Question

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 5.5%. The probability distributions of therisky funds are:

	Expected return	Standard Deviation
Stock Fund (S)	15%	32%
Bond Fund (B)	9	23

The correlation between the fund returns is .15.

If you were to use only the two risky funds and still require an expected return of 12%,what would be the investment proportions of your portfolio? Compare its standarddeviation to that of the optimal portfolio in the previous problem. What do youconclude?

Short answer

The efficient portfolio with a mean of 12% has a standard deviation of only 20.61%.Using the CAL reduces the standard deviation by 45 basis points.

Step-by-step solution

Using only the stock and bond funds to achieve a mean of 12%

Using only the stock and bond funds to achieve a mean of 12% we solve:

12 = 15w_S + 9(1 -w_S ) = 9 + 6w_Sw_S = 0.5

Calculation of standard deviation with a mean of 12%

Investing 50% in stocks and 50% in bonds yields a mean of 12% and standard deviationof:

σ_P = [(0.50²x 1024) + (0.50²x 529) + (2 x 0.50 x 0.50 x 110.4)] ^1/2 = 21.06%

The efficient portfolio with a mean of 12% has a standard deviation of only 20.61%.

Using the CAL reduces the standard deviation by 45 basis points.