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 4.4%. The probability distributions of the risky funds are:
Expected Return Standard Deviation
Stock fund (S) 14% 34%
Bond fund (B) 5% 28%
The correlation between the fund returns is .14.
a) Solve the proportions of each asset and the expected return and standard deviation of the optimal risky portfolio. What is the reward-to-volatility ratio of the best feasible CAL?
b) Suppose now that your portfolio must yield an expected return of 13% and be efficient, that is, on the best feasible CAL.
b1). What is the standard deviation of your portfolio?
b2) What is the proportion invested in the T-bill fund and each of the two risky funds?
c) If you were to use only the two risky funds and still require an expected return of 13%, 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?