(a) Explain why it is difficult to estimate correct Sharpe ratios for funds when the fund manager engages in market timing where he moves the fund’s capital in and out of risky assets often?

(b) You are given the following data. Fund Average return Standard deviation Beta Risk free asset 3% 0 0 Market index 8% 30% 1 Portfolio A 12% 50% 1.4 Portfolio B 9% 30% 1.2 Are the data in the table reasonable? What is the Sharpe ratio and the Treynor ratio for A and B? Would you recommend these two portfolios to investors? 

(c) You are given the following data on 4 stocks A, B, C, and D. Stock Beta Total variance A 1.2 0.12 B 1.2 0.12 C 1.2 0.12 D 1.2 0.2 The total variance of the market portfolio is 0.09. Assume the idiosyncratic risk is independent across the four stocks. What portfolio consisting of the four stocks has the smallest total variance? What is the idiosyncratic risk of this portfolio?