2010-2015 FRM Practice Exams

G L O B A L A S S O C I AT I O N O F R I S K P R O F E S S I O N A L S

Financial Risk ® Manager (FRM ) Examination 2010 Practice Exam PART I / PART II

2010 FRM Examination Practice Exam / PART I / PART II

TABLE OF CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

2010 FRM Practice Exam Part I Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

2010 FRM Practice Exam Part I Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

2010 FRM Practice Exam Part I Correct Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

2010 FRM Practice Exam Part I Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

2010 FRM Practice Exam Part II Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59

2010 FRM Practice Exam Part II Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61

2010 FRM Practice Exam Part II Correct Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79

2010 FRM Practice Exam Part II Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81

© GARP, Global Association of Risk Professionals, Inc., 2010 It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.

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2010 FRM Examination Practice Exam / PART I / PART II

INTRODUCTION

The FRM® Exam is a practice-oriented examination. Its questions are derived from a combination of theory, as set forth in the core readings, and “real-world” work experience. Candidates are expected to understand risk management concepts and approaches and how they would apply to a risk manager’s day-to-day activities. The FRM Examination is also a comprehensive examination, testing a risk professional on a number of risk management concepts and approaches. It is very rare that a risk manager will be faced with an issue that can immediately be slotted into one category. In the real world, a risk manager must be able to identify any number of risk-related issues and be able to deal with them effectively. The 2010 FRM Practice Exams I and II have been developed to aid candidates in their preparation for the FRM Examination in November 2010. These practice exams are based on a sample of questions from the 2009 FRM Examination and are representative of the questions that will be in the 2010 FRM Examination. Wherever necessary and possible, questions, answers and references have been updated to better reflect the topics and core readings listed in the 2010 FRM Examination Study Guide. The 2010 FRM Practice Exam I for Part I and the 2010 FRM Practice Exam II for Part II each contain 40 multiple-choice questions. Note that the 2010 FRM Examination will consist of a morning and afternoon session, each containing 70 multiple-choice questions. The practice exams were designed to be shorter to allow candidates to calibrate their preparedness without being overwhelming. The 2010 FRM Practice Exam for Part I does not necessarily cover all topics to be tested in the 2010 FRM Examination. For a complete list of topics and core readings, candidates should refer to the 2010 FRM Examination Study Guide. Core readings were selected by the FRM Committee to assist candidates in their review of the subjects covered by the exam. Questions for the FRM examination are derived from the “core” readings. It is strongly suggested that candidates review these readings in depth prior to sitting for the exam.

Suggested Use of Practice Exams To maximize the effectiveness of the practice exams, candidates are encouraged to follow these recommendations: 1. Plan a date and time to take each practice exam. Set dates appropriately to give sufficient study/review time for the practice exam and prior to the actual exam. 2. Simulate the test environment as closely as possible. • Take each practice exam in a quiet place. • Have only the practice exam, candidate answer sheet, calculator, and writing instruments (pencils, erasers) available. • Minimize possible distractions from other people, cell phones and study material. • Allocate 90 minutes for the practice exam and set an alarm to alert you when 90 minutes have passed. Complete the exam but note the questions answered after the 90 minute mark. • Follow the FRM calculator policy. You may only use a Texas Instruments BA II Plus (including the BA II Plus Professional) calculator or a Hewlett Packard 12C (including the HP 12C Platinum) calculator. 3. After completing the practice exam, • Calculate your score by comparing your answer sheet with the practice exam answer key. Only include questions completed in the first 90 minutes. • Use the practice exam Answers and Explanations to better understand correct and incorrect answers and to identify topics that require additional review. Consult referenced core readings to prepare for exam. • Pass/fail status for the actual exam is based on the distribution of scores from all candidates, so use your scores only to gauge your own progress and preparedness.


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Financial Risk ® Manager (FRM ) Examination 2010 Practice Exam PART I

2010 FRM Examination Practice Exam / PART I

2010 FRM PRACTICE EXAM PART I: ANSWER SHEET

a.

b.

c.

a.

d.

1.

23.

2.

24.

3.

25.

4.

26.

5.

27.

6.

28.

7.

29.

8.

30.

9.

31.

10.

32.

11.

33.

12.

34.

13.

35.

14.

36.

15.

37.

16.

38.

17.

39.

18.

40.

b.

c.

d.

19. 20.

Correct way to complete 1.

21. 22.

✓

✘

Wrong way to complete 1.


1.

Which of the following statements about simulation is invalid? a. The historical simulation approach is a nonparametric method that makes no specific assumption about the distribution of asset returns. b. When simulating asset returns using Monte Carlo simulation, a sufficient number of trials must be used to ensure simulated returns are risk neutral. c. Bootstrapping is an effective simulation approach that naturally incorporates correlations between asset returns and non-normality of asset returns, but does not generally capture autocorrelation of asset returns. d. Monte Carlo simulation can be a valuable method for pricing derivatives and examining asset return scenarios.

2.

Portfolio Q has a beta of 0.7 and an expected return of 12.8%. The market risk premium is 5.25%. The risk-free rate is 4.85%. Calculate Jensen’s Alpha measure for Portfolio Q. a. b. c. d.

3.

7.67% 2.70% 5.73% 4.27%

A corporation is faced with the decision to choose between the two following projects: Project A B

Investment 100 80

Perpetual Annual Cash Flow 20 55

Cash Flow at Risk 50 200

Assuming that there is no systematic risk and the projects are mutually exclusive, under what circumstances would project A be selected over project B? a. Project A should never be chosen because it requires a larger initial investment and generates lower perpetual annual cash flows. b. Project A could be preferred over Project B if Project A’s cash flows are negatively correlated with the firm’s existing cash flows while the cash flows of Project B are highly positively correlated with the firm’s existing cash flows. c. Project A should be chosen if the opportunity cost of funds is low, and Project B should be chosen otherwise. d. Project A should be chosen if the net present value of the project is positive.


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4.

If the lease rate of commodity A is less than the risk-free rate, what is the market structure of commodity A? a. b. c. d.

5.

Sarah is a risk manager responsible for the fixed income portfolio of a large insurance company. The portfolio contains a 30-year zero coupon bond issued by the US Treasury (STRIPS) with a 5% yield. What is the bond’s DV01? a. b. c. d.

6.

0.0161 0.0665 0.0692 0.0694

Currently, shares of ABC Corp. trade at USD 100. The monthly risk neutral probability of the price increasing by USD 10 is 30%, and the probability of the price decreasing by USD 10 is 70%.What are the mean and standard deviation of the price after 2 months if price changes on consecutive months are independent?

a. b. c. d.

8

Backwardation Contango Flat Inversion

Mean 70 70 92 92

Standard Deviation 11.32 12.96 11.32 12.96



7.

Which of the following statements about the ordinary least squares regression model (or simple regression model) with one independent variable are correct? i. In the ordinary least squares (OLS) model, the random error term is assumed to have zero mean and constant variance. ii. In the OLS model, the variance of the independent variable is assumed to be positively correlated with the variance of the error term. iii. In the OLS model, it is assumed that the correlation between the dependent variable and the random error term is zero. iv. In the OLS model, the variance of the dependent variable is assumed to be constant. a. b. c. d.

8.

Bob tests the null hypothesis that the population mean is less than or equal to 45. From a population size of 3,000,000 people, 81 observations are randomly sampled. The corresponding sample mean is 46.3 and sample standard deviation is 4.5.What is the value of the appropriate test statistic for the test of the population mean, and what is the correct decision at the 1 percent significance level? a. b. c. d.

9.

i, ii, iii, and iv ii and iv only i and iv only i, ii, and iii only

z = 0.29, and fail to reject the null hypothesis z = 2.60, and reject the null hypothesis t = 0.29, and accept the null hypothesis t = 2.60, and neither reject nor fail to reject the null hypothesis

Which one of the following four statements about hypothesis testing holds true if the level of significance decreases from 5% to 1%? a. b. c. d.

It becomes more difficult to reject a null hypothesis when it is actually true. The probability of making a type I error increases. The probability of making a type II error decreases. The failure to reject the null hypothesis when it is actually false decreases to 1%.


9


10.

Mr. Black has been asked by a client to write a large put option on the S&P 500 index. The option has an exercise price and a maturity that are not available for options traded on exchanges. He, therefore, has to hedge the position dynamically. Which of the following statements about the risk of his position are not correct? a. He can make his portfolio delta neutral by shorting index futures contracts. b. There is a short position in an S&P 500 futures contract that will make his portfolio insensitive to both small and large moves in the S&P 500. c. A long position in a traded option on the S&P 500 will help hedge the volatility risk of the option he has written. d. To make his hedged portfolio gamma neutral, he needs to take positions in options as well as futures.

11.

On March 13, 2008, William Tell, a fund manager for the Rossini fund, takes a short position in the March Treasury bond (T-bond) futures contract. He plans to deliver the cheapest-to-deliver Treasury bond with a coupon of 4.5% payable semiannually on May 15 and November 15 (182 days between), a conversion factor of 1.3256, and a face value of USD 100,000. The delivery date is Friday, March 15 (121 days after November 15 coupon payment date). The settlement price for the cheapest-to-deliver Treasury bond on March 13 is 68 2/32. Which of the following is the best estimate of the invoice price? a. b. c. d.

12.

The yield curve is upward sloping, and a portfolio manager has a long position in 10-year Treasury Notes funded through overnight repurchase agreements. The risk manager is concerned with the risk that market rates may increase further and reduce the market value of the position. What hedge could be put on to reduce the position’s exposure to rising rates? a. b. c. d.

10

USD 90,118.87 USD 91,719.53 USD 92,367.75 USD 95,619.47

Enter into a 10-year pay fixed and receive floating interest rate swap. Enter into a 10-year receive fixed and pay floating interest rate swap. Establish a long position in 10-year Treasury Note futures. Buy a call option on 10-year Treasury Note futures.



13.

14.

Jennifer Durrant is evaluating the existing risk management system of Silverman Asset Management. She is asked to match the following events to the corresponding type of risk. Identify each numbered event as a market risk, credit risk, operational risk, or legal risk event.

1. 2. 3. 4.

Event Insufficient training leads to misuse of order management system. Credit spreads widen following recent bankruptcies. Option writer does not have the resources required to honor a contract. Credit swaps with counterparty cannot be netted because they originated in multiple jurisdictions.

a. b. c. d.

1: legal risk, 2: credit risk, 3: operational risk, 4: credit risk 1: operational risk, 2: credit risk, 3: operational risk, 4: legal risk 1: operational risk, 2: market risk, 3: credit risk, 4: legal risk 1: operational risk, 2: market risk, 3: operational risk, 4: legal risk

Which one of the following four statements on models for estimating volatility is incorrect? a. In the RiskMetrics™ EWMA model, some positive weight is assigned to the long-run average variance rate. b. In the RiskMetrics™ EWMA model, the weights assigned to observations decrease exponentially as the observations become older. c. In the GARCH (1, 1) model, a positive weight is estimated for the long-run average variance rate. d. In the GARCH (1, 1) model, the weights estimated for observations decrease exponentially as the observations become older.

15.

The table below gives the closing prices and yields of a particular liquid bond over the past few days. Day Monday Tuesday Wednesday

Price 106.3 105.8 106.1

Yield 4.25% 4.20% 4.23%

What is the approximate duration of the bond? a. b. c. d.

18.8 9.4 4.7 1.9


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16.

Bond A B

Yield

Maturity in Years

5% 3%

2 13

Standard Deviation of the Yield – Annual 5% 12%

Exposure USD 25.00 USD 75.00

The correlation between the two returns is 0.25. From a risk management perspective, what is the gain from diversification for a VaR estimated at the 95% level for the next 10 days? Assume there are 250 trading days in a year. a. b. c. d.

17.

Assume that a random variable follows a normal distribution with a mean of 100 and a standard deviation of 17.5. What is the probability that this random variable is between 82.5 and 135? a. b. c. d.

18.

76,500 283,000 382,300 1,413,000

68.0% 81.9% 82.8% 95.0%

The following table gives the prices of two out of three US Treasury notes for settlement on August 30, 2008. All three notes will mature exactly one year later on August 30, 2009. Assume annual coupon payments and that all three bonds have the same coupon payment date. Coupon 2 7/8 4 1/2 6 1/4

Price 98.40 ? 101.30

Approximately what would be the price of the 4 1/2 US Treasury note? a. b. c. d.

12

99.20 99.40 99.80 100.20



19.

A newly issued non-callable, fixed-rate bond with 30-year maturity carries a coupon rate of 5.5% and trades at par. Its duration is 15.33 years and its convexity is 321.03.Which of the following statements about this bond is true? a. b. c. d.

20.

If the bond were to start trading at a discount, its duration would decrease. If the bond were to start trading at a premium, its duration would decrease. If the bond were to start trading at a discount, its duration would not change. If the bond were to remain at par, its duration would increase as the bond aged.

Rational Investment Inc. is estimating a daily VaR for its fixed income portfolio currently valued at USD 800 million. Using returns for the last 400 days (ordered in decreasing order, from highest daily return to lowest daily return), the daily returns are the following: 1.99%, 1.89%, 1.88%, 1.87%,…, -1.76%, -1.82%, -1.84%, -1.87%, -1.91%. At the 99% confidence level, what is your estimate of the daily dollar VaR using the historical simulation method? a. b. c. d.

21.

USD 14.08mm USD 14.56mm USD 14.72mm USD 15.04mm

A market risk manager uses historical information on 1,000 days of profit/loss information to calculate a daily VaR at the 99th percentile, of USD 8 million. Loss observations beyond the 99th percentile are then used to estimate the conditional VaR. If the losses beyond the VaR level, in millions, are USD 9, USD 10, USD 11, USD 13, USD 15, USD 18, USD 21, USD 24, and USD 32, then what is the conditional VaR? a. b. c. d.

USD 9 million USD 32 million USD 15 million USD 17 million


13


22.

23.

In looking at the frequency distribution of weekly crude oil price changes between 1984 and 2008, an analyst notices that the frequency distribution has a surprisingly large number of observations for extremely large positive price changes and a smaller number, but still a surprising one, of observations for extremely large negative price changes. The analyst provides you with the following statistical measures. Which measures would help you identify these characteristics of the frequency distribution? i. ii. iii. iv.

Serial correlation of weekly price changes Variance of weekly price changes Skewness of weekly price changes Kurtosis of weekly price changes

a. b. c. d.

i, ii, iii, and iv ii only iii and iv only i, iii, and iv only

Let X and Y be two random variables representing the annual returns of two different portfolios. If E[ X ] = 3, E[ Y ] = 4 and E[ XY ] = 11, then what is Cov[ X, Y ]? a. b. c. d.

24.

The current price of stock ABC is USD 42 and the call option with a strike at USD 44 is trading at USD 3. Expiration is in one year. The put option with the same exercise price and same expiration date is priced at USD 2. Assume that the annual risk-free rate is 10% and that there is a risk-free bond paying the risk-free rate that can be shorted costlessly. There are no transaction costs. Which of the following trading strategies will result in arbitrage profits? a. b. c. d.

14

-1 0 11 12

Long position in both the call option and the stock, and short position in the put option and risk-free bond. Long position in both the call option and the put option, and short position in the stock and risk-free bond. Long position in both the call option and risk-free bond, and short position in the stock and the put option. Long position in both the put option and the risk-free bond, and short position in the stock and the call option.



25.

Nicholas is responsible for the asset and liability management of JerseyBeech Bank, a small retail bank with USD 300 million in interest-bearing assets that yield approximately 70 bp above LIBOR. The duration of the interest-bearing assets is 2.5 years. Due to the recent financial turmoil, the bank seeks to reduce potential negative impacts on earnings from adverse moves in interest rates. Thus, the bank decides to hedge 50% of its interest rate exposures using Treasury bond futures. Nicholas decides to use September T-bond futures that trade at 106-22 and will mature in three months; the cheapest-to-deliver bond associated with this contract is a 7-year, 10% coupon, with a current duration of 5 years. At the maturity of the futures contract, the duration of the bank’s interest rate sensitive assets will not change; however, the duration of the cheapest-to-deliver bond will fall to 4.9. How many contracts should Nicholas buy or sell? a. b. c. d.

26.

Bonds issued by the XYZ Corp. are currently callable at par value and trade close to par. The bonds mature in 8 years and have a coupon of 8%. The yield on the XYZ bonds is 175 basis points over 8-year US Treasury securities, and the Treasury spot yield curve has a normal, rising shape. If the yield on bonds comparable to the XYZ bond decreases sharply, the XYZ bonds will most likely exhibit: a. b. c. d.

27.

Buy 703 contracts. Sell 703 contracts. Buy 717 contracts. Sell 717 contracts.

negative convexity increasing modified duration increasing effective duration positive convexity

A risk analyst seeks to find out the yield-to-maturity on a BB-rated, 2-year zero coupon bond issued by a multinational petroleum company. If the prevailing annual risk-free rate is 3%, the default rate for BB-rated bonds is 7% per year, and the loss given default is 60%, then the yield-to-maturity of the bond is: a. b. c. d.

2.57% 5.90% 7.45% 7.52%


15


28.

Your supervisor is an expert in market and credit risk. He recruits you to manage the operational risk department. He would like to use VaR to measure the firm’s operational risk and proposes that you use the same VaR framework previously developed for market and credit risk. Which of the following arguments is a valid argument for why it is difficult to estimate an operational VaR using the same framework as market and credit VaR? a. Market risk events are easier to map to risk factors than operational risk events. b. Quantitative methods for estimating operational risk VaR do not exist. c. Market and credit VaRs are estimated using only a frequency distribution, but operational VaR is estimated using both a frequency distribution and a severity distribution. d. Monte Carlo techniques cannot be used for an operational risk VaR because the underlying risk factors are not normally distributed.

29.

One of the traders whose risk you monitor put on a carry trade where he borrows in yen and invests in some emerging market bonds whose performance is independent of yen. Which of the following risks should you not worry about? a. b. c. d.

30.

John Flag, the manager of a USD 150 million distressed bond portfolio, conducts stress tests on the portfolio. The portfolio’s annualized return is 12%, with an annualized return volatility of 25%. In the last two years, the portfolio encountered several days when the daily value change of the portfolio was more than 3 standard deviations. If the portfolio suffered a 4-sigma daily event, which of the following is the best estimate of the change in the value of this portfolio? Assume that there are 250 trading days in a year. a. b. c. d.

16

Unexpected devaluation of the yen. A currency crisis in one of the emerging markets the trader invests in. Unexpected downgrading of the sovereign rating of a country in which the trader invests. Possible contagion to emerging markets of a credit crisis in a major country.

USD 9.48 million USD 23.70 million USD 37.50 million USD 150 million



31.

32.

The current spot price of cotton is USD 0.7409 per pound. The cost of storing and insuring cotton is USD 0.0042 per pound per month payable at the beginning of every month. The risk-free rate is 5%. A 3-month forward contract trades at USD 0.7415 per pound. If there is an arbitrage opportunity, how would you capitalize on it to make a profit? Assume there are no restrictions on short selling cotton. i. ii. iii. iv. v. vi.

short the futures contract borrow at the risk-free rate buy cotton at the spot price go long in the futures contract invest at the risk-free rate sell cotton at the spot price

a. b. c. d.

There is no arbitrage opportunity here. The arbitrage opportunity involves i, ii, and iii. The arbitrage opportunity involves iv, v, and vi. The arbitrage opportunity involves ii, iv, and vi.

There are many reasons why risk management increases shareholder wealth. Which of the following risk management policies is least likely to increase shareholder wealth? a. b. c. d.

Hedging strategies to lower the probability of financial distress and bankruptcy. Risk management policies designed to reduce the probability of debt overhang. Well-designed compensation structure for managers that sets incentives for managers to take appropriate risks. Risk management policies designed to eliminate projects with high volatility.


17


33.

In late 1993, Metallgesellschaft reported losses of approximately USD 1.5 billion in connection with the implementation of a hedging strategy in the oil futures market. In 1992, the company had begun a new strategy to sell petroleum to independent retailers, on a monthly basis, at fixed prices above the prevailing market price for periods of up to 5 and even 10 years. At the same time, Metallgesellschaft implemented a hedging strategy using a large number of short-term derivative contracts such as swaps and futures on crude oil, heating oil, and gasoline on several exchanges and markets. Its approach was to buy on the derivatives market exposure to one barrel of oil for each barrel it had committed to deliver. Because of its choice of a hedge ratio, the company suffered significant losses with its hedging strategy when oil market conditions abruptly changed to: a. b. c. d.

34.

The current share price and daily volatility of a stock are USD 10 and 2%, respectively. Using the delta-normal approximation, the 95% VaR on a long at-the-money call on this stock over a one-day holding period is: a. b. c. d.

35.

USD 0.1645 USD 0.3290 USD 1.645 USD 16.45

In country X, the probability that a letter sent through the postal system reaches its destination is 2/3. Assume that each postal delivery is independent of every other postal delivery, and assume that if a wife receives a letter from her husband, she will certainly mail a response to her husband. Suppose a man in country X mails a letter to his wife (also in country X) through the postal system. If the man does not receive a response letter from his wife, what is the probability that his wife received his letter? a. b. c. d.

18

Contango, which occurs when the futures price is above the spot price. Contango, which occurs when the futures price is below the spot price. Normal backwardation, which occurs when the futures price is above the spot price. Normal backwardation, which occurs when the futures price is below the spot price.

1/3 3/5 2/3 2/5



36.

Basis risk is a common problem faced by hedgers because the underlying and the hedging instrument may not always move in perfect correlation. Which of the following strategies has the least basis risk? a. b. c. d.

37.

Straddle strategy Hedging individual equities using index futures Stack and roll strategy Delta hedging strategy

Which one of the following four trading strategies limits the investor’s upside potential and downside risk? a. A long position in a put combined with a long position in a stock. b. A short position in a put combined with a short position in a stock. c. Buying a call option on a stock with a certain strike price and selling a call option on the same stock with a higher strike price and the same expiration date. d. Buying a call and a put with the same strike price and expiration date.

38.

Which of the following statements are correct about the early exercise of American options? i. ii. iii. iv.

It is never optimal to exercise an American call option on a non-dividend-paying stock before the expiration date. It can be optimal to exercise an American put option on a non-dividend-paying stock early. It can be optimal to exercise an American call option on a non-dividend-paying stock early. It is never optimal to exercise an American put option on a non-dividend-paying stock before the expiration date.

a. b. c. d.

i and ii i and iv ii and iii iii and iv


19


39.

In 2006, UBS reported no exceedances on its daily 99% VaR. In 2007, UBS reported 29 exceedances. To test whether the VaR was biased, you consider using a binomial test. Assuming no serial correlation, 250 trading days, and an accurate VaR measure, you calculate the probability of observing n exceedances, for n = 0, 1, . . . n 0 1 2 3 4

Prob(observing n exceedances) 7.9% 20.2% 25.6% 21.6% 13.6%

n 5 6 7 8 9


Which of the following statements is not correct? a. At the 5% probability level, you cannot reject that the VaR was unbiased in 2006 using a binomial test. b. The lack of exceedances in 2006 demonstrates that UBS failed to take into account the existence of fat tails in estimating the distribution of its market risk. c. It is difficult to evaluate the implications of the lack of exceedances if the VaR is forecasted for a static portfolio and it is compared against the trading P&L. d. At the 5% probability level, you can reject that the VaR was unbiased in 2007 using a binomial test.

40.

An asset manager analyzes a position consisting of a put option sold on an underlying asset, which is a hedge fund pursuing a fixed income strategy. This hedge fund, which the asset manager does not own, reports daily returns to the asset manager. Due to the credit crisis, return volatility of the hedge fund has been increasing, which makes the manager nervous about the short option position. When the asset manager entered this trade, he set a guideline limiting the 95% 1-day VaR exposure of this trade to 1.0% of the fund’s NAV. Assuming the hedge fund returns are normally distributed and that there are 250 trading days per year, what is the lowest level of annualized return volatility that exceeds the guideline? a. b. c. d.

20

Any volatility over 6% Any volatility over 7% Any volatility over 8% Any volatility over 10%



2010 ERP PRACTICE EXAM PART I: CORRECT ANSWER SHEET

a.

b.

c.

1.

a.

d. 23.

2.

25.

4.

26.

5.

27.

7.

8. 9.

28.

29.

30.

31.

32.

11.

33.

34.

13. 14.

36.

15.

37.

16.

38.

17.

39.

18. 19. 20.

40.


✓

✘

21. 22.

35.

d.

10.

12.

c.

24.

3.

6.

b.

Wrong way to complete

1.


Financial Risk ® Manager (FRM ) Examination 2010 Practice Exam Answers and Explanations PART I


1.

Which of the following statements about simulation is invalid? a. The historical simulation approach is a nonparametric method that makes no specific assumption about the distribution of asset returns. b. When simulating asset returns using Monte Carlo simulation, a sufficient number of trials must be used to ensure simulated returns are risk neutral. c. Bootstrapping is an effective simulation approach that naturally incorporates correlations between asset returns and non-normality of asset returns, but does not generally capture autocorrelation of asset returns. d. Monte Carlo simulation can be a valuable method for pricing derivatives and examining asset return scenarios. Answer: b

Explanation: Risk neutrality has nothing to do with sample size. Topic: Quantitative Analysis Subtopic: Simulation methods. Reference: Jorion, chapter 12.

2.

Portfolio Q has a beta of 0.7 and an expected return of 12.8%. The market risk premium is 5.25%. The risk-free rate is 4.85%. Calculate Jensen’s Alpha measure for Portfolio Q. a. b. c. d.

7.67% 2.70% 5.73% 4.27%

Answer: d Explanation: Jensen’s alpha is defined by: E(RP ) − RF = αP + βP(E(RM) − RF) αP = E(RP ) − RF - βP(E(RM) − RF) = 0.128 – 0.0485 – 0.7 * (0.0525 + 0.0485 – 0.0485) = 0.0427 a. Incorrect. Forgets to subtract the risk-free rate for the excess market return. b. Incorrect. Forgets to multiply the excess market return by beta. c. Incorrect. Forgets to subtract the risk-free rate for both the excess market return and the excess portfolio return. d. Correct. Topic: Foundation of Risk Management Subtopic: Market efficiency, equilibrium and CAPM. Reference: Amenc and LeSourd, Chapter 4.


23


3.

A corporation is faced with the decision to choose between the two following projects: Project A B

Investment 100 80

Perpetual Annual Cash Flow 20 55

Cash Flow at Risk 50 200

Assuming that there is no systematic risk and the projects are mutually exclusive, under what circumstances would project A be selected over project B? a. Project A should never be chosen because it requires a larger initial investment and generates lower perpetual annual cash flows. b. Project A could be preferred over Project B if Project A’s cash flows are negatively correlated with the firm’s existing cash flows while the cash flows of Project B are highly positively correlated with the firm’s existing cash flows. c. Project A should be chosen if the opportunity cost of funds is low, and Project B should be chosen otherwise. d. Project A should be chosen if the net present value of the project is positive. Answer: b Explanation: Project A should be chosen only if the cash flow at risk of the project has low or negative correlation with the other projects the company currently has or plans. The overall cash flow position of the firm has to be evaluated as a result. Topic: Foundations of Risk Management Subtopic: Creating value with risk management Reference: Stulz, chapter 3

24



4.

If the lease rate of commodity A is less than the risk-free rate, what is the market structure of commodity A? a. b. c. d.

Backwardation Contango Flat Inversion

Answer: b Explanation: 1. Contango occurs when futures prices are higher than current spot, so in this case the risk-free rate is greater than the lease rate. 2. Backwardation occurs when futures prices are less than spot, so in this case the lease rate is greater than risk-free rate. So, if the lease rate is less than the risk-free rate, the futures price is above the current spot price. Topic: Financial Markets and Products Subtopic: Derivatives on commodities Reference: MacDonald, Chapter 6

5.

Sarah is a risk manager responsible for the fixed income portfolio of a large insurance company. The portfolio contains a 30-year zero coupon bond issued by the US Treasury (STRIPS) with a 5% yield. What is the bond’s DV01? a. b. c. d.

0.0161 0.0665 0.0692 0.0694

Answer: b Explanation: The DV01 of a zero-coupon is DV01 = 30 / 100 (1 + y/2)2T+1 100 (1 + 5%/2)61 = 0.0665 Topic: Valuation and Risk Models Subtopic: DV01, duration and convexit Reference: Tuckman, Chapter 5


25


6.

Currently, shares of ABC Corp. trade at USD 100. The monthly risk neutral probability of the price increasing by USD 10 is 30%, and the probability of the price decreasing by USD 10 is 70%.What are the mean and standard deviation of the price after 2 months if price changes on consecutive months are independent?

a. b. c. d.

Mean 70 70 92 92

Standard Deviation 11.32 12.96 11.32 12.96

Answer: d Explanation: Develop a 2 step tree. Mean = 9% (120) + 42% (100) + 49% (80) = 92 Variance = 9% (120 – 92)2 + 42% (100 – 92)2 + 49% (80 – 92)2 = 168 Thus, standard deviation = 12.96 Topic: Valuation and Risk Models Subtopic: Binomial Trees Reference: John C. Hull, Options, Futures, and Other Derivatives, 6th Edition (New York: Prentice Hall, 2006).

26



7.

Which of the following statements about the ordinary least squares regression model (or simple regression model) with one independent variable are correct? i. In the ordinary least squares (OLS) model, the random error term is assumed to have zero mean and constant variance. ii. In the OLS model, the variance of the independent variable is assumed to be positively correlated with the variance of the error term. iii. In the OLS model, it is assumed that the correlation between the dependent variable and the random error term is zero. iv. In the OLS model, the variance of the dependent variable is assumed to be constant. a. b. c. d.

i, ii, iii, and iv ii and iv only i and iv only i, ii, and iii only

Answer: c Explanation: i. Is correct. In Simple Linear Regression model, the random error term is assumed to be stationary. It means that the Variance of random error term must be constant, or by using another term: it is assumed that there is no heteroskedasticity in linear regression model. ii. Is incorrect. In Simple Linear Regression model, the independent variable and the error term have constant variances. iii. Is incorrect. The dependent variable is allowed to be correlated with the error term. iv. Is correct. In Simple Linear Regression model, the variance of the dependent variable is assumed to be constant. Thus, the correct option is option C. Topic: Quantitative Analysis. Subtopic: Linear regression. Reference: Gujarati, chapter 7, pp. 140-145.


27


8.

Bob tests the null hypothesis that the population mean is less than or equal to 45. From a population size of 3,000,000 people, 81 observations are randomly sampled. The corresponding sample mean is 46.3 and sample standard deviation is 4.5.What is the value of the appropriate test statistic for the test of the population mean, and what is the correct decision at the 1 percent significance level? a. b. c. d.

z = 0.29, and fail to reject the null hypothesis z = 2.60, and reject the null hypothesis t = 0.29, and accept the null hypothesis t = 2.60, and neither reject nor fail to reject the null hypothesis

Answer: b Explanation: a. is incorrect. The denominator of the z-test statistic is standard error instead of standard deviation. If the denominator takes the value of standard deviation 4.5, instead of standard error 4.5/sqrt(81), the z-test statistic computed will be z = 0.29, which is incorrect. b. is correct. The population variance is known and the sample size is large (>30). The test statistics is: z = (46.345)/(4.5/(sqrt(81)) = 2.60. Decision rule: reject Ho if zcomputed > zcritical. Therefore, reject the null hypothesis because the computed test statistics of 2.60 exceeds the critical z-value of 2.33. c. is incorrect because z-test (instead of t-test) should be used for sample size (81) >= 30 d. is incorrect because z-test (instead of t-test) should be used for sample size (81) >= 30 Topic: Quantitative Analysis Subtopic: Hypothesis testing Reference: Damodar N. Gujarati, Essentials of Econometrics, 3rd ed., (New York: McGraw-Hill, 2006)

28



9.

Which one of the following four statements about hypothesis testing holds true if the level of significance decreases from 5% to 1%? a. b. c. d.

It becomes more difficult to reject a null hypothesis when it is actually true. The probability of making a type I error increases. The probability of making a type II error decreases. The failure to reject the null hypothesis when it is actually false decreases to 1%.

Answer: a Explanation: Type I error: The rejection of the null hypothesis when it is actually true. Type II error: The failure to reject the null hypothesis when it is actually false. The significance level is the probability of making a type I error. a. is correct. Decreasing the probability level makes it more difficult to reject the null when it is true. b. is incorrect. Decreases the probability of making a type I error. c. is incorrect. All else being equal, the decrease in the probability of making a Type I error comes at the cost of increasing the probability of making a Type II error. d. is incorrect. Increases the probability of making a Type II error, in other words, the probability of failing to reject the null hypothesis when it is actually false decreased Topic: Quantitative Analysis Subtopic: Hypothesis testing Reference: Damodar N Gujarati, Essentials of Econometrics, 3rd Edition.


29


10.

Mr. Black has been asked by a client to write a large put option on the S&P 500 index. The option has an exercise price and a maturity that are not available for options traded on exchanges. He, therefore, has to hedge the position dynamically. Which of the following statements about the risk of his position are not correct? a. He can make his portfolio delta neutral by shorting index futures contracts. b. There is a short position in an S&P 500 futures contract that will make his portfolio insensitive to both small and large moves in the S&P 500. c. A long position in a traded option on the S&P 500 will help hedge the volatility risk of the option he has written. d. To make his hedged portfolio gamma neutral, he needs to take positions in options as well as futures. Answer: b

Explanation: The short index futures makes the portfolio delta neutral. It does not help with large moves, though. Topic: Valuation and Risk Models Subtopic: Greeks Reference: Hull, Chapter 17.

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11.

On March 13, 2008, William Tell, a fund manager for the Rossini fund, takes a short position in the March Treasury bond (T-bond) futures contract. He plans to deliver the cheapest-to-deliver Treasury bond with a coupon of 4.5% payable semiannually on May 15 and November 15 (182 days between), a conversion factor of 1.3256, and a face value of USD 100,000. The delivery date is Friday, March 15 (121 days after November 15 coupon payment date). The settlement price for the cheapest-to-deliver Treasury bond on March 13 is 68 2/32. Which of the following is the best estimate of the invoice price? a. b. c. d.

USD 90,118.87 USD 91,719.53 USD 92,367.75 USD 95,619.47

Answer: b The invoice is based on a settlement price of 68 2/32 or 68.0625. The accrued interest is calculated on the basis of the number of days since the last coupon payment date, November 15, and the delivery date, March 15. That is 121. During the current six-month period between coupon payment dates, November 15 to May 15, there are 182 days. Thus the accrued interest on USD 100,000 face value of the bond is 121/182 * USD 100,000 * 0.045/2 = USD 1,495.88 Explanation: The invoice price is USD 100,000 * 0.680625 * 1.3256 + USD 1,495.88 = 91,719.53 Topic: Financial Markets and Products Subtopic: Cheapest to deliver bond, conversion factors Reference: Bruce Tuckman, Fixed Income Securities, 2nd Edition.


31


12.

The yield curve is upward sloping, and a portfolio manager has a long position in 10-year Treasury Notes funded through overnight repurchase agreements. The risk manager is concerned with the risk that market rates may increase further and reduce the market value of the position. What hedge could be put on to reduce the position’s exposure to rising rates? a. b. c. d.

Enter into a 10-year pay fixed and receive floating interest rate swap. Enter into a 10-year receive fixed and pay floating interest rate swap. Establish a long position in 10-year Treasury Note futures. Buy a call option on 10-year Treasury Note futures.

Answer: a Explanation: a. is correct. An increase in rates will increase the value of the hedge position and offset the loss in value from the Bond position. b. is incorrect. An increase in rates will decrease the value of the hedge position and add to the loss in value from the Bond position. c. is incorrect. An increase in rates will decrease the value of the futures position and add to the loss in value from the Bond position. d. is incorrect. An increase in rates (all else equal), will decrease the value of the call option and add to the loss in value from the Bond position. Topic: Financial Markets and Products Subtopic: Futures, forwards, swaps and options Reference: John Hull, Options, Futures, and Other Derivatives, 6th Edition (New York: Prentice Hall, 2006) Chapter 7 – Swaps

32



13.

Jennifer Durrant is evaluating the existing risk management system of Silverman Asset Management. She is asked to match the following events to the corresponding type of risk. Identify each numbered event as a market risk, credit risk, operational risk, or legal risk event.

1. 2. 3. 4.

Event Insufficient training leads to misuse of order management system. Credit spreads widen following recent bankruptcies. Option writer does not have the resources required to honor a contract. Credit swaps with counterparty cannot be netted because they originated in multiple jurisdictions.

a. b. c. d.

1: legal risk, 2: credit risk, 3: operational risk, 4: credit risk 1: operational risk, 2: credit risk, 3: operational risk, 4: legal risk 1: operational risk, 2: market risk, 3: credit risk, 4: legal risk 1: operational risk, 2: market risk, 3: operational risk, 4: legal risk

Answer: c Explanation: a, b and d are incorrect. c is correct. 1. Insufficient training leads to misuse of order management system is an example of operational risk. 2. Widening of credit spreads represents an increase in market risk. 3. An option writer not honoring the obligation in a contract is a credit risk event. 4. When a contract is originated in multiple jurisdictions leading to problems with enforceability, there is legal risk. Topic: Foundations of Risk Management Subtopic: Creating value with risk management, risk management failures Reference: Jorion, “Value at Risk”, Chapter 1


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14.

Which one of the following four statements on models for estimating volatility is incorrect? a. In the RiskMetrics™ EWMA model, some positive weight is assigned to the long-run average variance rate. b. In the RiskMetrics™ EWMA model, the weights assigned to observations decrease exponentially as the observations become older. c. In the GARCH (1, 1) model, a positive weight is estimated for the long-run average variance rate. d. In the GARCH (1, 1) model, the weights estimated for observations decrease exponentially as the observations become older. Answer: a

Explanation: a. is incorrect. The RiskMetrics model does not involve the long-run average variance rate in updating volatility, in other words, the weight assigned to the long-run average variance rate is zero. b. is correct. In the RiskMetrics model, the weights assigned to observations decrease exponentially as the observations become older. c. is correct. In the GARCH (1, 1) model, some positive weight is assigned to the long-run average variance rate. d. is correct. In the GARCH (1, 1) model, the weights assigned to observations decrease exponentially as the observations become older. Topic: Quantitative Analysis Subtopic: EWMA, GARCH models Reference: Hull, Chapter 21.

34



15.

The table below gives the closing prices and yields of a particular liquid bond over the past few days. Day Monday Tuesday Wednesday

Price 106.3 105.8 106.1

Yield 4.25% 4.20% 4.23%

What is the approximate duration of the bond? a. b. c. d.

18.8 9.4 4.7 1.9

Answer: b Explanation: The duration can be approximated from the price changes. (106.3 – 105.8)/106.3/.0005 = 9.4 (106.3 – 106.1)/106.3/.0002 = 9.4 Topic: Valuation and Risk Models Subtopic: DV01, duration and convexity Reference: Tuckman, chapter 5


35


16.

Bond A B

Yield

Maturity in Years

5% 3%

2 13

Standard Deviation of the Yield – Annual 5% 12%

Exposure USD 25.00 USD 75.00

The correlation between the two returns is 0.25. From a risk management perspective, what is the gain from diversification for a VaR estimated at the 95% level for the next 10 days? Assume there are 250 trading days in a year. a. b. c. d.

76,500 283,000 382,300 1,413,000

Answer: b Explanation: 1. Calculate the undiversified VaR VaRundiv = 1.645 * 5%*√(10/250) * 25 + 1.645 * 12% √10/250 *75 = 0.4113 + 2.9610 = 3.3723 2. Calculate the diversified VaR 1.645 √0.25 2 * 5% 2 + 0.75 2 * 12% + 2 * 0.25 * 0.75 * 5% * 12% * 0.25 * √(10/250) * 100 = 1.645 * 0.0939 * √10/250 * 100 = 3.0893 3. Difference is 0.283 Topic: Valuation and Risk Models Subtopic: VaR for fixed income securities Reference: Allen, Boudoukh, Saunders, Understanding market, Credit and Operational Risk: The Value at Risk Approach, Chapters 2, 3

36



17.

Assume that a random variable follows a normal distribution with a mean of 100 and a standard deviation of 17.5.What is the probability that this random variable is between 82.5 and 135? a. b. c. d.

68.0% 81.9% 82.8% 95.0%

Answer: b Explanation: Prob (-1*σ < X < 2*σ) = (1 – 0.0228) – 0.1587 = 0.8185 a. is incorrect. Almost 68% of the observations will be within the interval from one standard deviations below the mean to one standard deviations above the mean, which is within the interval [100 – 17.5; 100 + 17.5]. b. is correct. 82.5 = 100 – 17.5 and 135 = 100 + 2 * 17.5. So, the percentage is 34% on the left hand side of the mean, plus 95%/2 on the right hand side of the mean. c. is incorrect. Almost 95% of the items will lie within the interval from two standard deviations below the means to two standard deviations above the mean, that is within the interval [100 – 2 *17.5;100 + 2 * 17.5]. d. is incorrect. This answer assumes wrongly that 97.5% of the observations will be within [100 – 2 * 17.5;100 + 2 * 17.5]. Topic: Quantitative analysis Subtopic: Probability Distributions Reference: Damodar N Gujarati, Essentials of Econometrics, 3rd Edition (New York: McGraw-Hill, 2006), chapter 4, pp. 80-84.


37


18.

The following table gives the prices of two out of three US Treasury notes for settlement on August 30, 2008. All three notes will mature exactly one year later on August 30, 2009. Assume annual coupon payments and that all three bonds have the same coupon payment date. Coupon 2 7/8 4 1/2 6 1/4

Price 98.40 ? 101.30

Approximately what would be the price of the 4 1/2 US Treasury note? a. b. c. d.

99.20 99.40 99.80 100.20

Answer: c Explanation: 2.875% * x + 6.25% *(1 – x) = 4.5% X = 52% The portfolio that has cash flows identical to the 4 1/2 bond consists of 52% of the 2 7/8 and 48% of the 6 1/4 bonds. As this portfolio has cash flows identical to the 4 1/2 bond, precluding arbitrage, the price of the portfolio should equal to 52% * 98.4 + 48% * 101.30 or 99.80 Topic: Valuation and Risk Models Subtopic: Bond prices, spot rates, forward rates Reference: Tuckman, Chapter 1

38



19.

A newly issued non-callable, fixed-rate bond with 30-year maturity carries a coupon rate of 5.5% and trades at par. Its duration is 15.33 years and its convexity is 321.03.Which of the following statements about this bond is true? a. b. c. d.

If the bond were to start trading at a discount, its duration would decrease. If the bond were to start trading at a premium, its duration would decrease. If the bond were to start trading at a discount, its duration would not change. If the bond were to remain at par, its duration would increase as the bond aged.

Answer: a Explanation: a. is correct. At higher interest rates, the bond/price relationship is closer to linear than it is when rates are low. So, the new duration would be lower than 15. Alternatively, one can think of duration as a weighted average of the times when cash flows are made, where the weights are the percentage of the total value of the bond. When rates rise, the present values associated with the later payments are relatively smaller and the duration falls. b. is incorrect because it is the exact opposite of a, the correct answer. c. is incorrect. It fails to recognize the logic stated in a. d. is incorrect because duration is mainly a function of duration and, all else constant, duration would decrease as the bond’s maturity shortened. Topic: Valuation and Risk Models Subtopic: Duration and convexity Reference: Bruce Tuckman, Fixed Income Securities, 2nd edition, Chapter 5


39


20.

Rational Investment Inc. is estimating a daily VaR for its fixed income portfolio currently valued at USD 800 million. Using returns for the last 400 days (ordered in decreasing order, from highest daily return to lowest daily return), the daily returns are the following: 1.99%, 1.89%, 1.88%, 1.87%,…, -1.76%, -1.82%, -1.84%, -1.87%, -1.91%. At the 99% confidence level, what is your estimate of the daily dollar VaR using the historical simulation method? a. b. c. d.

USD 14.08mm USD 14.56mm USD 14.72mm USD 15.04mm

Answer: b Explanation: VaR = 1.82% * 800 = 14.56 million Topic: Valuation and Risk Models Subtopic: Value-at-Risk—Historic simulation Reference: Allen, Boudoukh, Saunders: chapter 2,3.

21.

A market risk manager uses historical information on 1,000 days of profit/loss information to calculate a daily VaR at the 99th percentile, of USD 8 million. Loss observations beyond the 99th percentile are then used to estimate the conditional VaR. If the losses beyond the VaR level, in millions, are USD 9, USD 10, USD 11, USD 13, USD 15, USD 18, USD 21, USD 24, and USD 32, then what is the conditional VaR? a. b. c. d.

USD 9 million USD 32 million USD 15 million USD 17 million

Answer: d Explanation: a. is incorrect. This is the minimum. b. is incorrect. This is the maximum. c. is incorrect. This is the median. d. is correct. Conditional VaR is the “mean” of the losses beyond the VaR level. Topic: Valuation and Risk Models Subtopic: Value-at-Risk—Definition and methods Reference: Allen, Boudoukh, Saunders: chapter 2,3.

40



22.

In looking at the frequency distribution of weekly crude oil price changes between 1984 and 2008, an analyst notices that the frequency distribution has a surprisingly large number of observations for extremely large positive price changes and a smaller number, but still a surprising one, of observations for extremely large negative price changes. The analyst provides you with the following statistical measures. Which measures would help you identify these characteristics of the frequency distribution? i. ii. iii. iv.

Serial correlation of weekly price changes Variance of weekly price changes Skewness of weekly price changes Kurtosis of weekly price changes

a. b. c. d.

i, ii, iii, and iv ii only iii and iv only i, iii, and iv only

Answer: c Explanation: The question considers a skewed leptokurtic distribution. To measure the magnitude of these skewed tails, the analyst needs to consider both the skewness and kurtosis Topic: Quantitative Analysis Subtopic: Mean, standard deviation, skewness and kurtosis Reference: Damodar N. Gujarati, Essentials of Econometrics, 3rd ed., (New York: McGraw-Hill, 2006) 3rd chapter


41


23.

Let X and Y be two random variables representing the annual returns of two different portfolios. If E[ X ] = 3, E[ Y ] = 4 and E[ XY ] = 11, then what is Cov[ X, Y ]? a. b. c. d.

-1 0 11 12

Answer: a Explanation: We can rewrite Cov[ X, Y ] as E[ XY ] – E[ X ]E[ Y ]. Then, Cov[ X, Y ] = 11 – 3 * 4 = -1. a. is correct because the above formula was used correctly, E[ XY ] - E[ X ]E[ Y ]. b. is incorrect because it assumes zero covariance, which is false when above the formula is used. c. is incorrect because the product of the 2 expectations of X and Y was not subtracted from the joint expectation E[ XY ]. d. is incorrect because the covariance is not the product of the 2 expectations of X and Y. Topic: Quantitative Analysis Subtopic: Mean, standard deviation, skewness and kurtosis Reference: Damodar N. Gujarati, Essentials of Econometrics, 3rd ed., (New York: McGraw-Hill, 2006) 3rd chapter, p. 59.

42



24.

The current price of stock ABC is USD 42 and the call option with a strike at USD 44 is trading at USD 3. Expiration is in one year. The put option with the same exercise price and same expiration date is priced at USD 2. Assume that the annual risk-free rate is 10% and that there is a risk-free bond paying the risk-free rate that can be shorted costlessly. There are no transaction costs. Which of the following trading strategies will result in arbitrage profits? a. b. c. d.

Long position in both the call option and the stock, and short position in the put option and risk-free bond. Long position in both the call option and the put option, and short position in the stock and risk-free bond. Long position in both the call option and risk-free bond, and short position in the stock and the put option. Long position in both the put option and the risk-free bond, and short position in the stock and the call option.

Answer: c Explanation: a. is incorrect as this would not yield arbitrage profit b. is incorrect as this would not yield arbitrage profit c. is correct The put call parity relation is: stock + put = pv(strike) + call Therefore for no arbitrage opportunity the following relation should hold 42 + 2 = (44/1.10) + 3 But 44 > 43 Therefore there is an arbitrage opportunity. The arbitrage profit is 44 – 43 = 1 by taking a long position in call and buying the risk-free bond and going short on the stock and the put. d. is incorrect as this would not yield arbitrage profit Topic: Financial Markets and Products Subtopic: Derivatives on equities Reference: John Hull, Options, Futures and other Derivatives, Chapter 9


43


25.

Nicholas is responsible for the asset and liability management of JerseyBeech Bank, a small retail bank with USD 300 million in interest-bearing assets that yield approximately 70 bp above LIBOR. The duration of the interest-bearing assets is 2.5 years. Due to the recent financial turmoil, the bank seeks to reduce potential negative impacts on earnings from adverse moves in interest rates. Thus, the bank decides to hedge 50% of its interest rate exposures using Treasury bond futures. Nicholas decides to use September T-bond futures that trade at 106-22 and will mature in three months; the cheapest-to-deliver bond associated with this contract is a 7-year, 10% coupon, with a current duration of 5 years. At the maturity of the futures contract, the duration of the bank’s interest rate sensitive assets will not change; however, the duration of the cheapest-to-deliver bond will fall to 4.9. How many contracts should Nicholas buy or sell? a. b. c. d.

Buy 703 contracts. Sell 703 contracts. Buy 717 contracts. Sell 717 contracts.

Answer: d Explanation: N = Exposure to hedge * Duration of assets to be hedged Price of futures contract * Duration of futures contract = 150 mil * 2.5 = 375 mil = 375 717 contracts 106 22/32 * 0.1 mil * 4.9 106.6875 * 0.1 mil * 4.9 0.52276875 Since he is long in the asset, he should sell 717 contracts. The answer with 703 contracts comes from not using the duration at the maturity of the futures contract. Topic: Financial Markets and Products Subtopic: Futures, forwards, swaps and options Reference: John Hull, Options, Futures, and Other Derivatives, 6th Edition (New York: Prentice Hall, 2006), Chapter 6 – Interest Rate Futures

44



26.

Bonds issued by the XYZ Corp. are currently callable at par value and trade close to par. The bonds mature in 8 years and have a coupon of 8%. The yield on the XYZ bonds is 175 basis points over 8-year US Treasury securities, and the Treasury spot yield curve has a normal, rising shape. If the yield on bonds comparable to the XYZ bond decreases sharply, the XYZ bonds will most likely exhibit: a. b. c. d.

negative convexity increasing modified duration increasing effective duration positive convexity

Answer: a Explanation: a. is correct. As yields in the market declines, the probability that the call option will get exercised increases. The issuer will not necessarily exercise the call option as soon as the market yield drops below the coupon rate. Yet the value of the embedded call option increases causing the price to reduce relative to an otherwise comparable option free bond. This is negative convexity. b. is incorrect. Modified duration does not take into account the effect of embedded options. c. is incorrect. As the interest rates decline, the call option becomes more valuable therefore effective duration may decrease because the expected cash flows can decrease. d. is incorrect. When interest rates decline below the coupon rate, callable bonds show negative convexity. Topic: Financial Markets and Products Subtopic: Corporate bonds Reference: Frank Fabozzi, The Handbook of Fixed Income Securities, 7th edition, Chapter 13.


45


27.

A risk analyst seeks to find out the yield-to-maturity on a BB-rated, 2-year zero coupon bond issued by a multinational petroleum company. If the prevailing annual risk-free rate is 3%, the default rate for BB-rated bonds is 7% per year, and the loss given default is 60%, then the yield-to-maturity of the bond is: a. b. c. d.

2.57% 5.90% 7.45% 7.52%

Answer: c Explanation: The correct answer is obtained using the equation: (1 + rfr)T – (1 + r *)T [(1 – π)T + f(1 – (1 -π)T)] = 0. (1 + 3%)2 – (1 + r *)2 [(1 – 7% )2 + 40%(1 – (1 – 7%)2)] = 0. 1.0609 1.0609 (1 + r *)2 = = 2 2 0.93 + 40%(1 – (0.93) ) 0.8649 + 40% * 0.1351 1.0609 = 1.0609 (1 + r *)2 = 0.8649 + 40% * 0.1351 0.9189 1.0609 r* = – 1 = 7.45% √ 0.9189

a. b. c. d.

using rfr instead of r* uses LGD instead of RR correct fails to adjust for time horizon (i.e, T = 1)

Topic: Valuation and Risk Models Reference: Arnaud de Servigny and Olivier Renault, Measuring and Managing Credit Risk

46



28.

Your supervisor is an expert in market and credit risk. He recruits you to manage the operational risk department. He would like to use VaR to measure the firm’s operational risk and proposes that you use the same VaR framework previously developed for market and credit risk. Which of the following arguments is a valid argument for why it is difficult to estimate an operational VaR using the same framework as market and credit VaR? a. Market risk events are easier to map to risk factors than operational risk events. b. Quantitative methods for estimating operational risk VaR do not exist. c. Market and credit VaRs are estimated using only a frequency distribution, but operational VaR is estimated using both a frequency distribution and a severity distribution. d. Monte Carlo techniques cannot be used for an operational risk VaR because the underlying risk factors are not normally distributed. Answer: a

Explanation: a. is correct. Operational losses are not easy to map to risk factors. b. is incorrect. Operational VaR can be calculated. c. is incorrect. Operational VaR is calculated by both severity and frequency distribution. d. is incorrect. Monte Carlo techniques can be used for other distributions than the normal distribution. Topic: Valuation and Risk Models Subtopic: Applications of VaR for market, credit and operational risks Reference: Allen, Boudoukh, and Saunders, Understanding Market, Credit and Operational Risk, Chapter 5

29.

One of the traders whose risk you monitor put on a carry trade where he borrows in yen and invests in some emerging market bonds whose performance is independent of yen. Which of the following risks should you not worry about? a. b. c. d.

Unexpected devaluation of the yen. A currency crisis in one of the emerging markets the trader invests in. Unexpected downgrading of the sovereign rating of a country in which the trader invests. Possible contagion to emerging markets of a credit crisis in a major country.

Answer: a Explanation: A devaluation would result in a gain to the trader because he is short yen. Topic: Financial Markets and Products Subtopic: Foreign exchange risk Reference: Saunders, Cornett, Financial Institutions Management: A Risk Management Approach, 6th Edition, Chapter 14.


47


30.

John Flag, the manager of a USD 150 million distressed bond portfolio, conducts stress tests on the portfolio. The portfolio’s annualized return is 12%, with an annualized return volatility of 25%. In the last two years, the portfolio encountered several days when the daily value change of the portfolio was more than 3 standard deviations. If the portfolio suffered a 4-sigma daily event, which of the following is the best estimate of the change in the value of this portfolio? Assume that there are 250 trading days in a year. a. b. c. d.

USD 9.48 million USD 23.70 million USD 37.50 million USD 150 million

Answer: a Explanation: Daily volatility is equal to 0.25 x √1/250 = 0.0158. A 4-sigma event therefore implies a loss equal to 4 x 0.0158 x 150 = 9,486,832. b. Calculates the daily volatility and multiplies the volatility with the value of the portfolio. c. Multiplies the portfolio value by its annual volatility, or divides the portfolio value by 4. d. Attempts the short-cut of reducing the portfolio value by 4 times 25%, which is 100%, i.e, the value of the portfolio. Topic: Valuation and Risk Models Subtopic: Stress testing and scenario analysis Reference: Jorion, Value-at-Risk, 3rd edition, Chapter 14.

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31.

The current spot price of cotton is USD 0.7409 per pound. The cost of storing and insuring cotton is USD 0.0042 per pound per month payable at the beginning of every month. The risk-free rate is 5%. A 3-month forward contract trades at USD 0.7415 per pound. If there is an arbitrage opportunity, how would you capitalize on it to make a profit? Assume there are no restrictions on short selling cotton. i. ii. iii. iv. v. vi.

short the futures contract borrow at the risk-free rate buy cotton at the spot price go long in the futures contract invest at the risk-free rate sell cotton at the spot price

a. b. c. d.

There is no arbitrage opportunity here. The arbitrage opportunity involves i, ii, and iii. The arbitrage opportunity involves iv, v, and vi. The arbitrage opportunity involves ii, iv, and vi.

Answer: c Explanation: a. is incorrect as there exists an arbitrage opportunity on account of price differentials. b. is incorrect. As the futures price is lower than the observed price (future spot price), you need to long the futures and not short it. c. is correct because such a strategy results in profit, as shown below. The future spot price is USD 0.7428: [ 0.7409 e 0.05 * (3/12) ] + [ 0.0042 (1+0.05/12)3 + 0.0042 (1+0.05/12)2 + 0.0042 (1+0.05/12) ] = 0.7301 + 0.0127 = USD 0.7428 The futures price is USD 0.7415, which is lower than USD 0.7428. Hence you need to buy the futures, sell cotton spot and invest the funds in a risk-free bond so as to obtain a riskless profit of USD 0.0013 per pound. d. is incorrect because borrowing and buying cotton spot do not result in a profit. Topic: Financial Markets and Products Subtopic: Futures, forwards, swaps and options Reference: John C. Hull, Options, Futures & Other Derivatives, 6th edition.


49


32.

There are many reasons why risk management increases shareholder wealth. Which of the following risk management policies is least likely to increase shareholder wealth? a. b. c. d.

Hedging strategies to lower the probability of financial distress and bankruptcy. Risk management policies designed to reduce the probability of debt overhang. Well-designed compensation structure for managers that sets incentives for managers to take appropriate risks. Risk management policies designed to eliminate projects with high volatility.

Answer: d Explanation: The first three are examples of where risk management can increase firm value. The last one is invalid because reducing volatility per se could just eliminate projects with extremely high payoffs. Topic: Foundations of Risk Management Subtopic: Creating value with risk management Reference: Stulz, Chapter 3.

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33.

In late 1993, Metallgesellschaft reported losses of approximately USD 1.5 billion in connection with the implementation of a hedging strategy in the oil futures market. In 1992, the company had begun a new strategy to sell petroleum to independent retailers, on a monthly basis, at fixed prices above the prevailing market price for periods of up to 5 and even 10 years. At the same time, Metallgesellschaft implemented a hedging strategy using a large number of short-term derivative contracts such as swaps and futures on crude oil, heating oil, and gasoline on several exchanges and markets. Its approach was to buy on the derivatives market exposure to one barrel of oil for each barrel it had committed to deliver. Because of its choice of a hedge ratio, the company suffered significant losses with its hedging strategy when oil market conditions abruptly changed to: a. b. c. d.

Contango, which occurs when the futures price is above the spot price. Contango, which occurs when the futures price is below the spot price. Normal backwardation, which occurs when the futures price is above the spot price. Normal backwardation, which occurs when the futures price is below the spot price.

Answer: a Explanation: Oil prices fell in the fall of 1993 because of OPEC’s problems adhering to its production quotas, so the market changed into one of contango so c and d are incorrect. In contango, the futures price is above the spot price and as a result Metallgesellchaft incurred losses on its short-dated long futures contracts so b is incorrect and a is correct. Topic: Foundations of Risk Management Subtopic: Case studies Reference: Steven Allen, “Financial Risk Management: A practitioners Guide”, Chapter 4 – Financial Disasters.


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34.

The current share price and daily volatility of a stock are USD 10 and 2%, respectively. Using the delta-normal approximation, the 95% VaR on a long at-the-money call on this stock over a one-day holding period is: a. b. c. d.

USD 0.1645 USD 0.3290 USD 1.645 USD 16.45

Answer: a Explanation: This question requires candidates to know the formula for the delta-normal VaR approximation, and also to know that the delta of an at-the-money call is 0.5. VaR = 0.5 x 1.645 x 0.02 x 10 = 0.1645 a. the correct answer. b. uses a delta of 1. c. confuses the decimal point. d. uses 2 instead of 2% for the volatility. Topic: Valuation and Risk Models Subtopic: Value-at-Risk—delta normal valuation Reference: Jorion, Value-at-Risk, 3rd edition

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35.

In country X, the probability that a letter sent through the postal system reaches its destination is 2/3. Assume that each postal delivery is independent of every other postal delivery, and assume that if a wife receives a letter from her husband, she will certainly mail a response to her husband. Suppose a man in country X mails a letter to his wife (also in country X) through the postal system. If the man does not receive a response letter from his wife, what is the probability that his wife received his letter? a. b. c. d.

1/3 3/5 2/3 2/5

Answer: d Explanation: A = Event that the wife receives the man’s letter B = Event that the man does not receive a response from his wife We need to find P(A|B). First, we know P(A) = 2/3. To get P(B), note that there are three possible scenarios. 1. His letter does not get to his wife → probability is 1/3. 2. Her response letter does not get to him → 2/9 (= 2/3 * 1/3, probability that she gets his letter times the probability that her letter gets lost) 3. Her response letter does get to him → 4/9 (= 2/3 * 2/3, probability that she gets his letter times the probability that her letter gets to him). He does not receive a response in scenarios 1 and 2, so P(B) = 5/9 Next, we also know P(B|A) = 1/3 (if she receives the letter, she responds and so he only does not get a response if the letter is lost which happens with probability 1/3) Then, by Bayes’ rule, P(A|B) = P(B|A) * P(A) / P(B) = (1/3) * (2/3) / (5/9) = 2/5 Topic: Quantitative Analysis Subtopic: Probability distributions Reference: Damodar N Gujarati, Essentials of Econometrics, 3rd Edition


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36.

Basis risk is a common problem faced by hedgers because the underlying and the hedging instrument may not always move in perfect correlation. Which of the following strategies has the least basis risk? a. b. c. d.

Straddle strategy Hedging individual equities using index futures Stack and roll strategy Delta hedging strategy

Answer: a Explanation: A straddle involves buying a call and a put for the same underlying at a given strike price. There is no basis risk. The other strategies have basis risk. Topic: Financial Markets and Products Subtopic: Futures, forwards, swaps and options Reference: McDonald, chapter 6.

37.

Which one of the following four trading strategies limits the investor’s upside potential and downside risk? a. A long position in a put combined with a long position in a stock. b. A short position in a put combined with a short position in a stock. c. Buying a call option on a stock with a certain strike price and selling a call option on the same stock with a higher strike price and the same expiration date. d. Buying a call and a put with the same strike price and expiration date. Answer: c

Explanation: Long position in a put combined with long position in a stock could limit only the downside risk; A is incorrect. Short position in a put combined with short position in a stock could limit only the upside risk; B is incorrect. Buying a call option on a stock with a certain strike price and selling a call option on the same stock with a higher strike price and the same expiration date could limit both the upside and downside risk; C is correct. Buying a call and put with the same strike price and expiration date could limit only the downside risk; D is incorrect. Topic: Financial Markets and Products Subtopic: Derivatives on fixed‐income securities, interest rates, foreign exchange, equities, and commodities Reference: John Hull, Options, Futures, and Other Derivatives, 7th edition.

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38.

Which of the following statements are correct about the early exercise of American options? i. ii. iii. iv.

It is never optimal to exercise an American call option on a non-dividend-paying stock before the expiration date. It can be optimal to exercise an American put option on a non-dividend-paying stock early. It can be optimal to exercise an American call option on a non-dividend-paying stock early. It is never optimal to exercise an American put option on a non-dividend-paying stock before the expiration date.

a. b. c. d.

i and ii i and iv ii and iii iii and iv

Answer: a Explanation: There are no advantages to exercising early if the investor plans to keep the stock for the remaining life of the call option, because the early exercise would sacrifice the interest that would be earned if the strike price is paid out later on expiration date after the early exercise, the investor may suffer the risk that the stock price will fall below the strike price as the stock pays no dividend, the early exercise will earn no income from the stock. So it is never optimal to exercise an American call option on a nondividend-paying stock before the expiration date. At any given time during its life, a put option should always be exercised early if it is sufficiently deep in the money. So it can be optimal to exercise an American put option on a non-dividend-paying stock early. As a result, answer A is correct. Topic: Financial Markets and Products Subtopic: American Options, effects of dividends, early exercise Reference: John Hull, Options, Futures, and Other Derivatives, 6th Edition, Chapter 9


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39.

In 2006, UBS reported no exceedances on its daily 99% VaR. In 2007, UBS reported 29 exceedances. To test whether the VaR was biased, you consider using a binomial test. Assuming no serial correlation, 250 trading days, and an accurate VaR measure, you calculate the probability of observing n exceedances, for n = 0, 1, . . . n 0 1 2 3 4


n 5 6 7 8 9


Which of the following statements is not correct? a. At the 5% probability level, you cannot reject that the VaR was unbiased in 2006 using a binomial test. b. The lack of exceedances in 2006 demonstrates that UBS failed to take into account the existence of fat tails in estimating the distribution of its market risk. c. It is difficult to evaluate the implications of the lack of exceedances if the VaR is forecasted for a static portfolio and it is compared against the trading P&L. d. At the 5% probability level, you can reject that the VaR was unbiased in 2007 using a binomial test. Answer: b Explanation: A and D are correct. Using 250 days in a year, the binomial test rejects for 2006 at the 8% level and for 2006 at less than the 1% level. C is correct since the trading P&L includes intra-day trading as well as market-making income. B is wrong since exceedances alone tell us nothing about the existence of fat tails. Topic: Valuation and Risk Models Subtopic: Value-at-Risk definition and methods Reference: Allen, Boudoukh, Saunders, Understanding Market, Credit and Operational Risk, chapters 2, 3.

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40.

An asset manager analyzes a position consisting of a put option sold on an underlying asset, which is a hedge fund pursuing a fixed income strategy. This hedge fund, which the asset manager does not own, reports daily returns to the asset manager. Due to the credit crisis, return volatility of the hedge fund has been increasing, which makes the manager nervous about the short option position. When the asset manager entered this trade, he set a guideline limiting the 95% 1-day VaR exposure of this trade to 1.0% of the fund’s NAV. Assuming the hedge fund returns are normally distributed and that there are 250 trading days per year, what is the lowest level of annualized return volatility that exceeds the guideline? a. b. c. d.

Any volatility over 6% Any volatility over 7% Any volatility over 8% Any volatility over 10%

Answer: d Explanation: 95% 1-day VAR of the Fund should not exceed 1.0% on Fund's NAV From this we can conclude that (assuming there are 250 trading days in the calendar year): 1-day VAR = 1.645 * Annualized Volatility * sqrt (1/250) * FundNAV < 1% * FundNAV Therefore: Annualized Volatility < 1% * sqrt(250) / 1.645 Volatility < 9.61% So the officer will be nervous if the volatility of the returns of the fund were to increase over 10% and not otherwise. Topic: Risk Management and Investment Management Subtopic: Setting Risk Limits Reference: Jorion, Chapter 7.


57


Financial Risk ® Manager (FRM ) Examination 2010 Practice Exam PART II

2010 FRM Examination Practice Exam / PART II

2010 FRM PRACTICE EXAM PART II: ANSWER SHEET

a.

b.

c.

a.

d.

1.

23.

2.

24.

3.

25.

4.

26.

5.

27.

6.

28.

7.

29.

8.

30.

9.

31.

10.

32.

11.

33.

12.

34.

13.

35.

14.

36.

15.

37.

16.

38.

17.

39.

18.

40.

b.

c.

d.

19. 20.


21. 22.

✓

✘



1.

You are the risk manager of a pension fund. You are asked to evaluate how the correlation among hedge funds and between hedge funds and other asset classes, respectively, has evolved over time. Which of the following statements are correct? a. In recent years, correlations between hedge fund strategies have increased, while correlations of hedge funds with broad market indices have decreased. b. In recent years, correlations between hedge fund strategies have increased, and correlations of hedge funds with broad market indices have also increased. c. In recent years, correlations between hedge fund strategies have decreased, and correlations of hedge funds with broad market indices have also decreased. d. In recent years, correlations between hedge fund strategies have decreased, while correlations of hedge funds with broad market indices have increased.

2.

Which of the following is not a drawback of the Basel II Foundation Internal Ratings Based (IRB) approach? a. b. c. d.

3.

Probabilities of default (PDs) and losses given default (LGDs) are assumed to be uncorrelated. Asset correlations decrease with increasing PDs. The portfolio of the financial institution is assumed to be infinitely granular. The approach uses a single risk factor portfolio model instead of a multiple risk factor model.

The Basel II risk weight function for the Internal Ratings Based Approach (IRB) is based on the Asymptotic Single Risk Factor (ASRF) model, under which the system-wide risks that affect all obligors are modeled with only one systematic risk factor. The major reason for using the ASRF is: a. The model should not depend on the granularity of the portfolio. b. The model should be portfolio invariant so that the capital required for any given loan depends only on the risk of that loan and does not depend on the portfolio it is added to. c. The model should not be portfolio invariant and the capital required for any given loan should not depend on the risk of other loans. d. The model corresponds to the one-year Value at Risk at a 99.9% confidence level.


61


4.

FASB 140, “Accounting for Transfers and Servicing of Financial Assets and Extinguishment of Liabilities,” sets out standards for qualified SPEs (QSPEs). Which of the following is not a requirement under FASB 140 that an SPE must satisfy in order to receive the QSPE designation? a. b. c. d.

5.

The SPE must be demonstrably different from the originator and any affiliates of the originator. The SPE cannot use derivatives. Sale and disposition of assets in the QSPE must be defined in the deal documents and may never be discretionary. Sale and disposition of passive financial assets and passive derivatives in the QSPE must be defined in the deal documents and may never be discretionary.

You are asked to mark to market a book of plain vanilla stock options. The trader is short deep out-of-money options and long at-the-money options. There is a pronounced smile for these options. The trader’s bonus increases as the value of his book increases. Which approach should you use to mark the book? a. Use the implied volatility of at-the-money options because the estimation of the volatility is more reliable. b. Use the average of the implied volatilities for the traded options for which you have data because all options should have the same implied volatility with Black-Scholes and you don’t know which one is the right one. c. For each option, use the implied volatility of the most similar option traded on the market. d. Use the historical volatility because doing so corrects for the pricing mistakes in the option market.

6.

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As a risk practitioner, Leo realizes that model risk can never be eliminated, although he may find some ways to protect against it. Which of the following measures help reduce model risk? i. ii. iii. iv.

All else equal, choose the model with the fewest parameters. Have regularly scheduled model reviews that involve careful back-testing and stress-testing. Identify and evaluate key model assumptions, and ignore small but persistent problems. Validate the model using simple problems for which answers are independently known.

a. b. c. d.

ii only i, ii, and iii i, ii, and iv iii and iv



7.

Randy Bartell has collected operational loss data to calibrate frequency and severity distributions. Generally, he regards all data points as a sample from an underlying distribution and therefore gives each data point the same weight or probability in the statistical analysis. However, external loss data is inherently biased. Which of the following biases is not typically associated with external loss data? a. b. c. d.

8.

Mortgage-backed securities (MBS) are a class of securities where the underlying is a pool of mortgages. Assume that the mortgages are insured, so that they do not have default risk. The mortgages have prepayment risk because the borrower has the option to repay the loan early (at any time) usually due to favorable interest rate changes. From an investor’s point of view, a mortgage-backed security is equivalent to holding a long position in a non-prepayable mortgage pool and which of the following? a. b. c. d.

9.

Data capture bias Scale bias Truncation bias Omitted-variable bias

A long American call option on the underlying pool of mortgages. A short American call option on the underlying pool of mortgages. A short European put option on the underlying pool of mortgages. A long American put option on the underlying pool of mortgages.

You are a risk manager for a hedge fund. You are told that the TED spread increased sharply. Which of the following statements best describes the change in your situation? a. An increase in the TED spread indicates that the US Federal Reserve will push interest rates up, so the duration of the portfolios should be reduced. b. An increase in the TED spread indicates a bigger gap between the Fed Funds rate and Treasuries, so that the US Federal Reserve will choose to increase liquidity in the markets, which will increase prices of securities as demand will increase. c. An increase in the TED spread could indicate greater concerns about bank solvency, so that you should review your counterparty exposures and possibly hedge some exposure to banks. d. An increase in the TED spread could indicate more willingness of banks to lend since they get paid more for lending, so that we should use the opportunity to renegotiate lines of credit.


63


10.

According to the Basel II Accord, “At the discretion of their national authority, banks may also use a third tier of capital (Tier 3), consisting of short-term subordinated debt for the sole purpose of meeting a proportion of the capital requirements for,” which of the following? a. b. c. d.

11.

12.

Market risk charges only Credit risk charges only Market risk and credit risk charges All types of risk charges

Unexpected loss (UL) represents the standard deviation of losses, and expected loss (EL) represents the average losses over the same time horizon. Further define LGD as expected loss given default and EDF as expected default frequency. Which of the following statements are true? i. ii. iii. iv.

EL increases linearly with increasing EDF. EL is often higher than UL. With increasing EDF, UL increases at a much faster rate than EL. The lower the LGD, the higher the percentage loss for both the EL and UL.

a. b. c. d.

i only i and ii i and iii ii and iv

Suppose that you want to estimate the implied default probability for a BB-rated discount corporate bond. • • •

The T-bond (a risk-free bond) yields 12% per year. The one-year BB-rated discount bond yields 15.8% per year. The two-year BB-rated discount bond yields 18% per year.

If the recovery rate on a BB-rated bond is expected to be 0%, and the marginal default probability in year one is 5%, which of the following is the best estimate of the risk-neutral probability that the BB-rated discount bond defaults within the next two years? a. b. c. d.

64

6.85% 3.28% 9.91% 10.14%



13.

A credit manager overseeing the structured credit book of a bank works on identifying the frictions in the securitization process that caused the recent subprime mortgage crisis in the United States. Of the following frictions in the securitization process, which one was not a cause of the subprime crisis? a. b. c. d.

14.

Paul sells a put option on HRTB stock with a time to expiration of 6 months, a strike price of USD 125, an underlying asset price of USD 98, implied volatility of 20% and a risk-free rate of 4%. What is Paul’s credit exposure from this transaction? a. b. c. d.

15.

