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 rate of 6%. The probability distribution of the risky funds is as follows:

	Expected Return			Standard Deviation
Stock fund (S)		24	%		33	%
Bond fund (B)		14			22

The correlation between the fund returns is 0.14.

You require that your portfolio yield an expected return of 16%, and that it be efficient, on the best feasible CAL.

a. What is the standard deviation of your portfolio? (Round your answer to 2 decimal places.)   

b. What is the proportion invested in the T-bill fund and each of the two risky funds? (Round your answers to 2 decimal places.)

	Proportion Invested
T-Bill Fund		%
Stocks		%
Bonds		%

Answer 1

Using the given paramters the expected return and std of optimal portfolio is below

Return=19.34% and std=21.60%

The equation use to solve this is
Expected return=Risk free+sharpe ratio*std
sharpe ratio=(return-risk free)/std
=(19.34%-6%)/21.6%=0.6178
std of our portfolio=(16%-6%)/0.6178=16.19%

Let amount invested in risk free be (1-y) so in portfolio is y
16%=((1-y)*6%)+y*19.34%
y=74.94% and 1-y=25.06%
proportion in stocks=74.94%*53.44%=40.05%
in bonds=74.94%*46.56%=34.89%
Risk free asset=25.06%