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 4.7%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	17%	37%
Bond fund (B)	8%	31%

The correlation between the fund returns is 0.1065.

What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Expected return % Standard deviation %

Answer 1

Sol:

	Stock fund	Bond fund	T-bill money market fund
Expected returns	17%	8%	4.70%
Standard deviation	37%	31%
Correlation between the fund returns	0.1065
Stock fund variance	0.1369
Bond fund variance	0.0961
Covariance of stock and bond fund	0.0122
Minimum variance of the portfolio = (Stock fund + Bond fund)
Stock fund weight	0.4022
Bond fund weight	0.5978
Expected return of minimum variance portfolio	11.62%
Standard deviation of minimum variance portfolio	24.97%

Workings