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 4.3%. The probability distributions of the risky funds are:

  

	Expected Return	Standard Deviation
Stock fund (S)	13%	34%
Bond fund (B)	6%	27%

  

The correlation between the fund returns is .0630.

  

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

Minimum variance portfolio is the portfolio which has the highest Sharpe ratio.

Respective fund weights have to be found using Solver to maximize the Sharpe ratio.

We do this by first creating the covariance/variance matrix and then using it to calculate the portfolio return and standard deviation. After which, Sharpe ratio is calculated and then Solver is used to find the weights at which Sharpe ratio is maximized.

Formulas:

Minimum variance portfolio:

Expected return = 11.67%

Standard deviation = 28.34%