Problem 1 (30 pts)

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. What are the investment proportions of the minimum-variance portfolio of the two risky funds, and what is the expected value and standard deviation of its rate of return? (4pts)