Financial Risk Management “Whether we like it or not, mankind now has a completely integrated, international financial and informational marketplace capable of moving money and ideas to any place on this planet in minutes.” “Believe me the secret of reaping the greatest fruitfulness and the greatest enjoyment from life is to live dangerously” Friedrich Wilhelm Nietzsche Financial Engineering Computational finance, also called financial engineering, is a cross-disciplinary field which relies on computational intelligence, mathematical finance, numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of those decisions. Utilizing various methods, practitioners of computational finance aim to precisely determine the financial risk that certain financial instruments create.
“To be alive at all involve some Risk” (Harold Macmillan)
Khurasan Institute of Higher Education Jalalabad, Afghanistan.
By Imran Khan
MBA (Finance), CIA, CQC
Financial Risk Management
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What Is Risk?
Risk is the chance of financial loss, or more formally the variability of returns associated with a given
asset. Risk provides the basis for opportunity. The terms risk and exposure have slight differences in
their meaning. Risk refers to the probability of loss, while exposure (experience, contact) is the possibility of loss, although they are often used interchangeably. Risk arises as a result of exposure. Exposure to financial markets affects most organizations, either directly or indirectly. When an organization has financial market exposure, there is a possibility of loss but also an opportunity for gain or profit. Financial market exposure may provide strategic or competitive benefits. Risk is the likelihood of losses resulting from events such as changes in market prices. Events with a low probability of occurring, but that may result in a high loss, are particularly troublesome because they are often not anticipated. Put another way, risk is the probable variability of returns. Potential Size of Loss Potential for Large Loss Potential for Small Loss
Probability of Loss High Probability of Occurrence Low Probability of Occurrence
Since it is not always possible or desirable to eliminate risk, understanding it is an important step in determining how to manage it. Identifying exposures and risks forms the basis for an appropriate financial risk management strategy. Investment A commitment of funds made in the expectation of the positive rate of returns. Returns: investment is made with the aim of returns. Returns= yield +capital appreciations. Risk Its inherent May be capital loss Or not receiving the interest payments or dividends. Longer maturity higher risk Credit worthiness of the firm Risk varies with nature of investment.
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Return time.
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Return can be defined as the total gain or loss experienced on an investment over a given period of
Financial Risk Management
Risk in Investment Investors like return and dislike risk than the returns that were expected. Risk is the variability of the in returns of a security
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Risk in holding securities is generally associated with the possibility that realized returns will be less
How Does Financial Risk Arise? Financial risk arises through countless transactions of a financial nature, including sales and purchases, investments and loans, and various other business activities. It can arise as a result of legal transactions, new projects, mergers and acquisitions, debt financing, the energy component of costs, or through the activities of management, stakeholders, competitors, foreign governments, or weather. When financial prices change dramatically, it can increase costs, reduce revenues, or otherwise adversely impact the profitability of an organization. Financial fluctuations may make it more difficult to plan and budget, price goods and services, and allocate capital. There are three main sources of financial risk: 1. Financial risks arising from an organization’s exposure to changes in market prices, such as interest rates, exchange rates, and commodity prices. 2. Financial risks arising from the actions of, and transactions with, other organizations such as vendors, customers, and counterparties in derivatives transactions 3. Financial risks resulting from internal actions or failures of the organization, particularly people, processes, and systems. These are discussed in more detail in subsequent chapters. What Is Financial Risk Management? Financial risk management is a process to deal with the uncertainties resulting from financial markets. It involves assessing the financial risks facing an organization and developing management strategies consistent with internal priorities and policies. Addressing financial risks proactively may provide an organization with a competitive advantage. It also ensures that management, operational staff, stakeholders, and the board of directors are in agreement on key issues of risk. Managing financial risk necessitates making organizational decisions about risks that are acceptable versus those that are not. The passive strategy of taking no action is the acceptance of all risks by default. 4|Page
Financial Risk Management
Organizations manage financial risk using a variety of strategies and products. It is important to understand how these products and strategies work to reduce risk within the context of the 201213
organization’s risk tolerance (acceptance) and objectives.
Strategies for risk management often involve derivatives. Derivatives are traded widely among financial institutions and on organized exchanges. The value of derivatives contracts, such as futures, forwards,
options, and swaps, is derived from the price of the underlying asset. Derivatives trade on interest rates, exchange rates, commodities, equity and fixed income securities, credit, and even weather. The products and strategies used by market participants to manage financial risk are the same ones used by speculators to increase leverage and risk. Although it can be argued that widespread use of derivatives increases risk, the existence of derivatives enables those who wish to reduce risk to pass it along to those who seek risk and its associated opportunities. The ability to estimate the possibility of a financial loss is highly desirable. However, standard theories of probability often fail in the analysis of financial markets. Risks usually do not exist in isolation, and the interactions of several exposures may have to be considered in developing an understanding of how financial risk arises. Sometimes, these interactions are difficult to forecast, since they ultimately depend on human behavior. The process of financial risk management is an ongoing one. Strategies need to be implemented and refined as the market and requirements change. Refinements may reflect changing expectations about market rates, changes to the business environment, or changing international political conditions, for example. In general, the process can be summarized as follows: •
Identify and prioritize key financial risks.
•
Determine an appropriate level of risk tolerance.
•
Implement risk management strategy in accordance with policy.
•
Measure, report, monitor, and refine as needed.
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Financial Risk Management
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Risk Classification TYPES OF RISK: Thus far, our discussion has concerned the total risk of an asset, which is one important consideration in investment analysis. However, modern investment analysis categorizes the traditional sources of risk identified previously as .causing variability in returns into two
General types: those that are pervasive in nature, such as market risk or interest rate risk, and those that are specific to a particular security issue, such as business or financial risk. Therefore, we must consider these two categories of total risk. Dividing total risk into its two components, a general (market) component and a specific (issuer) component, we have systematic risk and nonsystematic risk, which are additive: Total risk = General risk + Specific risk = Market risk + Issuer risk = Systematic risk + Nonsystematic risk
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Financial Risk Management
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Risk Classification Total Risk
Systematic Risk
Market Risk
Interest Rate Risk
Unsystematic Risk
Purchasing Power Risk
Business Risk
Financial Risk
A. Systematic Risk Systematic (Market) Risk, (Non-diversifiable Risk): Risk attributable to broad macro factors affecting all securities. Acting according to a fixed plan or system Systematic risk is caused by system wide factors that affect the entire community. •
Change in economic conditions
•
Change in political system
•
Change in social system
The effect of such system wide factors which are beyond the control of individual, business establishments and which affect all the business establishments in the system called “Systematic Risk”.
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Financial Risk Management
Systematic Risk is an investor can construct a diversified portfolio and eliminate pan of the total risk, the diversifiable or non-market part. What is left is the non-diversifiable portion or the movements in the general market or economy is called systematic (market) risk.
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market risk. Variability in a security's total returns that is directly associated with overall
Virtually all securities have some systematic risk, whether bonds or stocks, because systematic risk directly encompasses the interest rate, market, and inflation risks. The investor cannot escape this part of the risk, because no matter how well he or she diversifies, the risk of the overall market cannot be avoided. If the stock market declines sharply, most stocks will be adversely affected; if it rises strongly, as in the last few months of 1982, most stocks will appreciate in value. These movements occur regardless of what any single investor does. Clearly, market risk is critical to all investors. 1. Market Risk This arises out of changes in demand and supply pressures in the markets, following the changing flow of information or expectations. The totality of investor perception and subjective factors influence the events in the market which are unpredictable and give rise to risk, which is not controllable. The basis for the reaction is a set of real, tangible events –political, social or economic Intangible events are related to market psychology 2. Interest Rate Risk The return on an investment depends on the interest rate promised on it and changes in market rates of interest from time to time. The cost of funds borrowed by companies or stockbrokers depends on interest rates. The market activity and investor perception change with the changes in interest rates. Lower interest rates make it easier for people to borrow in order to buy cars and homes. Purchases of homes, in turn, increase the demand for other items, such as furniture and appliances, thus providing an additional boost to the economy. Lower interest rates mean that consumers spend less on interest costs, leaving them with more of their income to spend on goods and services.
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Financial Risk Management
3. Purchasing Power Risk It is also known as inflation risk inflation and deflation periods Inflation: Rising prices on goods and services
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This risk is arises out of change in the prices of goods and services and technically it covers both
Deflation: Falling prices on goods and services Purchasing power risk= Inflation + Deflation B. Unsystematic Risk
Nonsystematic (Non-market) Risk, (Diversifiable Risk): Risk attributable to factors unique to the security Nonsystematic Risk is the variability in a security's total returns not related to overall market variability is called the nonsystematic (non-market) risk. This risk 1s unique to a particular security and is associated with such factors as business and financial risk as well as liquidity risk. Although all securities tend to have some nonsystematic risk, it is generally connected with common stocks. Unsystematic risk emerges out of the known and controllable factors, internal to issuer of the securities or companies. Factors such as management capability, consumer preferences and labor strikes can cause unsystematic variability of returns for a company’s stock. The uncertainty surrounding the ability of the issuer to make payments on securities stops from two sources: 1. The operating environment of the business- Business Risk 2. The financing of the firm- Financial risk 1
Business Risk This relates to the variability of the business, sales, income, profits etc. which in turn depend on the market conditions for the product mix, input supplies, strength of competitors, etc. This Business risk is sometimes external to the company due to changes in govt. policy or strategies of competitors or unforeseen market conditions They may be internal due to fall in production, labor problems, raw material problems or inadequate 9|Page
Financial Risk Management
supply of electricity etc. The internal business risk leads to fall in revenues and in profit of the company, but can be corrected
2. Financial Risk
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by certain changes in the company’s policies.
This relates to the method of financing, adopted by the company, high leverage leading to larger debt servicing problems or short-term liquidity problems due to bad debts, delayed receivables and fall in current assets or rise in current liabilities. These problems could no doubt be solved, but they may lead to fluctuations in earnings, profits and dividends to shareholders. Sometimes, if the company runs into losses or reduced profits, these may lead to fall in returns to investors or negative returns. Proper financial planning and other financial adjustments can be used to correct this risk and as such it is controllable. Risk management: Nature & Importance Risk Management – The entire process of identifying, evaluating, controlling and reviewing risks, to make sure that the organization is exposed to only those risks that it needs to take to achieve its primary objectives. Risk management is Proactive (practical) process, As different markets, different types of risks so, the risk management procedures and techniques vary in their application ways but target is same; putting the risks under control and accomplishing the mission as expected.
Ways to Conduct Risk Management There can be three approaches or sets of actions and within them the various instruments that are available to firms for risk management. •
Eliminate/Avoid
A firm can decide to eliminate certain risks that are not consistent with its desired financial characteristics or not essential to a financial asset created. Moreover, the firm like a bank can use portfolio diversification in order to eliminate specific risk. Additionally, it can decide to buy insurance, for event risks. Furthermore, the firm can choose to avoid certain risk types up front by setting certain business practices/policies (e.g., underwriting standards, 10 | P a g e
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process control) to reduce the chances of certain losses and/or to eliminate certain risks ex ante. If the firm has no comparative advantage in managing a specific kind of risk, there is no reason to absorb •
Absorb/Manage
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and/or manage such a risk.