Frictions between the mortgagor and the originator: predatory lending. Frictions between the originator and the arranger: predatory borrowing and lending. Frictions between the servicer and asset manager: moral hazard. Frictions between the asset manager and investor: principal-agent conflict.

USD 0.00 USD 0.38 USD 1.75 USD 24.90

Which of the following approaches can be used to compute regulatory capital under the internal ratings-based (IRB) approach for securitization exposures under the Basel II framework? i. ii. iii. iv.

Ratings-Based Approach (RBA) Supervisory Formula (SF) Internal Assessment Approach (IAA) Internal Models Approach (IMA)

a. b. c. d.

i and ii i, ii, and iii ii, iii, and iv i, iii, and iv


65


16.

The following statements concern differences between market and operational risk VaR models. Which of the following statements is false? a. Market risk models are primarily driven by historical data, whereas operational risk models often incorporate more qualitative information. b. Market risk VaR estimates a specific quantile of the loss distribution, whereas operational risk VaR estimates the frequency of specific losses. c. Backtesting is generally a more useful form of validation for market risk models than for operational risk models. d. The time horizon over which VaR is evaluated differs between market and operational risk models.

17.

The bank’s trading book consists of the following two assets: Asset A B

Annual Return 10% 20%

Volatility of Annual Return 25% 20%

Value 100 50

Correlation (A, B) 0.2 How would the daily VaR at 99% level change if the bank sells 50 worth of asset A and buys 50 worth of asset B? Assume there are 250 trading days in a year. a. b. c. d.

66

0.2286 0.4581 0.7705 0.7798



18.

Joan Berkeley is an investment analyst for a U.S.-based pension fund that considers adding a large capitalization equity mutual fund to its asset mix. To assess these funds better, Joan conducts detailed quantitative analysis on four mutual funds that claim to be large-capitalization funds. The quantitative results are shown in Exhibits 1 and 2. Exhibit 1: Style Analysis Results for the Four Funds Andromeda Russell 1000 Value Index (large-cap) 98% Russell 1000 Growth Index (large-cap) 0% Russell 2000 Value Index (small-cap) 2% Russell 2000 Growth Index (small-cap) 0% Total 100% R2 99.0%

Borealis 10% 78% 1% 11% 100% 89.7%

Crux 34% 5% 28% 33% 100% 85.5%

Draco 69% 22% 9% 0% 100% 67.5%

Exhibit 2: Performance Measurement of the Four Funds Benchmark S&P 500 Andromeda Annual return (gross) 6.8% 7% Sharpe ratio 0.42 0.47 Treynor ratio 0.34 0.36 Tracking error — 8%

Borealis 7.3% 0.49 0.34 8.6%

Crux 7.9% 0.46 0.32 9.1%

Draco 8.5% 0.47 0.38 9.5%

Based on the above results, Joan made several comments. Which of the following statements is least likely to be correct? a. b. c. d.

Andromeda is a passively managed fund. The pension fund should invest in the Borealis fund because it has the highest Sharpe ratio. Crux’s investment style has drifted to small-capitalization. Draco has the highest Information Ratio.


67


19.

In examining some of the features of a two-asset credit portfolio, consisting of two correlated credits, credit A and credit B, let the following notation be given: • • •

RCA, RCB is the risk contribution of credit A and credit B, respectively. ELP, ELA, ELB is the expected loss of a portfolio consisting of credits A and B, credit A, and credit B, respectively. ULP, ULA, ULB is the unexpected loss of a portfolio consisting of credits A and B, credit A, and credit B, respectively.

Using the notation above and assuming that the two assets’ defaults are correlated, which of the following equations is correct? a. b. c. d.

20.

Widget, Inc., is considering an investment in a new business line. The company calculates the RAROC for the new business line to be 12%. Suppose the risk-free rate is 5%, the expected rate of return on the market is 11.0%, and the systematic risk of the company is 1.5. If the company only invests in new businesses for which the ARAROC (adjusted RAROC) exceeds the expected excess rate of return on the market, what return will this new business earn for Widget, Inc.? a. b. c. d.

68

ELP = ELA + ELB ULP = ULA + ULB ULP > RCA + RCB RCA + RCB > ULA + ULB

0.0% 12.0% 4.7% 6.0%



21.

Redhat is a small bank whose only business line is retail banking.With the Basel II Standardized Approach for calculating operational risk capital charges, the beta factors for each business line are given in the following table: Business Line Corporate finance Trading and sales Retail banking Commercial banking Payment and settlement Agency services Asset management Retail brokerage

Beta Factor 18% 18% 12% 15% 18% 15% 12% 12%

Assuming Redhat is eligible to choose any Basel II approach for operational risk, which Basel II approach will minimize Redhat’s operational risk capital charge? a. b. c. d.

22.

Basic Indicator Approach. Standardized Approach. Foundation Internal Ratings-Based Approach (FIRB). Both the Basic Indicator Approach and the Standardized Approach have the same operational risk charge for Redhat.

In a synthetic CDO, a. b. c. d.

The SPV gains credit exposure by buying securities. The SPV gains credit exposure by selling credit default swaps. The SPV gains credit exposure by buying credit default swaps. The SPV gains credit exposure by selling risk-free bonds.


69


23.

Consider the following two asset portfolios: Asset A B Portfolio

Position Value Return Standard Deviation (%) (in thousands of USD) 400 3.60 600 8.63 1,000 5.92

Beta 0.5 1.2 1.0

Calculate the component VaR of asset A and marginal VaR of asset B, respectively, at 95% confidence level? a. b. c. d.

24.

USD 21,773 and 0.1306 USD 21,773 and 0.1169 USD 19,477 and 0.1169 USD 19,477 and 0.1306

Which of the options below properly classifies each model risk error into a model risk category? Model Risks • Risk 1: Failure to consider a sufficient number of trials in a Monte Carlo simulation. • Risk 2: Use of the mid-quote price rather than the bid price to value long positions in financial instruments. • Risk 3: Failure to fully account for time-variation of volatility. Model Risk Categorization • Implementation risk • Incorrect model calibration • Incorrect model application a. b. c. d.

70

Risk 1 = Incorrect model calibration, Risk 2 = Implementation risk, Risk 3 = Incorrect model calibration Risk 1 = Implementation risk, Risk 2 = Incorrect model application, Risk 3 = Incorrect model calibration Risk 1 = Incorrect model application, Risk 2 = Implementation risk, Risk 3 = Incorrect model calibration Risk 1 = Incorrect model application, Risk 2 = Implementation risk, Risk 3 = Implementation risk



25.

Looking at a risk report, Mr.Woo finds that the options book of Ms. Yu has only long positions and yet has a negative delta. He asks you to explain how that is possible. What is a possible explanation? a. b. c. d.

26.

The book has a long position in up-and-in call options. The book has a long position in binary options. The book has a long position in up-and-out call options. The book has a long position in down-and-out call options.

John Grea has just been appointed the CFO of a bank and wants to construct a composite risk picture following a “building block” approach that aggregates risk at three successive levels in his organization. • Level I: Aggregates the standalone risks within a single risk factor. • Level II: Aggregates risk across different risk factors within a single business line. • Level III: Aggregates risk across different business lines. However, he understands that there might be different degrees of diversification benefits for each level. Empirically, which level in the “building block” approach has the greatest degree of diversification benefit? a. b. c. d.

Level I — single risk factor level Level II — single business line level Level III — different business lines level The degree of diversification benefits are the same for each level


71


27.

The capital structure of HighGear Corporation consists of two parts: one 5-year zero-coupon bond with a face value of USD 100 million and the rest is equity. The current market value of the firm’s assets (MVA) is USD 130 million and the expected rate of change of the firm’s value is 25%. The firm’s assets have an annual volatility of 30%. Assume that firm value is log-normally distributed with constant volatility. The firm’s risk management division estimates the distance to default (in terms of number of standard deviations) using the Merton Model, or

( ) ( FVB

MVA

–

δ –

1 2

σ 2A

)

Τ

σ A T0.5 Given the distance to default, the estimated risk-neutral default probability is: a. b. c. d.

28.

There are different commercially available credit risk models. These models exhibit significant differences as well as similarities. Which of the following models builds on transition probabilities determined by macro factors? a. b. c. d.

72

2.74% 12.78% 12.79% 30.56%

CreditMetrics KMV’s PortfolioManager CreditRisk+ CreditPortfolioView



29.

John Smith is a bank supervisor responsible for the oversight of Everbright Group, a large banking conglomerate. Everbright Group now determines its credit risk profile according to the foundation IRB approach and assesses operational risk according to the standardized approach as described in the Basel II Capital Accord. Which of the following are specific issues that should be addressed as part of Smith’s supervisory review process of Everbright Group? i. Review the bank’s internal control systems. ii. Check compliance with transparency requirements as described in Pillar 3 of Basel II Accord. iii. Make sure that the bank estimates for LGD and EAD for its corporate loans are in compliance with supervisory estimates. iv. Evaluate the impact of interest rate risk by assessing the impact of a 200 basis point interest rate shock to the bank’s capital position. a. b. c. d.

30.

i and iii only ii and iv only i, ii, and iv only i, ii, iii, and iv

Silo Bank begins its risk measurement process by calculating VaR for market, credit, and operational risk individually, and then aggregates the three measures to produce a firm-wide VaR. Correlation between risk types is a key input for calculating firm-wide VaR. Which of the following statements about correlation are valid? i.

When market and credit risks involve securities issued by firms such as bonds, warrants, and stocks, correlation estimates for market and credit risk can be derived using equity returns if Merton’s model for the pricing of debt holds. ii. If correlations between highly adverse market, credit, and operational outcomes are high, there is diversification across risk categories and therefore the firm-wide VaR is substantially less than the sum of the market, credit, and operational risk VaRs. iii. With non-normal distributions, the use of correlations estimated using historical data from a stable period may not adequately capture how extreme returns for one type of risk are related to extreme returns of another type of risk. a. b. c. d.

i, ii and iii i only ii and iii only None of the statements are valid.


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31.

The Trading Desk of Global Bank PLC presents its risk manager with a potential trade. The trade is to provide support through a bank guarantee to the AAA tranche issued by a Special Purpose Vehicle (SPV). The SPV’s assets are restricted to residential mortgage loans that have been sold by other originating banks into the pool, making the bond issued by the SPV an RMBS. As far as the bank knows, no further relationship is known to exist between the originating banks and the SPV issuing the AAA tranche of the RMBS in question. As a risk manager, the first decision is to evaluate the potential for counterparty risk in this transaction. Taking into account that no additional external credit enhancements are available here, which party involved in the complex securitization transaction would expose Global Bank PLC to counterparty risk? a. There is only counterparty exposure with the regional banks that originated the mortgages that are securitized in the SPV because in providing the bank guarantee to the AAA tranche on this RMBS, Global Bank PLC is exposed to the credit quality of these banks. b. There is counterparty exposure to both the regional banks and the SPV issuing the RMBS, and any default in either would directly affect Global Bank PLC. c. There is only counterparty exposure to the SPV because if the mortgages in the SPV were to default, the SPV would not be able to continue to make payments. d. There is no counterparty exposure as the bank guarantee to be provided by Global Bank PLC is only a contingent exposure.

32.

A credit risk manager of Esta Bank is reviewing the credit risk of a EUR 400,000 loan to KidCo, which is a subsidiary of Pattern Inc. Assume that KidCo will default if Pattern Inc. defaults, but Pattern Inc. will not necessarily default if KidCo defaults. If Pattern Inc. has a 1-year probability of default of 1% and KidCo has a 1-year probability of default of 5% given that Pattern Inc. does not default, what is the probability that KidCo defaults in the next year? a. b. c. d.

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5.00% 6.00% 5.95% 4.95%



33.

The spread on a one-year BBB-rated bond relative to the risk-free treasury of similar maturity is 1.4%. It is estimated that the contribution to this spread by all noncredit factors (e.g., liquidity risk, taxes) is 0.4%. Assuming the loss given default rate for the underlying credit is 40%, what is, approximately, the implied default probability for this bond? a. b. c. d.

34.

1.67% 2.33% 3.50% 2.50%

The following table lists the default probabilities for an A-rated issue by a company facing the risk of imminent downgrade. Year 1 2 3

Default Probability 0.300% 0.450% 0.550%

Assume that defaults, if they take place, only happen at the end of the year. Based on the information in the table above, calculate the cumulative default rate at the end of each of the next three years. a. b. c. d.

0.300%, 0.750%, 1.300% 0.300%, 0.150%, 0.250% 0.300%, 0.749%, 1.295% 0.300%, 0.449%, 0.548%


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35.

Which of the following statements are true? i.

Hedge fund manager compensation is often symmetric (i.e., a dollar of gain has the opposite impact on compensation as a dollar of loss), while the compensation of mutual fund managers is almost always asymmetric. ii. Leverage obtained through lines of credit increases the risk of a hedge fund more than leverage obtained by issuing debt, because unexpected cancellation of a line of credit by a lender during troubled times can force a fund to liquidate its positions in illiquid markets. iii. A hedge fund investor should pay performance-based compensation to the manager for producing alpha, but should not pay performance-based compensation to a hedge fund manager who has done well because the fund invests in risk factors that mirror the performance of his style or strategy, and the style or strategy has performed well. iv. The lack of hedge fund transparency is particularly problematic for investors with fiduciary responsibilities such as pension fund managers, and to secure funding from these investors, hedge fund managers often have to provide more information to these investors. a. b. c. d.

36.

i, ii, and iv only. ii, iii, and iv only. ii and iv only. i and iii only.

Which of the following statements does not identify a potential factor that played a role in the subprime crisis? a. Many products offered to subprime borrowers were very complex and subject to misunderstanding and/or misrepresentation. b. Credit ratings were assigned to subprime MBS with significant error. Even though the rating agencies publicly disclosed their rating criteria for subprime, investors lacked the ability to evaluate the efficacy of these models. c. Existing investment mandates often distinguished between structured and corporate ratings, forcing asset managers to evaluate structured debt issues and corporate debt issues with the same credit rating but different coupons. d. Without due diligence by the asset manager, the arranger’s incentives to conduct its own due diligence are reduced.

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37.

Which of the following instruments has or have the most potential counterparty credit risk when the final exchange draws near maturity? i. An FX forward contract in which the bank will pay USD 1.1 million and receive EUR 0.77 million on December 1, 2008. ii. A EUR 10 million interest rate swap with one remaining payment due December 1, 2008, in which the bank pays EURIBOR + 1.0% and receives 4.5%. iii. A cross-currency swap with final payments due December 1, 2008, in which the bank pays 5% annually on a notional USD 1.1 million and receives 10% annually on a notional value of EUR 0.7 million. a. b. c. d.

38.

i only ii and iii i and iii ii only

You have a long position in a digital call option – an option that is also called cash-or-nothing – on shares in Global Enterprises. The digital call has a strike price of USD 20 with one year remaining to expiration. Assume that the shares currently trade at USD 22 and annual return volatility of Global Enterprises shares is 15%.Which of the following sensitivities would be associated with this option? i. ii. iii. iv.

Delta is positive. Gamma is positive. Vega is negative. Vega is positive.

Which statements are true? a. b. c. d.

i and iii iv only i, ii, and iv ii and iii


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39.

The Merton model is used to predict default. It builds on several very strong assumptions and its applicability is hampered by practical difficulties. Which of the following statements does not correctly identify limiting assumptions or practical difficulties of using the model? a. b. c. d.

40.

The current yield-to-maturity on a 1-year zero coupon bond with a face value of 1,000 is 3%. There is an equal probability that, in the coming 6 months, the yield will either increase or decrease by 50 bp, respectively (to 2.5% and 3.5%, respectively). Using this information, what is the expected discounted value of the zero-coupon bond? a. b. c. d.

78

The Merton Model relies on a simplistic capital structure consisting of only one debt issue. The Merton Model asset value volatility cannot be estimated because firm value does not trade. The Merton Model assumes that debt does not pay a coupon while most publicly-trade debt is coupon debt. The Merton Model assumes a constant riskless interest rate.

969.45 970.67 982.80 985.23



2010 FRM PRACTICE EXAM PART II: CORRECT ANSWER SHEET

a.

b.

c.

a.

d.

b.

c.

1.

23.

2.

24.

3.

25.

4.

26.

5.

27.

6.

28.

7.

8.

10.

31.

32.

33.

12.

34.

13.

35.

29.

11.

14.

30.

9.

36.

15.

37.

16.

38.

17.

39.

18.

40.

19.

20.

d.


21.

22.

✓

✘



Financial Risk ® Manager (FRM ) Examination 2010 Practice Exam Answers and Explanations PART II


1.

You are the risk manager of a pension fund. You are asked to evaluate how the correlation among hedge funds and between hedge funds and other asset classes, respectively, has evolved over time. Which of the following statements are correct? a. In recent years, correlations between hedge fund strategies have increased, while correlations of hedge funds with broad market indices have decreased. b. In recent years, correlations between hedge fund strategies have increased, and correlations of hedge funds with broad market indices have also increased. c. In recent years, correlations between hedge fund strategies have decreased, and correlations of hedge funds with broad market indices have also decreased. d. In recent years, correlations between hedge fund strategies have decreased, while correlations of hedge funds with broad market indices have increased. Answer: b

Explanation: In recent years, correlations between hedge fund strategies have increased, and correlations of hedge funds with broad market indices have also increased. Topic: Risk Management and Investment Management AIMS: Reference: René M. Stulz, "Hedge Funds: Past, Present and Future".


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2.

Which of the following is not a drawback of the Basel II Foundation Internal Ratings Based (IRB) approach? a. b. c. d.

Probabilities of default (PDs) and losses given default (LGDs) are assumed to be uncorrelated. Asset correlations decrease with increasing PDs. The portfolio of the financial institution is assumed to be infinitely granular. The approach uses a single risk factor portfolio model instead of a multiple risk factor model.

Answer: b Explanation: a. Incorrect. This is a drawback of the Basel II prescribed IRB model as there can exist correlation between the PDs and LGDs which is not considered in the Basel model b. Correct. This is NOT a drawback of the Basel II prescribed IRB model as the higher the PD, the higher the idiosyncratic (individual) risk components of a borrower. The default risk depends less on the overall state of the economy and more on individual risk drivers c. Incorrect. This is a drawback of the Basel II prescribed IRB model as the portfolio of the financial institutions need not be completely granular d. Incorrect. This is a drawback of the Basel II prescribed IRB model as there can be many systematic risk factor affecting the exposure instead of one single risk factor Topic: Operational and Integrated Risk Management Subtopic: Regulation and Basel II Accord Reference: “An Explanatory Note on the Basel II IRB Risk Weight Functions” (Basel Committee on Banking Supervision Publication, July 2005)

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3.

The Basel II risk weight function for the Internal Ratings Based Approach (IRB) is based on the Asymptotic Single Risk Factor (ASRF) model, under which the system-wide risks that affect all obligors are modeled with only one systematic risk factor. The major reason for using the ASRF is: a. The model should not depend on the granularity of the portfolio. b. The model should be portfolio invariant so that the capital required for any given loan depends only on the risk of that loan and does not depend on the portfolio it is added to. c. The model should not be portfolio invariant and the capital required for any given loan should not depend on the risk of other loans. d. The model corresponds to the one-year Value at Risk at a 99.9% confidence level. Answer: b

Explanation: a. Is incorrect since granularity though an issue, is not the major factor here since the model assumes infinitely granular portfolios. b. Portfolio invariance is the only correct option above for the use of the ASRF in the Basel II model. c. This statement is incorrect but put here to confuse unprepared candidates. d. This statement is not correct since the model is based on a VaR minus Expected Loss approach to computing capital to cover Unexpected Losses (UL) under credit risk exposures. Type of question: Operational and Integrated Risk Management. Subtopic: Regulation and Basel II Accord Reference: An Explanatory Note on the Basel II IRB Risk Weight Functions (Basel Committee on Banking Supervision Publication, July 2005).


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4.

FASB 140, “Accounting for Transfers and Servicing of Financial Assets and Extinguishment of Liabilities,” sets out standards for qualified SPEs (QSPEs).Which of the following is not a requirement under FASB 140 that an SPE must satisfy in order to receive the QSPE designation? a. b. c. d.

The SPE must be demonstrably different from the originator and any affiliates of the originator. The SPE cannot use derivatives. Sale and disposition of assets in the QSPE must be defined in the deal documents and may never be discretionary. Sale and disposition of passive financial assets and passive derivatives in the QSPE must be defined in the deal documents and may never be discretionary.

Answer: b Explanation: The SPE may hold only passive financial assets and passive derivatives for hedging. Statement B is incorrect; all others are correct. Topic: Credit Risk Measurement and Management Subtopic: Securitization Reference: Christopher L. Culp, Structured Finance and Insurance: The Art of Managing Capital and Risk Chapter 16 – Securitization

5.

You are asked to mark to market a book of plain vanilla stock options. The trader is short deep out-of-money options and long at-the-money options. There is a pronounced smile for these options. The trader’s bonus increases as the value of his book increases. Which approach should you use to mark the book? a. Use the implied volatility of at-the-money options because the estimation of the volatility is more reliable. b. Use the average of the implied volatilities for the traded options for which you have data because all options should have the same implied volatility with Black-Scholes and you don’t know which one is the right one. c. For each option, use the implied volatility of the most similar option traded on the market. d. Use the historical volatility because doing so corrects for the pricing mistakes in the option market. Answer: c

Explanation: The prices obtained with C are the right ones because they correspond to prices at which you could sell or buy the options. Topic: Market Risk Measurement and Management Subtopic: Volatility smiles, Exotic Options Reference: John Hull, Options, Futures, and Other Derivatives.

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6.

As a risk practitioner, Leo realizes that model risk can never be eliminated, although he may find some ways to protect against it. Which of the following measures help reduce model risk? i. ii. iii. iv.

All else equal, choose the model with the fewest parameters. Have regularly scheduled model reviews that involve careful back-testing and stress-testing. Identify and evaluate key model assumptions, and ignore small but persistent problems. Validate the model using simple problems for which answers are independently known.

a. b. c. d.

ii only i, ii, and iii i, ii, and iv iii and iv

Answer: c Explanation: i. is correct. First and foremost, practitioners should simply be aware of the model risk; It is true that unnecessary complexity is never a virtue in model selection. ii. is correct. Practitioners should evaluate model adequacy using stress tests and backtests; models should be recalibrated and re-estimated on a regular basis, and the methods used should be kept up to date. iii. is incorrect. Users should explicitly set out the key assumptions on which a model is based, evaluate the extent to which the model’s results depend on these assumptions; But he should never ignore the small problems because small discrepancies are often good warning signals of larger problems. iv. is correct. It is always a good idea to check a model on simple problems to which one already knows the answer, and many problems can be distilled to simple special cases that have knows answers. Topic: Operation and Integrated Risk Management Subtopic: Model Risk Reference: Kevin Dowd, Measuring Market Risk 2nd., (West Sussex:Wiley & Sons, 2005) Chapter 16


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7.

Randy Bartell has collected operational loss data to calibrate frequency and severity distributions. Generally, he regards all data points as a sample from an underlying distribution and therefore gives each data point the same weight or probability in the statistical analysis. However, external loss data is inherently biased. Which of the following biases is not typically associated with external loss data? a. b. c. d.

Data capture bias Scale bias Truncation bias Omitted-variable bias

Answer: d Explanation: a. is incorrect. Data capture bias – Data is usually captured with a systematic bias. This problem is particularly pronounced with publicly available data. b. is incorrect. Scale bias – Scalability refers to the fact that operational risk is dependent on the size of the bank, i.e. the scale of operations. A bigger bank is exposed to more opportunity for operational failures and therefore to a higher level of operational risk. c. is incorrect. Truncation bias – Banks collect data above certain thresholds. It is generally not possible to guarantee that these thresholds are uniform. d. is correct. Survivorship bias is not a problem that is typically associated only with external data collection. Topic: Operational Risk Management/Data Collection Bias Subtopic: Evaluating the performance of risk management systems Reference: Falko Aue and Michael Kalkbrener, 2007, “LDA at Work”, Deutsche Bank White Paper.

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8.

Mortgage-backed securities (MBS) are a class of securities where the underlying is a pool of mortgages. Assume that the mortgages are insured, so that they do not have default risk. The mortgages have prepayment risk because the borrower has the option to repay the loan early (at any time) usually due to favorable interest rate changes. From an investor’s point of view, a mortgage-backed security is equivalent to holding a long position in a non-prepayable mortgage pool and which of the following? a. b. c. d.

A long American call option on the underlying pool of mortgages. A short American call option on the underlying pool of mortgages. A short European put option on the underlying pool of mortgages. A long American put option on the underlying pool of mortgages.

Answer: b Explanation: Prepayment risk is equivalent to an American call option because the borrower can repay at any time and the position is short because the option lies with the borrower. Topic: Market Risk Measurement and Management Subtopic: Mortgages and Mortgage Backed Securities Reference: Tuckman, Fixed Income Securities, Chapter 21.

9.

You are a risk manager for a hedge fund. You are told that the TED spread increased sharply. Which of the following statements best describes the change in your situation? a. An increase in the TED spread indicates that the US Federal Reserve will push interest rates up, so the duration of the portfolios should be reduced. b. An increase in the TED spread indicates a bigger gap between the Fed Funds rate and Treasuries, so that the US Federal Reserve will choose to increase liquidity in the markets, which will increase prices of securities as demand will increase. c. An increase in the TED spread could indicate greater concerns about bank solvency, so that you should review your counterparty exposures and possibly hedge some exposure to banks. d. An increase in the TED spread could indicate more willingness of banks to lend since they get paid more for lending, so that we should use the opportunity to renegotiate lines of credit. Answer: c

Topic: Credit Risk Measurement and Management Subtopic: Counterparty Risk Reference: “Studies on credit risk concentration: an overview of the issues and a synopsis of the results from the Research Task Force project” (Basel Committee on Banking Supervision Publication, November 2006).


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10.

According to the Basel II Accord, “At the discretion of their national authority, banks may also use a third tier of capital (Tier 3), consisting of short-term subordinated debt for the sole purpose of meeting a proportion of the capital requirements for,” which of the following? a. b. c. d.

Market risk charges only Credit risk charges only Market risk and credit risk charges All types of risk charges

Answer: a Explanation: Tier 3 capital can only be used to satisfy capital requirements resulting from market risk charges and cannot be applied to credit risk charges. Other choices are incorrect except choice A. Topic: Operational and Integrated Risk Management Subtopic: Basel II accord Reference:“Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework – Comprehensive Version” (Basel Committee on Banking Supervision Publication, June 2006).

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11.

Unexpected loss (UL) represents the standard deviation of losses, and expected loss (EL) represents the average losses over the same time horizon. Further define LGD as expected loss given default and EDF as expected default frequency. Which of the following statements are true? i. ii. iii. iv.

EL increases linearly with increasing EDF. EL is often higher than UL. With increasing EDF, UL increases at a much faster rate than EL. The lower the LGD, the higher the percentage loss for both the EL and UL.

a. b. c. d.

i only i and ii i and iii ii and iv

Answer: c Explanation: Over the same fixed horizon, we have the following equations: EL = AE × LGD × EDF UL = AE × AE – adjusted exposure at default i. ii. iii. iv.

is correct, EL increases linearly with increasing EDF is incorrect, EL is often lower than UL(EL < UL) is correct, UL increases much faster than EL with increasing EDF is incorrect, the lower the LGD( the higher the recovery rate), the lower is the percentage loss for both EL and UL

Topic: Credit Risk Measurement and Management Subtopic: Credit risk/expected loss/unexpected loss/LGD/EAD Reference: Michael Ong, Internal Credit Risk Models: Capital Allocation and Performance Measurement, Chapter 6


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12.

Suppose that you want to estimate the implied default probability for a BB-rated discount corporate bond. • • •

The T-bond (a risk-free bond) yields 12% per year. The one-year BB-rated discount bond yields 15.8% per year. The two-year BB-rated discount bond yields 18% per year.

If the recovery rate on a BB-rated bond is expected to be 0%, and the marginal default probability in year one is 5%, which of the following is the best estimate of the risk-neutral probability that the BB-rated discount bond defaults within the next two years? a. b. c. d.

6.85% 3.28% 9.91% 10.14%

Answer: c Explanation: (1 + 0.12)2 = PD * (1 + 0.18)2 → PD = 9.91% Topic: Credit Risk Measurement and Management Subtopic: Probability of Default Reference: Hull; Opitions, Futures and Other Derivatives.

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13.

A credit manager overseeing the structured credit book of a bank works on identifying the frictions in the securitization process that caused the recent subprime mortgage crisis in the United States. Of the following frictions in the securitization process, which one was not a cause of the subprime crisis? a. b. c. d.

Frictions between the mortgagor and the originator: predatory lending. Frictions between the originator and the arranger: predatory borrowing and lending. Frictions between the servicer and asset manager: moral hazard. Frictions between the asset manager and investor: principal-agent conflict.

Answer: c Explanation: a. is incorrect. Frictions between the mortgagor and the originator: predatory lending – have been identified as key frictions that caused the subprime mortgage crisis. b. is incorrect. Frictions between the originator and the arranger: predatory borrowing and lending – have been identified as key frictions that caused the subprime mortgage crisis. c. is correct. Frictions between the servicer and asset manager or credit ratings agency: moral hazard – although important these frictions have not been identified as key frictions that caused the subprime mortgage crisis. d. is incorrect. Frictions between the asset manager and investor: principal-agent – have been identified as key frictions that caused the subprime mortgage crisis. Topic: Credit Risk Measurement and Management Subtopic: Securitization, Risk Mitigation Reference: Adam Ashcroft and Til Schuermann, “Understanding the Securitization of Subprime Mortgage Credit”, 2007


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14.

Paul sells a put option on HRTB stock with a time to expiration of 6 months, a strike price of USD 125, an underlying asset price of USD 98, implied volatility of 20% and a risk-free rate of 4%. What is Paul’s credit exposure from this transaction? a. b. c. d.

USD 0.00 USD 0.38 USD 1.75 USD 24.90

Answer: a Explanation: Selling a put option exposes you to zero credit risk as the premium is paid up front. The correct answer is therefore a. All the information necessary to price the option is provided but it is not necessary. The value of the put option is USD 24.90 (answer D) while the value of a call option with the same terms is USD 0.38 (Answer B). Answer C is the value of a call option with 1 year to expiration. Topic: Credit Risk Measurement and Management Subtopic: Counterparty Credit Risk. Reference: Hull; Options, Futures and Other Derivatives.

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15.

Which of the following approaches can be used to compute regulatory capital under the internal ratings-based (IRB) approach for securitization exposures under the Basel II framework? i. ii. iii. iv.

Ratings-Based Approach (RBA) Supervisory Formula (SF) Internal Assessment Approach (IAA) Internal Models Approach (IMA)

a. b. c. d.

i and ii i, ii, and iii ii, iii, and iv i, iii, and iv

Answer: b Explanation: a. Is incorrect since IAA is missing. b. Correct since the RBA, SF and IAA are the correct approaches. c. Is incorrect since RBA is missing and IMA is wrong since it is for Market Risk. d. Is incorrect since IMA is used for Market Risk. Topic: Operational and Integrated Risk Management Subtopic: Basel II accord Reference: Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework – Comprehensive Version”


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16.

The following statements concern differences between market and operational risk VaR models. Which of the following statements is false? a. Market risk models are primarily driven by historical data, whereas operational risk models often incorporate more qualitative information. b. Market risk VaR estimates a specific quantile of the loss distribution, whereas operational risk VaR estimates the frequency of specific losses. c. Backtesting is generally a more useful form of validation for market risk models than for operational risk models. d. The time horizon over which VaR is evaluated differs between market and operational risk models. Answer: b

Explanation: a. is true. Operational risk models often rely heavily on scenarios and other forms of judgment in addition to historical loss data. Operational risk models often incorporate more qualitative information. b. is false. Operational risk models do define VaR as a specific quantile of the loss distribution, typically either 99.9 or 99.97. c. is true. The high soundness standard typically used in operational risk models together with the limited time series of data available make backtesting of limited value. d. is true. Operational risk VaRs are typically calculated at a 1 year time horizon, whereas market risk VaRs are typically calculated at shorter horizons. Topic: Operational and Integrated Risk Management Subtopic: Correlations across market, credit and operational risk. Reference: Nocco and Stulz, Enterprise Risk Management: Theory and Practice.

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17.

The bank’s trading book consists of the following two assets: Asset A B

Annual Return 10% 20%

Volatility of Annual Return 25% 20%

Value 100 50

Correlation (A, B) = 0.2 How would the daily VaR at 99% level change if the bank sells 50 worth of asset A and buys 50 worth of asset B? Assume there are 250 trading days in a year. a. b. c. d.

0.2286 0.4581 0.7705 0.7798

Answer: b Explanation: The trade will decrease the VaR by 0.4581 Topic: Valuation and Risk Models Subtopic: Value-at-Risk; definition and methods Reference: Allen, Boudoukh, Saunders: chapter 2, 3


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18.

Joan Berkeley is an investment analyst for a U.S.-based pension fund that considers adding a large capitalization equity mutual fund to its asset mix. To assess these funds better, Joan conducts detailed quantitative analysis on four mutual funds that claim to be large-capitalization funds. The quantitative results are shown in Exhibits 1 and 2. Exhibit 1: Style Analysis Results for the Four Funds Andromeda Russell 1000 Value Index (large-cap) 98% Russell 1000 Growth Index (large-cap) 0% Russell 2000 Value Index (small-cap) 2% Russell 2000 Growth Index (small-cap) 0% Total 100% R2 99.0%

Borealis 10% 78% 1% 11% 100% 89.7%

Crux 34% 5% 28% 33% 100% 85.5%

Draco 69% 22% 9% 0% 100% 67.5%

Exhibit 2: Performance Measurement of the Four Funds Benchmark S&P 500 Andromeda Annual return (gross) 6.8% 7% Sharpe ratio 0.42 0.47 Treynor ratio 0.34 0.36 Tracking error — 8%

Borealis 7.3% 0.49 0.34 8.6%

Crux 7.9% 0.46 0.32 9.1%

Draco 8.5% 0.47 0.38 9.5%

Based on the above results, Joan made several comments. Which of the following statements is least likely to be correct? a. b. c. d.

Andromeda is a passively managed fund. The pension fund should invest in the Borealis fund because it has the highest Sharpe ratio. Crux’s investment style has drifted to small-capitalization. Draco has the highest Information Ratio.

Answer: b Explanation: Choice a: The high R2 indicate low residuals, and the fund is probably being passively managed. Choice b: The Sharpe ratio is not the right metric in this context because a fund is added to an existing portfolio and the fund has to be a large cap fund. Choice c: Although Crux claims to be large-capitalization fund, its weight in Russell 2000 Value Index and Russell 2000 Growth Index sum up to over 60%. So style drifting occurs. Choice d: Information ratio = (fund return – S&P 500 return)/tracking error. Draco has the highest IR. Topic: Risk Management and Investment Management Subtopic: Risks of Specific Strategies References: Lars Jaeger (ed), The New Generation of Risk Management for Hedge Funds and Private Equity Investments (London: Euromoney Institutional Investor, 2003), Chapter 27.

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19.

In examining some of the features of a two-asset credit portfolio, consisting of two correlated credits, credit A and credit B, let the following notation be given: • • •

RCA, RCB is the risk contribution of credit A and credit B, respectively. ELP, ELA, ELB is the expected loss of a portfolio consisting of credits A and B, credit A, and credit B, respectively. ULP, ULA, ULB is the unexpected loss of a portfolio consisting of credits A and B, credit A, and credit B, respectively.

Using the notation above and assuming that the two assets’ defaults are correlated, which of the following equations is correct? a. b. c. d.

ELP = ELA + ELB ULP = ULA + ULB ULP > RCA + RCB RCA + RCB > ULA + ULB

Answer: a Explanation: a. is correct. Two different risky assets with average losses due to a credit event at some time during the analysis horizon have an aggregate average loss equal to the sum of the two average losses. b. is incorrect. The unexpected loss of the portfolio is not equal to the sum of the individual unexpected losses of the risky assets that make up the aggregate portfolio due to (default) correlation. ULP = (ULA * ULA + ULB * ULB + 2 ULA * ULB *corr)0.5 c. is incorrect. The sum of all the risk contributions from all the assets in the portfolio is the portfolio unexpected loss; ULP = RCA + RCB d. is incorrect. The portfolio unexpected loss is very much smaller than the sum of the individual unexpected losses due to the diversification effect. ULP = (ULA * ULA + ULB * ULB + 2 ULA * ULB *corr)0.5 Topic: Credit Risk Measurement and Management Subtopic: Credit risk/portfolio expected loss/portfolio unexpected loss/risk contribution. Reference: Michael Ong, Internal Credit Risk Models: Capital Allocation and Performance Measurement, Chapter 6


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20.

Widget, Inc., is considering an investment in a new business line. The company calculates the RAROC for the new business line to be 12%. Suppose the risk-free rate is 5%, the expected rate of return on the market is 11.0%, and the systematic risk of the company is 1.5. If the company only invests in new businesses for which the ARAROC (adjusted RAROC) exceeds the expected excess rate of return on the market, what return will this new business earn for Widget, Inc.? a. b. c. d.

0.0% 12.0% 4.7% 6.0%

Answer: a Explanation: a. is correct. ARAROC=(12%-5%)/1.5=0.047=4.7% the expected excess rate of return on the market=11%-5%=6%. 4.7%< 6%. So as a rational company, it will reject the project, the contribution will be 0. b. is incorrect. There is no reason for 5%-4.7%=0.3% c. is incorrect 4.7% is ARAROC. d. is incorrect. 6% is the expected excess rate of return on the market. Topic: Operational and Integrated Risk Management Subtopic: Firm wide risk measurement and management Reference: Michael Crouhy, Dan Galai, and Robert Mark, Risk Management (New York: McGraw‐Hill, 2001), Chapter 14

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21.

Redhat is a small bank whose only business line is retail banking.With the Basel II Standardized Approach for calculating operational risk capital charges, the beta factors for each business line are given in the following table: Business Line Corporate finance Trading and sales Retail banking Commercial banking Payment and settlement Agency services Asset management Retail brokerage

Beta Factor 18% 18% 12% 15% 18% 15% 12% 12%

Assuming Redhat is eligible to choose any Basel II approach for operational risk, which Basel II approach will minimize Redhat’s operational risk capital charge? a. b. c. d.

Basic Indicator Approach. Standardized Approach. Foundation Internal Ratings-Based Approach (FIRB). Both the Basic Indicator Approach and the Standardized Approach have the same operational risk charge for Redhat.

Answer: b Explanation: a. is incorrect. For all business lines, the Basic Indicator Approach uses a 15% Beta factor which is higher than retail banking beta factor of the Standardized approach. b. is correct. Redhat’s only business line is retail banking. Using the Standardized Approach will use a lower beta factor than Basic Indicator Approach. c. is not correct FIRB and AIRB are credit risk capital approach. d. is not correct because of above. Topic: Operational and Integrated Risk Management Subtopic: Economic Capital Reference: “Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework – Comprehensive Version” (Basel Committee on Banking Supervision Publication, June 2006).


99


22.

In a synthetic CDO, a. b. c. d.

The SPV gains credit exposure by buying securities. The SPV gains credit exposure by selling credit default swaps. The SPV gains credit exposure by buying credit default swaps. The SPV gains credit exposure by selling risk-free bonds.

Answer: b Explanation: a. incorrect answer: This is the case in a cash CDO. b. correct answer: in this case the SPV is synthetically short protection c. incorrect answer: in this case the SPV is synthetically long protection d. incorrect answer: SPV sells credit protection and uses the funds to purchase risk-free bonds Topic: Credit Risk Measurement and Management Subtopic: Collateralized Debt Obligations Reference: Culp, Chapters 17,18

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23.

Consider the following two asset portfolios: Asset A B Portfolio

Position Value Return Standard Deviation (%) (in thousands of USD) 400 3.60 600 8.63 1,000 5.92

Beta 0.5 1.2 1.0

Calculate the component VaR of asset A and marginal VaR of asset B, respectively, at 95% confidence level? a. b. c. d.

USD 21,773 and 0.1306 USD 21,773 and 0.1169 USD 19,477 and 0.1169 USD 19,477 and 0.1306

Answer: c Explanation: Diversified VAR (DVAR) = z * standard deviation * portfolio value = 1.645 * 0.0592 * USD 1,000,000 = USD 97,384 Component VAR = DVAR * beta (A) * weight (A) = USD 97,384 * 0.5 * 0.4 = USD 19,477 Marginal VAR = DVAR * beta (B) / portfolio value = USD 97,384 * 1.2 / USD 1,000,000 = 0.1169 a. Incorrect. Uses confidence level of 99% b. Incorrect. Uses undiversified VAR (= 400,000 * 0.036 * 1.645 + 600,000 * 0.0863 * 1.645) c. Correct. d. Incorrect. Uses VaR of asset A (400000 * 0.036 * 1.645) as component VAR of A, and uses weight instead of beta in marginal VAR calculation. Topic: Risk Management and Investment Management Subtopic: Portfolio Construction Reference: Philippe Jorion, Value at Risk, 3rd Edition. Chapter 7


101


24.

Which of the options below properly classifies each model risk error into a model risk category? Model Risks • Risk 1: Failure to consider a sufficient number of trials in a Monte Carlo simulation. • Risk 2: Use of the mid-quote price rather than the bid price to value long positions in financial instruments. • Risk 3: Failure to fully account for time-variation of volatility. Model Risk Categorization • Implementation risk • Incorrect model calibration • Incorrect model application a. b. c. d.

Risk 1 = Incorrect model calibration, Risk 2 = Implementation risk, Risk 3 = Incorrect model calibration Risk 1 = Implementation risk, Risk 2 = Incorrect model application, Risk 3 = Incorrect model calibration Risk 1 = Incorrect model application, Risk 2 = Implementation risk, Risk 3 = Incorrect model calibration Risk 1 = Incorrect model application, Risk 2 = Implementation risk, Risk 3 = Implementation risk

Answer: c Explanation: Implementation risk refers to model risk pertinent to implementation, it assumes the model is correctly specified and calibrated. It usually pertains to valuation errors, e.g. mark to market vs. mark to model, usage of mid-quote vs. bid-ask spread, hence it corresponds to Risk 2. Incorrect model calibration risk refers to model risk pertinent to non-calibration or inaccurate calibration of (usually correctly specified) models under changing circumstances. An example is unexpected rise in volatility, causing banks to experience higher losses than suggested under original risk models (past cases include LTCM, Natwest, BZW and Bank of Tokyo Mitsubishi cases), hence it corresponds to risk 3. Incorrect model application risk refers to model risk pertinent to improper application of a risk model. An example is consideration of an insufficient number of trials in a Monte Carlo simulation. The wrong answers A, B and D capture cases when candidates do not fully understand correct classification and application of model risks. Topic: Operational and Integrated Risk Management Subtopic: Implementation and Model Risk Reference: Kevin Dowd, Measuring Market Risk, Chapter 16 – Model risk

102



25.

Looking at a risk report, Mr.Woo finds that the options book of Ms. Yu has only long positions and yet has a negative delta. He asks you to explain how that is possible. What is a possible explanation? a. b. c. d.

The book has a long position in up-and-in call options. The book has a long position in binary options. The book has a long position in up-and-out call options. The book has a long position in down-and-out call options.

Answer: c Explanation: As the underlying assets’ price increases the up-and-out call options become more vulnerable since they will cease to exist when the barrier is reached. Hence their price decreases. This is negative delta. Topic: Market Risk Measurement and Management Subtopic: Exotic Derivatives Reference: John C. Hull, Options, Futures and Derivatives, 7th Edition.

26.

John Grea has just been appointed the CFO of a bank and wants to construct a composite risk picture following a “building block” approach that aggregates risk at three successive levels in his organization. • Level I: Aggregates the standalone risks within a single risk factor. • Level II: Aggregates risk across different risk factors within a single business line. • Level III: Aggregates risk across different business lines. However, he understands that there might be different degrees of diversification benefits for each level. Empirically, which level in the “building block” approach has the greatest degree of diversification benefit? a. b. c. d.

Level I — single risk factor level Level II — single business line level Level III — different business lines level The degree of diversification benefits are the same for each level

Answer: a Explanation: Empirically, diversification effects are greatest within a single risk factor (Level I), decrease at the business line level (Level II), and are smallest across business lines (Level III). Topic: Operational Risk Measurement and Management Subtopic: Economic Capital and Risk Aggregation. Reference: Andrew Kuritzkes, Til Schuermann and Scott M.Weiner. “Risk Measurement, Risk Management and Capital Adequacy in Financial Conglomerates.” © GARP, Global Association of Risk Professionals, Inc., 2010 It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.

103


27.

The capital structure of HighGear Corporation consists of two parts: one 5-year zero-coupon bond with a face value of USD 100 million and the rest is equity. The current market value of the firm’s assets (MVA) is USD 130 million and the expected rate of change of the firm’s value is 25%. The firm’s assets have an annual volatility of 30%. Assume that firm value is log-normally distributed with constant volatility. The firm’s risk management division estimates the distance to default (in terms of number of standard deviations) using the Merton Model, or

( ) ( FVB

MVA

–

δ –

1 2

σ 2A

)

Τ

σ A T0.5 Given the distance to default, the estimated risk-neutral default probability is: a. b. c. d.

2.74% 12.78% 12.79% 30.56%

Answer: a Explanation: According to the Merton model, the default probability is N[Ln(100/130) – (25% – (30%2)/2) * 5}/(30% * sqrt(5))] = 2.74% a. Is correct b. Incorrect N[Ln(130/100) + (25% + (30%2)/2) * 5}/(30% * sqrt(5))] = 12.78% c. Incorrect N[Ln(100/130) + (25% – (30%)/2) * 5}/(30% * sqrt(5))] = 12.79% d. Incorrect – N[Ln(100/130) – (25% + (30%2)/2) * 5}/(30% * (5))] = 30.56% Topic: Credit Risk Measurement and Management Subtopic: Credit Derivatives Reference: Rene M. Stulz, Risk Management and Derivatives (Mason, Ohio: South-Western, 2003), Chapters 18

104



28.

There are different commercially available credit risk models. These models exhibit significant differences as well as similarities. Which of the following models builds on transition probabilities determined by macro factors? a. b. c. d.

CreditMetrics KMV’s PortfolioManager CreditRisk+ CreditPortfolioView

Answer: b Explanation: CreditMetrics, PortfolioManager, and CreditRisk+ use constant transition probabilities; CreditPortfolioView uses transition probabilities determined by macro factors. Topic: Credit Risk Measurement and Management Subtopic: Credit risk management models Reference: Arnaud de Servigny and Olivier Renault, Measuring and Managing Credit Risk.


105


29.

John Smith is a bank supervisor responsible for the oversight of Everbright Group, a large banking conglomerate. Everbright Group now determines its credit risk profile according to the foundation IRB approach and assesses operational risk according to the standardized approach as described in the Basel II Capital Accord. Which of the following are specific issues that should be addressed as part of Smith’s supervisory review process of Everbright Group? i. Review the bank’s internal control systems. ii. Check compliance with transparency requirements as described in Pillar 3 of Basel II Accord. iii. Make sure that the bank estimates for LGD and EAD for its corporate loans are in compliance with supervisory estimates. iv. Evaluate the impact of interest rate risk by assessing the impact of a 200 basis point interest rate shock to the bank’s capital position. a. b. c. d.

i and iii only ii and iv only i, ii, and iv only i, ii, iii, and iv

Answer: c Explanation: The supervisor’s duties as part of the supervisory review process include: Check compliance with Pillars I and III of Basel II Accord, which would include credit risk mitigation and transparency requirements. Review internal control systems. Access internal capital management methods employed by the bank. So I and II are correct. Note that the foundation IRB approach, the bank provides its estimates for PD but uses supervisory estimates for LGD and EAD for corporate loans. So III is incorrect. Also, the impact of interest rate risk on the bank’s capital position must be accessed by determining the impact of a 200 basis point shock or its equivalent. So IV is also correct. Therefore, the correct answer for this question is choice C. Topic: Operational and Integrated Risk Management Subtopic: Basel II Accord Reference:“Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework – Comprehensive Version” (Basel Committee on Banking Supervision Publication, June 2006)

106



30.

Silo Bank begins its risk measurement process by calculating VaR for market, credit, and operational risk individually, and then aggregates the three measures to produce a firm-wide VaR. Correlation between risk types is a key input for calculating firm-wide VaR. Which of the following statements about correlation are valid? i.

When market and credit risks involve securities issued by firms such as bonds, warrants, and stocks, correlation estimates for market and credit risk can be derived using equity returns if Merton’s model for the pricing of debt holds. ii. If correlations between highly adverse market, credit, and operational outcomes are high, there is diversification across risk categories and therefore the firm-wide VaR is substantially less than the sum of the market, credit, and operational risk VaRs. iii. With non-normal distributions, the use of correlations estimated using historical data from a stable period may not adequately capture how extreme returns for one type of risk are related to extreme returns of another type of risk. a. b. c. d.

i, ii and iii i only ii and iii only None of the statements are valid.

Answer: b Explanation: i. is true. ii. is false – if correlations are low, there is diversification benefit. iii. is false – asset correlations tend to be higher in times of stress. Topic: Operational and Integrated Risk Management Subtopic: Economic capital and risk aggregation Reference: Nocco and Stulz; “Enterprise Risk Management: Theory and Practice”.


107


31.

The Trading Desk of Global Bank PLC presents its risk manager with a potential trade. The trade is to provide support through a bank guarantee to the AAA tranche issued by a Special Purpose Vehicle (SPV). The SPV’s assets are restricted to residential mortgage loans that have been sold by other originating banks into the pool, making the bond issued by the SPV an RMBS. As far as the bank knows, no further relationship is known to exist between the originating banks and the SPV issuing the AAA tranche of the RMBS in question. As a risk manager, the first decision is to evaluate the potential for counterparty risk in this transaction. Taking into account that no additional external credit enhancements are available here, which party involved in the complex securitization transaction would expose Global Bank PLC to counterparty risk? a. There is only counterparty exposure with the regional banks that originated the mortgages that are securitized in the SPV because in providing the bank guarantee to the AAA tranche on this RMBS, Global Bank PLC is exposed to the credit quality of these banks. b. There is counterparty exposure to both the regional banks and the SPV issuing the RMBS, and any default in either would directly affect Global Bank PLC. c. There is only counterparty exposure to the SPV because if the mortgages in the SPV were to default, the SPV would not be able to continue to make payments. d. There is no counterparty exposure as the bank guarantee to be provided by Global Bank PLC is only a contingent exposure. Answer: c

Explanation: a. Is Incorrect. There is only counterparty exposure with the regional banks that originated the mortgages that are securitized in the SPV because in providing the bank guarantee to the AAA tranche on this RMBS, Global Bank PLC is exposed to the credit quality of these banks. b. Is Incorrect. There is counterparty exposure to both the regional banks and the SPV issuing the RMBS and any default in either would directly affect Global Bank PLC. c. Correct. There is only counterparty exposure to the SPV because if the mortgages in the SPV were to default, the SPV would not be able to continue to make payments. d. Is Incorrect. There is no counterparty exposure as the bank guarantee to be provided by Global Bank PLC is only a contingent exposure. Topic: Credit Risk Measurement and Management Subtopic: Structured finance, securitization, tranching and subordination. Reference: Adam Ashcroft and Til Schuermann, “Understanding the Securitization of Subprime Mortgage Credit”, 2007.

108



32.

A credit risk manager of Esta Bank is reviewing the credit risk of a EUR 400,000 loan to KidCo, which is a subsidiary of Pattern Inc. Assume that KidCo will default if Pattern Inc. defaults, but Pattern Inc. will not necessarily default if KidCo defaults. If Pattern Inc. has a 1-year probability of default of 1% and KidCo has a 1-year probability of default of 5% given that Pattern Inc. does not default, what is the probability that KidCo defaults in the next year? a. b. c. d.

5.00% 6.00% 5.95% 4.95%

Answer: c Explanation: This question tests that candidates understand conditional probability in the context of a credit risk question. Here are 4 possible scenarios and probabilities: Scenario Pattern Inc. defaults, KidCo does not default

Probability 0.0%

Explanation By assumption, KidCo defaults if Pattern Inc. defaults

Pattern Inc. defaults, KidCo defaults

1.0%

Pattern Inc. has a 1% probability of default in the next year

Pattern Inc. does not default, KidCo defaults

4.95%

Pattern Inc. does not default with probability 99%, KidCo defaults with probability 5%

Pattern Inc. does not default, KidCo does not default

94.05%

Pattern Inc. does not default with probability 99%, KidCo does not default with probability 95%

KidCo defaults in scenarios 2 and 3 with probability 5.95%. a. b. c. d.

This is the probability KidCo defaults, given Pattern Inc. does not default This is the probability KidCo defaults, given Pattern Inc. does not default plus the probability that Pattern Inc. defaults Correct. This is the probability both KidCo and Pattern Inc. do not default

Topic: Credit Risk Measurement and Management Subtopic: Structured finance, securitization, tranching and subordination. Reference: Culp; Chapters 13,16; Hull, Chapter 23.


109


33.

The spread on a one-year BBB-rated bond relative to the risk-free treasury of similar maturity is 1.4%. It is estimated that the contribution to this spread by all noncredit factors (e.g., liquidity risk, taxes) is 0.4%. Assuming the loss given default rate for the underlying credit is 40%, what is, approximately, the implied default probability for this bond? a. b. c. d.

1.67% 2.33% 3.50% 2.50%

Answer: d Explanation: The probability of default equals the credit risk spread divided by the loss given default. PD = spread / LGD Here, the spread due to credit risk equals 1.4% - 0.4% or 1.0% and the loss given default is 40%. The probability of default is then 2.5%. a. is incorrect. Incorrectly sets PD = 1.0/0.6 = 1.67. b. is incorrect. Incorrectly sets PD = 1.4/0.6 = 2.33. c. is incorrect . Incorrectly sets PD = 1.4/0.4 = 3.50. Topic: Credit Risk Measurement and Management Subtopic: Probability of default, loss given default and recovery rates. Reference: Arnaud de Servigny and Oliver Renault, Measuring and Managing Credit Risk, (New York: McGraw-Hill, 2004) chapter 3, 4

110



34.

The following table lists the default probabilities for an A-rated issue by a company facing the risk of imminent downgrade. Year 1 2 3

Default Probability 0.300% 0.450% 0.550%

Assume that defaults, if they take place, only happen at the end of the year. Based on the information in the table above, calculate the cumulative default rate at the end of each of the next three years. a. b. c. d.

0.300%, 0.750%, 1.300% 0.300%, 0.150%, 0.250% 0.300%, 0.749%, 1.295% 0.300%, 0.449%, 0.548%

Answer: c Explanation: Assume that dt signifies default by the end of the year. d1 = 0.300% d2 = 0.450% d3 = 0.550%. At the end of the first year, the survival rate is S1= 1-d1=1-0.300% = 99.700%. At the end of the second year, the survival rate is S2 = S1 × (1-d2) =0.997×(1-0.00450) = 0.992514. The default is C2 = 1-S2 =1-0.992514 = 0.00749 At the end of the third year, the survival rate is S3 = S2 × (1-d3) =0. 992514×(1-0.00550) = 0.987055 The default is C3 = 1- S3 = 1- S2×(1- d3) = 1- 0.992514×(1-0.00550) = 0.01295. a. is incorrect because the calculations assume the survival rate is at 100%. b. is incorrect because the calculations assume that the increments in the default probability are equal to the cumulative default rates. c. is correct. d. is incorrect because of calculation errors. Topic: Credit Risk Measurement and Management Subtopic: Probability of default, loss given default and recovery rates. Reference: Arnaud de Servigny and Oliver Renault, Measuring and Managing Credit Risk, (New York: McGraw-Hill, 2004) chapter 3, 4


111


35.

Which of the following statements are true? i.

Hedge fund manager compensation is often symmetric (i.e., a dollar of gain has the opposite impact on compensation as a dollar of loss), while the compensation of mutual fund managers is almost always asymmetric. ii. Leverage obtained through lines of credit increases the risk of a hedge fund more than leverage obtained by issuing debt, because unexpected cancellation of a line of credit by a lender during troubled times can force a fund to liquidate its positions in illiquid markets. iii. A hedge fund investor should pay performance-based compensation to the manager for producing alpha, but should not pay performance-based compensation to a hedge fund manager who has done well because the fund invests in risk factors that mirror the performance of his style or strategy, and the style or strategy has performed well. iv. The lack of hedge fund transparency is particularly problematic for investors with fiduciary responsibilities such as pension fund managers, and to secure funding from these investors, hedge fund managers often have to provide more information to these investors. a. b. c. d.

i, ii, and iv only. ii, iii, and iv only. ii and iv only. i and iii only.

Answer: b Explanation: Statements ii, iii and iv are true. Statement i is false – the opposite is true. Topic: Risk Management and Investment Management Subtopic: Hedge fund risk management References: René M. Stulz, "Hedge Funds: Past, Present and Future".

112



36.

Which of the following statements does not identify a potential factor that played a role in the subprime crisis? a. Many products offered to subprime borrowers were very complex and subject to misunderstanding and/or misrepresentation. b. Credit ratings were assigned to subprime MBS with significant error. Even though the rating agencies publicly disclosed their rating criteria for subprime, investors lacked the ability to evaluate the efficacy of these models. c. Existing investment mandates often distinguished between structured and corporate ratings, forcing asset managers to evaluate structured debt issues and corporate debt issues with the same credit rating but different coupons. d. Without due diligence by the asset manager, the arranger’s incentives to conduct its own due diligence are reduced. Answer: c

Explanation: Existing investment mandates failed to consider the rating in relation to the type of security considered and assumed that an AAA rating for a corporate and an AAA rating for a CDO could be treated exactly the same. Existing investment mandates did not adequately distinguish between structured and corporate ratings. Asset managers had an incentive to reach for yield by purchasing structured debt issues with the same credit rating but higher coupons as corporate debt issues. Topic: Credit Risk Measurement and Management Subtopic: Securitization Reference: Adam Ashcroft and Til Schuermann, “Understanding the Securitization of Subprime Mortgage Credit”


113


37.

Which of the following instruments has or have the most potential counterparty credit risk when the final exchange draws near maturity? i. An FX forward contract in which the bank will pay USD 1.1 million and receive EUR 0.77 million on December 1, 2008. ii. A EUR 10 million interest rate swap with one remaining payment due December 1, 2008, in which the bank pays EURIBOR + 1.0% and receives 4.5%. iii. A cross-currency swap with final payments due December 1, 2008, in which the bank pays 5% annually on a notional USD 1.1 million and receives 10% annually on a notional value of EUR 0.7 million. a. b. c. d.

i only ii and iii i and iii ii only

Answer: c Explanation: FX forwards and Cross currency swaps with final exchange involves exchanging two currencies at rates fixed at inception. Because of this, the potential future credit exposure profile peaks at maturity for both these instruments. In case of interest rate swaps, there is no exchange of notional amounts. Therefore, the profile tends to peak well before maturity. Topic: Credit Risk Measurement and Management Subtopic: Counterparty risk

114



38.

You have a long position in a digital call option – an option that is also called cash-or-nothing – on shares in Global Enterprises. The digital call has a strike price of USD 20 with one year remaining to expiration. Assume that the shares currently trade at USD 22 and annual return volatility of Global Enterprises shares is 15%.Which of the following sensitivities would be associated with this option? i. ii. iii. iv.

Delta is positive. Gamma is positive. Vega is negative. Vega is positive.

Which statements are true? a. b. c. d.

i and iii iv only i, ii, and iv ii and iii

Answer: a Explanation: A call spread replicates a cash-or-nothing option. Such long call spread is constituted by a long call C1 with a strike K-epsilon, and a short call C2 with a strike K+epsilon where epsilon is small. The strategy is market bullish, the delta is always positive so I is true. Furthermore, the vega and gamma can be positive or negative depending on the spot level. When the underlying price is bigger than the strike price, the vega is negative and the gamma as well corresponding to C2’s Greeks. So, II is wrong and III is true. Topic: Market Risk Measurement and Management Subtopic: Exotic derivatives Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition.


115


39.

The Merton model is used to predict default. It builds on several very strong assumptions and its applicability is hampered by practical difficulties. Which of the following statements does not correctly identify limiting assumptions or practical difficulties of using the model? a. b. c. d.

The Merton Model relies on a simplistic capital structure consisting of only one debt issue. The Merton Model asset value volatility cannot be estimated because firm value does not trade. The Merton Model assumes that debt does not pay a coupon while most publicly-trade debt is coupon debt. The Merton Model assumes a constant riskless interest rate.

Answer: b Explanation: Firm asset volatility can be estimated using equity and call option on equity, so firm asset value does not have to trade. Topic: Credit Risk Measurement and Management Subtopic: Credit risk management models Reference: Arnaud de Servigny and Olivier Renault, Measuring and Managing Credit Risk Chapter 3 – Default Risk: Quantitative Methodologies

40.

The current yield-to-maturity on a 1-year zero coupon bond with a face value of 1,000 is 3%. There is an equal probability that, in the coming 6 months, the yield will either increase or decrease by 50 bp, respectively (to 2.5% and 3.5%, respectively). Using this information, what is the expected discounted value of the zero-coupon bond? a. b. c. d.

969.45 970.67 982.80 985.23

Answer: b Explanation: The other alternatives are either intermediate steps or random incorrect number. Topic: Market Risk Measurement and Management Subtopic: Term structure models Reference: Tuckman – Chapter 9

116


Creating a culture of risk awareness.TM

Global Association of Risk Professionals 111 Town Square Place Suite 1215 Jersey City, New Jersey 07310 USA + 1 201.719.7210 Minster House, 1st Floor 42 Mincing Lane London EC3R 7AE UK + 44 (0) 20 7397 9631 www.garp.org

© 2010 Global Association of Risk Professionals. All rights reserved. GARP1036 2-10

FINANCIAL RISK MANAGER (FRM®) EXAMINATION • 2010 PRACTICE EXAM

Financial Risk Manager (FRM®) Examination 2011 Practice Exam Part I / Part II

2011 Financial Risk Manager Examination (FRM®) Practice Exam

TABLE OF CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 2011 FRM Part I Practice Exam 1 Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . .3 2011 FRM Part I Practice Exam 1 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 2011 FRM Part I Practice Exam 1 Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . . .15 2011 FRM Part I Practice Exam 1 Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 2011 FRM Part I Practice Exam 2 Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . .35 2011 FRM Part I Practice Exam 2 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 2011 FRM Part I Practice Exam 2 Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . .47 2011 FRM Part I Practice Exam 2 Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 2011 FRM Part II Practice Exam 1 Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . .67 2011 FRM Part II Practice Exam 1 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69 2011 FRM Part II Practice Exam 1 Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . .77 2011 FRM Part II Practice Exam 1 Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79 2011 FRM Part II Practice Exam 2 Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . .93 2011 FRM Part II Practice Exam 2 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95 2011 FRM Part II Practice Exam 2 Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . .103 2011 FRM Part II Practice Exam 2 Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105

© 2011 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.

3


INTRODUCTION

Core readings were selected by the FRM Committee to assist candidates in their review of the subjects covered by

The FRM Exam is a practice-oriented examination. Its

the exam. Questions for the FRM examination are derived

questions are derived from a combination of theory, as set

from the “core” readings. It is strongly suggested that

forth in the core readings, and “real-world” work experience.

candidates review these readings in depth prior to sitting

Candidates are expected to understand risk management

for the exam.

concepts and approaches and how they would apply to a risk manager’s day-to-day activities. The FRM Examination is also a comprehensive examination, testing a risk professional on a number of risk manage-

Suggested Use of Practice Exams To maximize the effectiveness of the practice exams, candidates are encouraged to follow these recommendations:

ment concepts and approaches. It is very rare that a risk manager will be faced with an issue that can immediately

1. Plan a date and time to take each practice exam.

be slotted into one category. In the real world, a risk man-

Set dates appropriately to give sufficient study/

ager must be able to identify any number of risk-related

review time for the practice exam prior to the

issues and be able to deal with them effectively.

actual exam.

The 2011 FRM Practice Exams I and II have been developed to aid candidates in their preparation for the FRM

2. Simulate the test environment as closely as possible.

Examination in May and November 2011. These practice

•

Take each practice exam in a quiet place.

exams are based on a sample of questions from the 2009

•

Have only the practice exam, candidate answer sheet, calculator, and writing instruments (pencils,

FRM Examination and are suggestive of the questions that

erasers) available.

will be in the 2011 FRM Examination. Each of the 2011 FRM Practice Exams for Part I contain

•

cell phones and study material.

25 multiple-choice questions and each of the 2011 FRM Practice Exams for Part II contain 20 multiple-choice

Minimize possible distractions from other people,

•

Allocate 90 minutes for the practice exam and

questions. Note that the 2011 FRM Examination Part I will

set an alarm to alert you when 90 minutes have

contain 100 multiple-choice questions and the 2011 FRM

passed. Complete the exam but note the questions

Examination Part II will contain 80 multiple-choice ques-

answered after the 90 minute mark.

tions. The practice exams were designed to be shorter to

•

Follow the FRM calculator policy. You may only use

allow candidates to calibrate their preparedness without

a Texas Instruments BA II Plus (including the BA II

being overwhelming.

Plus Professional), Hewlett Packard 12C (including the HP 12C Platinum), Hewlett Packard 10B II or

The 2011 FRM Practice Exams do not necessarily cover

Hewlett Packard 20B calculator.

all topics to be tested in the 2011 FRM Examination as the material covered in the 2011 Study Guide may be different from that covered by the 2009 Study Guide. The questions selected for inclusion in the Practice Exams were chosen to

3. After completing the practice exam, •

sheet with the practice exam answer key. Only

be broadly reflective of the material assigned for 2011 as well

include questions completed in the first 90 minutes.

as to represent the style of question that the FRM Committee considers appropriate based on assigned material.

Calculate your score by comparing your answer

•

Use the practice exam Answers and Explanations to better understand correct and incorrect

For a complete list of current topics, core readings, and

answers and to identify topics that require addi-

key learning objectives candidates should refer to the 2011

tional review. Consult referenced core readings to

FRM Examination Study Guide and AIM Statements.

prepare for exam.


1

Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART I / EXAM 1

Answer Sheet


a.

b.

c.

d.

a.

1.

16.

2.

17.

3.

18.

4.

19.

5.

20.

6.

21.

7.

22.

8.

23.

9.

24.

10.

25.

b.

c.

d.

3

8

11. 12.

Correct way to complete

13.

1.

14.


15.

1.


3


Questions


1.

Assume that a random variable follows a normal distribution with a mean of 50 and a standard deviation of 10. What percentage of this distribution is between 55 and 65? a. b. c. d.

2.

Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift μ = 0.02, volatility σ = 0.18 and time step Δt = 0.05. Let St be the price of the stock at time t. If S0 = 100, and the first two simulated (randomly selected) standard normal variables are ε1 = 0.253, ε2 = -0.675, what is the simulated stock price after the second step? a. b. c. d.

3.

96.79 98.47 101.12 103.70

A population has a known mean of 500. Suppose 400 samples are randomly drawn with replacement from this population. The mean of the observed samples is 508.7, and the standard deviation of the observed samples is 30. What is the standard error of the sample mean? a. b. c. d.

4.

4.56% 8.96% 18.15% 24.17%

0.015 0.15 1.5 15

The following GARCH(1,1) model is used to forecast the daily return variance of an asset: 2 σn2 = 0.000005 + 0.05u2n-1 + 0.92σn-1

Suppose the estimate of the volatility today is 5.0% and the asset return is -2.0%. What is the estimate of the long-run average volatility per day? a. b. c. d.

1.29% 1.73% 1.85% 1.91%


5


5.

John is forecasting a stock’s price in 2011 conditional on the progress of certain legislation in the United States Congress. He divides the legislative outcomes into three categories of “Passage”, “Stalled” and “Defeated” and the stock’s performance into three categories of “increase”, “constant” and “decrease” and estimates the following events:

Probability of legislative outcome Probability of increase in stock price given legislative outcome Probability of decrease in stock price given legislative outcome

Passage 20%

Stalled 50%

Defeated 30%

10%

40%

70%

60%

30%

10%

A portfolio manager would like to know that if the stock price does not change in 2011, what the probability that the legislation passed is. Based on John’s estimates, this probability is: a. b. c. d.

6.

15.5% 19.6% 22.2% 38.7%

Roy Thomson, a global investment risk manager of FBN Bank, is assessing markets A and B using a twofactor model. In order to determine the covariance between markets A and B, Thomson developed the following factor covariance matrix for global assets: Factor Covariance Matrix for Global Assets

Global Equity Factor Global Bond Factor

Global Equity Factor 0.3543 -0.0132

Global Bond Factor -0.0132 0.0089

Suppose the factor sensitivities to the global equity factor are 0.75 for market A and 0.45 for market B, and the factor sensitivities to the global bond factors are 0.20 for market A and 0.65 for market B. The covariance between market A and market B is closest to: a. b. c. d.

6

-0.215 -0.113 0.113 0.215



7.

John Diamond is evaluating the existing risk management system of Rome Asset Management and identified the following two risks. I. II.

Rome Asset Management’s derivative pricing model consistently undervalues call options Swaps with counterparties exceed counterparty credit limit

These two risks are most likely to be classified as: a. b. c. d.

8.

If the daily, 90% confidence level, Value-at-Risk (VaR) of a portfolio is correctly estimated to be USD 5,000, one would expect that in one out of: a. b. c. d.

9.

Market Credit Liquidity Operational

10 days, the portfolio value will decline by USD 5,000 or less. 90 days, the portfolio value will decline by USD 5,000 or less. 10 days, the portfolio value will decline by USD 5,000 or more. 90 days, the portfolio value will decline by USD 5,000 or more.

Tim is evaluating 4 funds run by 4 independent managers relative to a benchmark portfolio that has an expected return of 7.4% and volatility of 14%. He is interested in investing in the fund with the highest information ratio that also meets the following conditions in his investment guidelines: • •

Expected residual return must be at least 2% Residual risk relative to the benchmark portfolio must be less than 2.5%

Based on the following information, which fund should he choose? Fund Fund Fund Fund Fund a. b. c. d.

Expected Return 9.3%

A B C D

Fund Fund Fund Fund

9.4%

Volatility 15.3% 16.4% 15.8%

Residual Risk 2.4% 1.5% 1.8%

Information Ratio 0.8 0.9 1.3

A B C D


7


10.

A bank had entered into a 3-year interest rate swap for a notional amount of USD 300 million, paying a fixed rate of 7.5% per year and receiving LIBOR annually. Just after the payment was made at the end of the first year, the continuously compounded 1-year and 2-year annualized LIBOR rates were 7% per year and 8% per year, respectively. The value of the swap to the bank at that time was closest to which of the following choices? a. b. c. d.

11.

b. c. d.

Decreases Increases Stays the same Insufficient information to determine.

On Nov 1, Jimmy Walton, a fund manager of an USD 60 million US medium-to-large cap equity portfolio, considers locking up the profit from the recent rally. The S&P 500 index and its futures with the multiplier of 250 are trading at USD 900 and USD 910, respectively. Instead of selling off his holdings, he would rather hedge two-thirds of his market exposure over the remaining 2 months. Given that the correlation between Jimmy’s portfolio and the S&P 500 index futures is 0.89 and the volatilities of the equity fund and the futures are 0.51 and 0.48 per year respectively, what position should he take to achieve his objective? a. b. c. d.

8

An airline company hedging exposure to a rise in jet fuel prices with heating oil futures contracts may face basis risk. Choices left to the seller about the physical settlement of the futures contract in terms of grade of the commodity, location, chemical attributes may result in basis risk. Basis risk exists when futures and spot prices change by the same amount over time and converge at maturity of the futures contract. Basis risk is zero when variances of both the futures and spot process are identical and the correlation coefficient between spot and futures prices is equal to one.

If the volatility of the interest rate decreases, the value of a callable convertible bond to an investor: a. b. c. d.

13.

million million million million

Which of the following statements about basis risk is incorrect? a.

12.

USD -14 USD -4 USD 4 USD 14

Sell Sell Sell Sell

250 futures contracts of S&P 500 169 futures contracts of S&P 500 167 futures contracts of S&P 500 148 futures contracts of S&P 500



14.

Alan bought a futures contract on a commodity on the New York Commodity Exchange on June 1. The futures price was USD 500 per unit and the contract size was 100 units per contract. Alan set up a margin account with initial margin of USD 2,000 per contract and maintenance margin of USD 1000 per contract. The futures price of the commodity varied as shown below. What was the balance in Alan’s margin account at the end of day on June 5? Day June June June June June a. b. c. d.

15.

Futures Price (USD) 497.30 492.70 484.20 471.70 468.80

1 2 3 4 5

-USD 1,120 USD 0 USD 880 USD 1,710

The yield curve is upward sloping. You have a short T-Bond interest rate futures position. The following bonds are eligible for delivery: Bonds A B C

Spot–Price (USD) 102.44 106.59 98.38

Conversion Factor 0.98 1.03 0.95

Coupon Rate 4% 5% 3%

The futures price is 103 -17/32 and the maturity date of the contract is September 1. The bonds pay their coupon amount semi-annually on June 30 and December 31. With these data, the cheapest-to-deliver bond is: a. b. c. d.

Bond A Bond B Bond C Insufficient information to determine.


9


16.

On the OTC market there are two options available on Microsoft stock: a European put with premium of USD 2.25 and an American call option with premium of USD 0.46. Both options have a strike price of USD 24 and an expiration date 3 months from now. Microsoft’s stock price is currently at USD 22 and no dividend is due during the next 6 months. Assuming that there is no arbitrage opportunity, which of the following choices is closest to the level of the risk- free rate: a. b. c. d.

17.

0.25% 1.76% 3.52% Insufficient information to determine.

