Discuss the differences between the expected return estimates from the single-factor model and those from the multifactor model. Which estimates are most likely to be more useful in practice? What sort of exposure might MACRO2 represent? Given the estimated factor betas, is it really reasonable to consider it a common (i.e., systematic) risk factor? 5. Suppose that three stocks (A, B, and C) and two common risk factors (1 and 2) have the following relationship: E(RA ) = (1.1)λ1 + (0.8)λ2 E(RB) = (0.7)λ1 + (0.6)λ2 E(RC) = (0.3)λ1 + (0.4)λ2 If λ1 = 4% and λ2 = 2%, what are the prices expected next year for each of the stocks? Assume that all three stocks currently sell for $30 and will not pay a dividend in the next year. Suppose that you know that next year the prices for Stocks A, B, and C will actually be $31.50, $35.00, and $30.50. Create and demonstrate a riskless, arbitrage investment to take advantage of these priced securities. What is the profit from your investment? You may assume that you can use the proceeds from any necessary short sale. 7. a. Using regression analysis, calculate the factor betas of each stock associated with each of the common risk factors. Which of these coefficients are statistically significant? b. How well does the factor model explain the variation in portfolio returns? On what basis can you make an evaluation of this nature? c. Suppose you are now told that the three factors in Exhibit 9.12 represent the risk exposures in the Fama-French characteristic-based model (i.e., excess market, SMB, and HML.) Based on your regression results, which one of these factors is the most likely to be the market factor? Explain why. d. Suppose it is further revealed that Factor 3 is the HML factor. Which of the two portfolios is most likely to be a growth-oriented fund and which is a value-oriented fund? Explain why. CHAPTER 10
Discuss the differences between the expected return estimates from the single-factor model and those from the multifactor model. Which estimates are most likely to be more useful in practice? What sort of exposure might MACRO2 represent? Given the estimated factor betas, is it really reasonable to consider it a common (i.e., systematic) risk factor? 5. Suppose that three stocks (A, B, and C) and two common risk factors (1 and 2) have the following relationship: E(RA ) = (1.1)λ1 + (0.8)λ2 E(RB) = (0.7)λ1 + (0.6)λ2 E(RC) = (0.3)λ1 + (0.4)λ2 If λ1 = 4% and λ2 = 2%, what are the prices expected next year for each of the stocks? Assume that all three stocks currently sell for $30 and will not pay a dividend in the next year. Suppose that you know that next year the prices for Stocks A, B, and C will actually be $31.50, $35.00, and $30.50. Create and demonstrate a riskless, arbitrage investment to take advantage of these priced securities. What is the profit from your investment? You may assume that you can use the proceeds from any necessary short sale. 7. a. Using regression analysis, calculate the factor betas of each stock associated with each of the common risk factors. Which of these coefficients are statistically significant? b. How well does the factor model explain the variation in portfolio returns? On what basis can you make an evaluation of this nature? c. Suppose you are now told that the three factors in Exhibit 9.12 represent the risk exposures in the Fama-French characteristic-based model (i.e., excess market, SMB, and HML.) Based on your regression results, which one of these factors is the most likely to be the market factor? Explain why. d. Suppose it is further revealed that Factor 3 is the HML factor. Which of the two portfolios is most likely to be a growth-oriented fund and which is a value-oriented fund? Explain why. CHAPTER 10