A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a risk-free rate (for this question, assume that the T-bill fund is a risk-free investment). The return characteristics are the following:

a. [4pts] What are the investment proportions in the minimum variance portfolio (MVP) of the two risky funds, and what are the expected value and standard deviation of its rate of return? What is the Sharpe ratio of the portfolio?

b. [4pts] Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. What is the Sharpe ratio of the tangency portfolio?

c. [5pts] A client requires that her portfolio yields an expected return of 15%, and that it be efficient, on the best feasible capital allocation line. What is the standard deviation of her portfolio? What is the proportion invested in the T-bill fund and each of the two risky funds?

d. [4pts] A client requires that her portfolio give her the greatest utility and that it be efficient, on the best feasible capital allocation line. Her utility function is U(,) = 1/2 2, where her risk aversion is 4. What is the proportion invested in the T-bill fund and each of the two risky funds?

Asset Expected return Stock fund (S) 25% Bond fund (B) 10% Riskless Asset 3% Correlation(B, S) = 0.6 Standard deviation 40% 20%