A risk manager for bank XYZ, Mark is considering writing a 6 month American put option on a non-dividend paying stock ABC. The current stock price is USD 50 and the strike price of the option is USD 52. In order to find the no-arbitrage price of the option, Mark uses a two-step binomial tree model. The stock price can go up or down by 20% each period. Mark’s view is that the stock price has an 80% probability of going up each period and a 20% probability of going down. The risk-free rate is 12% per annum with continuous compounding. What is the risk-neutral probability of the stock price going up in a single step? a. b. c. d.

18.

Assume that options on a non dividend paying stock with price of USD 100 have a time to expiry of half a year and a strike price of USD 110. The risk-free rate is 10%. Further, N(d1) = 0.457185 and N(d2) = 0.374163. Which of the following values is closest to the Black-Scholes values of these options? a. b c. d.

10

34.5% 57.6% 65.5% 80.0%

Value Value Value Value

of of of of

American American American American

call call call call

option option option option

is is is is

USD USD USD USD

6.56 and of American put option is USD 12.0 5.50 and of American put option is USD 12.0 6.56 and of American put option is USD 10.0 5.50 and of American put option is USD 10.0



19.

An analyst is doing a study on the effect on option prices of changes in the price of the underlying asset. The analyst wants to find out when the deltas of calls and puts are most sensitive to changes in the price of the underlying. Assume that the options are European and that the Black-Scholes formula holds. An increase in the price of the underlying has the largest absolute value impact on delta for: a. b. c. d.

20.

A 5-year corporate bond paying an annual coupon of 8% is sold at a price reflecting a yield-to-maturity of 6% per year. One year passes and the interest rates remain unchanged. Assuming a flat term structure and holding all other factors constant, the bond’s price during this period will have a. b. c. d.

21.

Deep in-the-money calls and deep out-of-the-money puts. Deep in-the-money puts and calls. Deep out-of-the-money puts and calls. At-the-money puts and calls.

Increased Decreased Remained constant Insufficient information to determine.

Which of the following statements is incorrect, given the following one-year rating transition matrix? From/To (%) AAA AA A BBB BB B CCC/C a. b. c. d.

AAA 87.44 0.60 0.05 0.02 0.04 0.00 0.08

AA 7.37 86.65 2.05 0.21 0.08 0.07 0.00

A 0.46 7.78 86.96 3.85 0.33 0.20 0.31

BBB 0.09 0.58 5.50 84.13 5.27 0.28 0.39

BB 0.06 0.06 0.43 4.39 75.73 5.21 1.31

B 0.00 0.11 0.16 0.77 7.36 72.95 9.74

CCC/C 0.00 0.02 0.03 0.19 0.94 4.23 46.83

D 0.00 0.01 0.04 0.29 1.20 5.71 28.83

Non Rated 4.59 4.21 4.79 6.14 9.06 11.36 12.52

BBB loans have a 4.08% chance of being upgraded in one year. BB loans have a 75.73% chance of staying at BB for one year. BBB loans have an 88.21% chance of being upgraded in one year. BB loans have a 5.72% chance of being upgraded in one year.


11


22.

You are the risk manager of a fund. You are using the historical method to estimate VaR. You find that the worst 10 daily returns for the fund over the period of last 100 trading days are -1.0%, -0.3%, -0.6%, -0.2%, -2.7%, -1.0%, -2.9%, 0.1%, -1.1%, -3.0%. What is the daily VaR for the portfolio at the 95% confidence level? a. b. c. d.

23.

-2.9% -1.1% -1.0% -3.0%

Consider a bond with par value of EUR 1,000, maturity in 3 years, and that pays a coupon of 5% annually. The spot rate curve is as follows: Term 1 2 3

Annual Spot Interest Rates 6% 7% 8%

The value of the bond is closest to: a. b. c. d.

24.

904 924 930 950

Assume that portfolio daily returns are independently and identically normally distributed. Sam Neil, a new quantitative analyst, has been asked by the portfolio manager to calculate the portfolio Value-at-Risk (VaR) measure for 10, 15, 20 and 25 day periods. The portfolio manager notices something amiss with Sam’s calculations displayed below. Which one of following VaRs on this portfolio is inconsistent with the others? a. b. c. d.

12

EUR EUR EUR EUR

VaR(10-day) = USD 316M VaR(15-day) = USD 465M VaR(20-day) = USD 537M VaR(25-day) = USD 600M



25.

For the monthly returns plot of the fund tracked below in 2010, which period had a negative tracking error?

a. b. c. d.

1/2009 – 5/2009 6/2009 – 10/2009 1/2009 – 10/2009 None of the above


13


Answers


a.

b.

c.

1.

2.

a.

18.

b.

c.

19.

5.

20.

6.

21.

22.

7.

8.

10.

11.

12.

15.

1.

24.


14.

25.

13.

23.

9.

d.

16. 17.

3. 4.

d.

3

8



15


Explanations


1.

Assume that a random variable follows a normal distribution with a mean of 50 and a standard deviation of 10. What percentage of this distribution is between 55 and 65? a. b. c. d.

4.56% 8.96% 18.15% 24.17%

Answer: d. Explanation: Prob(mean + 0.5*σ < X < mean + 1.5*σ) = Prob( X < mean + 1.5*σ) - Prob( X < mean + 0.5*σ) = 0.9332 - 0.6915 = 0.2417 Topic: Quantitative Analysis Subtopic: Probability Distributions AIMS: Describe the key properties of the normal, standard normal, multivariate normal, Chi-squared, Student t, and F distributions. Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition, (Boston: Pearson Education, 2008), Chapter 2—Review of Probability.

2.

Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift μ = 0.02, volatility σ = 0.18 and time step Δt = 0.05. Let St be the price of the stock at time t. If S0 = 100, and the first two simulated (randomly selected) standard normal variables are ε1 = 0.253, ε2 = -0.675, what is the simulated stock price after the second step? a. b. c. d.

96.79 98.47 101.12 103.70

Answer: b. Explanation: In the simulation, St is assumed to move as follows over an interval of time of length Δt: ΔSt+i /St+i -1 = (μ Δt + σ εi (Δt)1/2) where εi is a standard normal random variable. Therefore, S1 = 100 + 100 * (0.02 * 0.05 + 0.18 * 0. 253 * sqrt(0.05)) = 101.1183 S2 = 101.1183 + 101.1183 * (0.02 * 0.05 + 0.18 * -0. 675 * sqrt(0.05)) = 98.4722 Topic: Quantitative Analysis Subtopic: Monte Carlo Methods AIMS: Describe how to simulate a price path using a geometric Brownian motion model. Reference: Jorion (2005), Value-at-Risk: the New Benchmark for Managing Financial Risk, 3rd Edition, New York: McGraw-Hill, Chapter 12—Monte Carlo Methods.


17


3.


0.015 0.15 1.5 15

Answer: c. Explanation: The standard error of the sample mean is estimated by dividing the standard deviation of the sample by the square root of the sample size: sx = s / (n)1/2 = 30 / (400)1/2 = 30 / 20 = 1.5. (the population mean is irrelevant.) Topic: Quantitative Analysis Subtopic: Estimating the parameters of distributions AIMS: Define, calculate, and interpret the sample variance, sample standard deviation, and standard error. Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition, (Boston: Pearson Education, 2008), Chapter 3—Review of Statistics.

4.


Suppose the estimate of the volatility today is 5.0% and the asset return is -2.0%. What is the estimate of the long-run average volatility per day? a. b. c. d.

1.29% 1.73% 1.85% 1.91%

Answer: a. Explanation: The model corresponds to α = 0.05, β = 0.92, and ω = 0.000005. Because γ = 1− α− β, it follows that γ = 0.03. Because the long-run average variance, VL, can be found by VL = ω / γ , it follows that VL = 0.000167. In other words, the long-run average volatility per day implied by the model is sqrt(0. 000167) = 1.29%. Topic: Quantitative Analysis Subtopic: EWMA, GARCH model AIMS: Estimate volatility using the GARCH(p,q) model. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition, (New York: Prentice Hall, 2009), Chapter 21—Estimating Volatilities and Correlations.

18



5.

John is forecasting a stock’s price in 2011 conditional on the progress of certain legislation in the United States Congress. He divides the legislative outcomes into three categories of “Passage”, “Stalled” and “Defeated” and the stock’s performance into three categories of “increase”, “constant” and “decrease” and estimates the following events:

Probability of legislative outcome Probability of increase in stock price given legislative outcome Probability of decrease in stock price given legislative outcome

Passage 20%

Stalled 50%

Defeated 30%

10%

40%

70%

60%

30%

10%

A portfolio manager would like to know that if the stock price does not change in 2011, what the probability that the legislation passed is. Based on John’s estimates, this probability is: a. b. c. d.

15.5% 19.6% 22.2% 38.7%

Answer: c. Explanation: Use Bayes’ Theorem: P(Passage | NoChange) = P(NoChange | Passage) * P(Passage) / P(NoChange) = (0.3 * 0.2) / (0.2 * 0.3 + 0.5 * 0.3 + 0.3 * 0.2) = 0.222 Topic: Quantitative Analysis Subtopic: Probability Distributions AIMS: Describe joint, marginal, and conditional probability functions. Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition, (Boston: Pearson Education, 2008), Chapter 2—Review of Probability.


19


6.

Roy Thomson, a global investment risk manager of FBN Bank, is assessing markets A and B using a twofactor model. In order to determine the covariance between markets A and B, Thomson developed the following factor covariance matrix for global assets: Factor Covariance Matrix for Global Assets


Global Equity Factor 0.3543 -0.0132

Global Bond Factor -0.0132 0.0089

Suppose the factor sensitivities to the global equity factor are 0.75 for market A and 0.45 for market B, and the factor sensitivities to the global bond factors are 0.20 for market A and 0.65 for market B. The covariance between market A and market B is closest to: a. b. c. d.

-0.215 -0.113 0.113 0.215

Answer: c. Explanation: Cov (A, B)

= βA,1 βB,1 σ2F1 + βA,2 βB,2 σ2F2 + (βA,1 βB,2 + βA,2 βB,1) Cov (F1, F2) = (0.75) (0.45) (0.3543) + (0.20) (0.65) (0.0089) + [(0.75) (0.65) + (0.20) (0.45)] (-0.0132) = 0.1131

Topic: Foundation of Risk Management Subtopic: Factor models and Arbitrage Pricing Theory AIMS: Use the APT to calculate the expected returns on an asset. Reference: Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann, Modern Portfolio Theory and Investment Analysis, 7th Edition, (Hoboken, NJ: John Wiley & Sons, 2007), Chapter 16—The Arbitrage Pricing Model APT—A New Approach to Explaining Asset Prices.

20



7.


Rome Asset Management’s derivative pricing model consistently undervalues call options Swaps with counterparties exceed counterparty credit limit

These two risks are most likely to be classified as: a. b. c. d.

Market Credit Liquidity Operational

Answer: d. Explanation: I is a model failure and II is an internal failure. These are types of operational risks Topic: Foundation of Risk Management Subtopic: Creating Value with Risk Management AIMS: Define and describe the four major types of financial risks: market, liquidity, credit, and operational. Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, (New York: McGraw‐Hill, 2007), Chapter 1—The Need for Risk Management.

8.



Answer: c. Explanation: If the daily, 90% confidence level Value-at-Risk (VaR) of a portfolio is correctly estimated to be USD 5,000, one would expect that 90% of the time (9 out of 10), the portfolio will lose less than USD 5,000; equivalently, 10% of the time (1 out of 10) the portfolio will lose USD 5,000 or more. Topic: Foundation of Risk Management Subtopic: Creating Value with Risk Management AIMS: Define Value-at-Risk (VaR) and describe how it is used in risk management. Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, (New York: McGraw-Hill, 2007), Chapter 1—The Need for Risk Management.


21


9.

Tim is evaluating 4 funds run by 4 independent managers relative to a benchmark portfolio that has an expected return of 7.4% and volatility of 14%. He is interested in investing in the fund with the highest information ratio that also meets the following conditions in his investment guidelines: • •

Expected residual return must be at least 2% Residual risk relative to the benchmark portfolio must be less than 2.5%

Based on the following information, which fund should he choose? Fund Fund Fund Fund Fund a. b. c. d.


A B C D

Fund Fund Fund Fund

9.4%

Volatility 15.3% 16.4% 15.8%



A B C D

Answer: d. Explanation: Information ratio = Expected residual return / residual risk = E(RP – RB) / σ(RP – RB) Fund A: Expected residual return = 9.3% - 7.4% = 1.9%, which does not meet the requirement of minimum residual return of 2%. Fund B: Expected residual return = information ratio * residual risk = 0.9 * 2.4% = 2.16%, so it meets both requirements Fund C: Expected residual return = information ratio * residual risk = 1.3 * 1.5% = 1.95%, does not meet residual return of 2% Fund D: This fund also meets both the residual return and residual risk requirements. Expected residual return = 9.4% - 7.4% = 2.0% Information ratio = 2.0% / 1.8% = 1.11 Both funds B and D meet the requirements. Fund D has the higher information ratio. Topic: Foundation of Risk Management Subtopic: Sharpe ratio and information ratio AIMS: Compute and interpret tracking error, the information ratio, and the Sortino ratio. Reference: Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England: John Wiley & Sons, 2003), Chapter 4, Section 4.2 only—Applying the CAPM to Performance Measurement: SingleIndex Performance Measurement Indicators.

22



10.

A bank had entered into a 3-year interest rate swap for a notional amount of USD 300 million, paying a fixed rate of 7.5% per year and receiving LIBOR annually. Just after the payment was made at the end of the first year, the continuously compounded 1-year and 2-year annualized LIBOR rates were 7% per year and 8% per year, respectively. The value of the swap to the bank at that time was closest to which of the following choices? a. b. c. d.

USD -14 USD -4 USD 4 USD 14

million million million million

Answer: c. Explanation: Fixed rate coupon = USD 300 million x 7.5% = USD 22.5 million Value of the fixed payment = Bfix = 22.5 e(-0.07)+322.5 e(-0.08*2) = USD 295.80 million Value of the floating payment = Bfloating = USD 300 million. Since the payment has just been made the value of the floating rate is equal to the notional amount. Value of the swap = Bfloating - Bfix = USD 300 – USD 295.80 = USD 4.2 million Topic: Financial Markets and Products Subtopic: Futures, forwards, swaps and options AIMS: Value a plain vanilla interest rate swap based on two simultaneous bond positions. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 7—Swaps.


23


11.

Which of the following statements about basis risk is incorrect? a. b. c. d.

An airline company hedging exposure to a rise in jet fuel prices with heating oil futures contracts may face basis risk. Choices left to the seller about the physical settlement of the futures contract in terms of grade of the commodity, location, chemical attributes may result in basis risk. Basis risk exists when futures and spot prices change by the same amount over time and converge at maturity of the futures contract. Basis risk is zero when variances of both the futures and spot process are identical and the correlation coefficient between spot and futures prices is equal to one.

Answer: c. Explanation: Statement a is incorrect: as it is a correct statement: An Airline company hedging jet fuel with heating oil futures may face basis risk due to difference in the underlying assets. Statement b is incorrect: as it is a correct statement: optionalities left to the seller at maturity gives the seller flexibility resulting in the buyer of the contract facing basis risk. Statement c is correct: as it is an incorrect statement: Basis risk exists when futures and spot prices do not change by the same amount over time and possibly will not converge at maturity of the futures contract. Statement d is incorrect: as it is a correct statement: The magnitude of basis risk depends mainly on the degree of correlation between cash and futures prices. If the correlation is one then by definition there is no basis risk Topic: Financial Markets and Products Subtopic: Basis Risk AIMS: Define the various sources of basis risk and explain how basis risks arise when hedging with futures. Reference: Hull, Options, Futures, and Other Derivatives, 7th Edition, Chapter 3—Hedging Strategies Using Futures.

12.

If the volatility of the interest rate decreases, the value of a callable convertible bond to an investor: a. b. c. d.

Decreases Increases Stays the same Insufficient information to determine.

Answer: b. Explanation: A decrease in the interest rate volatility will decrease the value of embedded call on the bond and increase the value of the convertible bond. Topic: Financial Markets and Products Subtopic: Corporate Bonds, Derivatives on fixed‐income securities, interest rates, foreign exchange and equities AIMS: Identify the six factors that affect an option's price and discuss how these six factors affect the price for both European and American options. Describe the mechanisms by which corporate bonds can be retired before maturity, including: Call provisions. Reference: Hull, Options, Futures, and Other Derivatives, 7th Edition, Chapter 9—Properties of Stock Options Frank Fabozzi, The Handbook of Fixed Income Securities, 7th Edition, (New York: McGraw-Hill, 2005). Chapter 13— Corporate Bonds.

24



13.

On Nov 1, Jimmy Walton, a fund manager of an USD 60 million US medium-to-large cap equity portfolio, considers locking up the profit from the recent rally. The S&P 500 index and its futures with the multiplier of 250 are trading at USD 900 and USD 910, respectively. Instead of selling off his holdings, he would rather hedge two-thirds of his market exposure over the remaining 2 months. Given that the correlation between Jimmy’s portfolio and the S&P 500 index futures is 0.89 and the volatilities of the equity fund and the futures are 0.51 and 0.48 per year respectively, what position should he take to achieve his objective? a. b. c. d.

Sell Sell Sell Sell


Answer: c. Explanation: The calculation is as follows: Two-thirds of the equity fund is worth USD 40 million. The Optimal hedge ratio is given by h = 0.89 * 0.51 / 0.48 = 0.945 The number of futures contracts is given by N=0.945 * 40,000,000 / (910 * 250) = 166.26 ≈ 167, round up to nearest integer. Topic: Financial Markets and Products Subtopic: Minimum Variance Hedge Ratio AIMS: Define, compute and interpret the optimal number of futures contracts needed to hedge an exposure, including a “tailing the hedge” adjustment. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 3—Hedging Strategies Using Futures.

14.

Alan bought a futures contract on a commodity on the New York Commodity Exchange on June 1. The futures price was USD 500 per unit and the contract size was 100 units per contract. Alan set up a margin account with initial margin of USD 2,000 per contract and maintenance margin of USD 1,000 per contract. The futures price of the commodity varied as shown below. What was the balance in Alan’s margin account at the end of day on June 5? Day June June June June June a. b. c. d.

1 2 3 4 5

Futures Price (USD) 497.30 492.70 484.20 471.70 468.80

-USD 1,120 USD 0 USD 880 USD 1,710

Answer: d.


25


Explanation: Day June June June June June

1 2 3 4 5

Futures Price 497.30 492.70 484.20 471.70 468.80

Daily Gain (Loss) (270) (460) (850) (1250) (290)

Cumulative Gain (Loss) (270) (730) (1580) (2830) (3120)

Margin Account Balance 1730 1270 420 750 1710

Margin Call

1580 1250

Topic: Financial Markets and Products Subtopic: Futures, forwards, swaps, and options AIMS: Describe the rationale for margin requirements and explain how they work. Reference: Hull, Options, Futures, and Other Derivatives, 7th Edition, Chapter 2—Mechanics of Futures Markets.

15.


Spot–Price (USD) 102.44 106.59 98.38



The futures price is 103 -17/32 and the maturity date of the contract is September 1. The bonds pay their coupon amount semi-annually on June 30 and December 31. With these data, the cheapest-to-deliver bond is: a. b. c. d.


Answer: b. Explanation: Cheapest to deliver bond is the bond with the lowest cost of delivering. Cost of delivering = Quoted price – (Current Futures price x Conversion Factor) Cost of bond A = 102.44 – (103.53 x .98) = 0.98 Cost of bond B = 106.59 – (103.53 x 1.03) = -0.04 Cost of bond C = 98.38 – (103.53 x 0.95) = 0.02 Hence, bond B is the cheapest to deliver bond. Topic: Financial Markets and Products Subtopic: Cheapest to deliver bond, conversion factors AIMS: Describe the impact of the level and shape of the yield curve on the cheapest‐to‐deliver bond decision. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 6—Interest Rate Futures.

26



16.

On the OTC market there are two options available on Microsoft stock: a European put with premium of USD 2.25 and an American call option with premium of USD 0.46. Both options have a strike price of USD 24 and an expiration date 3 months from now. Microsoft’s stock price is currently at USD 22 and no dividend is due during the next 6 months. Assuming that there is no arbitrage opportunity, which of the following choices is closest to the level of the risk- free rate: a. b. c. d.

0.25% 1.76% 3.52% Insufficient information to determine.

Answer: c. Explanation: Due to the fact that the American call option under consideration is on the stock which does not pay dividends, its value is equal to European call option with the same parameters. Thus, we can apply put-call parity to determine the level of interest rate. C – P = S – K e-rT 0.46 – 2.25 = 22 – 24 e-0.25r - 23.79 = -24e-0.25r r = 3.52% Topic: Financial Markets and Products Subtopic: American options, effects of dividends, early exercise AIMS: Explain put‐call parity and calculate, using the put‐call parity on a non‐dividend‐paying stock, the value of a European and American option, respectively. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 9—Properties of Stock Options, Chapter 10—Trading Strategies Involving Options.

17.

A risk manager for bank XYZ, Mark is considering writing a 6 month American put option on a non-dividend paying stock ABC. The current stock price is USD 50 and the strike price of the option is USD 52. In order to find the no-arbitrage price of the option, Mark uses a two-step binomial tree model. The stock price can go up or down by 20% each period. Mark’s view is that the stock price has an 80% probability of going up each period and a 20% probability of going down. The risk-free rate is 12% per annum with continuous compounding. What is the risk-neutral probability of the stock price going up in a single step? a. b. c. d.

34.5% 57.6% 65.5% 80.0%

Answer: b.


27


Explanation: b. is correct. pup = (erΔt – d)/(u - d) = (e0.12*3/12 – 0.8)/(1.2 – 0.8) = 57.61% Topic:: Valuation and Risk Models Subtopic: Binomial trees AIMS: Calculate the value of a European call or put option using the one‐step and two‐step binomial model. Reference: John Hull, Options, Futures and Other Derivatives, 7th Edition (New York: Prentice Hall, 2009), Chapter 11—Binomial Trees.

18.

Assume that options on a non dividend paying stock with price of USD 100 have a time to expiry of half a year and a strike price of USD 110. The risk-free rate is 10%. Further, N(d1) = 0.457185 and N(d2) = 0.374163. Which of the following values is closest to the Black-Scholes values of these options? a. b c. d.


of of of of


call call call call


is is is is

USD USD USD USD


Answer: a. Explanation: a: is correct. With the given data, the value of a European call option is USD 6.56 and the value of a European put option is USD 11.20. We know that American options are never less than corresponding European option in valuation. Also, the American call option price is exactly the same as the European call option price under the usual Black-Scholes world with no dividend. Thus only ‘a’ is the correct option. Topic: Valuation and Risk Models Subtopic: Black‐Scholes‐Merton model AIMS: Compute the value of a European option using the Black‐Scholes‐Merton model on a non‐dividend‐paying stock. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 13—The Black-Scholes-Merton Model.

28



19.

An analyst is doing a study on the effect on option prices of changes in the price of the underlying asset. The analyst wants to find out when the deltas of calls and puts are most sensitive to changes in the price of the underlying. Assume that the options are European and that the Black-Scholes formula holds. An increase in the price of the underlying has the largest absolute value impact on delta for: a. b. c. d.

Deep in-the-money calls and deep out-of-the-money puts. Deep in-the-money puts and calls. Deep out-of-the-money puts and calls. At-the-money puts and calls.

Answer: d. Explanation: a: is incorrect. When calls are deep in-the-money and puts are deep out-of-the-money, deltas are NOT most sensitive to changes in the underlying asset. b: is incorrect. When both calls and puts are deep in-the-money, deltas are NOT most sensitive to changes in the underlying asset. c: is incorrect. When both calls and puts are deep out-of-the-money, deltas are NOT most sensitive to changes in the underlying asset. d: is correct. When both calls and puts are at-the-money, deltas are most sensitive to changes in the underlying asset. (Gammas are largest when options are at-the-money) Topic: Valuation and Risk Models Subtopic: Greek Letters AIMS: Define, compute and describe delta, theta, gamma, vega, and rho for option positions. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 17—The Greek Letters.

20.

A 5-year corporate bond paying an annual coupon of 8% is sold at a price reflecting a yield-to-maturity of 6% per year. One year passes and the interest rates remain unchanged. Assuming a flat term structure and holding all other factors constant, the bond’s price during this period will have a. b. c. d.

Increased Decreased Remained constant Insufficient information to determine.

Answer: b. Explanation: Since yield-to-maturity < coupon, the bond is sold at a premium. As time passes, the bond price will move towards par. Hence the price will decrease. Topic: Valuation and Risk Models Subtopic: Bond prices, spot rates, forward rates AIMS: Discuss the impact of maturity on the price of a bond and the returns generated by bonds. Reference: Bruce Tuckman, Fixed Income Securities, 2nd Edition, (Hoboken, NJ: John Wiley & Sons, 2002), Chapter 2—Bond Prices, Spot Rates, and Forward Rates.


29


21.


AAA 87.44 0.60 0.05 0.02 0.04 0.00 0.08

AA 7.37 86.65 2.05 0.21 0.08 0.07 0.00

A 0.46 7.78 86.96 3.85 0.33 0.20 0.31

BBB 0.09 0.58 5.50 84.13 5.27 0.28 0.39

BB 0.06 0.06 0.43 4.39 75.73 5.21 1.31

B 0.00 0.11 0.16 0.77 7.36 72.95 9.74

CCC/C 0.00 0.02 0.03 0.19 0.94 4.23 46.83

D 0.00 0.01 0.04 0.29 1.20 5.71 28.83

Non Rated 4.59 4.21 4.79 6.14 9.06 11.36 12.52

BBB loans have a 4.08% chance of being upgraded in one year. BB loans have a 75.73% chance of staying at BB for one year. BBB loans have an 88.21% chance of being upgraded in one year. BB loans have a 5.72% chance of being upgraded in one year.

Answer: c. Explanation: a: is incorrect. b: is incorrect. c: is correct. d: is incorrect.

The chance of BBB loans being upgraded over 1 year is 4.08% (0.02 + 0.21 + 3.85). The chance of BB loans staying at the same rate over 1 year is 75.73%. 88.21% represents the chance of BBB loans staying at BBB or being upgraded over 1 year. The chance of BB loans being downgraded over 1 year is 5.72% (0.04 + 0.08 + 0.33 + 5.27).

Topic: Valuation and Risk Models Subtopic: Credit transition matrices AIMS: Define and explain a ratings transition matrix and its elements. Reference: Caouette, Altman, Narayanan and Nimmo, Managing Credit Risk, 2nd Edition. Chapter 6—The Rating Agencies.

30



22.

You are the risk manager of a fund. You are using the historical method to estimate VaR. You find that the worst 10 daily returns for the fund over the period of last 100 trading days are -1.0%, -0.3%, -0.6%, -0.2%, -2.7%, -1.0%, -2.9%, 0.1%, -1.1%, -3.0%. What is the daily VaR for the portfolio at the 95% confidence level? a. b. c. d.

-2.9% -1.1% -1.0% -3.0%

Answer: c. Explanation: While some authors differ on the exact point on a discrete distribution at which to define VaR, it would be either the fifth worst loss, the sixth worst loss, or some interpolated value in between in this case. FRM questions and answer choices will be structured as to avoid confusion in this matter. Topic: Valuation and Risk Models Subtopic: Value‐at‐Risk (VaR) Definition and methods AIMS: Explain the various approaches for estimating VaR. Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition, (West Sussex, England: John Wiley & Sons, 2005, Chapter 2—Measures of Financial Risk.

23.

Consider a bond with par value of EUR 1,000, maturity in 3 years, and that pays a coupon of 5% annually. The spot rate curve is as follows: Term 1 2 3



EUR EUR EUR EUR

904 924 930 950

Answer: b. Explanation: Using spot rates, the value of the bond is: 50/(1.06) + 50/[(1.07)^2] + 1050/[(1.08)^3] = 924.37 Topic: Valuation and Risk Models Subtopic: Discount factors, arbitrage, yield curves AIMS: Calculate the value of a bond using spot rates. Reference: Bruce Tuckman, Fixed Income Securities, 2nd Edition, (Hoboken, NJ: John Wiley & Sons, 2002), Chapter 2—Bond Prices, Spot Rates, and Forward Rates.


31


24.

Assume that portfolio daily returns are independently and identically normally distributed. Sam Neil, a new quantitative analyst, has been asked by the portfolio manager to calculate the portfolio Value-at-Risk (VaR) measure for 10, 15, 20 and 25 day periods. The portfolio manager notices something amiss with Sam’s calculations displayed below. Which one of following VaRs on this portfolio is inconsistent with the others? a. b. c. d.

VaR(10-day) = USD 316M VaR(15-day) = USD 465M VaR(20-day) = USD 537M VaR(25-day) = USD 600M

Answer: a. Explanation: Calculate VaR(1-day) from each choice: VaR(10-day) = 316 → VaR(1-day) = 316/sqrt(10) = 100 VaR(15-day) = 465 → VaR(1-day) = 465/sqrt(15) = 120 VaR(20-day) = 537 → VaR(1-day) = 537/sqrt(20) = 120 VaR(25-day) = 600 → VaR(1-day) = 600/sqrt(25) = 120 VaR(1-day) from Answer A is different from those from other answers. Thus, VaR from answer A is inconsistent. Topic: Valuation and Risk Models Subtopic: Value‐at‐Risk (VaR) Definition and methods AIMS: Explain the various approaches for estimating VaR. Reference: Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, Chapter 14— Stress Testing.

32



25.

For the monthly returns plot of the fund tracked below in 2010, which period had a negative tracking error?

a. b. c. d.

1/2009 – 5/2009 6/2009 – 10/2009 1/2009 – 10/2009 None of the above

Answer: d. Explanation: The definition of tracking error is σ(Rp–Rb) where Rp and Rb are the return of the portfolio and benchmark respectively. This value can never be negative. Topic: Foundation of Risk Management Subtopic: Tracking error AIMS: Compute and interpret tracking error, the information ratio, and the Sortino ratio. Reference: Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England: John Wiley & Sons, 2003), Chapter 4, Section 4.2—Applying the CAPM to Performance Measurement: Single-Index Performance Measurement Indicators.


33


Answer Sheet


a.

b.

c.

d.

a.

1.

16.

2.

17.

3.

18.

4.

19.

5.

20.

6.

21.

7.

22.

8.

23.

9.

24.

10.

25.

b.

c.

d.

3

8

11. 12.


13.

1.

14.


15.

1.


35


Questions


1.

You built a linear regression model to analyze annual salaries for a developed country. You incorporated two independent variables, age and experience, into your model. Upon reading the regression results, you noticed that the coefficient of “experience” is negative which appears to be counter-intuitive. In addition you have discovered that the coefficients have low t-statistics but the regression model has a high R2. What is the most likely cause of these results? a. b. c. d.

2.

Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift μ = 0, volatility σ = 0.2 and time step Δt = 0.01. Let St be the price of the stock at time t. If S0 = 50, and the first two simulated (randomly selected) standard normal variables are ε1 = -0.521, ε2 = 1.225, by what percent will the stock price change in the second step of the simulation? a. b. c. d.

3.

Incorrect standard errors Heteroskedasticity Serial correlation Multicollinearity

-1.04% 0.43% 1.12% 2.45%


0.095 0.95 9.5 95


37


4.


Suppose the estimate of the volatility on day n-1 is 2.5% and that on day n-1, the asset return was -1.5%. What is the estimate of the long-run average volatility per day? a. b. c. d.

5.

0.80% 1.21% 1.85% 2.42%

John is forecasting a stock’s performance in 2010 conditional on the state of the economy of the country in which the firm is based. He divides the economy’s performance into three categories of “GOOD”, “NEUTRAL” and “POOR” and the stock’s performance into three categories of “increase”, “constant” and “decrease”. He estimates: • •

•

The probability that the state of the economy is GOOD is 20%. If the state of the economy is GOOD, the probability that the stock price increases is 80% and the probability that the stock price decreases is 10%. The probability that the state of the economy is NEUTRAL is 30%. If the state of the economy is NEUTRAL, the probability that the stock price increases is 50% and the probability that the stock price decreases is 30%. If the state of the economy is POOR, the probability that the stock price increases is 15% and the probability that the stock price decreases is 70%.

Billy, his supervisor, asks him to estimate the probability that the state of the economy is NEUTRAL given that the stock performance is constant. John’s best assessment of that probability is closest to: a. b. c. d.

6.

Suppose that a quiz consists of 10 true-false questions. A student has not studied for the exam and just randomly guesses the answers. What is the probability that the student will get at least three questions correct? a. b. c. d.

38

6.0% 15.5% 20.0% 38.7%

5.47% 33.66% 78.62% 94.53%



7.

A global investment risk manager is assessing an investment’s performance using a two-factor model. In order to determine the volatility of the investment, the risk manager developed the following factor covariance matrix for global assets: Factor Covariance Matrix for Global Assets


Global Equity Factor 0.24500 0.00791

Global Bond Factor 0.00791 0.01250

Suppose the factor sensitivity to the global equity factor is 0.75 for the investment and the factor sensitivity to the global bond factor is 0.20 for the investment. The volatility of the investment is closest to: a. b. c. d.

8.

11.5% 24.2% 37.5% 42.2%


Credit spreads widen following recent bankruptcies The bid-ask spread of an asset suddenly widens

Which of these can be identified as liquidity risk? a. b. c. d.

9.

I only II only Both Neither




39


10.

Tom is evaluating 4 funds run by 4 independent managers relative to a benchmark portfolio that has an expected return of 6.4% and volatility of 12%. He is interested in investing in the fund with the highest information ratio that also meets the following conditions in his investment guidelines: I. II.

Expected residual return must be at least 2% The Sharpe ratio must be at least 0.2

Based on the following information and a risk free rate of 5%, which fund should he choose? Fund Fund Fund Fund Fund a. b. c. d.

11.

Fund Fund Fund Fund



A B C D

Differences between the asset whose price is being hedged and the asset underlying the futures contract. Uncertainty about the exact date when the asset being hedged will be bought or sold. The inability of managers to forecast the price of the underlying. The need to close the futures contract before its delivery date.

On Nov 1, Dane Hudson, a fund manager of an USD 50 million US large cap equity portfolio, considers locking up the profit from the recent rally. The S&P 500 index and its futures with the multiplier of 250 are trading at USD 1,000 and USD 1,100, respectively. Instead of selling off his holdings, he would rather hedge his market exposure over the remaining 2 months. Given that the correlation between Dane’s portfolio and the S&P 500 index futures is 0.92 and the volatilities of the equity fund and the futures are 0.55 and 0.45 per year respectively, what position should he take to achieve his objective? a. b. c. d.

40

8.5%

Volatility 14.3% 16.4% 17.8% 19.1%

Which of the following is not a source of basis risk when using futures contracts for hedging? a. b. c. d.

12.


A B C D

Sell Sell Sell Sell




13.

In late June, Simon purchased two September silver futures contracts. Each contract size is 5,000 ounces of silver and the futures price on the date of purchase was USD 18.62 per ounce. The broker requires an initial margin of USD 6,000 and a maintenance margin of USD 4,500. You are given the following price history for the September silver futures: Day June 29 June 30 July 1 July 2 July 6 July 7 July 8

Futures Price (USD) 18.62 18.69 18.03 17.72 18.00 17.70 17.60

Daily Gain (Loss) 0 700 -6,600 -3,100 2,800 -3,000 -1,000

On which days did Simon receive a margin call? a. b. c. d.

14.

July July July July

1 only 1 and July 2 only 1, July 2 and July 7 only 1, July 2 and July 8 only


Spot–Price(USD) 102.40 100.40 99.60



The futures price is USD 104 and the maturity date of the contract is September 1. The bonds pay their coupon amount semi-annually on June 30 and December 31. With these data, which bond is cheapest-todeliver? a. b. c. d.



41


15.

A stock index is valued at USD 800 and pays a continuous dividend at the rate of 3% per year. The 6-month futures contract on that index is trading at USD 758. The continuously compounded risk free rate is 2.5% per year. There are no transaction costs or taxes. Is the futures contract priced so that there is an arbitrage opportunity? If yes, which of the following numbers comes closest to the arbitrage profit you could realize by taking a position in one futures contract? a. b. c. d.

16.

38 40 42 There is no arbitrage opportunity.

Below is a table of term structure of swap rates Maturity in Years 1 2 3 4 5

Swap Rate 3.50% 4.00% 4.50% 5.00% 5.50%

What is the 2-year forward rate starting in three years? a. b. c. d.

17.

A stock is trading at USD 100. A box spread with 1 year to expiration and strikes at USD 120 and USD 150 is trading at USD 20. The price of a 1-year European call option with strike USD 120 is USD 5 and the price of a European put option with same strike and expiration is USD 25. What strategy exploits an arbitrage opportunity, if any? a. b. c. d.

42

4.50% 5.50% 6.51% 7.02%

Short one put, short one unit of spot, buy one call, and buy six units box-spread. Buy one put, short one unit of spot, short one call, and buy four units of box-spread. Buy one put, buy one unit of spot, short one call, and short six units of box-spread. There is no arbitrage opportunity.



18.

A trader in your bank has sold 200 call option contracts each on 100 shares of General Motors with time to maturity of 60 days at USD 2.10. The delta of the option on one share is 0.50. As a risk manager, what action must you take on the underlying stock in order to hedge the option exposure and keep it delta neutral? a. b. c. d.

19.

A non-dividend paying stock is currently trading at USD 25. You are looking to find a no-arbitrage price for a 1 year American call using a two-step binomial tree model for which the stock can go up or down by 25%. The risk free rate is 10% and you believe that there is an equal chance of the stock price going up or down. What is the risk-neutral probability of the stock price going down in a single step? a. b. c. d.

20.

22.6% 39.8% 50.0% 68.3%

Assume that options on a non dividend paying stock with price of USD 150 expire in a year and all have a strike price of USD 140. The risk-free rate is 8%. Which of the following values is closest to the Black-Scholes values of these options assuming N(d1) = 0.7327 and N(d2) = 0.6164 a. b. c. d.

21.

Buy 10,000 shares of General Motors. Sell 10,000 shares of General Motors. Buy 1,000 shares of General Motors. Sell 1,000 shares of General Motors.


of of of of


call call call call


is is is is

USD USD USD USD


Which of the following portfolios would have the highest vega assuming all options involved are of the same strikes and maturities? a. b. c. d.

Long a call Short a put Long a put and long a call A short of the underlying, a short in a put, and a long in a call


43


22.


23.

AAA 87.44 0.60 0.05 0.02 0.04 0.00 0.08

AA 7.37 86.65 2.05 0.21 0.08 0.07 0.00

A 0.46 7.78 86.96 3.85 0.33 0.20 0.31

BBB 0.09 0.58 5.50 84.13 5.27 0.28 0.39

BB 0.06 0.06 0.43 4.39 75.73 5.21 1.31

B 0.00 0.11 0.16 0.77 7.36 72.95 9.74

CCC/C 0.00 0.02 0.03 0.19 0.94 4.23 46.83

D Non Rated 0.00 4.59 0.01 4.21 0.04 4.79 0.29 6.14 1.20 9.06 5.71 11.36 28.83 12.52

‘AAA’ loans have 0% chance of ever defaulting. ‘AA’ loans have a 86.65% chance of staying at AA for one year. ‘A’ loans have a 13.04% chance of receiving a ratings change. ‘BBB’ loans have a 4.08% chance of being upgraded in one year.

A bond with par value of USD 100 and 3 years to maturity pays 7% annual coupons. The spot rate curve is as follows: Term 1 2 3



44

USD USD USD USD

95.25 97.66 99.25 101.52



24.

Sam Neil, a new quantitative analyst, has been asked by the portfolio manager to calculate the portfolio 1-day 98% Value-at-Risk (VaR) measure based on the past 100 trading days. What will this be if worst 5 losses in the past 100 trading days are 316M, 385M, 412M, 422M and 485M in USD? a. b. c. d.

25.

USD USD USD USD

31.6M 41.2M 316M 412M

Which of the following statements is correct? I. II.

The Rho of a call option changes with the passage of time and tends to approach zero as expiration approaches, but this is not true for the Rho of put options. Theta is always negative for long calls and long puts and positive for short calls and short puts.

a. b. c. d.



45


Answers


a.

b.

c.

d.

a.

1.

16.

2.

17.

18.

3. 4.

20.

6.

21.

7.

8.

24.

25.

11.

12.

d.

23.

9. 10.

22.

c.

19.

5.

b.


13.

1.

14.


15.

1.


3

8

47


Explanations


1.

You built a linear regression model to analyze annual salaries for a developed country. You incorporated two independent variables, age and experience, into your model. Upon reading the regression results, you noticed that the coefficient of “experience” is negative which appears to be counter-intuitive. In addition you have discovered that the coefficients have low t-statistics but the regression model has a high R2. What is the most likely cause of these results? a. b. c. d.

Incorrect standard errors Heteroskedasticity Serial correlation Multicollinearity

Answer: d. Explanation: Age and experience are highly correlated and would lead to multicollinearity. In fact, low t-statistics but a high R2 do suggest this problem also. Answers a, b and c are not likely causes and are therefore incorrect. Topic: Quantitative Analysis Subtopic: Linear regression and correlation, hypothesis testing AIMS: Explain the concept of imperfect and perfect multicollinearity and its implications. Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition, (Boston: Pearson Education, 2008), Chapter 6—Linear Regression with Multiple Regressors.

2.

Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with drift μ = 0, volatility σ = 0.2 and time step Δt = 0.01. Let St be the price of the stock at time t. If S0 = 50, and the first two simulated (randomly selected) standard normal variables are ε1 = -0.521, ε2 = 1.225, by what percent will the stock price change in the second step of the simulation? a. b. c. d.

-1.04% 0.43% 1.12% 2.45%

Answer: d. Explanation: In the simulation, St is assumed to move as follows over an interval of time of length Δt: ΔSt+i /St+i -1 = (μ Δt + σ εi (Δt)1/2) where εi is a standard normal random variable. Therefore, (S2 - S1)/S1 = 0.2 * 1.225 * sqrt(0.01) = 0.0245 Topic: Quantitative Analysis Subtopic: Monte Carlo Methods AIMS: Describe how to simulate a price path using a geometric Brownian motion model. Reference: Jorion (2005), Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, New York: McGraw-Hill, Chapter 12—Monte Carlo Methods.


49


3.


0.095 0.95 9.5 95

Answer: b. Explanation: The standard error of the sample mean is estimated by dividing the standard deviation of the sample by the square root of the sample size: sx = s / (n)1/2 = 60 / (4000)1/2 = 60 / 63 = 0.95 (the population mean is irrelevant.) Topic: Quantitative Analysis Subtopic: Estimating the parameters of distributions AIMS: Define, calculate, and interpret the sample variance, sample standard deviation, and standard error. Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition, (Boston: Pearson Education, 2008), Chapter 3—Review of Statistics.

4.

The following GARCH(1,1) model is used to forecast the daily return variance of an asset: 2 σn2 = 0.000007 + 0.12u2n-1 + 0.77σn-1 Suppose the estimate of the volatility on day n-1 is 2.5% and that on day n-1, the asset return was -1.5%. What is the estimate of the long-run average volatility per day? a. b. c. d.

0.80% 1.21% 1.85% 2.42%

Answer: a. Explanation: The model corresponds to α = 0.12, β = 0.77, and ω = 0.000007. Because γ = 1− α − β, it follows that γ = 0.11. The long-run average variance, VL, can be found with VL = ω /γ, it follows that VL = 0.00006364. In other words, the long-run average volatility per day implied by the model is sqrt(0.00006364) = 0.798%. Topic: Quantitative Analysis Subtopic: EWMA, GARCH model AIMS: Estimate volatility using the GARCH(p,q) model. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition, (New York: Prentice Hall, 2009), Chapter 21—Estimating Volatilities and Correlations.

50



5.

John is forecasting a stock’s performance in 2010 conditional on the state of the economy of the country in which the firm is based. He divides the economy’s performance into three categories of “GOOD”, “NEUTRAL” and “POOR” and the stock’s performance into three categories of “increase”, “constant” and “decrease”. He estimates: • •

•

The probability that the state of the economy is GOOD is 20%. If the state of the economy is GOOD, the probability that the stock price increases is 80% and the probability that the stock price decreases is 10%. The probability that the state of the economy is NEUTRAL is 30%. If the state of the economy is NEUTRAL, the probability that the stock price increases is 50% and the probability that the stock price decreases is 30%. If the state of the economy is POOR, the probability that the stock price increases is 15% and the probability that the stock price decreases is 70%.

Billy, his supervisor, asks him to estimate the probability that the state of the economy is NEUTRAL given that the stock performance is constant. John’s best assessment of that probability is closest to: a. b. c. d.

6.0% 15.5% 20.0% 38.7%

Answer: d. Explanation: Use Bayes’ Theorem: P(NEUTRAL | Constant) = P(Constant | NEUTRAL) * P(NEUTRAL) / P(Constant) = 0.2 * 0.3 / (0.1 * 0.2 + 0.2 * 0.3 + 0.15 * 0.5) = 0.387 a: b: c:

This is the Prob(Constant & NEUTRAL) This is the Prob(Constant) This is the Prob(NEUTRAL | Decrease)

Topic: Quantitative Analysis Subtopic: Probability Distributions AIMS: Describe joint, marginal, and conditional probability functions. Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition, (Boston: Pearson Education, 2008), Chapter 2—Review of Probability.


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6.

Suppose that a quiz consists of 10 true-false questions. A student has not studied for the exam and just randomly guesses the answers. What is the probability that the student will get at least three questions correct? a. b. c. d.

5.47% 33.66% 78.62% 94.53%

Answer: d Explanation: Calculate for no questions correct, 1 question correct, and 2 questions correct: (10C0 + 10C1 + 10C2)*0.510 = (1 + 10 + 45) )*0.510 = 5.469% 1 - 0.05469 = 94.53% Topic: Quantitative Analysis Subtopic: Probability and Probability Distributions AIMS: Define the probability of an event. Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition, (Boston: Pearson Education, 2008), Chapter 2—Review of Probability.

7.

A global investment risk manager is assessing an investment’s performance using a two-factor model. In order to determine the volatility of the investment, the risk manager developed the following factor covariance matrix for global assets: Factor Covariance Matrix for Global Assets


Global Equity Factor 0.24500 0.00791

Global Bond Factor 0.00791 0.01250

Suppose the factor sensitivity to the global equity factor is 0.75 for the investment and the factor sensitivity to the global bond factor is 0.20 for the investment. The volatility of the investment is closest to: a. b. c. d.

11.5% 24.2% 37.5% 42.2%

Answer: c.

52



Explanation: 2 2 2 2 VaR (Inv) = β1 σF1 + β2 σF2 + 2 β1 β2 Cov (F1, F2) = (0.75)2 (0.245) + (0.20)2 (0.0125) + 2 (0.75) (0.20) (0.00791) = 0.1407 σ = sqrt(0.1407) = 37.5% Topic: Foundation of Risk Management Subtopic: Factor models and Arbitrage Pricing Theory AIMS: Calculate the mean and variance of sums of random variables. Use the APT to calculate the expected returns on an asset. Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition, (Boston: Pearson Education, 2008), Chapter 2—Review of Probability; Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann, Modern Portfolio Theory and Investment Analysis, 7th Edition, (Hoboken, NJ: John Wiley & Sons, 2007), Chapter 16—The Arbitrage Pricing Model APT—A New Approach to Explaining Asset Prices.

8.


Credit spreads widen following recent bankruptcies The bid-ask spread of an asset suddenly widens

Which of these can be identified as liquidity risk? a. b. c. d.


Answer: b. Explanation: I is market risk, II is liquidity risk. Topic: Foundation of Risk Management Subtopic: Creating Value with Risk Management AIMS: Define and describe the four major types of financial risks: market, liquidity, credit, and operational. Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, (New York: McGraw‐Hill, 2007), Chapter 1—The Need for Risk Management.


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9.



Answer: d. Explanation: If the daily, 95% confidence level Value-at-Risk (VaR) of a portfolio is correctly estimated to be USD 10,000, one would expect that 95% of the time (19 out of 20), the portfolio will lose less than USD 10,000; equivalently, 5% of the time (1 out of 20) the portfolio will lose USD 10,000 or more. Topic: Foundation of Risk Management Subtopic: Creating Value with Risk Management AIMS: Define Value-at-Risk (VaR) and describe how it is used in risk management. Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, (New York: McGraw-Hill, 2007), Chapter 1—The Need for Risk Management.

10.

Tom is evaluating 4 funds run by 4 independent managers relative to a benchmark portfolio that has an expected return of 6.4% and volatility of 12%. He is interested in investing in the fund with the highest information ratio that also meets the following conditions in his investment guidelines: I. II.

Expected residual return must be at least 2% The Sharpe ratio must be at least 0.2

Based on the following information and a risk free rate of 5%, which fund should he choose? Fund Fund Fund Fund Fund a. b. c. d.


A B C D

Fund Fund Fund Fund

8.5%

Volatility 14.3% 16.4% 17.8% 19.1%



A B C D

Answer: a.

54



Explanation: Sharpe Ratio = Return Premium over Risk Free Rate / Volatility = E(RP – Rf) / σ Fund A: Fund B: Fund C: Fund D:

Expected residual return = 8.4% - 6.4% = 2.0%, Sharpe Ratio = (8.4% - 5%)/14.3% = 0.238 Expected residual return = information ratio * residual risk = 0.9 * 2.4% = 2.16% Sharpe Ratio = (2.16% + 6.4% - 5%)/16.4% = 0.217 Expected residual return = information ratio * residual risk = 1.3 * 1.5% = 1.95% Expected residual return = 8.5% - 6.4% = 2.1% Information ratio = 2.1% / 1.8% = 1.16 Sharpe Ratio = (8.5% - 5%)/19.1% = 0.183

Both funds A and B meet the requirements. Fund A has the higher information ratio. Topic: Foundation of Risk Management Subtopic: Sharpe ratio and information ratio AIMS: Compute and interpret tracking error, the information ratio, and the Sortino ratio. Reference: Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England: John Wiley & Sons, 2003), Chapter 4, Section 4.2 only—Applying the CAPM to Performance Measurement: SingleIndex Performance Measurement Indicators.

11.

Which of the following is not a source of basis risk when using futures contracts for hedging? a. b. c. d.

Differences between the asset whose price is being hedged and the asset underlying the futures contract. Uncertainty about the exact date when the asset being hedged will be bought or sold. The inability of managers to forecast the price of the underlying. The need to close the futures contract before its delivery date.

Answer: c. Explanation: The inability of managers to forecast the price of the underlying is an argument for hedging but does not increase basis risk. Topic: Financial Markets and Products Subtopic: Basis risk AIMS: Define the various sources of basis risk and explain how basis risk arises when hedging with futures. Reference: John Hull, Options, Futures and Other Derivatives, 7th Edition, (New York: Pearson, 2009), Chapter 3— Hedging strategies using futures.


55


12.

On Nov 1, Dane Hudson, a fund manager of an USD 50 million US large cap equity portfolio, considers locking up the profit from the recent rally. The S&P 500 index and its futures with the multiplier of 250 are trading at USD 1,000 and USD 1,100, respectively. Instead of selling off his holdings, he would rather hedge his market exposure over the remaining 2 months. Given that the correlation between Dane’s portfolio and the S&P 500 index futures is 0.92 and the volatilities of the equity fund and the futures are 0.55 and 0.45 per year respectively, what position should he take to achieve his objective? a. b. c. d.

Sell Sell Sell Sell


Answer: c. Explanation: The calculation is as follows: The equity fund is worth USD 50 million. The Optimal hedge ratio is given by h = 0.92 * 0.55 / 0.45 = 1.124 The number of futures contracts is given by N = 1.124 * 50,000,000 / (1,100 * 250) = 204.36 ≈ 205, round up to nearest integer. Topic: Financial Markets and Products Subtopic: Minimum Variance Hedge Ratio AIMS: Define, compute and interpret the optimal number of futures contracts needed to hedge an exposure, including a “tailing the hedge” adjustment. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 3—Hedging Strategies Using Futures.

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13.

In late June, Simon purchased two September silver futures contracts. Each contract size is 5,000 ounces of silver and the futures price on the date of purchase was USD 18.62 per ounce. The broker requires an initial margin of USD 6,000 and a maintenance margin of USD 4,500. You are given the following price history for the September silver futures: Day June 29 June 30 July 1 July 2 July 6 July 7 July 8

Futures Price (USD) 18.62 18.69 18.03 17.72 18.00 17.70 17.60

Daily Gain (Loss) 0 700 -6,600 -3,100 2,800 -3,000 -1,000

On which days did Simon receive a margin call? a. b. c. d.

July July July July

1 only 1 and July 2 only 1, July 2 and July 7 only 1, July 2 and July 8 only

Answer: b. Explanation: Here is the complete history of the margin account and margin calls: Day 6/29/2010 6/30/2010 7/1/2010 7/2/2010 7/6/2010 7/7/2010 7/8/2010

Futures Price 18.62 18.69 18.03 17.72 18.00 17.70 17.60

Daily Gain (Loss)

Cumulative Gain (Loss)

700 -6,600 -3,100 2,800 -3,000 -1,000

700 -5,900 -9,000 -6,200 -9,200 -10,200

Margin Account Balance 6,000 6,700 100 2,900 8,800 5,800 4,800

Margin Call 0 0 5,900 3,100 0 0 0

Margin calls happened on July 1 and July 2 only. Topic: Financial Markets and Products Subtopic: Futures, forwards, swaps and options AIMS:Describe the rationale for margin requirements and explain how they work. Reference: John Hull, Options, Futures and Other Derivatives, 7th Edition, (New York: Pearson, 2009), Chapter 2— Mechanics of Futures Markets.


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14.


Spot–Price(USD) 102.40 100.40 99.60



The futures price is USD 104 and the maturity date of the contract is September 1. The bonds pay their coupon amount semi-annually on June 30 and December 31. With these data, which bond is cheapest-todeliver? a. b. c. d.


Answer: b. Explanation: Cheapest to deliver bond is the bond with the lowest cost of delivering. Cost of delivering = Quoted price – (Current Futures price x Conversion Factor) Cost of bond A = 102.40 – (104 x .8) = 19.2 Cost of bond B = 100.40 – (104 x 1.5) = -55.6 Cost of bond C = 99.6 – (104 x 1.1) = -14.8 Hence, bond B is the cheapest to deliver bond. Topic: Financial Markets and Products Subtopic: Cheapest to deliver bond, conversion factors AIMS: Describe the impact of the level and shape of the yield curve on the cheapest‐to‐deliver bond decision. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 6—Interest Rate Futures.

15.

A stock index is valued at USD 800 and pays a continuous dividend at the rate of 3% per year. The 6-month futures contract on that index is trading at USD 758. The continuously compounded risk free rate is 2.5% per year. There are no transaction costs or taxes. Is the futures contract priced so that there is an arbitrage opportunity? If yes, which of the following numbers comes closest to the arbitrage profit you could realize by taking a position in one futures contract? a. b. c. d.

38 40 42 There is no arbitrage opportunity.

Answer: b.

58



Explanation: With the given data, the no-arbitrage futures price should be; 800e(0.025-0.03)*0.50 =798 Since the market price of the futures contract is lower than this price there is an arbitrage opportunity. The futures contract could be purchased and the index sold. Arbitrage profit is 798 - 758 = 40 Topic: Financial Markets and Products Subtopic: Futures, Forwards and Swaps and Options AIMS: Calculate the forward price, given the underlying asset’s price, with or without short sales and/or consideration to the income or yield of the underlying asset. Describe an arbitrage argument in support of these prices. Reference: Hull, Options, Futures and Other Derivatives, 7th Edition, Chapter 5—Determination of Forward and Futures Prices.

16.

Below is a table of term structure of swap rates Maturity in Years 1 2 3 4 5

Swap Rate 3.50% 4.00% 4.50% 5.00% 5.50%

What is the 2-year forward rate starting in three years? a. b. c. d.

4.50% 5.50% 6.51% 7.02%

Answer: d. Explanation: Statement d is correct. To calculate the 2-year forward rate starting in 3 years, use the relation: [ (1.055^5 / 1.045^3)^(1/2) - 1 = 7.02% ] Topic: Financial Markets and Products Subtopic: Futures, forwards, swaps, and options AIMS: Explain how the discount rates in a plain vanilla interest rate swap are computed. Reference: John Hull, Options, Futures and Other Derivatives, 7th Edition, (New York: Prentice Hall, 2009), Chapter 4—Interest Rates.


59


17.

A stock is trading at USD 100. A box spread with 1 year to expiration and strikes at USD 120 and USD 150 is trading at USD 20. The price of a 1-year European call option with strike USD 120 is USD 5 and the price of a European put option with same strike and expiration is USD 25. What strategy exploits an arbitrage opportunity, if any? a. b. c. d.

Short one put, short one unit of spot, buy one call, and buy six units box-spread. Buy one put, short one unit of spot, short one call, and buy four units of box-spread. Buy one put, buy one unit of spot, short one call, and short six units of box-spread. There is no arbitrage opportunity.

Answer: a. Explanation: The key concept here is the box-spread. A box-spread with strikes at USD 120 and USD 150, gives you a pay-off of USD 30 at expiration irrespective of the spot price. Now recall the put call parity relation: p + S = c + price of zero coupon bond with face value of strike redeeming at the maturity of the options Since, the strike is USD 120, price of a zero coupon bond with face value of USD 120 can be expressed as 4 units of box spread. Strategy A is correct Short one put: +25 Short one spot: +100 Buy one call: -5 Buy six box-spreads: -120 Net cash flow: 0 At expiry, if spot is greater than 120, call is exercised and if it is less than 120, put is exercised. In either case you end up buying one spot at 120. This can be used to close the short position. The six spreads will provide a cash flow of 6*30 = 180. The net profit is therefore = 180 – 120 = 60. Topic: Financial Markets and Products Subtopic: Trading Strategies using options AIMS: Describe and explain the use and payoff functions of spread strategies, including bull spread, bear spread, box spread, calendar spread, butterfly spread, and diagonal spread. Reference: Hull, Options, Futures, and Other Derivatives, 7th Edition, Chapter 10—Trading Strategies Involving Options.

60



18.

A trader in your bank has sold 200 call option contracts each on 100 shares of General Motors with time to maturity of 60 days at USD 2.10. The delta of the option on one share is 0.50. As a risk manager, what action must you take on the underlying stock in order to hedge the option exposure and keep it delta neutral? a. b. c. d.

Buy 10,000 shares of General Motors. Sell 10,000 shares of General Motors. Buy 1,000 shares of General Motors. Sell 1,000 shares of General Motors.

Answer: a. Explanation: Number of Calls = 200 Contracts * 100 = 20,000 Calls Hedged by 20000 * .50 = 10000 shares So, one needs to buy 10,000 shares in order to keep the position delta neutral. Topic: Valuation and Risk Models Subtopic: Greek Letters AIMS: Discuss the dynamic aspects of delta hedging. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition, (New York: Prentice Hall, 2009), Chapter 17—The Greek Letters.

19.

A non-dividend paying stock is currently trading at USD 25. You are looking to find a no-arbitrage price for a 1 year American call using a two-step binomial tree model for which the stock can go up or down by 25%. The risk free rate is 10% and you believe that there is an equal chance of the stock price going up or down. What is the risk-neutral probability of the stock price going down in a single step? a. b. c. d.

22.6% 39.8% 50.0% 68.3%

Answer: b. Explanation: pup = (erΔt – d)/(u - d) = (e0.10*6/12 – 0.75)/(1.25 – 0.75) = 60.25% pdown = 1 – pup = 39.75% Topic: Valuation and Risk Models Subtopic: Binomial trees AIMS: Calculate the value of a European call or put option using the one‐step and two‐step binomial model. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition, (New York: Prentice Hall, 2009), Chapter 11—Binomial Trees.


61


20.

Assume that options on a non dividend paying stock with price of USD 150 expire in a year and all have a strike price of USD 140. The risk-free rate is 8%. Which of the following values is closest to the Black-Scholes values of these options assuming N(d1) = 0.7327 and N(d2) = 0.6164 a. b. c. d.


of of of of


call call call call


is is is is

USD USD USD USD


Answer: a. Explanation: a: is correct. With the given data the value of European call option is USD 30.25 and value of European put option is USD 9.48. We know that American options are never less than corresponding European option in valuation. Also, the American call option price is exactly the same as the European call option price under the usual Black-Scholes world with no dividend. Thus only ‘a’ is the correct option. Topic: Valuation and Risk Models Subtopic: Black‐Scholes‐Merton model AIMS: Compute the value of a European option using the Black‐Scholes‐Merton model on a non‐dividend‐paying stock. Reference: Hull, Options, Futures, and Other Derivatives, 7th Edition, Chapter 13—The Black-Scholes-Merton Model.

21.

Which of the following portfolios would have the highest vega assuming all options involved are of the same strikes and maturities? a. b. c. d.

Long a call Short a put Long a put and long a call A short of the underlying, a short in a put, and a long in a call

Answer: c. Explanation: a and b are standard call/put, c is a straddle, d is a collar. A collar limits exposure to volatility, while a straddle increases this exposure. Vega is the sensitivity of a portfolio to volatility. Topic: Valuation and Risk Models Subtopic: Greek Letters AIMS: Define, compute and describe delta, theta, gamma, vega, and rho for option positions. Reference: Hull, Options, Futures, and Other Derivatives, 7th Edition, Chapter 17—The Greek Letters.

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22.


AAA 87.44 0.60 0.05 0.02 0.04 0.00 0.08

AA 7.37 86.65 2.05 0.21 0.08 0.07 0.00

A 0.46 7.78 86.96 3.85 0.33 0.20 0.31

BBB 0.09 0.58 5.50 84.13 5.27 0.28 0.39

BB 0.06 0.06 0.43 4.39 75.73 5.21 1.31

B 0.00 0.11 0.16 0.77 7.36 72.95 9.74

CCC/C 0.00 0.02 0.03 0.19 0.94 4.23 46.83

D 0.00 0.01 0.04 0.29 1.20 5.71 28.83

Non Rated 4.59 4.21 4.79 6.14 9.06 11.36 12.52

‘AAA’ loans have 0% chance of ever defaulting. ‘AA’ loans have a 86.65% chance of staying at AA for one year. ‘A’ loans have a 13.04% chance of receiving a ratings change. ‘BBB’ loans have a 4.08% chance of being upgraded in one year.

Answer: a. Explanation: AAA loans can default eventually, through consecutive downgrading, even though they are calculated to not default in one year. AA → AA is 86.65% A → A is 86.96% BBB → AAA/AA/A (sum) = 4.08% Topic: Valuation and Risk Models Subtopic: Credit transition matrices AIMS: Define and explain a ratings transition matrix and its elements. Reference: Caouette, Altman, Narayanan and Nimmo, Managing Credit Risk, 2nd Edition, Chapter 6—The Rating Agencies.


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23.

A bond with par value of USD 100 and 3 years to maturity pays 7% annual coupons. The spot rate curve is as follows: Term 1 2 3



USD USD USD USD

95.25 97.66 99.25 101.52

Answer: b. Explanation: Using spot rates, the value of the bond is: 7/(1.06) + 7/[(1.07)^2] + 107/[(1.08)^3] = 97.66 Topic: Valuation and Risk Models Subtopic: Discount factors, arbitrage, yield curves AIMS: Calculate the value of a bond using spot rates. Reference: Bruce Tuckman, Fixed Income Securities, 2nd Edition, (Hoboken, NJ: John Wiley & Sons, 2002), Chapter 1—Bond Prices, Discount Factors, and Arbitrage.

24.

Sam Neil, a new quantitative analyst, has been asked by the portfolio manager to calculate the portfolio 1-day 98% Value-at-Risk (VaR) measure based on the past 100 trading days. What will this be if worst 5 losses in the past 100 trading days are 316M, 385M, 412M, 422M and 485M in USD? a. b. c. d.

USD USD USD USD

31.6M 41.2M 316M 412M

Answer: d. Explanation: In the ordered list of 100 trading day returns, the 3rd worst loss, USD 412M, corresponds to the 98th worst return and therefore the 98% 1-day VaR. Topic: Valuation and Risk Models Subtopic: Value‐at‐Risk (VaR) Definition and methods AIMS: Explain the various approaches for estimating VaR. Reference: Jorion, Value-at-Risk, 3rd Edition, Chapter 14—Stress Testing.

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25.

Which of the following statements is correct? I. II.

The Rho of a call option changes with the passage of time and tends to approach zero as expiration approaches, but this is not true for the Rho of put options. Theta is always negative for long calls and long puts and positive for short calls and short puts.

a. b. c. d.


Answer: b. Explanation: Statement I is false—rho of a call and a put will change, with expiration of time and it tends to approach zero as expiration approaches. Statement II is true Topic: Valuation and Risk Models Subtopic: Greek Letters AIMS: Define, compute and describe delta, theta, gamma, vega, and rho for option positions. Reference: John Hull, Options, Futures and Other Derivatives, 7th Edition, (New York: Prentice Hall, 2009), Chapter 17—The Greek Letters.


65

Financial Risk ® Manager (FRM ) Examination 2011 Practice Exam PART II / EXAM 1

Answer Sheet


a.

b.

c.

d.

a.

1.

14.

2.

15.

3.

16.

4.

17.

5.

18.

6.

19.

7.

20.

b.

c.

d.

3

8

8.

9.


10.

1.

11.


12.

1.

13.


67


Questions


1.

After estimating the 99%, 1-day VaR of a bank’s portfolio to be USD 1,484 using historical simulation with 1,000 past trading days, you are concerned that the VaR measure is not providing enough information about tail losses. You decide to re-examine the simulation results and sort the simulated daily P&L from worst to best giving the following worst 15 scenarios: Scenario Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Daily P/L USD -2,833 USD -2,333 USD -2,228 USD -2,084 USD -1,960 USD -1,751 USD -1,679 USD -1,558 USD -1,542 USD -1,484 USD -1,450 USD -1,428 USD -1,368 USD -1,347 USD -1,319

What is the 99%, 1-day expected shortfall of the portfolio? a. b. c. d.

2.

USD USD USD USD

433 1,285 1,945 2,833

Which of following statement about mortgage-backed securities (MBS) is correct? I. II.

The price of a MBS is more sensitive to yield curve twists than zero-coupon bonds. When the yield is higher than the coupon rate of a MBS, the MBS behaves similar to corporate bonds as interest rates change.

a. b. c. d.



69


3.

A fixed-income portfolio with market value of USD 60 million, modified duration of 2.53 years and yielding 4.7% compounded semiannually. What would be the change in the value of this portfolio after a parallel rate decline of 20 basis points in the yield curve? a. b. c. d.

4.

loss of USD 607,200 loss of USD 303,600 gain of USD 303,600 gain of USD 607,200

Assuming equal strike prices and expiration dates, which of the following options should be the least expensive? a. b. c. d.

5.

A A A A

American call option Shout call option European call option Lookback call option

Edward Art, a CFO of Bank of Mitsubishi, has recently proposed to increase the bank’s liquidity by securitizing existing credit card receivables. Edward’s proposed securitization includes tranches with multiple internal credit enhancements as shown in Exhibit 1 below. The total value of the collateral for the structure is USD 680 million, the lockout period is two years, and the subordinated tranche B bond class is the first loss piece: Exhibit 1. Proposed ABS Structure Bond Class Senior tranche Junior tranche A Junior tranche B Subordinated tranche A Subordinated tranche B Total

Par Value USD 270 million USD 230 million USD 80 million USD 60 million USD 40 million USD 680 million

At the end of the fourteenth month after the securities were issued, the underlying credit card accounts have prepaid USD 300 million in principal in addition to regularly scheduled principal and interest payments. What is the amount of the prepaid principal paid out to the holders of the junior tranche A bond class? a. b. c. d.

70

USD USD USD USD

0 million 30 million 120 million 230 million



6.

Miller Castello is the head of credit derivatives trading at an investment bank. He is monitoring a new credit default swap basket that is made up of 20 bonds each with a 1% probability of default. Assuming the probability of any one bond defaulting is completely independent of what happens to the other bonds in the basket what is the probability that exactly one bond defaults? a. b. c. d.

7.

8.

Capital Bank is concerned about its counterparty credit exposure to City Bank. Which of the following trades by Capital Bank would increase its credit exposure to City Bank? I. II.

Buying a put option from City Bank Buying a loan extended to Sunny Inc. from City Bank

a. b. c. d.


A bank has booked a loan with total commitment of USD 50,000 of which 80% is currently outstanding. The default probability of the loan is assumed to be 2% for the next year and loss given default (LGD) is estimated at 50%. The standard deviation of LGD is 40% and the standard deviation of the default event indicator is 7%. Drawdown on default is assumed to be 60%. The expected losses for the bank are: a. b. c. d.

9.

2.06% 3.01% 16.5% 30.1%

USD USD USD USD

380 420 460 500

An investor has sold default protection on the most senior tranche of a CDO. If the default correlation decreases sharply, assuming everything else is unchanged, the investor’s position will a. b. c. d.

Gain significant value since the probability of exercising the protection falls. Lose significant value since his protection will gain value. Neither gain nor lose value since only expected default losses matter and correlation does not affect expected default losses. It depends on the pricing model used and the market conditions.


71


10.

11.

Which of the following are methods of credit risk mitigation? I. II.

Collateral agreements Netting

a. b. c. d.


As a risk manager for Bank ABC, John is asked to calculate the market risk capital charge of the bank’s trading portfolio under the internal models approach using the information given in the table below. Assuming the return of the bank’s trading portfolio is normally distributed, what is the market risk capital charge of the trading portfolio? VaR (95%, 1-day) of last trading day Average VaR (95%, 1-day) for last 60 trading days Multiplication Factor a. b. c. d.

12.

84,582 134,594 189,737 222,893

The CEO of Merlion Holdings, a large diversified conglomerate, is keen to enhance shareholder value using an enterprise risk management framework. You are asked to assist senior management to quantify and manage the risk-return tradeoff for the entire firm. Specifically, the CEO wants to know which risks to retain and which risks to lay off and how to decentralize the risk-return trade-off decisions within the company. Which of the following statements is/are correct? I. II.

a. b. c. d.

72

USD USD USD USD

USD 40,000 USD 25,000 2

Management should retain strategic and business risks in which the company has a comparative advantage but diversify risks that can be hedged inexpensively through the capital markets. When proposing new projects, business unit managers must evaluate all major risks in the context of the marginal impact of the project on the firm’s total risk. I only II only Both Neither



13.

You are a manager of a renowned hedge fund and are analyzing a 1,000 share position in an undervalued but illiquid stock BNA, which has a current stock price of USD 72 (expressed as the midpoint of the current bid-ask spread). Daily return for BNA has an estimated volatility of 1.24%. The average bid-ask spread is USD 0.16. Assuming returns of BNA are normally distributed, what is the estimated liquidity-adjusted daily 95% VaR, using the constant spread approach? a. b. c. d.

14.

1,389 1,469 1,549 1,629

In March 2009, the Basel Committee published the consultative document “Guidelines for computing capital for incremental risk in the trading book.” The incremental risk charge (IRC) defined in that document aims to complement additional standards being applied to the Value-at-Risk modeling framework which address a number of perceived shortcomings in the 99%/10-day VaR framework. Which of the following statements about the IRC is/are correct? I.

15.

USD USD USD USD

II.

For all IRC-covered positions, a bank’s IRC model must measure losses due to default and migration over a one-year capital horizon at a 99% confidence level. A bank must calculate the IRC measure at least weekly, or more frequently as directed by its supervisor.

a. b. c. d.


Operational risk loss data is not easy to collect within an institution, especially for extreme loss data. Therefore, financial institutions usually attempt to obtain external data, but doing so may create biases in estimating loss distributions. Which of the following statements regarding characteristics of external loss data is incorrect? a. b. c. d.

External loss data often exhibits scale bias as operational risk losses tend to be positively related to the size of the institution (i.e., scale of its operations). External loss data often exhibits truncation bias as minimum loss thresholds for collecting loss data are not uniform across all institutions. External loss data often exhibits data capture bias as the likelihood that an operational risk loss is reported is positively related to the size of the loss. The biases associated with external loss data are more important for large losses in relation to a bank’s assets or revenue than for small losses.


73


16.

You are the head of the Independent Risk Oversight (IRO) unit of XYZ bank. Your first task is to review the following existing policies relating to model implementation. I. II.

The remuneration of the staff of the IRO unit is dependent on how frequently the traders of XYZ bank use models vetted by the IRO. Model specifications assume that markets are perfectly liquid.

Which of the existing policies are sources of model risk? a. b. c. d.

17.

You want to construct a portfolio so that all of the alphas are benchmark-neutral. Stock XYZ has a volatility of 40%, an information coefficient of 0.10, an alpha of 60 basis points, and a beta of 1.63. The benchmark has an alpha of 5.7 basis points. The appropriate benchmark-neutral alpha for stock XYZ is: a. b. c. d.

18.

44.0 basis points 50.7 basis points 54.3 basis points 56.0 basis points

When identifying factors that contributed to the recent financial crisis, many commentators have pointed to the principal-agent problem associated with securitization, namely that the agent, the originator, can have poor incentives to act in the interest of the principal, the ultimate investor. An example of this would include which of the following? a. b. c. d.

74


The lack of liquid hedging instruments in the securitized mortgage market. Optimistic correlation assumptions embedded in rating agency models. The failure of originators to retain sufficient holdings of residual interest risk. Lack of sufficient subordination in securitized mortgage products.



19.

