A pension fund manager is considering four mutual funds. The first is a US stock fund, the second a long-term government and corporate bond fund, the third is a commodity funds, and the fourth a T-bill money market fund that yields a rate of 6%. You know the following information about the risky funds:

Expected return (ER) Standard deviation (SD)

Stock Fund (S) - ER-16% , SD -25%

Bond fund (B): ER- 12% , SD- 15%

Commodity fund (C) ER- 10% , SD-10%

The correlation between the stock and fund return is 0.4. The correlation between the stock and commodity return is 0.1. The correlation between the bond and commodity return is 0.2.

a. What are the investment proportions in the minimum-variance portfolio of the three risky funds, and what is the expected value and standard deviation of its rate of return?

b. What are the proportions of each asset and the expected return and standard deviation of the tangency portfolio?

c. What is the Sharpe ratio of the best feasible CAL?

d. You require that your portfolio yields an expected return of 11%, and that it be efficient, on the best feasible CAL. What is the proportion invested in the T-bill fund and each of the three risky funds? What it the standard deviation of your portfolio?

e. Youre risk aversion coefficient is 6 and your preferences are described by quadratic utility function. What is an optimal portfolio weights if you can invest both in risky and risk-free assets?

f. If you were to use only the three risky funds, and still require an expected return of 11%, what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimized portfolio in 1d). What do you conclude?