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 the risky funds are:

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

The correlation between the fund returns is 0.15.

a. What would be the investment proportions of your portfolio if you were limited to only the stock and bond funds and the portfolio has to yield an expected return of 12%?

b. Calculate the standard deviation of the portfolio which yields an expected return of 12%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer (a):

Let us assume investment proportion of Stock fund is Ws.

Hence:

Investment proportion of Bond fund will be = 100% - Ws

Expected return of portfolio = 12%

As such:

=> Ws*15% + (100% - Ws) * 9% = 12%

=> 15% Ws + 9% - 9% Ws =12%

=> 6% Ws = 12% -9% = 3%

=> Ws = 3% / 6% = 50%

Investment proportion of Bond fund will be = 100% - Ws = 100% - 50% = 50%

Hence:

Investment proportions of your portfolio in the stock fund = 50%

Investment proportions of your portfolio in the bond fund = 50%

Answer (b):

The correlation between the fund returns is 0.15.

Formula for Standard deviation of portfolio (of Asset A and B) is:

Standard deviation of portfolio

= SQRT (50% ² * 32% ² + 50% ² * 23% ² + 2 * 50% * 50% * 0.15 * 32% * 23%)

= 21.06%

Standard deviation of the portfolio which yields an expected return of 12% = 21.06%