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You are currently 100% invested in the S&P500. You are evaluating two trading strategies. You have historical data on the returns to these strategies and the S&P500. After analyzing the data you come up with the following estimated quantities ("1" refers to the first strategy, "2" refers to the second strategy, rf is the risk-free rate and S&P refers to the S&P500):
E(r1) = 15% σ1 = 0.50 ρ1, S&P = 0.35 E(r2) = 6% σ2 = 0.30 ρ2,S&P = 0.25 ρ1,2 = 0.4 E(rS&P ) = 12% σS&P = 0.15 rf = 5%
(a) Let's examine how the CAPM performs when using the S&P500 as a proxy for the market portfolio. What are the alphas and betas of the two strategies?
(b) Recall that you are currently holding the S&P500. Describe in words how you would adjust your portfolio in response to the alphas calculated in part (a)?
(c) Find a combination of the two strategies that would make you react to market risk the way S&P 500 does. What is the expected return to this portfolio? What is the alpha of this portfolio? What is the idiosyncratic risk of the portfolio?
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