Rick Masler is considering the performance of the managers of two funds, the HCM Fund and the GRT Fund. He uses a linear regression of each manager’s excess returns (ri) against the excess returns of a peer group (rB): ri = ai + bi * rB + εi The information he compiles is as follows: Fund HCM

Initial Equity USD 100

Borrowed Funds USD 0

Total Investment Pool USD 100

ai 0.0150 (t = 4.40)

bi 0.9500 (t = 12.1)

GRT

USD 500

USD 3,000

USD 3,500

0.0025 (t = 0.002)

3.4500 (t = 10.20)

Based on this information, which of the following statements is correct? a. b. c. d.

20.

The regression suggests that both managers have greater skill than the peer group. The ai term measures the extent to which the manager employs greater or lesser amounts of leverage than do his/her peers. If the GRT Fund were to lose 10% in the next period, the return on equity (ROE) would be -60%. The sensitivity of the GRT fund to the benchmark return is much higher than that of the HCM fund.

In response to the recent crisis, rigorous stress testing has been emphasized as an important component of risk measurement and management that has been poorly implemented by many financial institutions in the recent past. Which of the following statements concerning steps banks can take to improve the value of stress testing exercises is/are correct? I. II.

a. b. c. d.

Regular dialogue with executive management about the results of stress tests and contingency plans to address such scenarios. Regular evaluation of a well-defined, common set of scenarios that include a broad range of possible stresses. I only II only Both Neither


75


Answers


a.

b.

c.

d.

a.

b.

1.

14.

2.

15.

3.

16.

4.

17.

5.

7.

10.

20.

8.

9.

19.

d.

18.

6.

c.


1.

11.

12.

13.

3

8


1.


77


Explanations


1.

After estimating the 99%, 1-day VaR of a bank’s portfolio to be USD 1,484 using historical simulation with 1,000 past trading days, you are concerned that the VaR measure is not providing enough information about tail losses. You decide to re-examine the simulation results and sort the simulated daily P&L from worst to best giving the following worst 15 scenarios: Scenario Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Daily P/L USD -2,833 USD -2,333 USD -2,228 USD -2,084 USD -1,960 USD -1,751 USD -1,679 USD -1,558 USD -1,542 USD -1,484 USD -1,450 USD -1,428 USD -1,368 USD -1,347 USD -1,319

What is the 99%, 1-day expected shortfall of the portfolio? a. b. c. d.

USD USD USD USD

433 1,285 1,945 2,833

Answer: c. Explanation: Expected Shortfall = Average of the worst 10 daily P&L = USD 1945. Topic: Market Risk Measurement and Management Subtopic: Expected shortfall and coherent risk measures AIMS: Estimate expected shortfall given P/L or return data. Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition, (West Sussex, England: Wiley, 2005), Chapter 3— Estimating Market Measures.


79


2.


The price of a MBS is more sensitive to yield curve twists than zero-coupon bonds. When the yield is higher than the coupon rate of a MBS, the MBS behaves similar to corporate bonds as interest rates change.

a. b. c. d.


Answer: c. Explanation: I. This statement is correct. MBS’ cash flows are like annuities, which are more sensitive to yield curve twist because of reinvestment risk. Normal bond has a lump sum payment at maturity, which implies less reinvestment risk. II. This statement is correct. When yield is higher than MBS’ coupon rate, the embedded call option is out of the money. It is much the same as a normal bond. Topic: Market Risk Measurement and Management Subtopic: Mortgage-backed securities: structure and valuation AIMS: Describe the various risk associated with mortgages and mortgage backed securities and explain risk based pricing. Reference: Frank Fabozzi, Handbook of Mortgage Backed Securities, 6th Edition, (New York: McGraw-Hill, 2006), Chapter 1—An Overview of Mortgages and the Mortgage Market.

3.

A fixed-income portfolio with market value of USD 60 million, modified duration of 2.53 years and yielding 4.7% compounded semiannually. What would be the change in the value of this portfolio after a parallel rate decline of 20 basis points in the yield curve? a. b. c. d.

A A A A

loss of USD 607,200 loss of USD 303,600 gain of USD 303,600 gain of USD 607,200

Answer: c. Explanation: By definition, Dmod = (-1/P) * (dP/dy). So as a linear approximation, ΔP = -1 * Δy * Dmod * P = -1 * -0.0020 * 2.53 * 60 = 0.3036 million Topic: Market Risk Measurement and Management Subtopic: Duration, DV01, and convexity AIMS: Define and calculate yield‐based DV01, modified duration, and Macaulay duration. Reference: Tuckman, Fixed Income Securities, 2nd Edition, Chapter 6—Measures of Price Sensitivity Based on Parallel Yield Shifts.

80



4.

Assuming equal strike prices and expiration dates, which of the following options should be the least expensive? a. b. c. d.

American call option Shout call option European call option Lookback call option

Answer: c. Explanation: c is correct. The shout call option and lookback call option are clearly wrong, since they grant more rights to the buyer than the European call option. American calls also offer more to the buyer than the European calls. Topic: Market Risk Measurement and Management Subtopic: Exotic options AIMS: List and describe the characteristics and pay‐off structure of barrier options, shout options and lookback options. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition, (New York: Prentice Hall, 2009), Chapter 24—Exotic Options.

5.

Edward Art, a CFO of Bank of Mitsubishi, has recently proposed to increase the bank’s liquidity by securitizing existing credit card receivables. Edward’s proposed securitization includes tranches with multiple internal credit enhancements as shown in Exhibit 1 below. The total value of the collateral for the structure is USD 680 million, the lockout period is two years, and the subordinated tranche B bond class is the first loss piece: Exhibit 1. Proposed ABS Structure Bond Class Senior tranche Junior tranche A Junior tranche B Subordinated tranche A Subordinated tranche B Total



USD USD USD USD


Answer: a.


81


Explanation: a: is correct. The securities have a two-year lockout period; all principal prepayments within the first two years will be used to fund new loans. No security tranche will receive principal prepayments until after the 24 months lockout period. Credit card prepayments are usually just rolled into new loans (not repaid to bondholders). Topic: Credit Risk Measurement and Management Subtopic: Structured finance, securitization, tranching and subordination AIMS: Explain the structure of the securitization process of the subprime mortgage loans. Reference: Adam Ashcroft and Til Schuermann, "Understanding the Securitization of Subprime Mortgage Credit", Federal Reserve Bank of New York Staff Reports, no. 318 (March 2008).

6.

Miller Castello is the head of credit derivatives trading at an investment bank. He is monitoring a new credit default swap basket that is made up of 20 bonds each with a 1% probability of default. Assuming the probability of any one bond defaulting is completely independent of what happens to the other bonds in the basket what is the probability that exactly one bond defaults? a. b. c. d.

2.06% 3.01% 16.5% 30.1%

Answer: c. Explanation: C120p1(1 - p)19 = 20 x 0.01 x (1 - 0.01)19 = 0.1652 The right choice is c. Topic: Credit Risk Measurement and Management Subtopic: Default risk: quantitative methodologies AIMS: Compute the value of a CDS, given unconditional default probabilities, survival probabilities, market yields, recovery rates and cash flows. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition, (NY: Pearson, 2009), Chapter 23—Credit Derivatives.

82



7.

Capital Bank is concerned about its counterparty credit exposure to City Bank. Which of the following trades by Capital Bank would increase its credit exposure to City Bank? I. II.

Buying a put option from City Bank Buying a loan extended to Sunny Inc. from City Bank

a. b. c. d.


Answer: a. Explanation: I. Buying a put option creates credit risk exposure to City Bank as it is subject to the performance of counterparty City Bank. For example, City Bank may default to deliver the underlying asset when Capital Bank exercises the option. II. Buying a loan extended to Sunny Inc does not create credit risk exposure to City Bank as it is not subject to performance of counterparty City Bank but Sunny Inc. It creates credit risk exposure to Sunny Inc instead. Topic: Credit Risk Measurement and Management Subtopic: Counterparty risk and OTC derivatives AIMS: Describe counterparty credit risk in derivatives markets and explain how it affects valuation. Reference: Hull, Options, Futures, and Other Derivatives, 7th Edition, Chapter 22—Credit Risk.

8.

A bank has booked a loan with total commitment of USD 50,000 of which 80% is currently outstanding. The default probability of the loan is assumed to be 2% for the next year and loss given default (LGD) is estimated at 50%. The standard deviation of LGD is 40% and the standard deviation of the default event indicator is 7%. Drawdown on default is assumed to be 60%. The expected losses for the bank are: a. b. c. d.

USD USD USD USD

380 420 460 500

Answer: c.


83


Explanation: Standard deviation of LGD = 0.4, Standard deviation of the default event indicator = .07 Adjusted Exposure (AE) = Outstanding + (Commitment – Outstanding) x Draw Down on default AE = (0.8 x 50,000) + {50,000 – (0.8 x 50000)} x 0.6 = 46,000 Expected Loss = AE x default probability x LGD = 46,000 x .02 x 0.5 = 460 Topic: Credit Risk Measurement and Management Subtopic: Expected and unexpected loss AIMS: Define, calculate and interpret expected and unexpected portfolio loss. Reference: Ong, Internal Credit Risk Models, Chapter 6—Portfolio Effects: Risk Contributions and Unexpected Losses.

9.

An investor has sold default protection on the most senior tranche of a CDO. If the default correlation decreases sharply, assuming everything else is unchanged, the investor’s position will a. b. c. d.

Gain significant value since the probability of exercising the protection falls. Lose significant value since his protection will gain value. Neither gain nor lose value since only expected default losses matter and correlation does not affect expected default losses. It depends on the pricing model used and the market conditions.

Answer: a. Explanation: The Senior tranche will gain value if the default correlation decreases. High correlation means that if one name defaults, a large number of other names will default. Low correlation means that if one name default, it will not affect the default probability of the other names. A seller of protection on a senior tranche will prefer a small number of highly probable defaults rather that an unlikely large number of defaults so that it becomes less likely that he makes a payment. Topic: Credit Risk Measurement and Management Subtopic: Structured finance, securitization, tranching and subordination AIMS: Describe portfolio credit default swaps, including basket CDS, Nth to Default CDS, Senior and Subordinated Basket CDS. Reference: Christopher Culp, Structured Finance and Insurance: The Art of Managing Capital and Risk (Hoboken: John Wiley & Sons, 2006), Chapter 12—Credit Derivatives and Credit-Linked Notes.

84



10.

Which of the following are methods of credit risk mitigation? I. II.

Collateral agreements Netting

a. b. c. d.


Answer: c. Explanation: Both collateral and netting agreements are methods of mitigating credit risk. Topic: Credit Risk Measurement and Management Subtopic: Credit Risk Mitigation AIMS: Describe credit mitigation techniques. Reference: Eduardo Canabarro and Darrell Duffie: "Measuring and Marking Counterparty risk" in ALM of Financial Institutions, ed. Leo Tilman (London: Euro-money Institutional Investor, 2003).

11.

As a risk manager for Bank ABC, John is asked to calculate the market risk capital charge of the bank’s trading portfolio under the internal models approach using the information given in the table below. Assuming the return of the bank’s trading portfolio is normally distributed, what is the market risk capital charge of the trading portfolio? VaR (95%, 1-day) of last trading day Average VaR (95%, 1-day) for last 60 trading days Multiplication Factor a. b. c. d.

USD USD USD USD

USD 40,000 USD 25,000 2

84,582 134,594 189,737 222,893

Answer: d. Explanation: Market Risk Capital Charge = MAX(40,000 x SQRT(10)/1.65 x 2.326, 2 x 25,000 x SQRT(10)/1.65 x 2.326) = 222893 Candidate is required to convert the VaR (95%, 1-day) to a 95% 10-day VaR. Topic: Operational and Integrated Risk Management Subtopic: Regulation and the Basel II Accord: minimum capital requirements AIMS: Describe and contrast the major elements—including a description of the risks covered—of the two options available for the calculation of market risk: Standardized Measurement Method and Internal Models Approach. Reference: “Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework—Comprehensive Version” (Basel Committee on Banking Supervision Publication, June 2006).


85


12.

The CEO of Merlion Holdings, a large diversified conglomerate, is keen to enhance shareholder value using an enterprise risk management framework. You are asked to assist senior management to quantify and manage the risk-return tradeoff for the entire firm. Specifically, the CEO wants to know which risks to retain and which risks to lay off and how to decentralize the risk-return trade-off decisions within the company. Which of the following statements is/are correct? I. II.

a. b. c. d.

Management should retain strategic and business risks in which the company has a comparative advantage but diversify risks that can be hedged inexpensively through the capital markets. When proposing new projects, business unit managers must evaluate all major risks in the context of the marginal impact of the project on the firm’s total risk. I only II only Both Neither

Answer: c. Explanation: In the context of using an ERM framework to decentralize the risk-reward tradeoff in a company, statements I and II are both correct. Topic: Operational and Integrated Risk Management Subtopic: Enterprise risk management (ERM) AIMS: Discuss how an ERM program can be used to determine the right amount of risk. Reference: Brian Nocco and René Stulz, “Enterprise Risk Management: Theory and Practice,” Journal of Applied Corporate Finance 18, No. 4 (2006): 8–20.

13.


USD USD USD USD

1,389 1,469 1,549 1,629

Answer: c.

86



Explanation: The constant spread approach adds half of the bid-ask spread (as a percent) to the VaR calculation: Daily 95% VaR = 72,000 * (1.645 * 0.0124) = USD 1469 Liquidity cost = 72,000 * (0.5 * 0.16/72) = 80 LVaR = VaR + LC = 1549 Topic: Operational and Integrated Risk Management Subtopic: Estimating liquidity risk AIMS: Describe and calculate LVaR using the Constant Spread approach and the Exogenous Spread approach. Reference: Dowd, Measuring Market Risk, 2nd Edition, (West Sussex, England: John Wiley & Sons, 2005), Chapter 14—Estimating Liquidity Risks.

14.

In March 2009, the Basel Committee published the consultative document “Guidelines for computing capital for incremental risk in the trading book.” The incremental risk charge (IRC) defined in that document aims to complement additional standards being applied to the Value-at-Risk modeling framework which address a number of perceived shortcomings in the 99%/10-day VaR framework. Which of the following statements about the IRC is/are correct? I. II.

For all IRC-covered positions, a bank’s IRC model must measure losses due to default and migration over a one-year capital horizon at a 99% confidence level. A bank must calculate the IRC measure at least weekly, or more frequently as directed by its supervisor.

a. b. c. d.


Answer: b. Explanation: i is incorrect. Specifically, for all IRC-covered positions, a bank’s IRC model must measure losses due to default and migration at the 99.9% confidence interval over a capital horizon of one year, taking into account the liquidity horizons applicable to individual trading positions or sets of positions. ii is correct. A bank must calculate the IRC measure at least weekly, or more frequently as directed by its supervisor. Topic: Operational and Integrated Risk Management Subtopic: Regulation and the Basel II Accord: methods for calculating credit, market, and operational risk AIMS: Define the risks captured by the incremental risk charge and the key supervisory parameters for computing the incremental risk charge; Define the frequency with which banks must calculate the incremental risk charge; Calculate the capital charge for incremental risk as a function of recent increment risk charge measures. Reference: “Guidelines for Computing Capital for Incremental Risk in the Trading Book—Consultative Document” (Basel Committee on Banking Supervision Publication, January 2009).


87


15.

Operational risk loss data is not easy to collect within an institution, especially for extreme loss data. Therefore, financial institutions usually attempt to obtain external data, but doing so may create biases in estimating loss distributions. Which of the following statements regarding characteristics of external loss data is incorrect? a. b. c. d.

External loss data often exhibits scale bias as operational risk losses tend to be positively related to the size of the institution (i.e., scale of its operations). External loss data often exhibits truncation bias as minimum loss thresholds for collecting loss data are not uniform across all institutions. External loss data often exhibits data capture bias as the likelihood that an operational risk loss is reported is positively related to the size of the loss. The biases associated with external loss data are more important for large losses in relation to a bank’s assets or revenue than for small losses.

Answer: d. Explanation: The biases associated with external loss data are important for all losses in relation to a bank’s assets or revenue. Topic: Operational and Integrated Risk Management Subtopic: Operational loss data: data sufficiency AIMS: Discuss issues related to external and internal operational loss data sets. Reference: Mo Chaudhury, "A review of the key issues in operational risk capital modeling", The Journal of Operational Risk, Volume 5/Number 3, Fall 2010: pp. 37-66.

16.


The remuneration of the staff of the IRO unit is dependent on how frequently the traders of XYZ bank use models vetted by the IRO. Model specifications assume that markets are perfectly liquid.

Which of the existing policies are sources of model risk? a. b. c. d.


Answer: b.

88



Explanation: I. Incorrect. Even though this is a risk that can increase exposure to model risk, the policy itself is regarding compensation and not the model itself. II. Correct. This assumption can lead to major error where market liquidity is limited. Topic: Operational and Integrated Risk Management Subtopic: Evaluating the performance of risk management systems AIMS: Identify and discuss sources of model risk. Reference: Dowd, Measuring Market Risk, 2nd Edition, (West Sussex, England: John Wiley & Sons, 2005), Chapter 16.

17.

You want to construct a portfolio so that all of the alphas are benchmark-neutral. Stock XYZ has a volatility of 40%, an information coefficient of 0.10, an alpha of 60 basis points, and a beta of 1.63. The benchmark has an alpha of 5.7 basis points. The appropriate benchmark-neutral alpha for stock XYZ is: a. b. c. d.


Answer: b. Explanation: To make the alpha benchmark neutral, you subtract the product of the beta of the stock and the alpha of the benchmark from the original alpha of the stock [0.60 – (1.63*0.057)] = 0.507. Topic: Risk Management and Investment Management Subtopic: Portfolio construction AIMS: Describe neutralization and methods for refining alphas to be neutral. Reference: Grinold and Kahn, Active Portfolio Management: A Quantitative Approach for Providing Superior Returns and Controlling Risk, 2nd Edition, Chapter 14—Portfolio Construction.

18.

When identifying factors that contributed to the recent financial crisis, many commentators have pointed to the principal-agent problem associated with securitization, namely that the agent, the originator, can have poor incentives to act in the interest of the principal, the ultimate investor. An example of this would include which of the following? a. b. c. d.

The lack of liquid hedging instruments in the securitized mortgage market. Optimistic correlation assumptions embedded in rating agency models. The failure of originators to retain sufficient holdings of residual interest risk. Lack of sufficient subordination in securitized mortgage products.

Answer: c.


89


Explanation: Only c is an illustration of the principal-agent problem. Topic: Current Issues in Risk Management Subtopic: Causes and consequences of the current crisis AIMS: Discuss the argument that the traditional originate-to-hold model of credit markets to the originate-todistribute model was a primary driver of the current crisis. Reference: John Martin, “A Primer on the Role of Securitization in the Credit Market Crisis of 2007,” (January 2009).

19.

Rick Masler is considering the performance of the managers of two funds, the HCM Fund and the GRT Fund. He uses a linear regression of each manager’s excess returns (ri) against the excess returns of a peer group (rB): ri = ai + bi * rB + εi The information he compiles is as follows: Fund HCM

Initial Equity USD 100

Borrowed Funds USD 0

Total Investment Pool USD 100

ai 0.0150 (t = 4.40)

bi 0.9500 (t = 12.1)

GRT

USD 500

USD 3,000

USD 3,500

0.0025 (t = 0.002)

3.4500 (t = 10.20)

Based on this information, which of the following statements is correct? a. b. c. d.

The regression suggests that both managers have greater skill than the peer group. The ai term measures the extent to which the manager employs greater or lesser amounts of leverage than do his/her peers. If the GRT Fund were to lose 10% in the next period, the return on equity (ROE) would be -60%. The sensitivity of the GRT fund to the benchmark return is much higher than that of the HCM fund.

Answer: d. Explanation: Statement d is correct as can be seen from the bi coefficient. It is higher for GRT and lower for HCM. This indicates that the sensitivity of the GRT fund to the benchmark return is much higher than that of the HCM fund. Topic: Risk Management and Investment Management Subtopic: Risk monitoring and performance measurement AIMS: Describe common features of a performance measurement framework including comparisons with benchmark portfolios and peer groups. Reference: Robert Litterman and the Quantitative Resources Group, Modern Investment Management: An Equilibrium Approach (Hoboken, NJ: John Wiley & Sons: 2003), Chapter 17—Risk Monitoring and Performance Measurement.

90



20.

In response to the recent crisis, rigorous stress testing has been emphasized as an important component of risk measurement and management that has been poorly implemented by many financial institutions in the recent past. Which of the following statements concerning steps banks can take to improve the value of stress testing exercises is/are correct? I. II.

a. b. c. d.

Regular dialogue with executive management about the results of stress tests and contingency plans to address such scenarios. Regular evaluation of a well-defined, common set of scenarios that include a broad range of possible stresses. I only II only Both Neither

Answer: c. Explanation: Both of the statements are correct. Topic: Current Issues in Financial Markets Subtopic: Causes and consequences of the current crisis AIMS: Discuss methods for improving stress testing among financial institutions. Reference: Andrew G. Haldane, “Why Banks Failed the Stress Test,” (February 2009).


91


Answer Sheet


a.

b.

c.

d.

a.

1.

14.

2.

15.

3.

16.

4.

17.

5.

18.

6.

19.

7.

20.

b.

c.

d.

3

8

8.

9.


10.

1.

11.


12.

1.

13.


93


Questions


1.

A 1-year forward contract on a stock with a forward price of USD 100 is available for USD 1.50. The table below lists the prices of some barrier options on the same stock with a maturity of 1 year and strike of USD 100. Assuming a continuously compounded risk-free rate of 5% per year what is the price of a European put option on the stock with a strike of USD 100. Option Up-and-in barrier call, barrier USD 95 Down-and-in barrier put, barrier USD 80 a. b. c. d.

2.

3.

USD USD USD USD

Price USD 5.21 USD 3.50

2.00 3.50 3.71 6.71


As yield volatility increases, the value of a MBS grows as well. A rise in interest rates increases the duration of a MBS.

a. b. c. d.


John Snow’s portfolio has a fixed-income position with market value of USD 70 million with modified duration of 6.44 years and yielding 6.7% compounded semiannually. If there is a positive parallel shift in the yield curve of 25 basis points, which of the following answers best estimates the resulting change in the value of John’s portfolio? a. b. c. d.

USD USD USD USD

-11,725 -1,127,000 -1,134,692 -1,164,755


95


4.

5.

George Smith is an analyst in the risk management department and he is reviewing a pool of mortgages. Prepayment risk introduces complexity to the valuation of mortgages. Which of the two factors is generally considered to affect prepayment risk for a mortgage? I. II.

Changes to interest rates Amount of principal outstanding

a. b. c. d.


National United Bank has recently increased the bank’s liquidity through securitization of existing credit card receivables. The proposed securitization includes tranches with multiple internal credit enhancements as shown in Exhibit 1 below. The total value of the collateral for the structure is USD 600 million, no lockout period, and the subordinated tranche B bond class is the first loss piece: Exhibit 1. Proposed ABS Structure Bond Class Senior tranche Junior tranche A Junior tranche B Subordinated tranche A Subordinated tranche B Total



96

USD USD USD USD




6.

The 1-year risk-free rate is 4%, and the yield on a 1-year zero-coupon corporate bond is 7% per year. Assuming a recovery rate of zero, what is the implied probability of default? a. b. c. d.

7.

8.

2.80% 3.23% 11.00% 11.28%

Which of the following two transactions increases counterparty credit exposure? I. II.

Selling a forward contract to the counterparty Selling a call option to the counterparty

a. b. c. d.


You are given the following data for a firm: Current market value of firm = 4,500 Expected market value of the firm one year from now = 5,000 Short term debt = 1,000 Long term debt = 1,300 Annualized volatility of firm’s assets = 22%. According to KMV model, what is the distance-to-default one year from now? a. b. c. d.

3.045 3.350 3.583 3.612


97


9.

You have been asked by the Chief Risk Officer of your bank to determine how much should be set aside as a loan-loss reserve for a 1-year horizon on a USD 100 million line of credit that has been extended to a large corporate borrower. Of the original balance, USD 20 million has already been drawn and due to deteriorating economic conditions the bank is concerned that the borrower might find itself in a liquidity crisis causing it to draw on the remaining commitment and default. Given the following information from the bank’s internal credit risk models what is an appropriate loan loss reserve to cover this eventuality? 1-year default probability = 0.35% Drawdown given default = 80% Loss given default = 60% a. b. c. d.

10.

b. c. d.

The probability of default can be mitigated by collateral and exposure at default can be mitigated by netting. The probability of default can be mitigated by netting and exposure at default can be mitigated by collateral. Loss given default can be mitigated by collateral and exposure at default can be mitigated by netting. Loss given default can be mitigated by netting and exposure at default can be mitigated by collateral.

An investor has sold default protection on the most junior tranche of a CDO. If the default correlation decreases sharply and changes from a positive to a negative correlation, assuming everything else is unchanged, the investor’s position will: a. b. c. d.

98

210,000 176,400 140,000 117,600

Credit risk is a function of the probability of default, exposure at default, and loss given default. Assuming that the individual exposures at default with a counterparty are fixed, which of the following statements is correct? a.

11.

USD USD USD USD

Gain value Lose value Neither gain nor lose value It depends on the pricing model used and the market conditions.



12.

As a risk manager for Bank ABC is asked to calculate the market risk capital charge of the bank’s trading portfolio under the internal models approach using the information given in the table below. Assuming the return of the bank’s trading portfolio is normally distributed, what is the market risk capital charge of the trading portfolio? VaR (95%, 1-day) of last trading day Average VaR (95%, 1-day) for last 60 trading days Multiplication Factor a. b. c. d.

13.

84,582 134,594 189,737 267,471


14.

USD USD USD USD

USD 30,000 USD 20,000 3

USD USD USD USD

1,389 2,076 3,324 4,351

Which of the following statements regarding characteristics of operational risk loss data and operational risk modeling is correct? a. b. c. d.

Operational risk losses tend to be negatively related to the size of the institution. External loss data often exhibits capture bias as minimum loss thresholds for collecting loss data are uni form across all institutions. The likelihood that an operational risk loss is reported is positively related to the size of the loss. Operational risk losses are modeled using techniques that are used in interest rate modeling.


99


15.

Brisk Holdings, a large conglomerate is implementing the enterprise risk management (ERM) framework to quantify and manage the risk-return tradeoff for the entire firm. Which of the following statements about the ERM framework is/are correct? I.

16.

II.

The performance of each business unit should be evaluated on a stand-alone basis and the unit should be allocated more capital if its net income is positive. The ERM framework tries to minimize the aggregate risk taken by the firm.

a. b. c. d.



The IRO unit of XYZ bank only re-evaluates previously implemented models when a problem is identified. The IRO unit evaluates and checks the key assumptions of all the models used by XYZ bank.

Which of the existing policies is/are sources of model risk? a. b. c. d.

17.

You want to construct a portfolio so that all of the alphas are benchmark-neutral. Stock XYZ has a volatility of 30%, an information coefficient of 0.20, an alpha of 90 bps, and a beta of 1.94. The benchmark has an alpha of 3.7 basis points. The appropriate benchmark-neutral alpha for stock XYZ is: a. b. c. d.

100





The next two questions are based on the following information. A risk manager assumes that the joint distribution of returns is multivariate normal and calculates the following risk measures for a 2-asset portfolio: Asset 1 2 Portfolio

18.

Marginal VaR 0.176 0.440

VaR Contribution USD 17.6 USD 44.0 USD 61.6

USD USD USD USD

15.0 38.3 44.0 46.6

Let βi = ρip * σi / σp, where ρip denotes the correlation between the return of asset i and the return of the portfolio, σi is the volatility of the return of asset i and σp is the volatility of the return of the portfolio. What is β2? a. b. c. d.

20.

Individual VaR USD 23.3 USD 46.6 USD 61.6

If asset 1 is dropped from the portfolio, what will be the reduction in portfolio VaR? a. b. c. d.

19.

Position USD 100 USD 100 USD 200

0.714 1.429 1.513 Insufficient information to determine.

Rigorous stress testing has been emphasized as an important component of risk measurement and management that has been poorly implemented by many financial institutions in the recent past. Which of the following statements concerning steps banks should consider to improve the value of stress testing exercises is/are correct? I. II.

Banks do not need to consider potential second round effects of stress scenarios on the broader financial network. It is inappropriate for banks to conduct “reverse” stress tests.

a. b. c. d.



101


Answers


a.

b.

c.

d.

1.

a.

15.

3.

16.

18.

6.

19.

7.

20.

8.

9.

11.

13.

1.

3

8


12.


10.

d.

17.

5.

c.

14.

2.

4.

b.

1.


103


Explanations


1.

A 1-year forward contract on a stock with a forward price of USD 100 is available for USD 1.50. The table below lists the prices of some barrier options on the same stock with a maturity of 1 year and strike of USD 100. Assuming a continuously compounded risk-free rate of 5% per year what is the price of a European put option on the stock with a strike of USD 100. Option Up-and-in barrier call, barrier USD 95 Down-and-in barrier put, barrier USD 80 a. b. c. d.

USD USD USD USD

Price USD 5.21 USD 3.50

2.00 3.50 3.71 6.71

Answer: c. Explanation: When the barrier is below the strike price, the value of an up-and-in call is the same as the value of a European call with the same strike price. The put-call parity theorem gives put= call - forward (with same strikes and maturities). Thus put = USD 5.21 - USD 1.50 = USD 3.71. Topic: Market Risk Measurement and Management Subtopic: Exotic options AIMS: List and describe the characteristics and pay-off structures of barrier options. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition, (New York: Pearson 2009), Chapter 24—Exotic Options.


105


2.


As yield volatility increases, the value of a MBS grows as well. A rise in interest rates increases the duration of a MBS.

a. b. c. d.


Answer: b. Explanation: I. This statement is false. Holding MBS is equivalent to holding a similar duration bond and selling a call option. As yield volatility increases, the value of embedded call option increases. Thus the value of MBS decreases. II. This statement is true. A rise in interest rates reduces the prepayments and hence increases the duration of a MBS. Topic: Market Risk Measurement and Management Subtopic: Mortgage-backed securities: structure and valuation AIMS: Describe the various risk associated with mortgages and mortgage backed securities and explain risk based pricing. Reference: Frank Fabozzi, Handbook of Mortgage Backed Securities 6th Edition, (New York: McGraw-Hill, 2006), Chapter 1—An Overview of Mortgages and the Mortgage Market.

3.

John Snow’s portfolio has a fixed-income position with market value of USD 70 million with modified duration of 6.44 years and yielding 6.7% compounded semiannually. If there is a positive parallel shift in the yield curve of 25 basis points, which of the following answers best estimates the resulting change in the value of John’s portfolio? a. b. c. d.

USD USD USD USD

-11,725 -1,127,000 -1,134,692 -1,164,755

Answer: b. Explanation: a: is correct. By definition, Dmod = (-1/P) * (dP/dy). So as a linear approximation, ΔP = -1 * Δy * Dmod * P = -1 * 0.0025 * 6.44 * 70 = -1.127 million Topic: Market Risk Measurement and Management Subtopic: Duration, DV01, and convexity AIMS: Define and calculate yield‐based DV01, modified duration, and Macaulay duration. Reference: Tuckman, Fixed Income Securities, 2nd Edition, Chapter 6—Measures of Price Sensitivity Based on Parallel Yield Shifts.

106



4.

George Smith is an analyst in the risk management department and he is reviewing a pool of mortgages. Prepayment risk introduces complexity to the valuation of mortgages. Which of the two factors is generally considered to affect prepayment risk for a mortgage? I. II.

Changes to interest rates Amount of principal outstanding

a. b. c. d.


Answer: c. Explanation: Both are factors affecting prepayment Topic: Market Risk Measurement and Management Subtopic: Mortgage-backed securities: structure and valuation AIMS: Describe the impact of interest rate changes on the value of the prepayment option and discuss non‐interest rate factors that may trigger mortgage prepayments. Reference: Bruce Tuckman, Fixed Income Securities, 2nd Edition, (Hoboken, NJ: Wiley & Sons, 2002). Chapter 21— Mortgage‐Backed Securities.


107


5.

National United Bank has recently increased the bank’s liquidity through securitization of existing credit card receivables. The proposed securitization includes tranches with multiple internal credit enhancements as shown in Exhibit 1 below. The total value of the collateral for the structure is USD 600 million, no lockout period, and the subordinated tranche B bond class is the first loss piece: Exhibit 1. Proposed ABS Structure Bond Class Senior tranche Junior tranche A Junior tranche B Subordinated tranche A Subordinated tranche B Total



USD USD USD USD


Answer: b. Explanation: USD 50 million is calculated by USD 300 - USD 250 = USD 50, since prepayments are first distributed to the senior tranches. Since the period is past the lockout period, the distribution is made. Topic: Credit Risk Measurement and Management Subtopic: Structured finance, securitization, tranching and subordination AIMS: Discuss the securitization process for mortgage‐backed securities and asset‐backed commercial paper. Reference: Christopher Culp, Structured Finance and Insurance: The Art of Managing Capital and Risk (Hoboken: John Wiley & Sons, 2006), Chapter 16—Securitization.

108



6.

The 1-year risk-free rate is 4%, and the yield on a 1-year zero-coupon corporate bond is 7% per year. Assuming a recovery rate of zero, what is the implied probability of default? a. b. c. d.

2.80% 3.23% 11.00% 11.28%

Answer: a. Explanation: The probability of default (PD) is = 1 - ((1+risk-free rate)/(1 + corp bond rate)) = 1-((1 + 4%)/(1 + 7%)) = 2.80% Topic: Credit Risk Measurement and Management Subtopic: Probability of default, loss given default and recovery rates AIMS: Estimate the probability of default for a company from its bond price. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition, (NY: Pearson, 2009). Chapter 22— Credit Risk.

7.

Which of the following two transactions increases counterparty credit exposure? I. II.

Selling a forward contract to the counterparty Selling a call option to the counterparty

a. b. c. d.


Answer: a. Explanation: I. Selling of forward contract creates credit risk exposure to the counterparty as it is subject to the performance of the counterparty, which may default to pay at expiry date. II. Selling an option (for both call and put) does not create credit risk as it is not subject to the performance of the counterparty. The option premium has already been collected when the transaction is made and default of the counterparty will have no negative impact on the seller. Topic: Credit Risk Measurement and Management Subtopic: Counterparty risk and OTC derivatives AIMS: Describe counterparty credit risk in derivatives markets and explain how it affects valuation. Reference: Hull, Options, Futures, and Other Derivatives, 7th Edition, Chapter 22—Credit Risk.


109


8.

You are given the following data for a firm: Current market value of firm = 4,500 Expected market value of the firm one year from now = 5,000 Short term debt = 1,000 Long term debt = 1,300 Annualized volatility of firm’s assets = 22%. According to KMV model, what is the distance-to-default one year from now? a. b. c. d.

3.045 3.350 3.583 3.612

Answer: a. Explanation: According to KMV, default value X = ST+0.5LT if LT/ST < = 1.5 X = 1000 + 0.5*1300 = 1650 Distance to default = (Market value of Asset after 1 year-default point) / Annualized Asset volatility = (5000 - 1650)/(5000*0.22) = 3.045 Topic: Credit Risk Measurement and Management Subtopic: Default risk: quantitative methodologies AIMS: Describe the Moody’s KMV Credit Monitor Model to estimate probability of default using equity prices. Reference: De Servigny and Renault, Measuring and Managing Credit Risk, Chapter 3—Default Risk: Quantitative Methodologies.

9.

You have been asked by the Chief Risk Officer of your bank to determine how much should be set aside as a loan-loss reserve for a 1-year horizon on a USD 100 million line of credit that has been extended to a large corporate borrower. Of the original balance, USD 20 million has already been drawn and due to deteriorating economic conditions the bank is concerned that the borrower might find itself in a liquidity crisis causing it to draw on the remaining commitment and default. Given the following information from the bank’s internal credit risk models what is an appropriate loan loss reserve to cover this eventuality? 1-year default probability = 0.35% Drawdown given default = 80% Loss given default = 60% a. b. c. d.

USD USD USD USD

210,000 176,400 140,000 117,600

Answer: b.

110



Explanation: The risky portion of the asset value at the horizon is Outstanding + (Commitment – Outstanding)*Drawdown Given Default = USD 20,000,000 + (USD 100,000,000 - USD 20,000,000)*0.80 = USD 84,000,000. This is the adjusted exposure on default (AE). The expected loss EL = AE*EDF*LGD, or USD 84,000,000*0.0035*0.6 = USD 176,400. This is the amount that the bank should set aside as a loss reserve. Topic: Credit Risk Measurement and Management Subtopic: Expected and unexpected loss AIMS: Define, calculate and interpret expected and unexpected portfolio loss. Explain how the recovery rate, credit quality, and expected default frequency affect the expected and unexpected loss, respectively. Reference: Michael Ong, Internal Credit Risk Models: Capital Allocation and Performance Measurement (London: Risk Books, 2003), Chapter 6—Portfolio Effects: Risk Contributions and Unexpected Losses.

10.

Credit risk is a function of the probability of default, exposure at default, and loss given default. Assuming that the individual exposures at default with a counterparty are fixed, which of the following statements is correct? a. b. c. d.

The probability of default can be mitigated by collateral and exposure at default can be mitigated by netting. The probability of default can be mitigated by netting and exposure at default can be mitigated by collateral. Loss given default can be mitigated by collateral and exposure at default can be mitigated by netting. Loss given default can be mitigated by netting and exposure at default can be mitigated by collateral.

Answer: c. Explanation: a: is incorrect. Probability of default depends on credit events which can’t be controlled by collateral because credit events depend on ability to pay and willingness to pay. Both of them are independent to collateral. b: is incorrect. Probability of default depends on credit events which can’t be controlled by netting because credit events depend on ability to pay and willingness to pay. Both of them are independent to netting. Collateral can’t reduce exposure at default. However, it can be claimed later so that collateral reduce loss given default. c: is correct. Collateral can be claimed to reduce loss given default. Netting reduces the settlement amount if the counterparty is in default so that netting reduces exposure at default. d: is incorrect. Collateral can’t reduce exposure at default. However, it can be claimed later so that collateral reduce loss given default. Topic: Credit Risk Measurement and Management Subtopic: Counterparty risk and OTC derivatives AIMS: Describe the credit mitigation techniques of netting and collateralization. Reference: Hull, Options, Futures, and Other Derivatives, 7th Edition, Chapter 22—Credit Risk.


111


11.

An investor has sold default protection on the most junior tranche of a CDO. If the default correlation decreases sharply and changes from a positive to a negative correlation, assuming everything else is unchanged, the investor’s position will: a. b. c. d.

Gain value Lose value Neither gain nor lose value It depends on the pricing model used and the market conditions.

Answer: b. Explanation: The junior tranche will become riskier and more likely to absorb a default since it is now more likely that a single asset default will happen and be absorbed by the junior tranche. This is in contrast to having a high correlation, which would imply a more likely default of many assets at once, and less likely default of any single one. Topic: Credit Risk Measurement and Management Subtopic: Structured finance, securitization, tranching and subordination AIMS: Describe portfolio credit default swaps, including basket CDS, Nth to Default CDS, Senior and Subordinated Basket CDS. Reference: Christopher Culp, Structured Finance and Insurance: The Art of Managing Capital and Risk (Hoboken: John Wiley & Sons, 2006), Chapter 12—Credit Derivatives and Credit-Linked Notes.

12.

As a risk manager for Bank ABC is asked to calculate the market risk capital charge of the bank’s trading portfolio under the internal models approach using the information given in the table below. Assuming the return of the bank’s trading portfolio is normally distributed, what is the market risk capital charge of the trading portfolio? VaR (95%, 1-day) of last trading day Average VaR (95%, 1-day) for last 60 trading days Multiplication Factor a. b. c. d.

USD USD USD USD

USD 30,000 USD 20,000 3

84,582 134,594 189,737 267,471

Answer: d.

112



Explanation: Market Risk Capital Charge = MAX(30,000 x SQRT(10)/1.65x2.326, 3 x 20,000 x SQRT(10)/1.65 x 2.326) = 267,471 Candidate is required to convert the VaR (95%, 1-day) to a 95% 10-day VaR. Topic: Operational and Integrated Risk Management Subtopic: Regulation and the Basel II Accord: minimum capital requirements AIMS: Describe and contrast the major elements—including a description of the risks covered—of the two options available for the calculation of market risk: Standardized Measurement Method and Internal Models Approach. Reference: “Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework—Comprehensive Version” (Basel Committee on Banking Supervision Publication, June 2006).

13.


USD USD USD USD

1,389 2,076 3,324 4,351

Answer: b. Explanation: The constant spread approach adds half of the bid-ask spread (as a percent) to the VaR calculation: Daily 95% VaR = 80,000 * (1.645 * 0.0154) = USD 2026.64 Liquidity cost (LC) = 80,000 * (0.5 * 0.10/80) = 50 LVaR = VaR + LC = 2076.64 Topic: Operational and Integrated Risk Management Subtopic: Estimating liquidity risk AIMS: Describe and calculate LVaR using the Constant Spread approach and the Exogenous Spread approach. Reference: Dowd, Measuring Market Risk, 2nd Edition, (West Sussex, England: John Wiley & Sons, 2005), Chapter 14—Estimating Liquidity Risks.


113


14.

Which of the following statements regarding characteristics of operational risk loss data and operational risk modeling is correct? a. b. c. d.

Operational risk losses tend to be negatively related to the size of the institution. External loss data often exhibits capture bias as minimum loss thresholds for collecting loss data are uniform across all institutions. The likelihood that an operational risk loss is reported is positively related to the size of the loss. Operational risk losses are modeled using techniques that are used in interest rate modeling.

Answer: c. Explanation: Statement c is correct: The likelihood that an operational risk loss is reported is positively related to the size of the loss. This is referred to as data capture bias. Topic: Operational and Integrated Risk Management Subtopic: Operational loss data: data sufficiency AIMS: Discuss issues related to external and internal operational loss data sets. Reference: Mo Chaudhury, "A review of the key issues in operational risk capital modeling", The Journal of Operational Risk, Volume 5/Number 3, Fall 2010: pp. 37-66.

15.

Brisk Holdings, a large conglomerate is implementing the enterprise risk management (ERM) framework to quantify and manage the risk-return tradeoff for the entire firm. Which of the following statements about the ERM framework is/are correct? I. The performance of each business unit should be evaluated on a stand-alone basis and the unit should be allocated more capital if its net income is positive. II. The ERM framework tries to minimize the aggregate risk taken by the firm. a. b. c. d.


Answer: d. Explanation: Statement I is incorrect. Management must avoid a silo approach in its evaluation of the performance of each business unit but should take into account the contributions of each the units to the firm’s total risk. This can be done by assigning a level of additional imputed capital to reflect incremental risk of the project. Statement II is incorrect. The purpose of an ERM program is not to minimize or eliminate the firm’s probability of distress. Rather, it should optimize the firm’s risk portfolio by trading off the probability of large shortfalls and its associated costs and with expected gains from taking strategic and business risks. Topic: Operational and Integrated Risk Management Subtopic: Enterprise risk management (ERM) AIMS: Discuss how an ERM program can be used to determine the right amount of risk. Reference: Brian Nocco and René Stulz, “Enterprise Risk Management: Theory and Practice,” Journal of Applied Corporate Finance 18, No. 4 (2006): 8–20.

114



16.


The IRO unit of XYZ bank only re-evaluates previously implemented models when a problem is identified. The IRO unit evaluates and checks the key assumptions of all the models used by XYZ bank.

Which of the existing policies is/are sources of model risk? a. b. c. d.


Answer: a. Explanation: I. Correct. Models should be reviewed regularly and not just as problems with the model are identified. II. Incorrect. Evaluating and checking key assumptions will reduce model risk. Topic: Operational and Integrated Risk Management Subtopic: Sources of model risk AIMS: Identify and discuss sources of model risk. Reference: Dowd, Measuring Market Risk, 2nd Edition, (West Sussex, England: John Wiley & Sons, 2005), Chapter 16—Model Risk.

17.

You want to construct a portfolio so that all of the alphas are benchmark-neutral. Stock XYZ has a volatility of 30%, an information coefficient of 0.20, an alpha of 90 bps, and a beta of 1.94. The benchmark has an alpha of 3.7 basis points. The appropriate benchmark-neutral alpha for stock XYZ is: a. b. c. d.


Answer: d. Explanation: To make the alpha benchmark neutral, you subtract the product of the beta of the stock and the alpha of the benchmark from the original alpha of the stock [0.90 – (1.94*0.037)] = 0.828. Topic: Risk Management and Investment Management Subtopic: Portfolio construction AIMS: Describe neutralization and methods for refining alphas to be neutral. Reference: Grinold and Kahn, Active Portfolio Management: A Quantitative Approach for Providing Superior Returns and Controlling Risk, 2nd Edition, Chapter 14—Portfolio Construction.


115


The next two questions are based on the following information. A risk manager assumes that the joint distribution of returns is multivariate normal and calculates the following risk measures for a 2-asset portfolio: Asset 1 2 Portfolio

18.

Position USD 100 USD 100 USD 200

Individual VaR USD 23.3 USD 46.6 USD 61.6

Marginal VaR 0.176 0.440

VaR Contribution USD 17.6 USD 44.0 USD 61.6

If asset 1 is dropped from the portfolio, what will be the reduction in portfolio VaR? a. b. c. d.

USD USD USD USD

15.0 38.3 44.0 46.6

Answer: a. Explanation: a is correct: The new portfolio VaR is that of asset 2 alone (USD 46.6), which implies a reduction in portfolio VaR of USD 61.6 - USD 46.6 = USD 15.0. Topic: Risk Management and Investment Management Subtopic: Portfolio construction AIMS: Define and distinguish between individual VaR, incremental VaR and diversified portfolio VaR. Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, (New York: McGraw‐Hill, 2007), Chapter 7—Portfolio Risk: Analytical Methods.

19.

Let βi = ρip * σi / σp, where ρip denotes the correlation between the return of asset i and the return of the portfolio, σi is the volatility of the return of asset i and σp is the volatility of the return of the portfolio. What is β2? a. b. c. d.

0.714 1.429 1.513 Cannot determine from information provided.

Answer: b.

116



Explanation: Marginal VaRi = βi * Portfolio VaR / Portfolio Value So, βi = Marginal VaRi * Portfolio Value / Portfolio VaR β2 = 0.44 * 200 / 61.6 = 1.429 Topic: Risk Management and Investment Management Subtopic: Risk decomposition and performance attribution AIMS: Define, compute, and explain the uses of marginal VaR, incremental VaR, and component VaR. Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, (New York: McGraw‐Hill, 2007), Chapter 7—Portfolio Risk: Analytical Methods.

20.

Rigorous stress testing has been emphasized as an important component of risk measurement and management that has been poorly implemented by many financial institutions in the recent past. Which of the following statements concerning steps banks should consider to improve the value of stress testing exercises is/are correct? I. II.

Banks do not need to consider potential second round effects of stress scenarios on the broader financial network. It is inappropriate for banks to conduct “reverse” stress tests.

a. b. c. d.


Answer: d. Explanation: Both statements are incorrect. I—Banks need to examine possible systemic risk implications. II—Banks should stress test for events that can cause major downturns. Topic: Current Issues in Financial Markets Subtopic: Causes and consequences of the current crisis AIMS: Discuss methods for improving stress testing among financial institutions. Reference: Andrew G. Haldane, “Why Banks Failed the Stress Test,” (February 2009).


117

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© 2011 Global Association of Risk Professionals. All rights reserved. 6-11

Financial Risk Manager (FRM®) Examination 2012 Practice Exam Part I / Part II


TABLE OF CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 2012 FRM Part I Practice Exam Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . .3 2012 FRM Part I Practice Exam Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 2012 FRM Part I Practice Exam Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . . . .15 2012 FRM Part I Practice Exam Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

2012 FRM Part II Practice Exam Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . .35 2012 FRM Part II Practice Exam Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 2012 FRM Part II Practice Exam Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . . .45 2012 FRM Part II Practice Exam Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47


i


INTRODUCTION



the Exam. Questions for the FRM Examination are derived






for the Exam.


Suggested Use of Practice Exams To maximize the effectiveness of the Practice Exams, candidates are encouraged to follow these recommendations:


1. Plan a date and time to take each Practice Exam.


Set dates appropriately to give sufficient study/


review time for the Practice Exam prior to the

issues and be able to deal with them effectively.

actual Exam.



Examination in May and November 2012. These Practice

•

Take each Practice Exam in a quiet place.

Exams are based on a sample of questions from the 2010

•

Have only the practice exam, candidate answer

and 2011 FRM Examinations and are suggestive of the

sheet, calculator, and writing instruments (pencils,

questions that will be in the 2012 FRM Examination.

erasers) available.

The 2012 FRM Practice Exam for Part I contain 25

•


•

Allocate 90 minutes for the Practice Exam and


multiple-choice questions and the 2012 FRM Practice Exam for Part II contains 20 multiple-choice questions. Note that the 2012 FRM Examination Part I will contain 100 multiple-


choice questions and the 2012 FRM Examination Part II will


contain 80 multiple-choice questions. The Practice Exams


were designed to be shorter to allow candidates to calibrate

•

Follow the FRM calculator policy. You may only use a Texas Instruments BA II Plus (including the BA II

their preparedness without being overwhelming.

Plus Professional), Hewlett Packard 12C (including

The 2012 FRM Practice Exams do not necessarily cover all topics to be tested in the 2012 FRM Examination as the

the HP 12C Platinum and the Anniversary Edition),

material covered in the 2012 Study Guide may be different

Hewlett Packard 10B II, Hewlett Packard 10B II+ or

from that that covered by the 2010 and 2011 Study Guides.


The questions selected for inclusion in the Practice Exams were chosen to be broadly reflective of the material assigned for 2012 as well as to represent the style of question that

3. After completing the Practice Exam, •


the FRM Committee considers appropriate based on

sheet with the Practice Exam answer key. Only

assigned material.

include questions completed in the first 90 minutes. •


Use the Practice Exam Answers and Explanations to better understand correct and incorrect




tional review. Consult referenced core readings to prepare for Exam.


1


Answer Sheet


a.

b.

c.

d.

a.

1.

16.

2.

17.

3.

18.

4.

19.

5.

20.

6.

21.

7.

22.

8.

23.

9.

24.

10.

25.

b.

c.

d.

✓

✘

11. 12.


13.

1.

14.


15.

1.


3


Questions


1.

You have been asked to estimate the VaR of an investment in Big Pharma Inc. The company’s stock is trading at USD 23 and the stock has a daily volatility of 1.5%. Using the delta-normal method, the VaR at the 95% confidence level of a long position in an at-the-money put on this stock with a delta of -0.5 over a 1-day holding period is closest to which of the following choices? a. b. c. d.

2.

USD USD USD USD

0.28 0.40 0.57 2.84

Alan bought a futures contract on a commodity on the New York Commodity Exchange on June 1. The futures price was USD 500 per unit and the contract size was 100 units per contract. Alan set up a margin account with initial margin of USD 2,000 per contract and maintenance margin of USD 1,000 per contract. The futures price of the commodity varied as shown below. What was the balance in Alan’s margin account at end of June 5? Day

Futures Price (USD)

June June June June June

a. b. c. d.

1 2 3 4 5

USD USD USD USD

497.30 492.70 484.20 471.70 468.80

-1,120 0 880 1,710


5


3.

Gregory is analyzing the historical performance of two commodity funds tracking the Reuters/Jefferies-CRB® Index (CRB) as benchmark. He collated the data on the monthly returns and decided to use the information ratio (IR) to assess which fund achieved higher returns more efficiently and presented his findings.

Average monthly returns Average excess return Standard deviation of returns Tracking error

Fund I

Fund II

Benchmark returns

1.488% 0.073% 0.294% 0.344%

1.468% 0.053% 0.237% 0.341%

1.415% 0.000% 0.238% 0.000%

What is the information ratio for each fund and what conclusion can be drawn? a. b. c. d.

4.

Fund Fund Fund Fund

I I I I

= = = =

0.212, IR for Fund II = 0.155; Fund II performed better as it has a lower IR. 0.212, IR for Fund II = 0.155; Fund I performed better as it has a higher IR. 0.248, IR for Fund II = 0.224; Fund I performed better as it has a higher IR. 0.248, IR for Fund II = 0.224; Fund II performed better as it has a lower IR.

Both Both Both Both

bond bond bond bond

prices prices prices prices

will will will will

move move move move

up by roughly the same amount. up, but bond B will gain more than bond A. down by roughly equal amounts. down, but bond B will lose more than bond A.

You have a portfolio of USD 50 million and you have to hedge it using index futures. The correlation coefficient between the portfolio and index futures being used is 0.65. The standard deviation of the portfolio is 7% and that of the hedging instrument is 6%. The price of the index futures is USD 150 and one contract size is 100 futures. Among the following positions, which position reduces the risk the most? a. b. c. d.

6

for for for for

A trading portfolio consists of two bonds, A and B. Both have modified duration of three years and face value of USD 1000, but A is a zero-coupon bond and its current price is USD 900, and bond B pays annual coupons and is priced at par. What do you expect will happen to the market prices of A and B if the risk-free yield curve moves up by 1 basis point? a. b. c. d.

5.

IR IR IR IR

Long 3364 futures contracts Short 3364 futures contracts Long 2527 futures contracts Short 2527 futures contracts



6.

An analyst gathered the following information about the return distributions for two portfolios during the same time period: Portfolio A B

Skewness -1.6 0.8

Kurtosis 1.9 3.2

The analyst states that the distribution for Portfolio A is more peaked than a normal distribution and that the distribution for Portfolio B has a long tail on the left side of the distribution. Which of the following is correct? a. b. c. d.

The The The The

analyst’s assessment is correct. analyst’s assessment is correct for Portfolio A and incorrect for portfolio B. analyst’s assessment is incorrect for Portfolio A but is correct for portfolio B. analyst is incorrect in his assessment for both portfolios.

Common text for questions 7 and 8: A risk manager for Bank XYZ, Mark, is considering writing a 6-month American put option on a non-dividend-paying stock ABC. The current stock price is USD 50 and the strike price of the option is USD 52. In order to find the no-arbitrage price of the option Mark uses a two-step binomial tree model. The stock price can go up or down by 20% each period. Mark’s view is that the stock price has an 80% probability of going up each period and a 20% probability of going down. The annual risk-free rate is 12% with continuous compounding. 7.

What is the risk-neutral probability of the stock price going up in a single step? a. b. c. d.

8.

34.5% 57.6% 65.5% 80.0%

The no-arbitrage price of the option is closest to: a. b. c. d.

USD USD USD USD

2.00 2.93 5.22 5.86


7


9.

For non-dividend-paying stocks, according to put-call parity, the payoff on a long stock position can be synthetically created with: a. b. c. d.

10.

b. c. d.

No, this is not a violation of the GARP Code of Conduct because neither Manzoor nor the firm is aware of the changes to risk measurement approaches. No, this is not a violation as the methodology worked when Manzoor took his FRM exams. This is only a violation of the GARP Code of Conduct if investment decisions are made based on Manzoor’s risk reports. Yes, this is a violation of the GARP Code of Conduct.

When testing a hypothesis, which of the following statements is correct when the level of significance of the test is decreased? a. b. c. d.

8

long call, a short put and a long position in a risk-free discount bond short call, a short put and a long position in a risk-free discount bond long call, a long put and a long position in a risk-free discount bond long call, a short put and a short position in a risk-free discount bond

Junaid Manzoor has been hired as head of risk management by KDB Asset Management, a small investment firm in Pakistan. Manzoor implements a risk measurement framework to gauge portfolio risk for the firm. Unfortunately, the methodology he implements for risk measurement has changed considerably in recent years and is no longer used internationally. Neither Manzoor nor anyone else at the firm is aware of the changes to risk measurement approaches. As a GARP member, has Junaid violated the GARP Code of Conduct? a.

11.

a a a a

The The The The

likelihood of rejecting the null hypothesis when it is true decreases. likelihood of making a Type I error increases. null hypothesis is rejected more frequently, even when it is actually false. likelihood of making a Type II error decreases.



12.

Howard Freeman manages a portfolio of investment securities for a regional bank. The portfolio has a current market value equal to USD 6,247,000 with a daily variance of 0.0002. Assuming there are 250 trading days in a year and that the portfolio returns follow a normal distribution, the estimate of the annual VaR at the 95% confidence level is closest to which of the following? a. b. c. d.

13.

14.

USD USD USD USD

32,595 145,770 2,297,854 2,737,868

An investor finds that the gold lease rate is 5% and the corresponding risk free rate is 6%. Under these conditions, which of the following charts of forward prices (y-axis) versus time (x-axis) best indicates the structure of the forward market for gold? a.

b.

c.

d.

A multiple choice exam has ten questions, with five choices per question. If you need at least three correct answers to pass the exam, what is the probability that you will pass simply by guessing? a. b. c. d.

0.8% 20.1% 67.8% 32.2%


9


15.

You are using key rate shifts to analyze the effect of yield changes on bond prices. Suppose that the 10-year yield has increased by 10 basis points and that this shock decreases linearly to zero for the 20-year yield. What is the effect of this shock on the 14-year yield? a. b. c. d.

16.

10

of of of of

0 basis points 4 basis points 6 basis points 10 basis points

All else held constant and assuming no change in the value of the underlying, what impact should an increase in interest rates have on the price of stock index futures? a. b. c. d.

17.

increase increase increase increase

Increase futures prices Reduce futures prices Have no impact on futures prices Make futures prices same as spot

Which of the following methods will generally be effective in reducing the likelihood that your firm is exposed to “hidden risks”? i. ii. iii. iv.

Reducing the flexibility traders have to respond to market events Creating a culture of risk awareness throughout the organization Structuring compensation to be aligned with the risk appetite of the firm Investing heavily in quantitative risk models

a. b. c. d.

i only iv only ii and iii only i, ii, and iii only



18.

A hedge fund has invested USD 100 million in mortgage backed securities. The risk manager is concerned about prepayment risk if interest rates fall. Which of the following strategies is an effective hedge against the potential loss due to a drop in interest rates? a. b. c. d.

19.

Sam Seel has a small portfolio of options. Since the options are currently in-the-money, he is considering the possibility of early exercise. Which of the following statements is correct? a. b. c. d.

20.

It is never optimal to exercise European call options early. It is best to exercise a put option when it is just in-the-money. Early exercise of put options becomes more attractive when interest rates rise. Early exercise of put options becomes more attractive when interest rates decline.

Portfolio A has an expected return of 8%, volatility of 20%, and beta of 0.5. Assume that the market has an expected return of 10% and volatility of 25%. Also assume a risk-free rate of 5%. What is Jensen’s alpha for portfolio A? a. b. c. d.

21.

Short forward rate agreement (FRA), long T-bond futures Long FRA, short T-bond futures Long FRA, long T-bond futures Short FRA, short T-bond futures

0.5% 1.0% 10% 15%

Half of the mortgages in a portfolio are considered subprime. The principal balance of half of the subprime mortgages and one-quarter of the non-subprime mortgages exceeds the value of the property used as collateral. If you randomly select a mortgage from the portfolio for review and its principal balance exceeds the value of the collateral, what is the probability that it is a subprime mortgage? a. b. c. d.

1/4 1/3 1/2 2/3


11


22.

John Holt is managing a fixed-income portfolio worth USD 10 million. The duration of the portfolio today is 5.9 years and in six months it is expected to be 6.2 years. The 6-month Treasury bond futures contract is trading at USD 98.47. The bond that is expected to be cheapest-to-deliver has a duration of 4.0 years today and an expected duration of 4.8 years at the maturity of the futures contract. How many futures contracts should John short to hedge against changes in interest rates over the next six months? Each futures contract is for the delivery of USD 100,000 face value of bonds. a. b. c. d.

23.

24.

Which of the following are potential consequences of violating the GARP Code of Conduct once a formal determination that such a violation has occurred is made? i. ii. iii. iv.

Suspension of the GARP Member from GARP’s Membership roles. Suspension of the GARP Member’s right to work in the risk management profession. Removal of the GARP Member’s right to use the FRM designation or any other GARP granted designation. Required participation in ethical training.

a. b. c. d.

i and ii only i and iii only ii and iv only iii and iv only

In comparison to the bottom-up approach to measuring operational risk exposure, the top-down approach would be most appropriate for which of the following: a. b. c. d.

12

125 contracts 131 contracts 150 contracts 157 contracts

Determining firm-wide economic capital levels Designing risk reduction techniques at the business-unit level Diagnosing specific weak points in a process Incorporating changes in the risk environment



25.

HedgeFund has been in existence for two years. Its average monthly return has been 6% with a standard deviation of 5%. HedgeFund has a stated objective of controlling volatility as measured by the standard deviation of monthly returns. You are asked to test the null hypothesis that the volatility of HedgeFund’s monthly returns is equal to 4% versus the alternative hypothesis that the volatility is greater than 4%. Assuming that all monthly returns are independently and identically normally distributed, and using the tables below, what is the correct test to be used and what is the correct conclusion at the 2.5% level of significance? t Table: Inverse of the one-tailed probability of the Student’s t-distribution Df

One-tailed Probability = 5.0%


22 23 24

1.717 1.714 1.711

2.074 2.069 2.064

Chi-Square Table: Inverse of the one-tailed probability of the Chi-Squared distribution Df



22 23 24

33.9244 35.1725 36.4151

36.7807 38.0757 39.3641

a. b. c. d.

t-test; reject the null hypothesis Chi-square test; reject the null hypothesis t-test; do not reject the null hypothesis Chi-square test; do not reject the null hypothesis


13


Answers


a.

1.

b.

c.

d.

16.

2.

3.

a.

18.

19.

5.

20.

6.

21.

8. 9.

10. 11.

23.

25.


1.

14. 15.

12. 13.

d.

22.

24.

c.

17.

4.

7.

b.

✓

✘



15


Explanations


1.

You have been asked to estimate the VaR of an investment in Big Pharma Inc. The company’s stock is trading at USD 23 and the stock has a daily volatility of 1.5%. Using the delta-normal method, the VaR at the 95% confidence level of a long position in an at-the-money put on this stock with a delta of -0.5 over a 1-day holding period is closest to which of the following choices? a. b. c. d.

USD USD USD USD

0.28 0.40 0.57 2.84

Answer: a Explanation: VaR = |delta| * 1.645 * sigma * S = 0.5 * 1.645 * 0.015 * 23 = 0.28. The delta of an at-the-money put is -0.5 and the absolute value of the delta is 0.5. Topic: Valuation and Risk Models Subtopic: Delta‐normal valuation, full revaluation, historical simulation, Monte Carlo simulation methods AIMS: Describe the delta‐normal approach to calculating VaR for non‐linear derivatives. Reference: Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach (Oxford: Blackwell Publishing, 2004), Chapter 3

2.

Alan bought a futures contract on a commodity on the New York Commodity Exchange on June 1. The futures price was USD 500 per unit and the contract size was 100 units per contract. Alan set up a margin account with initial margin of USD 2,000 per contract and maintenance margin of USD 1,000 per contract. The futures price of the commodity varied as shown below. What was the balance in Alan’s margin account at end of June 5? Day

Futures Price (USD)


a. b. c. d.

1 2 3 4 5

USD USD USD USD

497.30 492.70 484.20 471.70 468.80

-1,120 0 880 1,710

Answer: d


17


Explanation: (USD) Date

Daily Price

Gain (Loss)

Cumulative Gain (Loss)

Margin Balance


497.30 492.70 484.20 471.70 468.80

(270) (460) (850) (1,250) (290)

(270) (730) (1,580) (2,830) (3,120)

1,730 1,270 420 750 1,710

1 2 3 4 5

Margin Call

1,580 1,250

The margin balance at the end of June 5 is USD 1,710. There is a margin call each time the margin account drops below the maintenance margin amount of USD 1,000. Each time there is a margin call, the balance has to be brought back to the initial margin level of USD 2,000. Topic: Financial Markets and Products Subtopic: Futures, forwards, swaps, and options AIMS: Describe the rationale for margin requirements and explain how they work. Reference: Hull, Options, Futures and Other Derivatives, 7th edition, Chapter 2

3.

Gregory is analyzing the historical performance of two commodity funds tracking the Reuters/Jefferies-CRB® Index (CRB) as benchmark. He collated the data on the monthly returns and decided to use the information ratio (IR) to assess which fund achieved higher returns more efficiently and presented his findings.

Average monthly returns Average excess return Standard deviation of returns Tracking error

Fund I

Fund II

Benchmark returns

1.488% 0.073% 0.294% 0.344%

1.468% 0.053% 0.237% 0.341%

1.415% 0.000% 0.238% 0.000%

What is the information ratio for each fund and what conclusion can be drawn? a. b. c. d.

IR IR IR IR

for for for for

Fund Fund Fund Fund

I I I I

= = = =

0.212, IR for Fund II = 0.155; Fund II performed better as it has a lower IR. 0.212, IR for Fund II = 0.155; Fund I performed better as it has a higher IR. 0.248, IR for Fund II = 0.224; Fund I performed better as it has a higher IR. 0.248, IR for Fund II = 0.224; Fund II performed better as it has a lower IR.

Answer: b

18



Explanation: The information ratio may be calculated by either a comparison of the residual return to residual risk, or the excess return to tracking error. The higher the IR, the better ‘informed’ the manager is at picking assets to invest in. Since neither residual return nor risk is given, only the latter is an option. IR = E(Rp – Rb)/Tracking Error. For Fund I: IR = 0.00073 / 0.00344 = 0.212; For Fund II: IR = 0.00053 / 0.00341 = 0.155 Topic: Foundation of Risk Management Subtopic: Sharpe ratio and information ratio AIMS: Compute and interpret tracking error, the information ratio, and the Sortino ratio. Reference: Richard Grinold and Ronald Kahn, Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk, 2nd Edition (McGraw-Hill, 1999)

4.

A trading portfolio consists of two bonds, A and B. Both have modified duration of three years and face value of USD 1000, but A is a zero-coupon bond and its current price is USD 900, and bond B pays annual coupons and is priced at par. What do you expect will happen to the market prices of A and B if the risk-free yield curve moves up by 1 basis point? a. b. c. d.

Both Both Both Both

bond bond bond bond

prices prices prices prices

will will will will

move move move move

up by roughly the same amount. up, but bond B will gain more than bond A. down by roughly equal amounts. down, but bond B will lose more than bond A.

Answer: d Explanation: Assuming parallel movements to the yield curve, the expected price change is: ΔP = -PΔy * D where P is the current price or net present value Δy is the yield change D is duration All else equal, a negative impact of yield curve move is stronger in absolute terms at the bond which is currently priced higher. Upward parallel curve movements makes bonds cheaper. Topic: Valuation and Risk Models Subtopic: DV01, duration and convexity, duration based hedging AIMS: Define and compute the DV01 of a fixed income security given a change in yield and the resulting change in price. Reference: Bruce Tuckman, Fixed Income Securities, 2nd Edition, Chapter 5


19


5.

You have a portfolio of USD 50 million and you have to hedge it using index futures. The correlation coefficient between the portfolio and index futures being used is 0.65. The standard deviation of the portfolio is 7% and that of the hedging instrument is 6%. The price of the index futures is USD 150 and one contract size is 100 futures. Among the following positions, which position reduces the risk the most? a. b. c. d.

Long 3364 futures contracts Short 3364 futures contracts Long 2527 futures contracts Short 2527 futures contracts

Answer: d Explanation: The optimal hedge ratio is the product of the coefficient of correlation and the ratio of the standard deviations of the portfolio and the index futures, respectively. Computing the optimal hedge ratio: h = ρ(σs / σf) where ρ is the coefficient of correlation, and σs and σf are standard deviations of portfolio and standard deviation of index futures, respectively. h= 0.65 * (0.07/0.06) = 0.758 The number of futures contract to be shorted: N= h * (Portfolio value)/ (Futures contract size) N= 0.758 * 50000000/(150 * 100) N= 2526.67 Æ 2527 Since you are long in the portfolio, you have to short the index futures to hedge it. Topic: Financial Markets and Products Subtopic: Minimum variance hedge ratio AIMS: Define, compute and interpret the optimal number of futures contracts needed to hedge an exposure, including a “tailing the hedge” adjustment. Reference: Hull, Options, Futures and other Derivatives, 7th Edition, Chapter 3—Hedging Strategies using Futures

6.

An analyst gathered the following information about the return distributions for two portfolios during the same time period: Portfolio A B

Skewness -1.6 0.8

Kurtosis 1.9 3.2

The analyst states that the distribution for Portfolio A is more peaked than a normal distribution and that the distribution for Portfolio B has a long tail on the left side of the distribution. Which of the following is correct? a. b. c. d.

The The The The

analyst’s assessment is correct. analyst’s assessment is correct for Portfolio A and incorrect for portfolio B. analyst’s assessment is incorrect for Portfolio A but is correct for portfolio B. analyst is incorrect in his assessment for both portfolios.

Answer: d

20



Explanation: The analyst’s statement is incorrect in reference to either portfolio. Portfolio A has a kurtosis of less than 3, indicating that it is less peaked than a normal distribution (platykurtic). Portfolio B is positively skewed (long tail on the right side of the distribution). Topic: Quantitative Analysis Subtopic: Mean, standard deviation, correlation, skewness, and kurtosis AIMS: Define, calculate and interpret the skewness and kurtosis of a random variable; Describe and identify a platykurtic and leptokurtic distribution; Define the skewness and kurtosis of a normally distributed random variable. Reference: Damodar Gujarati, Essentials of Econometrics, 3th Edition, Chapter 3.

Common text for questions 7 and 8: A risk manager for Bank XYZ, Mark, is considering writing a 6-month American put option on a non-dividend-paying stock ABC. The current stock price is USD 50 and the strike price of the option is USD 52. In order to find the no-arbitrage price of the option Mark uses a two-step binomial tree model. The stock price can go up or down by 20% each period. Mark’s view is that the stock price has an 80% probability of going up each period and a 20% probability of going down. The annual risk-free rate is 12% with continuous compounding. 7.

What is the risk-neutral probability of the stock price going up in a single step? a. b. c. d.

34.5% 57.6% 65.5% 80.0%

Answer: b ert – d Explanation: Calculation follows: Pup =

e0.12 * 3/12 – 0.8 =

u–d

1.2 – 0.8

= 57.61% Pdown = 1 – Pup = 42.39%

Topic: Valuation and Risk Models Subtopic: Binomial trees AIMS: Calculate the value of a European call or put option using the one‐step and two‐step binomial model. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition (Prentice Hall, 2009), Chapter 11.

8.

The no-arbitrage price of the option is closest to: a. b. c. d.

USD USD USD USD

2.00 2.93 5.22 5.86

Answer: d


21


Explanation: The risk neutral probability of an up move is 57.61% (calculated in the previous question).

D 1.2 * 50 = 60 1.65

A

50

•

1.2 * 1.2 * 50 = 72 max(0, 52 - 72) = 0

•

1.2 * 0.8 * 50 = 48 max(0, 52 - 48) = 4

•

0.8 * 0.8 * 50 = 32 max(0, 52 - 32) = 20

• B

•

E C

5.86

• 0.8 * 50 = 40 max(10.46, 12) = 12

F

The figure shows the stock price and the respective option value at each node. At the final nodes the value is calculated as max(0, K - S). Node B: (0.5761 * 0 + 0.4239 * 4) * exp(-0.12 * 3/12) = 1.65, which is greater than the intrinsic value of the option at this node equal to max(0, 52 - 60)=0, so the option should not be exercised early at this node. Node C: (0.5761 * 4 + 0.4239 * 20) * exp(-0.12 * 3/12) = 10.46, which is lower than the intrinsic value of the option at this node equal to max(0, 52 - 40) = 12, so the option should be exercised early at node C, and the value of the option at node C is 12. Node A: (0.5761 * 1.65 + 0.4239 * 12) * exp(-0.12 * 3/12) = 5.86, which is greater than the intrinsic value of the option at this node equal to max(0, 52 - 50) = 2, so the option should not be exercised early at this node. Topic: Valuation and Risk Models Subtopic: Binomial trees AIMS: Calculate the value of a European call or put option using the one-step and two-step binomial model. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition (Prentice Hall, 2009), Chapter 11

9.

For non-dividend-paying stocks, according to put-call parity, the payoff on a long stock position can be synthetically created with: a. b. c. d.

a a a a

long call, a short put and a long position in a risk-free discount bond short call, a short put and a long position in a risk-free discount bond long call, a long put and a long position in a risk-free discount bond long call, a short put and a short position in a risk-free discount bond

Answer: a

22



Explanation: According to put-call parity: S = C – P + Xe-rt Topic: Financial Markets and Products Subtopic: Futures, Forwards, Swaps, and Options AIMS: Explain put-call parity and calculate, using put-call parity on a non-dividend paying stock, the value of a European and American option. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition (Pearson 2009), Chapter 9

10.

Junaid Manzoor has been hired as head of risk management by KDB Asset Management, a small investment firm in Pakistan. Manzoor implements a risk measurement framework to gauge portfolio risk for the firm. Unfortunately, the methodology he implements for risk measurement has changed considerably in recent years and is no longer used internationally. Neither Manzoor nor anyone else at the firm is aware of the changes to risk measurement approaches. As a GARP member, has Junaid violated the GARP Code of Conduct? a. b. c. d.

No, this is not a violation of the GARP Code of Conduct because neither Manzoor nor the firm is aware of the changes to risk measurement approaches. No, this is not a violation as the methodology worked when Manzoor took his FRM exams. This is only a violation of the GARP Code of Conduct if investment decisions are made based on Manzoor’s risk reports. Yes, this is a violation of the GARP Code of Conduct.

Answer: d Explanation: The GARP Code of Conduct states that GARP members should be familiar with current generally accepted risk management practices. Topic: Foundations Subtopic: Ethics AIMS: Describe the responsibility of each GARP member with respect to professional integrity, ethical conduct, conflicts of interest, confidentiality of information and adherence to generally accepted practices in risk management. Reference: GARP Code of Conduct


23


11.

