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 0.10.
1. 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%. What expected return and standard deviation does your graph show for the minimum-variance portfolio?
2. What is the reward-to-volatility ratio of the best feasible CAL?
3. Suppose now that your portfolio must yield an expected return of 12% and be efficient, that is, 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
4. If you were to use only the two risky funds and still require an expected return of 12%, what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimal portfolio in the previous problem. What do you conclude?