You are an investor with mean-variance preferences and a risk-aversion coefficient of A. You have the following three investment options to choose from. The first is a growth fund, the second is a value fund, and the third is a T-bill money market fund that yields a rate of 6%. The probability distribution of the risky funds is as follows: Expected return Standard deviation 25% 8% Growth fund (S) Value fund (B) 40% 16% The correlation between the fund returns is 0.20. (a) (6 points) Determine the proportion of each asset class of the optimal risky port- folio. (b) (6 points) Suppose A = 3. Determine the proportion of each asset class in the portfolio that maximizes your expected utility. (c) (6 points) Suppose A = 3. Determine the proportion of each asset class in the portfolio that maximizes your expected utility if you're only allowed to invest in the risky funds. (d) (6 points) Suppose A = 3. For this question only, suppose that your portfolio is not allowed to have a standard deviation of more than 10%. Determine the proportion of each asset class in the portfolio that maximizes your expected utility in this case. Calculate the expected utility obtained from this portfolio. How much expected utility is lost compared to the expected utility given by the portfolio in 1b? (e) (6 points) Suppose A = 3. Determine the proportion of each asset class in the portfolio that satisfies all of the following conditions: i. it gives you the same expected utility as the portfolio found in 1c ii. it has the best Sharpe ratio possible, iii. and it has the smallest risk. (f) (6 points) Suppose that the portfolio that maximizes your expected utility has either zero or a short position in the risk-free bond. Find the maximum value that your risk-aversion coefficient A can be.