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Problem Set #7 1. (a) (b) (c) (d) In a multifactor APT model, the coefficients on the macro factors are often called: systemic risk. firm-specific risk. idiosyncratic risk. factor betas. 2. Consider the multifactor APT with two factors. Stock A has an expected return of 17.6%, a beta of 1.45 on factor 1, and a beta of .86 on factor 2. The risk premium on the factor 1 portfolio is 3.2%. The risk-free rate of return is 5%. What is the risk-premium on factor 2 if no arbitrage opportunities exist? (a) 9.26% (b) 3% (c) 4% (d) 7.75% 3. The exploitation of security mispricing in such a way that risk-free economic profits may be earned is called (a) arbitrage. (b) capital asset pricing. (c) factoring. (d) fundamental analysis. (e) none of the above. 4. Consider the one-factor APT. The variance of returns on the factor portfolio is 6%. The beta of a well-diversified portfolio on the factor is 1.1. The variance of returns on the welldiversified portfolio is approximately (a) 3.6% (b) 6.0% (c) 7.3% (d) 10.1% 5. Consider the multifactor APT with two factors. Stock A has an expected return of 16.4%, a beta of 1.4 on factor 1 and a beta of .8 on factor 2. The risk premium on the factor 1 portfolio is 3%. The risk-free rate of return is 6%. What is the risk-premium on factor 2 if no arbitrage opportunities exist? (a) 2% (b) 3% (c) 4% (d) 7.75% 6. Suppose that two factors have been identified for the U.S. economy: the growth rate of industrial production, IP, and the inflation rate, IR. IP is expected to be 3%, and IR 4.0%. A stock with a beta of 1.4 on IP and 0.9 on IR currently is expected to provide a rate of return of 10%. If industrial production actually grows by 7%, while the inflation rate turns out to be 5.0%, what is your revised estimate of the expected rate of return on the stock? (Do not round intermediate calculations. Round your answer to 1 decimal place. Omit the "%" sign in your response.) 7. Assume that security returns are generated by the single-index model, Ri = i + iRM + ei where Ri is the excess return for security i and RM is the market's excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security A 0.9 B 1.2 C 1.5 i 9% 12 15 E(Ri) 22% 8 17 (ei) a. If M = 18%, calculate the variance of returns of securities A, B, and C. (Do not round intermediate calculations. Round your answers to the nearest whole number.) b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number. Omit the "%" sign in your response.) 8. Consider the following multifactor (APT) model of security returns for a particular stock. Factor Inflation Industrial production Oil prices Factor Beta 1.5 1.0 0.5 Factor Risk Premium 6% 7 5 a. If T-bills currently offer a 6% yield, find the expected rate of return on this stock if the market views the stock as fairly priced. (Do not round intermediate calculations. Round your answer to 1 decimal place. Omit the "%" sign in your response.) b. Suppose that the market expected the values for the three macro factors given in column 1 below, but that the actual values turn out as given in column 2. Calculate the revised expectations for the rate of return on the stock once the "surprises" become known. (Do not round intermediate calculations. Round your answer to 1 decimal place. Omit the "%" sign in your response.) Factor Inflation Industrial production Oil prices Expected Rate of Change 8% 6 5 Actual Rate of Change 6% 9 0 9. Suppose that the market can be described by the following three sources of systematic risk with associated risk premiums. Factor Industrial production (I) Interest rates (R) Consumer confidence (C) Risk Premium 6% 4 5 The return on a particular stock is generated according to the following equation: r = 14% + 1.2I + 0.6R + 0.80C + e a-1. Find the equilibrium rate of return on this stock using the APT. The T-bill rate is 4%. (Do not round intermediate calculations. Omit the "%" sign in your response.) a-2. Is the stock over- or underpriced? 10. Assume that security returns are generated by the single-index model, Ri = i + iRM + ei where Ri is the excess return for security i and RM is the market's excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security A B C i 0.8 1.0 1.2 E(Ri) 10% 12 14 (ei) 25% 10 20 a. If M = 20%, calculate the variance of returns of securities A, B, and C. (Do not round intermediate calculations. Round your answers to the nearest whole number.) b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number. Omit the "%" sign in your response.)