When testing a hypothesis, which of the following statements is correct when the level of significance of the test is decreased? a. b. c. d.

The The The The

likelihood of rejecting the null hypothesis when it is true decreases. likelihood of making a Type I error increases. null hypothesis is rejected more frequently, even when it is actually false. likelihood of making a Type II error decreases.

Answer: a Explanation: Decreasing the level of significance of the test decreases the probability of making a Type I error and hence makes it more difficult to reject the null when it is true. However, the decrease in the chance of making a Type I error comes at the cost of increasing the probability of making a Type II error, because the null is rejected less frequently, even when it is actually false. Topic: Quantitative Analysis Subtopic: Linear regression and correlation, hypothesis testing AIMS: Define, calculate and interpret Type I and Type II errors. Reference: Damodar Gujarati, Essentials of Econometrics, 3rd Edition (McGraw-Hill, 2006)

12.

Howard Freeman manages a portfolio of investment securities for a regional bank. The portfolio has a current market value equal to USD 6,247,000 with a daily variance of 0.0002. Assuming there are 250 trading days in a year and that the portfolio returns follow a normal distribution, the estimate of the annual VaR at the 95% confidence level is closest to which of the following? a. b. c. d.

USD USD USD USD

32,595 145,770 2,297,854 2,737,868

Answer: c Explanation: Daily standard deviation = sqrt(0.0002) = 0.01414. Annual VaR = 6,247,000 x sqrt(250) x 0.01414 x 1.645 = 2,297,854. Topic: Valuation and Risk Models Subtopic: Value-at-Risk (VaR) AIMS: Explain and give examples of linear and non-linear derivatives. Explain how to calculate VaR for linear derivatives. Reference: Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach (Oxford: Blackwell Publishing, 2004), Chapter 3—Putting VaR to Work

24



13.

An investor finds that the gold lease rate is 5% and the corresponding risk free rate is 6%. Under these conditions, which of the following charts of forward prices (y-axis) versus time (x-axis) best indicates the structure of the forward market for gold? a.

b.

c.

d.

Answer: a Explanation: Forward price = Spot price * exp[(risk free rate – lease rate) * T]. Since lease rate is lower than the risk free rate, it will show a positive sloped forward curve. “b” is a curve that indicates backwardation, and the other two choices both show a two-stage market structure which is not indicated in the question. Topic: Financial Markets and Products Subtopic: Commodity Derivatives, Cost of Carry, Lease Rate, Convenience Yield AIMS: Define the lease rate and how it determines the no-arbitrage values for commodity forwards and futures, and explain the relationship between lease rates and contango, and lease rates and backwardation. Reference: Robert McDonald, Derivatives Markets (Addison-Wesley, 2003), Chapter 6

14.

A multiple choice exam has ten questions, with five choices per question. If you need at least three correct answers to pass the exam, what is the probability that you will pass simply by guessing? a. b. c. d.

0.8% 20.1% 67.8% 32.2%

Answer: d


25


Explanation: The probability of an event is between 0 and 1. If these are mutually exclusive events, the probability of individual occurrences are summed. This probability follows a binomial distribution with a p-parameter of 0.2. The probability of getting at least three questions correct is 1 - (p(0) + p(1) + p(2)) = 32.2%. Topic: Quantitative Analysis Subtopic: Probability Distributions AIMS: Define the probability of an event. Reference: Damodar Gujarati, Essentials of Econometrics, 3rd Edition (McGraw‐Hill, 2006), Chapter 2—Review of Statistics: Probability and Probability Distributions

15.

You are using key rate shifts to analyze the effect of yield changes on bond prices. Suppose that the 10-year yield has increased by 10 basis points and that this shock decreases linearly to zero for the 20-year yield. What is the effect of this shock on the 14-year yield? a. b. c. d.

increase increase increase increase

of of of of


Answer: c Explanation: The 10 basis point shock to the 10-year yield is supposed to decline linearly to zero for the 20 year yield. Thus, the shock decreases by 1 basis point per year and will result in an increase of 6 basis points for the 14 year yield. Topic: Valuation and Risk Models Subtopic: Term Structure of Interest Rates AIMS: Define, interpret, and apply a bond’s yield-to-maturity (YTM) to bond pricing. Reference: Bruce Tuckman, Fixed Income Securities, 2nd Edition (Hoboken, NJ: Wiley & Sons, 2002), Chapter 3— Yield to Maturity

16.

All else held constant and assuming no change in the value of the underlying, what impact should an increase in interest rates have on the price of stock index futures? a. b. c. d.

Increase futures prices Reduce futures prices Have no impact on futures prices Make futures prices same as spot

Answer: a

26



Explanation: The formula to compute futures price on a stock index future is: F0 = S * e(r-q)T All else held constant if r rises, so should F. Topic: Financial Markets and Products Subtopic: Futures, Forwards, Swaps, and Options AIMS: Calculate the forward price, given the underlying asset’s price, with or without short sales and/or consideration to the income yield of the underlying asset. Describe an arbitrage argument in support of these prices. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition (Pearson 2009), Chapter 5

17.

Which of the following methods will generally be effective in reducing the likelihood that your firm is exposed to “hidden risks”? i. ii. iii. iv.

Reducing the flexibility traders have to respond to market events Creating a culture of risk awareness throughout the organization Structuring compensation to be aligned with the risk appetite of the firm Investing heavily in quantitative risk models

a. b. c. d.

i only iv only ii and iii only i, ii, and iii only

Answer: c Explanation: Besides eliminating flexibility within the firm, risk monitoring is costly so that at some point, tighter risk monitoring is not efficient. The effectiveness of risk monitoring and control depends crucially on an institution’s culture and incentives. If risk is everybody’s business in an organization, it is harder for pockets of risk to be left unobserved. If employees’ compensation is affected by how they take risks, they will take risk more judiciously. The best risk models in a firm with poor culture and poor incentives will be much less effective than in a firm where the incentives of employees are better aligned with the risk-taking objectives of the firm. Topic: Foundations of Risk Management Subtopic: Risk Management Failures: What are They and When Do They Happen? AIMS: Define the role of risk management and explain why a large financial loss is not necessarily a failure of risk management. Explain how firms can fail to take known and unknown risks into account in making strategic decisions. Reference: Rene Stulz, “Risk Management Failures: What are They and When Do They Happen?” Fisher College of Business Working Paper Series (Oct. 2008)


27


18.

A hedge fund has invested USD 100 million in mortgage backed securities. The risk manager is concerned about prepayment risk if interest rates fall. Which of the following strategies is an effective hedge against the potential loss due to a drop in interest rates? a. b. c. d.

Short forward rate agreement (FRA), long T-bond futures Long FRA, short T-bond futures Long FRA, long T-bond futures Short FRA, short T-bond futures

Answer: a Explanation: When rates drop, the long position in the futures and the short position in the FRA both gain. Topic: Valuation and Risk Models Subtopic: Bond prices, spot prices, forward rates AIMS: Define and describe reinvestment risk. Reference: Bruce Tuckman, Fixed Income Securities, 2nd Edition (Hoboken, NJ: Wiley & Sons, 2002). Chapter 3— Yield to Maturity

19.

Sam Seel has a small portfolio of options. Since the options are currently in-the-money, he is considering the possibility of early exercise. Which of the following statements is correct? a. b. c. d.

It is never optimal to exercise European call options early. It is best to exercise a put option when it is just in-the-money. Early exercise of put options becomes more attractive when interest rates rise. Early exercise of put options becomes more attractive when interest rates decline.

Answer: c Explanation: When interest rates rise, stock prices have a tendency to fall. This increases the value of a put option on a stock. All options benefit from high volatility. Topic: Financial Markets and Products Subtopic: American Options, Effects of Dividends, Early Exercise AIMS: Discuss the effects dividends have on the put‐call parity, the bounds of put and call option prices, and on the early exercise feature of American options. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition (Prentice Hall, 2009), Chapter 9— Properties of Stock Options

28



20.

Portfolio A has an expected return of 8%, volatility of 20%, and beta of 0.5. Assume that the market has an expected return of 10% and volatility of 25%. Also assume a risk-free rate of 5%. What is Jensen’s alpha for portfolio A? a. b. c. d.

0.5% 1.0% 10% 15%

Answer: a Explanation: The Jensen measure of a portfolio, or Jensen’s alpha, is computed as follows: αp = E(Rp) – RF – β x [E(RM) – RF] = 8% - 5% - 0.5 x (10% - 5%) = 0.5% Topic: Foundation of Risk Management Subtopic: Market efficiency, equilibrium and the Capital Asset Pricing Model (CAPM), performance measurement and attribution AIMS: Calculate, compare, and evaluate the Treynor measure, the Sharpe measure, and Jensen's alpha. Reference: Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (John Wiley & Sons, 2003), Chapter 4—The Capital Asset Pricing Model and Its Application to Performance Measurement

21.

Half of the mortgages in a portfolio are considered subprime. The principal balance of half of the subprime mortgages and one-quarter of the non-subprime mortgages exceeds the value of the property used as collateral. If you randomly select a mortgage from the portfolio for review and its principal balance exceeds the value of the collateral, what is the probability that it is a subprime mortgage? a. b. c. d.

1/4 1/3 1/2 2/3

Answer: d


29


Explanation: Assume: A = event that the loan is subprime B = event that the face value of the loan exceeds that the property P(A) = ½ P(A’) = 1/2 P(B|A) = ½ P(B|A’) = 1/4 P(A|B) = P(B|A)*P(A)/[P(B|A)*P(A) + P(B|A')*P(A')] P(A|B) = (1/2 * 1/2)/(1/2 * 1/2 + 1/4 * 1/2) = (1/4) / (1/4 + 1/8) = (1/4)/(3/8) = 8/12 = 2/3 Topic: Quantitative Analysis. Subtopic: Probability distributions AIMS: Define the Bayes’ Theorem and apply Bayes’ formula to determine the probability of an event. Reference: Damodar Gujarati, Essentials of Econometrics, 3rd Edition (McGraw-Hill, 2006), Chapter 2

22.

John Holt is managing a fixed-income portfolio worth USD 10 million. The duration of the portfolio today is 5.9 years and in six months it is expected to be 6.2 years. The 6-month Treasury bond futures contract is trading at USD 98.47. The bond that is expected to be cheapest-to-deliver has a duration of 4.0 years today and an expected duration of 4.8 years at the maturity of the futures contract. How many futures contracts should John short to hedge against changes in interest rates over the next six months? Each futures contract is for the delivery of USD 100,000 face value of bonds. a. b. c. d.

125 contracts 131 contracts 150 contracts 157 contracts

Answer: b Explanation: The correct number of futures contracts to short is computed as follows: 10,000,000 * 6.2 / (.9847 * 100,000 * 4.8) = 131.17 Topic: Financial Markets and Products Subtopic: Minimum Variance Hedge Ratio AIMS: Calculate the duration‐based hedge ratio and describe a duration‐based hedging strategy using interest rate futures. Reference: John Hull, Options, Futures, and Other Derivatives, 7th Edition (Prentice Hall, 2009), Chapter 6—Interest Rate Futures

30



23.

Which of the following are potential consequences of violating the GARP Code of Conduct once a formal determination that such a violation has occurred is made? i. ii. iii. iv.

Suspension of the GARP Member from GARP’s Membership roles. Suspension of the GARP Member’s right to work in the risk management profession. Removal of the GARP Member’s right to use the FRM designation or any other GARP granted designation. Required participation in ethical training.

a. b. c. d.

i and ii only i and iii only ii and iv only iii and iv only

Answer: b Explanation: According to the GARP Code of Conduct, violation(s) of the Code may result in the temporary suspension or permanent removal of the GARP Member from GARP’s Membership roles, and may also include temporarily or permanently removing from the violator the right to use or refer to having earned the FRM designation or any other GARP granted designation, following a formal determination that such a violation has occurred. Topic: Foundations of Risk Management Subtopic: Ethics AIMS: Describe the potential consequences of violating the GARP Code of Conduct. Reference: GARP Code of Conduct, Applicability and Enforcement section


31


24.

In comparison to the bottom-up approach to measuring operational risk exposure, the top-down approach would be most appropriate for which of the following: a. b. c. d.

Determining firm-wide economic capital levels Designing risk reduction techniques at the business-unit level Diagnosing specific weak points in a process Incorporating changes in the risk environment

Answer: a Explanation: Top-down operational risk measurement techniques may be appropriate for the determination of overall economic levels for the firm. However, top-down operational risk techniques tend to be of little use in designing procedures to reduce operational risk in any particularly vulnerable area of the firm. That is, they do not incorporate any adjustment for the implementation of operational risk controls, nor can they advise management about specific weak points in the production process. They over-aggregate the firm’s processes and procedures and are thus poor diagnostic tools. Top-down techniques are also backward looking and cannot incorporate changes in the risk environment that might affect the operational loss distribution over time. Topic: Valuation and Risk Models. Subtopic: Applications of VaR for market, credit and operational risk AIMS: Compare and contrast top-down and bottom-up approaches to measuring operational risk. Reference: Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach (Oxford: Blackwell Publishing, 2004), Chapter 5

32



25.

HedgeFund has been in existence for two years. Its average monthly return has been 6% with a standard deviation of 5%. HedgeFund has a stated objective of controlling volatility as measured by the standard deviation of monthly returns. You are asked to test the null hypothesis that the volatility of HedgeFund’s monthly returns is equal to 4% versus the alternative hypothesis that the volatility is greater than 4%. Assuming that all monthly returns are independently and identically normally distributed, and using the tables below, what is the correct test to be used and what is the correct conclusion at the 2.5% level of significance? t Table: Inverse of the one-tailed probability of the Student’s t-distribution Df



22 23 24

1.717 1.714 1.711

2.074 2.069 2.064

Chi-Square Table: Inverse of the one-tailed probability of the Chi-Squared distribution Df



22 23 24

33.9244 35.1725 36.4151

36.7807 38.0757 39.3641

a. b. c. d.

t-test; reject the null hypothesis Chi-square test; reject the null hypothesis t-test; do not reject the null hypothesis Chi-square test; do not reject the null hypothesis

Answer: d Explanation: The correct test is: Null Hypothesis s2 = 4%2 = .0016

Alternative Hypothesis s2 > .0016

Critical Region, reject the null if: (24 – 1)(.05) ^ 2 2 > c2.5,24 – 1 ➞ 36 > 38 (.04) ^ 2

Therefore, you would not reject the null hypothesis. A chi-square test is a statistical hypothesis test whereby the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. Topic: Quantitative Analysis Subtopic: Statistical Inference and Hypothesis Testing. AIMS: Describe and interpret the chi-square test of significance and the F-test of significance. Reference: Damodar Gujarati, Essentials of Econometrics, 3rd Edition (McGraw-Hill, 2006), Chapter 5


33


Answer Sheet


a.

b.

c.

d.

a.

1.

14.

2.

15.

3.

16.

4.

17.

5.

18.

6.

19.

7.

20.

b.

c.

d.

✓

✘

8. 9.


10.

1.

11.


12.

1.

13.


35


Questions


1.

In an effort to hedge some of your portfolio’s commodity exposure, you purchased a look-back put on 100,000 pounds of copper for the period from June 30, 2009 through June 30, 2010. The price of copper over this period is shown in the chart below. What was the payoff at expiration of this option?

a. b. c. d.

2.

USD USD USD USD

0 100,000 200,000 300,000

Which of the following statements about correlation and copula are correct? i.

Copula enables the structures of correlation between variables to be calculated separately from their marginal distributions. ii. Transformation of variables does not change their correlation structure. iii. Correlation can be a useful measure of the relationship between variables drawn from a distribution without a defined variance. iv. Correlation is a good measure of dependence when the measured variables are distributed as multivariate elliptical. a. b. c. d.

i and iv only ii, iii, and iv only i and iii only ii and iv only


37


3.

Which of the following about the duration of a mortgage-backed, interest-only security (IO) is correct? a. b. c. d.

4.

The Chief Risk Officer of Martingale Investments Group is planning a change in methodology for some of the risk management models used to estimate risk measures. His aim is to move from models that use the normal distribution of returns to models that use the distribution of returns implied by market prices. Martingale Group has a large long position in the German equity stock index DAX which has a volatility smile that slopes downward to the right. How will the change in methodology affect the estimate of expected shortfall (ES)? a. b. c. d.

5.

USD USD USD USD

932 93,263 111,122 131,892

An analyst is using Moody’s KMV model to estimate the distance to default of a large public firm, Shoos Inc., a firm that designs, manufactures and sells athletic shoes. The firm’s capital structure consists of USD 40 million in short-term debt, USD 20 million in long-term debt, and there are one million shares of stock currently trading at USD 10 per share. The asset volatility is 20% per year. What is the normalized distance to default for Shoos Inc.? a. b. c. d.

38

ES with the updated models will be larger than the old estimate. ES with the updated models will be smaller than the old estimate. ES will remain unchanged. Insufficient information to determine.

A portfolio manager owns a portfolio of options on a non-dividend paying stock RTX. The portfolio is made up of 10,000 deep in-the-money call options on RTX and 50,000 deep out-of-the money call options on RTX. The portfolio also contains 20,000 forward contracts on RTX. RTX is trading at USD 100. If the volatility of RTX is 30% per year, which of the following amounts would be closest to the 1-day VaR of the portfolio at the 95 percent confidence level, assuming 252 trading days in a year? a. b. c. d.

6.

An IO has positive duration. An IO has negative duration. An IO has exactly the same duration as a mortgage-backed security (MBS) with the same coupon. An IO has exactly the same duration as a mortgage-backed, principal-only security stripped off the same MBS.

0.714 1.430 2.240 5.000



7.

You are evaluating the credit risk in a portfolio comprised of Loan A and Loan B. In particular, you are interested in the risk contribution of each of the loans to the unexpected loss of the portfolio. Given the information in the table below, and assuming that the correlation of default between Loan A and Loan B is 20%, what is the risk contribution of Loan A to the risk of the portfolio? Adjusted Exposure Loan A Loan B

a. b. c. d.

8.

Volatility of Expected Default Frequency

Loss Given Default

Volatility of Loss Given Default

1.5% 3.5%

7.0% 12.0%

30% 45%

20% 30%

39,587 62,184 96,794 120,285

A hedge fund is considering taking positions in various tranches of a collateralized debt obligation (CDO). The fund’s chief economist predicts that the default probability will decrease significantly and that the default correlation will increase. Based on this prediction, which of the following is a good strategy to pursue? a. b. c. d.

9.

USD USD USD USD

USD 3,000,000 USD 2,000,000

Expected Default Frequency

Buy the senior tranche and buy the equity tranche. Buy the senior tranche and sell the equity tranche. Sell the senior tranche and sell the equity tranche. Sell the senior tranche and buy the equity tranche.

Sacks Bank has many open derivative positions with Lake Investments. A description and current market values are displayed in the table below: Positions

Market Price (USD)

Long swaptions Long credit default swaps Short currency derivatives

10 million -25 million 25 million

In the event that Lake defaults, what would be the loss to Sacks if netting is used? a. b. c. d.

USD USD USD USD



39


10.

Mike Merton is the head of credit derivatives trading at an investment bank. He is monitoring a new credit default swap basket that is made up of 20 bonds, each with a 1% annual probability of default. Assuming the probability of any one bond defaulting is completely independent of what happens to other bonds in the basket, what is the probability that exactly one bond defaults in the first year? a. b. c. d.

11.

12.

2.06% 3.01% 16.5% 30.1%

The Basel Committee recommends that banks use a set of early warning indicators in order to identify emerging risks and potential vulnerabilities in its liquidity position. Which of the following are not early warning indicators of a potential liquidity problem? i. ii. iii. iv.

Rapid asset growth Negative publicity Credit rating downgrade Increased asset diversification

a. b. c. d.

ii and iii iv only i and iv i, ii and iv

Using approved approaches, Barlop Bank has calculated the following values: Risk-weighted assets for credit risk, RWAc: Market risk capital requirement, CRm: Operational risk capital requirement, CRo:

USD 47 million USD 3.2 million USD 2.8 million

Assuming Tier 3 capital is USD 0, in which scenario below does Barlop Bank meet the Basel II minimum capital requirement?

a. b. c. d.

40

(all figures in USD million) Tier 1 Capital Tier 2 Capital 6.8 3.2 6.2 4.8 6.2 8.4 4.8 6.2

Deductions 0.4 0.8 2.8 0.0



13.

Jeremy Park and Brian Larksen are both portfolio managers who hold identical long positions worth GBP 100 million in the FTSE 1000 index. To hedge their respective portfolios, Park shorts FTSE 1000 futures contracts while Larksen buys put options on the FTSE 1000. Who has a higher Liquidity-at-Risk (LaR) measure? a. b. c. d.

14.

15.

Larksen Park Both have the same LaR Insufficient information to determine

Based on “Supervisory Guidance for Assessing Banks’ Financial Instrument Fair Value Practices” issued by the Basel Committee, which of the following factors should be considered in determining whether the sources of fair values are reliable and relevant? i. ii. iii. iv.

Frequency and availability of prices / quotes Maturity of the market Agreement of values with those generated by internal models Number of independent sources that produce the prices / quotes

a. b. c. d.

i and ii only iii and iv only i, ii and iii only i, ii, and iv only

Major Investments is an asset management firm with USD 25 billion under management. It owns 20% of the stock of a company. Major Investments’ risk manager is concerned that, in the event the entire position needs to be sold, its size would affect the market price. His estimate of the price elasticity of demand is -0.5. What is the increase in Major Investments’ Value-at-Risk estimate for this position if a liquidity adjustment is made? a. b. c. d.

4% 10% 15% 20%


41


16.

Which of the following statements about convertible arbitrage hedge fund strategies is correct? a. b. c. d.

17.

18.

Credit risk plays only a minor role in convertible arbitrage hedge funds. Investing in convertible arbitrage does not require an understanding of liquidity considerations as the market for convertible securities is sufficiently liquid today. Gamma trading entails significant directional exposure to the equity markets. Re-hedging after a large gain yields trading gains for a typical hedged position in convertible arbitrage hedge funds.

You are evaluating the performance of Valance, an equity fund designed to mimic the performance of the Russell 2000 Index. Based upon the information provided below, what is the best estimate of the tracking error of Valance relative to the Russell 2000 Index? • • •

Annual volatility of Valance: Annual volatility of the Russell 2000 Index: Correlation between Valance and the Russell 2000 Index:

a. b. c. d.

3.1% 17.5% 39.6% 53.2%

35% 40% 0.90

Consider a USD 1 million portfolio with an equal investment in two funds, Alpha and Omega, with the following annual return distributions: Fund

Expected Return

Volatility

Alpha Omega

5% 7%

20% 25%

Assuming the returns follow the normal distribution and that there are 252 trading days per year, what is the maximum possible daily 95% Value-at-Risk (VaR) estimate for the portfolio? a. b. c. d.

42

USD USD USD USD

16,587 23,316 23,459 32,973



19.

Which of the following statements about the impact of rising home prices on mortgages is incorrect? a. b. c. d.

20.

Negative convexity limits mortgage price appreciation. Higher prepayment penalties increase the payout to banks in the event mortgagors refinance to “cash out” on their equity. The expected life of a mortgage with a low teaser rate increases as the size of the step-up rate increases. Expected losses decrease as the value of mortgage collateral increases.

A simplified version of New Pavonia Bank is shown below. Which of the following statements about the bank is correct? Assets (USD)

Liabilities (USD)

100,000,000

Deposits: Repos: Long Term Debt: Equity:

40,000,000 30,000,000 22,000,000 8,000,000

Total Assets: 100,000,000

Total Liabilities and Equity:

100,000,000

a. b. c. d.

New Pavonia Bank clearly meets its Basel II capital requirements. The risks that threaten New Pavonia Bank are on the asset side because it has diversified its sources of financing. A bank such as New Pavonia Bank could have been threatened during the crisis if there was strong information asymmetry about the value of the securities it used for repos. Deposit runs are the most likely type of run that could threaten New Pavonia Bank.


43


Answers


a.

b.

a.

b.

c.

15.

16.

17.

5.

18.

6.

19.

7.

20.

8. 9.

d.

14.

3. 4.

d.

1. 2.

c.


10.

1.

11.


12.

1.

13.


✓

✘

45


Explanations


1.

In an effort to hedge some of your portfolio’s commodity exposure, you purchased a look-back put on 100,000 pounds of copper for the period from June 30, 2009 through June 30, 2010. The price of copper over this period is shown in the chart below. What was the payoff at expiration of this option?

a. b. c. d.

USD USD USD USD

0 100,000 200,000 300,000

Answer: c Explanation: Look-back options are options which the holder can buy/sell the underlying asset at the lowest/highest price achieved during the life of the option. A put look-back option is the option to sell at the highest price. The payoffs from look-back options depend on the maximum or minimum price reached during the life of the option. The payoff of a look-back put is the difference between the maximum price of the underlying asset over the time period covered by the option (USD 4), less the price at expiration (USD 2): 100,000 * (USD 4 – USD 2) = USD 200,000 Topic: Market Risk Measurement and Management Subtopic: Exotic Options AIMS: List and describe the characteristics and pay-off structures of look-back options. Reference: John Hull: Options, Futures, and Other Derivatives, 7th Edition (New York: John Wiley, 2009), Chapter 24: Exotic Options


47


2.

Which of the following statements about correlation and copula are correct? i.

Copula enables the structures of correlation between variables to be calculated separately from their marginal distributions. ii. Transformation of variables does not change their correlation structure. iii. Correlation can be a useful measure of the relationship between variables drawn from a distribution without a defined variance. iv. Correlation is a good measure of dependence when the measured variables are distributed as multivariate elliptical. a. b. c. d.

i and iv only ii, iii, and iv only i and iii only ii and iv only

Answer: a Explanation: “i” is true. Using the copula approach, we can calculate the structures of correlation between variables separately from the marginal distributions. “iv” is also true. Correlation is a good measure of dependence when the measured variables are distributed as multivariate elliptical. “ii” is false. The correlation between transformed variables will not always be the same as the correlation between those same variables before transformation. Data transformation can sometimes alter the correlation estimate. “iii” is also false. Correlation is not defined unless variances are finite. Topic: Market Risk Measurement and Management Subtopic: Modeling Dependence: Correlations and Copulas—Copulas and Tail Dependence AIMS: Explain the drawbacks of using correlation to measure dependence. Describe how copulas provide an alternative measure of dependence. Reference: Kevin Dowd: Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley, 2005), Chapter 5: Modeling Dependence: Correlations and Copulas

48



3.

Which of the following about the duration of a mortgage-backed, interest-only security (IO) is correct? a. b. c. d.

An IO has positive duration. An IO has negative duration. An IO has exactly the same duration as a mortgage-backed security (MBS) with the same coupon. An IO has exactly the same duration as a mortgage-backed, principal-only security stripped off the same MBS.

Answer: b Explanation: The IO holder benefits from rising rates. If rates are rising, prepays slow. Thus, IOs have negative duration and can be used for hedging purposes. An IO’s price moves in the same direction as interest rate changes, implying negative duration. An MBS has positive duration, as it is inversely proportional to interest rate changes. Likewise, a PO has positive duration, as it is inversely proportional to interest rate changes. Topic: Market Risk Measurement and Management Subtopic: Mortgages and Mortgage-Backed Securities AIMS: Discuss the impact of interest rates and prepayments on different portions of CMOs, IO and PO strips. Reference: Bruce Tuckman: Fixed Income Securities: Tools for Today’s Markets, 2nd Edition (Hoboken, NJ: John Wiley, 2002), Chapter 21: Mortgage-Backed Securities


49


4.

The Chief Risk Officer of Martingale Investments Group is planning a change in methodology for some of the risk management models used to estimate risk measures. His aim is to move from models that use the normal distribution of returns to models that use the distribution of returns implied by market prices. Martingale Group has a large long position in the German equity stock index DAX which has a volatility smile that slopes downward to the right. How will the change in methodology affect the estimate of expected shortfall (ES)? a. b. c. d.

ES with the updated models will be larger than the old estimate. ES with the updated models will be smaller than the old estimate. ES will remain unchanged. Insufficient information to determine.

Answer: a Explanation: A volatility smile is a common graphical shape that results from plotting the strike price and implied volatility of a group of options with the same expiration date. Since the volatility smile is downward sloping to the right, the implied distribution has a fatter left tail compared to the lognormal distribution of returns. This means that an extreme decrease in the DAX has a higher probability of occurrence under the implied distribution than the lognormal. The ES will therefore be larger when the methodology is modified. Topic: Market Risk Measurement and Management Subtopic: Volatility Smiles and Volatility Term Structures AIMS: Explain and calculate expected shortfall (ES), and compare and contrast VaR and ES. Relate the shape of the volatility smile (or skew) to the shape of the implied distribution of the underlying asset price. References: Kevin Dowd: Measuring Market Risk, 2nd Edition (John Wiley, 2005), Chapter 3: Estimating Market Risk Measures: An Introduction and Overview, and John Hull: Options, Futures, and Other Derivatives, 7th Edition (New York: John Wiley, 2009), Chapter 18: Volatility Smiles

50



5.

A portfolio manager owns a portfolio of options on a non-dividend paying stock RTX. The portfolio is made up of 10,000 deep in-the-money call options on RTX and 50,000 deep out-of-the money call options on RTX. The portfolio also contains 20,000 forward contracts on RTX. RTX is trading at USD 100. If the volatility of RTX is 30% per year, which of the following amounts would be closest to the 1-day VaR of the portfolio at the 95 percent confidence level, assuming 252 trading days in a year? a. b. c. d.

USD USD USD USD

932 93,263 111,122 131,892

Answer: b Explanation: We need to map the portfolio to a position in the underlying stock RTX. A deep in-the-money call has a delta of approximately 1, a deep out-of-the-money call has delta of approximately 0 and forwards have a delta of 1. The net portfolio has a delta of about 30,000 and is approximately gamma neutral. The 1-day VaR estimate at 95 percent confidence level is computed as follows: a x S x Δ x σ x sqrt(1/T) = 1.645 x 100 x 30,000 x 0.30 x .sqrt(1/252) = 93,263 Topic: Market Risk Measurement and Management Subtopic: VaR Mapping—Mapping Financial Instruments to Risk Factors AIMS: Describe the method of mapping forwards, commodity forwards, forward rate agreements, and interest rate swaps. Describe the method of mapping options. Reference: Philippe Jorion: Value at Risk: The New Benchmark for Managing Financial Risk, 3rd Edition (New York: McGraw-Hill, 2007), Chapter 11: VaR Mapping


51


6.

An analyst is using Moody’s KMV model to estimate the distance to default of a large public firm, Shoos Inc., a firm that designs, manufactures and sells athletic shoes. The firm’s capital structure consists of USD 40 million in short-term debt, USD 20 million in long-term debt, and there are one million shares of stock currently trading at USD 10 per share. The asset volatility is 20% per year. What is the normalized distance to default for Shoos Inc.? a. b. c. d.

0.714 1.430 2.240 5.000

Answer: b Explanation: Moody’s KMV model is a model for predicting private company defaults. It covers many geographic specific models, and each model reflects the unique lending, regulatory, and accounting practices of that region. Moody’s KMV computes the normalized distance to default as: DD =

A–K AsA

where “K” (floor) is defined as the value of all short term liabilities (one year and under) plus one half of the book value of all long term debt: 40 million + 0.5 x 20 million = 50 million “A” is the value of assets: Market value of equity (1 million shares x 10/share = 10 million) plus the book value of all debt (60 million) = 70 million thus AsA = 20% x 70 million = 14 million DD = (70 million – 50 million) / 14 = 1.429 standard deviations Topic: Credit Risk Measurement and Management Subtopic: Credit Risks and Credit Derivatives—Credit Spreads AIMS: Discuss the fundamental differences between CreditRisk+, CreditMetrics and KMV credit portfolio models. Reference: Rene Stulz: Risk Management and Derivatives, 1st Edition (South-Western, 2003), Chapter 18: Credit Risks and Credit Derivatives

52



7.

You are evaluating the credit risk in a portfolio comprised of Loan A and Loan B. In particular, you are interested in the risk contribution of each of the loans to the unexpected loss of the portfolio. Given the information in the table below, and assuming that the correlation of default between Loan A and Loan B is 20%, what is the risk contribution of Loan A to the risk of the portfolio? Adjusted Exposure Loan A Loan B

a. b. c. d.

USD USD USD USD

USD 3,000,000 USD 2,000,000

Expected Default Frequency

Volatility of Expected Default Frequency

Loss Given Default

Volatility of Loss Given Default

1.5% 3.5%

7.0% 12.0%

30% 45%

20% 30%

39,587 62,184 96,794 120,285

Answer: b Explanation: Risk contribution is a critical risk measure for assessing credit risk. The risk contribution of a risky assets “RC” to the portfolio unexpected loss, is defined as the incremental risk that the exposure of a single asset contributes to the portfolio’s total risk. Mathematically: RCA = (ULA2 + p x ULA x ULB)/ULP UL = V x sqrt(EDF x VARLGD + LGD2 x VAREDF) therefore: ULA = 3,000,000 x sqrt(1.5% x 20%2 + 30%2 x 7%2) = 96,793.59 ULB = 2,000,000 x sqrt(3.5% x 30%2 + 45%2 x 12%2) = 155,769.06 ULP = sqrt(96793.592 + 155,769.062 + 2 x 20% x 96,793.59 x 155,769.06) = 199,158.17 RCA = (96,793.592 + 20% x 96,793.59 x 155,769.06) / 199,158.17 = 62,184.19 Topic: Credit Risk Measurement and Management Subtopic: Portfolio Effects: Risk Contribution and Unexpected Losses—Expected and Unexpected Losses AIMS: Define, calculate and interpret expected and unexpected portfolio loss. Reference: Michael Ong: Internal Credit Risk Models: Capital Allocation and Performance Measurement (London: Risk Books, 1999), Chapter 6: Portfolio Effects: Risk Contributions and Unexpected Losses


53


8.

A hedge fund is considering taking positions in various tranches of a collateralized debt obligation (CDO). The fund’s chief economist predicts that the default probability will decrease significantly and that the default correlation will increase. Based on this prediction, which of the following is a good strategy to pursue? a. b. c. d.

Buy the senior tranche and buy the equity tranche. Buy the senior tranche and sell the equity tranche. Sell the senior tranche and sell the equity tranche. Sell the senior tranche and buy the equity tranche.

Answer: d Explanation: The decrease in probability of default would increase the value of the equity tranche. Also, a default of the equity tranche would increase the probability of default of the senior tranche, due to increased correlation, reducing its value. Thus, it is better to go long the equity tranche and short the senior tranche. Topic: Credit Risk Measurement and Management Subtopic: Credit Derivatives—Default and Default-time Correlations AIMS: Describe asset backed securities including collateralized debt obligations (CDOs) and explain tranches role of correlation in valuing CDOs. Reference: John Hull: Options, Futures, and Other Derivatives, 7th Edition (New York: Pearson, 2009), Chapter 23: Credit Derivatives

54



9.

Sacks Bank has many open derivative positions with Lake Investments. A description and current market values are displayed in the table below: Positions

Market Price (USD)

Long swaptions Long credit default swaps Short currency derivatives

10 million -25 million 25 million

In the event that Lake defaults, what would be the loss to Sacks if netting is used? a. b. c. d.

USD USD USD USD


Answer: b Explanation: Netting means that the payments between the two counterparties are netted out, so that only a net payment has to be made. With netting, Sacks is not required to make the payout of 25 million. Hence the loss will be reduced to: 35 million – 25 million = 10 million Topic: Credit Risk Measurement and Management Subtopic: Credit Risk – Risk Mitigation Techniques AIMS: Describe the following credit mitigation techniques: netting. Reference: John Hull: Options, Futures, and Other Derivatives, 7th Edition (New York: Pearson, 2009), Chapter 22: Credit Risk


55


10.

Mike Merton is the head of credit derivatives trading at an investment bank. He is monitoring a new credit default swap basket that is made up of 20 bonds, each with a 1% annual probability of default. Assuming the probability of any one bond defaulting is completely independent of what happens to other bonds in the basket, what is the probability that exactly one bond defaults in the first year? a. b. c. d.

2.06% 3.01% 16.5% 30.1%

Answer: c Explanation: C20p1 (1 – p)19 = 20 x 0.01 x (1 – 0.01)19 = 0.1652 1

Topic: Credit Risk Measurement and Management Subtopic: Credit Derivatives—Probability of Default, Loss Given Default and Recovery Rates AIMS: Compute the value of a CDS, given unconditional default probabilities, survival probabilities, market yields, recovery rates and cash flows. Reference: John Hull: Options, Futures, and Other Derivatives, 7th Edition (New York: Pearson, 2009), Chapter 23: Credit Derivatives

56



11.

The Basel Committee recommends that banks use a set of early warning indicators in order to identify emerging risks and potential vulnerabilities in its liquidity position. Which of the following are not early warning indicators of a potential liquidity problem? i. ii. iii. iv.

Rapid asset growth Negative publicity Credit rating downgrade Increased asset diversification

a. b. c. d.

ii and iii iv only i and iv i, ii and iv

Answer: b Explanation: Rapid asset growth, negative publicity and credit rating downgrade are all early warnings of a potential liquidity problem. Increased asset diversification is not an early warning indicator of liquidity. Topic: Operational Risk Measurement and Management Subtopic: Liquidity Risk AIMS: Describe the principles involved in the governance of liquidity risk, the measurement and management of liquidity risk and public disclosure. Reference: Principles of Sound Liquidity Risk Management and Supervision” (Basel Committee on Banking Supervision Publication, September 2008)


57


12.

Using approved approaches, Barlop Bank has calculated the following values: Risk-weighted assets for credit risk, RWAc: Market risk capital requirement, CRm: Operational risk capital requirement, CRo:

USD 47 million USD 3.2 million USD 2.8 million

Assuming Tier 3 capital is USD 0, in which scenario below does Barlop Bank meet the Basel II minimum capital requirement?

a. b. c. d.

(all figures in USD million) Tier 1 Capital Tier 2 Capital 6.8 3.2 6.2 4.8 6.2 8.4 4.8 6.2

Deductions 0.4 0.8 2.8 0.0

Answer: b Explanation: The total risk-weighted assets are: RWAt = RWAc + 12.5 x (CRm + CRo) = 47 + 12.5 x (3.2 + 2.8) = USD 122 million Eligible regulatory capital is: RC = Tier 1 + Tier 2 – Deductions In addition, Tier 2 capital must be less than or equal to Tier 1 capital. Minimum capital requirement is: RC / RWAt >= 8%. In this case, RC >= 0.08 x 122 = 9.76 RC = 6.8 + min(3.2, 6.8) – 0.4 = 9.6 RC = 6.2 + min(4.8, 6.2) – 0.8 = 10.2 RC = 6.2 + min(8.4, 6.2) – 2.8 = 9.6 RC = 4.8 + min(6.2, 4.8) – 0.0 = 9.6

(Fails to meet the minimum capital requirement) (Meets the minimum capital requirement) (Fails to meet the minimum capital requirement) (Fails to meet the minimum capital requirement)

Topic: Operational and Integrated Risk Management Subtopic: Regulation—Basel II Accord AIMS: Define in the context of Basel II and calculate: Capital ratio and capital charge Risk weights and risk-weighted assets Tier 1 capital, Tier 2 capital and Tier 3 capital Reference: “Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework—Comprehensive Version” (Basel Committee on Banking Supervision Publication, June 2006)

58



13.

Jeremy Park and Brian Larksen are both portfolio managers who hold identical long positions worth GBP 100 million in the FTSE 1000 index. To hedge their respective portfolios, Park shorts FTSE 1000 futures contracts while Larksen buys put options on the FTSE 1000. Who has a higher Liquidity-at-Risk (LaR) measure? a. b. c. d.

Larksen Park Both have the same LaR Insufficient information to determine

Answer: b Explanation: The futures positions are exposed to margin calls in the event that the FTSE 1000 increases. Park, with the short futures position, is thus exposed more to liquidity risk (cash flow risk). The Park portfolio, hedged with the short futures contract, will thus have the higher LaR. Topic: Operational and Integrated Risk Management Subtopic: Estimating Liquidity Risks AIMS: Describe Liquidity at Risk (LaR) and discuss the factors that affect future cash flows. Reference: Kevin Dowd: Measuring Market Risk, 2nd Edition (John Wiley, 2005), Chapter 14: Estimating Liquidity Risks

14.

Based on “Supervisory Guidance for Assessing Banks’ Financial Instrument Fair Value Practices” issued by the Basel Committee, which of the following factors should be considered in determining whether the sources of fair values are reliable and relevant? i. ii. iii. iv.

Frequency and availability of prices / quotes Maturity of the market Agreement of values with those generated by internal models Number of independent sources that produce the prices / quotes

a. b. c. d.

i and ii only iii and iv only i, ii and iii only i, ii, and iv only

Answer: d Explanation: Agreement with internally generated values is not necessary or relevant. The other three factors should be considered in determining the reliability and relevancy of the sources of fair values. Topic: Operational and Integrated Risk Management Subtopic: Regulation—Fair Value Reference: “Supervisory Guidance for Assessing Bank’s Financial Instrument Fair Value Practices” (Basel Committee on Banking Supervision, April 2009).


59


15.

Major Investments is an asset management firm with USD 25 billion under management. It owns 20% of the stock of a company. Major Investments’ risk manager is concerned that, in the event the entire position needs to be sold, its size would affect the market price. His estimate of the price elasticity of demand is -0.5. What is the increase in Major Investments’ Value-at-Risk estimate for this position if a liquidity adjustment is made? a. b. c. d.

4% 10% 15% 20%

Answer: b Explanation: What is needed is a liquidity adjustment that reflects the response of the market to a possible trade. The formula to use is the ratio of LVaR to VaR: LVaR VaR

=1–

ΔP P

=1–h

ΔN N

The ratio of LVaR to VaR depends on the elasticity of demand h and the size of the trade, relative to the size of the market (ΔN/N). We are given: dN/N = .2 and that the price elasticity is -0.5. Thus dP/P = elasticity x dN/N = -0.1. Therefore LVaR/VaR = 1 – dP/P = 1 + 0.1 = 1.1 The liquidity adjustment increases the VaR by 10%. Topic: Operational and Integrated Risk Management Subtopic: Estimating Liquidity Risks AIMS: Discuss Endogenous Price approaches to LVaR, its motivation and limitations. Reference: Kevin Dowd: Measuring Market Risk, 2nd Edition (John Wiley, 2005), Chapter 14: Estimating Liquidity Risks

60



16.

Which of the following statements about convertible arbitrage hedge fund strategies is correct? a. b. c. d.

Credit risk plays only a minor role in convertible arbitrage hedge funds. Investing in convertible arbitrage does not require an understanding of liquidity considerations as the market for convertible securities is sufficiently liquid today. Gamma trading entails significant directional exposure to the equity markets. Re-hedging after a large gain yields trading gains for a typical hedged position in convertible arbitrage hedge funds.

Answer: d Explanation: Re-hedging after significant moves of the underlying stock price is the essence of gamma trading. Credit risk plays an important role in the risk profile of convertible arbitrage hedge funds. Liquidity considerations are essential. Ignorance of this risk can lead to devastating losses as the 2008 financial crisis showed. Gamma trading means frequent re-hedging of directional exposure after market moves. Topic: Risk Management and Investment Management Subtopic: Individual Hedge Fund Strategies – Risks of Specific Strategies AIMS: Describe the underlying characteristics, sources of returns and risk exposures of various hedge fund strategies including convertible arbitrage strategies. Reference: Lars Jaeger: Through the Alpha Smoke Screens: A Guide to Hedge Fund Returns (New York: Euromoney Institutional Investor Books, 2005), Chapter 5: Individual Hedge Fund Strategies


61


17.

You are evaluating the performance of Valance, an equity fund designed to mimic the performance of the Russell 2000 Index. Based upon the information provided below, what is the best estimate of the tracking error of Valance relative to the Russell 2000 Index? • • •

Annual volatility of Valance: Annual volatility of the Russell 2000 Index: Correlation between Valance and the Russell 2000 Index:

a. b. c. d.

3.1% 17.5% 39.6% 53.2%

35% 40% 0.90

Answer: b Explanation: ω2 = σ(p - B)2 = σ(p)2 + σ(B)2 – 2 x σ(p) x σ(B) x ρ = 0.352 + 0.42 – 2 x 0.35 x 0.4 x 0.9 = 0.0305 ω = 17.5% where p = B = ρ =

portfolio returns benchmark returns correlation between benchmark and portfolio

Topic: Risk Management and Investment Management Subtopic: VaR and Risk Budgeting in Investment Management—Risk decomposition and performance attribution AIMS: Define and calculate tracking error. Reference: Philippe Jorion: Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition (New York: McGraw‐Hill, 2007), Chapter 17: VaR and Risk Budgeting in Investment Management

62



18.

Consider a USD 1 million portfolio with an equal investment in two funds, Alpha and Omega, with the following annual return distributions: Fund

Expected Return

Volatility

Alpha Omega

5% 7%

20% 25%

Assuming the returns follow the normal distribution and that there are 252 trading days per year, what is the maximum possible daily 95% Value-at-Risk (VaR) estimate for the portfolio? a. b. c. d.

USD USD USD USD

16,587 23,316 23,459 32,973

Answer: b Explanation: This question tests that the candidate understands correlation in calculating portfolio VaR. From the table, we can get daily volatility for each fund: Fund Alpha volatility: 0.20 / 2520.5 = 1.260% Fund Omega volatility: 0.25 / 2520.5 = 1.575% Portfolio variance: 0.52 * 0.012592 + 0.52 * 0.015742 + 2 x 0.5 x 0.5 x 0.01259 x 0.01574 x ρ Portfolio volatility = (portfolio variance)0.5 Portfolio volatility is least when ρ = -1 → portfolio volatility = 0.1575% Portfolio volatility is greatest when ρ = 1 → portfolio volatility = 1.4175% Therefore, 95% VaR maximum is 1.645 x 0.014175 x 1,000,000 = USD23,316 Topic: Risk Management and Investment Management Subtopic: Portfolio Risk: Analytical Methods—Risk Decomposition and Performance Attribution AIMS: Compute diversified VaR, individual VaR, and undiversified VaR of a portfolio. Reference: Philippe Jorion: Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition (New York: McGraw‐Hill, 2007), Chapter 7: Portfolio Risk: Analytical Methods


63


19.

Which of the following statements about the impact of rising home prices on mortgages is incorrect? a. b. c. d.

Negative convexity limits mortgage price appreciation. Higher prepayment penalties increase the payout to banks in the event mortgagors refinance to “cash out” on their equity. The expected life of a mortgage with a low teaser rate increases as the size of the step-up rate increases. Expected losses decrease as the value of mortgage collateral increases.

Answer: c Explanation: Low teaser rates with high step-ups increase the desire of those who can refinance to do so, if home prices rise. Thus, the expected life of mortgages is shorter if home prices rise. Topic: Current Issues in Financial Markets AIMS: List differences between prime and subprime mortgages and borrowers. Reference: Gary Gorton: "The Panic of 2007," (August 2008)

64



20.

A simplified version of New Pavonia Bank is shown below. Which of the following statements about the bank is correct? Assets (USD)

Liabilities (USD)

100,000,000

Deposits: Repos: Long Term Debt: Equity:

40,000,000 30,000,000 22,000,000 8,000,000

Total Assets: 100,000,000

Total Liabilities and Equity:

100,000,000

a. b. c. d.

New Pavonia Bank clearly meets its Basel II capital requirements. The risks that threaten New Pavonia Bank are on the asset side because it has diversified its sources of financing. A bank such as New Pavonia Bank could have been threatened during the crisis if there was strong information asymmetry about the value of the securities it used for repos. Deposit runs are the most likely type of run that could threaten New Pavonia Bank.

Answer: c Explanation: Information about the securities’ values is asymmetric, meaning that the current holders have better information than potential buyers. There is not enough information in the problem to determine if the bank meets its Basel II capital requirements. Also, a run on repos is possible. Topic: Current Issues in Financial Markets AIMS: Explain how the ABX information together with the lack of information about the location of risks led to a loss in confidence on the part of banks. Reference: Gary Gorton: "The Panic of 2007," (August 2008)


65



Global Association of Risk Professionals 111 Town Square Place Suite 1215 Jersey City, New Jersey 07310 USA + 1 201.719.7210 2nd Floor Bengal Wing 9A Devonshire Square London, EC2M 4YN UK + 44 (0) 20 7397 9630 www.garp.org

About GARP | The Global Association of Risk Professionals (GARP) is a not-for-profit global membership organization dedicated to preparing professionals and organizations to make better informed risk decisions. Membership represents over 150,000 risk management practitioners and researchers from banks, investment management firms, government agencies, academic institutions, and corporations from more than 195 countries and territories. GARP administers the Financial Risk Manager (FRM®) and the Energy Risk Professional (ERP®) Exams; certifications recognized by risk professionals worldwide. GARP also helps advance the role of risk management via comprehensive professional education and training for professionals of all levels. www.garp.org.

© 2012 Global Association of Risk Professionals. All rights reserved. 02-12

2013

FRM Examination Practice Exam PART I and PART II


TABLE OF CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 2013 FRM Part I Practice Exam Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . .3 2013 FRM Part I Practice Exam Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 2013 FRM Part I Practice Exam Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . . . .15 2013 FRM Part I Practice Exam Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

2013 FRM Part II Practice Exam Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . .39 2013 FRM Part II Practice Exam Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 2013 FRM Part II Practice Exam Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . . .49 2013 FRM Part II Practice Exam Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51


i


INTRODUCTION



the Exam. Questions for the FRM Examination are derived






for the Exam.


Suggested Use of Practice Exams To maximize the effectiveness of the Practice Exams, candidates are encouraged to follow these recommendations:




Set dates appropriately to give sufficient study/



issues and be able to deal with them effectively.

actual Exam.



Examination in May and November 2013. These Practice

•


Exams are based on a sample of questions from the 2010

•


through 2012 FRM Examinations and are suggestive of the

erasers) available.

questions that will be in the 2013 FRM Examination. The 2013 FRM Practice Exam for Part I contains 25

•


•



multiple-choice questions and the 2013 FRM Practice Exam for Part II contains 20 multiple-choice questions. Note that the 2013 FRM Examination Part I will contain 100 multiple-


choice questions and the 2013 FRM Examination Part II will


contain 80 multiple-choice questions. The Practice Exams


were designed to be shorter to allow candidates to calibrate

•




The 2013 FRM Practice Exams do not necessarily cover all topics to be tested in the 2013 FRM Examination as the


material covered in the 2013 Study Guide may be different


from that that covered by the 2010 through 2012 Study


Guides. The questions selected for inclusion in the Practice Exams were chosen to be broadly reflective of the material assigned for 2013 as well as to represent the style of question



that the FRM Committee considers appropriate based on


assigned material.

include questions completed in the first 60 minutes. •

Use the Practice Exam Answers and Explanations


to better understand correct and incorrect






1


Answer Sheet


a.

b.

c.

d.

a.

1.

16.

2.

17.

3.

18.

4.

19.

5.

20.

6.

21.

7.

22.

8.

23.

9.

24.

10.

25.

b.

c.

d.

✓

✘

11. 12.


13.

1.

14.


15.

1.


3


Questions


1.

You are deciding between buying a futures contract on an exchange and buying a forward contract directly from a counterparty on the same underlying asset. Both contracts would have the same maturity and delivery specifications. You find that the futures price is less than the forward price. Assuming no arbitrage opportunity exists, what single factor acting alone would be a realistic explanation for this price difference? a. b. c. d.

2.

futures contract is more liquid and easier to trade. forward contract counterparty is more likely to default. asset is strongly negatively correlated with interest rates. transaction costs on the futures contract are less than on the forward contract.

Eric Meyers is a trader in the arbitrage unit of a multinational bank. He finds that an asset is trading at USD 1,000, the price of a 1-year futures contract on that asset is USD 1,010, and the price of a 2-year futures contract is USD 1,025. Assume that there are no cash flows from the asset for 2 years. If the term structure of interest rates is flat at 1% per year, which of the following is an appropriate arbitrage strategy? a. b. c. d.

3.

The The The The

Short Short Short Short

2-year futures and long 1-year futures 1-year futures and long 2-year futures 2-year futures and long the underlying asset funded by borrowing for 2 years 1-year futures and long the underlying asset funded by borrowing for 1 year

The price of a six-month European call option on a stock is USD 3. The stock price is USD 24. A dividend of USD 1 is expected in three months. The continuously compounded risk-free rate for all maturities is 5% per year. Which of the following is closest to the value of a put option on the same underlying stock with a strike price of USD 25 and a time to maturity of six months? a. b. c. d.

USD USD USD USD

3.60 2.40 4.37 1.63


5


4.

Which of the following statements regarding the trustee named in a corporate bond indenture is correct? a. b. c. d.

5.

trustee trustee trustee trustee

has the authority to declare a default if the issuer misses a payment. may take action beyond the indenture to protect bondholders. must act at the request of a sufficient number of bondholders. is paid by the bondholders or their representatives.

Pear, Inc. is a manufacturer that is heavily dependent on plastic parts shipped from Malaysia. Pear wants to hedge its exposure to plastic price shocks over the next 7 ½ months. Futures contracts, however, are not readily available for plastic. After some research, Pear identifies futures contracts on other commodities whose prices are closely correlated to plastic prices. Futures on Commodity A have a correlation of 0.85 with the price of plastic, and futures on Commodity B have a correlation of 0.92 with the price of plastic. Futures on both Commodity A and Commodity B are available with 6-month and 9-month expirations. Ignoring liquidity considerations, which contract would be the best to minimize basis risk? a. b. c. d.

6.

The The The The

Futures Futures Futures Futures

on on on on

Commodity Commodity Commodity Commodity

A with 6 months to expiration A with 9 months to expiration B with 6 months to expiration B with 9 months to expiration

You are examining the exchange rate between the U.S. dollar and the euro and are given the following information regarding the USD/EUR exchange rate and the respective domestic risk-free rates: Current USD/EUR exchange rate is 1.25 Current USD-denominated 1-year risk-free interest rate is 4% per year Current EUR-denominated 1-year risk-free interest rate is 7% per year According to the interest rate parity theorem, what is the 1-year forward USD/EUR exchange rate? a. b. c. d.

6

0.78 0.82 1.21 1.29



7.

An investor sells a January 2014 call on the stock of XYZ Limited with a strike price of USD 50 for USD 10, and buys a January 2014 call on the same underlying stock with a strike price of USD 60 for USD 2. What is the name of this strategy, and what is the maximum profit and loss the investor could incur at expiration?

a. b. c. d.

8.

Strategy Bear spread Bull spread Bear spread Bull spread

Maximum Profit USD 8 USD 8 Unlimited USD 8

Maximum Loss USD 2 Unlimited USD 2 USD 2

Samantha Xiao is trying to get some insight into the relationship between the return on stock LMD (RLMD,t) and the return on the S&P 500 index (RS&P,t). Using historical data she estimates the following: Annual mean return for LMD: Annual mean return for S&P 500 index: Annual volatility for S&P 500 index: Covariance between the returns of LMD and S&P 500 index:

11% 7% 18% 6%

Assuming she uses the same data to estimate the regression model given by: RLMD,t = α + βR

S&P,t

+ εt

Using the ordinary least squares technique, which of the following models will she obtain? a. b. c. d.

RLMD,t RLMD,t RLMD,t RLMD,t

= -0.02 + 0.54RS&P,t + εt = -0.02 + 1.85RS&P,t + εt = 0.04 + 0.54RS&P,t + εt = 0.04 + 1.85RS&P,t + εt


7


9.

For a sample of 400 firms, the relationship between corporate revenue (Yi) and the average years of experience per employee (Xi) is modeled as follows: Yi = β1 + β2 Xi + εi, i = 1, 2,...,400

You wish to test the joint null hypothesis that β1 = 0 and β2 = 0 at the 95% confidence level. The p-value for the t-statistic for β1 is 0.07, and the p-value for the t-statistic for β2 is 0.06. The p-value for the F-statistic for the regression is 0.045. Which of the following statements is correct? a. b. c. d.

10.

can reject the null hypothesis because each β is different from 0 at the 95% confidence level. cannot reject the null hypothesis because neither β is different from 0 at the 95% confidence level. can reject the null hypothesis because the F-statistic is significant at the 95% confidence level. cannot reject the null hypothesis because the F-statistic is not significant at the 95% confidence level.

A fixed income portfolio manager currently holds a portfolio of bonds of various companies. Assuming all these bonds have the same annualized probability of default and that the defaults are independent, the number of defaults in this portfolio over the next year follows which type of distribution? a. b. c. d.

11.

You You You You

Bernoulli Normal Binomial Exponential

A portfolio manager has asked each of four analysts to use Monte Carlo simulation to price a path-dependent derivative contract on a stock. The derivative expires in nine months and the risk-free rate is 4% per year compounded continuously. The analysts generate a total of 20,000 paths using a geometric Brownian motion model, record the payoff for each path, and present the results in the table shown below.

Analyst

Number of Paths

Average Derivative Payoff per Path (USD)

1

2,000

43

2

4,000

44

3

10,000

46

4

4,000

45

What is the estimated price of the derivative? a. b. c. d.

8

USD USD USD USD

43.33 43.77 44.21 45.10



12.

Suppose that the correlation of the return of a portfolio with the return of its benchmark is 0.8, the volatility of the return of the portfolio is 5%, and the volatility of the return of the benchmark is 4%. What is the beta of the portfolio? a. b. c. d.

13.

Firms commonly incentivize their management to increase the firm’s value by granting managers securities tied to the firm’s stock. Some securities, however, can reduce managerial incentives to manage risk within the firm. Which is likely the best example of this type of security? a. b. c. d.

14.

1.00 0.80 0.64 -1.00

Deep in-the-money call option on the firm’s stock At-the-money call option on the firm’s stock Deep out-of-the-money call option on the firm’s stock Long position in the firm’s stock

You have been asked to check for arbitrage opportunities in the Treasury bond market by comparing the cash flows of selected bonds with the cash flows of combinations of other bonds. If a 1-year zero-coupon bond is priced at USD 96.12 and a 1-year bond paying a 10% coupon semi-annually is priced at USD 106.20, what should be the price of a 1-year Treasury bond that pays a coupon of 8% semi-annually? a. b. c. d.

USD USD USD USD

98.10 101.23 103.35 104.18


9


15.

If the current market price of a stock is USD 50, which of the following options on the stock has the highest gamma? a. b. c. d.

16.

Call option expiring in 30 days with strike price of USD 50 Call option expiring in 5 days with strike price of USD 30 Call option expiring in 5 days with strike price of USD 50 Put option expiring in 30 days with strike price of USD 30

John Starwood is an investment advisor at Metuchen Investment Advisors (MIA). Starwood is advising Michael Cooke, a wealthy client of MIA. Cooke would like to invest USD 500,000 in a bond rated at least AA. Starwood is considering bonds issued by IBM, GE, and Microsoft, and wants to choose a bond that satisfies Cooke’s rating requirement, but also has the highest yield to maturity. He has access to the following information:

IBM

GE

Microsoft

S&P Bond Rating

AA+

A+

AAA

Semiannual Coupon

1.75%

1.78%

1.69%

Term to Maturity in years

5

5

5

Price (USD)

975

973

989

Par value (USD)

1000

1000

1000

Which bond should Starwood purchase for Cooke? a. b. c. d.

17.

After evaluating the results of your firm’s stress tests, you are recommending that the firm allocate additional economic capital and purchase selective insurance protection to guard against particular events. In order to give management a fully informed assessment, it is important that you note the following, related to this strategy: a. b. c. d.

10

GE bond IBM bond Microsoft bond Either the Microsoft bond or the GE bond

While While While While

decreasing decreasing decreasing decreasing

liquidity risk exposure, it will likely increase market risk exposure. correlation risk exposure, it will likely increase credit risk exposure. market risk exposure, it will likely increase credit risk exposure. credit risk exposure, it will likely increase model risk exposure.



18.

A bank’s foreign loan portfolio contains a large concentration of loans to a country whose government has been running large external deficits. To evaluate the transfer risk that might exist in the event of stress, the greatest concern should be given to the possibility that the sovereign will impose restrictions on which of the following? a. b. c. d.

19.

A portfolio manager bought 1,000 call options on a non-dividend-paying stock, with a strike price of USD 100, for USD 6 each. The current stock price is USD 104 with a daily stock return volatility of 1.89%, and the delta of the option is 0.6. Using the delta-normal approach to calculate VaR, what is an approximation of the 1-day 95% VaR of this position? a. b. c. d.

20.

USD USD USD USD

112 1,946 3,243 5,406

Which of the following statements concerning the measurement of operational risk is correct? a. b. c. d.

21.

Imports Interest rates Exports Currency convertibility

Economic capital should be sufficient to cover both expected and worst-case operational risk losses. Loss severity and loss frequency tend to be modeled with lognormal distributions. Operational loss data available from data vendors tend to be biased towards small losses. The standardized approach used by banks in calculating operational risk capital allows for different beta factors to be assigned to different business lines.

The proper selection of factors to include in an ordinary least squares estimation is critical to the accuracy of the result. When does omitted variable bias occur? a. b. c. d.

Omitted variable bias occurs when the omitted determinant of the dependent variable. Omitted variable bias occurs when the omitted not a determinant of the dependent variable. Omitted variable bias occurs when the omitted determinant of the dependent variable. Omitted variable bias occurs when the omitted not a determinant of the dependent variable.

variable is correlated with the included regressor and is a variable is correlated with the included regressor but is variable is independent of the included regressor and is a variable is independent of the included regressor but is


11


22.

Assume that you are only concerned with systematic risk. Which of the following would be the best measure to use to rank order funds with different betas based on their risk-return relationship with the market portfolio? a. b. c. d.

23.

The collapse of Long Term Capital Management (LTCM) is a classic risk management case study. Which of the following statements about risk management at LTCM is correct? a. b. c. d.

24.

Formal notification to the GARP Member’s employer of such a violation Suspension of the GARP Member’s right to work in the risk management profession Removal of the GARP Member’s right to use the FRM designation Required participation in ethical training

Which of the following is assumed in the multiple least squares regression model? a. b. c. d.

12

LTCM had no active risk reporting. At LTCM, stress testing became a risk management department exercise that had little influence on the firm’s strategy. LTCM’s use of high leverage is evidence of poor risk management. LTCM failed to account properly for the illiquidity of its largest positions in its risk calculations.

Which of the following is a potential consequence of violating the GARP Code of Conduct once a formal determination is made that such a violation has occurred? a. b. c. d.

25.

Treynor ratio Sharpe ratio Jensen’s alpha Sortino ratio

The The The The

dependent variable is stationary. independent variables are not perfectly multicollinear. error terms are heteroskedastic. independent variables are homoskedastic.




13


Answers


a.

b.

c.

d.

a.

1.

16.

2.

17.

3.

18.

4.

6. 7.

8.

22.

23.

10.

25.

11.


1.

14. 15.

24.

13.

21.

d.

20.

9.

12.

c.

19.

5.

b.

✓

✘



15


Explanations


1.

You are deciding between buying a futures contract on an exchange and buying a forward contract directly from a counterparty on the same underlying asset. Both contracts would have the same maturity and delivery specifications. You find that the futures price is less than the forward price. Assuming no arbitrage opportunity exists, what single factor acting alone would be a realistic explanation for this price difference? a. b. c. d.

The The The The

futures contract is more liquid and easier to trade. forward contract counterparty is more likely to default. asset is strongly negatively correlated with interest rates. transaction costs on the futures contract are less than on the forward contract.

Correct answer: c Explanation: When an asset is strongly negatively correlated with interest rates, futures prices will tend to be slightly lower than forward prices. When the underlying asset increases in price, the immediate gain arising from the daily futures settlement will tend to be invested at a lower than average rate of interest due to the negative correlation. In this case futures would sell for slightly less than forward contracts, which are not affected by interest rate movements in the same manner since forward contracts do not have a daily settlement feature. The other three choices would all most likely result in the futures price being higher than the forward price. Reference: John Hull, Options, Futures and Other Derivatives, 8th Edition (New York: Pearson, 2012), Chapter 5. AIMS: Explain the relationship between forward and futures prices; Describe the differences between forward and futures contracts and explain the relationship between forward and spot prices. Section: Financial Markets and Products


17


2.

Eric Meyers is a trader in the arbitrage unit of a multinational bank. He finds that an asset is trading at USD 1,000, the price of a 1-year futures contract on that asset is USD 1,010, and the price of a 2-year futures contract is USD 1,025. Assume that there are no cash flows from the asset for 2 years. If the term structure of interest rates is flat at 1% per year, which of the following is an appropriate arbitrage strategy? a. b. c. d.


2-year futures and long 1-year futures 1-year futures and long 2-year futures 2-year futures and long the underlying asset funded by borrowing for 2 years 1-year futures and long the underlying asset funded by borrowing for 1 year

Correct answer: c Explanation: The 1-year futures price should be 1000 * e0.01 = 1010.05. The 2-year futures price should be 1000 * e0.01 = 1020.20. The current 2-year futures price in the market is overvalued compared to the theoretical price. To lock in a profit, you would short the 2 year futures, borrow USD 1000 at 1%, and buy the underlying asset. At the end of 2 years, you will sell the asset at USD 1025 and return the borrowed money with interest, which would be 1000* e0.02 = USD 1020.20, resulting in a USD 4.80 gain. Reference: John Hull, Options, Futures and Other Derivatives, 8th Edition (New York: Pearson, 2012), Chapter 5, p. 92. AIMS: Calculate the forward price, given the underlying asset’s price, with or without short sales and/or consideration to the income or yield of the underlying asset. Describe an arbitrage argument in support of these prices. Section: Financial Markets and Products

18



3.

The price of a six-month European call option on a stock is USD 3. The stock price is USD 24. A dividend of USD 1 is expected in three months. The continuously compounded risk-free rate for all maturities is 5% per year. Which of the following is closest to the value of a put option on the same underlying stock with a strike price of USD 25 and a time to maturity of six months? a. b. c. d.

USD USD USD USD

3.60 2.40 4.37 1.63

Correct answer: c Explanation: From the equation for put-call parity, this can be solved by the following equation: p = c + PV (K) + PV (D) — S0 where PV represents the present value, so that PV (K) = Ke-rT and PV (D) = De-rT Where: p represents the put price, c is the call price, K is the strike price of the put option, D is the dividend, S0 is the current stock price. T is the time to maturity of the option, and T is the time to the next dividend distribution.

Calculating PV (K), the present value of the strike price, results in a value of 25 * e-0.05*0.5 or 24.38, while PV (D) is equal to 1.00e-0.05*0.25, or 0.99. Hence p = 3 + 24.38 + 0.99 — 24 = US 4.37. Reference: John Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson 2012), Chapter 10, p. 158. AIM: Explain the effects of dividends on the put-call parity, the bounds of put and call option prices, and the early exercise feature of American options. Section: Financial Markets and Products


19


4.

Which of the following statements regarding the trustee named in a corporate bond indenture is correct? a. b. c. d.

The The The The

trustee trustee trustee trustee

has the authority to declare a default if the issuer misses a payment. may take action beyond the indenture to protect bondholders. must act at the request of a sufficient number of bondholders. is paid by the bondholders or their representatives.

Correct answer: a Explanation: According to the Trust Indenture Act, if a corporate issuer fails to pay interest or principal, the trustee may declare a default and take such action as may be necessary to protect the rights of bondholders. Trustees can only perform the actions indicated in the indenture, but are typically under no obligation to exercise the powers granted by the indenture even at the request of bondholders. The trustee is paid by the debt issuer, not by bondholders or their representatives. Reference: Frank Fabozzi, The Handbook of Fixed Income Securities, 8th Edition (New York: McGraw Hill, 2012), Chapter 12. AIM: Describe a bond indenture and explain the role of the corporate trustee in a bond indenture. Section: Financial Markets and Products

5.

Pear, Inc. is a manufacturer that is heavily dependent on plastic parts shipped from Malaysia. Pear wants to hedge its exposure to plastic price shocks over the next 7 ½ months. Futures contracts, however, are not readily available for plastic. After some research, Pear identifies futures contracts on other commodities whose prices are closely correlated to plastic prices. Futures on Commodity A have a correlation of 0.85 with the price of plastic, and futures on Commodity B have a correlation of 0.92 with the price of plastic. Futures on both Commodity A and Commodity B are available with 6-month and 9-month expirations. Ignoring liquidity considerations, which contract would be the best to minimize basis risk? a. b. c. d.

Futures Futures Futures Futures

on on on on

Commodity Commodity Commodity Commodity

A with 6 months to expiration A with 9 months to expiration B with 6 months to expiration B with 9 months to expiration

Correct answer: d Explanation: In order to minimize basis risk, one should choose the futures contract with the highest correlation to price changes, and the one with the closest maturity, preferably expiring after the duration of the hedge. Reference: John Hull, Options, Futures and Other Derivatives, 8th Edition (New York: Pearson, 2012), Chapter 3 — “Hedging Strategies Using Futures”, p. 47. AIM: Define the basis and the various sources of basis risk, and explain how basis risks arise when hedging with futures. Section: Financial Markets and Products

20



6.

You are examining the exchange rate between the U.S. dollar and the euro and are given the following information regarding the USD/EUR exchange rate and the respective domestic risk-free rates: Current USD/EUR exchange rate is 1.25 Current USD-denominated 1-year risk-free interest rate is 4% per year Current EUR-denominated 1-year risk-free interest rate is 7% per year According to the interest rate parity theorem, what is the 1-year forward USD/EUR exchange rate? a. b. c. d.

0.78 0.82 1.21 1.29

Correct answer: c Explanation: The forward rate, FT, is given by the interest rate parity equation: Ft =S0 * e(r-rf)T where S0 is the spot exchange rate, is the domestic (USD) risk-free rate, and rf is the foreign (EUR) risk-free rate T is the time to delivery r

Substituting the values in the equation: Ft = 1.25 * e(0.04-0.07) = 1.21 Reference: Anthony Saunders and Marcia Millon Cornett, Financial Institutions Management: A Risk Management Approach, 7th Edition (New York: McGraw-Hill, 2010), Chapter 15, p. 236. AIM: Describe how a no-arbitrage assumption in the foreign exchange markets leads to the interest rate parity theorem; use this theorem to calculate forward foreign exchange rates. Section: Financial Markets and Products


21


7.

An investor sells a January 2014 call on the stock of XYZ Limited with a strike price of USD 50 for USD 10, and buys a January 2014 call on the same underlying stock with a strike price of USD 60 for USD 2. What is the name of this strategy, and what is the maximum profit and loss the investor could incur at expiration?

a. b. c. d.

Strategy Bear spread Bull spread Bear spread Bull spread

Maximum Profit USD 8 USD 8 Unlimited USD 8

Maximum Loss USD 2 Unlimited USD 2 USD 2

Correct answer: a Explanation: This strategy of buying a call option at a higher strike price and selling a call option at lower strike price with the same maturity is known as a bear spread. To establish a bull spread, one would buy the call option at a lower price and sell a call on the same security with the same maturity at a higher strike price. The cost of the strategy will be: USD -10 + USD 2 = USD -8 (a negative cost, which represents an inflow of USD 8 to the investor) The maximum payoff occurs when the stock price ST ≤ USD 50 and is equal to USD 8 (the cash inflow from establishing the position) as none of the options will be exercised. The maximum loss occurs when the stock price ST ≥ 60 at expiration, as both options will be exercised. The investor would then be forced to sell XYZ shares at 50 to meet the obligations on the call option sold, but could exercise the second call to buy the shares back at 60 for a loss of USD -10. However, since the investor received an inflow of USD 8 by establishing the strategy, the total profit would be USD 8 - USD 10 = USD -2. When the stock price is USD 50 < ST ≤ USD 60, only the call option sold by the investor would be exercised, hence the payoff will be 50 — ST. Since the inflow from establishing the original strategy was USD 8, the net profit will be 58 — ST, which would always be higher than USD -2. Reference: John Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson 2012), Chapter 10, pp. 167-168. AIM: Identify, interpret and compute upper and lower bounds for option prices. Section: Financial Markets and Products

22



8.

Samantha Xiao is trying to get some insight into the relationship between the return on stock LMD (RLMD,t) and the return on the S&P 500 index (RS&P,t). Using historical data she estimates the following: Annual mean return for LMD: Annual mean return for S&P 500 index: Annual volatility for S&P 500 index: Covariance between the returns of LMD and S&P 500 index:

11% 7% 18% 6%

Assuming she uses the same data to estimate the regression model given by: RLMD,t = α + βR

S&P,t

+ εt

Using the ordinary least squares technique, which of the following models will she obtain? a. b. c. d.

= -0.02 + 0.54RS&P,t + εt = -0.02 + 1.85RS&P,t + εt = 0.04 + 0.54RS&P,t + εt = 0.04 + 1.85RS&P,t + εt

RLMD,t RLMD,t RLMD,t RLMD,t

Correct answer: b Explanation: The regression coefficients for a model specified by Y = b X + a + ε are obtained using the formula: 2 X

b = SXY/S

In this example: SXY = 0.06 Sx = 0.18 E(Y) = 0.11 Then: b = 0.06 / (0.18)2 = 1.85 a = E(Y) – b*E(X) = 0.11 – (1.85*0.07) = -0.02 where ε represents the error term.

Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008), Chapter 4, p. 64. AIM: Explain how regression analysis in econometrics measures the relationship between dependent and independent variables. Section: Quantitative Analysis


23


9.

For a sample of 400 firms, the relationship between corporate revenue (Yi) and the average years of experience per employee (Xi) is modeled as follows: Yi = β1 + β2 Xi + εi, i = 1, 2,...,400

You wish to test the joint null hypothesis that β1 = 0 and β2 = 0 at the 95% confidence level. The p-value for the t-statistic for β1 is 0.07, and the p-value for the t-statistic for β2 is 0.06. The p-value for the F-statistic for the regression is 0.045. Which of the following statements is correct? a. b. c. d.

