An administrator of an annuity agency is considering three mutual funds for investment. The first is stock funds, the second is long-term government bonds and bond funds, and the third is T-bill money market funds, which provide a firm yield of 5.5 percent. The probability distribution of these risk funds is as follows. The correlation between fund yields is 0.15.

8. Minimum diversified portfolios of the two risk funds

Make a table and draw a picture. Suppose that the investment ratio of stock funds increases by 20 percent from 0 percent to 100 percent. The expected rate of return and standard deviation of the minimum dispersion portfolio are shown in the graph.

9. Draw a tangent line from the risk-free return to the investment opportunity set. What does the graph show about the expected returns and standard deviations of the optimal risk portfolio?

10. What is the percentage of the sharpest possible CAL?

11. From now on, your portfolio should be efficient with an expected return of 12%. In other words, suppose that it should be on the most feasible CAL.

a) What is your portfolio standard deviation?

b) What is the ratio of investment in each of the T-bill funds and the two risk funds?

12. If investors can only use two risk funds and still demand an expected return of 12%, what should happen to their portfolio investment ratios? Compare the standard deviation of this portfolio with the standard deviation of the best portfolio in the previous problem. What is the conclusion?

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