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 sure rate of 4.5%. The probability distributions of the risky funds are:

Bond Fund Stock Fund

Expected return 8% 16.5%

Standard deviation 12% 42%

The correlation coefficient between the fund returns is 0.32

Required

1-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 10%.

Highlight the efficient frontier.

2-What expected return and standard deviation does your graph show for the minimum-variance portfolio?

3-Draw a tangent from the risk-free rate to the opportunity set. What does your graph show for the expected return and standard deviation of the optimal risky portfolio?

4-Suppose now that your portfolio must yield an expected return of 9% and be efficient, that is, on the best feasible CAL.

What is the standard deviation of your portfolio?

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

5-If you were to use only the two risky funds and still require an expected return of 9%, what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimal portfolio in question 4. What do you conclude?