Problem 3. The following data apply to the problems below. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term govern- ment 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 in 0.10.

Suppose that you can invest in the three mutual funds as an individual investor. Sup- pose further that you have a mean-variance utility function, U = E[r] 0.5 A^2 , and your risk aversion coefficient is A = 4.

(a)(5 points) Determine the proportion of each asset class in the portfolio that maximizes your expected utility.

(b)(5 points) Determine the proportion of each asset class in the portfolio that max- imizes your expected utility if you're only allowed to invest in the risky funds.