Introduction to Multifactor Models – Question Bank
LO.a: Describe arbitrage pricing theory (APT), including its underlying assumptions and its relation to multifactor models.
1. Which of the following statements about arbitrage pricing theor y (APT) is most likely likely true? A. APT represents an asset’s risk as a linear function of factors representing unsystematic risk. B. The number of underlying factors in APT is fixed. C. A key assumption of APT is that there are many investable assets such that asset specific risk can be diversified. LO.b: Define arbitrage opportunity and determine whether an arbitrage opportunity exists.
2. An arbitrage opportunity is: A. a transaction that generates a risk-free return as a guaranteed pay-off. B. a transaction that is risk-free and requires no net investment of mo ney but earns an expected positive net profit. C. a transaction that earns a return in excess of the risk-free rate with minimal risk. 3. The one year futures of DMX Co. are selling at $11. The current stock price is $10 and the risk-free rate is 8%. There are no further costs or benefits of holding the future contracts. John Harper is considering shorting futures. Which of the following statements is most likely likely true? A. There exists an arbitrage opportunity as the transaction will yield a return higher than the risk-free rate without assuming any risk. B. There is no arbitrage opportunity because the transaction does not yield a return higher than the risk-free rate. C. There is no arbitrage opportunity because the transaction is not risk-free. LO.c: Calculate Calculate the expected return on an asset given an asset’s factor sensitivities and the factor risk premiums.
4. The following table shows the factor sensitivities and expected returns of three welldiversified portfolios each sensitive to the same factor: Portfolio A B C
Factor Sensitivity 0.5 -0.6 0.7
Expected Return 6.5% 3.2% 7.1%
Assuming a single factor explains returns and no arbitrage a rbitrage opportunity exists, a risk-free rate of 5%, the factor risk premium of is closest to: to: A. 3.0%. B. 5.1%. C. 11.4%.
Introduction to Multifactor Models – Question Bank
5. Belta Inc. has an expected return of 9%. The risk-free rate is 3%. The only factor representing systematic risk is Factor X with an expected return of 5%. The company’s sensitivity to Factor X is closest to: A. 0.0 B. 1.2 C. 1.0 LO.d: Describe and compare macroeconomic factor models, fundamental factor models, and statistical factor models.
6. Which of the following statements regarding multi factor models is most likely most likely true? A. Fundamental factor models present sensitivities of the company to external economic factors that affect its fundamentals B. Factor analysis models and principal component models mode ls are instances of fundamental factor models C. Macro-economic factor model includes factors such as interest rates and in flation 7. A potential difference between macroeconomic factor models and an d fundamental factor models is that: A. macroeconomic factor models explain past returns whereas fundamental factor models explain expected return. B. macroeconomic factor models use regression to estimate sensitivities whereas fundamental factor models do not use regression. C. in macroeconomic models the factor is stated as a surprise whereas in fundamental factor models the factor is stated as a return. LO.e: Explain sources of active risk and interpret tracking risk and the information ratio.
8. Active risk is due to: A. different-from-benchmark exposures relative to factors specified in the risk model only. B. different-from-benchmark weights on individual assets only. C. both different-from-benchmark exposures to factors in the model and different-fromdifferent-from benchmark weights of individual assets. 9. The active risk decomposition of two portfolios, po rtfolios, A and B is given below: Portfolio
Active Factor Active Specific Industry Style factor A 15 10 17 B 5 8 2 Note: Entries are in % squared Which of the following statements is most likely true? A. Style factor contributed more to Portfolio B’s active risk than Portfolio A. B. Portfolio B’s active risk is higher than that of portfolio A. C. The low active specific risk of portfolio B suggests a passively managed portfolio.
Introduction to Multifactor Models – Question Bank
10. The track record of three fund managers is given below: Average Active return Tracking Error Fund Manager A 5% 2% Fund Manager B 2% 1% Fund Manager C 6% 4% Based on the data, which fund manager has the best risk-adjusted record? A. Fund Manager A. B. Fund Manager B. C. Fund Manager C. LO.f: Describe uses of multifactor models and interpret the output of analyses based on multifactor models.
11. Which of the following statements regarding multifactor models is most likely likely true? A. Multifactor models can be used to predict alpha in passively managed portfolios. B. Factor models have sensitivity of -1 to a particular pa rticular factor and 0 to all other factors. C. Multifactor models can be used to replicate a be nchmark’s risk exposures for a passively managed portfolio. LO.g: Describe the potential benefits for investors in considering multiple risk dimensions when modeling asset returns.
12. Which of the following is least likely mod eling asset least likely a benefit of using multifactor models in modeling returns? A. Investors can better analyze their comparative advantage in bearing risk. B. Investors can achieve better-diversified bet ter-diversified portfolios. C. Investors can determine the optimum allocation between a risk-free asset and market portfolio.
Introduction to Multifactor Models – Question Bank Solutions
1. C is correct. APT explains an asset ’s return based on factors representing systematic risk only. It assumes that asset specific risk can be diversified away. Section 3. 2. B is correct. An arbitrage opportunity is an opportunity to conduct a transaction that is risk-free and requires no net investment of money but earns ea rns an expected positive net profit. Section S ection 3. 3. A is correct. Buying the stock and shorting the futures gives a guaranteed return of 10% i.e. 11/10 -1 = 10%. The R F rate is 8%. The transaction gives a pay-off, i.e. risk-free. As the expected return is higher than the R F rate, an arbitrage opportunity exists. Section 3. 4. A is correct. Because the single factor explains returns, E(R p p) = R F + 0.5 x factor risk premium (λ ) given E(R A) = 0.065 = 0.05 + 0.5(λ). λ = (0.065 - 0.05)/0.5 = 0.03 = 3%. Section 3. 5. B is correct. 9% = 3% + Factor sensitivity (5%). Factor sensitivity is therefore 1.2. Section 3. 6. C is correct. Macroeconomic models represent asset returns correlated to surprises in some factors related to macroeconomic variables. These include interest rates, inflation risk, business cycle risk, GDP growth etc. Section 4.1.
7. C is correct. In macro-economic models the factor is stated as a surprise whereas in fundamental factor models the factor is stated as a return. Section 4.3. 8. C is correct. Active risk has two components: 1) active a ctive factor risk which is the risk due to portfolio’s different-from-benchmark exposures relative to factors specified in the risk model and 2) asset selection risk which is the risk resulting from the portfolio’s active weights o f individual assets. Section 5.2. 9. A is correct. Style contributed 10/42 = 23.8% 23 .8% to portfolio A’s active risk and 8/15=53.3% to portfolio B’s active risk. Section 5.2. 10. A is correct. Fund Manager A’s IR (information (information ratio) is 5/2 = 2.5, Fund Manager B’s IR is 2/1 = 2 and Fund Manager C’s IR is is 6/4 = 1.5. Fund Manager A has the highest IR. Section 5.2. 11. C is correct. Multifactor models can be used to replicate re plicate risk exposures of a benchmark for a passively managed portfolio when number of stocks in a benchmark may be too high or investing in all stocks is not possible. Section 5.3. 12. C is correct. Multifactor models do not provide an optimum allocation rather they are used to understand the varying sources of risk in a portfolio. portfolio. This can lead to more efficient efficient portfolios. Section 5.4.