Some risks must or should be absorbed and managed at the firm level, because they have one or more of the following characteristics: •
They cannot be traded or hedged easily
•
They have a complex, illiquid, or proprietary structure that is difficult, expensive, or impossible to reveal to others
•
They are a business necessity. Some risks play a central role in the bank’s business purpose and should therefore not be eliminated or transferred
•
Transfer
The transfer of risks to other market participants is decided on the basis of whether or not the firm has a competitive advantage in a specific (risk) segment. Any element of the systematic risk that is not required or desired can be either shed; •
by selling it in the spot market or
•
hedged by using derivative instruments such as futures, forwards, or swaps
In all such circumstances, the bank needs to actively manage these risks by using one of the following instruments: •
Diversification: The bank is supposed to have superior skills (competitive advantages), because it can provide diversification more efficiently/at a lower cost than individual investors could do on their own. This might be the case in illiquid areas where shareholders cannot hedge on their own. Management of their credit portfolio is necessary, because the performance of a credit portfolio is determined not only by exogenous factors but also by endogenous factors such as superior ex ante screening capabilities and ex post monitoring skills. Diversification, typically, reduces the frequency of both worst-case and best-case outcomes, which generally reduces the bank’s probability of failure.
Holding capital: For all other risks that cannot be diversified away or insured internally and which the bank decides to absorb, it has to make sure that it holds a sufficient amount of capital in order to ensure that its probability of default is kept at a sufficiently low level. 11 | P a g e
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Note that equity finance is costly
•
The cost of economic capital and the decision of not eliminating risk provide a trade-off
•
Both risk and return need to be monitored
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•
In dealing with the challenge of risk management, the following interrelated guidelines should be considered; Understanding the firm’s strategic exposure Employing a mix of real and financial tools Proactively managing uncertainty Aligning risk management with corporate strategy Learning when it is worth reducing risk
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Financial Risk Management
Risk Management Process The process of financial risk management comprises strategies that enable an organization to 201213
manage the risks associated with financial markets. Risk management is a dynamic process that
should evolve with an organization and its business. It involves and impacts many parts of an organization including treasury, sales, marketing, legal, tax, commodity, and corporate finance. The risk management process involves both internal and external analysis. The first part of the process involves identifying and prioritizing the financial risks facing an organization and understanding their relevance. It may be necessary to examine the organization and its products, management, customers, suppliers, competitors, pricing, industry trends, balance sheet structure, and position in the industry. It is also necessary to consider stakeholders and their objectives and tolerance for risk. Once a clear understanding of the risks emerges, appropriate strategies can be implemented in conjunction with risk management policy. For example, it might be possible to change where and how business is done, thereby reducing the organization’s exposure and risk. Alternatively, existing exposures may be managed with derivatives. Another strategy for managing risk is to accept all risks and the possibility of losses. There are three broad alternatives for managing risk: •
Do nothing and actively, or passively by default, accept all risks.
•
Hedge a portion of exposures by determining which exposures can and should be hedged.
•
Hedge all exposures possible. Measurement and reporting of risks provides decision makers with information to execute decisions and monitor outcomes, both before and after strategies are taken to mitigate them. Since the risk management process is ongoing, reporting and feedback can be used to refine the system by modifying or improving strategies. An active decision-making process is an important component of risk management. Decisions about potential loss and risk reduction provide a forum for discussion of important issues and the varying perspectives of stakeholders.
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Financial Risk Management
Factors that Impact Financial Rates and Prices that impact markets because those factors, in turn, impact the potential risk of an organization. A
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Financial rates and prices are affected by a number of factors. It is essential to understand the factors
Factors that Affect Interest Rates
Interest rates are a key component in many market prices and an important economic barometer. They are comprised of the real rate plus a component for expected inflation, since inflation reduces the purchasing power of a lender’s assets. The greater the term to maturity, the greater the uncertainty. Interest rates are also reflective of supply and demand for funds and credit risk. Interest rates are particularly important to companies and governments because they are the key ingredient in the cost of capital. Most companies and governments require debt financing for expansion and capital projects. When interest rates increase, the impact can be significant on borrowers. Interest rates also affect prices in other financial markets, so their impact is farreaching. Other components to the interest rate may include a risk premium to reflect the creditworthiness of a borrower. For example, the threat of political or sovereign risk can cause interest rates to rise, sometimes substantially, as investors demand additional compensation for the increased risk of default. Factors that influence the level of market interest rates include: •
Expected levels of inflation
•
General economic conditions
•
Monetary policy and the stance of the central bank
•
Foreign investor demand for debt securities
•
Levels of sovereign debt outstanding
•
Financial and political stability
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Factors that Affect Foreign Exchange Rates
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B
Foreign exchange rates are determined by supply and demand for currencies. Supply and demand, in turn, are influenced by factors in the economy, foreign trade, and the activities of international
investors. Capital flows, given their size and mobility, are of great importance in determining exchange rates. Factors that influence the level of interest rates also influence exchange rates among floating or market-determined currencies. Currencies are very sensitive to changes or anticipated changes in interest rates and to sovereign risk factors. Some of the key drivers that affect exchange rates include: • Interest rate differentials net of expected inflation • Trading activity in other currencies • International capital and trade flows • International institutional investor sentiment • Financial and political stability • Monetary policy and the central bank • Domestic debt levels (e.g., debt-to-GDP ratio) • Economic fundamentals
C
Factors that Affect Commodity Prices
Physical commodity prices are influenced by supply and demand. Unlike financial assets, the value of commodities is also affected by attributes such as physical quality and location. Commodity supply is a function of production. Supply may be reduced if problems with production or delivery occur, such as crop failures or labor disputes. In some commodities, seasonal variations of supply and demand are usual and shortages are not uncommon. 15 | P a g e
Financial Risk Management
Demand for commodities may be affected if final consumers are able to obtain substitutes at a lower cost. There may also be major shifts in consumer taste over the long term if there are supply or Commodity traders are sensitive to the inclination of certain commodity prices to vary according to the stage of the economic cycle. For example, base metals prices may rise late in the economic
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cost issues.
cycle as a result of increased economic demand and expansion. Prices of these commodities are monitored as a form of leading indicator. Commodity prices may be affected by a number of factors, including: • Expected levels of inflation, particularly for precious metals • Interest rates • Exchange rates, depending on how prices are determined • General economic conditions • Costs of production and ability to deliver to buyers • Availability of substitutes and shifts in taste and consumption patterns • Weather, particularly for agricultural commodities and energy • Political stability, particularly for energy and precious metals
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Calculation of Return
We are going to assess risk on the basis of variability of return, we need to be certain we know what return is and how to measure it. The return is the total gain or loss experienced on an investment over a given period of time. It is commonly measure as cash distributions during the period plus the change in value expressed as a percentage of the beginning of period investment value. The expression for calculating the rate of return earned on any asset over period, commonly defined as:
i
=
C + PC - PB PB
where: i
=
rate of return
C
=
cash flow received from the investment
PB
=
price (value) of asset at beginning
PC
=
price (value) of asset after changes
Example: Mr. Moody wishes to determine the return of two video machines, C and D. C was purchased 1 year ago for $ 20,000 and currently has a market value of $ 21,500. During the year it generated $ 800 of after tax cash receipts. D was purchased 4 years ago, its value in the year just completed declined from m$ 12,000 to $ 11,800. During the year it generated $ 1,700 of after tax cash receipts. We can calculate the annual rate of return i for each video machine. For video machine C i
=
C + PC - PB
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PB i
=
800 + 21,500 - 20,000
i
=
2,300
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20,000
20,000 i
=
11.5%
For video machine D i
=
C + PC - PB PB
i
=
1,700 + 11,800 - 12,000 12,000
i
=
1,500 12,000
i
=
12.5%
Although the market value of D declined during the year, its cash flow caused it to earn higher rate of return than C earned during the same period. Clearly the combined impact of cash flow changes in value as measured by the rate of return is important.
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Financial Risk Management
Risk Preferences Feelings about risk differ among managers and firms. Thus it is important to specify a generally risk seeking are explained below: A
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acceptable level of risk. The three basic risk preference behaviors risk averse, risk indifferent and
Risk Indifferent
Risk Indifferent is the attitude toward risk in which no change in return would be required for an increase risk. For the risk indifferent manager the required return does not change as risk goes from x1 to x2. In essence no change in return would be required for the increase in risk. B
Risk Averse
It is the attitude toward risk in which increased return would be required for an increase in risk. For the risk averse manager the required return increases for an increase in risk. Because they shy away from risk, these managers require expected returns to compensate them for taking greater risk. C
Risk Seeking
Risk seeking is the attitude toward risk in which a decreased return would be accepted for an increase in risk. For the risk seeking manager, the required return decreases for an increase in risk. Theoretically because they enjoy risk these managers are willing to give up some return to take more risk. However such behavior would not be likely to benefit the firm. Most managers are risk averse; for a given increase in risk they require an increase in return. They generally tend to be conservative rather than aggressive hen accepting risk for their firm. Accordingly a risk averse financial manager requiring higher returns for greater risk is assumed throughout this text.
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Financial Risk Management
Risk of a single asset The concept of risk can be developed by first considering a single asset held in isolation. We can
Risk Assessment
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look at expected return behaviors to assess risk, and statistics can be used to measure it.
Sensitivity analysis and probability distributions can be used to assess the general level of risk embodied in a given asset. Sensitivity analysis An approach for assessing risk that uses several possible return estimates to obtain a sense of the variability among outcomes. Sensitivity analysis uses several possible return estimates to obtain a sense of the variability among outcomes. One common method involve s making pessimistic worst, most likely expected and optimistic best estimates of the returns associated with a given asset. In this case the assets risk can be measured by the range of returns. The range is found by subtracting the pessimistic outcome from the optimistic outcome. The greater the range the more variability or risk the asset is said to have. Example Norman company a golf equipment manufacturer, wants to choose the better two investments, A and B. each requires an initial outlay of Rs. 10,000 and each has a most likely annual rate of return of 15%. Management has made pessimistic an optimistic estimates of the returns associated with each. The three estimates for each asset along with its range are given below: Assets A and B
Initial Investment
Asset A
Asset B
Rs 100,000
Rs 100,000
Annual rate of return Pessimistic
13%
7%
Most likely
15%
15%
Optimistic
17%
23%
Range
4%
16%
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Asset A appears to be less risky than asset B, its range of 4 percent (17% - 13%) is less than the B, because A offers the same most likely return as B 15% with lower risk smaller range.
