Consider the following two-factor model for the returns of three well-diversified assets (i.e., with no idiosyncratic...
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Consider the following two-factor model for the returns of three well-diversified assets (i.e., with no idiosyncratic risk): = 0.12 +6F₁ +4F2, 0.04 + 1F₁+2F2, 0.01 - 1F₁ + 3F2. ΤΑ TB = rc = (a) (10 points) Compute the expected return of factor replicating portfolio 1 (FRP1), the expected return of factor replicating portfolio 2 (FRP2), and the risk-free rate. [Note: Recall that FRP1 has b1,FRP1 = 1, b2,FRP1 = 0 and FRP2 has b₁,FRP2 = 0, b2,FRP2 = 1.] (b) (5 points) Assume that we have a new asset, asset D (also with no idiosyncratic risk), with exposures plus 1 to factor 1 (F₁) and plus 2 to factor 2 (F2). What is its expected return? (c) (5 points) Assume that the standard deviation of factor 1 is 11%, the standard deviation of factor 2 is 5%, and the standard deviation of D is 25%. Additionally, relax earlier assumption and assume D might have idiosyncratic risk. What the standard deviation of the idiosyncratic risk in portfolio D? Make sure you justify each step in this calculation. (d) (10 points) What are the Sharpe Ratios of assets FPR1, FRP2, and D? Consider the following two-factor model for the returns of three well-diversified assets (i.e., with no idiosyncratic risk): = 0.12 +6F₁ +4F2, 0.04 + 1F₁+2F2, 0.01 - 1F₁ + 3F2. ΤΑ TB = rc = (a) (10 points) Compute the expected return of factor replicating portfolio 1 (FRP1), the expected return of factor replicating portfolio 2 (FRP2), and the risk-free rate. [Note: Recall that FRP1 has b1,FRP1 = 1, b2,FRP1 = 0 and FRP2 has b₁,FRP2 = 0, b2,FRP2 = 1.] (b) (5 points) Assume that we have a new asset, asset D (also with no idiosyncratic risk), with exposures plus 1 to factor 1 (F₁) and plus 2 to factor 2 (F2). What is its expected return? (c) (5 points) Assume that the standard deviation of factor 1 is 11%, the standard deviation of factor 2 is 5%, and the standard deviation of D is 25%. Additionally, relax earlier assumption and assume D might have idiosyncratic risk. What the standard deviation of the idiosyncratic risk in portfolio D? Make sure you justify each step in this calculation. (d) (10 points) What are the Sharpe Ratios of assets FPR1, FRP2, and D?
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a The expected return of factor replicating portfolio 1 FRPI is 6b1FRPI 4b2FRPI 61 40 6 Th... View the full answer
Related Book For
Understanding Basic Statistics
ISBN: 9781111827021
6th Edition
Authors: Charles Henry Brase, Corrinne Pellillo Brase
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