[Chapter 7: Very challenging. Try your best but don't be frustrated if you cannot get the right answers for some questions] A pension fund manager is...

1.    [Chapter 7: Very challenging. Try your best but don't be frustrated if you cannot get the right answers for some questions] 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 rate of 8%. The probability distribution of the risky funds is as follows:

The correlation between the fund returns is .10.

a.      The proportions of the stock fund and the bond fund in the optimal risky portfolio are 45.16% and 54.84%, respectively. Solve numerically for the expected return and standard deviation of the optimal risky portfolio.

b.     What is the Sharpe ratio of the tangent CAL?

c.      You require that your portfolio yield an expected return of 14%, and that it lies on the tangent 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?

d.     If you were to use only the two risky funds, and require an expected return of 14%, what would be the investment proportions of your portfolio?