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range of 16% (23% - 7%) for asset B. the risk averse decision maker would prefer asset A over asset
Although the use of sensitivity analysis and the range is rather crude, it does give the decision maker a feel for the behavior of returns, which can be used to estimate the risk involved. Probability Distributions Probability means the chance that a given outcome will occur. Probability distributions provide a more quantitative insight into an assets risk. The probability of a given outcome is its chance of occurring. An outcome with an 80% probability of occurrence would be expected to occur 8 out of 10 times. An outcome with a probability of 100 percent is certain to occur. Outcomes with a probability of zero will never occur. A probability distribution is a model that relates probabilities to the associated outcomes. The simplest type of probability distribution is the bar chart, which shows only a limited number of outcome probability coordinates. The bar charts for Norman company’s assets A and B are show in the following figure. Although both assets have the same most likely return, the range of return is much greater or more dispersed for asset B than for asset A- 16 percent versus 4 percent. Bar charts for asset A’s and B’s returns Continuous probability distribution A probability distribution showing all the possible outcomes and associated probabilities for a given event. If we knew all the possible outcomes and associated probabilities, we could develop a continuous probability distribution. This type of distribution can be thought of as a bar chart for a very large number of outcomes. Following figure represents continuous probability distributions for assets A and B. note that although assets A and B have the same most likely return 15%, the distribution of returns for asset B has much greater dispersion than the distribution for asset A. clearly asset B is more risky than asset A. Risk of a Portfolio
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Financial Risk Management
In real world situations, the risk of any single investment would not be viewed independently of other assets. We did so for teaching purposes. New investments must be considered in light of their efficient portfolio, one that maximizes return for a given level of risk or minimizes risk for a given level of return. We therefore need a way to measure the return and the standard deviation of a
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impact on the risk and return of the portfolio of assets. The financial manager’s goal is to create an
portfolio of assets. Once we can do that we will look at the statistical concept of correlation, which underlies the process of diversification that is used to develop an efficient portfolio. Efficient portfolio A portfolio that maximizes return for a given level of risk or minimizes risk for a given level of return. Correlation A statistical measure of the relationship between any two series of numbers representing data of any kind. The numbers may represent data of any kind from returns to test scores. Positively correlated If two series move in the same direction they are positively correlated. Or describes two series that move in the same direction. Negatively correlated If the series move in opposite directions they are negatively correlated. Or describes two series that move in opposite directions. Hedging and Correlation Hedging is the business of seeking assets or events that offset, or have weak or negative correlation to, an organization’s financial exposures. Correlation measures the tendency of two assets to move, or not move, together. This tendency is quantified by a coefficient between -1 and +1. Correlation of +1.0 signifies perfect positive correlation and means that two assets can be expected to move together. Correlation of -1.0 signifies perfect negative correlation, which means that two assets can be expected to move together but in opposite directions. 22 | P a g e
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The concept of negative correlation is central to hedging and risk management. Risk management involves pairing a financial exposure with an instrument or strategy that is negatively correlated to 201213
the exposure.
A long futures contract used to hedge a short underlying exposure employs the concept of negative correlation. If the price of the underlying (short) exposure begins to rise, the value of the (long) futures contract will also increase, offsetting some or all of the losses that occur. The extent of
the protection offered by the hedge depends on the degree of negative correlation between the two.
Derivatives Definition of Derivatives
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One of the most significant events in the securities markets has been the development and expansion of financial derivatives. The term “derivatives” is used to refer to financial be equities (shares), debt (bonds, T-bills, and notes), currencies, and even indices of these various assets, such as the Nifty 50 Index. Derivatives derive their names from their respective
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instruments which derive their value from some underlying assets. The underlying assets could
underlying asset. Thus if a derivative’s underlying asset is equity, it is called equity derivative and so on. Derivatives can be traded either on a regulated exchange, such as the NSE or off the exchanges, i.e., directly between the different parties, which is called “over-the-counter” (OTC) trading. The basic purpose of derivatives is to transfer the price risk (inherent in fluctuations of the asset prices) from one party to another; they facilitate the allocation of risk to those who are willing to take it. In so doing, derivatives help mitigate the risk arising from the future uncertainty of prices. For example, on November 1, 2009 a rice farmer may wish to sell his harvest at a future date (say January 1, 2010) for a pre-determined fixed price to eliminate the risk of change in prices by that date. Such a transaction is an example of a derivatives contract. The price of this derivative is driven by the spot price of rice which is the "underlying". Origin of derivatives While trading in derivatives products has grown tremendously in recent times, the earliest evidence of these types of instruments can be traced back to ancient Greece. Even though derivatives have been in existence in some form or the other since ancient times, the advent of modern day derivatives contracts is attributed to farmers’ need to protect themselves against a decline in crop prices due to various economic and environmental factors. Thus, derivatives contracts initially developed in commodities. The first “futures” contracts can be traced to the Yodoya rice market in Osaka, Japan around 1650. The farmers were afraid of rice prices falling in the future at the time of harvesting. To lock in a price (that is, to sell the rice at a predetermined fixed price in the future), the farmers entered into contracts with the buyers. These were evidently standardized contracts, much like today’s futures contracts. In 1848, the Chicago Board of Trade (CBOT) was established to facilitate trading of forward contracts on various commodities. From then on, futures contracts on commodities have remained more or less in the same form, as we know them today. While the basics of derivatives are the same for all assets
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Financial Risk Management
such as equities, bonds, currencies, and commodities, we will focus on derivatives in the equity markets and all examples that we discuss will use stocks and index (basket of stocks).
Before discussing derivatives, it would be useful to be familiar with two terminologies relating to
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Two important terms
the underlying markets. These are as follows: Spot Market In the context of securities, the spot market or cash market is a securities market in which securities are sold for cash and delivered immediately. The delivery happens after the settlement period. Let us describe this in the context of India. The NSE’s cash market segment is known as the Capital Market (CM) Segment. Index Stock prices fluctuate continuously during any given period. Prices of some stocks might move up while that of others may move down. In such a situation, what can we say about the stock market as a whole? Has the market moved up or has it moved down during a given period? Similarly, have stocks of a particular sector moved up or down? To identify the general trend in the market (or any given sector of the market such as banking), it is important to have a reference barometer which can be monitored. Market participants use various indices for this purpose. An index is a basket of identified stocks, and its value is computed by taking the weighted average of the prices of the constituent stocks of the index. A market index for example consists of a group of top stocks traded in the market and its value changes as the prices of its constituent stocks change. Definitions of Basic Derivatives There are various types of derivatives traded on exchanges across the world. They range from the very simple to the most complex products. The following are the three basic forms of derivatives, which are the building blocks for many complex derivatives instruments (the latter are beyond the scope of this book): Forwards 25 | P a g e
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Futures Options 201213
Swaps Knowledge of these instruments is necessary in order to understand the basics of derivatives. We shall now discuss each of them in detail. A
Forwards
A forward contract or simply a forward is a contract between two parties to buy or sell an asset at a certain future date for a certain price that is pre-decided on the date of the contract. The future date is referred to as expiry date and the pre-decided price is referred to as Forward Price. It may be noted that Forwards are private contracts and their terms are determined by the parties involved. A forward contract is a particularly simple derivative. It is an agreement to buy or sell an asset at a certain future time at a certain price. It can be contrasted with a spot contract, which is an agreement to buy or sell an asset today. A forward contract is traded in the over-the-counter market, usually between two financial institutions or between a financial institution and one of its clients. One of the parties to a forward contract assumes a long position and agrees to buy the underlying asset on a certain specified future date for a certain specified price. The other party assumes a short position and agrees to sell the underlying asset on the same for the same price. The price in a forward contract is known as the delivery price. Forward contracts are commonly used to hedge foreign currency risk.
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A forward is thus an agreement between two parties in which one party, the buyer, enters into an agreement with the other party, the seller that he would buy from the seller an underlying asset engage in a transaction at a later date with the price set in advance. This is different from a spot
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on the expiry date at the forward price. Therefore, it is a commitment by both the parties to
market contract, which involves immediate payment and immediate transfer of asset. The party that agrees to buy the asset on a future date is referred to as a long investor and is said to have a long position. Similarly the party that agrees to sell the asset in a future date is referred to as a short investor and is said to have a short position. The price agreed upon is called the delivery price or the Forward Price. Forward contracts are traded only in Over the Counter (OTC) market and not in stock exchanges. OTC market is a private market where individuals/institutions can trade through negotiations on a one to one basis.
Example 1:
(Hedging Currency Risk with a Forward Contract)
Suppose it is April 5 of a certain year and the treasurer of a U.S. Corporation knows that the corporation will receive 1 million EUROs in three months (on July 5th), and wants to hedge against the exchange rate moves. The treasurer could contact a bank, and find out that the exchange rate for a 3-month forward contract on EURO is $1.25, and agree to sell 1 million EUROs. In this case, the corporation takes a short forward position (agrees to sell), whereas the bank assumes a long forward position (agrees to buy). This forward contract eliminates all exchange rate risk, since the corporation will receive $1.25 million no matter what happens to the Euro currency rate in the course of the next three months. Settlement of forward contracts When a forward contract expires, there are two alternate arrangements possible to settle the obligation of the parties: physical settlement and cash settlement. Both types of settlements happen on the expiry date and are given below. Physical Settlement A forward contract can be settled by the physical delivery of the underlying asset by a short investor (i.e. the seller) to the long investor (i.e. the buyer) and the payment of the agreed 27 | P a g e
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forward price by the buyer to the seller on the agreed settlement date. The following example will help us understand the physical settlement process.
Consider two parties (A and B) enter into a forward contract on 1 August, 2009 where, A agrees
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Example II
to deliver 1000 stocks of Unitech to B, at a price of Rs. 100 per share, on 29 the August, 2009 (the expiry date). In this contract, A, who has committed to sell 1000 stocks of Unitech at Rs. 100 per share on 29 the August, 2009 has a short position and B, who has committed to buy 1000 stocks at Rs. 100 per share is said to have a long position. In case of physical settlement, on 29th August, 2009 (expiry date), A has to actually deliver 1000 Unitech shares to B and B has to pay the price (1000 * Rs. 100 = Rs. 10,000) to A. Incase A does not have 1000 shares to deliver on 29th August, 2009, he has to purchase it from the spot market and then deliver the stocks to B. On the expiry date the profit/loss for each party depends on the settlement price, that is, the closing price in the spot market on 29 August, 2009. The closing price on any given day is the weighted average price of the underlying during the last half an hour of trading in that day. Depending on the closing price, three different scenarios of profit/loss are possible for each party. They are as follows: Scenario I
Closing spot price on 29 August, 2009 (S T) is greater than the Forward price
(FT) Assume that the closing price of Unitech on the settlement date 29 August, 2009 is Rs. 105. Since the short investor has sold Unitech at Rs. 100 in the Forward market on 1 August, 2009, he can buy 1000 Unitech shares at Rs. 105 from the market and deliver them to the long investor. Therefore the person who has a short position makes a loss of (100 – 105) X 1000 = Rs. 5000. If the long investor sells the shares in the spot market immediately after receiving them, he would make an equivalent profit of (105 – 100) X 1000 = Rs. 5000. Scenario II
Closing Spot price on 29 August (S T), 2009 is the same as the Forward price
(FT) The short seller will buy the stock from the market at Rs. 100 and give it to the long investor. As the settlement price is same as the Forward price, neither party will gain or lose anything. 28 | P a g e
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Scenario III Closing Spot price (S T) on 29 August is less than t he futures price (F T) Assume that the closing price of Unitech on 29 August, 2009 is Rs. 95. The short investor, who has sold at Rs. 95 and deliver it to the long investor. Therefore the person who has a short position would make a profit of (100 – 95) X 1000 = Rs. 5000 and the person who has long position in the
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Unitech at Rs. 100 in the Forward market on 1 August, 2009, will buy the stock from the market
contract will lose an equivalent amount (Rs. 5000), if he sells the shares in the spot market immediately after receiving them. The main disadvantage of physical settlement is that it results in huge transaction costs in terms of actual purchase of securities by the party holding a short position (in this case A) and transfer of the security to the party in the long position (in this case B). Further, if the party in the long position is actually not interested in holding the security, then she will have to incur further transaction cost in disposing off the security. An alternative way of settlement, which helps in minimizing this cost, is through cash settlement.