You You You You

can reject the null hypothesis because each β is different from 0 at the 95% confidence level. cannot reject the null hypothesis because neither β is different from 0 at the 95% confidence level. can reject the null hypothesis because the F-statistic is significant at the 95% confidence level. cannot reject the null hypothesis because the F-statistic is not significant at the 95% confidence level.

Correct answer: c Explanation: The T-test would not be sufficient to test the joint hypothesis. In order to test the joint null hypothesis, examine the F-statistic, which in this case is statistically significant at the 95% confidence level. Thus the null can be rejected. Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief edition (Boston, Pearson Education, 2008), Chapter 7, pp. 128-129. AIM: Describe and interpret tests of single restrictions involving multiple coefficients, Define and interpret the F-statistic. Section: Quantitative Analysis

24



10.

A fixed income portfolio manager currently holds a portfolio of bonds of various companies. Assuming all these bonds have the same annualized probability of default and that the defaults are independent, the number of defaults in this portfolio over the next year follows which type of distribution? a. b. c. d.

Bernoulli Normal Binomial Exponential

Correct answer: c Explanation: The result would follow a Binomial distribution as there is a fixed number of random variables, each with the same annualized probability of default. It is not a Bernoulli distribution, as a Bernoulli distribution would describe the likelihood of default of one of the individual bonds rather than of the entire portfolio (i.e. a Binomial distribution essentially describes a group of Bernoulli distributed variables). A normal distribution is used to model continuous variables, while in this case the number of defaults within the portfolio is discrete. References: Michael Miller, Mathematics and Statistics for Financial Risk Management (Hoboken, NJ: John Wiley & Sons, 2012), Chapter 4. Svetlozar Rachev, Christian Menn, and Frank Fabozzi (2005), Chapter 3: Continuous Probability Distributions, Fat-Tailed and Skewed Asset Return Distributions: Implications for Risk Management, Portfolio Selection and Option Pricing (Hoboken, NJ: Wiley and Sons, 2005), Chapter 2: Discrete Probability Distributions. AIM: Describe the key properties of the uniform distribution, Bernoulli distribution, Binomial distribution, Poisson distribution, normal distribution and lognormal distribution, and identify common occurrences of each distribution. Section: Quantitative Analysis


25


11.

A portfolio manager has asked each of four analysts to use Monte Carlo simulation to price a path-dependent derivative contract on a stock. The derivative expires in nine months and the risk-free rate is 4% per year compounded continuously. The analysts generate a total of 20,000 paths using a geometric Brownian motion model, record the payoff for each path, and present the results in the table shown below.

Analyst

Number of Paths

Average Derivative Payoff per Path (USD)

1

2,000

43

2

4,000

44

3

10,000

46

4

4,000

45

What is the estimated price of the derivative? a. b. c. d.

USD USD USD USD

43.33 43.77 44.21 45.10

Correct answer: b Explanation: Following the risk neutral valuation methodology, the price of the derivative is obtained by calculating the weighted average nine month payoff and then discounting this figure by the risk free rate. Average payoff calculation: (2000*43 + 4000*44 +10000*46 + 4000*45)/20000 = 45.10 Discounted payoff calculation: 45.10*e(-0.04*(9/12)) = 43.77 Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition (New York: McGraw-Hill, 2007), Chapter 12: Monte Carlo Methods, pp. 167, 170. AIM: Explain how simulations can be used for computing VaR and pricing options. Section: Quantitative Analysis

26



12.

Suppose that the correlation of the return of a portfolio with the return of its benchmark is 0.8, the volatility of the return of the portfolio is 5%, and the volatility of the return of the benchmark is 4%. What is the beta of the portfolio? a. b. c. d.

1.00 0.80 0.64 -1.00

Correct answer: a Explanation: The following equation is used to calculate beta: β=ρ*

σ(portfolio) σ(benchmark)

= 0.8 *

0.05 0.04

= 1.00.

where ρ represents the correlation coefficient and σ the volatility. Reference: Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England: Wiley, 2003), Chapter 4, section 4.2. AIM: Define beta and calculate the beta of a portfolio. Section: Foundations of Risk Management


27


13.

Firms commonly incentivize their management to increase the firm’s value by granting managers securities tied to the firm’s stock. Some securities, however, can reduce managerial incentives to manage risk within the firm. Which is likely the best example of this type of security? a. b. c. d.

Deep in-the-money call option on the firm’s stock At-the-money call option on the firm’s stock Deep out-of-the-money call option on the firm’s stock Long position in the firm’s stock

Correct answer: c Explanation: Deep out-of-the-money calls have no value unless the firm value increases substantially, so providing deep out-of-the-money calls as an incentive could cause managers to take substantially higher risks and perform less hedging. With an at-the-money call, managers could still be incentivized to take greater risks but they would not have to aim for as large of a stock price increase to recognize significant value from their options, so the danger of mismanaging risk is less. A deep in-the-money call would have a similar investment profile as a long equity position and both of the latter choices would provide the least managerial incentive to reduce risk management. References: “Risk Taking: A Corporate Governance Perspective,” (International Finance Corporation, World Bank Group, June 2012.) John Hull, Options, Futures and Other Derivatives, 8th Edition, Chapter 1. René Stulz, Risk Management & Derivatives (Florence, KY: Thomson South-Western, 2002), Chapter 3, p. 30. AIM: Identify the methods a firm can use to exploit risk better than its competitors, and explain how an organization can create a culture of prudent risk-taking among its employees. AIM: Calculate and identify option and forward contract payoffs. Sections: Foundations of Risk Management, Financial Markets and Products

28



14.

You have been asked to check for arbitrage opportunities in the Treasury bond market by comparing the cash flows of selected bonds with the cash flows of combinations of other bonds. If a 1-year zero-coupon bond is priced at USD 96.12 and a 1-year bond paying a 10% coupon semi-annually is priced at USD 106.20, what should be the price of a 1-year Treasury bond that pays a coupon of 8% semi-annually? a. b. c. d.

USD USD USD USD

98.10 101.23 103.35 104.18

Correct answer: d Explanation: The solution is to replicate the 1 year 8% bond using the other two treasury bonds. In order to replicate the cash flows of the 8% bond, you could solve a system of equations to determine the weight factors, F1 and F2, which correspond to the proportion of the zero and the 10% bond to be held, respectively. The two equations are as follows: (100 * F1) + (105 * F2) = 104

(replicating the cash flow including principal and interest payments at the end of 1 year),

and (5*F2) = 4

(replicating the cash flow from the coupon payment in 6 months.)

Solving the two equations gives us F1 = 0.2 and F2 = 0.8. Thus the price of the 8% bond should be 0.2 (96.12) + 0.8 (106.2) = 104.18. Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: Wiley & Sons, 2011), Chapter 1. Originally based on the 2nd Edition. AIM: Derive a replicating portfolio using multiple fixed income securities in order to match the cash flows of a single given fixed income security. Section: Valuation and Risk Models


29


15.

If the current market price of a stock is USD 50, which of the following options on the stock has the highest gamma? a. b. c. d.

Call option expiring in 30 days with strike price of USD 50 Call option expiring in 5 days with strike price of USD 30 Call option expiring in 5 days with strike price of USD 50 Put option expiring in 30 days with strike price of USD 30

Correct answer: c Explanation: Gamma is defined as the rate of change of an option’s delta with respect to the price of the underlying asset, or the second derivative of the option price with respect to the asset price. Therefore the highest gamma is observed in shorter maturity and at-the-money options, since options with these characteristics are much more sensitive to changes in the underlying asset price. The correct choice is a call option both at-the-money and with the shorter maturity. Reference: John Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson, 2012), Chapter 18 — The Greek Letters, p. 104. AIM: Define and describe theta, gamma, vega, and rho for option positions. Section: Valuation and Risk Models

30



16.

John Starwood is an investment advisor at Metuchen Investment Advisors (MIA). Starwood is advising Michael Cooke, a wealthy client of MIA. Cooke would like to invest USD 500,000 in a bond rated at least AA. Starwood is considering bonds issued by IBM, GE, and Microsoft, and wants to choose a bond that satisfies Cooke’s rating requirement, but also has the highest yield to maturity. He has access to the following information:

IBM

GE

Microsoft

S&P Bond Rating

AA+

A+

AAA

Semiannual Coupon

1.75%

1.78%

1.69%

Term to Maturity in years

5

5

5

Price (USD)

975

973

989

Par value (USD)

1000

1000

1000

Which bond should Starwood purchase for Cooke? a. b. c. d.

GE bond IBM bond Microsoft bond Either the Microsoft bond or the GE bond

Correct answer: b Explanation: To reach the correct answer, find the bond with the highest yield to maturity (YTM) that qualifies for inclusion in Cooke’s portfolio. Although we can calculate the YTM for each bond using a modern business calculator, it is unnecessary to do so in this case. Of the three bonds, the GE bond does not qualify for the portfolio as its rating of A+ is below the AA rating required by Cooke. This leaves the IBM bond and the Microsoft bond. Comparing the two bonds, the IBM bond pays a higher coupon than the Microsoft bond, yet it is cheaper as well. Therefore the yield on the IBM bond is higher. To formally calculate the yield, you could also use the following equation describing the relationship between price and yield:

P=

[( )]

1 c 11 + y/2 y

2T

1 1 + y/2

2T

( )

+F

Using this equation (or an equivalent calculator function), the YTM for the IBM bond equals 4.057%, while the YTM for the Microsoft bond equals 3.62%. Reference: Bruce Tuckman, Fixed Income Securities, 2nd Edition (Hoboken, NJ: Wiley & Sons, 2002), Chapter 3 — Yield to Maturity. AIM: Compute a bond's YTM given a bond structure and price. Section: Valuation and Risk Models


31


17.

After evaluating the results of your firm’s stress tests, you are recommending that the firm allocate additional economic capital and purchase selective insurance protection to guard against particular events. In order to give management a fully informed assessment, it is important that you note the following, related to this strategy: a. b. c. d.

While While While While

decreasing decreasing decreasing decreasing

liquidity risk exposure, it will likely increase market risk exposure. correlation risk exposure, it will likely increase credit risk exposure. market risk exposure, it will likely increase credit risk exposure. credit risk exposure, it will likely increase model risk exposure.

Correct answer: c Explanation: The purchase of insurance protection can transform market risk into counterparty credit risk. Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition (New York: McGraw-Hill 2007), Chapter 14, p. 264. AIM: Explain how the results of a stress test can be used to improve our risk analysis and risk management systems. Section: Valuation and Risk Models

18.

A bank’s foreign loan portfolio contains a large concentration of loans to a country whose government has been running large external deficits. To evaluate the transfer risk that might exist in the event of stress, the greatest concern should be given to the possibility that the sovereign will impose restrictions on which of the following? a. b. c. d.

Imports Interest rates Exports Currency convertibility

Correct answer: d Explanation: Transfer risk arises when central banks or governments impose restrictions on currency convertibility. The consequences include payment defaults and debt restructurings. Reference: John Caouette, Edward Altman, Paul Narayanan and Robert Nimmo (2008), Managing Credit Risk: The Great Challenge for the Global Financial Markets, 2nd Edition, (Hoboken, NJ: John Wiley & Sons, 2008), Chapter 23, p. 176. AIM: Define and differentiate between country risk and transfer risk and describe some of the factors that might lead to each. Describe some of the challenges in country risk analysis. Section: Valuation and Risk Models

32



19.

A portfolio manager bought 1,000 call options on a non-dividend-paying stock, with a strike price of USD 100, for USD 6 each. The current stock price is USD 104 with a daily stock return volatility of 1.89%, and the delta of the option is 0.6. Using the delta-normal approach to calculate VaR, what is an approximation of the 1-day 95% VaR of this position? a. b. c. d.

USD USD USD USD

112 1,946 3,243 5,406

Correct answer: b Explanation: The delta of the option is 0.6. The VaR of the underlying is: 1.89% * 1.65 * 104 = 3.24 Therefore, the VaR of one option is: 0.6*3.24=1.946, and multiplying by 1,000 provides the VaR of the entire position: 1,946. Reference: Linda Allen, Jacob Boudoukh and Anthony Saunders (2004), Understanding Market, Credit and Operational Risk: The Value at Risk Approach (Oxford, Blackwell Publishing, 2004), Chapter 3. AIM: Describe the delta-normal approach to calculating VaR for non-linear derivatives. Section: Valuation and Risk Models

20.

Which of the following statements concerning the measurement of operational risk is correct? a. b. c. d.

Economic capital should be sufficient to cover both expected and worst-case operational risk losses. Loss severity and loss frequency tend to be modeled with lognormal distributions. Operational loss data available from data vendors tend to be biased towards small losses. The standardized approach used by banks in calculating operational risk capital allows for different beta factors to be assigned to different business lines.

Correct answer: d Explanation: In the standardized approach to calculating operational risk, a bank’s activities are divided up into several different business lines, and a beta factor is calculated for each line of business. Economic capital covers the difference between the worst-case loss and the expected loss. Loss severity tends to be modeled with a lognormal distribution, but loss frequency is typically modeled using a Poisson distribution. Operational loss data available from data vendors tends to be biased towards large losses. Reference: John Hull, Risk Management and Financial Institutions, 2nd Edition (Boston: Pearson Prentice Hall, 2010), Chapter 18 — Operational Risk, p. 243. AIM: Describe the allocation of operational risk capital and the use of scorecards. Section: Valuation and Risk Models


33


21.

The proper selection of factors to include in an ordinary least squares estimation is critical to the accuracy of the result. When does omitted variable bias occur? a. b. c. d.

Omitted variable bias occurs when the omitted determinant of the dependent variable. Omitted variable bias occurs when the omitted not a determinant of the dependent variable. Omitted variable bias occurs when the omitted determinant of the dependent variable. Omitted variable bias occurs when the omitted not a determinant of the dependent variable.

variable is correlated with the included regressor and is a variable is correlated with the included regressor but is variable is independent of the included regressor and is a variable is independent of the included regressor but is

Correct answer: a Explanation: Omitted variable bias occurs when a model improperly omits one or more variables that are critical determinants of the dependent variable and are correlated with one or more of the other included independent variables. Omitted variable bias results in an over- or under-estimation of the regression parameters. Reference: James Stock and Mark Watson (2008), Introduction to Econometrics, Brief Edition (Boston, Pearson Education, 2008), Chapter 6, pp. 186-190 AIM: Define, interpret, and describe methods for addressing omitted variable bias. Section: Quantitative Analysis

34



22.

Assume that you are only concerned with systematic risk. Which of the following would be the best measure to use to rank order funds with different betas based on their risk-return relationship with the market portfolio? a. b. c. d.

Treynor ratio Sharpe ratio Jensen’s alpha Sortino ratio

Correct answer: a Explanation: Systematic risk of a portfolio is that risk which is inherent in the market and thus cannot be diversified away. In this situation you should seek a measure which ranks funds based on systematic risk only, which is reflected in the beta as defined below: βP =(ρPM * σP * σM)/σ2M where ρ PM is the correlation coefficient between the portfolio and the market, σp represents the standard deviation of the portfolio and σM represents the standard deviation of the market. In a well diversified portfolio (where one is normally only concerned with systematic risk), it can be assumed that the correlation coefficient is close to 1, therefore beta can be approximated to an even simpler equation: βP ≈ σP /σM In either case, beta explains the volatility of the portfolio compared to the volatility of the market, which captures only systematic risk. The Treynor ratio is the correct ratio to use in this case. The formula is: Tρ = [E(Rρ) - Rf] / βρ which describes the difference between the expected return of the portfolio, E(Rρ) and the risk free rate Rf divided by the portfolio beta β. Therefore, it plots excess return over systematic risk. Reference: Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England: Wiley, 2003), Chapter 4, Section 4.2 — Applying the CAPM to Performance Measurement: Single-Index Performance Measurement Indicators, page 151. AIM: Calculate, compare, and evaluate the Treynor measure, the Sharpe measure, and Jensen's alpha. Section: Foundations of Risk Management


35


23.

The collapse of Long Term Capital Management (LTCM) is a classic risk management case study. Which of the following statements about risk management at LTCM is correct? a. b. c. d.

LTCM had no active risk reporting. At LTCM, stress testing became a risk management department exercise that had little influence on the firm’s strategy. LTCM’s use of high leverage is evidence of poor risk management. LTCM failed to account properly for the illiquidity of its largest positions in its risk calculations.

Correct answer: d Explanation: A major contributing factor to the collapse of LTCM is that it did not account properly for the illiquidity of its largest positions in its risk calculations. LTCM received valuation reports from dealers who only knew a small portion of LTCM’s total position in particular securities, therefore understating LTCM’s true liquidity risk. When the markets became unsettled due to the Russian debt crisis in August 1998 and a separate firm decided to liquidate large positions which were similar to many at LTCM, the illiquidity of LTCM’s positions forced it into a situation where it was reluctant to sell and create an even more dramatic adverse market impact even as its equity was rapidly deteriorating. To avert a full collapse, LTCM’s creditors finally stepped in to provide $3.65 billion in additional liquidity to allow LTCM to continue holding its positions through the turbulent market conditions in the fall of 1998. However, as a result, investors and managers in LTCM other than the creditors themselves lost almost all their investment in the fund. Reference: Steve Allen, Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk (New York: John Wiley & Sons, 2003), Chapter 4 — Financial Disasters, pp. 178-182. AIM: Describe the key factors that led to and the lessons learned from the following risk management case studies: • Long Term Capital Management Section: Foundations of Risk Management

36



24.

Which of the following is a potential consequence of violating the GARP Code of Conduct once a formal determination is made that such a violation has occurred? a. b. c. d.

Formal notification to the GARP Member’s employer of such a violation Suspension of the GARP Member’s right to work in the risk management profession Removal of the GARP Member’s right to use the FRM designation Required participation in ethical training

Correct answer: c Explanation: According to the GARP Code of Conduct, violation(s) of this Code may result in, among other things, the temporary suspension or permanent removal of the GARP Member from GARP’s Membership roles, and may also include temporarily or permanently removing from the violator the right to use or refer to having earned the FRM designation or any other GARP granted designation, following a formal determination that such a violation has occurred. Reference: GARP Code of Conduct, Applicability and Enforcement section. AIM: Describe the potential consequences of violating the GARP Code of Conduct. Section: Foundations of Risk Management

25.

Which of the following is assumed in the multiple least squares regression model? a. b. c. d.

The The The The

dependent variable is stationary. independent variables are not perfectly multicollinear. error terms are heteroskedastic. independent variables are homoskedastic.

Correct answer: b Explanation: One of the assumptions of the multiple regression model of least squares is that no perfect multicollinearity is present. Perfect multicollinearity would exist if one of the regressors is a perfect linear function of the other regressors. None of the other choices are assumptions of the multiple least squares regression model. Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston, Pearson Education, 2008), Chapter 6, pp. 202-204. AIM: Explain the assumptions of the multiple linear regression model. Section: Quantitative Analysis


37


Answer Sheet


a.

b.

c.

d.

a.

1.

14.

2.

15.

3.

16.

4.

17.

5.

18.

6.

19.

7.

20.

b.

c.

d.

✓

✘

8. 9.


10.

1.

11.


12.

1.

13.


39


Questions


1.

You are examining a sample of return data. As a first step, you construct a QQ plot of the data as shown below:

Based on an examination of the QQ plot, which of the following statements is correct? a. b. c. d.

2.

returns are normally distributed. return distribution has thin tails relative to the normal distribution. return distribution is negatively skewed relative to the normal distribution. return distribution has fat tails relative to the normal distribution.

The annual mean and volatility of a portfolio are 10% and 40%, respectively. The current value of the portfolio is GBP 1,000,000. How does the 1-year 95% VaR that is calculated using a normal distribution assumption (normal VaR) compare with the 1-year 95% VaR that is calculated using the lognormal distribution assumption (lognormal VaR)? a. b. c. d.

3.

The The The The

Lognormal Lognormal Lognormal Lognormal

VaR VaR VaR VaR

is is is is

greater than normal VaR by GBP 13,040 greater than normal VaR by GBP 17,590 less than normal VaR by GBP 13,040 less than normal VaR by GBP 17,590

Bennett Bank extends a 5% APR (annual percentage rate) USD 100,000 30-year mortgage requiring monthly payments. If the mortgage is structured so that it requires interest-only payments for the first 5 years, after which point it becomes a self-amortizing mortgage, what would be the portion of the monthly payment applied to the principal in the 61st month? a. b. c. d.

USD USD USD USD

167.92 174.60 584.59 591.27


41


4.

Let X be a random variable representing the daily loss of your portfolio. The “peaks over threshold” (POT) approach considers a threshold value, u, of X and the distribution of excess losses over this threshold. Which of the following statements about this application of extreme value theory is correct? a. b. c. d.

5.

A risk analyst is comparing the use of parametric and non-parametric approaches for calculating VaR and is concerned about some of the characteristics present in the loss data. Which of the following distribution characteristics would make parametric approaches the favored method to use? a. b. c. d.

6.

Skewness in the distribution Fat tails in the distribution Scarcity of high magnitude loss events Heteroskedasticity in the distribution

Lin Ping is valuing a 1-year credit default swap (CDS) contract which will pay the buyer 75% of the face value of a bond issued by Xiao Corp. immediately after a default by Xiao. To purchase this CDS, the buyer will pay the CDS spread, which is a percentage of the face value, once at the end of the year. Lin estimates that the risk-neutral default probability for Xiao is 5% per year. The risk-free rate is 3% per year. Assuming defaults can only occur halfway through the year and that the accrued premium is paid immediately after a default, what is the estimate for the CDS spread? a. b. c. d.

42

To apply the POT approach, the distribution of X must be elliptical and known. If X is normally distributed, the distribution of excess losses requires the estimation of only one parameter, β, which is a positive scale parameter. To apply the POT approach, one must choose a threshold, u, which is high enough that the number of observations in excess of u is zero. As the threshold, u, increases, the distribution of excess losses over u converges to a generalized Pareto distribution.




7.

You are the risk manager at Vision, a small fixed-income hedge fund that specializes in bank debt. Vision’s strategy utilizes both relative value and long-only trades using credit default swaps (CDS) and bonds. One of the new traders has the positions described in the table below.

Bank

Position

Credit Rating

SBU

Long USD 10 million CDS

A

Stanos

Long USD 5 million bond

BB+

CAB

Short USD 10 million CDS

A

Some of Vision’s newest clients are restricted from withdrawing their funds for three years. You are currently evaluating the impact of various default scenarios to estimate future asset liquidity. You have estimated that the marginal probability of default of the Stanos bond is 5% in Year 1, 10% in Year 2, and 15% in Year 3. What is the probability that the bond makes coupon payments for 3 years and then defaults at the end of Year 3? a. b. c. d.

8.

Consider a 1-year maturity zero-coupon bond with a face value of USD 1,000,000 and a 0% recovery rate issued by Company A. The bond is currently trading at 80% of face value. Assuming the excess spread only captures credit risk and that the risk-free rate is 5% per annum, the risk-neutral 1-year probability of default on Company A is closest to which of the following? a. b. c. d.

9.

13% 15% 27% 73%

2% 14% 16% 20%

Portland General Electric (PGE) was an Enron subsidiary that was able to survive after the Enron implosion. At that time, there was a trend towards electric utility downgrades, particularly for those utilities operating within larger corporate structures. PGE survived in part due to ring-fencing. Which of the following statements about ring fencing is correct? a. b. c. d.

A ring-fencing assets approach is typically only useful when a low quality firm wants to finance a high-quality project. When ring-fencing assets, options for credit enhancement include overcollateralization and financial guarantees provided by the parent against default of the subsidiary. A subsidiary holding the ring-fenced assets may be able to gain a higher credit rating than the parent, allowing it to issue bonds on the assets at a lower cost. Because the parent does not retain an equity interest in the subsidiary holding the ring-fenced assets, the subsidiary is not consolidated on the parent’s balance sheet.


43


10.

Bank A, a large international bank, engages in trading with counterparties throughout the world. Recently, it has started to pay more attention to wrong-way risk in its trading book. Which one of the following four scenarios would serve as an example of wrong-way risk from Bank A's perspective? a. b. c. d.

11.

Bank A has a large exposure to Bank B's equity, and Bank B offers to sell put options with long maturities on its own equity to Bank A. Bank A enters into a medium-term repurchase agreement with Bank B using several different types of debt issued by bank B as collateral. Bank A actively manages its credit portfolio using credit default swaps, and decides to sell long-term credit protection to Bank B. Bank A enters into a forward rate agreement with Bank B to deliver at LIBOR+2.5%.

The Chief Risk Officer of your bank has put you in charge of operational risk management. As a first step, you collect internal data to estimate the frequency and severity of operational-risk-related losses. The table below summarizes your findings:

Frequency Distribution

Severity Distribution

Number of Occurrences

Probability

Loss (USD)

Probability

0

0.6

1,000

0.5

1

0.3

100,000

0.4

2

0.1

1,000,000

0.1

Based on this information, what is your estimate of the expected loss due to operational risk? a. b. c. d.

12.

20,000 70,250 130,600 140,500

In its efforts to enhance its enterprise risk management function, Countryside Bank introduced a new decisionmaking process based on economic capital that involves assessing sources of risk across different business units and organizational levels. Which of the following statements regarding the correlations between these risks is correct? a. b. c. d.

44

USD USD USD USD

Correlations between the risks in the asset and liability sides of the balance sheet can be changed by management decisions. Generally, correlations between broad risk types such as credit, market, and operational risk are well understood and are easy to estimate at the individual firm level. Correlations between business units are only relevant in deciding total firm-wide economic capital levels and are not relevant for decisions at the individual business unit or project level. The introduction of correlations into firm-wide risk evaluation will result in a total VaR that, in general, is greater than or equal to the sum of individual business unit VaRs. © 2013 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.


13.

In recent years, large dealer banks financed significant fractions of their assets using short-term, often overnight, repurchase (repo) agreements in which creditors held bank securities as collateral against default losses. The table below shows the quarter-end financing of four broker-dealer banks. All values are in USD billions:

Bank A

Bank B

Bank C

Bank D

Financial instruments owned

823

629

723

382

Pledged as collateral

272

289

380

155

In the event that repo creditors become nervous about a bank’s solvency, which bank is least vulnerable to a liquidity crisis? a. b. c. d.

14.

A B C D

Galileo Vehicles (GV) and Leonardo Motors (LM) are both leading car manufacturers in hybrid car designs. Earlier this year, both companies introduced new hybrid models that are comparable to each other in almost every category. However, after both companies release pricing for their new models, LM’s model is 20% less expensive than GV’s. As a result, GV’s stock price declined sharply while LM’s stock price rose dramatically. Subsequently LM and GV announce that they have entered into merger discussions where the terms of the planned merger would give GV shareholders 1 share of LM per 3 shares of GV previously held. Post the announcement, GV’s stock is trading at USD 20 and LM’s stock is trading at USD 58. If you are confident that the merger will be completed, assuming zero transaction costs, which of the following investments should you make? a. b. c. d.

15.

Bank Bank Bank Bank

Buy 300 shares of GV and short 100 shares of LM. Short 300 shares of GV and buy 100 shares of LM. Buy 300 shares of GV and buy 100 shares of LM. Short 300 shares of GV and short 100 shares of LM.

At the end of 2007, Chad & Co.’s pension had USD 350 million worth of assets that were fully invested in equities and USD 180 million in fixed-income liabilities with a modified duration of 14. In 2008, the widespread effects of the subprime crisis hit the pension fund, causing its investment in equities to lose 50% of their market value. In addition, the immediate response from the government — cutting interest rates — to salvage the situation, caused bond yields to decline by 2%. What was the change in the pension fund’s surplus in 2008? a. b. c. d.

USD USD USD USD

-55.4 million -124.6 million -225.4 million -230.4 million


45


16.

As investors found out that highly-rated securities backed by subprime mortgages were not risk-free, the subprime crisis affected other asset classes. Which of the following mechanisms played an important role in the transmission of the crisis from the subprime sector to other asset classes? a. b. c. d.

17.

In the years leading up to the collapse of the Icelandic banking system, how did the relationship between the Central Bank of Iceland (CBI) and the Icelandic banks change? a. b. c. d.

18.

The CBI supplemented credit ratings from the major rating agencies with market-implied ratings when determining the liquidity to provide to the banks. The CBI began to issue loans to the banks that were denominated in Euros. The CBI began to issue more loans to the banks that were collateralized by the bonds of other Icelandic banks. The CBI began to issue loans to the banks that were denominated in U.S. dollars.

A portfolio has USD 2 million invested in Stock A and USD 1 million invested in Stock B. The 95% 1-day VaR for each individual position is USD 40,000. The correlation between the returns of Stock A and Stock B is 0.5. While rebalancing, the portfolio manager decides to sell USD 1 million of Stock A to buy USD 1 million of Stock B. Assuming that returns are normally distributed and that the rebalancing does not affect the volatility of the individual stocks, what effect will this have on the 95% 1-day portfolio VaR? a. b. c. d.

46

Impact of cross-default clauses linking industrial bonds and commercial mortgages held by banks Increase in repo haircuts causing banks to sell off assets to meet collateral calls Tightening of discount window lending standards by the U.S. Federal Reserve Exercise of credit default swap contracts tied to subprime mortgage pools held in off-balance sheet vehicles

There will be no effect. It will increase by USD 20,370. It will increase by USD 21,370. It will increase by USD 22,370.



19.

In calculating its risk-adjusted return on capital, your bank uses a capital charge of 2.50% for revolving credit facilities with a loan equivalent factor of 0.35 assigned to the undrawn portion. Recently, you have become concerned that the protective covenants embedded in these loans are weak and may not prevent customers from drawing on the facilities during times of stress. As such, you have recommended doubling the loan equivalent factor to 0.70. This recommendation has met with resistance from the loan origination team, and senior management has asked you to quantify the impact of your recommendation. For a typical facility that has an original principal of USD 1 billion and is 30% drawn, how much additional economic capital would have to be allocated if you increase the loan equivalent factor from 0.35 to 0.70? a. b. c. d.

20.

USD USD USD USD

3.50 million 6.13 million 8.75 million 13.63 million

Which of the following statements regarding frictions in the securitization of subprime mortgages is correct? a. b. c. d.

The arranger will typically have an information advantage over the originator with regard to the quality of the loans securitized. The originator will typically have an information advantage over the arranger, which can create an incentive for the originator to collaborate with the borrower in filing false loan applications. The major credit rating agencies are paid by investors for their rating service of mortgage-backed securities, and this creates a potential conflict of interest. The use of escrow accounts for insurance and tax payments eliminates the risk of foreclosure.


47


Answers


a.

b.

c.

1.

2. 3.

d.

a.

17.

5.

18.

6.

19.

20.

7.

8.

9.

10.


11.

d.

16.

c.

14. 15.

4.

b.

1.

12.


13.

1.


✓

✘

49


Explanations


1.

You are examining a sample of return data. As a first step, you construct a QQ plot of the data as shown below:

Based on an examination of the QQ plot, which of the following statements is correct? a. b. c. d.

The The The The

returns are normally distributed. return distribution has thin tails relative to the normal distribution. return distribution is negatively skewed relative to the normal distribution. return distribution has fat tails relative to the normal distribution.

Correct answer: d Explanation: This Q-Q plot has steeper slopes at the tails of the plot, which indicate fat tails in the distribution. A normal distribution would result in a linear QQ plot. A distribution with thin tails would produce a QQ plot with less steep slopes at the tails of the plot than a linear relationship, while this one is steeper at the tails. It is not a negatively skewed distribution, as the Q-Q plot is symmetric. Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition, Chapter 3, pp. 75, 77. AIM: Describe the use of QQ plots for identifying the distribution of data. Section: Market Risk Management and Measurement


51


2.

The annual mean and volatility of a portfolio are 10% and 40%, respectively. The current value of the portfolio is GBP 1,000,000. How does the 1-year 95% VaR that is calculated using a normal distribution assumption (normal VaR) compare with the 1-year 95% VaR that is calculated using the lognormal distribution assumption (lognormal VaR)? a. b. c. d.

Lognormal Lognormal Lognormal Lognormal

VaR VaR VaR VaR

is is is is

greater than normal VaR by GBP 13,040 greater than normal VaR by GBP 17,590 less than normal VaR by GBP 13,040 less than normal VaR by GBP 17,590

Correct answer: c Explanation: Normal VaR is calculated as follows: Normal VaR = 0.1 – (1.645 * 0.4) = 0.558 (dropping negative sign) and lognormal VaR is calculated as follows: Lognormal VaR = 1 – exp [0.1 – (1.645 * 0.4)] = 0.4276 Hence, Lognormal VaR is smaller than Normal VaR by: 13.04% per year. With a portfolio of GBP 1,000,000 this translates to GBP 13,040. Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition, Chapter 3. AIMS: Calculate VaR using a parametric estimation approach assuming that the return distribution is either normal or lognormal. Section: Market Risk Management and Measurement

52



3.

Bennett Bank extends a 5% APR (annual percentage rate) USD 100,000 30-year mortgage requiring monthly payments. If the mortgage is structured so that it requires interest-only payments for the first 5 years, after which point it becomes a self-amortizing mortgage, what would be the portion of the monthly payment applied to the principal in the 61st month? a. b. c. d.

USD USD USD USD

167.92 174.60 584.59 591.27

Correct answer: a Explanation: The principal payment for the 61st month is equal to the total monthly payment for the 61st month minus the total interest only payment for that month. First calculate the total monthly payment as shown below: Total Monthly Payment = Mortgage payment factor * Principal balance Mortgage payment factor: r(1+r)n/(1+r)n - 1 where r = the interest rate, and n = the number of payments over the loan term. Note that the interest rate corresponds to the frequency of the payment, so when using a monthly payment as in this example, the annual percentage rate (APR) must be divided by 12. In this case, given that the monthly interest rate equals 0.0041667 (0.05 / 12) and 300 monthly payments will be made in the 25 remaining years of the loan, the mortgage payment factor is: 300

[0.0041667 * (1.0041667)

300

] / (1.0041667

− 1) = .0058459.

So the total monthly payment equals .0058459 * 100,000 or USD 584.59. Next, compute the monthly interest payment, which is equal to 100,000 * (0.05 / 12) or USD 416.67. Hence, the correct answer is 584.59 – 416.67 or 167.92, which reflects the principal portion of the 61st month’s payment. Reference: Frank Fabozzi, Anand Bhattacharya, and William Berliner, Mortgage Backed Securities, 2nd Edition (Hoboken: John Wiley & Sons, 2006), Chapter 1, p. 13. AIMS: Calculate the mortgage payment factor. Understand the allocation of loan principal and interest over time for various loan types. Section: Market Risk Management and Measurement


53


4.

Let X be a random variable representing the daily loss of your portfolio. The “peaks over threshold” (POT) approach considers a threshold value, u, of X and the distribution of excess losses over this threshold. Which of the following statements about this application of extreme value theory is correct? a. b. c. d.

To apply the POT approach, the distribution of X must be elliptical and known. If X is normally distributed, the distribution of excess losses requires the estimation of only one parameter, β, which is a positive scale parameter. To apply the POT approach, one must choose a threshold, u, which is high enough that the number of observations in excess of u is zero. As the threshold, u, increases, the distribution of excess losses over u converges to a generalized Pareto distribution.

Correct answer: d Explanation: The distribution of excess losses over u converges to a generalized Pareto distribution as the threshold value u increases. The distribution of X itself can be any of the commonly used distributions: normal, lognormal, t, etc., and will usually be unknown. The distribution of excess losses requires the estimation of two parameters, a positive scale parameter β and a shape or tail index parameter ξ. Οne must choose a threshold u that is high enough so that the theory applies but also low enough so that there are observations in excess of u. Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition (Wiley, 2005), Chapter 7 — Parametric Approaches (II): Extreme Value, pp. 201-202. AIM: Describe the peaks over threshold (POT) approach. Section: Market Risk Management and Measurement

54



5.

A risk analyst is comparing the use of parametric and non-parametric approaches for calculating VaR and is concerned about some of the characteristics present in the loss data. Which of the following distribution characteristics would make parametric approaches the favored method to use? a. b. c. d.

Skewness in the distribution Fat tails in the distribution Scarcity of high magnitude loss events Heteroskedasticity in the distribution

Correct answer: c Explanation: Non-parametric approaches can accommodate fat tails, skewness, and any other non-normal features that can cause problems for parametric approaches. However, if the data period that is used in estimation includes few losses or losses with low magnitude, non-parametric methods will often produce risk measures that are too low. Hence parametric methods would be more appropriate in those situations. Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005), Chapter 4. AIM: Describe the advantages and disadvantages of non-parametric estimation methods. Section: Market Risk Management and Measurement


55


6.

Lin Ping is valuing a 1-year credit default swap (CDS) contract which will pay the buyer 75% of the face value of a bond issued by Xiao Corp. immediately after a default by Xiao. To purchase this CDS, the buyer will pay the CDS spread, which is a percentage of the face value, once at the end of the year. Lin estimates that the risk-neutral default probability for Xiao is 5% per year. The risk-free rate is 3% per year. Assuming defaults can only occur halfway through the year and that the accrued premium is paid immediately after a default, what is the estimate for the CDS spread? a. b. c. d.


Correct answer: c Explanation: The key to CDS valuation is to equate the present value (PV) of payments to the PV of expected payoff in the event of default. Let s denote the CDS spread. π = probability of default during year 1 = 5% C = contingent payment in case of default = 75% -0.03 x 1 di = discount factor = e for 1-year and e-0.03 x 0.5 for half a year = 0.97044 and 0.98511 s = CDS spread (to be solved) The premium leg, which includes the spread payment and accrual, is: s*(0.5d0.5* π +d1 (1-π) = s*(0.02463+0.92192) = s*0.94655 The payoff leg is: C * (d0.5) * π = 0.03694 Solving for the spread: s*0.94655 = 0.03694 → s = 0.03902 or a spread of 390 basis points. Reference: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011), chapter 7, pp. 250-253. AIM: Define the different ways of representing spreads. Compare and differentiate between the different spread conventions and compute one spread given others when possible. Section: Credit Risk Measurement and Management

56



7.

You are the risk manager at Vision, a small fixed-income hedge fund that specializes in bank debt. Vision’s strategy utilizes both relative value and long-only trades using credit default swaps (CDS) and bonds. One of the new traders has the positions described in the table below.

Bank

Position

Credit Rating

SBU

Long USD 10 million CDS

A

Stanos

Long USD 5 million bond

BB+

CAB

Short USD 10 million CDS

A

Some of Vision’s newest clients are restricted from withdrawing their funds for three years. You are currently evaluating the impact of various default scenarios to estimate future asset liquidity. You have estimated that the marginal probability of default of the Stanos bond is 5% in Year 1, 10% in Year 2, and 15% in Year 3. What is the probability that the bond makes coupon payments for 3 years and then defaults at the end of Year 3? a. b. c. d.

13% 15% 27% 73%

Correct answer: a Explanation: The probability that the bond defaults in year 3 can be modeled as a Bernoulli trial given by the following equation, where MP stands for marginal probability: P (Default at end of year 3) = (1-MP

) * (1 - MP

year 1 default

)* MP

year 2 default

year 3 default

= (1- 0.05) * (1 – 0.10) * 0.15 = 0.1283 or 12.83%. References: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011), chapter 7, p. 236. John Hull, Options, Futures and Other Derivatives, 8th Edition (New York: Pearson Prentice Hall, 2012), chapter 23. AIM: Explain how default risk for a single company can be modeled as a Bernoulli trial. Section: Credit Risk Measurement and Management


57


8.

Consider a 1-year maturity zero-coupon bond with a face value of USD 1,000,000 and a 0% recovery rate issued by Company A. The bond is currently trading at 80% of face value. Assuming the excess spread only captures credit risk and that the risk-free rate is 5% per annum, the risk-neutral 1-year probability of default on Company A is closest to which of the following? a. b. c. d.

2% 14% 16% 20%

Correct answer: c Explanation: This can be calculated by using the formula which equates the future value of a risky bond with yield (y) and default probability (π) to a risk free asset with yield (r): 1 + r = (1 - π) * (1 + y) + πR π = Probability of default; R = Recovery rate In the situation where the recovery rate is assumed to be zero, the risk-neutral probability of default can be derived from the following equation: 1 + r = (1 - π) * (1 + y) - ( 1 - π) * (FV/MV) where MV = market value and FV = face value. Inputting the data into this equation yields π = 1 - (800,000*1.05)/1,000,000 = 0.16. Reference: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011), chapter 6, p. 203. AIM: Explain the relationship between the yield spread and the probability of default and calculate default probability of a debt security using the credit spread. Section: Credit Risk Management and Measurement

58



9.

Portland General Electric (PGE) was an Enron subsidiary that was able to survive after the Enron implosion. At that time, there was a trend towards electric utility downgrades, particularly for those utilities operating within larger corporate structures. PGE survived in part due to ring-fencing. Which of the following statements about ring fencing is correct? a. b. c. d.

A ring-fencing assets approach is typically only useful when a low quality firm wants to finance a high-quality project. When ring-fencing assets, options for credit enhancement include overcollateralization and financial guarantees provided by the parent against default of the subsidiary. A subsidiary holding the ring-fenced assets may be able to gain a higher credit rating than the parent, allowing it to issue bonds on the assets at a lower cost. Because the parent does not retain an equity interest in the subsidiary holding the ring-fenced assets, the subsidiary is not consolidated on the parent’s balance sheet.

Correct answer: c Explanation: Ring fencing is often undertaken to provide a higher credit rating to a subsidiary than is available to the parent. Derivative product companies or unregulated subsidiaries of investment banks are examples of this structure. There are other reasons for ring fencing assets, including freeing the assets from restrictions, taxes or other laws specific to a particular country. Ring-fencing can be useful in two main situations: either when a low-quality firm cannot finance a high-quality project, or when a high-quality firm does not want to run the risk of being the sole financier of a low-quality project. The parent cannot guarantee the ring fenced assets, as this would allow creditors of the subsidiary to seek relief through the parent in the event of default of the subsidiary. The purpose of ring fencing assets is to create a structure that is bankruptcy remote from the parent. The retention of equity is a common feature of ring fencing. A subsidiary may remain consolidated on the parent company’s balance sheet in cases where the parent retains a substantial equity interest. Reference: Christopher Culp, The Structuring Process, Structured Finance and Insurance: The Art of Managing Capital and Risk (Hoboken, NJ: John Wiley & Sons, 2006), Chapter 13 pp. 274-279. AIM: Describe the process and benefits of ring-fencing assets. Section: Credit Risk Measurement and Management


59


10.

Bank A, a large international bank, engages in trading with counterparties throughout the world. Recently, it has started to pay more attention to wrong-way risk in its trading book. Which one of the following four scenarios would serve as an example of wrong-way risk from Bank A's perspective? a. b. c. d.

Bank A has a large exposure to Bank B's equity, and Bank B offers to sell put options with long maturities on its own equity to Bank A. Bank A enters into a medium-term repurchase agreement with Bank B using several different types of debt issued by bank B as collateral. Bank A actively manages its credit portfolio using credit default swaps, and decides to sell long-term credit protection to Bank B. Bank A enters into a forward rate agreement with Bank B to deliver at LIBOR+2.5%.

Correct answer: a Explanation: According to Section 101 of Basel III, "a bank is exposed to “specific wrong-way risk” if future exposure to a specific counterparty is highly correlated with the counterparty’s probability of default. For example, a company writing put options on its own stock creates wrong-way exposures for the buyer that is specific to the counterparty." Reference: Basel Committee on Banking Supervision (February 16, 2012), Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems (December 2010, revised June 2011) Note: www.bis.org/publ/bcbs189.pdf. AIM: Describe changes to the regulatory capital framework, including changes to: Risk coverage, the use of stress tests, the treatment of counter-party risk with credit valuations adjustments, the use of external ratings, and the use of leverage ratios. Section: Operational and Integrated Risk Management

60



11.

The Chief Risk Officer of your bank has put you in charge of operational risk management. As a first step, you collect internal data to estimate the frequency and severity of operational-risk-related losses. The table below summarizes your findings:

Frequency Distribution

Severity Distribution

Number of Occurrences

Probability

Loss (USD)

Probability

0

0.6

1,000

0.5

1

0.3

100,000

0.4

2

0.1

1,000,000

0.1

Based on this information, what is your estimate of the expected loss due to operational risk? a. b. c. d.

USD USD USD USD

20,000 70,250 130,600 140,500

Correct answer: b Explanation: The expected loss can be calculated by multiplying the expected frequency and the expected severity. Expected frequency is equal to: (0 * 0.6) + (1 * 0.3) + (2 * 0.1) = 0.5, Expected severity is equal to: (1000 * 0.5) + (100,000 * 0.4) + (1,000,000 * 0.1) = 140,500 The expected loss is therefore: 0.5 * 140,500 = 70,250 Reference: Mo Chaudhury, “A Review of the Key Issues in Operational Risk Capital Modeling”, The Journal of Operational Risk, Volume 5/Number 3, Fall 2010: pp. 37-66. AIM: Describe how a loss distribution is obtained from frequency and severity distributions. Section: Operational and Integrated Risk Management


61


12.

In its efforts to enhance its enterprise risk management function, Countryside Bank introduced a new decisionmaking process based on economic capital that involves assessing sources of risk across different business units and organizational levels. Which of the following statements regarding the correlations between these risks is correct? a. b. c. d.

Correlations between the risks in the asset and liability sides of the balance sheet can be changed by management decisions. Generally, correlations between broad risk types such as credit, market, and operational risk are well understood and are easy to estimate at the individual firm level. Correlations between business units are only relevant in deciding total firm-wide economic capital levels and are not relevant for decisions at the individual business unit or project level. The introduction of correlations into firm-wide risk evaluation will result in a total VaR that, in general, is greater than or equal to the sum of individual business unit VaRs.

Correct answer: a Explanation: Management has the ability to influence the correlations between these risks by changing the asset/liability mix, so management decision-making is indeed quite relevant. Reference: Brian Nocco and René Stulz, “Enterprise Risk Management: Theory and Practice,” Journal of Applied Corporate Finance 18, No. 4 (2006): pp. 8-20. AIM: Describe the role of and issues with correlation in risk aggregation. Section: Operational and Integrated Risk Management

62



13.

In recent years, large dealer banks financed significant fractions of their assets using short-term, often overnight, repurchase (repo) agreements in which creditors held bank securities as collateral against default losses. The table below shows the quarter-end financing of four broker-dealer banks. All values are in USD billions:

Bank A

Bank B

Bank C

Bank D

Financial instruments owned

823

629

723

382

Pledged as collateral

272

289

380

155

In the event that repo creditors become nervous about a bank’s solvency, which bank is least vulnerable to a liquidity crisis? a. b. c. d.

Bank Bank Bank Bank

A B C D

Correct answer: a Explanation: A liquidity crisis could materialize if repo creditors become nervous about a bank’s solvency and choose not to renew their positions. If enough creditors choose not to renew, the bank could likely be unable to raise sufficient cash by other means on such short notice, thereby precipitating a crisis. However, this vulnerability is directly related to the proportion of assets a bank has pledged as collateral. Bank A is least vulnerable since it has the least dependence on short-term repo financing (i.e. the lowest percentage of its assets out of the four banks is pledged as collateral: 272/823, or 33% Reference: Darrell Duffie (2010), “Failure Mechanics of Dealer Banks”, Journal of Economic Perspectives (24:1), pp. 51-72. AIM: Identify factors that can precipitate or accelerate a liquidity crisis at a dealer bank and what prudent risk management steps can be taken to mitigate these risks. Section: Operational and Integrated Risk Management


63


14.

Galileo Vehicles (GV) and Leonardo Motors (LM) are both leading car manufacturers in hybrid car designs. Earlier this year, both companies introduced new hybrid models that are comparable to each other in almost every category. However, after both companies release pricing for their new models, LM’s model is 20% less expensive than GV’s. As a result, GV’s stock price declined sharply while LM’s stock price rose dramatically. Subsequently LM and GV announce that they have entered into merger discussions where the terms of the planned merger would give GV shareholders 1 share of LM per 3 shares of GV previously held. Post the announcement, GV’s stock is trading at USD 20 and LM’s stock is trading at USD 58. If you are confident that the merger will be completed, assuming zero transaction costs, which of the following investments should you make? a. b. c. d.

Buy 300 shares of GV and short 100 shares of LM. Short 300 shares of GV and buy 100 shares of LM. Buy 300 shares of GV and buy 100 shares of LM. Short 300 shares of GV and short 100 shares of LM.

Correct answer: b Explanation: If the merger goes through, the companies’ prices should correspond on a 3:1 basis, with 1 share of LM corresponding to 3 shares of GV. However, at the given trading prices the ratio does not hold, with one share of LM being equal to USD 58 / USD 20, or 2.9 shares of GV. This shows that LM is undervalued compared to GV given the terms of the merger agreement. If the merger is completed, LM’s stock will appreciate and/or GV’s stock will depreciate relative to each other until the ratio reaches 3:1. In order to exploit this potential arbitrage opportunity, you can short 300 shares of the relatively overvalued stock GV, resulting in a cash inflow of USD 6000, while buying 100 shares of the relatively undervalued stock LM for USD 5800, resulting in a net cash inflow of USD 200. If the merger is completed, then the long and the short positions will exactly offset each other given the 3:1 ratio and the trade will be closed. The original cash inflow of USD 200 would be your profit from this arbitrage trade if the merger is completed. Reference: David P. Stowell (2010), An Introduction to Investment Banks, Hedge Funds, and Private Equity, Chapter 12. AIM: Describe and interpret a numerical example of the following strategies: merger arbitrage, pairs trading, distressed investing and global macro strategy. Section: Risk Management and Investment Management

64



15.

At the end of 2007, Chad & Co.’s pension had USD 350 million worth of assets that were fully invested in equities and USD 180 million in fixed-income liabilities with a modified duration of 14. In 2008, the widespread effects of the subprime crisis hit the pension fund, causing its investment in equities to lose 50% of their market value. In addition, the immediate response from the government — cutting interest rates — to salvage the situation, caused bond yields to decline by 2%. What was the change in the pension fund’s surplus in 2008? a. b. c. d.

USD USD USD USD

-55.4 million -124.6 million -225.4 million -230.4 million

Correct answer: c Explanation: The change in the pension fund’s surplus for the year 2008 is equal to the initial surplus S0 at the end of 2007 less the ending surplus S1 at the end of 2008. The initial surplus is calculated as S0 = A0 – L0 = 350 – 180 = 170, where A0 = the firm’s initial assets and L0 the firm’s initial liabilities. Next we have to calculate the surplus at the end of 2008. Given the 50% decline in the equity market, the new level of assets A1 at the end of 2008 is equal to: (1 – 0.5) * 350, or 175 The new level of liabilities L1 can be calculated as: L1 = ( 1 – (MD * Δy)) * L0 where MD is the modified duration, and Δy is the change in yield. Liabilities at end of 2008 are equal to: L1 = (1 – (14 * -0.02)) * 180 = 230.4. Therefore the 2008 surplus S1 is equal to A1 – L1 = 175 – 230.4 = -55.4 (which implies the pension fund is actually in a deficit situation at the end of 2008). The change in surplus for 2008 is hence S1 – S0 = -55.4 – 170 = -225.4 million. Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition (New York: McGraw-Hill, 2007), Chapter 17 — VaR and Risk Budgeting in Investment Management, p. 433. AIM: Describe the investment process of large investors such as pension funds. Section: Risk Management and Investment Management


65


16.

As investors found out that highly-rated securities backed by subprime mortgages were not risk-free, the subprime crisis affected other asset classes. Which of the following mechanisms played an important role in the transmission of the crisis from the subprime sector to other asset classes? a. b. c. d.

Impact of cross-default clauses linking industrial bonds and commercial mortgages held by banks Increase in repo haircuts causing banks to sell off assets to meet collateral calls Tightening of discount window lending standards by the U.S. Federal Reserve Exercise of credit default swap contracts tied to subprime mortgage pools held in off-balance sheet vehicles

Correct answer: b Explanation: A brief excerpt from the article provides a summary: "Uncertain about the solvency of counterparties, repo depositors became concerned that the collateral bonds might not be liquid; if all firms wanted to hold cash — a flight to quality — then collateral would have to decline in price to find buyers. This is the crucial link between the subprime shock and other asset categories”. This decline in the value of collateral became evident in the rapid increase in the “repo haircut”, which is the percentage difference between the market value of the pledged collateral and the amount of funds lent. For example, with a 5% “repo haircut”, a bank would only allow a USD 95 deposit against USD 100 face value of collateral. This repo haircut rose dramatically in late 2007 and 2008, from zero at the beginning of August 2007 to almost 10% in early 2008 and reaching over 45% by early 2009. As the value of collateral began to fall, this led to a deterioration in valuations across asset classes which also commenced in August 2007 when the LIBOR-OIS spread jumped. This occurred even though the subprime fundamentals (as measured by the ABX index of credit derivatives) had been deteriorating for months prior to that. Reference: Gary Gorton (05-2009), Slapped in the Face by the Invisible Hand: Banking and the Panic of 2007, p. 33. AIMS: Explain the function of and define repos, and discuss their use as the primary mechanism driving shadow banking. Explain how the shock from the subprime mortgage collapse affected asset classes that were unrelated and evolved into the 2007 banking system panic. Section: Current Issues in Financial Markets

66



17.

In the years leading up to the collapse of the Icelandic banking system, how did the relationship between the Central Bank of Iceland (CBI) and the Icelandic banks change? a. b. c. d.

The CBI supplemented credit ratings from the major rating agencies with market-implied ratings when determining the liquidity to provide to the banks. The CBI began to issue loans to the banks that were denominated in Euros. The CBI began to issue more loans to the banks that were collateralized by the bonds of other Icelandic banks. The CBI began to issue loans to the banks that were denominated in U.S. dollars.

Correct answer: c Explanation: In 2007 and 2008, the amount of Icelandic banks’ debt held by other Icelandic banks grew dramatically, from around one percent of GDP in January 2007 to almost 30% of GDP by September 2008. In turn, a large proportion of these bonds was used as collateral at the CBI. One example occurred in 2008 when the Icelandic banks issued debt to the savings bank, Icebank, which then used the debt as collateral at the CBI. Other banks such as Kaupthing and Glitnir also issued covered bonds which were used for collateralized loans at the CBI. CBI’s rules for the credit standards of eligible collateral were broadly similar to the rules of the European System of Central Banks (ESCB), stating that unsecured bonds and bills were required to have a minimum long-term rating of “A-“ by S&P or Fitch or “A3” by Moody’s, as well as having their securities traded on a regulated market in the EEA. There was no use of market-implied ratings. The CBI only issued loans to the banks that were denominated in krona. Reference: Arthur M. Berd (editor), Lessons From the Financial Crisis (London: Risk Books, 2010), Chapter 4: The Collapse of the Icelandic Banking System, pp. 111. AIMS: Describe the severity of the banking crisis, the currency crisis, and the public debt crisis. Understand how banks funded their risky business models before and after the 2006 mini-crisis. Section: Current Issues in Financial Markets


67


18.

A portfolio has USD 2 million invested in Stock A and USD 1 million invested in Stock B. The 95% 1-day VaR for each individual position is USD 40,000. The correlation between the returns of Stock A and Stock B is 0.5. While rebalancing, the portfolio manager decides to sell USD 1 million of Stock A to buy USD 1 million of Stock B. Assuming that returns are normally distributed and that the rebalancing does not affect the volatility of the individual stocks, what effect will this have on the 95% 1-day portfolio VaR? a. b. c. d.

There will be no effect. It will increase by USD 20,370. It will increase by USD 21,370. It will increase by USD 22,370.

Correct answer: d Explanation: The first step is to calculate the VaR of the original portfolio. This can be done by using the following equation: VaR Port (A,B) =

(VaRA2 + VaR B 2 + (2ρ * VaRA * VaRB )

where ρ is the correlation coefficient. Portfolio VaR (before): 400002 + 400002 + (2 * 0.5 * 40000 * 40000) = USD 69,282. After the rebalance, the market value of the position in Stock A is halved, so VaR(A) is now equal to $20,000. Meanwhile the market value for the position in B has doubled so that VaR(B) is now $80,000. Hence we can now calculate the VaR of the new portfolio as follows: Portfolio VaR (after) =

200002 + 800002 + (2 * 0.5 * 20000 * 80000) = USD 91,652.

So the VaR will increase by (91,652 – 69,282), or USD 22,370. Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, Chapter 7: Portfolio Risk — Analytical Methods, pp. 161-164. AIM: Compute diversified VaR, individual VaR, and undiversified VaR of a portfolio. Section: Risk Management and Investment Management

68



19.

In calculating its risk-adjusted return on capital, your bank uses a capital charge of 2.50% for revolving credit facilities with a loan equivalent factor of 0.35 assigned to the undrawn portion. Recently, you have become concerned that the protective covenants embedded in these loans are weak and may not prevent customers from drawing on the facilities during times of stress. As such, you have recommended doubling the loan equivalent factor to 0.70. This recommendation has met with resistance from the loan origination team, and senior management has asked you to quantify the impact of your recommendation. For a typical facility that has an original principal of USD 1 billion and is 30% drawn, how much additional economic capital would have to be allocated if you increase the loan equivalent factor from 0.35 to 0.70? a. b. c. d.

USD USD USD USD


Correct answer: b Explanation: The required economic capital to support a loan in the RAROC model can be calculated using the following formula: Required Capital=[BDRAWN + (BUNDRAWN * LEF )]*CF where LEF represents the loan equivalent factor and CF represents the capital factor. Therefore the initial required economic capital is calculated as follows: [(1 billion * 0.3) + (1 billion * 0.7 * 0.35)] * 2.5% = USD 13.625 million, and the required capital if the change is implemented would be: [(1 billion * 0.3) + (1 billion * 0.7 * 0.70)] * 2.5% = USD 19.75 million. Hence the additional required economic capital would be 19.75 – 13.625 or 6.13 million. Reference: Michel Crouhy, Dan Galai and Robert Mark, Risk Management (New York: McGraw-Hill, 2001), Chapter 14, p. 550. AIM: Compute and interpret the RAROC for a loan or loan portfolio, and use RAROC to compare business unit performance. Section: Operational and Integrated Risk Management


69


20.

Which of the following statements regarding frictions in the securitization of subprime mortgages is correct? a. b. c. d.

The arranger will typically have an information advantage over the originator with regard to the quality of the loans securitized. The originator will typically have an information advantage over the arranger, which can create an incentive for the originator to collaborate with the borrower in filing false loan applications. The major credit rating agencies are paid by investors for their rating service of mortgage-backed securities, and this creates a potential conflict of interest. The use of escrow accounts for insurance and tax payments eliminates the risk of foreclosure.

Correct answer: b Explanation: One of the key frictions in the process of securitization involves an information problem between the originator and arranger. In particular, the originator has an information advantage over the arranger with regard to the quality of the borrower. Without adequate safeguards in place, an originator can have the incentive to collaborate with a borrower in order to make significant misrepresentations on the loan application. Depending on the situation, this could be either construed as predatory lending (where the lender convinces the borrower to borrow too large of a sum given the borrower’s financial situation) or predatory borrowing (the borrower convinces the lender to lend too large a sum). The major rating agencies are not paid by the investors. Escrow accounts can forestall but not eliminate the risk of foreclosure. Reference: Adam Ashcroft and and Til Schuermann, “Understanding the Securitization of Subprime Mortgage Credit”, FRB of NY Staff reports, No. 318 (March 2008), page i. AIM: Identify and describe key frictions in subprime mortgage securitization, and assess the relative contribution of each factor to the subprime mortgage problems. Section: Credit Risk Measurement and Management

70


Creating a culture of risk awareness.®

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About GARP | The Global Association of Risk Professionals (GARP) is a not-for-profit global membership organization dedicated to preparing professionals and organizations to make better informed risk decisions. Membership represents over 150,000 Members and Affiliates from banks, investment management firms, government agencies, academic institutions, and corporations from more than 195 countries and territories. GARP administers the Financial Risk Manager (FRM®) and the Energy Risk Professional (ERP®) Exams; certifications recognized by risk professionals worldwide. GARP also helps advance the role of risk management via comprehensive professional education and training for professionals of all levels. www.garp.org.

© 2013 Global Association of Risk Professionals. All rights reserved. 12-03-12

2014

FRM Examination Practice Exam PART I and PART II


TABLE OF CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Reference Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 Special instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 2014 FRM Part I Practice Exam Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . .3 2014 FRM Part I Practice Exam Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 2014 FRM Part I Practice Exam Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . . . .15 2014 FRM Part I Practice Exam Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17



i


INTRODUCTION

Core readings were selected by the FRM Committee to assist candidates in their review of the subjects covered

The FRM Exam is a practice-oriented examination. Its questions

by the Exam. Questions for the FRM Exam are derived

are derived from a combination of theory, as set forth in the


core readings, and “real-world” work experience. Candidates


are expected to understand risk management concepts and

for the Exam.

approaches and how they would apply to a risk manager’s day-to-day activities. The FRM Exam is also a comprehensive examination, testing a risk professional on a number of risk management


concepts and approaches. It is very rare that a risk manager will be faced with an issue that can immediately be slotted


into one category. In the real world, a risk manager must be


able to identify any number of risk-related issues and be


able to deal with them effectively.

actual Exam.

The 2014 FRM Practice Exams I and II have been developed to aid candidates in their preparation for the FRM Exam in


May and November 2014. These Practice Exams are based

•


on a sample of questions from the 2010 through 2013 FRM

•


Exams and are suggestive of the questions that will be in

erasers) available.

the 2014 FRM Examination. The 2014 FRM Practice Exam for Part I contains 25

•


multiple-choice questions and the 2014 FRM Practice Exam for Part II contains 20 multiple-choice questions. Note that


•


the 2014 FRM Exam Part I will contain 100 multiple-choice


questions and the 2014 FRM Exam Part II will contain


80 multiple-choice questions. The Practice Exams were


designed to be shorter to allow candidates to calibrate

•




The 2014 FRM Practice Exams do not necessarily cover all topics to be tested in the 2014 FRM Exam as the material


covered in the 2014 Study Guide may be different from that


that covered by the 2010 through 2012 Study Guides. The


questions selected for inclusion in the Practice Exams were chosen to be broadly reflective of the material assigned for 2014 as well as to represent the style of question that the



FRM Committee considers appropriate based on


assigned material.



For a complete list of current topics, core readings, and key learning


objectives candidates should refer to the 2014 FRM Exam Study Guide


and AIM Statements.



1


Reference Table: Let Z be a standard normal random variable.

2



Special Instructions and Definitions 1. Unless otherwise indicated, interest rates are assumed to be continuously compounded. 2. Unless otherwise indicated, option contracts are assumed to be on one unit of the underlying asset. 3. VaR = value-at-risk 4. ES = expected shortfall 5. GARCH = generalized auto-regressive conditional heteroskedasticity 6. CAPM = capital asset pricing model 7. LIBOR = London interbank offer rate 8. The following acronyms are used for selected currencies:

Acronym

Currency

ARS

Argentine peso

AUD

Australian dollar

BRL

Brazilian real

CAD

Canadian dollar

CHF

Swiss franc

EUR

euro

GBP

British pound sterling

HKD

Hong Kong dollar

INR

Indian rupee

JPY

Japanese yen

MXN

Mexican peso

SGD

Singapore dollar

USD

US dollar


3


Answer Sheet


a.

b.

c.

d.

a.

1.

16.

2.

17.

3.

18.

4.

19.

5.

20.

6.

21.

7.

22.

8.

23.

9.

24.

10.

25.

b.

c.

d.

✓

✘

11. 12.


13.

1.

14.


15.

1.


5


Questions


1.

An analyst is preparing a valuation report on Wacha Corporation, a conglomerate which consists of three separate business units. The analyst has already estimated the unlevered beta of each of the firm’s business units based on data from the unit’s closest competitors, but would like to construct a beta metric that reflects the composite risk profile of the firm, taking into consideration its financing. According to its most recent financial statements, the firm has a debt to equity ratio of 1.1 and an effective corporate tax rate of 32.0%. Additional information about the firm’s three business units is as follows: Business Unit Telecom Internet Services Software

Percentage of Revenues 35% 40% 25%

Unlevered Beta 0.49 1.73 1.47

Based on this information, what is the levered beta of the firm? a. b. c. d.

2.

The board of directors plays a key role in the process of creating a strong culture of risk management at an organization. As part of this role, one function that should be fulfilled by the board of directors is to: a. b. c. d.

3.

1.75 1.92 2.15 2.33

Monitor the effectiveness of the company’s governance practices and make changes, if necessary, to ensure proper compliance. Ensure that the interests of the company’s stakeholders are prioritized above its executives’ interests in order to maximize the potential return on investment. Address issues that could potentially represent a conflict of interest by assigning committees composed exclusively of executive board members. Establish a policy to address individual risk factors by either reducing, hedging, or avoiding exposure to each risk.

A bank’s risk manager is considering different viewpoints for reporting data quality metrics within a data quality scorecard: a data quality issues viewpoint, a business process viewpoint, and a business impact viewpoint. For which of the following purposes would a business process viewpoint be most effective? a. b. c. d.

Aggregating the business impacts of poor quality data across different business processes. Creating a high-level overview of risks associated with data issues on the trading desk. Isolating the point at which data issues begin to arise in a foreign exchange hedging procedure. Identifying organizational processes that require enhanced monitoring and control.


7


4.

Suppose the S&P 500 has an expected annual return of 7.6% and volatility of 10.8%. Suppose the Atlantis Fund has an expected annual return of 8.3% and volatility of 8.8% and is benchmarked against the S&P 500. If the riskfree rate is 2.0% per year, what is the beta of the Atlantis Fund according to the Capital Asset Pricing Model? a. b. c. d.

5.

In October 1994, General Electric sold Kidder Peabody to Paine Webber, which eventually dismantled the firm. Which of the following led up to the sale? a. b. c. d.

6.

0.81 0.89 1.13 1.23

Kidder Peabody had its primary dealer status revoked by the Federal Reserve after it was found to have submitted fraudulent bids at US Treasury auctions. Kidder Peabody reported a large quarterly loss from highly leveraged positions, which left the company insolvent and on the verge of bankruptcy. Kidder Peabody suffered a large loss when counterparties to its CDS portfolio could not honor their contracts, which left the company with little equity. Kidder Peabody reported a sudden large accounting loss to correct an error in the firm's accounting system, which called into question the management team's competence.

You are evaluating the performance of a portfolio of Mexican equities that is benchmarked to the IPC Index. You collect the information about the portfolio and the benchmark index shown in the table below: Expected return on the portfolio Volatility of returns on the portfolio Expected return on the IPC Index Volatility of returns on the IPC Index Risk-free rate of return Beta of portfolio relative to IPC Index

6.6% 13.1% 4.0% 8.7% 1.5% 1.4

What is the Sharpe ratio for this portfolio? a. b. c. d.

8

0.036 0.047 0.389 0.504



7.

You have estimated a regression of your firm’s monthly portfolio returns against the returns of three U.S. domestic equity indexes: the Russell 1000 index, the Russell 2000 index, and the Russell 3000 index. The results are shown below. Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

0.951 0.905 0.903 0.009 192

Regression Output

Coefficients

Standard Error

t Stat

P-value

Intercept Russell 1000 Russell 2000 Russell 3000

0.0023 0.1093 0.1055 0.3533

0.0006 1.5895 0.1384 1.7274

3.5305 0.0688 0.7621 0.2045

0.0005 0.9452 0.4470 0.8382

Correlation Matrix

Portfolio Returns

Russell 1000

Russell 2000

Russell 3000

Portfolio Returns Russell 1000 Russell 2000 Russell 3000

1.000 0.937 0.856 0.945

1.000 0.813 0.998

1.000 0.845

1.000

Based on the regression results, which statement is correct? a. b. c. d.

The estimated coefficient of 0.3533 indicates that the returns of the Russell 3000 index are more statistically significant in determining the portfolio returns than the other two indexes. The high adjusted R2 indicates that the estimated coefficients on the Russell 1000, Russell 2000, and Russell 3000 indexes are statistically significant. The high p-value of 0.9452 indicates that the regression coefficient of the returns of Russell 1000 is more statistically significant than the other two indexes. The high correlations between each pair of index returns indicate that multicollinearity exists between the variables in this regression.


9


8.

You are examining a portfolio that consists of 600 subprime mortgages and 400 prime mortgages. Of the subprime mortgages, 120 are late on their payments. Of the prime mortgages, 40 are late on their payments. If you randomly select a mortgage from the portfolio and it is currently late on its payments, what is the probability that it is a subprime mortgage? a. b. c. d.

9.

Emanuel Lee is analyzing his new credit portfolio, which consists of a large number of companies. He assumes that the time, measured in years, between successive defaults follows an exponential distribution. If N denotes the number of defaults over the next year, what is the appropriate probability distribution of N? a. b. c. d.

10.

60% 67% 75% 80%

Poisson Generalized Pareto Weibull Gamma

Sarah Wong is testing her hypothesis that the beta, 𝛽, of stock CDM is 1. She runs an ordinary least squares regression of the monthly returns of CDM, RCDM, on the monthly returns of the S&P 500 index, Rm, and obtains the following relation: 𝑅𝐶𝐷𝑀 = 0.86 𝑅𝑚 − 0.32 Sarah also observes that the standard error of the coefficient of Rm is 0.80. In order to test the hypothesis H0: 𝛽 = 1 against H1: 𝛽 ≠ 1, what is the correct statistic to calculate? a. b. c. d.

10

t-statistic Chi-square test statistic Jarque-Bera test statistic Sum of squared residuals



11.

Which of the following statements about the exponentially weighted moving average (EWMA) model and the generalized autoregressive conditional heteroscedasticity (GARCH(1,1)) model is correct? a. b. c. d.

12.

The EWMA model is a special case of the GARCH(1,1) model with the additional assumption that the longrun volatility is zero. A variance estimate from the EWMA model is always between the prior day’s estimated variance and the prior day’s squared return. The GARCH(1,1) model always assigns less weight to the prior day’s estimated variance than the EWMA model. A variance estimate from the GARCH(1,1) model is always between the prior day’s estimated variance and the prior day’s squared return.

A risk manager is examining a Hong Kong trader’s profit and loss record for the last week, as shown in the table below: Trading Day Monday Tuesday Wednesday Thursday Friday

Profit/Loss (HKD million) 10 80 90 -60 30

The profits and losses are normally distributed with a mean of 4.5 million HKD and assume that transaction costs can be ignored. Part of the t-table is provided below: Percentage Point of the t Distribution P(T>t) = α α Degrees of Freedom 0.3 0.2 0.15 4 0.569 0.941 1.19 5 0.559 0.92 1.156 According to the information provided above, what is the probability that this trader will record a profit of at least HKD 30 million on the first trading day of next week? a. b. c. d.

About About About About

15% 20% 80% 85%


11


13.

An experienced commodities risk manager is examining corn futures quotes from the CME Group. Which of the following observations would the risk manager most likely view as a potential problem with the quotation data? a. b. c. d.

14.

A portfolio manager controls USD 88 million par value of zero-coupon bonds maturing in 5 years and yielding 4%. The portfolio manager expects that interest rates will increase. To hedge the exposure, the portfolio manager wants to sell part of the 5-year bond position and use the proceeds from the sale to purchase zero-coupon bonds maturing in 1.5 years and yielding 3%. What is the market value of the 1.5-year bonds that the portfolio manager should purchase to reduce the duration on the combined position to 3 years? a. b. c. d.

15.

USD USD USD USD


A 15-month futures contract on an equity index is currently trading at USD 3,767.52. The underlying index is currently valued at USD 3,625 and has a continuously-compounded dividend yield of 2% per year. The continuously compounded risk-free rate is 5% per year. Assuming no transactions costs, what is the potential arbitrage profit per contract and the appropriate strategy? a. b. c. d.

12

The volume in a specific contract is greater than the open interest. The prices indicate a mixture of normal and inverted markets. The settlement price for a specific contract is above the high price. There is no contract with maturity in a particular month.

USD USD USD USD

189, buy the futures contract and sell the underlying. 4, buy the futures contract and sell the underlying. 189, sell the futures contract and buy the underlying. 4, sell the futures contract and buy the underlying.



16.

Savers Bancorp entered into a swap agreement over a 2-year period on August 9, 2008, with which it received a 4.00% fixed rate and paid LIBOR plus 1.20% on a notional amount of USD 6.5 million. Payments were to be made every 6 months. The table below displays the actual annual 6-month LIBOR rates over the 2-year period. Date

6-month LIBOR

Aug 9, 2008 Feb 9, 2009 Aug 9, 2009 Feb 9, 2010 Aug 9, 2010

3.11% 1.76% 0.84% 0.39% 0.58%

Assuming no default, how much did Savers Bancorp receive on August 9, 2010? a. b. c. d.

17.

72,150 78,325 117,325 156,650

The six-month forward price of commodity X is USD 1,000. Six-month, risk-free, zero-coupon bonds with face value USD 1,000 trade in the fixed income market. When taken in the correct amounts, which of the following strategies creates a synthetic long position in commodity X for a period of 6 months? a. b. c. d.

18.

USD USD USD USD

Short the forward contract and short the zero-coupon bond. Short the forward contract and buy the zero-coupon bond. Buy the forward contract and short the zero-coupon bond. Buy the forward contract and buy the zero-coupon bond.

A call provision embedded in a corporate bond can be viewed as an option held by the ______, and therefore, the price of a callable bond will be _____ than the price of a similar noncallable bond. a. b. c. d.

issuer, greater issuer, lower investor, greater investor, lower


13


19.

