Question 8 (Optimal complete portfolio 3pt) 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 8%. The probability distribution of the risky funds is as follows: Standard Deviation Expected Return 20% 12% Stock fund (S) Bond fund (B) The correlation between the fund returns is 0.1. 30% 15% 1. What are the investment proportions in the minimum-variance portfolio of the two risky funds, and what is the expected value and standard deviation of its rate of return? (0.5pt) 2. Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of 0% to 100% in increments of 20%. (0.5pt) 3. Draw a tangent from the risk-free rate to the opportunity set. What is the expected return and standard deviation of the tangent portfolio? (1pt) 4. You have risk aversion coefficient of 4, so your utility is 4 U = E[rp] - p. rp 2 What is the optimal complete portfolio that you will hold? Please give the portfolio weight on risk-free asset and the risky assets. (1pt)

Question 8 (Optimal complete portfolio 3pt) 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 8%. The probability distribution of the risky funds is as follows: The correlation between the fund returns is 0.1. 1. What are the investment proportions in the minimum-variance portfolio of the two risky funds, and what is the expected value and standard deviation of its rate of return? (0.5pt) 2. Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of 0% to 100% in increments of 20%. (0.5pt) 3. Draw a tangent from the risk-free rate to the opportunity set. What is the expected return and standard deviation of the tangent portfolio? (1pt) 4. You have risk aversion coefficient of 4 , so your utility is U=E[rP]24rP2. What is the optimal complete portfolio that you will hold? Please give the portfolio weight on risk-free asset and the risky assets. (1pt)