19.Carrie Marcel, CFA, has long used the Capital Asset Pricing Model (CAPM) as an investment tool. Marcel has recently begun to appreciate the advantages of arbitrage pricing theory (APT) She used reliable techniques and data to create the following two-factor APT equation: E(RP) = 6.0% + 12.0%βp,ΔGDP – 3.0%βp,ΔINF . Where ΔGDP is the change in GDP and ΔINF is the change in inflation. She then determines the sensitivities to the factors of three diversified portfolios that are available for investment as well as a benchmark index. Portfolio
| Sensitivity to ΔGDP
| Sensitivity to ΔINF
| Q | 2.00 | 0.75 | R | 1.25 | 0.50 | S | 1.50 | 0.25 | Benchmark Index | 1.80 | 1.00 |
Marcel is investigating several strategies. She decides to determine how to create a portfolio from Q, R, and S that only has an exposure to ΔGDP. She also wishes to create a portfolio out of Q, R, and S that can replicate the benchmark. Marcel also believes that a hedge fund, which is composed of long and short positions, could be created with a portfolio that is equally weighted in Q, R, S and the benchmark index. The hedge fund would produce a return in excess of the risk-free return but would not have any risk. All of the following statements describe characteristics of the Arbitrage Pricing Theory (APT) and the Capital Asset Pricing Model (CAPM) EXCEPT:
A) the APT is more flexible than the CAPM because it allows for multiple factors. B) under the framework of CAPM, investors who are more risk averse should hold less of the market portfolio and more of the risk-free asset. C) both models assume firm-specific risk can be diversified away. D) both models require the ability to invest in the market portfolio. The correct answer was D) The CAPM can be thought of as a subset of the APT, multifactor model. Therefore, fewer assumptions are needed for the APT model than the CAPM. Although it could be included as a factor, the APT does not require an investment in the market portfolio. APT can be thought of as a k factor model, while the CAPM is based on the risk-free asset and the market portfolio. 20.What is the APT expected return on a factor portfolio exposed only to ΔGDP? A) 12.0%. B) 18.0%. C) 15.0%. D) 3.0%. The correct answer was B) A factor portfolio is a portfolio with a factor sensitivity of one to a particular factor and zero to all other factors. The expected return on a “factor 1” portfolio is E(RR) = 6.0% + 12.0% (1.00) - 3.0%(0.00) = 18.0%. 21.Jennifer Watkins, CFA, is a portfolio manager at Q-Metrics. She has derived a 2-factor arbitrage pricing theory (APT) model of expected returns she intends to use in her portfolio management strategies. The two-factor APT equation, in which the two factors are confidence risk and industrial production, is: E(RP) = RT-bill + 0.06βp,CONF + 0.09βp,PROD Watkins determines the sensitivity to each of the two factors for three diversified portfolios as well as for her benchmark, the Wilshire 5000. The results of her analysis are shown in the table below. Portfolio | Sensitivity to Conf. Risk Factor | Sensitivity to Indust. Prod. Factor | J | 1.50 | 1.00 | K | 0.80 | 1.20 | L | 1.00 | 2.00 | Wilshire 5000 | 1.00 | 1.50 |
βp,CONF: a market confidence factor βp,PROD: industrial production factor RT-bill: the Treasury bill rate of return, assumed equal to 4%. Watkins compares her data and results to that of a colleague who uses the CAPM to analyze the same portfolios. She determines that her analysis is more appropriate for the given portfolios. What is the expected return on Portfolio K according to the APT equation? A) 19.6%. B) 22.0%. C) 18.4%. D) 15.6%. The correct answer was A) The β's in the APT equation are the factor sensitivities. The expected return on portfolio K is E(RK) = 0.04 + 0.06(0.80) + 0.09(1.20) = 19.6%. 22.Which of the following would be a valid reason for concluding that the APT analysis of Watkins is more appropriate than the CAPM analysis of her colleague? A) Investors can borrow and lend at the risk-free rate. B) The security returns have a kurtosis equal to three. C) Investors have quadratic utility functions. D) The APT model is less restrictive than the CAPM. The correct answer was D) The true market portfolio contains all securities. The CAPM is a more restrictive model and requires that such a portfolio be mean/variance efficient while the APT does not. The Wilshire 5000 is a very diversified portfolio, but it does not contain all securities. 23.Which of the following is NOT one of the three equations needed to solve for the Industrial Production factor portfolio combination of J, K and L? A) wJ + wK + wL = 1 B) 1.50wJ + 0.80wK + 1.00wL = 0. C) 1.00wJ + 1.20wK + 2.00wL = 1. D) 1.50wJ + 1.20wK + 2.00wL = 0. The correct answer was D) A factor portfolio has a sensitivity of one to one factor and a sensitivity of zero for all other factors (in this case, a pure bet on industrial production). We need to create a factor portfolio (a combination of portfolios J, K and L) that has a factor sensitivity of zero to the confidence risk factor and a sensitivity of one to the industrial production factor. The three simultaneous equations to solve are: Eq. 1: wJ + wK + wL = 1 (portfolio weights sum to 1) Eq. 2: 1.50wJ + 0.80wK + 1.00wL = 0 (confidence risk portfolio sensitivity equals 0) Eq. 3: 1.00wJ + 1.20wK + 2.00wL = 1 (production portfolio sensitivity equals 1) 24.Given a three-factor arbitrage pricing theory APT model, what is the expected return on the Freedom Fund? §
The factor risk premiums to factors 1, 2, and 3 are 10%, 7% and 6%, respectively. §
The Freedom Fund has sensitivities to the factors 1, 2, and 3 of 1.0, 2.0 and 0.0, respectively. §
The risk-free rate is 6.0%. A) 30.0%. B) 24.0%. C) 33.0%. D) 36.0%. The correct answer was A) The expected return on the Freedom Fund is 6% + (10.0%)(1.0) + (7.0%)(2.0) + (6.0%)(0.0) = 30.0%. 25.An arbitrage pricing theory (APT) model has the following characteristics: §
The risk free rate is 3.8 percent. §
Factor risk premiums are: A. (7 percent) B. (4 percent) C. (2 percent) D. (10 percent) Assume Silver Linings Fund has the following sensitivities to the factors: §
Sensitivity to A is 0.5. §
Sensitivity to B is 1.2. §
Sensitivity to C is 2.1. §
Sensitivity to D is 0.2. The expected return on the Silver Linings Fund is: A) 14.5 percent. B) 20.1 percent. C) 18.3 percent. D) 16.8 percent. The correct answer was C) E(R) = 3.8 + (0.5 * 7) + (1.2 * 4) + (2.1 * 2) + (0.2 * 10) = 18.3. | 
发表于 2008-4-16 14:49
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