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 2%. The expected return of stock fund and bond fund are 28% and 12%, respectively. The standard deviations of stock fund and bond fund are 30% and 18% respectively. The correlation between the fund returns is 0.35. Assume you have a quadratic utility in the form of [ = ( ) ] and a risk aversion coefficient equal to 4.

1. In this question, assume you are to invest in the stock fund and bond fund only (the two risky funds only). Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio that will maximize your utility. What will be your utility? (5pts)
2. If you require that your portfolio has 30% invested in the stock fund and that it be efficient, on the best feasible CAL. What is the rate of return of your portfolio? What is the standard deviation of your portfolio? What is the proportion invested in the T-bill fund and the bond funds?
3. If you require that your portfolio maximizes your utility and that it be efficient, on the best feasible CAL. What is the rate of return of your portfolio? What is the standard deviation of your portfolio? What is the proportion invested in the T-bill fund and each of the two risky funds? What will be your utility?