Cash Settlement Cash settlement does not involve actual delivery or receipt of the security. Each party either pays (receives) cash equal to the net loss (profit) arising out of their respective position in the contract. So, in case of Scenario I mentioned above, where the spot price at the expiry date (ST) was greater than the forward price (FT), the party with the short position will have to pay an amount equivalent to the net loss to the part y at the long position. In our example, A will simply pay Rs. 5000 to B on the expiry date. The opposite is the case in Scenario (III), when ST < FT. The long party will be at a loss and have to pay an amount equivalent to the net loss to the short party. In our example, B will have to pay Rs. 5000 to A on the expiry date. In case of Scenario (II) where S T = FT, there is no need for any party to pay anything to the other party. Please note that the profit and loss position in case of physical settlement and cash settlement is the same except for the transaction costs which is involved in the physical settlement.
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Default risk in forward contracts A drawback of forward contracts is that they are subject to default risk. Regardless of whether not honor the contract. It could be either the buyer or the seller. This results in the other party
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the contract is for physical or cash settlement, there exists a potential for one party to default, i.e. suffering a loss. This risk of making losses due to any of the two parties defaulting is known as counter party risk. The main reason behind such risk is the absence of any mediator between the parties, who could
have undertaken the task of ensuring that both the parties fulfill their obligations arising out of the contract. Default risk is also referred to as counter party risk or credit risk. Forward Prices and Arbitrage Arbitrage involves locking in a profit by simultaneously entering into transactions in two or more markets to exploit a pricing anomaly. Such opportunities to make riskless profits are quite rare, since when the traders start moving to exploit them the prices adjust accordingly so that the arbitrage opportunity disappears.
Example III (Arbitrage with a Forward Contract on Gold). This example illustrates the possibility of arbitrage when the delivery price on a forward contract is too high or too low. Consider a trader who owns one ounce of gold today. Suppose the spot prices for gold is such that in the spot market traders can buy an ounce of gold at PB = $100 and sell at PS = $95. Furthermore, suppose that the 1-year borrowing and lending rates are such that traders can borrow at RB = 5% and lend at RL = 4% a year. Suppose first that the delivery price for a one year forward contract on gold is F = $107. In this case, the following arbitrage strategy yields a riskless profit. Borrow $100 at 5%, buy one ounce of gold in the spot market and take a short position in the forward contract.
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To see why, note that at time of delivery for the forward, the trader will sell the gold she bought for $107, whereas she has to pay back the loan at $100(1+0.05) = $105, which leaves her with
Note that once traders start exploiting this arbitrage opportunity by taking short forward
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$107 − $105 = $2 profits.
positions, there will be an excess supply to deliver gold at $107, which will drive the 1-year gold forward delivery price down. For the arbitrage opportunity to disappear, the delivery price F should be less than F < PB (1 + RB) = $100(1 + 0.05) = $105 ⇒ F < $105. Example III
(continued)
Suppose now that the delivery price for a one year forward contract on gold is F = $96. In this case, the following arbitrage strategy yields a riskless profit (recall that our trader own one ounce of gold to begin with). Sell the gold today at PS = $95, lend the proceeds at RL = 4%, and take a LONG position in the forward contract. To see why, note that at time of delivery for the forward contract, the trader will BUY the gold at F = $96, whereas she will receive $95(1 + 0.04) = $98.8 (for the funds she invested at 4%), which leaves her with $98.8 − $96 = $2.8 profits. Note that once traders start exploiting this arbitrage opportunity by taking long forward positions, there will be an excess demand to be delivered gold at $96, which will drive the 1-year gold forward delivery price up. For the arbitrage opportunity to disappear, the delivery price F should be more than F > PS (1 + RL) = $95(1 + 0.04) = $98.8 ⇒ F > $98.8
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Practice Problems Problem 1
A U.S. Company expects to pay 1 million Euros in six months. How can they use
Problem 2
The price of gold is currently $500 per ounce. The forward price for delivery in
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forward contracts to hedge against the exchange rate risk?
one year is $700. An arbitrage trader can borrow money at 10% per annum. Identify an arbitrage strategy. Problem 3
A traders owns one unit of gold. The trader can buy gold at $50 per ounce and sell
it at $40 per ounce in the spot market. She can borrow money at 6% per year and can invest money at 5% per year. For what range of one-year gold forward price F does this trader have no arbitrage opportunities?
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B
Futures 201213
Like a forward contract, a futures contract is an agreement between two parties in which the buyer agrees to buy an underlying asset from the seller, at a future date at a price that is agreed
upon today. However, unlike a forward contract, a futures contract is not a private transaction but gets traded on a recognized stock exchange. In addition, a futures contract is standardized by the exchange. All the terms, other than the price, are set by the stock exchange (rather than by individual parties as in the case of a forward contract). Also, both buyer and seller of the futures contracts are protected against the counter party risk by an entity called the Clearing Corporation. The Clearing Corporation provides this guarantee to ensure that the buyer or the seller of a futures contract does not suffer as a result of the counter party defaulting on its obligation. In case one of the parties defaults, the Clearing Corporation steps in to fulfill the obligation of this party, so that the other party does not suffer due to non-fulfillment of the contract. To be able to guarantee the fulfillment of the obligations under the contract, the Clearing Corporation holds an amount as a security from both the parties. This amount is called the Margin money and can be in the form of cash or other financial assets. Also, since the futures contracts are traded on the stock exchanges, the parties have the flexibility of closing out the contract prior to the maturity by squaring off the transactions in the market. The basic flow of a transaction between three parties, namely Buyer, Seller and Clearing Corporation is depicted in the diagram below:
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What is the difference between forward and futures contracts? Fundamentally, forward and futures contracts have the same function: both types of contracts allow people to buy or sell a specific type of asset at a specific time at a given price. Forwards
Futures
Privately negotiated contracts
Traded on an exchange
Not standardized
Standardized contracts
Settlement dates can be set by the parties
Fixed settlement dates as declared by the exchange
High counter party risk
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C
Options
Like forwards and futures, options are derivative instruments that provide the opportunity to buy and a seller, where one party (say First Party) gives to the other (say Second Party) the right, but
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or sell an underlying asset on a future date. An option is a derivative contract between a buyer not the obligation, to buy from (or sell to) the First Party the underlying asset on or before a specific day at an agreed -upon price. In return for granting the option, the party granting the
option collects a payment from the other party. This payment collected is called the “premium” or price of the option. The right to buy or sell is held by the “option buyer” (also called the option holder); the party granting the right is t he “option seller” or “option writer”. Unlike forwards and futures contracts, options require a cash payment (called the premium) upfront from the option buyer to the option seller. This payment is called option premium or option price. Options can be traded either on the stock exchange or in over the counter (OTC) markets. Options traded on the exchanges are backed by the Clearing Corporation thereby minimizing the risk arising due to default by the counter parties involved. There are two types of options, call options and put options, which are explained below: Call option A call option is an option granting the right to the buyer of the option to buy the underlying asset on a specific day at an agreed upon price, but not the obligation to do so. It is the seller who grants this right to the buyer of the option. It may be noted that the person who has the right to buy the underlying asset is known as the “buyer of the call option”. The price at which the buyer has the right to buy the asset is agreed upon at the time of entering the contract. This price is known as the strike price of the contract (call option strike price in this case). Since the buyer of the call option has the right (but no obligation) to buy the underlying asset, he will exercise his right to buy the underlying asset if and only if the price of the underlying asset in the market is more than the strike price on or before the expiry date of the contract. The buyer of the call option does not have an obligation to buy if he does not want to.
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Put option A put option is a contract granting the right to the buyer of the option to sell the underlying asset who grants this right to the buyer of the option. The person who has the right to sell the
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on or before a specific day at an agreed upon price, but not the obligation to do so. It is the seller underlying asset is known as the “buyer of the put option”. The price at which the buyer has the right to sell the asset is agreed upon at the time of entering the contract. This price is known as the strike price of the contract (put option strike price in this case). Since the buyer of the put option has the right (but not the obligation) to sell the underlying asset, he will exercise his right to sell the underlying asset if and only if the price of the underlying asset in the market is less than the strike price on or before the expiry date of the contract. The buyer of the put option does not have the obligation to sell if he does not want to. Illustration Suppose A has “bought a call option” of 2000 shares of Unilever at a strike price of Rs 260 per share at a premium of Rs 10. This option gives A, the buyer of the option, the right to buy 2000 shares of Unilever from the seller of the option, on or before August 27, 2009 (expiry date of the option). The seller of the option has the obligation to sell 2000 shares of Unilever at Rs 260 per share on or before August 27, 2009 (i.e. whenever asked by the buyer of the option). Suppose instead of buying a call, A has “sold a put option” on 100 Reliance Industries (RIL) shares at a strike price of Rs 2000 at a premium of Rs 8. This option is an obligation to A to buy 100 shares of Reliance Industries (RIL) at a price of Rs 2000 per share on or before August 27 (expiry date of the option) i.e., as and when asked by the buyer of the put option. It depends on
the option buyer as to when he exercises the option. As stated earlier, the buyer does not have the obligation to exercise the option.
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Differences between futures and options:
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Terminology of Derivatives In this section we explain the general terms and concepts related to derivatives. Spot price (ST) Spot price of an underlying asset is the price that is quoted for immediate delivery of the asset. For example, at the National Stock Exchange of India (NSE), the spot price of Reliance Ltd. at any given time is the price at which Reliance Ltd. shares are being traded at that time in the Cash Market Segment of the NSE. Spot price is also referred to as cash price sometimes. Forward price or futures price (F)
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Forward price or futures price is the price that is agreed upon at the date of the contract for the delivery of an asset at a specific future date. These prices are dependent on the spot price, the
Strike price (K)
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prevailing interest rate and the expiry date of the contract.
