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 sure rate of 5.5%. The probability distributions of the risky funds are:
Expected Return Standard Deviation
Stock fund (S) 15% 32%
Bond fund (B) 9% 23%
The correlation between the fund returns is 0.15.
a. 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?
b. 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 risky portfolio?
c. What is the reward-to-volatility ratio of the best feasible CAL?
d. Suppose now that your portfolio must yield an expected return of 12% and be efficient, that is, 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?
e. 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 (d). What do you conclude?