Please help the question 7

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 0.10.7. 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 = Er] - ;Ao, and your risk aversion coefficient is A = 4. (a) (5 points) Determine the proportion of each asset class in the portfolio that max- imizes 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. Hint. You will need to solve for the optimal weights that the maximize expected utility when fully invested in two risky assets. The process is similar to what we did to solve for the minimum-variance portfolio in class. (c) (5 points) Draw the following on the same graph: The efficient frontier, the minimum-variance portfolio, the tangency portfolio, the portfolio found in [7] and the portfolio found in 71. (d) (5 points) A feasible standard deviation - expected return pair, denoted by (o, E[r]), is one that can be obtained from some portfolio of the three classes of assets. Is (0.05, 0.12) a feasible standard deviation - expected return pair? Why or why not? If not, does there exist a feasible standard deviation - expected return pair that will offer you the same utility as that hypothetical portfolio