The price at which the buyer of an option can buy the stock (in the case of a call option) or sell the stock (in the case of a put option) on or before the expiry date of option contracts is called strike price. It is the price at which the stock will be bought or sold when the option is exercised. Strike price is used in the case of options only; it is not used for futures or forwards. Expiration date (T) In the case of Futures, Forwards and Index Options, Expiration Date is the only date on which settlement takes place. In case of stock options, on the other hand, Expiration date (or simply expiry), is the last date on which the option can be exercised. It is also called the final settlement date. Contract size As futures and options are standardized contracts traded on an exchange, they have a fixed contract size. One contract of a derivatives instrument represents a certain number of shares of the underlying asset. For example, if one contract of BHEL consists of 300 shares of BHEL, then if one buys one futures contract of BHEL, then for every Re 1 increase in BHEL’s futures price, the buyer will make a profit of 300 X 1 = Rs 300 and for every Re 1 fall in BHEL’s futures price, he will lose Rs 300. Contract Value Contract value is notional value of the transaction in case one contract is bought or sold. It is the contract size multiplied but the price of the futures. Contract value is used to calculate margins etc. for contracts. In the example above if BHEL futures are trading at Rs. 2000 the contract value would be Rs. 2000 x 300 = Rs. 6 lacs.
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Margins
the stock) to the seller. For example, if Infosys is trading at Rs. 2000 a share and an investor
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In the spot market, the buyer of a stock has to pay the entire transaction amount (for purchasing
wants to buy 100 Infosys shares, then he has to pay Rs. 2000 X 100 = Rs. 2,00,000 to the seller. The settlement will take place on T+2 basis; that is, two days after the transaction date. In a derivatives contract, a person enters into a trade today (buy or sell) but the settlement happens on a future date. Because of this, there is a high possibility of default by any of the parties. Futures and option contracts are traded through exchanges and the counter party risk is taken care of by the clearing corporation. In order to prevent any of the parties from defaulting on his trade commitment, the clearing corporation levies a margin on the buyer as well as seller of the futures and option contracts. This margin is a percentage (approximately 20%) of the total contract value. Thus, for the aforementioned example, if a person wants to buy 100 Infosys futures, then he will have to pay 20% of the contract value of Rs 2,00,000 = Rs 40,000 as a margin to the clearing corporation. This margin is applicable to both, the buyer and the seller of a futures contract.
Moneyness of an Option “Moneyness” of an option indicates whether an option is worth exercising or not i.e. if the option is exercised by the buyer of the option whether he will receive money or not. “Moneyness” of an option at any given time depends on where the spot price of the underlying is at that point of time relative to the strike price. The premium paid is not taken into consideration while calculating moneyness of an Option, since the premium once paid is a sunk cost and the profitability from exercising the option does not depend on the size of the premium. Therefore, the decision (of the buyer of the option) whether to exercise the option or not is not affected by the size of the premium. The following three terms are used to define the moneyness of an option.
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In-the-money option
for the buyer. Thus, Call Options are in-the-money when the value of spot price of the
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An option is said to be in-the-money if on exercising the option, it would produce a cash inflow underlying exceeds the strike price. On the other hand, Put Opt ions are in-the- money when the
spot price of the underlying is lower than the strike price. Moneyness of an option should not be confused with the profit and loss arising from holding an option contract. It should be noted that while moneyness of an option does not depend on the premium paid, profit/loss do. Thus a holder of an in-the-money option need not always make profit as the profitability also depends on the premium paid. Out-of- the-money option An out-of-the-money option is an opposite of an in-the-money option. An option-holder will not exercise the option when it is out-of-the-money. A Call option is out-of-the-money when its strike price is greater than the spot price of the underlying and a Put option is out-of-the-money when the spot price of the underlying is greater than the option’s strike price. At- the-money option An at-the-money-option is one in which the spot price of the underlying is equal to the strike price. It is at the stage where with any movement in the spot price of the underlying, the option will either become in-the-money or out-of-the-money. Illustration Consider some Call and Put options on stock XYZ. As on 13 August, 2009, XYZ is trading at Rs 116.25. The table below gives the information on closing prices of four options, expiring in September and December, and with strike prices of Rs. 115 and Rs. 117.50.
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Moneyness of call and put options 201213
Suppose the spot price of the underlying (closing share price) as at end of September is Rs. 116 and at end of December is Rs. 118. On the basis of the rules stated above, which options is inthe-money and which ones is out-of-the-money are given in the following table. Moneyness of call and put options
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asset.
Applications of Derivatives We look at the participants in the derivatives markets and how they use derivatives contracts. Participants in the Derivatives Market As equity markets developed, different categories of investors started participating in the market. Equity market participants currently include retail investors, corporate investors, mutual funds, banks, foreign institutional investors etc. Each of these investor categories uses the derivatives market to as a part of risk management, investment strategy or speculation. Based on the applications that derivatives are put to, these investors can be broadly classified into three groups: Hedgers Speculators, and Arbitrageurs We shall now look at each of these categories in detail. 1
Hedgers
These investors have a position (i.e., have bought stocks) in the underlying market but are worried about a potential loss arising out of a change in the asset price in the future. Hedgers participate in the derivatives market to lock the prices at which they will be able to transact in the future. Thus, they try to avoid price risk through holding a position in the derivatives market. Different hedgers take different positions in the derivatives market based on their exposure in the underlying market. A hedger normally takes an opposite position in the derivatives market to what he has in the underlying market. Hedging in futures market can be done through two positions, viz. short hedge and long hedge. 42 | P a g e
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Short Hedge A short hedge involves taking a short position in the futures market. Short hedge position is underlying asset.
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taken by someone who already owns the underlying asset or is expecting a future receipt of the
For example, an investor holding Reliance shares may be worried about adverse future price movements and may want to hedge the price risk. He can do so by holding a short position in the derivatives market. The investor can go short in Reliance futures at the NSE. This protects him from price movements in Reliance stock. In case the price of Reliance shares falls, the investor will lose money in the shares but will make up for this loss by the gain made in Reliance Futures. Note that a short position holder in a futures contract makes a profit if the price of the underlying asset falls in the future. In this way, futures contract allows an investor to manage his price risk. Similarly, a sugar manufacturing company could hedge against any probable loss in the future due to a fall in the prices of sugar by holding a short position i n the futures/ forwards market. If the prices of sugar fall, the company may lose on the sugar sale but the loss will be offset by profit made in the futures contract. Long Hedge A long hedge involves holding a long position in the futures market. A Long position holder agrees to buy the underlying asset at the expiry date by paying the agreed futures/ forward price. This strategy is used by those who will need to acquire the underlying asset in the future. For example, a chocolate manufacturer who needs to acquire sugar in the future will be worried about any loss that may arise if the price of sugar increases in the future. To hedge against this risk, the chocolate manufacturer can hold a long position in the sugar futures. If the price of sugar rises, the chocolate manufacture may have to pay more to acquire sugar in the normal market, but he will be compensated against this loss through a profit that will arise in the futures market. Note that a long position holder in a futures contract makes a profit if the price of the underlying asset increases in the future. Long hedge strategy can also be used by those investors who desire to purchase the underlying asset at a future date (that is, when he acquires the cash to
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purchase the asset) but wants to lock the prevailing price in the market. This may be because he thinks that the prevailing price is very low.
expecting to have Rs. 250 at the end of the month. The investor feels that Wipro Ltd. is at a very
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For example, suppose the current spot price of Wipro Ltd. is Rs. 250 per stock. An investor is attractive level and he may miss the opportunity to buy the stock if he waits till the end of the month. In such a case, he can buy Wipro Ltd. in the futures market. By doing so, he can lock in
the price of the stock. Assuming that he buys Wipro Ltd. in the futures market at Rs. 250 (this becomes his locked-in price), there can be three probable scenarios: Scenario I:
Price of Wipro Ltd. in the cash market on expiry date is Rs. 300. As futures price
is equal to the spot price on the expiry day, the futures price of Wipro would be at Rs. 300 on expiry day. The investor can sell Wipro Ltd in the futures market at Rs. 300. By doing this, he has made a profit of 300 – 250 = Rs. 50 in the futures trade. He can now buy Wipro Ltd in the spot market at Rs. 300. Therefore, his total investment cost for buying one share of Wipro Ltd equals Rs.300 (price in spot market) – 50 (profit in futures market) = Rs.250. This is the amount of money he was expecting to have at the end of the month. If the investor had not bought Wipro Ltd futures, he would have had only Rs. 250 and would have been unable to buy Wipro Ltd shares in the cash market. The futures contract helped him to lock in a price for the shares at Rs. 250. Scenario II: Price of Wipro Ltd in the cash market on expiry day is Rs. 250. As futures price tracks spot price, futures price would also be at Rs. 250 on expiry day. The investor will sell Wipro Ltd in the futures market at Rs. 250. By doing this, he has made Rs. 0 in the futures trade. He can buy Wipro Ltd in the spot market at Rs. 250. His total investment cost for buying one share of Wipro will be = Rs. 250 (price in spot market) + 0 (loss in futures market) = Rs. 250. Scenario III: Price of Wipro Ltd in the cash market on expiry day is Rs. 200. As futures price tracks spot price, futures price would also be at Rs. 200 on expiry day. The investor will sell Wipro Ltd in the futures market at Rs. 200. By doing this, he has made a loss of 200 – 250 = Rs. 50 in the futures trade. He can buy Wipro in the spot market at Rs. 200. Therefore, his total investment cost for buying one share of Wipro Ltd will be = 200 (price in spot market) + 50 (loss
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in futures market) = Rs. 250. Thus, in all the three scenarios, he has to pay only Rs. 250. This is an example of a Long Hedge. Speculators
A Speculator is one who bets on the derivatives market based on his views on the potential
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2
movement of the underlying stock price. Speculators take large, calculated risks as they trade based on anticipated future price movements. They hope to make quick, large gains; but may not always be successful. They normally have shorter holding time for their positions as compared to hedgers. If the price of the underlying moves as per their expectation they can make large profits. However, if the price moves in the opposite direction of their assessment, the losses can also be enormous. Illustration Currently ICICI Bank Ltd (ICICI) is trading at, say, Rs. 500 in the cash market and also at Rs. 500 in the futures market (assumed values for the example only). A speculator feels that post the RBI’s policy announcement, the share price of ICICI will go up. The speculator can buy the stock in the spot market or in the derivatives market. If the derivatives contract size of ICICI is 1000 and if the speculator buys one futures contract of ICICI, he is buying ICICI futures worth Rs 500 X 1000 = Rs. 5,00,000. For this he will have to pay a margin of say 20% of the contract value to the exchange. The margin that the speculator needs to pay to the exchange is 20% of Rs. 5,00,000 = Rs. 1,00,000. This Rs. 1,00,000 is his total investment for the futures contract. If the speculator would have invested Rs. 1,00,000 in the spot market, he could purchase only 1,00,000 / 500 = 200 shares. Let us assume that post RBI announcement price of ICICI share moves to Rs. 520. With one lakh investment each in the futures and the cash market, the profits would be: (520 – 500) X 1,000 = Rs. 20,000 in case of futures market and (520 – 500) X 200 = Rs. 4000 in the case of cash market. It should be noted that the opposite will result in case of adverse movement in stock prices, wherein the speculator will be losing more in the futures market than in the spot market. This is because the speculator can hold a larger position in the futures market where he has to pay only the margin money. 45 | P a g e
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3
Arbitrageurs
Arbitrageurs attempt to profit from pricing inefficiencies in the market by making simultaneous profit in case there is price discrepancy between the stock price in the cash and the derivatives
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trades that offset each other and captures a risk-free profit. An arbitrageur may also seek to make markets. For example, if on 1st August, 2009 the SBI share is trading at Rs. 1780 in the cash market and the futures contract of SBI is trading at Rs. 1790, the arbitrageur would buy the SBI shares (i.e. make an investment of Rs. 1780) in the spot market and sell the same number of SBI futures contracts. On expiry day (say 24 August, 2009), the price of SBI futures contracts will close at the price at which SBI closes in the spot market. In other words, the settlement of the futures contract will happen at the closing price of the SBI shares and that is why the futures and spot pr ices are said to converge on the expiry day. On expiry day, the arbitrageur will sell the SBI stock in the spot market and buy the futures contract, both of which will happen at the closing price of
SBI in the spot market. Since the arbitrageur has entered into off-setting positions, he will be able to earn Rs. 10 irrespective of the prevailing market price on the expiry date. There are three possible price scenarios at which SBI can close on expiry day. Let us calculate the profit/ loss of the arbitrageur in each of the scenarios where he had initially (1 August) purchased SBI shares in the spot market at Rs 1780 and sold the futures contract of SBI at Rs. 1790: Scenario I:
SBI shares closes at a price greater than 1780 (say Rs. 2000) in the spot market
on expiry day (24 August 2009) SBI futures will close at the same price as SBI in spot market on the expiry day i.e., SBI futures will also close at Rs. 2000. The arbitrageur reverses his previous transaction entered into on 1 August 2009. Profit/ Loss (–) in spot market = 2000 – 1780 = Rs. 220 Profit/ Loss (–) in futures market = 1790 – 2000 = Rs. (–) 210 Net profit/ Loss (–) on both transactions combined = 220 – 210 = Rs. 10 profit.