Bank A and Bank B are two competing investment banks that are calculating the 1-day 99% VaR for an at-themoney call on a non-dividend-paying stock with the following information: • • • •

Current stock price: USD 120 Estimated annual stock return volatility: 18% Current Black-Scholes-Merton option value: USD 5.20 Option delta: 0.6

To compute VaR, Bank A uses the linear approximation method, while Bank B uses a Monte Carlo simulation method for full revaluation. Which bank will estimate a higher value for the 1-day 99% VaR? a. b. c. d.

20.

Portfolio A has a 1-day 95% VaR, denoted by VaR(A), and Portfolio B has a 1-day 95% VaR, denoted by VaR(B). If Portfolio A and Portfolio B are combined into a new Portfolio C with a 1-day 95% VaR denoted by VaR(C), which of the following statements will always be correct? a. b. c. d.

21.

VaR(C) ≤ VaR(A) + VaR(B) VaR(C) = VaR(A) + VaR(B) VaR(C) ≥ VaR(A) + VaR(B) None of the above.

In evaluating the dynamic delta hedging of a portfolio of short option positions, which of the following is correct? a. b. c. d.

14

Bank A. Bank B. Both will have the same VaR estimate. Insufficient information to determine.

The The The The

interest interest interest interest

cost cost cost cost

of of of of

carrying carrying carrying carrying

the the the the

delta delta delta delta

hedge hedge hedge hedge

will will will will

be be be be

highest when the options are deep out-of-the-money. highest when the options are deep in-the-money. lowest when the options are at-the-money. highest when the options are at-the-money.



QUESTIONS 22 AND 23 REFER TO THE FOLLOWING INFORMATION A risk manager is evaluating the price sensitivity of an investment-grade callable bond using the firm’s valuation system. The table below presents information on the bond as well as on the embedded option. The current interest rate environment is flat at 5%. Value in USD per USD 100 face value Interest Rate Level 4.98% 5.00% 5.02%

22.

Callable Bond

Call Option

102.07848 101.61158 100.92189

2.08719 2.05010 2.01319

The DV01 of a comparable bond with no embedded options having the same maturity and coupon rate is closest to: a. b. c. d.

0.0185 0.2706 0.2891 0.3077

SEE INFORMATION PRECEDING QUESTION 23 A risk manager is evaluating the price sensitivity of an investment-grade callable bond using the firm’s valuation system. The table below presents information on the bond as well as on the embedded option. The current interest rate environment is flat at 5%. Value in USD per USD 100 face value Interest Rate Level 4.98% 5.00% 5.02%

23.

Callable Bond

Call Option

102.07848 101.61158 100.92189

2.08719 2.05010 2.01319

The convexity of the callable bond can be estimated as: a. b. c. d.

-55,698 -54,814 -5.5698 -5.4814


15


24.

A portfolio contains a long position in an option contract on a US Treasury bond. The option exhibits positive convexity across the entire range of potential returns for the underlying bond. This positive convexity: a. b. c. d.

25.

An implementation principle recommended by the Basel Committee to banks for the governance of sound stress testing practices is that stress testing reports should: a. b. c. d.

16

Implies that the option’s value increases at a decreasing rate as the option goes further into the money. Makes a long option position a superior investment compared to a long bond position of equivalent duration. Can be effectively hedged by the sale of a negatively convex financial instrument. Implies that the option increases in value as market volatility increases.

Not be passed up to senior management without first being approved by middle management. Have limited input from their respective business areas to prevent biasing of the results. Challenge prior assumptions to help foster debate among decision makers. Be separated by business lines to help identify risk concentrations.




Answers


a.

b.

d.

1. 2.

c.

a.

18.

4.

19.

5.

6.

8.

10.

25.

14. 15.

23. 24.

12.

22.

20.

9.

11.

21.

7.

d.

17.

3.


13.

c.

16.

b.

1.

✓

✘


1.


19


Explanations


1.

An analyst is preparing a valuation report on Wacha Corporation, a conglomerate which consists of three separate business units. The analyst has already estimated the unlevered beta of each of the firm’s business units based on data from the unit’s closest competitors, but would like to construct a beta metric that reflects the composite risk profile of the firm, taking into consideration its financing. According to its most recent financial statements, the firm has a debt to equity ratio of 1.1 and an effective corporate tax rate of 32.0%. Additional information about the firm’s three business units is as follows: Business Unit Telecom Internet Services Software

Percentage of Revenues 35% 40% 25%

Unlevered Beta 0.49 1.73 1.47

Based on this information, what is the levered beta of the firm? a. b. c. d.

1.75 1.92 2.15 2.33

Correct answer: c Explanation: A levered equity beta can be calculated using the following formula: Levered Beta = Unlevered Beta * (1 + (1-tax rate) (Debt/Equity)) First, we should calculate the unlevered beta, which is the weighted average of the unlevered segment betas (weighted by proportion of revenues): (0.35 * 0.49) + (0.40 * 1.73) + (0.25 * 1.47) = 1.231. Inputting this factor along with the given tax rate and debt/equity ratio into the equation provides the levered beta: Levered beta = 1.231 * (1 + (1-.320) * 1.1) = 2.15 Section: Foundations of Risk Management Reference: Oliviero Roggi, Maxine Garvey, Aswath Damodaran (2012), Risk Taking: A Corporate Governance Perspective (International Finance Corporation: World Bank Group), pp. 20-21. AIMS: Describe the impact of leverage and taxes in the calculation of an equity beta for a firm.


21


2.

The board of directors plays a key role in the process of creating a strong culture of risk management at an organization. As part of this role, one function that should be fulfilled by the board of directors is to: a. b. c. d.

Monitor the effectiveness of the company’s governance practices and make changes, if necessary, to ensure proper compliance. Ensure that the interests of the company’s stakeholders are prioritized above its executives’ interests in order to maximize the potential return on investment. Address issues that could potentially represent a conflict of interest by assigning committees composed exclusively of executive board members. Establish a policy to address individual risk factors by either reducing, hedging, or avoiding exposure to each risk.

Correct answer: a Explanation: One of the key responsibilities of a board of directors should be to monitor the effectiveness of the firm’s governance practices and ensure proper compliance with these practices. Boards should ensure that the interest of management and stakeholders are aligned with neither group being prioritized, and should ideally address potential conflicts of interest by including a significant proportion of independent (non-executive) board members. A firm should not necessarily mitigate or avoid each risk factor it faces, as it can also add value in some situations by retaining specific risk factors in order to exploit those risks. Section: Foundations of Risk Management Reference: Oliviero Roggi, Maxine Garvey, Aswath Damodaran (2012), Risk Taking: A Corporate Governance Perspective, International Finance Corporation: World Bank Group. AIMS: Describe a risk profile and describe the role of risk governance in an organization.

22



3.

A bank’s risk manager is considering different viewpoints for reporting data quality metrics within a data quality scorecard: a data quality issues viewpoint, a business process viewpoint, and a business impact viewpoint. For which of the following purposes would a business process viewpoint be most effective? a. b. c. d.

Aggregating the business impacts of poor quality data across different business processes. Creating a high-level overview of risks associated with data issues on the trading desk. Isolating the point at which data issues begin to arise in a foreign exchange hedging procedure. Identifying organizational processes that require enhanced monitoring and control.

Correct answer: c Explanation: A business process view would be the best choice when the firm is looking to isolate the specific point within a business process where data quality issues are introduced, as in this example. Section: Foundations of Risk Management Reference: Anthony Tarantino and Deborah Cernauskas (2009), Chapter 3: Information Risk and Data Quality Management, Risk Management in Finance: Six Sigma and other Next Generation Techniques, Hoboken, NJ, John Wiley & Sons. AIMS: Describe the process of creating a data quality scorecard and compare three different viewpoints for reporting data via a data quality scorecard.

4.

Suppose the S&P 500 has an expected annual return of 7.6% and volatility of 10.8%. Suppose the Atlantis Fund has an expected annual return of 8.3% and volatility of 8.8% and is benchmarked against the S&P 500. If the riskfree rate is 2.0% per year, what is the beta of the Atlantis Fund according to the Capital Asset Pricing Model? a. b. c. d.

0.81 0.89 1.13 1.23

Correct answer: c Explanation: Since the correlation or covariance between the Atlantis Fund and the S&P 500 is not known, CAPM − − must be used to back out the beta: 𝑅𝑖 = 𝑅𝐹 + 𝛽𝑖∙(𝑅𝑀 − 𝑅𝐹). Therefore: (8.3% − 2.0%) 8.3% = 2.0% + 𝛽𝑖∙(7.6% − 2.0%); hence 𝛽𝑖 = or 1.13. (7.6% − 2.0%) Section: Foundations of Risk Management Reference: Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann, Modern Portfolio Theory and Investment Analysis, 7th Edition — Chapter 13. AIMS: Use the CAPM to calculate the expected return on an asset. Define beta and calculate the beta of a single asset or portfolio.


23


5.

In October 1994, General Electric sold Kidder Peabody to Paine Webber, which eventually dismantled the firm. Which of the following led up to the sale? a. b. c. d.

Kidder Peabody had its primary dealer status revoked by the Federal Reserve after it was found to have submitted fraudulent bids at US Treasury auctions. Kidder Peabody reported a large quarterly loss from highly leveraged positions, which left the company insolvent and on the verge of bankruptcy. Kidder Peabody suffered a large loss when counterparties to its CDS portfolio could not honor their contracts, which left the company with little equity. Kidder Peabody reported a sudden large accounting loss to correct an error in the firm's accounting system, which called into question the management team's competence.

Correct answer: d Explanation: Kidder Peabody’s accounting system failed to account for the present value of forward trades, which allowed trader Joseph Jett to book an instant, but fraudulent, accounting profit by purchasing cash bonds to be delivered at a later date. These profits would dissipate as the bonds approached their delivery date, but Jett covered this up by rolling the positions forward with increasingly greater positions and longer lengths to delivery, which created a higher stream of hypothetical profits due to the accounting flaw. Finally this stream of large profits was investigated and Kidder Peabody was forced to take a USD 350 million accounting loss to reverse the reported gains, which resulted in a loss of confidence in the firm and General Electric’s subsequent sale. Section: Foundations of Risk Management Reference: Steve Allen, Financial Risk Management: A Practitioner's Guide to Managing Market and Credit Risk (New York: John Wiley & Sons, 2012), Chapter 4: Financial Disasters. AIMS: Describe the key factors that led to and the lessons learned from the following risk management case studies: Kidder Peabody.

24



6.

You are evaluating the performance of a portfolio of Mexican equities that is benchmarked to the IPC Index. You collect the information about the portfolio and the benchmark index shown in the table below: Expected return on the portfolio Volatility of returns on the portfolio Expected return on the IPC Index Volatility of returns on the IPC Index Risk-free rate of return Beta of portfolio relative to IPC Index

6.6% 13.1% 4.0% 8.7% 1.5% 1.4

What is the Sharpe ratio for this portfolio? a. b. c. d.

0.036 0.047 0.389 0.504

Correct answer: c Explanation: The Sharpe ratio for the portfolio is

Expected Return on Portfolio — Risk Free Rate Volatility of Returns of Portfolio

=

6.6% − 1.5% 13.1%

= 0.389.

Section: Foundations of Risk Management Reference: Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England: Wiley, 2003), Chapter 4, Section 4.2 — Applying the CAPM to Performance Measurement: Single-Index Performance Measurement Indicators. AIMS: Calculate, compare, and evaluate the Treynor measure, the Sharpe measure, and Jensen's alpha.


25


7.

You have estimated a regression of your firm’s monthly portfolio returns against the returns of three U.S. domestic equity indexes: the Russell 1000 index, the Russell 2000 index, and the Russell 3000 index. The results are shown below. Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

0.951 0.905 0.903 0.009 192

Regression Output

Coefficients

Standard Error

t Stat

P-value

Intercept Russell 1000 Russell 2000 Russell 3000

0.0023 0.1093 0.1055 0.3533

0.0006 1.5895 0.1384 1.7274

3.5305 0.0688 0.7621 0.2045

0.0005 0.9452 0.4470 0.8382

Correlation Matrix

Portfolio Returns

Russell 1000

Russell 2000

Russell 3000

Portfolio Returns Russell 1000 Russell 2000 Russell 3000

1.000 0.937 0.856 0.945

1.000 0.813 0.998

1.000 0.845

1.000

Based on the regression results, which statement is correct? a. b. c. d.

The estimated coefficient of 0.3533 indicates that the returns of the Russell 3000 index are more statistically significant in determining the portfolio returns than the other two indexes. The high adjusted R2 indicates that the estimated coefficients on the Russell 1000, Russell 2000, and Russell 3000 indexes are statistically significant. The high p-value of 0.9452 indicates that the regression coefficient of the returns of Russell 1000 is more statistically significant than the other two indexes. The high correlations between each pair of index returns indicate that multicollinearity exists between the variables in this regression.

Correct answer: d Explanation: This is an example of multicollinearity, which arises when one of the regressors is very highly correlated with the other regressors. In this case, all three regressors are highly correlated with each other, so multicollinearity exists between all three. Since the variables are not perfectly correlated with each other this is a case of imperfect, rather than perfect, multicollinearity. Section: Quantitative Analysis Reference: Stock and Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008). • Chapter 6, Linear Regression with Multiple Regressors • Chapter 7, Hypothesis Tests and Confidence Intervals in Multiple Regression AIMS: Define and interpret the slope coefficient in a multiple regression. Interpret the R2 and adjusted-R2 in a multiple regression. Explain the concepts of imperfect and perfect multicollinearity and their implications.

26



8.

You are examining a portfolio that consists of 600 subprime mortgages and 400 prime mortgages. Of the subprime mortgages, 120 are late on their payments. Of the prime mortgages, 40 are late on their payments. If you randomly select a mortgage from the portfolio and it is currently late on its payments, what is the probability that it is a subprime mortgage? a. b. c. d.

60% 67% 75% 80%

Correct answer: c Explanation: In order to solve this conditional probability question, first calculate the probability that any one mortgage in the portfolio is late. This is: P(Mortgage is late) = (120 + 40)/1000 = 16%. Next use the conditional probability relationship as follows: P (Mortgage subprime | Mortgage is late) = P(Mortgage subprime and late) / P(Mortgage is late) Since P(Mortgage subprime and late) = 120/1000 = 12%; therefore P(Mortgage subprime | Mortgage is late) = 12% / 16% = 0.75 = 75%. Hence the probability that a random late mortgage selected from this portfolio turns out to be subprime is 75%. Section: Quantitative Analysis Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston, Pearson Education, 2008), Chapter 2. AIMS: Describe joint, marginal, and conditional probability functions.


27


9.

Emanuel Lee is analyzing his new credit portfolio, which consists of a large number of companies. He assumes that the time, measured in years, between successive defaults follows an exponential distribution. If N denotes the number of defaults over the next year, what is the appropriate probability distribution of N? a. b. c. d.

Poisson Generalized Pareto Weibull Gamma

Correct answer: a Explanation: The number of defaults in a given time period t with exponentially distributed default arrival times 𝑘 1 with density 𝑓(𝑥) = β 𝑒−𝑥/β are Poisson distributed with density 𝑃 (𝑥 = 𝑘) = 𝜆𝑘! 𝑒−𝜆 where λ = t/β. Section: Quantitative Analysis Reference: Michael Miller, Mathematics and Statistics for Financial Risk Management, 1st Edition (Wiley, 2012) Chapter 4: Distributions. AIMS: Describe the key properties of the following distributions: uniform distribution, Bernoulli distribution, Binomial distribution, Poisson distribution, normal distribution, lognormal distribution, Chi-squared distribution, Student’s t, and F-distributions, and identify common occurrences of each distribution.

28



10.

Sarah Wong is testing her hypothesis that the beta, 𝛽, of stock CDM is 1. She runs an ordinary least squares regression of the monthly returns of CDM, RCDM, on the monthly returns of the S&P 500 index, Rm, and obtains the following relation: 𝑅𝐶𝐷𝑀 = 0.86 𝑅𝑚 − 0.32 Sarah also observes that the standard error of the coefficient of Rm is 0.80. In order to test the hypothesis H0: 𝛽 = 1 against H1: 𝛽 ≠ 1, what is the correct statistic to calculate? a. b. c. d.

t-statistic Chi-square test statistic Jarque-Bera test statistic Sum of squared residuals

Correct answer: a Explanation: The correct test is the t test. The t statistic is defined by: t=

𝛽 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 −𝛽 𝑆𝐸 (𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝛽)

=

0.86 − 1 0.8

In this case t = -0.175. Since |t| < 1.96 we cannot reject the null hypothesis. Section: Quantitative Analysis Reference: Stock and Watson, Introduction to Econometrics, Chapter 5. AIMS: Define and interpret hypothesis tests about regression coefficients.


29


11.

Which of the following statements about the exponentially weighted moving average (EWMA) model and the generalized autoregressive conditional heteroscedasticity (GARCH(1,1)) model is correct? a. b. c. d.

The EWMA model is a special case of the GARCH(1,1) model with the additional assumption that the longrun volatility is zero. A variance estimate from the EWMA model is always between the prior day’s estimated variance and the prior day’s squared return. The GARCH(1,1) model always assigns less weight to the prior day’s estimated variance than the EWMA model. A variance estimate from the GARCH(1,1) model is always between the prior day’s estimated variance and the prior day’s squared return.

Correct answer: b Explanation: The EWMA estimate of variance is a weighted average of the prior day’s variance and prior day squared return. Section: Quantitative Analysis Reference: John Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson, 2012), Chapter 22: Estimating Volatilities and Correlations. AIMS: Describe the exponentially weighted moving average (EWMA) model for estimating volatility and its properties, and estimate volatility using the EWMA model. Describe the generalized autoregressive conditional heteroskedasticity (GARCH(p,q)) model for estimating volatility and its properties.

30



12.

A risk manager is examining a Hong Kong trader’s profit and loss record for the last week, as shown in the table below: Trading Day Monday Tuesday Wednesday Thursday Friday

Profit/Loss (HKD million) 10 80 90 -60 30

The profits and losses are normally distributed with a mean of 4.5 million HKD and assume that transaction costs can be ignored. Part of the t-table is provided below: Percentage Point of the t Distribution P(T>t) = α α Degrees of Freedom 0.3 0.2 0.15 4 0.569 0.941 1.19 5 0.559 0.92 1.156 According to the information provided above, what is the probability that this trader will record a profit of at least HKD 30 million on the first trading day of next week? a. b. c. d.

About About About About

15% 20% 80% 85%

Correct answer: b Explanation: When the population mean and population variance are not known, the t-statistic can be used to analyze the distribution of the sample mean. Sample mean = (10 + 80 + 90-60 + 30)/5 = 30 Unbiased sample variance = (1/4)[ (-20)^2 + 50^2 + 60^2 + (-90)^2 + 0^2 ] = 14600/4 = 3650 Unbiased sample standard deviation = 60.4152 Sample standard error = (sample standard deviation)/√5 = 27.0185 Population mean of return distribution = 4.5 (million HKD) Therefore the t-statistic = (Sample mean – population mean)/Sample standard error = (30-4.5)/27.02 = 0.9438. Because we are using the sample mean in the analysis, we must remove 1 degree of freedom before consulting the t-table; therefore 4 degrees of freedom are used. According to the table, the closest possibility is 0.2 = 20%. Section: Quantitative Analysis References: Michael Miller, Mathematics and Statistics for Financial Risk Management, 1st Edition (Wiley, 2012) Chapter 4: Distributions. Stock and Watson, Introduction to Econometrics, Brief Edition, Chapter 5: Regression with a Single Regressor AIMS: Define, describe, apply, and interpret the t-statistic when the sample size is small. © 2014 Global Association of Risk Professionals. All rights reserved. It is illegal to reproduce this material in any format without prior written approval of GARP, Global Association of Risk Professionals, Inc.

31


13.

An experienced commodities risk manager is examining corn futures quotes from the CME Group. Which of the following observations would the risk manager most likely view as a potential problem with the quotation data? a. b. c. d.

The volume in a specific contract is greater than the open interest. The prices indicate a mixture of normal and inverted markets. The settlement price for a specific contract is above the high price. There is no contract with maturity in a particular month.

Correct answer: c Explanation: The reported high price of a futures contract should reflect all prices for the day, so the settlement price should never be greater than the high price. Section: Financial Markets and Products Reference: John Hull, Options, Futures and Other Derivatives (New York, Pearson, 2012), Chapter 2: Mechanics of Futures Markets. AIMS: Define and describe the key features of a futures contract.

14.

A portfolio manager controls USD 88 million par value of zero-coupon bonds maturing in 5 years and yielding 4%. The portfolio manager expects that interest rates will increase. To hedge the exposure, the portfolio manager wants to sell part of the 5-year bond position and use the proceeds from the sale to purchase zero-coupon bonds maturing in 1.5 years and yielding 3%. What is the market value of the 1.5-year bonds that the portfolio manager should purchase to reduce the duration on the combined position to 3 years? a. b. c. d.

USD USD USD USD


Correct answer: a Explanation: In order to find the proper amount, we first need to calculate the current market value of the portfolio (P), which is: P = 88 * exp (-0.04 * 5) = 72.05 million. The desired portfolio duration (after the sale of the 5-year bond and purchase of the 1.5 year bond) can be expressed as: [5 * (P-X) + 1.5* X]/P = 3 where X represents the market value of the zero-coupon bond with a maturity of 1.5 years. This equation holds true when X = (4/7) * P, or 41.17 million. Section: Financial Markets and Products Reference: Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson, 2012), Chapter 4: Interest Rates. AIMS: Calculate the change in a bond’s price given its duration, its convexity, and a change in interest rates.

32



15.

A 15-month futures contract on an equity index is currently trading at USD 3,767.52. The underlying index is currently valued at USD 3,625 and has a continuously-compounded dividend yield of 2% per year. The continuously compounded risk-free rate is 5% per year. Assuming no transactions costs, what is the potential arbitrage profit per contract and the appropriate strategy? a. b. c. d.

USD USD USD USD

189, buy the futures contract and sell the underlying. 4, buy the futures contract and sell the underlying. 189, sell the futures contract and buy the underlying. 4, sell the futures contract and buy the underlying.

Correct answer: d Explanation: This is an example of index arbitrage. The no-arbitrage value of the futures contract can be calculated as the future value of the spot price: S0 * e(risk-free – dividend yield) x t, where S0 equals the current spot price and t equals the time in years. Future value of the spot price = S0 * exp[(risk free rate — dividend yield) * 1.25] = 3763.5 Since this value is different from the current futures contract price, a potential arbitrage situation exists. Since the futures price is higher than the future value of the spot price in this case, one can short sell the higher priced futures contract, and buy the underlying stocks in the index at the current price. The arbitrage profit would equal 3,767.52 - 3,763.52 = USD 4. Section: Financial Markets and Products Reference: John Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson, 2012), Chapter 5. AIMS: Calculate the forward price given the underlying asset’s spot price, and describe an arbitrage argument between spot and forward prices.


33


16.

Savers Bancorp entered into a swap agreement over a 2-year period on August 9, 2008, with which it received a 4.00% fixed rate and paid LIBOR plus 1.20% on a notional amount of USD 6.5 million. Payments were to be made every 6 months. The table below displays the actual annual 6-month LIBOR rates over the 2-year period. Date

6-month LIBOR

Aug 9, 2008 Feb 9, 2009 Aug 9, 2009 Feb 9, 2010 Aug 9, 2010

3.11% 1.76% 0.84% 0.39% 0.58%

Assuming no default, how much did Savers Bancorp receive on August 9, 2010? a. b. c. d.

USD USD USD USD

72,150 78,325 117,325 156,650

Correct answer: b Explanation: The proper interest rate to use is the 6-month LIBOR rate at February 9, 2010, since it is the 6-month LIBOR that will yield the payoff on August 9, 2010. Therefore the net settlement amount on August 9th, 2010 is as follows: Savers receives: 6,500,000 * 4.00% * 0.5 years, or USD 130,000 Savers pays 6,500,000 * (0.39% + 1.20%) * 0.5 , or USD 51,675. Therefore Savers would receive the difference, or 78,325. Section: Financial Markets and Products Reference: John Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson 2012), Chapter 7. AIMS: Explain the mechanics of a plain vanilla interest rate swap and compute its cash flows.

34



17.

The six-month forward price of commodity X is USD 1,000. Six-month, risk-free, zero-coupon bonds with face value USD 1,000 trade in the fixed income market. When taken in the correct amounts, which of the following strategies creates a synthetic long position in commodity X for a period of 6 months? a. b. c. d.

Short the forward contract and short the zero-coupon bond. Short the forward contract and buy the zero-coupon bond. Buy the forward contract and short the zero-coupon bond. Buy the forward contract and buy the zero-coupon bond.

Correct answer: d Explanation: A synthetic commodity position for a period of T years can be constructed by entering into a long forward contract with T years to expiration and buying a zero-coupon bond expiring in T years with a face value of the forward price. The payoff function is as follows: Payoff from long forward position = ST – F0,T , where ST is the spot price of the commodity at time T and F0,T is the current forward price. Payoff from zero coupon bond: F0,T at time T. Hence, the total payoff function equals (ST – F0,T ) + F0,T or ST. This creates a synthetic commodity position. Section: Financial Markets and Products Reference: Robert McDonald, Derivatives Markets (Boston: Addison-Wesley, 2013). Chapter 6. AIMS: Explain how to create a synthetic commodity position, and use it to explain the relationship between the forward price and the expected future spot price.

18.

A call provision embedded in a corporate bond can be viewed as an option held by the ______, and therefore, the price of a callable bond will be _____ than the price of a similar noncallable bond. a. b. c. d.

issuer, greater issuer, lower investor, greater investor, lower

Correct answer: b Explanation: Many corporate bonds contain an embedded option that gives the issuer the right to buy the bonds back at a fixed price either in whole or in part prior to maturity. The feature is known as a call provision. The ability to retire debt before its scheduled maturity date is a valuable option for the issuer for which bondholders will demand compensation. All else being equal, this compensation will come in the form of bondholders paying a lower price for a callable bond than an otherwise identical option-free (i.e., straight) bond. The difference between the price of an option-free bond and the callable bond is the value of the embedded call option. Section: Financial Markets and Products Reference: Frank Fabozzi, The Handbook of Fixed Income Securities, 8th Edition (New York: McGraw Hill, 2012), Chapter 12. AIMS: Describe the mechanisms by which corporate bonds can be retired before maturity.


35


19.

Bank A and Bank B are two competing investment banks that are calculating the 1-day 99% VaR for an at-themoney call on a non-dividend-paying stock with the following information: • • • •

Current stock price: USD 120 Estimated annual stock return volatility: 18% Current Black-Scholes-Merton option value: USD 5.20 Option delta: 0.6

To compute VaR, Bank A uses the linear approximation method, while Bank B uses a Monte Carlo simulation method for full revaluation. Which bank will estimate a higher value for the 1-day 99% VaR? a. b. c. d.

Bank A. Bank B. Both will have the same VaR estimate. Insufficient information to determine.

Correct answer: a Explanation: The option’s return function is convex with respect to the value of the underlying; therefore the linear approximation method will always underestimate the true value of the option for any potential change in price. Therefore the VaR will always be higher under the linear approximation method than a full revaluation conducted by Monte Carlo simulation analysis. The difference is the bias resulting from the linear approximation, and this bias increases in size with the change in the option price and with the holding period. Section: Valuation and Risk Models Reference: Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach (Oxford: Blackwell Publishing, 2004). Chapter 3. AIMS: Compare delta-normal and full revaluation approaches for computing VaR.

36



20.

Portfolio A has a 1-day 95% VaR, denoted by VaR(A), and Portfolio B has a 1-day 95% VaR, denoted by VaR(B). If Portfolio A and Portfolio B are combined into a new Portfolio C with a 1-day 95% VaR denoted by VaR(C), which of the following statements will always be correct? a. b. c. d.

VaR(C) ≤ VaR(A) + VaR(B) VaR(C) = VaR(A) + VaR(B) VaR(C) ≥ VaR(A) + VaR(B) None of the above.

Correct answer: d Explanation: This question tests the concept of subadditivity. With a subadditive risk measure, at any given confidence level, ρ(A + B) ≤ ρ(A) + ρ(B), where ρ reflects the portfolio risk. However, VaR is not a subadditive measure, which can be proved as follows: Assume that portfolio A and portfolio B each represent a USD 100 position in a single bond with a 1-year default probability of 4% and a recovery rate of zero, with the default probabilities of A and B independent of each other. Therefore, the individual 95% VaR of each portfolio is zero. However, when analyzing the combined portfolio, the probability of no loss is (1-0.04)2, or 0.9216, so the probability of one or more defaults is 1-0.9216, or 7.84%. Since the probability of a loss is greater than 5%, the 95% VaR of the combined portfolio is greater than zero. Therefore, none of the relationships given in choices a, b, and c are correct. Section: Valuation and Risk Models Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005). Chapter 2 — Measures of Financial Risk. AIMS: Explain why VaR is not a coherent risk measure.

21.

In evaluating the dynamic delta hedging of a portfolio of short option positions, which of the following is correct? a. b. c. d.

The The The The

interest interest interest interest

cost cost cost cost

of of of of

carrying carrying carrying carrying

the the the the

delta delta delta delta

hedge hedge hedge hedge

will will will will

be be be be

highest when the options are deep out-of-the-money. highest when the options are deep in-the-money. lowest when the options are at-the-money. highest when the options are at-the-money.

Correct answer: b Explanation: The deeper into-the-money the options are, the larger their deltas and therefore the more expensive to delta hedge. Section: Valuation and Risk Models Reference: John Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson Prentice Hall, 2012), Chapter 18. AIMS: Describe the dynamic aspects of delta hedging.


37


QUESTIONS 22 AND 23 REFER TO THE FOLLOWING INFORMATION A risk manager is evaluating the price sensitivity of an investment-grade callable bond using the firm’s valuation system. The table below presents information on the bond as well as on the embedded option. The current interest rate environment is flat at 5%. Value in USD per USD 100 face value Interest Rate Level 4.98% 5.00% 5.02%

22.

Callable Bond

Call Option

102.07848 101.61158 100.92189

2.08719 2.05010 2.01319

The DV01 of a comparable bond with no embedded options having the same maturity and coupon rate is closest to: a. b. c. d.

0.0185 0.2706 0.2891 0.3077

Correct answer: d Explanation: The call option reduces the bond price, therefore the bond with no embedded options will be the sum of the callable bond price and the call option price. Therefore the price of the bond with no embedded options at a rate of 4.98% would be 104.1657 and the price at a rate of 5.02% would be 102.9351. DV01 is a measure of price sensitivity of a bond. To calculate the DV01, the following equation is used: DV01 = -

∆𝑃 10,000 ∗ ∆𝑦

Where ∆P is the change in price and ∆y is the change in yield. Therefore DV01 = -

102.9351 − 104.1657 10000 ∗ (5.02% − 4.98%)

= 0.3077.

Section: Valuation and Risk Models Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken: John Wiley and Sons, 2011), Chapter 4. AIMS: Define and compute the DV01 of a fixed income security given a change in yield and the resulting change in price.

38



SEE INFORMATION PRECEDING QUESTION 23 A risk manager is evaluating the price sensitivity of an investment-grade callable bond using the firm’s valuation system. The table below presents information on the bond as well as on the embedded option. The current interest rate environment is flat at 5%. Value in USD per USD 100 face value Interest Rate Level 4.98% 5.00% 5.02%

23.

Callable Bond

Call Option

102.07848 101.61158 100.92189

2.08719 2.05010 2.01319

The convexity of the callable bond can be estimated as: a. b. c. d.

-55,698 -54,814 -5.5698 -5.4814

Correct answer: b Explanation: Convexity is defined as the second derivative of the price-rate function divided by the price of the bond. To estimate convexity, one must first estimate the difference in bond price per difference in the rate for two separate rate environments, one a step higher than the current rate and one a step lower. One must then estimate the change across these two values per difference in rate. This is given by the formula: 𝐶=

1 𝑃0

𝑃1 − 𝑃0 - 𝑃0 − 𝑃 − 1 ∆𝑟 ∆𝑟

∆𝑟

=

1 ∗ 𝑃0

∆𝑟2

𝑃1 − 2𝑃0 + 𝑃− 1

.

where ∆𝑟 is the change in the rate in one step; in this case, 0.02%. Therefore, the best estimate of convexity is: C=

1 101.61158

∗

100.92189 − (2 ∗ 1 01.61158) + 102.07848 (0.02%)2

= -54,814.

Section: Valuation and Risk Models Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken: John Wiley and Sons, 2011), Chapter 4. AIMS: Define, compute, and interpret the convexity of a fixed income security given a change in yield and the resulting change in price.


39


24.

A portfolio contains a long position in an option contract on a US Treasury bond. The option exhibits positive convexity across the entire range of potential returns for the underlying bond. This positive convexity: a. b. c. d.

Implies that the option’s value increases at a decreasing rate as the option goes further into the money. Makes a long option position a superior investment compared to a long bond position of equivalent duration. Can be effectively hedged by the sale of a negatively convex financial instrument. Implies that the option increases in value as market volatility increases.

Correct answer: d Explanation: The relationship between convexity and volatility for a security can be seen most clearly through the second-order Taylor approximation of the change in price given a small change in yield. The resulting change in price can be estimated as: 𝟏 ∆𝑷 ≈ − 𝑫∆𝒚 + 𝑪∆𝒚𝟐 𝟐 𝑷

where d is equal to the duration, c is the convexity and y is the change in the interest rate. Since ∆𝒚𝟐 is always positive, positive convexity will lead to an increase in return as long as interest rates move, with larger interest moves in either direction leading to a greater return benefit from the positive convexity. Therefore, a position in a security with positive convexity can be considered a long position in volatility. This relationship can also be explained graphically. The price curve of a security with positive convexity will lie above and tangentially to the price curve of the underlying. If volatility of the underlying increases, then so will the volatility of either a long call or a long put, but the deviation from the price of the underlying will be positive when there is positive convexity, and negative with negative convexity. Therefore, the expected terminal value over the in-the-money region will increase while the expected terminal value over the out-of-the-money region will remain zero, an aggregate effect of increasing the total expected value of the option. Section: Valuation and Risk Models Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken: John Wiley and Sons, 2011), Chapter 4. AIMS: Define, compute, and interpret the convexity of a fixed income security given a change in yield and the resulting change in price.

40



25.

An implementation principle recommended by the Basel Committee to banks for the governance of sound stress testing practices is that stress testing reports should: a. b. c. d.

Not be passed up to senior management without first being approved by middle management. Have limited input from their respective business areas to prevent biasing of the results. Challenge prior assumptions to help foster debate among decision makers. Be separated by business lines to help identify risk concentrations.

Correct answer: c Explanation: The Basel Committee states “At banks that were highly exposed to the financial crisis and fared comparatively well, senior management as a whole took an active interest in the development and operation of stress testing… stress testing at most banks, however, did not foster internal debate nor challenge prior assumptions…” Therefore, the Basel Committee recommends that prior assumptions used in stress testing be challenged to ensure that the stress test best captures the potential for extreme scenarios given current market conditions. Section: Valuation and Risk Models Reference: Basel Committee on Banking Supervision Publication (2009), Principles for Sound Stress Testing Practices and Supervision. AIMS: Describe weaknesses identified and recommendations for improvement in: The use of stress testing and integration in risk governance.


41


Answer Sheet


a.

b.

c.

d.

a.

1.

14.

2.

15.

3.

16.

4.

17.

5.

18.

6.

19.

7.

20.

b.

c.

d.

✓

✘

8. 9.


10.

1.

11.


12.

1.

13.


43


Questions


1.

A fund holds a portfolio of principal-only strips of mortgage-backed securities. All other things being equal, which of the following will most likely reduce the weighted average maturity of the portfolio? a. b. c. d.

2.

Which of the following statements concerning Asian options is correct? a. b. c. d.

3.

options options options options

are not suitable for hedging positions on underlying assets that trade very frequently. tend to be more expensive than otherwise comparable vanilla options. are not suitable for hedging exposures that involve regular cashflows. tend to have payoffs that are less volatile than those of comparable European options.

Copulas can be used to join marginal distributions to construct a multivariate distribution. Copulas can only be used with mixtures of normal distributions. Copulas require the estimation of only one parameter. Copulas necessarily provide better estimates of tail dependence than correlation estimates for multivariate

A risk manager is analyzing a 1-day 98% VaR model. Assuming 252 days in a year, what is the maximum number of daily losses exceeding the 1-day 98% VaR that is acceptable in a 1-year backtest to conclude, at a 95% confidence level, that the model is calibrated correctly? a. b. c. d.

5.

Asian Asian Asian Asian

A consultant has recommended using copulas to better account for dependencies in a portfolio. Which of the following statements about copula approaches is correct? a. b. c. d.

4.

An increase in interest rates. An increase in prepayment speed. A small decrease in the value of the homes backing the mortgage pool. A small decrease in the real incomes of the underlying mortgage holders.

5 9 10 12

Which of the following is not a VaR mapping method for fixed-income portfolios? a. b. c. d.

Principal mapping. Duration mapping. Convexity mapping. Cash mapping.


45


6.

A risk manager is constructing a term structure model and intends to use the Cox-Ingersoll-Ross Model. Which of the following describes this model? a. b. c. d.

7.

The model presumes that the volatility of the short rate will increase at a predetermined rate. The model presumes that the volatility of the short rate will decline exponentially to a constant level. The model presumes that the basis-point volatility of the short rate will be proportional to the rate. The model presumes that the basis-point volatility of the short rate will be proportional to the square root of the rate.

A firm has entered into a USD 20 million total return swap on the NASDAQ 100 Index as the index payer with ABC Corporation, which will pay 1-year LIBOR + 2.5%. The contract will last 1 year, and cash flows will be exchanged annually. Suppose the NASDAQ 100 Index is currently at 2,900 and LIBOR is 1.25%. The firm conducts a stress test on this total return swap using the following scenario: NASDAQ 100 in 1 year: 3,625 LIBOR in 1 year: 0.50% For this scenario, what is the firm's net cash flow in year 1? a. b. c. d.

8.

net cash outflow of USD 4.40 million. net cash outflow of USD 4.25 million. new cash inflow of USD 4.25 million. new cash inflow of USD 4.40 million.

An analyst is reviewing a bond for investment purposes. The bond is expected to have a default probability of 2%, with an expected loss of 80 bps in the event of default. If the current risk-free rate is 4%, what is the minimum coupon spread needed on the bond for its expected return to match the risk-free rate? a. b. c. d.

46

A A A A

90 bps 120 bps 200 bps 280 bps



9.

You are the credit risk manager for a bank and are looking to mitigate counterparty credit risk exposure to ABCO, an A-rated firm. Currently your bank has the following derivatives contracts with ABCO: Contract A B C D

Contract Value (HKD) 20,000,000 30,000,000 14,000,000 1,000,000

With the information provided, what is the most appropriate credit risk mitigation technique in this case? a. b. c. d.

10.

Implement a netting scheme. Use credit triggers. Sell credit default swaps on ABCO. Increase collateral.

The exhibit below presents a summary of bilateral mark-to-market (MtM) trades for three counterparties. If netting agreements exist between all pairs of counterparties shown, what is the correct order of net exposure per counterparty, from highest to lowest? MtM Trades for Four Counterparties (USD Million) Opposing Counterparty B C 10 10 -10 0

Counterparty A

Trades with positive MtM Trades with negative MtM

Counterparty B


A 10 -10

C 0 -5

Counterparty C


A 0 -10

B 5 0

a. b. c. d.

A-B-C A-C-B C-A-B C-B-A


47


11.

An underlying exposure with an effective annual price volatility of 6% is collateralized by a 10-year U.S. Treasury note with an effective price volatility of 8%. The correlation between the exposure and the U.S. Treasury note is zero. Changes in the value of the overall position (exposure plus collateral) are calculated for a 10-day horizon at a 95% confidence interval (assume a year of 250 days). Which of the following would one expect to observe from this analysis? a. b. c. d.

12.

A trader observes a quote for Stock ZZZ, and the midpoint of its current best bid and best ask prices is CAD 35. ZZZ has an estimated daily return volatility of 0.25% and average bid-ask spread of CAD 0.1. Assuming the returns of ZZZ are normally distributed, what is closest to the estimated liquidity-adjusted, 1-day 95% VaR, using the constant spread approach on a 10,000 share position? a. b. c. d.

13.

The presence of collateral increases the current exposure and increases the volatility of the exposure between remargining periods. The presence of collateral increases the current exposure, but decreases the volatility of the exposure between remargining periods. The presence of collateral decreases the current exposure, but increases the volatility of the exposure between remargining periods. The presence of collateral decreases the current exposure and decreases the volatility of the exposure between remargining periods.

CAD CAD CAD CAD

1,000 2,000 3,000 4,000

The risk management department at Southern Essex Bank is trying to assess the impact of the capital conservation and countercyclical buffers defined in the Basel III framework. They consider a scenario in which the bank’s capital and risk-weighted assets are as shown in the table below (all values are in EUR millions): Risk-weighted assets Common equity Tier 1 (CET1) capital Additional Tier 1 capital Total Tier 1 capital Tier 2 capital Tier 3 capital Total capital

3,110 230 34 264 81 345

Assuming that all Basel III phase-ins have occurred and that the bank’s required countercyclical buffer is 0.75%, which of the capital ratios does the bank satisfy? a. b. c. d.

48

The CET1 capital ratio only. The CET1 capital ratio plus the capital conservation buffer only. The CET1 capital ratio plus the capital conservation buffer and the countercyclical buffer. None of the above.



14.

An operational risk manager is trying to compute the aggregate loss distribution for a firm's investment banking division. When using Monte Carlo simulation, which of the following loss frequency and loss severity distribution pairs is the most appropriate to use? a. b. c. d.

15.

Under the proposals for Basel III, which of the following instruments would meet the criteria to be eligible to be considered as Tier II capital? a. b. c. d.

16.

A senior unsecured bond with a step-up coupon and six years left until maturity. A senior unsecured bond with 10 years left until maturity. A subordinated bond with original maturity of seven years and a call option exercisable after five years. A subordinated bond with nine years left until maturity that is guaranteed by a subsidiary of the issuing entity.

Even though risk managers cannot eliminate model risk, there are many ways managers can protect themselves against model risk. Which of the following statements about managing model risk is correct? a. b. c. d.

17.

Poisson, normal Poisson, lognormal Binomial, lognormal Binomial, normal

Models should be tested against known problems. It is not advisable to estimate model risk using simulations. Complex models are generally preferable to simple models. Small discrepancies in model outputs are always acceptable.

When marking-to-market an illiquid position for Basel II compliance, the least desirable source of price information would be: a. b. c. d.

An interpolation from trade prices on liquid securities similar to the one being valued. An average of price quotes given over the phone from three reputable independent brokers. A price from a broker screen. A price from an active exchange.


49


18.

A risk analyst is evaluating the risks of a portfolio of stocks. Currently, the portfolio is valued at EUR 110 million and contains EUR 10 million in stock A. The standard deviation of returns of stock A is 12% annually and that of the overall portfolio is 19% annually. The correlation of returns between stock A and the portfolio is 0.5. Assuming the risk analyst uses a 1-year 99% VaR and that returns are normally distributed, how much is the component VaR of stock A? a. b. c. d.

19.


Which of the following statements about risk management in the pension fund industry is correct? a. b. c. d.

20.

EUR EUR EUR EUR

A pension plan’s total VaR is equal to the sum of its policy-mix VaR and active-management VaR. Pension fund risk analysis does not consider performance relative to a benchmark. In most defined-benefit pension plans, if liabilities exceed assets, the shortfall does not create a risk for the plan sponsor. From the plan sponsor’s perspective, nominal pension obligations are similar to a short position in a long term bond.

A risk manager is evaluating a pairs trading strategy recently initiated by one of the firm’s traders. The strategy involves establishing a long position in Stock A and a short position in Stock B. The following information is also provided: • • •

1-day 99% VaR of Stock A is USD 100 million 1-day 99% VaR of Stock B is USD 125 million The estimated correlation between long positions in Stock A and Stock B is 0.8

Assuming that the returns of Stock A and Stock B are jointly normally distributed, the 1-day 99% VaR of the combined positions is closest to? a. b. c. d.

50

USD USD USD USD





Answers


a.

b.

c.

1.

4.

5.

8.

c.

d.

15. 16.

17.

19.

20.

9. 10.

b.

18.

6. 7.

a.

14.

2. 3.

d.


11.

1.

12.


13.

1.


✓

✘

53


Explanations


1.

A fund holds a portfolio of principal-only strips of mortgage-backed securities. All other things being equal, which of the following will most likely reduce the weighted average maturity of the portfolio? a. b. c. d.

An increase in interest rates. An increase in prepayment speed. A small decrease in the value of the homes backing the mortgage pool. A small decrease in the real incomes of the underlying mortgage holders.

Correct answer: b Explanation: An increase in prepayment speed will reduce the weighted average maturity of the portfolio, however, the rest of the choices will not have this effect. Section: Market Risk Measurement and Management Reference: Frank Fabozzi, Anand Bhattacharya, William Berliner, Mortgage Backed Securities: Products, Structuring and Analytical Techniques, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011). Chapter 2: Overview of the Mortgage-Backed Securities Market. AIMS: Explain the creation of agency (fixed rate and adjustable rate) and private-label MBS pools, pass-throughs, CMOs, and mortgage strips.

2.

Which of the following statements concerning Asian options is correct? a. b. c. d.

Asian Asian Asian Asian

options options options options

are not suitable for hedging positions on underlying assets that trade very frequently. tend to be more expensive than otherwise comparable vanilla options. are not suitable for hedging exposures that involve regular cashflows. tend to have payoffs that are less volatile than those of comparable European options.

Correct answer: d Explanation: While a European option payoff is a function of the difference between the strike and the underlying asset’s terminal price, an Asian option payoff is a function of the difference between the strike and the underlying asset’s average price over the life of the option. The average price is less volatile than the terminal price, so Asian options have lower expected payoff (and lower premium) than European options. Hedging the average price rather than the terminal price may be more appropriate for underlying assets which are either paying/receiving regular cash flows or trade frequently. Section: Market Risk Measurement and Management Reference: John Hull, Options, Futures, and Other Derivatives, 8th Edition (New York: Pearson Prentice Hall, 2012). Chapter 25: Exotic Options. AIMS: Define and contrast exotic derivatives and plain vanilla derivatives. Identify and describe the characteristics and pay-off structure of the following exotic options: forward start, compound, chooser, barrier, binary, lookback, shout, Asian, exchange, rainbow, and basket options.


55


3.

A consultant has recommended using copulas to better account for dependencies in a portfolio. Which of the following statements about copula approaches is correct? a. b. c. d.

Copulas can be used to join marginal distributions to construct a multivariate distribution. Copulas can only be used with mixtures of normal distributions. Copulas require the estimation of only one parameter. Copulas necessarily provide better estimates of tail dependence than correlation estimates for multivariate distributions.

Correct answer: a Explanation: Copulas can be used to join marginal distributions to construct a multivariate distribution. Section: Market Risk Measurement and Management Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005). Chapter 5: Appendix — Modeling Dependence: Correlations and Copulas. AIMS: Explain the drawbacks of using correlation to measure dependence. Describe how copulas provide an alternative measure of dependence. Explain how tail dependence can be investigated using copulas.

4.

A risk manager is analyzing a 1-day 98% VaR model. Assuming 252 days in a year, what is the maximum number of daily losses exceeding the 1-day 98% VaR that is acceptable in a 1-year backtest to conclude, at a 95% confidence level, that the model is calibrated correctly? a. b. c. d.

5 9 10 12

Correct answer: b Explanation: The risk manager will reject the hypothesis that the model is correctly calibrated if the number x of losses exceeding the VaR is such that: (x-pT)/sqrt(p(1-p)T) > 1.96 where p represents the failure rate and is equal to 1-98%, or 2%; and T is the number of observations, 252. Then 1.96 = two-tail confidence level quantile --> x > 1.96 * sqrt(2% * 98% * 252) + p * T = 9.40. So the maximum number of exceedances would be 9 to conclude that the model is calibrated correctly. Section: Market Risk Measurement and Management Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition. (New York: McGraw-Hill, 2007). Chapter 6: Backtesting VaR. AIMS: Explain the framework of backtesting models with the use of exceptions or failure rates.

56



5.

Which of the following is not a VaR mapping method for fixed-income portfolios? a. b. c. d.

Principal mapping. Duration mapping. Convexity mapping. Cash mapping.

Correct answer: c Explanation: Principal mapping, duration mapping and cash flow mapping are methods of VaR mapping for fixed income portfolios. Convexity mapping is not a method of VaR mapping for fixed income portfolios. Section: Market Risk Measurement and Management Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition. (New York: McGraw-Hill, 2007). Chapter 11: VaR Mapping. AIMS: List and describe the three methods of mapping portfolios of fixed income securities.

6.

A risk manager is constructing a term structure model and intends to use the Cox-Ingersoll-Ross Model. Which of the following describes this model? a. b. c. d.

The model presumes that the volatility of the short rate will increase at a predetermined rate. The model presumes that the volatility of the short rate will decline exponentially to a constant level. The model presumes that the basis-point volatility of the short rate will be proportional to the rate. The model presumes that the basis-point volatility of the short rate will be proportional to the square root of the rate.

Correct answer: d Explanation: In the CIR model, the basis-point volatility of the short rate is not independent of the short rate as other simpler models assume. The annualized basis-point volatility equals 𝜎√𝑟 and therefore increases as a function of the square root of the rate. Section: Market Risk Measurement and Management Reference: Tuckman, Fixed Income Securities, 3rd Edition. Chapter 10: The Art of Term Structure Models: Volatility and Distribution. AIMS: Describe the short-term rate process under the Cox-Ingersoll-Ross (CIR) and lognormal models.


57


7.

A firm has entered into a USD 20 million total return swap on the NASDAQ 100 Index as the index payer with ABC Corporation, which will pay 1-year LIBOR + 2.5%. The contract will last 1 year, and cash flows will be exchanged annually. Suppose the NASDAQ 100 Index is currently at 2,900 and LIBOR is 1.25%. The firm conducts a stress test on this total return swap using the following scenario: NASDAQ 100 in 1 year: 3,625 LIBOR in 1 year: 0.50% For this scenario, what is the firm's net cash flow in year 1? a. b. c. d.

A A A A

net cash outflow of USD 4.40 million. net cash outflow of USD 4.25 million. new cash inflow of USD 4.25 million. new cash inflow of USD 4.40 million.

Correct answer: b Explanation: The NASDAQ will increase 25%, or (3625/2900)-1, over the next year, so the index payer will pay USD 5 million (0.25 * 20 million) to ABC Corp. Since ABC Corp’s payments depend on today’s LIBOR, it will pay 3.75% (1.25% + 2.5%) or USD 0.75 million (0.0375 * 20 million). So the firm's net cash flow would be 0.75 million – 5 million = -USD 4.25 million. Section: Credit Risk Measurement and Management Reference: Christopher Culp, Structured Finance and Insurance: The Art of Managing Capital and Risk (Hoboken, NJ: John Wiley & Sons, 2006). Chapter 12: Credit Derivatives and Credit-Linked Notes. AIMS: Explain the mechanics of asset default swaps, equity default swaps, total return swaps and credit linked notes.

58



8.

An analyst is reviewing a bond for investment purposes. The bond is expected to have a default probability of 2%, with an expected loss of 80 bps in the event of default. If the current risk-free rate is 4%, what is the minimum coupon spread needed on the bond for its expected return to match the risk-free rate? a. b. c. d.

90 bps 120 bps 200 bps 280 bps

Correct answer: a Explanation: The credit risky bond is preferable when (1-PD) * (1 + r + z) + PD * RR > 1 + r where PD is the probability of default, RR is the recovery rate, r is the coupon paid by a risk-free bond, and z is the coupon spread for a risky bond that compensates for the default risk. Since expected loss (EL) = PD * the loss given default (LGD), LGD = (EL/PD). Also the recovery rate RR = 1-LGD. Therefore RR = 1-EL/PD = 0.6, and using the relationship above: (1-2%) * (1 + 4% + z) + 2% * 60% > 1 + 4%. Making the calculations simplifies the equation as follows: 0.98 * (1.04 + z) + 0.012 > 1.04; hence z >

(1.04 − 0.012) 0.98

− 1.04 so z > 0.00897 or 90 bps.

Section: Credit Risk Measurement and Management Reference: Allan Malz, Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011). Chapter 6: Credit and Counterparty Risk. AIMS: Calculate expected loss from recovery rates, the loss given default, and the probability of default.


59


9.

You are the credit risk manager for a bank and are looking to mitigate counterparty credit risk exposure to ABCO, an A-rated firm. Currently your bank has the following derivatives contracts with ABCO: Contract A B C D

Contract Value (HKD) 20,000,000 30,000,000 14,000,000 1,000,000

With the information provided, what is the most appropriate credit risk mitigation technique in this case? a. b. c. d.

Implement a netting scheme. Use credit triggers. Sell credit default swaps on ABCO. Increase collateral.

Correct answer: d Explanation: Increasing collateral would effectively reduce current credit exposure depending on the contract parameters, mainly minimum transfer amount and threshold. Section: Credit Risk Measurement and Management Reference: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets (West Sussex, UK: John Wiley & Sons, 2012). Chapter 3: Defining Counterparty Credit Risk. AIMS: Identify and describe the different ways institutions can manage and mitigate counterparty risk.

60



10.

The exhibit below presents a summary of bilateral mark-to-market (MtM) trades for three counterparties. If netting agreements exist between all pairs of counterparties shown, what is the correct order of net exposure per counterparty, from highest to lowest? MtM Trades for Four Counterparties (USD Million) Opposing Counterparty C B 10 10 -10 0

Counterparty A


Counterparty B


A 10 -10

C 0 -5


A 0 -10

B 5 0

Counterparty C

a. b. c. d.

A-B-C A-C-B C-A-B C-B-A

Correct answer: b Explanation: One must properly net the positive and negative trades per counterparty for all three counterparties shown. The properly netted amounts are: For counterparty A: exposure to B = USD 0, exposure to C = USD 10 for a sum of USD 10; For counterparty B: exposure to A = USD 0, exposure to C = USD 0 for a sum of USD 0; For counterparty C: exposure to A = USD 0, exposure to B = USD 5 for a sum of USD5. Therefore, the correct sequence is as shown above. Section: Credit Risk Measurement and Management Reference: Jon Gregory (2010), Counterparty Credit Risk: The New Challenge for Global Financial Markets, West Sussex, UK, John Wiley & Sons. AIMS: Describe the different ways institutions can manage counterparty risk.


61


11.

An underlying exposure with an effective annual price volatility of 6% is collateralized by a 10-year U.S. Treasury note with an effective price volatility of 8%. The correlation between the exposure and the U.S. Treasury note is zero. Changes in the value of the overall position (exposure plus collateral) are calculated for a 10-day horizon at a 95% confidence interval (assume a year of 250 days). Which of the following would one expect to observe from this analysis? a. b. c. d.

The presence of collateral increases the current exposure and increases the volatility of the exposure between remargining periods. The presence of collateral increases the current exposure, but decreases the volatility of the exposure between remargining periods. The presence of collateral decreases the current exposure, but increases the volatility of the exposure between remargining periods. The presence of collateral decreases the current exposure and decreases the volatility of the exposure between remargining periods.

Correct answer: c Explanation: Worse case change for the value of the collateral is: -1.96 * 8% * (10/250)0.5 = -3.136% The overall volatility of the position: (.06^2 + .08^2)^0.5 = 10% Thus the worst case change in the value of this position (exposure + collateral) is: -1.96 * 10% * (10/250)0.5 = -3.92% Thus, the collateral mitigates the exposure today while increasing the volatility of the position in the future. Section: Credit Risk Measurement and Management Reference: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets (West Sussex, UK: John Wiley & Sons, 2012). Chapter 8: Credit Exposure. AIMS: Identify factors that affect the calculation of the credit exposure profile and summarize the impact of collateral on exposure.

62



12.

A trader observes a quote for Stock ZZZ, and the midpoint of its current best bid and best ask prices is CAD 35. ZZZ has an estimated daily return volatility of 0.25% and average bid-ask spread of CAD 0.1. Assuming the returns of ZZZ are normally distributed, what is closest to the estimated liquidity-adjusted, 1-day 95% VaR, using the constant spread approach on a 10,000 share position? a. b. c. d.

CAD CAD CAD CAD

1,000 2,000 3,000 4,000

Correct answer: b Explanation: The daily 95% VaR = 35 *10,000 * (1.645 * 0.0025) = CAD 1,440 The constant spread approach adds half of the bid-ask spread (as a percent) to the VaR calculation, using the following formula: Liquidity Cost (LC) = ½ (Spread * P), where Spread is equal to the actual spread divided by the midpoint and P is the value of the position. Therefore the liquidity cost (LC) = 350,000 * (0.5 * 0.1/35) = CAD 500 Liquidity-adjusted VaR (LVaR) = VaR + LC = CAD 1,940. Section: Operational and Integrated Risk Management Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005). Chapter 14: Estimating Liquidity Risks. AIMS: Describe and calculate LVaR using the constant spread approach and the exogenous spread approach.


63


13.

The risk management department at Southern Essex Bank is trying to assess the impact of the capital conservation and countercyclical buffers defined in the Basel III framework. They consider a scenario in which the bank’s capital and risk-weighted assets are as shown in the table below (all values are in EUR millions): Risk-weighted assets Common equity Tier 1 (CET1) capital Additional Tier 1 capital Total Tier 1 capital Tier 2 capital Tier 3 capital Total capital

3,110 230 34 264 81 345

Assuming that all Basel III phase-ins have occurred and that the bank’s required countercyclical buffer is 0.75%, which of the capital ratios does the bank satisfy? a. b. c. d.

The CET1 capital ratio only. The CET1 capital ratio plus the capital conservation buffer only. The CET1 capital ratio plus the capital conservation buffer and the countercyclical buffer. None of the above.

Correct answer: b Explanation: The bank has CET1 capital ratio of (230/3110) or 7.4%. This ratio meets the 4.5% minimum and the additional 2.5% capital conservation buffer but not the additional countercyclical buffer of 0.75% (4.5% + 2.5% + 0.75 = 7.75%). Section: Operational and Integrated Risk Management Reference: “Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems—Revised Version,” (Basel Committee on Banking Supervision Publication, June 2011). AIMS: Describe changes to the regulatory capital framework, including changes to: the measurement, treatment, and calculation of Tier 1, Tier 2, and Tier 3 capital.

64



14.

An operational risk manager is trying to compute the aggregate loss distribution for a firm's investment banking division. When using Monte Carlo simulation, which of the following loss frequency and loss severity distribution pairs is the most appropriate to use? a. b. c. d.

Poisson, normal Poisson, lognormal Binomial, lognormal Binomial, normal

Correct answer: b Explanation: Pareto and lognormal distributions (fat-tailed) are generally used for loss severity, Poisson and Negative Binomial distributions are appropriate for loss frequency. Section: Operational and Integrated Risk Management Reference: Eric Cope, Giulio Mignola, Gianluca Antonini and Roberto Ugoccioni, “Challenges and Pitfalls in Measuring Operational Risk from Loss Data,” The Journal of Operational Risk, Volume 4/Number 4, Winter 2009/10: pp. 3-27. AIMS: Explain the loss distribution approach to modeling operational risk losses.

15.

Under the proposals for Basel III, which of the following instruments would meet the criteria to be eligible to be considered as Tier II capital? a. b. c. d.

A senior unsecured bond with a step-up coupon and six years left until maturity. A senior unsecured bond with 10 years left until maturity. A subordinated bond with original maturity of seven years and a call option exercisable after five years. A subordinated bond with nine years left until maturity that is guaranteed by a subsidiary of the issuing entity.

Correct answer: c Explanation: Choice c meets all of the Basel Committee’s proposed criteria for inclusion in Tier II capital while the others do not. In this case, the bond is subordinated, has a minimum original maturity of at least five years and it is callable at the initiative of the issuer only after a minimum of five years. Section: Operational and Integrated Risk Management Reference: “Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems—Revised Version,” (Basel Committee on Banking Supervision Publication, June 2011). AIMS: Describe changes to the regulatory capital framework, including changes to the measurement, treatment, and calculation of Tier 1, Tier 2, and Tier 3 capital.


65


16.

Even though risk managers cannot eliminate model risk, there are many ways managers can protect themselves against model risk. Which of the following statements about managing model risk is correct? a. b. c. d.

Models should be tested against known problems. It is not advisable to estimate model risk using simulations. Complex models are generally preferable to simple models. Small discrepancies in model outputs are always acceptable.

Correct answer: a Explanation: One way to protect against model risk is to test a model against known problems. It is always a good idea to check a model against simple problems to which one already knows the answer, and many problems can be distilled to simple special cases that have known answers. If the model fails to give the correct answer to a problem whose solution is already known, then this indicates that there is something wrong with it. Section: Operational and Integrated Risk Management Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005). Chapter 16: Model Risk. AIMS: Identify ways risk managers can protect against model risk.

17.

When marking-to-market an illiquid position for Basel II compliance, the least desirable source of price information would be: a. b. c. d.

An interpolation from trade prices on liquid securities similar to the one being valued. An average of price quotes given over the phone from three reputable independent brokers. A price from a broker screen. A price from an active exchange.

Correct answer: a Explanation: Marking-to-market is the process of valuing positions, at least daily, using readily available close out prices in orderly transactions that are sourced independently. Examples of readily available close out prices include exchange prices, screen prices, or quotes from several independent reputable brokers. Only where marking-to-market is not possible, should banks mark-to-model. Marking-to model is defined as any valuation which has to be benchmarked, extrapolated or otherwise calculated from a market input. Section: Operational and Integrated Risk Management Reference: “Revisions to the Basel II Market Risk Framework—Updated as of 31 December 2010,” (Basel Committee on Banking Supervision Publication, February 2011). AIMS: Describe the regulatory guidance on prudent valuation of illiquid positions.

66



18.

A risk analyst is evaluating the risks of a portfolio of stocks. Currently, the portfolio is valued at EUR 110 million and contains EUR 10 million in stock A. The standard deviation of returns of stock A is 12% annually and that of the overall portfolio is 19% annually. The correlation of returns between stock A and the portfolio is 0.5. Assuming the risk analyst uses a 1-year 99% VaR and that returns are normally distributed, how much is the component VaR of stock A? a. b. c. d.

EUR EUR EUR EUR


Correct answer: c Explanation: Let α(99%) represent the 99% confidence factor for the VaR estimate, which is 2.326. VaRA = wA * σA * α(99%) = EUR 10 million x 0.12 x 2.326 = EUR 2.792 million Component VaRA = ρ * VaRA = 0.5 x 2.792 = EUR 1.396 million Section: Risk Management and Investment Management Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition. (New York: McGraw-Hill, 2007). Chapter 7: Portfolio Risk: Analytical Methods. AIMS: Define, compute, and explain the uses of marginal VaR, incremental VaR and component VaR.

19.

Which of the following statements about risk management in the pension fund industry is correct? a. b. c. d.

A pension plan’s total VaR is equal to the sum of its policy-mix VaR and active-management VaR. Pension fund risk analysis does not consider performance relative to a benchmark. In most defined-benefit pension plans, if liabilities exceed assets, the shortfall does not create a risk for the plan sponsor. From the plan sponsor’s perspective, nominal pension obligations are similar to a short position in a long term bond.

Correct answer: d Explanation: Nominal pension obligations are similar to a short position in a bond. Section: Risk Management and Investment Management Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition. (New York: McGraw-Hill, 2007). Chapter 17: VaR and Risk Budgeting in Investment Management. AIMS: Define and describe the following types of risk: absolute risk, relative risk, policy-mix risk, active management risk, funding risk and sponsor risk.


67


20.

A risk manager is evaluating a pairs trading strategy recently initiated by one of the firm’s traders. The strategy involves establishing a long position in Stock A and a short position in Stock B. The following information is also provided: • • •

1-day 99% VaR of Stock A is USD 100 million 1-day 99% VaR of Stock B is USD 125 million The estimated correlation between long positions in Stock A and Stock B is 0.8

Assuming that the returns of Stock A and Stock B are jointly normally distributed, the 1-day 99% VaR of the combined positions is closest to? a. b. c. d.

USD USD USD USD


Correct answer: b 2 Explanation: (VaRA + VaR2B + 2∗ρ∗VaRA ∗VaRB) = (1002 + 1252 + 2∗ − 0.8∗100∗125) = USD 75 million Since this is a pairs trading strategy with a long and a short position, the proper correlation to use is -0.8.

Section: Risk Management and Investment Management Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition. (New York: McGraw-Hill, 2007). Chapter 7: Portfolio Risk: Analytical Methods. AIMS: Define, calculate, and distinguish between the following portfolio VaR measures: individual VaR, incremental VaR, marginal VaR, component VaR, undiversified portfolio VaR, and diversified portfolio VaR.

68


Creating a culture of risk awareness®

Global Association of Risk Professionals 111 Town Square Place 14th Floor Jersey City, New Jersey 07310 U.S.A. + 1 201.719.7210 2nd Floor Bengal Wing 9A Devonshire Square London, EC2M 4YN U.K. + 44 (0) 20 7397 9630 www.garp.org



2015

FRM Practice Exam

2015 Financial Risk Manager (FRM®) Practice Exam

TABLE OF CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Reference Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 Special instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

2015 FRM Part I Practice Exam Candidate Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . .5 2015 FRM Part I Practice Exam Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 2015 FRM Part I Practice Exam Answer Sheet/Answers . . . . . . . . . . . . . . . . . . . . . . . . .19 2015 FRM Part I Practice Exam Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21



i


INTRODUCTION

Core readings were selected by the FRM Committee to assist candidates in their review of the subjects covered

The FRM Exam is a practice-oriented examination. Its questions

by the Exam. Questions for the FRM Exam are derived

are derived from a combination of theory, as set forth in the


core readings, and “real-world” work experience. Candidates


are expected to understand risk management concepts and

for the Exam.

approaches and how they would apply to a risk manager’s day-to-day activities. The FRM Exam is also a comprehensive examination, testing a risk professional on a number of risk management


concepts and approaches. It is very rare that a risk manager will be faced with an issue that can immediately be slotted


into one category. In the real world, a risk manager must be


able to identify any number of risk-related issues and be


able to deal with them effectively.

actual Exam.

The 2015 FRM Practice Exams I and II have been developed to aid candidates in their preparation for the FRM Exam in


May and November 2015. These Practice Exams are based

•


on a sample of questions from the 2011 through 2014 FRM

•


Exams and are suggestive of the questions that will be in

erasers) available.

the 2015 FRM Examination. The 2015 FRM Practice Exam for Part I contains 25

•


multiple-choice questions and the 2015 FRM Practice Exam for Part II contains 20 multiple-choice questions. Note that


•


the 2015 FRM Exam Part I will contain 100 multiple-choice


questions and the 2015 FRM Exam Part II will contain


80 multiple-choice questions. The Practice Exams were


designed to be shorter to allow candidates to calibrate

•




The 2015 FRM Practice Exams do not necessarily cover all topics to be tested in the 2015 FRM Exam as the material


covered in the 2015 Study Guide may be different from


that covered by the 2011 through 2014 Study Guides. The


questions selected for inclusion in the Practice Exams were chosen to be broadly reflective of the material assigned for 2015 as well as to represent the style of question that the



FRM Committee considers appropriate based on assigned


material.



For a complete list of current topics, core readings, and key learning


objectives candidates should refer to the 2015 FRM Exam Study Guide


and Program Manual.



1


Reference Table: Let Z be a standard normal random variable.

2



Special Instructions and Definitions

1.

Unless otherwise indicated, interest rates are assumed to be continuously compounded.

2.

Unless otherwise indicated, option contracts are assumed to be on one unit of the underlying asset.

3.

VaR = value-at-risk

4.

ES = expected shortfall

5.

GARCH = generalized auto-regressive conditional heteroskedasticity

6.

CAPM = capital asset pricing model

7.

LIBOR = London interbank offer rate

8.

EWMA = exponentially weighted moving average

9.

CDS = credit default swap (s)

10. MBS = mortgage-backed security (securities) 11. CEO/CFO/CRO = Senior management positions: Chief Executive Officer, Chief Financial Officer, and Chief Risk Officer, respectively 12. The following acronyms are used for selected currencies:

Acronym

Currency

ARS

Argentine peso

AUD

Australian dollar

BRL

Brazilian real

CAD

Canadian dollar

CHF

Swiss franc

EUR

euro

GBP

British pound sterling

HKD

Hong Kong dollar

INR

Indian rupee

JPY

Japanese yen

MXN

Mexican peso

SGD

Singapore dollar

USD

US dollar


3

2015 ®

FRM Practice Exam Part I Answer Sheet


a.

b.

c.

d.

a.

1.

16.

2.

17.

3.

18.

4.

19.

5.

20.

6.

21.

7.

22.

8.

23.

9.

24.

10.

25.

b.

c.

d.

✓

✘

11. 12.


13.

1.

14.


15.

1.


5

2015 ®

FRM Practice Exam Part I Questions


1.

A risk manager performs an ordinary least squares (OLS) regression to estimate the sensitivity of a stock's return to the return on the S&P 500. This OLS procedure is designed to: a. b. c. d.

2.

Minimize Minimize Minimize Minimize

the the the the

square of the sum of differences between the actual and estimated S&P 500 returns. square of the sum of differences between the actual and estimated stock returns. sum of differences between the actual and estimated squared S&P 500 returns. sum of squared differences between the actual and estimated stock returns.

Using the prior 12 monthly returns, an analyst estimates the mean monthly return of stock XYZ to be -0.75% with a standard error of 2.70%. ONE-TAILED T-DISTRIBUTION TABLE Degrees of Freedom 0.10 8 1.397 9 1.383 10 1.372 11 1.363 12 1.356

α 0.05 1.860 1.833 1.812 1.796 1.782

0.025 2.306 2.262 2.228 2.201 2.179

Using the t-table above, the 95% confidence interval for the mean return is between: a. b. c. d.

3.

-6.69% and 5.19% -6.63% and 5.15% -5.60% and 4.10% -5.56% and 4.06%

Using data from a pool of mortgage borrowers, a credit risk analyst performed an ordinary least squares regression of annual savings (in GBP) against annual household income (in GBP) and obtained the following relationship: Annual Savings = 0.24 * Household Income - 25.66, R² = 0.50 Assuming that all coefficients are statistically significant, which interpretation of this result is correct? a. b. c. d.

For For For For

this sample data, the average error term is GBP -25.66. a household with no income, annual savings is GBP 0. an increase of GBP 1,000 in income, expected annual savings will increase by GBP 240. a decrease of GBP 2,000 in income, expected annual savings will increase by GBP 480.


7


4.

A risk analyst is estimating the variance of stock returns on day n, given by , using the equation where and represent the return and volatility on day n-1, respectively. If the values of α and β are as indicated below, which combination of values indicates that the variance follows a stable GARCH (1,1) process? a. b. c. d.

α α α α

= = = =

0.084427 0.084427 0.084427 0.090927

and and and and

β β β β

= = = =

0.909073 0.925573 0.925573 0.925573

The following information applies to questions 5 and 6. A portfolio manager holds three bonds in one of his portfolios and each bond has a 1-year default probability of 15%. The event of default for each of the bonds is independent. 5.

What is the probability of exactly two bonds defaulting over the next year? a. b. c. d.

6.

What is the mean and variance of the number of bonds defaulting over the next year? a. b. c. d.

8

1.9% 5.7% 10.8% 32.5%

Mean Mean Mean Mean

= = = =

0.15, variance = 0.32 0.45, variance = 0.38 0.45, variance = 0.32 0.15, variance = 0.38



7.

A risk manager is evaluating a portfolio of equities with an annual volatility of 12.1% per year that is benchmarked to the Straits Times Index. If the risk-free rate is 2.5% per year, based on the regression results given in the chart below, what is the Jensen's alpha of the portfolio?

y = 0.4936x + 3.7069 R2 = 0.5387

a. b. c. d.

8.

0.4936% 0.5387% 1.2069% 3.7069%

An investment advisor is analyzing the range of potential expected returns of a new fund designed to replicate the directional moves of the BSE Sensex Index but with twice the volatility of the index. The Sensex has an expected annual return of 12.3% and volatility of 19.0%, and the risk free rate is 2.5% per year. Assuming the correlation between the fund’s returns and that of the index is 1, what is the expected return of the fund using the capital asset pricing model? a. b. c. d.

18.5% 19.0% 22.1% 24.6%


9


9.

A risk analyst is reconciling customer account data held in two separate databases and wants to ensure the account number for each customer is the same in each database. Which dimension of data quality would she be most concerned with in making this comparison? a. b. c. d.

10.

The hybrid approach for estimating VaR is the combination of a parametric and a nonparametric approach. It specifically combines the historical simulation approach with: a. b. c. d.

11.

Completeness Accuracy Consistency Currency

The The The The

delta normal approach. exponentially weighted moving average approach. multivariate density estimation approach. generalized autoregressive conditional heteroskedasticity approach.

A non-dividend-paying stock is currently trading at USD 40 and has an expected return of 12% per year. Using the Black-Scholes-Merton (BSM) model, a 1-year, European-style call option on the stock is valued at USD 1.78. The parameters used in the model are: N(d1) = 0.29123

N(d2) = 0.20333

The next day, the company announces that it will pay a dividend of USD 0.5 per share to holders of the stock on an ex-dividend date 1 month from now and has no further dividend payout plans for at least 1 year. This new information does not affect the current stock price, but the BSM model inputs change, so that: N(d1) = 0.29928

N(d2) = 0.20333

If the risk-free rate is 3% per year, what is the new BSM call price? a. b. c. d.

10

USD USD USD USD

1.61 1.78 1.95 2.11



12.

