Please show all your calculations. Problem 1 (33 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 3.5%. The expected return of stock fund and bond fund are 32% and 12%, respectively. The standard deviations of stock fund and bond fund are 35% and 20% respectively. The correlation between the fund returns is 0.42. Assume you have a quadratic utility in the form of [U=E(rP)21AP2] and a risk aversion coefficient equal to 3 . a) 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) b) 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)