Please show all your calculations. Problem 1 (30 pts) A pension fund manager is considering three mutual funds. The rst is a stock fund, the second is a long-term government and corporate bond fund, and the third is a Tbill money market fund that yields a rate of 2%. The expected return of stock fund and bond nd are 28% and 12%, respectively. The standard deviations of stock nd and bond Jnd are 30% and 18% respectively. The correlation between the fund returns is 0.35. Assume you have a quadratic utility in the form of [U = E(rp) EA 0%] and a risk aversion coefficient equal to 4. a) b) g) 11) What are the investment proportions of the minimumvariance portfolio of the two risky funds, and what is the expected value and standard deviation of its rate of return? (4pts) 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? (Spts) Solve numerically for the proportions of each asset and for the expected return and standard deviation of the Optimal risky portfolio \"P\" for the best feasible CAL (the line extending from the riskfree rate and that is tangent to the opportunity set). What is the slope of the best feasible CAL? Draw the CAL. Indicate on the graph the Optimal risky portfolio 'P'. (8pts) If you require that your portfolio yield an expected return of 20 percent and that it be efcient, on the best feasible CAL. What is the standard deviation of your portfolio? What is the preportion invested in the Tbill md and each of the two risky funds? (4pts) If you require that your portfolio has 30% invested in the stock fund and that it be efcient, 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? (4pts) If you require that your portfolio maximizes your utility and that it be efcient, 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 Tbill fund and each of the two risky funds? What will be your utility? (4pts) Suppose your risk aversion is 3 instead of 4. If you require that your portfolio maximizes your utility and that it be efcient, on the best feasible CAL. What is the rate of return of your portfolio? What is the stande deviation of your portfolio? What is the proportion invested in the Tbill fund and each of the two risky mds? What will be your utility? (4pts) Compare the percentages invested in the stock fund estimated in question 'f' and ' g'. What can you conclude? (Zpts)