You are a Morgan Stanley portfolio manager of a risky portfolio with an expected rate of return of 14% and a standard deviation of 25%. The T-bill rate is 4%. Suppose your client decides to invest in your risky portfolio a proportion (y) of his total investment budget so that his overall portfolio will have a standard deviation of 20%.

a. What is the proportion y? (sample answer: 25.45%)

b. What will be the expected return of your clients portfolio? (sample answer: 25.45%)

c. What is the Sharpe ratio of your clients portfolio? (sample answer: 0.25)

d. Suppose your client is wondering if he should switch his money in your fund to a passive portfolio invested to mimic the S&P 500 stock index yields an expected rate of return of 10% with a standard deviation of 24%. Show your client the maximum fee you could charge (as a percent of the investment in your fund deducted at the end of the year) that would still leave him at least as well off investing in your fund as in the passive one. (Hint: The fee will lower the slope of your clients CAL by reducing the expected return net of the fee.) (sample answer: 3.45%)