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Scenario II: SBI shares close at Rs 1780 in the spot market on expiry day (24 August 2009) SBI futures will close at the same price as SBI in spot market on expiry day i.e., SBI futures will 2009.
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also close at Rs 1780. The arbitrageur reverses his previous transaction entered into on 1 August
Profit/ Loss (–) in spot market = 1780 – 1780 = Rs 0 Profit/ Loss (–) in futures market = 1790 – 1780 = Rs. 10 Net profit/ Loss (–) on both transactions combined = 0 + 10 = Rs. 10 profit. Scenario III: SBI shares close at Rs. 1500 in the spot market on expiry day (24 August 2009), Here also, SBI futures will close at Rs. 1500. The arbitrageur reverses his previous transaction entered into on 1 August 2009. Profit/ Loss (–) in spot market = 1500 – 1780 = Rs. (–) 280 Profit/ Loss (–) in futures market = 1790 – 1500 = Rs. 290 Net profit/ Loss (–) on both transactions combined = (–) 280 + 290 = Rs. 10 profit. Thus, in all three scenarios, the arbitrageur will make a profit of Rs. 10, which was the difference between the spot price of SBI and futures price of SBI, when the transaction was entered into. This is called a “risk less profit” since once the transaction is entered into on 1 August, 2009 (due to the price difference between spot and futures), the profit is locked. Irrespective of where the underlying share price closes on the expiry date of the contract, a profit of Rs. 10 is assured. The investment made by the arbitrageur is Rs. 1780 (when he buys SBI in the spot market). He makes this investment on 1 August 2009 and gets a return of Rs. 10 on this investment in 23 days (24 August). This means a return of 0.56% in 23 days. If we annualize this, it is a return of nearly 9% per annum. One should also note that this opportunity to make a risk-less return of 9% per annum will not always remain. The difference between the spot and futures price arose due to some inefficiency (in the market), which was exploited by the arbitrageur by buying shares in spot and selling futures. As more and more such arbitrage trades take place, the difference between spot and futures prices would narrow thereby reducing the attractiveness of further arbitrage. 47 | P a g e
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Uses of Derivatives 1
Risk management
an investor comprises of the following three processes:
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The most important purpose of the derivatives market is risk management. Risk management for
Identifying the desired level of risk that the investor is willing to take on his investments; Identifying and measuring the actual level of risk that the investor is carrying; and Making arrangements which may include trading (buying/selling) of derivatives contracts that allow him to match the actual and desired levels of risk. The example of hedging discussed above illustrates the process of risk management through futures. 2
Market efficiency
Efficient markets are fair and competitive and do not allow an investor to make risk free profits. Derivatives assist in improving the efficiency of the markets, by providing a self-correcting mechanism. Arbitrageurs are one section of market participants who trade whenever there is an opportunity to make risk free profits till the opportunity ceases to exist. Risk free profits are not easy to make in more efficient markets. When trading occurs, there is a possibility that some amount of mispricing might occur in the markets. The arbitrageurs step in to take advantage of this mispricing by buying from the cheaper market and selling in the higher market. Their actions quickly narrow the prices and thereby reducing the inefficiencies. 3
Price discovery
One of the primary functions of derivatives markets is price discovery. They provide valuable information about the prices and expected price fluctuations of the underlying assets in two ways: First, many of these assets are traded in markets in different geographical locations. Because of this, assets may be traded at different prices in different markets. In derivatives markets, the price of the contract often serves as a proxy for the price of the underlying asset. For example, gold 48 | P a g e
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may trade at different prices in Mumbai and Delhi but a derivatives contract on gold would have one value and so traders in Mumbai and Delhi can validate the prices of spot markets in their
Second, the prices of the futures contracts serve as prices that can be used to get a sense of the
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respective location to see if it is cheap or expensive and trade accordingly.
market expectation of future prices. For example, say there is a company that produces sugar and expects that the production of sugar will take two months from today. As sugar prices fluctuate daily, the company does not know if after two months the price of sugar will be higher or lower than it is today. How does it predict where the price of sugar will be in future? It can do this by monitoring prices of derivatives contract on sugar (say a Sugar Forward contract). If the forward price of sugar is trading higher than the spot price that means that the market is expecting the sugar spot price to go up in future. If there were no derivatives price, it would have to wait for two months before knowing the market price of sugar on that day. Based on derivatives price the management of the sugar company can make strategic and tactical decisions of how much sugar to produce and when.
Trading Options In this chapter we will discuss pay -outs for various strategies using options and strategies which can be used to improve returns by using options. Option Payout There are two sides to every option contract. On the one side is the option buyer who has taken a long position (i.e., has bought the option). On the other side is the option seller who has taken a short position (i.e., has sold the option). The seller of the option receives a premium from the buyer of the option. It may be noted that while computing profit and loss, premium has to be taken into consideration. Also, when a buyer makes profit, the seller makes a loss of equal magnitude and vice versa. In this section, we will discuss payouts for various strategies using options.
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A long position in a call option
price i.e., strike price (K) and the option seller has the obligation to sell the asset at the strike
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In this strategy, the investor has the right to buy the asset in the future at a predetermined strike price (K). If the settlement price (underlying stock closing price) of the asset is above the strike price, then the call option buyer will exercise his option and buy the stock at the strike price (K).
If the settlement price (underlying stock closing price) is lower than the strike price, the option buyer will not exercise the option as he can buy the same stock from the market at a price lower than the strike price. A long position in a put option In this strategy, the investor has bought the right to sell the underlying asset in the future at a predetermined strike price (K). If the settlement price (underlying stock closing price) at maturity is lower than the strike price, then the put option holder will exercise his option and sell the stock at the strike price (K). If the settlement price (underlying stock closing price) is higher than the strike price, the option buyer will not exercise the option as he can sell the same stock in the market at a price higher than the strike price. A short position in a call option In this strategy, the option seller has an obligation to sell the asset at a predetermined strike price (K) if the buyer of the option chooses to exercise the option. The buyer of the option will exercise the option if the spot price at maturity is any value higher than (K). If the spot price is lower than (K), the buyer of the option will not exercise his/her option. A short position in a put option In this strategy, the option seller has an obligation to buy the asset at a predetermined strike price (K) if the buyer of the option chooses to exercise his/her option. The buyer of the option will exercise his option to sell at (K) if the spot price at maturity is lower than (K). If the spot price is higher than (K), then the option buyer will not exercise his/her option. Explanation of pay-offs for long options 50 | P a g e
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The buyer’s profit is equal to the seller’s loss. Therefore, in the above table the seller’s loss is S T – K for a short call option if the spot price closes at a value above the strike price of the option and is K –S T for a short put option if the spot price closes at a value lower than the strike price of the option. The above four positions and their pay-offs are depicted in the figure below: Pay -off for a buyer of a call option
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The figure shows the profits/losses for a buyer of a three-month Nifty 2250 call option. As can be seen, as the spot Nifty rises, the call option is in-the-money. If upon expiration, Nifty closes above the strike of 2250, the buyer would exercise his option and profit to the extent of the difference between the Nifty-close and the strike price. The profits possible on this option are potentially unlimited. However, if Nifty falls below the strike of 2250, the buyer lets the option expire. His losses are limited to the extent of the premium that he paid for buying the option. Pay-off for a seller of option
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The figure shows the profits/losses for a seller of a three-month Nifty 2250 call option. As the spot Nifty rises, the call option is in-the-money and the writer starts making losses. If upon writer who would suffer a loss to the extent of the difference between the Nifty-close and the strike price. The loss that can be incurred by the writer of the option is potentially unlimited,
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expiration, Nifty closes above the strike of 2250, the buyer would exercise his option on the
whereas the maximum profit is limited to the extent of the upfront option premium charged by him. Pay-off for a buyer of a put option
The figure shows the profits/losses for a buyer of a three-month Nifty 2250 put option. As can be seen, as the spot Nifty falls, the put option is in-the-money. If upon expiration, Nifty closes below the strike of 2250, the buyer would exercise his option and profit to the extent of the difference between the strike price and Nifty-close. The profits possible on this option can be as high as the strike price. However, if Nifty rises above the strike of 2250, he lets the option expire. His losses are limited to the extent of the premium he paid for buying the option. Pay-off for a seller of a put option
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The figure shows the profits/losses for a seller of a three-month Nifty 2250 put option. As the spot Nifty falls, the put option is in-the-money and the writer starts making losses. If upon expiration, Nifty closes below the strike of 2250, the buyer would exercise his option on the writer who would suffer a loss to the extent of the difference between the strike price and Niftyclose. The loss that can be incurred by the writer of the option is a maximum extent of the strike price (since the worst that can happen is that the asset price can fall to zero) whereas the maximum profit is limited to the extent of the upfront option premium of charged by him. Option Strategies An option strategy is implemented to try and make gains from the movement in the underlying price of an asset. As discussed above, options are derivatives that give the buyer the right to exercise the option at a future date. Unlike futures and forwards which have linear pay -offs and do not require an initial outlay (upfront payment), options have non linear pay-offs and do require an initial outlay (or premium). In this section we discuss various strategies which can be used to maximize returns by using options. A
Long option strategy
A long option strategy is a strategy of buying an option according to the view on future price movement of the underlying. A person with a bullish opinion on the underlying will buy a call option on that asset/security, while a person with a bearish opinion on the underlying will buy a put option on that asset/security. An important characteristic of long option strategies is limited 54 | P a g e
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risk and unlimited profit potential. An option buyer can only lose the amount paid for the option premium. At the same time, theoretically, the profit potential is unlimited.
