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 percent. 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 0.10.

1. What are the investment proportions of the minimum-variance portfolio of the two risky funds, and what is the expected value and standard deviation of its rate of return?
2. Solve numerically for the proportions of each of the assets and for the expected return and standard deviation of the optimal risky portfolio.
3. What is the reward-to-variability ratio of the best feasible CAL?
4. You require that your portfolio yield an expected return of 14 percent and be efficient on the best feasible CAL.
   1. What is the standard deviation of your portfolio?
   2. What is the proportion invested in the T-bill fund and each of the two risky funds?
5. If you were to use only the two risky funds and will require an expected return of 14 percent, what must be the investment proportions of your portfolio? (Compare its standard deviation to that of the optimized portfolio in question 4.)

Answer 1