Question

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 rate of 8%. The probability distribution of the risky funds is as follows:

Expected Return Standard Deviation

Stock fund (S) 20% 30%

Bond fund (B) 12% 15%

The correlation between the fund returns is .10.

1. What are the investment proportions in the minimum-variance portfolio of the two risky funds, and what is the expected value and standard deviation of its rate of return?

2. Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of 0% to 100% in increments of 20%.

3. Draw a tangent from the risk-free rate to the opportunity set. What does your graph show for the expected return and standard deviation of the optimal portfolio?

4. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio.

5. What is the Sharpe ratio of the best feasible CAL?

6. You require that your portfolio yield an expected return of 14%, and that it be efficient, on the best feasible CAL.

a. What is the standard deviation of your portfolio?

b. What is the proportion invested in the T-bill fund and each of the two risky funds?

Answer 1