An at-the-money European call option on the DJ EURO STOXX 50 index with a strike of 2200 and maturing in 1 year is trading at EUR 350, where contract value is determined by EUR 10 per index point. The risk-free rate is 3% per year, and the daily volatility of the index is 2.05%. If we assume that the expected return on the DJ EURO STOXX 50 is 0%, the 99% 1-day VaR of a short position on a single call option calculated using the delta-normal approach is closest to: a. b. c. d.

13.

EUR EUR EUR EUR

8. 53. 84. 525.

The current stock price of a company is USD 80. A risk manager is monitoring call and put options on the stock with exercise prices of USD 50 and 5 days to maturity. Which of these scenarios is most likely to occur if the stock price falls by USD 1? Scenario A B C D

a. b. c. d.

Scenario Scenario Scenario Scenario

Call Value Decrease by Decrease by Decrease by Decrease by

USD USD USD USD

0.94 0.94 0.07 0.07

Put Value Increase by Increase by Increase by Increase by

USD USD USD USD

0.08 0.89 0.89 0.08

A B C D


11


14.

Below is a chart showing the term structure of risk-free spot rates:

Which of the following charts presents the correct derived forward rate curve?

12

a.

b.

c.

d.



15.

A hedge fund manager wants to change her interest rate exposure by investing in fixed-income securities with negative duration. Which of the following securities should she buy? a. b. c. d.

16.

maturity maturity maturity maturity

calls puts puts calls

on on on on

zero-coupon bonds with long maturity interest-only strips from long maturity conforming mortgages zero-coupon bonds with long maturity principal-only strips from long maturity conforming mortgages

A risk analyst is analyzing several indicators for a group of countries. If he specifically considers the Gini coefficient in his analysis, in which of the following factors is he most interested? a. b. c. d.

17.


Standard of living Peacefulness Perceived corruption Income inequality

A trader writes the following 1-year European-style barrier options as protection against large movements in a non-dividend paying stock that is currently trading at EUR 40.96. Option Up-and-in barrier call, with barrier at EUR 45 Up-and-out barrier call, with barrier at EUR 45 Down-and-in barrier put, with barrier at EUR 35 Down-and-out barrier put, with barrier at EUR 35

Price (EUR) 3.52 1.24 2.00 1.01

All of the options have the same strike price. Assuming the risk-free rate is 2% per annum, what is the common strike price of these options? a. b. c. d.

EUR EUR EUR EUR

39.00 40.00 41.00 42.00


13


18.

A fixed-income portfolio manager purchases a seasoned 5.5% agency mortgage-backed security with a weighted average loan age of 60 months. The current balance on the loans is USD 20 million, and the conditional prepayment rate is assumed to be constant at 0.4% per year. Which of the following is closest to the expected principal prepayment this month? a. b. c. d.

19.

AA/Aa A/A BBB/Baa BB/Ba

A French bank enters into a 6-month forward contract with an importer to sell GBP 40 million in 6 months at a rate of EUR 0.80 per GBP. If in 6 months the exchange rate is EUR 0.85 per GBP, what is the payoff for the bank from the forward contract? a. b. c. d.

14

1,000 7,000 10,000 70,000

The rating agencies have analyzed the creditworthiness of Company XYZ and have determined that the company currently has adequate payment capacity, although a negative change in the business environment could affect its capacity for repayment. The company has been given an investment grade rating by S&P and Moody’s. Which of the following S&P/Moody’s ratings has Company XYZ been assigned? a. b. c. d.

20.

USD USD USD USD

EUR EUR EUR EUR

-2,941,176 -2,000,000 2,000,000 2,941,176



21.

An oil driller recently issued USD 250 million of fixed-rate debt at 4.0% per annum to help fund a new project. It now wants to convert this debt to a floating-rate obligation using a swap. A swap desk analyst for a large investment bank that is a market maker in swaps has identified four firms interested in swapping their debt from floating-rate to fixed-rate. The following table quotes available loan rates for the oil driller and each firm: Firm Oil driller Firm A Firm B Firm C Firm D

Fixed-rate (in %) 4.0 3.5 6.0 5.5 4.5

Floating-rate (in %) 6-month LIBOR + 1.5 6-month LIBOR + 1.0 6-month LIBOR + 3.0 6-month LIBOR + 2.0 6-month LIBOR + 2.5

A swap between the oil driller and which firm offers the greatest possible combined benefit? a. b. c. d.

22.

Firm Firm Firm Firm

A B C D

Consider an American call option and an American put option, each with 3 months to maturity, written on a non-dividend-paying stock currently priced at USD 40. The strike price for both options is USD 35 and the risk-free rate is 1.5%. What are the lower and upper bounds on the difference between the prices of the call and put options? Scenario A B C D a. b. c. d.


Lower Bound (USD) 5.13 5.00 34.87 0.13

Upper Bound (USD) 40.00 5.13 40.00 34.87

A B C D


15


23.

A growing regional bank has added a risk committee to its board. One of the first recommendations of the risk committee is that the bank should develop a risk appetite statement. What best represents a primary function of a risk appetite statement? a. b. c. d.

24.

Take Take Take Take

a a a a

long position in the futures because rising interest rates lead to rising futures prices. short position in the futures because rising interest rates lead to rising futures prices. short position in the futures because rising interest rates lead to declining futures prices. long position in the futures because rising interest rates lead to declining futures prices.

Barings was forced to declare bankruptcy after reporting over USD 1 billion in unauthorized trading losses by a single trader, Nick Leeson. Which of the following statements concerning the collapse of Barings is correct? a. b. c. d.

16

quantify the level of variability for each risk metric that a firm is willing to accept state specific new business opportunities that a firm is willing to pursue assign risk management responsibilities to specific internal staff members state a broad level of acceptable risk to guide the allocation of the firm’s resources

A German housing corporation needs to hedge against rising interest rates. It has chosen to use futures on 10-year German government bonds. Which position in the futures should the corporation take, and why? a. b. c. d.

25.

To To To To

Leeson avoided reporting the unauthorized trades by convincing the head of his back office that they did not need to be reported. Management failed to investigate high levels of reported profits even though they were associated with a low-risk trading strategy. Leeson traded primarily in OTC foreign currency swaps which allowed Barings to delay cash payments on losing trades until the first payment was due. The loss at Barings was detected when several customers complained of losses on trades that were booked to their accounts.


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17

2015 ®

FRM Practice Exam Part I Answers


a.

b.

c.

1. 2.

3. 4.

d.

a.

17.

18.

20.

6.

21.

23.

9.

24.

25.

12.


14. 15.

11.

13.

22.

8.

d.

19.

7.

c.

16.

5.

10.

b.

✓

✘



19

2015 ®

FRM Practice Exam Part I Explanations


1.

A risk manager performs an ordinary least squares (OLS) regression to estimate the sensitivity of a stock's return to the return on the S&P 500. This OLS procedure is designed to: a. b. c. d.

Minimize Minimize Minimize Minimize

the the the the

square of the sum of differences between the actual and estimated S&P 500 returns. square of the sum of differences between the actual and estimated stock returns. sum of differences between the actual and estimated squared S&P 500 returns. sum of squared differences between the actual and estimated stock returns.

Correct Answer: d Rationale: The OLS procedure is a method for estimating the unknown parameters in a linear regression model. The method minimizes the sum of squared differences between the actual, observed, returns and the returns estimated by the linear approximation. The smaller the sum of the squared differences between observed and estimated values, the better the estimated regression line fits the observed data points. Section: Quantitative Analysis Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008). Chapter 4, “Linear Regression with One Regressor.” Learning Objective: Define an ordinary least squares (OLS) regression and calculate the intercept and slope of the regression.


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2.

Using the prior 12 monthly returns, an analyst estimates the mean monthly return of stock XYZ to be -0.75% with a standard error of 2.70%. ONE-TAILED T-DISTRIBUTION TABLE Degrees of Freedom 0.10 1.397 8 9 1.383 10 1.372 11 1.363 12 1.356

α 0.05 1.860 1.833 1.812 1.796 1.782

0.025 2.306 2.262 2.228 2.201 2.179

Using the t-table above, the 95% confidence interval for the mean return is between: a. b. c. d.

-6.69% and 5.19% -6.63% and 5.15% -5.60% and 4.10% -5.56% and 4.06%

Correct Answer: a Rationale: The confidence interval is equal to the mean monthly return plus or minus the t-statistic times the standard error. To get the proper t-statistic, the 0.025 column must be used since this is a two-tailed interval. Since the mean return is being estimated using the sample observations, the appropriate degrees of freedom to use is equal to the number of sample observations minus 1. Therefore we must use 11 degrees of freedom and therefore the proper statistic to use from the t-distribution is 2.201. The proper confidence interval is: -0.75% +/- (2.201 * 2.70%) or -6.69% to +5.19%. Section: Quantitative Analysis Reference: Michael Miller, Mathematics and Statistics for Financial Risk Management, 2nd Edition (Hoboken, NJ: John Wiley & Sons, 2013). Chapter 7, “Hypothesis Testing and Confidence Intervals.” Learning Objective: Construct and interpret a confidence interval.

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3.

Using data from a pool of mortgage borrowers, a credit risk analyst performed an ordinary least squares regression of annual savings (in GBP) against annual household income (in GBP) and obtained the following relationship: Annual Savings = 0.24 * Household Income - 25.66, R² = 0.50 Assuming that all coefficients are statistically significant, which interpretation of this result is correct? a. b. c. d.

For For For For

this sample data, the average error term is GBP -25.66. a household with no income, annual savings is GBP 0. an increase of GBP 1,000 in income, expected annual savings will increase by GBP 240. a decrease of GBP 2,000 in income, expected annual savings will increase by GBP 480.

Correct Answer: c Rationale: An estimated coefficient of 0.24 from a linear regression indicates a positive relationship between income and savings, and more specifically means that a one unit increase in the independent variable (household income) implies a 0.24 unit increase in the dependent variable (annual savings). Given the equation provided, a household with no income would be expected to have negative annual savings of GBP 25.66. The error term mean is assumed to be equal to 0. Section: Quantitative Analysis Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008), Chapter 4, “Linear Regression with One Regressor.” Learning Objective: Interpret a population regression function, regression coefficients, parameters, slope, intercept, and the error term.


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4.

A risk analyst is estimating the variance of stock returns on day n, given by , using the equation where and represent the return and volatility on day n-1, respectively. If the values of α and β are as indicated below, which combination of values indicates that the variance follows a stable GARCH (1,1) process? a. b. c. d.

α α α α

= = = =

0.084427 0.084427 0.084427 0.090927

and and and and

β β β β

= = = =

0.909073 0.925573 0.925573 0.925573

Correct Answer: a Rationale: For a GARCH (1,1) process to be stable, the sum of parameters α and β need to be below 1.0. Section: Quantitative Analysis Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition (New York: Pearson Prentice Hall, 2014), chapter 23, “Estimating Volatilities and Correlations for Risk Management.” Learning Objective: Describe the generalized auto regressive conditional heteroskedasticity (GARCH(p,q)) model for estimating volatility and its properties: • Calculate volatility using the GARCH(1,1) model • Explain mean reversion and how it is captured in the GARCH (1,1) model

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The following information applies to questions 5 and 6. A portfolio manager holds three bonds in one of his portfolios and each bond has a 1-year default probability of 15%. The event of default for each of the bonds is independent. 5.

What is the probability of exactly two bonds defaulting over the next year? a. b. c. d.

1.9% 5.7% 10.8% 32.5%

Correct Answer: b Rationale: Since the bond defaults are independent and identically distributed Bernoulli random variables, the Binomial distribution can be used to calculate the probability of exactly two bonds defaulting. The correct formula to use is = Where n = the number of bonds in the portfolio, p = the probability of default of each individual bond, and k = the number of defaults for which you would like to find the probability. In this case n = 3, p = 0.15, and k = 2. Entering the variables into the equation, this simplifies to 3 x 0.152 x 0.85 = .0574. Section: Quantitative Analysis Reference: Michael Miller, Mathematics and Statistics for Financial Risk Management, 2nd Edition (Hoboken, NJ: John Wiley & Sons, 2013). Chapter 4, “Distributions.” Learning Objective: Distinguish the key properties among the following distributions: uniform distribution, Bernoulli distribution, Binomial distribution, Poisson distribution, normal distribution, lognormal distribution, Chi-squared distribution, Student’s t, and F-distributions, and identify common occurrences of each distribution.


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6.

What is the mean and variance of the number of bonds defaulting over the next year? a. b. c. d.

Mean Mean Mean Mean

= = = =

0.15, variance = 0.32 0.45, variance = 0.38 0.45, variance = 0.32 0.15, variance = 0.38

Correct Answer: b Rationale: Letting n equal the number of bonds in the portfolio and p equal the individual default probability, the formulas to use are as follows: Mean = n x p = 3 x 15% = 0.45. Variance = n x p x (1-p) = 3 x .15 x .85 = 0.3825 Section: Quantitative Analysis Reference: Michael Miller, Mathematics and Statistics for Financial Risk Management, 2nd Edition (Hoboken, NJ: John Wiley & Sons, 2013), Chapter 4, “Distributions.” Learning Objective: Distinguish the key properties among the following distributions: uniform distribution, Bernoulli distribution, Binomial distribution, Poisson distribution, normal distribution, lognormal distribution, Chi-squared distribution, Student’s t, and F-distributions, and identify common occurrences of each distribution.

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7.

A risk manager is evaluating a portfolio of equities with an annual volatility of 12.1% per year that is benchmarked to the Straits Times Index. If the risk-free rate is 2.5% per year, based on the regression results given in the chart below, what is the Jensen's alpha of the portfolio?

y = 0.4936x + 3.7069 R2 = 0.5387

a. b. c. d.

0.4936% 0.5387% 1.2069% 3.7069%

Correct Answer: d Rationale: The correct answer is d. The Jensen's alpha is equal to the y-intercept, or the excess return of the portfolio when the excess market return is zero. Therefore it is 3.7069%. Section: Foundations of Risk Management Reference: Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England: John Wiley & Sons, 2003). Chapter 4, Section 4.2 only—”Applying the CAPM to Performance Measurement: SingleIndex Performance Measurement Indicators.” Learning Objective: Calculate, compare, and evaluate the Treynor measure, the Sharpe measure, and Jensen's alpha.


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8.

An investment advisor is analyzing the range of potential expected returns of a new fund designed to replicate the directional moves of the BSE Sensex Index but with twice the volatility of the index. The Sensex has an expected annual return of 12.3% and volatility of 19.0%, and the risk free rate is 2.5% per year. Assuming the correlation between the fund’s returns and that of the index is 1, what is the expected return of the fund using the capital asset pricing model? a. b. c. d.

18.5% 19.0% 22.1% 24.6%

Correct Answer: c Rationale: If the CAPM holds, then Ri = Rf + βi x (Rm – Rf), which is maximized at the greatest possible beta value which implies a correlation of 1 between the fund’s return and the index return. Since the volatility of the fund is twice that of the index, a correlation of 1 implies a maximum beta βi of 2. Therefore: Ri (max) = 2.5% + 2 x (12.3% - 2.5%) = 22.1%. Section: Foundations of Risk Management Reference: Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann, Modern Portfolio Theory and Investment Analysis, 9th Edition (Hoboken, NJ: John Wiley & Sons, 2014). Chapter 13, “The Standard Capital Asset Pricing Model.” Learning Objective: Apply the CAPM in calculating the expected return on an asset.

9.

A risk analyst is reconciling customer account data held in two separate databases and wants to ensure the account number for each customer is the same in each database. Which dimension of data quality would she be most concerned with in making this comparison? a. b. c. d.

Completeness Accuracy Consistency Currency

Correct Answer: c Rationale: Consistency refers to the comparison of one element of data across two or more different databases. Section: Foundations of Risk Management Reference: Anthony Tarantino and Deborah Cernauskas, Risk Management in Finance: Six Sigma and Other Next Generation Techniques (Hoboken, NJ: John Wiley & Sons, 2009). Chapter 3, “Information Risk and Data Quality Management.” Learning Objective: Identify some key dimensions of data quality.

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10.

The hybrid approach for estimating VaR is the combination of a parametric and a nonparametric approach. It specifically combines the historical simulation approach with: a. b. c. d.

The The The The

delta normal approach. exponentially weighted moving average approach. multivariate density estimation approach. generalized autoregressive conditional heteroskedasticity approach.

Correct Answer: b Rationale: The hybrid approach combines two approaches to estimating VaR, the historical simulation and the exponential smoothing approach (i.e. an EWMA approach). Similar to a historical simulation approach, the hybrid approach estimates the percentiles of the return directly, but it also uses exponentially declining weights on past data similar to the exponentially weighted moving average approach. Section: Valuation and Risk Models Reference: Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach, Chapter 2, “Quantifying Volatility in VaR Models.” Learning Objective: Compare and contrast different parametric and non-parametric approaches for estimating conditional volatility.


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11.

A non-dividend-paying stock is currently trading at USD 40 and has an expected return of 12% per year. Using the Black-Scholes-Merton (BSM) model, a 1-year, European-style call option on the stock is valued at USD 1.78. The parameters used in the model are: N(d1) = 0.29123

N(d2) = 0.20333

The next day, the company announces that it will pay a dividend of USD 0.5 per share to holders of the stock on an ex-dividend date 1 month from now and has no further dividend payout plans for at least 1 year. This new information does not affect the current stock price, but the BSM model inputs change, so that: N(d1) = 0.29928

N(d2) = 0.20333

If the risk-free rate is 3% per year, what is the new BSM call price? a. b. c. d.

USD USD USD USD

1.61 1.78 1.95 2.11

Correct Answer: c Rationale: The value of a European call is equal to S * N(d1) – Ke-rT * N(d2), where S is the current price of the stock. In the case that dividends are introduced, S in the formula is reduced by the present value of the dividends. Furthermore, the announcement would affect the values of S, d1 and d2. However, since we are given the new values, and d2 is the same, the change in the price of the call is only dependent on the term S * N(d1). Previous S * N(d1) = 40 * 0.29123 = 11.6492 New S * N(d1) = (40 – (0.5 * exp(-3%/12)) * 0.29928 = 11.8219 Change = 11.8219 – 11.6492 = 0.1727 So the new BSM call price would increase in value by 0.1727, which when added to the previous price of 1.78 equals 1.9527. Section: Valuation and Risk Models Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition, Chapter 15, “The Black-Scholes-Merton Model.” Learning Objective: Compute the value of a European option using the Black-Scholes-Merton model on a dividendpaying stock.

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12.

An at-the-money European call option on the DJ EURO STOXX 50 index with a strike of 2200 and maturing in 1 year is trading at EUR 350, where contract value is determined by EUR 10 per index point. The risk-free rate is 3% per year, and the daily volatility of the index is 2.05%. If we assume that the expected return on the DJ EURO STOXX 50 is 0%, the 99% 1-day VaR of a short position on a single call option calculated using the delta-normal approach is closest to: a. b. c. d.

EUR EUR EUR EUR

8. 53. 84. 525.

Correct Answer: d Rationale: Since the option is at-the-money, the delta is close to 0.5. Therefore a 1 point change in the index would translate to approximately 0.5 * EUR 10 = EUR 5 change in the call value. Therefore, the percent delta, also known as the local delta, defined as %D = (5/350) / (1/2200) = 31.4. So the 99% VaR of the call option = %D * VaR(99% of index) = %D * call price * alpha (99%) * 1-day volatility = 31.4 * EUR 350 * 2.33 * 2.05% = EUR 525. The term alpha (99%) denotes the 99th percentile of a standard normal distribution, which equals 2.33. There is a second way to compute the VaR. If we just use a conversion factor of EUR 10 on the index, then we can use the standard delta, instead of the percent delta: VaR(99% of Call) = D * index price * conversion * alpha (99%) * 1-day volatility = 0.5 * 2200 * 10 * 2.33 * 2.05% = EUR 525, with some slight difference in rounding. Both methods yield the same result. Section: Valuation and Risk Models Reference: Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach, Chapter 3, “Putting VaR to Work.” Learning Objective: Compare delta-normal and full revaluation approaches for computing VaR.


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13.

The current stock price of a company is USD 80. A risk manager is monitoring call and put options on the stock with exercise prices of USD 50 and 5 days to maturity. Which of these scenarios is most likely to occur if the stock price falls by USD 1? Scenario A B C D

a. b. c. d.


Call Value Decrease by Decrease by Decrease by Decrease by

USD USD USD USD

0.94 0.94 0.07 0.07

Put Value Increase by Increase by Increase by Increase by

USD USD USD USD

0.08 0.89 0.89 0.08

A B C D

Correct Answer: a Rationale: The call option is deep in-the-money and must have a delta close to one. The put option is deep out-ofthe-money and will have a delta close to zero. Therefore, the value of the in-the-money call will decrease by close to USD 1, and the value of the out-of-the-money put will increase by a much smaller amount close to 0. The choice that is closest to satisfying both conditions is A. Section: Valuation and Risk Models Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition, Chapter 19, “The Greek Letters.” Learning Objective: Describe the dynamic aspects of delta hedging.

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14.

Below is a chart showing the term structure of risk-free spot rates:

Which of the following charts presents the correct derived forward rate curve? a.

b.

c.

d.

Correct Answer: d Rationale: The forward curve will be above the spot curve when the spot curve is rising. The forward curve will also cross the spot curve when the spot curve reaches its maximum (or extreme) value. The forward curve will be below the spot curve when the spot curve is declining. The only chart that reflects these three conditions is choice D. Section: Valuation and Risk Models Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition, Chapter 2, “Spot, Forward, and Par Rates.” Learning Objective: Interpret the forward rate, and compute forward rates given spot rates.


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15.

A hedge fund manager wants to change her interest rate exposure by investing in fixed-income securities with negative duration. Which of the following securities should she buy? a. b. c. d.


maturity maturity maturity maturity

calls puts puts calls

on on on on

zero-coupon bonds with long maturity interest-only strips from long maturity conforming mortgages zero-coupon bonds with long maturity principal-only strips from long maturity conforming mortgages

Correct Answer: c Rationale: In order to change her interest rate exposure by acquiring securities with negative duration, the manager will need to invest in securities that decrease in value as interest rates fall (and increase in value as interest rates rise). Zero coupon bonds with long maturity will increase in value as interest rates fall, so calls on these bonds will increase in value as rates fall but puts on these bonds will decrease in value and this makes C the correct choice. Interest-only strips from long maturity conforming mortgages will decrease in value as interest rates fall, so puts on them will increase in value, while principal strips on these same mortgages will increase in value, so calls on them will also increase in value. Section: Valuation and Risk Models Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition, Chapter 4, “One-Factor Risk Metrics and Hedges.” Learning Objective: Define, compute and interpret the effective duration of a fixed income security given a change in yield and the resulting change in price. Section: Financial Markets and Products Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition, Chapter 20, "Mortgages and Mortgage-Backed Securities."

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16.

A risk analyst is analyzing several indicators for a group of countries. If he specifically considers the Gini coefficient in his analysis, in which of the following factors is he most interested? a. b. c. d.

Standard of living Peacefulness Perceived corruption Income inequality

Correct Answer: d Rationale: The Gini coefficient is commonly used to measure income inequality on a scale of zero to one, with zero being total equality and one being total inequality. Therefore, nations with lower Gini coefficients have a more even distribution of income, while higher Gini coefficients indicate a wider disparity between higher and lower income households. Section: Valuation and Risk Models Reference: Daniel Wagner, Managing Country Risk: A Practitioner’s Guide to Effective Cross-Border Risk Analysis, chapter 4, “Country Risk Assessment in Practice.” Learning Objective: Describe alternative measures and indices that can be useful in assessing country risk.


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17.

A trader writes the following 1-year European-style barrier options as protection against large movements in a non-dividend paying stock that is currently trading at EUR 40.96. Option Up-and-in barrier call, with barrier at EUR 45 Up-and-out barrier call, with barrier at EUR 45 Down-and-in barrier put, with barrier at EUR 35 Down-and-out barrier put, with barrier at EUR 35

Price (EUR) 3.52 1.24 2.00 1.01

All of the options have the same strike price. Assuming the risk-free rate is 2% per annum, what is the common strike price of these options? a. b. c. d.

EUR EUR EUR EUR

39.00 40.00 41.00 42.00

Correct Answer: b Rationale: The sum of the price of an up-and-in barrier call and an up-and-out barrier call is the price of an otherwise equivalent European call. The price of the European call is EUR 3.52 + EUR 1.24 = EUR 4.76. The sum of the price of a down-and-in barrier put and a down-and-out barrier put is the price of an otherwise equivalent European put. The price of the European put is EUR 2.00 + EUR 1.01 = EUR 3.01. Using put-call parity, where C represents the price of a call option and P the price of a put option, C + Ke-r = P + S K = er (P + S – C) Hence, K = e0.02 * (3.01 + 40.96 – 4.76) = 40.00. Section: Financial Markets and Products Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition, chapter 26, “Exotic Options.” Learning Objective: Identify and describe the characteristics and pay-off structure of the following exotic options: Chooser and barrier options

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18.

A fixed-income portfolio manager purchases a seasoned 5.5% agency mortgage-backed security with a weighted average loan age of 60 months. The current balance on the loans is USD 20 million, and the conditional prepayment rate is assumed to be constant at 0.4% per year. Which of the following is closest to the expected principal prepayment this month? a. b. c. d.

USD USD USD USD

1,000 7,000 10,000 70,000

Correct Answer: b Rationale: The expected principal prepayment is equal to: 20,000,000 * (1-((1-0.004)^(1/12))) = USD 6,679. Section: Financial Markets and Products Reference: Pietro Veronesi, Basics of Residential Mortgage Backed Securities, Chapter 8. Learning Objective: Describe and work through a simple cash flow example for the following types of MBS: Pass-through securities. Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition, Chapter 20, “Mortgages and Mortgage-Backed Securities.” Learning Objective: Calculate a fixed rate mortgage payment, and its principal and interest components. Describe the mortgage prepayment option and the factors that influence prepayments.


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19.

The rating agencies have analyzed the creditworthiness of Company XYZ and have determined that the company currently has adequate payment capacity, although a negative change in the business environment could affect its capacity for repayment. The company has been given an investment grade rating by S&P and Moody’s. Which of the following S&P/Moody’s ratings has Company XYZ been assigned? a. b. c. d.

AA/Aa A/A BBB/Baa BB/Ba

Correct Answer: c Rationale: The interpretation given by the above statement refers to a rating of BBB/Baa, which is a lower investment grade rating. A rating of BB/Ba is not investment grade, an AA/Aa rating is a very high investment grade rating and an A/A rating still reflects a strong capacity to make payments. Section: Financial Markets and Products Reference: John Caouette, Edward Altman, Paul Narayanan and Robert Nimmo, Managing Credit Risk, 2nd Edition, Chapter 6, “The Rating Agencies.” Learning Objectives: Describe Standard and Poor’s and Moody’s rating scales and distinguish between investment and noninvestment grade ratings. Describe a rating scale, define credit outlooks, and explain the difference between solicited and unsolicited ratings.

20.

A French bank enters into a 6-month forward contract with an importer to sell GBP 40 million in 6 months at a rate of EUR 0.80 per GBP. If in 6 months the exchange rate is EUR 0.85 per GBP, what is the payoff for the bank from the forward contract? a. b. c. d.

EUR EUR EUR EUR

-2,941,176 -2,000,000 2,000,000 2,941,176

Correct Answer: b Rationale: The value of the contract for the bank at expiration: 40,000,000 GBP * 0.80 EUR/GBP The cost to close out the contract for the bank at expiration: 40,000,000 GBP * 0.85 EUR/GBP Therefore, the final payoff in EUR to the bank can be calculated as: 40,000,000*(0.80 – 0.85) = -2,000,000 EUR. Section: Financial Markets and Products Reference: John Hull, Options, Futures and Other Derivatives, 9th Edition, Chapter 1, “Introduction.” Learning Objective: Calculate and compare the payoffs from hedging strategies involving forward contracts and options.

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21.

An oil driller recently issued USD 250 million of fixed-rate debt at 4.0% per annum to help fund a new project. It now wants to convert this debt to a floating-rate obligation using a swap. A swap desk analyst for a large investment bank that is a market maker in swaps has identified four firms interested in swapping their debt from floating-rate to fixed-rate. The following table quotes available loan rates for the oil driller and each firm: Firm Oil driller Firm A Firm B Firm C Firm D

Fixed-rate (in %) 4.0 3.5 6.0 5.5 4.5

Floating-rate (in %) 6-month LIBOR + 1.5 6-month LIBOR + 1.0 6-month LIBOR + 3.0 6-month LIBOR + 2.0 6-month LIBOR + 2.5

A swap between the oil driller and which firm offers the greatest possible combined benefit? a. b. c. d.

Firm Firm Firm Firm

A B C D

Correct Answer: c Rationale: Since the oil driller is swapping out of a fixed-rate and into a floating-rate, the larger the difference between the fixed spread and the floating spread the greater the combined benefit. See table below: Firm Oil driller Firm A Firm B Firm C Firm D

Fixed-rate 4.0 3.5 6.0 5.5 4.5

Floating-rate 1.5 1.0 3.0 2.0 2.5

Fixed-spread

Floating-spread

Possible Benefit

-0.5 2.0 1.5 0.5

-0.5 1.5 0.5 1.0

-0.0 0.5 1.0 -0.5

Section: Financial Markets and Products Reference: John Hull, Options, Futures and Other Derivatives, 9th Edition, Chapter 7, “Swaps.” Learning Objective: Describe the comparative advantage argument for the existence of interest rate swaps and evaluate some of the criticisms of this argument.


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22.

Consider an American call option and an American put option, each with 3 months to maturity, written on a non-dividend-paying stock currently priced at USD 40. The strike price for both options is USD 35 and the risk-free rate is 1.5%. What are the lower and upper bounds on the difference between the prices of the call and put options? Scenario A B C D a. b. c. d.


Lower Bound (USD) 5.13 5.00 34.87 0.13

Upper Bound (USD) 40.00 5.13 40.00 34.87

A B C D

Correct Answer: b Rationale: The put-call parity in case of American options leads to the inequality: S0 – X ≤ (C – P) ≤ S0 – Xe-rT The lower and upper bounds are given by— = 40 – 35 ≤ (C – P) ≤ 40 – 35e-0.015 x 3/12 = 5 ≤ (C – P) ≤ 5.13 Alternatively, the upper and lower bounds for American options are given by Option American Call American Put

Minimum Value c ≥ max(0, S0 - Xe-rT) = 5.13 p ≥ max(0, X - S0) = 0

Maximum Value S0 = 40 X= 35

Subtracting the put values from the call values in the table above, we get the same result— = 5 ≤ C – P ≤ 5.13 (Note- the minimum and maximum values are obtained by comparing the results of the subtraction of the put price from the call price. For instance, in this example, the upper bound is obtained by subtracting the minimum value of the American put option from the minimum value of the American call option and vice versa). Section: Financial Markets and Products Reference: John Hull, Options, Futures and Other Derivatives, 9th Edition, Chapter 11, “Properties of Stock Options.” Learning Objective: Identify and compute upper and lower bounds for option prices on non-dividend and dividend paying stocks. Explain put-call parity and apply it to the valuation of European and American stock options.

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23.

A growing regional bank has added a risk committee to its board. One of the first recommendations of the risk committee is that the bank should develop a risk appetite statement. What best represents a primary function of a risk appetite statement? a. b. c. d.

To To To To

quantify the level of variability for each risk metric that a firm is willing to accept state specific new business opportunities that a firm is willing to pursue assign risk management responsibilities to specific internal staff members state a broad level of acceptable risk to guide the allocation of the firm’s resources

Correct Answer: d Rationale: A risk appetite statement states a broad level of risk across the organization the firm is willing to accept in order to pursue value creation. The statement is typically broadly articulated and can be communicated across the organization, and helps to allocate resources to specific objectives at the firm. Section: Foundations of Risk Management Reference: “Understanding and Communicating Risk Appetite,” (COSO, Dr. Larry Rittenberg and Frank Martens, January 2012). Learning Objective: Define risk appetite and explain the role of risk appetite in corporate governance. Reference: Implementing Robust Risk Appetite Frameworks to Strengthen Financial Institutions,” Institute of International Finance, June 2011 (Executive Summary—Section 4, pp. 10–40). Learning Objective: Relate the use of risk appetite frameworks (RAF) to the management of risk in a firm. Define risk culture and assess the relationship between a firm’s risk appetite and its risk culture.


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24.

A German housing corporation needs to hedge against rising interest rates. It has chosen to use futures on 10-year German government bonds. Which position in the futures should the corporation take, and why? a. b. c. d.

Take Take Take Take

a a a a

long position in the futures because rising interest rates lead to rising futures prices. short position in the futures because rising interest rates lead to rising futures prices. short position in the futures because rising interest rates lead to declining futures prices. long position in the futures because rising interest rates lead to declining futures prices.

Correct Answer: c Rationale: Government bond futures decline in value when interest rates rise, so the housing corporation should short futures to hedge against rising interest rates. Section: Financial Markets and Products Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition, Chapter 3, “Hedging Strategies Using Futures.” Learning Objective: Define and differentiate between short and long hedges and identify their appropriate uses.

42



25.

Barings was forced to declare bankruptcy after reporting over USD 1 billion in unauthorized trading losses by a single trader, Nick Leeson. Which of the following statements concerning the collapse of Barings is correct? a. b. c. d.

Leeson avoided reporting the unauthorized trades by convincing the head of his back office that they did not need to be reported. Management failed to investigate high levels of reported profits even though they were associated with a low-risk trading strategy. Leeson traded primarily in OTC foreign currency swaps which allowed Barings to delay cash payments on losing trades until the first payment was due. The loss at Barings was detected when several customers complained of losses on trades that were booked to their accounts.

Correct Answer: b Rationale: Leeson was supposed to be running a low-risk, limited return arbitrage business out of his Singapore office, but in actuality he was investing in large speculative positions in Japanese stocks and interest rate futures and options. When Leeson fraudulently declared very substantial reported profits on his positions, management did not investigate the stream of large profits even thought it was supposed to be associated with a low-risk strategy. Section: Foundations of Risk Management Reference: Steve Allen, Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk, 2nd Edition (New York: John Wiley & Sons, 2013), Chapter 4, “Financial Disasters.” Learning Objective: Analyze the key factors that led to and derive the lessons learned from the following risk management case studies: Barings.


43

2015 ®

FRM Practice Exam Part II Answer Sheet


a.

b.

c.

d.

a.

1.

14.

2.

15.

3.

16.

4.

17.

5.

18.

6.

19.

7.

20.

b.

c.

d.

✓

✘

8. 9.


10.

1.

11.


12.

1.

13.


45

2015 ®

FRM Practice Exam Part II Questions


1.

The CEO of a regional bank understands that failing to anticipate cash flow needs is one of the most serious errors that a firm can make and demands that a good liquidity-at-risk (LaR) measurement system be an essential part of the bank's risk management framework. Which of the following statements concerning LaR is correct? a. b. c. d.

2.

Pillar 1 of the Basel II framework allows banks to use various approaches to calculate the capital requirements for credit risk, operational risk and market risk. Which of the following Basel II approaches allows a bank to explicitly recognize diversification benefits? a. b. c. d.

3.

The The The The

internal models approach for market risk internal ratings based approach for credit risk basic indicator approach for operational risk standardized approach for operational risk

Nordlandia is a country with a developed economy maintaining its own currency, the Nordlandian crown (NLC), and whose most important export is domestically produced oil and natural gas. In a recent stress test of Nordlandia's banking system, several scenarios were considered. Which of the following is most consistent with being part of a coherent scenario? a. b. c. d.

4.

Reducing the basis risk through hedging decreases LaR. Hedging using futures has the same impact on LaR as hedging using long option positions. For a hedged portfolio, the LaR can differ significantly from the VaR. A firm's LaR tends to decrease as its credit quality declines.

An increase in domestic inflation and appreciation of the NLC A significant increase in crude oil prices and a decrease in the Nordlandian housing price index A drop in crude oil prices and appreciation of the NLC A sustained decrease in natural gas prices and a decrease in the Nordlandian stock index

Which statement about risk control in portfolio construction is correct? a. b. c. d.

Quadratic programming allows for risk control through parameter estimation but generally requires many more inputs estimated from market data than other methods require. The screening technique provides superior risk control by concentrating stocks in selected sectors based on expected alpha. When using the stratification technique, risk control is implemented by overweighting the categories with lower risks and underweighting the categories with higher risks. When using the linear programming technique, risk is controlled by selecting the portfolio with the lowest level of active risk.


47


5.

An analyst reports the following fund information to the advisor of a pension fund that currently invests in government and corporate bonds and carries a surplus of USD 10 million: Pension Assets Amount (in USD million) Expected Annual Growth Modified Duration Annual Volatility of Growth

Pension 100 6% 12 10%

Liabilities 90 7% 10 5%

To evaluate the sufficiency of the fund's surplus, the advisor estimates the possible surplus values at the end of one year. The advisor assumes that annual returns on assets and the annual growth of the liabilities are jointly normally distributed and their correlation coefficient is 0.8. The advisor can report that, with a confidence level of 95%, the surplus value will be greater than or equal to: a. b. c. d.

6.

-11.4 million -8.3 million -1.7 million 0 million

A due diligence specialist is evaluating the risk management process of a hedge fund in which his company is considering making an investment. Which of the following statements best describes criteria used for such an evaluation? a. b. c. d.

48

USD USD USD USD

Because of the overwhelming importance of tail risk, the company should not invest in the fund unless it fully accounts for fat tails using extreme value theory at the 99.99% level when estimating VaR. Today's best practices in risk management require that a fund employ independent risk service providers and that these service providers play important roles in risk-related decisions. When considering a leveraged fund, the specialist should assess how the fund estimates risks related to leverage, including funding liquidity risks during periods of market stress. It is crucial to assess the fund's valuation policy, and in general if more than 10% of asset prices are based on model prices or broker quotes, the specialist should recommend against investment in the fund regardless of other information available about the fund.



7.

Cloudesdale Corporation is considering a project that has an estimated risk-adjusted return on capital (RAROC) of 13%. Suppose that the risk-free rate is 3% per year, the expected market rate of return is 11% per year, and the firm's equity beta is 1.3. Using the criterion of adjusted risk-adjusted return on capital (ARAROC), Cloudesdale should: a. b. c. d.

8.

Rarecom is a specialist company that only trades derivatives on rare commodities. Rarecom and a handful of other firms, all of whom have large notional outstanding contracts with Rarecom, dominate the market for such derivatives. Rarecom management would like to mitigate its overall counterparty exposure, with the goal of reducing it to almost zero. Which of the following methods, if implemented, could best achieve this goal? a. b. c. d.

9.

Reject the project because the ARAROC is higher than the market expected excess return. Accept the project because the ARAROC is higher than the market expected excess return. Reject the project because the ARAROC is lower than the market expected excess return. Accept the project because the ARAROC is lower than the market expected excess return.

Ensuring that sufficient collateral is posted by counterparties Diversifying among counterparties Cross-product netting on a single counterparty basis Purchasing credit derivatives, such as credit default swaps

Local Company, a frequent user of swaps, often enters into transactions with Global Bank, a major provider of swaps. Recently, Global Bank was downgraded from a rating of AA+ to a rating of A, while Local Company was downgraded from a rating of A to a rating of A-. During this time, the credit spread for Global Bank has increased from 20 bps to 150 bps, while the credit spread for Local Company has increased from 130 bps to 170 bps. Which of the following is the most likely action that the counterparties will request on their credit value adjustment (CVA)? a. b. c. d.

The credit qualities of the counterparties have migrated, but not significantly enough to justify amending existing CVA arrangements. Global Bank requests an increase in the CVA charge it receives. Local Company requests a reduction in the CVA charge it pays. CVA is no longer a relevant factor, and the counterparties should migrate to using other mitigants of counterparty risk.


49


10.

An analyst estimates that the hazard rate for a company is 0.1 per year. The probability of survival in the first year followed by a default in the second year is closest to: a. b. c. d.

11.

8.61%. 9.00%. 9.52%. 19.03%.

At the beginning of the year, a firm bought an AA-rated corporate bond at USD 110 per USD 100 face value. Using market data, the risk manager estimates the following year-end values for the bond based on interest rate simulations informed by the economics team: Rating

Year-end Bond Value (USD per USD 100 face value) 112 109 105 101 92 83 73 50

AAA AA A BBB BB B CCC Default

In addition, the risk manager estimates the 1-year transition probabilities on the AA-rated corporate bond: Rating AAA AA A BBB BB B CCC Default

Probability of State 3.00% 85.00% 7.00% 4.00% 0.35% 0.25% 0.15% 0.25%

What is the 1-year 95% credit VaR per USD 100 of face value closest to? a. b. c. d.

50

USD USD USD USD

9 18 30 36



12.

A risk manager is advising the trading desk about entering into a digital credit default swap as a way to obtain credit protection. Which cash flow and delivery requirement will the desk most likely experience in the event of a default of the underlying reference asset? a. b. c. d.

13.

the pre-agreed cash payment; deliver nothing. [(Par Value) - (Market Value of Reference Asset)]; deliver the reference asset. [(Par Value) - (Market Value of Reference Asset)]; deliver nothing. the pre-agreed cash payment; deliver the reference asset.

Computing VaR on a portfolio containing a very large number of positions can be simplified by mapping these positions to a smaller number of elementary risk factors. Which of the following mappings would be adequate? a. b. c. d.

14.

Receive Receive Receive Receive

USD/EUR forward contracts are mapped on the USD/JPY spot exchange rate. Each position in a corporate bond portfolio is mapped on the bond with the closest maturity among a set of government bonds. Government bonds paying regular coupons are mapped on zero-coupon government bonds. A position in the stock market index is mapped on a position in a stock within that index.

The dependence structure between the returns of financial assets plays an important role in risk measurement. For liquid markets, which of the following statements is incorrect? a. b. c. d.

Correlation is a valid measure of dependence between random variables for only certain types of return distributions. Even if the return distributions of two assets have a correlation of zero, the returns of these assets are not necessarily independent. Copulas make it possible to model marginal distributions and the dependence structure separately. With short time horizons (3 months or less), correlation estimates are typically very stable.


51


A risk manager is in the process of valuing several European option positions on a non-dividend-paying stock XYZ that is currently priced at GBP 30. The implied volatility skew, estimated using the Black-Scholes-Merton model and the current prices of actively traded European-style options on stock XYZ at various strike prices, is shown below:

Implied Volatility

15.

Strike Price (GBP)

Assuming that the implied volatility at GBP 30 is used to conduct the valuation, which of the following long positions will be undervalued? a. b. c. d.

16.

out-of-the-money call in-the-money call at-the-money put in-the-money put

A risk manager is pricing a 10-year call option on 10-year Treasuries using a successfully tested pricing model. Current interest rate volatility is high and the risk manager is concerned about the effect this may have on short-term rates when pricing the option. Which of the following actions would best address the potential for negative short-term interest rates to arise in the model? a. b. c. d.

52

An An An An

The risk manager uses a normal distribution of interest rates. When short-term rates are negative, the risk manager adjusts the risk-neutral probabilities. When short-term rates are negative, the risk manager increases the volatility. When short-term rates are negative, the risk manager sets the rate to zero.



17.

A large commercial bank is using VaR as its main risk measurement tool. Expected shortfall (ES) is suggested as a better alternative to use during market turmoil. What should be understood regarding VaR and ES before modifying current practices? a. b. c. d.

18.

Despite being more complicated to calculate, ES is easier to backtest than VaR. Relative to VaR, ES leads to more required economic capital for the same confidence level. While VaR ensures that the estimate of portfolio risk is less than or equal to the sum of the risks of that portfolio’s positions, ES does not. Both VaR and ES account for the severity of losses beyond the confidence threshold.

A risk management consultant is involved in evaluating the capital planning at a US-based bank holding company (BHC) with over USD 100 billion in total consolidated assets. The evaluation includes looking at the stress testing program that is integral to the capital planning process. In evaluating the BHC's design of stress scenarios, which of the following statements is correct? a. b. c. d.

Although the BHC may feel it is losing some of its independence, limiting the scenarios to those developed by the Federal Reserve will ensure regulatory compliance. To avoid introducing bias, if the BHC uses private sector third-party-defined scenarios, they should be implemented without alteration. In order to properly assess both right-way and wrong-way risk in stress environments, assumptions should be included that specifically benefit the BHC. When developing scenarios internally, it is acceptable to combine expert judgment with quantitative models rather than relying only on the models.


53


Question 19 refers to the following information: A profitable derivatives trading desk at a bank decides that its existing VaR model, which has been used broadly across the firm for several years, is too conservative. The existing VaR model uses a historical simulation over a three-year look-back period, weighting each day equally. A quantitative analyst in the group quickly develops a new VaR model, which uses the delta normal approach. The new model uses volatilities and correlations estimated over the past four years using the Riskmetrics EWMA method. For testing purposes, the new model is used in parallel with the existing model for four weeks to estimate the 1-day 95% VaR. After four weeks, the new VaR model has no exceedances despite consistently estimating VaR to be considerably lower than the existing model's estimates. The analyst argues that the lack of exceedances shows that the new model is unbiased and pressures the bank’s model evaluation team to agree. Following an overnight examination of the new model by one junior analyst instead of the customary evaluation that takes several weeks and involves a senior member of the team, the model evaluation team agrees to accept the new model for use by the desk.

19.

Which of the following statements about the risk management implications of this replacement is correct? a. b. c. d.

54

Delta-normal VaR is more appropriate than historical simulation VaR for assets with non-linear payoffs. Changing the look-back period and weighing scheme from three years, equally weighted, to four years, exponentially weighted, will understate the risk in the portfolio. The desk increased its exposure to model risk due to the potential for incorrect calibration and programming errors related to the new model. A 95% VaR model that generates no exceedances in four weeks is necessarily conservative.



20.

The CFO at a bank is preparing a report to the board of directors on its compliance with Basel requirements. The bank's average capital and total exposure for the most recent quarter is as follows: REGULATORY CAPITAL Total Common Equity Tier 1 Capital Additional Tier 1 Capital Prior to regulatory adjustments Regulatory adjustments

USD MILLIONS 108 28 34 6

Total Tier 1 Capital Tier 2 Capital Prior to regulatory adjustments Regulatory adjustments

136 36 45 9

Total Capital Total Average Exposure

172 3678

Using the Basel III framework, which of the following is the best estimate of the bank’s current leverage ratio? a. b. c. d.

2.94% 3.70% 4.68% 5.08%


55

2015 ®

FRM Practice Exam Part II Answers


a.

c.

a.

17.

18.

6.

19.

7.

20.

9. 10.


11.

1.

12.


13.

d.

16.

5.

8.

c.

15.

b.

14.

3. 4.

d.

1. 2.

b.

1.


✓

✘

57

2015 ®

FRM Practice Exam Part II Explanations


1.

The CEO of a regional bank understands that failing to anticipate cash flow needs is one of the most serious errors that a firm can make and demands that a good liquidity-at-risk (LaR) measurement system be an essential part of the bank's risk management framework. Which of the following statements concerning LaR is correct? a. b. c. d.

Reducing the basis risk through hedging decreases LaR. Hedging using futures has the same impact on LaR as hedging using long option positions. For a hedged portfolio, the LaR can differ significantly from the VaR. A firm's LaR tends to decrease as its credit quality declines.

Correct Answer: c Rationale: The LaR can differ substantially from the VaR in a hedged portfolio, and in different situations can be larger or smaller than the VaR. For example, consider a portfolio where futures contracts are used to hedge. While the hedge can reduce the VaR of the portfolio, the LaR can be larger than the VaR as the futures contracts create an exposure to margin calls and the potential for cash outflows. Alternatively, in situations where the hedging instruments do not result in potential cash outflows over the measurement period (e.g. a portfolio of European options which do not expire during the period), the LaR can be smaller than the VaR. Section: Operational and Integrated Risk Management Reference: Kevin Dowd, Measuring Market Risk, Chapter 14, “Estimating Liquidity Risks.” Learning Objective: Describe liquidity at risk (LaR) and compare it to VaR, describe the factors that affect future cash flows, and explain challenges in estimating and modeling LaR.


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2.

Pillar 1 of the Basel II framework allows banks to use various approaches to calculate the capital requirements for credit risk, operational risk and market risk. Which of the following Basel II approaches allows a bank to explicitly recognize diversification benefits? a. b. c. d.

The The The The

internal models approach for market risk internal ratings based approach for credit risk basic indicator approach for operational risk standardized approach for operational risk

Correct Answer: a Rationale: The internal models approach allows banks to use risk measures derived from their own internal risk management models, subject to a set of qualitative conditions and quantitative standards. In terms of risk aggregation within market risk, banks are explicitly allowed to recognize empirical correlations across broad market risk categories, and, thus, diversification benefits. Section: Operational and Integrated Risk Management Reference: “Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework—Comprehensive Version,” (Basel Committee on Banking Supervision Publication, June 2006).* John Hull, Risk Management and Financial Institutions, 3rd Edition, Chapter 12, “Basel I, Basel II and Solvency II.” Learning Objective: Describe and contrast the major elements—including a description of the risks covered—of the two options available for the calculation of market risk: Standardised Measurement Method and Internal Models Approach.

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3.

Nordlandia is a country with a developed economy maintaining its own currency, the Nordlandian crown (NLC), and whose most important export is domestically produced oil and natural gas. In a recent stress test of Nordlandia's banking system, several scenarios were considered. Which of the following is most consistent with being part of a coherent scenario? a. b. c. d.

An increase in domestic inflation and appreciation of the NLC A significant increase in crude oil prices and a decrease in the Nordlandian housing price index A drop in crude oil prices and appreciation of the NLC A sustained decrease in natural gas prices and a decrease in the Nordlandian stock index

Correct Answer: d Rationale: A scenario is coherent when a change in one factor influences other factors in a logical manner. In this case, choice d is a coherent scenario since the Nordlandian economy depends heavily on exports of oil and natural gas, so therefore a sustained decrease in natural gas prices should lead to a decrease in stock prices as the domestic economy weakens. In stress testing banks, it is often challenging to develop scenarios where all factors behave coherently. Section: Operational and Integrated Risk Management Reference: Til Schuermann. “Stress Testing Banks,” April 2012. Learning Objective: Explain challenges in designing stress test scenarios, including the problem of coherence in modeling risk factors.


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4.

Which statement about risk control in portfolio construction is correct? a. b. c. d.

Quadratic programming allows for risk control through parameter estimation but generally requires many more inputs estimated from market data than other methods require. The screening technique provides superior risk control by concentrating stocks in selected sectors based on expected alpha. When using the stratification technique, risk control is implemented by overweighting the categories with lower risks and underweighting the categories with higher risks. When using the linear programming technique, risk is controlled by selecting the portfolio with the lowest level of active risk.

Correct Answer: a Rationale: Quadratic programming requires many more inputs than other portfolio construction techniques because it entails estimating volatilities and pair-wise correlations between all assets in a portfolio. Quadratic programming is a powerful process, but given the large number of inputs it introduces the potential for noise and poor calibration given the less than perfect nature of most data. On the other hand, the screening technique strives for risk control by including a sufficient number of stocks that meet the screening parameters and by weighting them to avoid concentrations in any particular stock. However, screening does not necessarily select stocks evenly across sectors and can ignore entire sectors or classes of stocks entirely if they do not pass the screen. Therefore, risk control in a screening process is fragmentary at best. Stratification separates stocks into categories (for example, economic sectors) and implements risk control by ensuring that the weighting in each sector matches the benchmark weighting. Therefore, it does not allow for overweighting or underweighting specific categories. Linear programming does not necessarily select the portfolio with the lowest level of active risk. Rather, it attempts to improve on stratification by introducing many more dimensions of risk control and ensuring that the portfolio approximates the benchmark for all these dimensions. Section: Risk Management and Investment Management Reference: Richard Grinold and Ronald Kahn, Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk, 2nd Edition (New York: McGraw-Hill, 2000). Chapter 14, “Portfolio Construction.” Learning Objective: Evaluate the strengths and weaknesses of the following portfolio construction techniques: screens, stratification, linear programming, and quadratic programming.

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5.

An analyst reports the following fund information to the advisor of a pension fund that currently invests in government and corporate bonds and carries a surplus of USD 10 million: Pension Assets Amount (in USD million) Expected Annual Growth Modified Duration Annual Volatility of Growth

Pension 100 6% 12 10%

Liabilities 90 7% 10 5%

To evaluate the sufficiency of the fund's surplus, the advisor estimates the possible surplus values at the end of one year. The advisor assumes that annual returns on assets and the annual growth of the liabilities are jointly normally distributed and their correlation coefficient is 0.8. The advisor can report that, with a confidence level of 95%, the surplus value will be greater than or equal to: a. b. c. d.

USD USD USD USD

-11.4 million -8.3 million -1.7 million 0 million

Correct Answer: c Rationale: The lower bound of the 95% confidence interval is equal to: Expected Surplus - (95% confidence factor * Volatility of Surplus). The required variables can be calculated as follows: Variance of the surplus = 1002 * 10%2 + 902 * 5%2 - 2 * 100 * 90 * 10% * 5% * 0.8 = 48.25 Volatility of the surplus = √48.25 = 6.94, The expected surplus = 100 * 1.06 - 90 * 1.07 = 9.7. Therefore, the lower bound of the 95% confidence interval = 9.7 - 1.645 * 6.94 = -1.725 Section: Risk Management and Investment Management Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, Chapter 17, “VaR and Risk Budgeting in Investment Management.” Learning Objective: Distinguish among the following types of risk: absolute risk, relative risk, policy-mix risk, active management risk, funding risk, and sponsor risk.


63


6.

A due diligence specialist is evaluating the risk management process of a hedge fund in which his company is considering making an investment. Which of the following statements best describes criteria used for such an evaluation? a. b. c. d.

Because of the overwhelming importance of tail risk, the company should not invest in the fund unless it fully accounts for fat tails using extreme value theory at the 99.99% level when estimating VaR. Today's best practices in risk management require that a fund employ independent risk service providers and that these service providers play important roles in risk-related decisions. When considering a leveraged fund, the specialist should assess how the fund estimates risks related to leverage, including funding liquidity risks during periods of market stress. It is crucial to assess the fund's valuation policy, and in general if more than 10% of asset prices are based on model prices or broker quotes, the specialist should recommend against investment in the fund regardless of other information available about the fund.

Correct Answer: c Rationale: Generally speaking, with a leveraged fund, an investor will need to evaluate historical and current changes in leverage, as well as the level of liquidity of the portfolio, particularly during times of market stress. Certain strategies may in fact expose an investor to tail risk, so while an investor should inquire whether the manager believes that tail risk exists, and whether or not it is hedged, it is then up to the investor to decide whether to accept the risk unhedged or hedge it on their own. Many funds employ independent risk service providers to report risks to investors, but these firms do not get involved in risk related decision making. And finally, while it is important to know what percentage of the assets is exchange-traded and marked to market, what might be acceptable may differ depending on the strategy of the fund. Section: Risk Management and Investment Management Learning Objective: Describe criteria that can be evaluated in assessing a fund’s risk management process. Reference: Kevin R. Mirabile, Hedge Fund Investing: A Practical Approach to Understanding Investor Motivation, Manager Profits, and Fund Performance (Hoboken, NJ: Wiley Finance, 2013). Chapter 11, “Performing Due Diligence on Specific Managers and Funds.”

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7.

Cloudesdale Corporation is considering a project that has an estimated risk-adjusted return on capital (RAROC) of 13%. Suppose that the risk-free rate is 3% per year, the expected market rate of return is 11% per year, and the firm's equity beta is 1.3. Using the criterion of adjusted risk-adjusted return on capital (ARAROC), Cloudesdale should: a. b. c. d.

Reject the project because the ARAROC is higher than the market expected excess return. Accept the project because the ARAROC is higher than the market expected excess return. Reject the project because the ARAROC is lower than the market expected excess return. Accept the project because the ARAROC is lower than the market expected excess return.

Correct Answer: c Rationale: ARAROC = (RAROC – Rf) / β = (0.13 – 0.03) / 1.3 = 7.69%. Market excess return = Rm – Rf = 0.11 – 0.03 = 8%. As ARAROC < market excess return, the project should be rejected. Section: Operational and Integrated Risk Management Reference: Michel Crouhy, Dan Galai and Robert Mark, Risk Management (New York: McGraw-Hill, 2001). Chapter 14, Capital Allocation and Performance Measurement. Learning Objective: Compute the adjusted RAROC for a project to determine its viability.


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8.

Rarecom is a specialist company that only trades derivatives on rare commodities. Rarecom and a handful of other firms, all of whom have large notional outstanding contracts with Rarecom, dominate the market for such derivatives. Rarecom management would like to mitigate its overall counterparty exposure, with the goal of reducing it to almost zero. Which of the following methods, if implemented, could best achieve this goal? a. b. c. d.

Ensuring that sufficient collateral is posted by counterparties Diversifying among counterparties Cross-product netting on a single counterparty basis Purchasing credit derivatives, such as credit default swaps

Correct Answer: a Rationale: Counterparty exposure, in theory, can be almost completely neutralized as long as a sufficient amount of high quality collateral, such as cash or short-term investment grade government bonds, is held against it. If the counterparty were to default, the holder of an open derivative contract with exposure to that counterparty would be allowed to receive the collateral. Cross-product netting would only reduce the exposure to one of the counterparties, and purchasing credit derivatives would replace the counterparty risk from the individual counterparties with counterparty risk from the institution who wrote the CDS. Section: Credit Risk Measurement and Management Reference: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, Chapter 3, "Defining Counterparty Credit Risk." Learning Objective: Identify and describe the different ways institutions can manage and mitigate counterparty risk.

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9.

Local Company, a frequent user of swaps, often enters into transactions with Global Bank, a major provider of swaps. Recently, Global Bank was downgraded from a rating of AA+ to a rating of A, while Local Company was downgraded from a rating of A to a rating of A-. During this time, the credit spread for Global Bank has increased from 20 bps to 150 bps, while the credit spread for Local Company has increased from 130 bps to 170 bps. Which of the following is the most likely action that the counterparties will request on their credit value adjustment (CVA)? a. b. c. d.

The credit qualities of the counterparties have migrated, but not significantly enough to justify amending existing CVA arrangements. Global Bank requests an increase in the CVA charge it receives. Local Company requests a reduction in the CVA charge it pays. CVA is no longer a relevant factor, and the counterparties should migrate to using other mitigants of counterparty risk.

Correct Answer: c Rationale: Because Local Bank has a lower credit rating than Global Bank, it would typically pay a CVA charge to Global Bank which would be a function of the relative credit spread between the two banks. After the downgrades of both Global Bank and Local Bank, the credit spread between the two banks narrowed from 110 bps initially to only 20 bps after the downgrades. Therefore, with the spread much lower between the two banks, Local Bank would be in a position to request a reduction in the CVA charge that it pays. Section: Credit Risk Measurement and Management Reference: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, Chapter 12, "Credit Value Adjustment.” Learning Objective: Explain the motivation for and the challenges of pricing counterparty risk.


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10.

An analyst estimates that the hazard rate for a company is 0.1 per year. The probability of survival in the first year followed by a default in the second year is closest to: a. b. c. d.

8.61%. 9.00%. 9.52%. 19.03%.

Correct Answer: a Rationale: The probability that the firm defaults in the second year is conditional on its surviving the first year. Using λ to represent the given hazard rate, we can calculate the cumulative probability of default in the first year using the formula 1 - exp(-λ), which equals 0.09516. Then, the cumulative probability that the firm defaults in the second year is equal to 1-exp(-2 * λ) or 0.18127, and the conditional one year default probability given that the firm survived the first year is the difference between the two year cumulative probability of default and the one year probability: 0.18127 - 0.09516 = .08611. Section: Credit Risk Measurement and Management Reference: Allan Malz, Financial Risk Management: Models, History, and Institutions (1st ed.), Chapter 7, “Spread Risk and Default Intensity Models,” pp. 238-241. Learning Objective: Define the hazard rate and use it to define probability functions for default time and conditional default probabilities.

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11.

At the beginning of the year, a firm bought an AA-rated corporate bond at USD 110 per USD 100 face value. Using market data, the risk manager estimates the following year-end values for the bond based on interest rate simulations informed by the economics team: Rating

Year-end Bond Value (USD per USD 100 face value) 112 109 105 101 92 83 73 50

AAA AA A BBB BB B CCC Default

In addition, the risk manager estimates the 1-year transition probabilities on the AA-rated corporate bond: Rating AAA AA A BBB BB B CCC Default

Probability of State 3.00% 85.00% 7.00% 4.00% 0.35% 0.25% 0.15% 0.25%

What is the 1-year 95% credit VaR per USD 100 of face value closest to? a. b. c. d.

USD USD USD USD

9 18 30 36

Correct Answer: a Rationale: The 95% credit VaR corresponds to the unexpected loss at the 95th percentile minus the expected loss, or the expected future value at the 95% loss percentile minus the current value. Using the probabilities in the given ratings transition matrix, the 95% percentile corresponds to a downgrade to BBB, at which the value of the bond would be estimated at 101. Since cash flows for the bond are not provided, we cannot derive the precise expected and unexpected losses, but the credit VaR (the difference) is easily derived by subtracting the estimated value given a BBB rating from the current value. 95% credit VaR = 110 – 101 = 9. Section: Credit Risk Measurement and Management Reference: Allan Malz, Financial Risk Management: Models, History, and Institutions, 1st Edition, Chapter 6, “Credit and Counterparty Risk.” Learning Objective: Define and calculate Credit VaR.


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12.

A risk manager is advising the trading desk about entering into a digital credit default swap as a way to obtain credit protection. Which cash flow and delivery requirement will the desk most likely experience in the event of a default of the underlying reference asset? a. b. c. d.

Receive Receive Receive Receive

the pre-agreed cash payment; deliver nothing. [(Par Value) - (Market Value of Reference Asset)]; deliver the reference asset. [(Par Value) - (Market Value of Reference Asset)]; deliver nothing. the pre-agreed cash payment; deliver the reference asset.

Correct Answer: a Rationale: A digital CDS will pay off a pre-determined fixed amount in the event of a default. Digital CDS are often used against highly illiquid reference assets that would be difficult to price. Section: Credit Risk Measurement and Management Reference: Christopher Culp (2006), Structured Finance and Insurance: The Art of Managing Capital and Risk, 1st Edition, Chapter 12, “Credit Derivatives and Credit Linked Notes,” pp. 252-254. Learning Objective: Describe the mechanics and attributes of a single named credit default swap (CDS).

13.

Computing VaR on a portfolio containing a very large number of positions can be simplified by mapping these positions to a smaller number of elementary risk factors. Which of the following mappings would be adequate? a. b. c. d.

USD/EUR forward contracts are mapped on the USD/JPY spot exchange rate. Each position in a corporate bond portfolio is mapped on the bond with the closest maturity among a set of government bonds. Government bonds paying regular coupons are mapped on zero-coupon government bonds. A position in the stock market index is mapped on a position in a stock within that index.

Correct Answer: c Rationale: Mapping government bonds paying regular coupons onto zero coupon government bonds is an adequate process, because both categories of bonds are government issued and therefore have a very similar sensitivity to risk factors. However, this is not a perfect mapping since the sensitivity of both classes of bonds to specific risk factors (i.e. changes in interest rates) may differ. Section: Market Risk Measurement and Management Reference: Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, Chapter 11, “VaR Mapping.” Learning Objective: Explain the principles underlying VaR mapping, and describe the mapping process.

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14.

The dependence structure between the returns of financial assets plays an important role in risk measurement. For liquid markets, which of the following statements is incorrect? a. b. c. d.

Correlation is a valid measure of dependence between random variables for only certain types of return distributions. Even if the return distributions of two assets have a correlation of zero, the returns of these assets are not necessarily independent. Copulas make it possible to model marginal distributions and the dependence structure separately. With short time horizons (3 months or less), correlation estimates are typically very stable.

Correct Answer: d Rationale: Correlation estimates tend to be very volatile when short term time horizons are considered. Section: Market Risk Measurement and Management Reference: Kevin Dowd (2005), Measuring Market Risk, 2nd Edition, Chapter 5, Appendix: “Modeling Dependence: Correlations and Copulas.” Learning Objective: Explain the drawbacks of using correlation to measure dependence. Describe how copulas provide an alternative measure of dependence. Reference: Gunter Meissner, Correlation Risk Modeling and Management, Chapter 1, “Some Correlation Basics: Properties, Motivation, Terminology.” Learning Objective: Describe financial correlation risk and the areas in which it appears in finance.


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A risk manager is in the process of valuing several European option positions on a non-dividend-paying stock XYZ that is currently priced at GBP 30. The implied volatility skew, estimated using the Black-Scholes-Merton model and the current prices of actively traded European-style options on stock XYZ at various strike prices, is shown below:

Implied Volatility

15.

Strike Price (GBP)

Assuming that the implied volatility at GBP 30 is used to conduct the valuation, which of the following long positions will be undervalued? a. b. c. d.

An An An An

out-of-the-money call in-the-money call at-the-money put in-the-money put

Correct Answer: b Rationale: An in-the-money call has a strike price below 30. Therefore, using the chart above, its implied volatility is greater than the at-the-money volatility, so using the at-the-money implied volatility would result in pricing an in-the-money call option lower than its fair price. Section: Market Risk Measurement and Management Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition, Chapter 20, “Volatility Smiles.” Learning Objective: Compare the shape of the volatility smile (or skew) to the shape of the implied distribution of the underlying asset price and to the pricing of options on the underlying asset.

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16.

A risk manager is pricing a 10-year call option on 10-year Treasuries using a successfully tested pricing model. Current interest rate volatility is high and the risk manager is concerned about the effect this may have on short-term rates when pricing the option. Which of the following actions would best address the potential for negative short-term interest rates to arise in the model? a. b. c. d.

The risk manager uses a normal distribution of interest rates. When short-term rates are negative, the risk manager adjusts the risk-neutral probabilities. When short-term rates are negative, the risk manager increases the volatility. When short-term rates are negative, the risk manager sets the rate to zero.

Correct Answer: d Rationale: Negative short-term interest rates can arise in models for which the terminal distribution of interest rates follows a normal distribution. The existence of negative interest rates does not make much economic sense since market participants would generally not lend cash at negative interest rates when they can hold cash and earn a zero return. One method that can be used to address the potential for negative interest rates when constructing interest rate trees is to set all negative interest rates to zero. This localizes the change in assumptions to points in the distribution corresponding to negative interest rates and preserves the original rate tree for all other observations. In comparison, adjusting the risk neutral probabilities would alter the dynamics across the entire range of interest rates and therefore not be an optimal approach. When a model displays the potential for negative short-term interest rates, it can still be a desirable model to use in certain situations, especially in cases where the valuation depends more on the average path of the interest rate, such as in valuing coupon bonds. Therefore, the potential for negative rates does not automatically rule out the use of the model. Section: Market Risk Measurement and Management Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition, Chapter 9, “The Art of Term Structure Models: Drift.” Learning Objective: Describe methods for addressing the possibility of negative short-term rates in term structure models.


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17.

A large commercial bank is using VaR as its main risk measurement tool. Expected shortfall (ES) is suggested as a better alternative to use during market turmoil. What should be understood regarding VaR and ES before modifying current practices? a. b. c. d.

Despite being more complicated to calculate, ES is easier to backtest than VaR. Relative to VaR, ES leads to more required economic capital for the same confidence level. While VaR ensures that the estimate of portfolio risk is less than or equal to the sum of the risks of that portfolio’s positions, ES does not. Both VaR and ES account for the severity of losses beyond the confidence threshold.

Correct Answer: b Rationale: Expected shortfall is always greater than or equal to VaR for a given confidence level, since ES accounts for the severity of expected losses beyond a particular confidence level, while VaR measures the minimum expected loss at that confidence level. Therefore, ES would lead to a higher level of required economic capital than VaR for the same confidence level. In practice, however, regulators often correct for the difference between ES and VaR by lowering the required confidence level for banks using ES compared to those using VaR. Section: Market Risk Measurement and Management Reference: Basel Committee on Banking Supervision, Messages from the Academic Literature on Risk Measurement for the Trading Book, Working Paper No. 19, January 2011. Learning Objective: Compare VaR, expected shortfall, and other relevant risk measures.

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18.

A risk management consultant is involved in evaluating the capital planning at a US-based bank holding company (BHC) with over USD 100 billion in total consolidated assets. The evaluation includes looking at the stress testing program that is integral to the capital planning process. In evaluating the BHC's design of stress scenarios, which of the following statements is correct? a. b. c. d.

Although the BHC may feel it is losing some of its independence, limiting the scenarios to those developed by the Federal Reserve will ensure regulatory compliance. To avoid introducing bias, if the BHC uses private sector third-party-defined scenarios, they should be implemented without alteration. In order to properly assess both right-way and wrong-way risk in stress environments, assumptions should be included that specifically benefit the BHC. When developing scenarios internally, it is acceptable to combine expert judgment with quantitative models rather than relying only on the models.

Correct Answer: d Rationale: According to the Board of Governors of the Federal Reserve, bank holding companies with superior scenario-design practices generally use a combination of internal models and expert judgment rather than relying solely on either practice by itself. This allows the BHC to tailor scenarios or quantitative models to its own unique risk profile and vulnerabilities. Therefore, combining expert judgment with quantitative models is clearly acceptable. Section: Current Issues (Operational and Integrated Risk Management for 2015) Reading: “Capital Planning at Large Bank Holding Companies: Supervisory Expectations and Range of Current Practice,” Board of Governors of the Federal Reserve System, August 2013. Learning Objective: Describe practices which can result in a strong and effective capital adequacy process for a BHC in the following areas: Stress testing and stress scenario design.


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Question 19 refers to the following information: A profitable derivatives trading desk at a bank decides that its existing VaR model, which has been used broadly across the firm for several years, is too conservative. The existing VaR model uses a historical simulation over a three-year look-back period, weighting each day equally. A quantitative analyst in the group quickly develops a new VaR model, which uses the delta normal approach. The new model uses volatilities and correlations estimated over the past four years using the Riskmetrics EWMA method. For testing purposes, the new model is used in parallel with the existing model for four weeks to estimate the 1-day 95% VaR. After four weeks, the new VaR model has no exceedances despite consistently estimating VaR to be considerably lower than the existing model's estimates. The analyst argues that the lack of exceedances shows that the new model is unbiased and pressures the bank’s model evaluation team to agree. Following an overnight examination of the new model by one junior analyst instead of the customary evaluation that takes several weeks and involves a senior member of the team, the model evaluation team agrees to accept the new model for use by the desk.

19.

Which of the following statements about the risk management implications of this replacement is correct? a. b. c. d.

Delta-normal VaR is more appropriate than historical simulation VaR for assets with non-linear payoffs. Changing the look-back period and weighing scheme from three years, equally weighted, to four years, exponentially weighted, will understate the risk in the portfolio. The desk increased its exposure to model risk due to the potential for incorrect calibration and programming errors related to the new model. A 95% VaR model that generates no exceedances in four weeks is necessarily conservative.

Correct Answer: c Rationale: Given the quick implementation of the new VaR model and the insufficient amount of testing that was done, the desk has increased its exposure to model risk due to the increased potential for incorrect calibration and programming errors. This situation is similar to the JP Morgan London Whale case in 2012, where a new VaR model was very quickly introduced for its Synthetic Credit portfolio without appropriate time to test the model in response to increasing losses and multiple exceedances of the earlier VaR model limit in the portfolio. Section: Operational and Integrated Risk Management Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition, Chapter 16, “Model Risk.” Learning Objective: Define model risk; identify and describe sources of model risk. Reference: Allan Malz, Financial Risk Management: Models, History, and Institutions, Chapter 11, "Assessing the Quality of Risk Measures," section 11.1. Learning Objective: Describe ways that errors can be introduced into models.

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Section: Current Issues Reference: “JP Morgan Chase Whale Trades: A Case History of Derivatives Risks and Abuses—Executive Summary,” US Senate Subcommittee on Investigation, April 2013. Learning Objective: Summarize the deficiencies in risk management practices related to the SCP, including the VAR model change. Section: Market Risk Measurement and Management Reference: Kevin Dowd, Measuring Market Risk, 2nd Edition, Chapter 3, “Estimating Market Risk Measures.” Learning Objective: Calculate VaR using a parametric estimation approach assuming that the return distribution is either normal or lognormal.


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20.

The CFO at a bank is preparing a report to the board of directors on its compliance with Basel requirements. The bank's average capital and total exposure for the most recent quarter is as follows: REGULATORY CAPITAL Total Common Equity Tier 1 Capital Additional Tier 1 Capital Prior to regulatory adjustments Regulatory adjustments

USD MILLIONS 108 28 34 6

Total Tier 1 Capital Tier 2 Capital Prior to regulatory adjustments Regulatory adjustments

136 36 45 9

Total Capital Total Average Exposure

172 3678

Using the Basel III framework, which of the following is the best estimate of the bank’s current leverage ratio? a. b. c. d.

2.94% 3.70% 4.68% 5.08%

Correct Answer: b Rationale: For Basel III purposes, the leverage ratio is Tier 1 Capital / Total Exposure = 136 / 3,678= 3.70%. Section: Operational and Integrated Risk Management Reference: “Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems—Revised Version,” Basel Committee on Banking Supervision Publication, June 2011. Learning Objective: Describe changes to the regulatory capital framework, including changes to: Risk coverage, the use of stress tests, the treatment of counter-party risk with credit valuation adjustments, the use of external ratings, and the use of leverage ratios. Reference: John Hull, Risk Management and Financial Institutions, 3rd Edition, Chapter 13, “Basel 2.5, Basel III, and Dodd-Frank.” Learning Objective: Describe and calculate ratios intended to improve the management of liquidity risk, including the required leverage ratio, the liquidity coverage ratio, and the net stable funding ratio.

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