An investor having a bullish opinion on underlying can expect to have positive returns by buying
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Calls
a call option on that asset/security. When a call option is purchased, the call option holder is exposed to the stock performance in the spot market without actually possessing the stock and does so for a fraction of the cost involved i n purchasing the stock in the spot market. The cost incurred by the call option holder is the option premium. Thus, he can take advantage of a smaller investment and maximize his profits. Consider the purchase of a call option at the price (premium) c. We take S T = Spot price at time T K = Strike price The payout in two scenarios is as follows: Profit/Loss = – c , if S T = K Profit/Loss = (S T - K ) – c if S T = K Let us explain this with some examples. Mr. A buys a Call on an index (such as Nifty 50) with a strike price of Rs. 2000 for premium of Rs. 81. Consider the values of the index at expiration as 1800, 1900, 2100, and 2200. For S T = 1800, Profit/Loss = 0 – 81 = – 81 (maximum loss = premium paid) For S T = 1900, Profit/Loss = 0 – 81 = – 81 (maximum loss = premium paid) For S T = 2100, Profit/Loss = 2100 – 2000 – 81 = 19 For S T = 2200, Profit/Loss = 2200 – 2000 – 81 = 119
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As we can see from the example, the maximum loss suffered by the buyer of the Call option is Rs. 81, which is the premium that he paid t o buy the option. His maximum profits are unlimited
Puts
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and they depend on where the underlying price moves.
An investor having a bearish opinion on the underlying can expect to have positive returns by buying a put option on that asset/security. When a put option is purchased, the put option buyer has the right to sell the stock at the strike price on or before the expiry date depending on where the underlying price is. Consider the purchase of a put option at price (premium) p. We take S T = Spot price a t time T K = exercise price The payout in two scenarios is as follows: Profit/Loss = (K – S T ) – p if S T = K Profit/Loss = – p if S T = K Let us explain this with some examples. Mr. X buys a put at a strike price of Rs. 2000 for a premium of Rs. 79. Consider the values of the index at expiration at 1800, 1900, 2100, and 2200. For S T = 1800, Profit/Loss = 2000 – 1800 – 79 = 121 For S T = 1900, Profit/Loss = 2000 – 1900 – 79 = 21 For S T = 2100, Profit/Loss = – 79 (maximum loss is the premium paid) For S T = 2200, Profit/Loss = – 79 (maximum loss is the premium paid) As we can see from the example, the maximum loss suffered by the buyer of the Put option is Rs. 79, which is the premium that he paid to buy the option. His maximum profits are unlimited and depend o n where the underlying price moves.
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B
Short options strategy
A short options strategy is a strategy where options are sold to make money upfront with a view exercise the same and the seller can keep the premium). As opposed to a long options strategy, here a person with a bullish opinion on the underlying will sell a put option in the hope that prices will rise and the buyer will not exercise the option leading to profit for the seller. On the other hand, a person with a bearish view on the underlying will sell a call option in the hope that prices will fall and the buyer will not exercise the option leading to profit for the seller. As opposed to a long options strategy where the downside was limited to the price paid for the option, here the downside is unlimited and the profit is limited to the price of selling the option (the premium). Calls An investor with a bearish opinion on the underlying can take advantage of falling stock prices by selling a call option on the asset/security. If the stock price falls, the profit to the seller will be the premium earned by selling the option. He will lose in case the stock price increases above the strike price. Consider the selling of a call option at the price (premium) c. We take S T = Spot price at time T K = exercise price The payout in two scenarios is as follows: Profit/Loss = c if S T = K Profit/Loss = c – (S T – K) if S T = K Now consider this example: A sells a call at a strike price of Rs 2000 for a premium of Rs 81. Consider values of index at expiration at 1800, 1900, 2100, and 2200. For S T = 1800, Profit/Loss = 81 (maximum profit = premium received) 57 | P a g e
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that the options will expire out of money at the expiry date (i.e., the buyer of the option will not
Financial Risk Management
For S T = 1900, Profit/Loss = 81 (maximum profit = premium received) For S T = 2100, Profit/Loss = 81 – (2100 – 2000) = – 1 9 201213
For S T =2200, Profit/Loss = 81 – (2100 – 2200) = – 119
As we can see from the example above, the maximum loss suffered by the seller of the Call option is unlimited (this is the reverse of the buyer’s gains). His maximum profits are limited to the premium received. Puts An investor with a bullish opinion on the underlying can take advantage of rising prices by selling a put option on the asset/security. If the stock price rises, the profit to the seller will be the premium earned by selling the option. He will lose in case the stock price falls below the strike price. Consider the sale of a put option at the price (premium) p . We take: S T = Spot price at time T K = exercise price The payout in two scenarios is as follows: Profit/Loss = p – (K – ST) if S T = K Profit/Loss = p if S T = K We sell a put at a strike price of Rs. 2000 for Rs. 79. Consider values of index at expiration as 1800, 1900, 2100, and 2200. For S T = 1800, Profit/Loss = 79 – (2000 – 1800) = (– ) 121 For S T = 1900, Profit/Loss = 79 – (2000 – 1900) = (– ) 21 For S T = 2100, Profit/Loss = 79 (maximum profit = premium received) For S T = 2200, Profit/Loss = 79 (maximum profit = premium received) 58 | P a g e
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As we can see from the example above the maximum loss suffered by the seller of the Put option is unlimited (this is the reverse of the buyer’s gains). His maximum profits are limited to the
Determination of option prices
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premium received.
Like in case of any traded good, the price of any option is determined by the demand for and supply of that option. This price has two components: intrinsic value and time value. Intrinsic value and time value Intrinsic value of an option: Intrinsic value of an option at a given time is the amount the holder of the option will get if he exercises the option at that time. In other words, the intrinsic value of an option is the amount the option is in-the-money (ITM). If the option is out -of- the-money (OTM), its intrinsic value is zero. Putting it another way, the intrinsic value of a call is Max [0, (S t — K)] which means that the intrinsic value of a call is the greater of 0 or (St — K). Similarly, the intrinsic value of a put is Max [0, K — S t] i.e., the greater of 0 or (K — S t) where K is the strike price and S t is the spot price. Time value of an option In addition to the intrinsic value, the seller charges a ‘time value’ from the buyers of the option. This is because the more time there is for the contract to expire, the greater the chance that the exercise of the contract will become more profitable for the buyer. This is a risk for the seller and he seeks compensation for it by demanding a ‘time value’. The time value of an option can be obtained by taking the difference between its premium and its intrinsic value. Both calls and puts have time value. An option that is Out-of-the-money (OTM) or At-the-money (ATM) has only time value and no intrinsic value. Usually, the maximum time value exists when the option is ATM. The longer the time to expiration, the greater is an option’s time value, all else being equal. At expiration, an option has no time value.
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Illustration In the following two tables, five different examples are given for call option and put option show how intrinsic value and time value vary depending on underlying price, strike price and premium. Intrinsic and Time Value for Call Options: Examples
Intrinsic and Time Value for Put Options: Examples
Factors impacting option prices The supply and demand of options and hence their prices are influenced by the following factors: The underlying price, The strike price,
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respectively. As stated earlier, premium is determined by demand and supply. The examples
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The time to expiration, The underlying asset’s volatility, 201213
Risk free rate Underlying Prices Each of the five parameters has a different impact on the option pricing of a Call and a Put. The
underlying price: Call and Put options react differently to the movement in the underlying price. As the underlying price increases, intrinsic value of a call increases and value of a put decreases. Thus, in the case of a Call option, the higher the price of the underlying asset from strike price, the higher is the value (premium) of the call option. On the other hand, in case of a put option, the higher the price of the underlying asset, the lower is the value of the put option. The strike price The strike price is specified in the option contract and does not change over time. The higher the strike price, the smaller is the intrinsic value of a call option and the greater is the intrinsic value of a put option. Everything else remaining constant, as the strike price increases, the value of a call option decreases and the value of a put option increases. Similarly, as the strike price decreases, the price of the call option increases while that of a put option decreases. Time to expiration Time to expiration is the time remaining for the option to expire. Obviously, the time remaining in an option’s life moves constantly towards zero. Even if the underlying price is constant, the option price will still change since time reduces constantly and the time for which the risk is remaining is reducing. The time value of both call as well as put option decreases to zero (and hence, the price of the option falls to its intrinsic value) as the time to expiration approaches zero. As time passes and a call option approaches maturity, its value declines, all other parameters remaining constant. Similarly, the value of a put option also decreases as we approach maturity. This is called “time-decay”.
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Volatility Volatility is an important factor in the price of an option. Volatility is defined as the uncertainty of returns. The more volatile the underlying higher is the price of the option on the underlying. Whether we are discussing a call or a put, this relationship remains the same.
Risk free rate Risk free rate of return is the theoretical rate of return of an investment which has no risk (zero risk). Government securities are considered to be risk free since their return is assured by the Government. Risk free rate is the amount of return which an investor is guaranteed to get over the life time of an option without taking any risk. As we increase the risk free rate the price of the call option increases marginally whereas the price of the put option decreases marginally. It may however be noted that option prices do not change much with changes in the risk free rate. The impact of all the parameters which affect the price of an option is given in the table below:
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Even though option prices are determined by market demand and supply, there are various models of getting a fair value of the options, the most popular of which is the Black Scholes 201213
Merton Model. In this model, the theoretical value of the options is obtained by inputting into
formula values of the above-mentioned five factors. It may be noted that the prices arrived at by using this model are only indicative.
Real Options An alternative or choice that becomes available with a business investment opportunity. Real options can include opportunities to expand and cease projects if certain conditions arise, amongst other options. They are referred to as "real" because they usually pertain to tangible assets such as capital equipment, rather than financial instruments. Taking into account real options can greatly affect the valuation of potential investments. Oftentimes, however, valuation methods, such as NPV, do not include the benefits that real options provide. Note that this kind of option is not a derivative instrument, but an actual option (in the sense of "choice") that a business may gain by undertaking certain endeavors. For example, by investing in a particular project, a company may have the real option of expanding, downsizing or abandoning other projects in the future. Other examples of real options may be opportunities for R&D, M&A and licensing. Real Options Valuation (ROV) is revolutionizing corporate strategy and bridging the gap between finance and strategic planning. Just as an option gives its owner the right - but not the obligation - to take a particular course of action at some time in the future, flexibility embedded in capital investment projects and company strategies allows managers to take a staged approach to corporate strategy and react to changes in the business environment, so they can limit downside losses while fully capitalizing on upside potential opportunities. Real Options - Some Examples •
Defer - Investing now eliminates the option to defer (learning)
•
Expand - An option to defer part of the scale of investment
•
Contract - The flexibility to reduce the rate of output
•
Abandon - Stop investing, and liquidate existing assets
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Staging - Substitute a series of small investments for one large
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Techniques for Reasoning Through Decision Trees 1. Focus on the most important decisions. 2. Reason forward to construct the tree. 3. Track certainties and uncertainties at each decision point. 4. Calculate backward to evaluate choices. 5. Select the tree branch with the highest expected value.
