A manager of Black Hills pension fund is considering three mutual funds. He can only invest in two risky assets (the first one is a stock fund, and the second one is a long-term government and corporate bond fund), and one risk-free asset (a T-bill money market fund) because of restrictions in his company. The yield of a T-bill money market fund is 5.5%. The characteristics of two risky funds are as follows:

	Expected Return	Standard Deviation
Stock fund (S)	15%	32%
Bond fund (B)	9%	23%

The correlation between the fund returns is 0.15, and he try to figure out the expected portfolio return and standard deviation for the various investment opportunity sets.

a. What is the proportion invested in the minimum-variance portfolio? (5 points)

b. What is the mean and standard deviation of the minimum variance portfolio? (5 points)

c. Now, he would like to create a portfolio that includes two risky funds and a T-bill money market fund. What is the Sharpe ratio of a stock fund portfolio, bond fund portfolio, and minimum-variance portfolio? (8 points)

d. What is the expected return and standard deviation of the optimal risky portfolio (tangency portfolio)? What is the Shape ratio of the optimal CAL? (10 points)

e. Suppose now that his portfolio must yield an expected return of 12% and be efficient, that is, on the best feasible CAL.

What is the standard deviation of this portfolio? (10 points)

What is the proportion invested in the T-bill fund and each of the two risky funds? (10 points)