The following data apply to Problems 2 to 8: 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, and the third is a T-bill money market fund that yields a rate of 8%. The mean and the standard deviation of the risky funds is as follows:

	Expected Return	Standard Deviation
Stock fund (S)	20%	30%
Bond fund (B)	12%	15%

The correlation between the fund returns is 0.10.

Problem 2. What are the investment proportions in the minimum-variance portfolio of the two risky funds (i.e., stock and bond funds), and what is expected value and standard deviation of its rate of return?

Problem 3. Tabulate and draw the investment opportunity set of the two risky funds (i.e., the efficient frontier defined on the stock and bond funds). Use investment proportion for the stock fund of 0% to 100% in increments of 20%.

Problem 4. Solve for the weight of each risky fund and for the expected return and standard deviation of the optimal risky portfolio (i.e., the tangency portfolio constructed using the stock and bond funds). See the formula on slide #44 of the lecture handout entitled Portfolio Theory.

Problem 5. Draw the capital market line (i.e., the most efficient capital allocation line that is defined on the T-bill fund (or the risk-free asset) and the tangency portfolio. Note that expected return and standard deviation of the tangency portfolio are from your answers to problem 4. What is the Sharpe ratio of the capital market line, or the best feasible capital allocation line? How do you interpret the Sharpe ratio?

Problem 6. You require that your portfolio yield an expected return of 14%, and that it be the most efficient in terms of risk-return trade (i.e., on the best feasible CAL).

1. What is the standard deviation of your portfolio?
2. What is the proportion invested in the T-bill fund?

Problem 7. If you were to use only the two risky funds, and still require an expected return of 14%, what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimized portfolio in Problem 6. What do you conclude?

Problem 8. Your clients degree of risk aversion is A = 3.5. Given the utility function:

1. What proportion, y, of the total investment should be invested in the tangency portfolio so that your client can maximize his/her expected utility?
2. What is the expected value and standard deviation of the rate of return on your clients optimized portfolio?