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Decision Tree Example – Assumptions
•
Demand may be high (30%), medium (50%), low (20%).
•
Cost of large restaurant is $750,000.
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Cost of small restaurant is $600,000.
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Entrepreneur will invest $400,000, outside investor provides the rest.
•
Investor requires 1% of equity for each $10,000 invested.
•
If demand is high - PV large is $1,500,000, PV small is $800,000.
•
If demand is medium - PV large is $800,000, PV small is $800,000.
•
If demand is low - PV large is $300,000, PV small is $400,000.
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Consider an investment project where there is uncertainty about the state of the world. Suppose it can be either good or bad and it's as likely to be one as the other. The market research provides us the following data that:
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Accept/reject Decision to Invest in Restaurant Business 201213
Evaluation of Accept/Reject Alternatives •
Large-scale entry:
NPV conditional on high demand
= $575,000
NPV conditional on intermediate demand
= $120,000
NPV conditional on low demand
= ($205,000)
NPV = .3 x $575,000 + .5 x $120,000 – .2 x $205,000 = $191,500
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•
Small-scale entry: = $240,000
NPV conditional on intermediate demand
= $240,000
NPV conditional on low demand
= ($ 80,000)
NPV = .3 x $240,000 + .5 x $240,000 - .2 x $80,000 = $176,000 •
Do not enter:
NPV = $0 Restaurant Business Investment with an Option to Delay Investing
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NPV conditional on high demand
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Evaluation of Option to Delay •
Large-scale entry strategy: NPV = $191,500
•
Delay until uncertainty is resolved: –
–
–
•
•
High demand •
Build large restaurant
•
NPV conditional on high demand
Intermediate demand •
Build small restaurant
•
NPV conditional on intermediate demand
Low demand •
Do not enter
•
NPV conditional on low demand = $0
NPV of delay strategy: –
= .3 x $445,000 + .5 x $160,000 + .2 x $0
–
= $213,500
Value of Option to Delay = $213,500 - 191,500 –
= $445,000
= $22,000
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= $160,000
Financial Risk Management
Evaluation of Option to Expand •
Large-scale entry strategy: NPV = $191,500
•
Delay until uncertainty is resolved: NPV = $213,500
•
Build small, with Option to Expand: –
Conditional on High demand: •
NPV if Expand
•
NPV if Remain Small = $240,000
•
Conclusion: Expand if demand is high
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= $580,000
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Restaurant Business Investment with an Option to Expand Initial Investment
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–
Conditional on Intermediate demand: •
Conditional on Low demand: •
•
NPV of Remaining Small = ($80,000)
NPV of Small-scale entry with Option to Expand –
= .3 x $580,000 + .5 x $240,000 - .2 x $80,000
–
= $278,000
–
•
Value of Expansion Option = $86,500
•
Incremental value over Delay Option = $64,500
The Options are Mutually Exclusive
Evaluation of Option to Abandon •
Large-scale entry strategy: NPV =
•
Large-scale entry with Abandonment option: –
Convert to office with $600,000 value
–
NPV of converting for entrepreneur = ($10,000)
–
NPV with Abandonment Option: •
– •
$191,500
= .3 x $575,000 + .5 x $120,000 - .2 x $10,000 = $230,500
Would pay up to $39,000 extra for location that is convertible
Small-scale entry with Expansion and Abandonment Options: –
Convert to office with $300,000 value
–
NPV of converting for entrepreneur = ($160,000)
–
NPV with Abandonment Option: •
–
= .3 x $580,000 + .5 x $240,000 - .2 x $160,000 = $262,000
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–
NPV of Remaining Small = $240,000
Financial Risk Management
– •
A result of discreteness of the analysis
Conclusion: Build small with Expansion Option NPV = $278,000
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–
Financial Risk Management
Value-at-Risk
VaR was pioneered by major U.S. banks in the ’80s, as the derivative markets developed. The birth of derivatives represented a new challenge for risk management because traditional measures of exposure were clearly inadequate. For example, two derivative contracts with the same notional value could have very different risks. With VaR, banks had developed a general measure of economic loss that could equate risk across products and aggregate risk on a portfolio basis. The value of a portfolio of financial assets is subject to many risks: credit risks, market risks, etc. Value at Risk, VaR, is a statistical estimate of the market risk of a portfolio. VaR attempts to answer the following question. Given a certain confidence level and a specified time horizon, what is the maximum potential loss of the portfolio? Definition of VaR The value at risk (VaR) indicates the maximum percentage value of our multiple trading systems portfolio that could be lost during a fixed period (e.g. one day) within a certain confidence level (e.g. 95%). VaR is defined as the predicted worst-case loss at a specific confidence level (e.g., 95%) over a certain period of time (e.g., 1 day). For example, every afternoon, J.P. Morgan takes a snapshot of its global trading positions to estimate its Daily-Earnings-at-Risk (DEaR), which is a VaR measure that Morgan defines as the 95% confidence worst-case loss over the next 24 hours due to adverse market movements. One the major advantage of VaR Method is that it works across different asset classes such as bonds and stocks. The elegance of the VaR solution is that it works on multiple levels, from the position-specific micro level to the portfolio-based macro level. VaR has become a common language for communication about aggregate risk taking, both within an organization and outside (e.g., with analysts, regulators, rating agencies, and shareholders). Virtually all major financial institutions have adopted VaR as a cornerstone of day-to-day risk measurement. Now with the VaR method it is possible to measure the aggregated risk on a portfolio level. But there are some limitations of VaR model that is it can only be achieved under normal market condition. Three approaches for VaR calculation: •
Risk Metrics
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History of Value-at-Risk
Financial Risk Management
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Monte Carlo simulation
Risk Metrics
Risk metrics by definition is a set of financial models used by investors to determine portfolio risk. Risk measurement process Portfolio risk measurement can be broken down into steps. The first is modeling the market that drives changes in the portfolio's value. The market model must be sufficiently specified so that the portfolio can be revalued using information from the market model. The risk measurements are then extracted from the probability distribution of the changes in portfolio value. The change in value of the portfolio is typically referred to by portfolio managers as profit and loss, or P&L. Market models RiskMetrics describes two models for modeling the risk factors that define financial markets. Historical Simulation Monte Carlo simulation
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The RiskMetrics variance model (also known as exponential smoother) was first established in 1989, when Sir Dennis Weather stone’s, the new chairman of J.P. Morgan, asked for a daily report measuring and explaining the risks of his firm. Nearly four years later in 1992, J.P. Morgan launched the RiskMetrics methodology to the marketplace, making the substantive research and analysis that satisfied Sir Dennis Weather stone’s request freely available to all market participants.
Financial Risk Management
Historical Simulation
Suppose we want to calculate VaR for a portfolio using 1-day horizon, a 99% confidence level, and 500 days of data. Collect data on the daily movements in the given market variables.Conduct 500 trials assuming as if todays prices will change at a past rate of change in each of the 500 days 0 This way forecasted value for tomorrow will be: v vn i vi −1
Where Vn is today’s value of the variable Vi is the variable value in past days Vi-1 is the variable value one-day before the vi value After that, calculate the value of portfolio based on the trial values of each variable and find the difference between the forecasted values and today’s value of the portfolio in all 500 trials. Find the given percentile of these differences, and that will be the VaR estimate. The 1st percentile in 500 observations means the 5th worst loss in all 500 observations In Excel, we do this by:
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=percentile (range, .01) if it is for 1st percentile.
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HS involves using past data as a guide to what will happen in the future
Financial Risk Management
Monte Carlo simulation
Monte Carlo simulation furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action. It shows the extreme possibilities—the outcomes of going for out of business and for the most conservative decision—along with all possible consequences for middle-of-the-road decisions. Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making. How Monte Carlo simulation works: Monte Carlo simulation performs risk analysis by building models of possible results by substituting a range of values—a probability distribution—for any factor that has inherent uncertainty. It then calculates results over and over, each time using a different set of random values from the probability functions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens of thousands of recalculations before it is complete. Monte Carlo simulation produces distributions of possible outcome values. During a Monte Carlo simulation, values are sampled at random from the input probability distributions. Each set of samples is called iteration, and the resulting outcome from that sample is recorded. Monte Carlo simulation does this hundreds or thousands of times, and the result is a probability distribution of possible outcomes. In this way, Monte Carlo simulation provides a much more comprehensive view of what may happen. It tells you not only what could happen, but how likely it is to happen. Advantages Monte Carlo simulation provides a number of advantages over “single-point estimate” analysis: •
Probabilistic Results. Results show not only what could happen, but how likely each outcome is.
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Risk analysis is part of every decision we make. We are constantly faced with uncertainty, ambiguity, and variability. And even though we have unprecedented access to information, we can’t accurately predict the future. Monte Carlo simulation (also known as the Monte Carlo Method) lets you see all the possible outcomes of your decisions and assess the impact of risk, allowing for better decision making under uncertainty.
Financial Risk Management
Graphical Results. Because of the data a Monte Carlo simulation generates, it’s easy to create graphs of different outcomes and their chances of occurrence. This is important for communicating findings to other stakeholders.
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Sensitivity Analysis. With just a few cases, deterministic analysis makes it difficult to see which variables impact the outcome the most. In Monte Carlo simulation, it’s easy to see which inputs had the biggest effect on bottom-line results.
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Scenario Analysis: In deterministic models, it’s very difficult to model different combinations of values for different inputs to see the effects of truly different scenarios. Using Monte Carlo simulation, analysts can see exactly which inputs had which values together when certain outcomes occurred. This is very useful for pursuing further analysis.
Who uses Monte Carlo simulation? Many companies use Monte Carlo simulation as an important tool for decision-making. Here are some examples. General Motors, Procter and Gamble, and Eli Lilly use simulation to estimate both the average return and the riskiness of new products. At GM, this information is used by CEO Rick Waggoner to determine the products that come to market. GM uses simulation for activities such as forecasting net income for the corporation, predicting structural costs and purchasing costs, determining its susceptibility to different kinds of risk (such as interest rate changes and exchange rate fluctuations). Lilly uses simulation to determine the optimal plant capacity that should be built for each drug. Wall Street firms use simulation to price complex financial derivatives and determine the Value at RISK (VAR) of their investment portfolios. Procter and Gamble uses simulation to model and optimally hedge foreign exchange risk. Sears uses simulation to determine how many units of each product line should be ordered from suppliers — for example, how many pairs of Dockers should be ordered this year.
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