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 4.1%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	11%	33%
Bond fund (B)	8%	25%

The correlation between the fund returns is 0.1560.

What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds?

Answer 1

Minimum variance portfolio=

(sigma of b^2)-(sigma of a*sigma of b*correlation(a,b))/ (sigma of b^2+ sigma of a^2-(2*sigma of a*sigma of b*correlation(a,b))

((25^2)-(33*25*0.1560))/((25^2)+(33^2)-(2*25*33*0.1560))

0.34

So weight of b i.e. bond fund=0.34

weight of stock fund =0.66

(1-0.34)

Expected Return of portfolio =

(Return of stock A* weight of stock A) + (Return of stock B* weight of stock B)

=

(11%*0.66)+(8%*0.34)

=

9.98%

Standard Deviation of Portfolio=

[{(weight of A)^2 * (sigma of A)^2} + {(weight of B)^2 + (sigma of B)^2} + {2*(weight of A)*(weight of B)*(Correlation of A&B * sigma of A* sigma of B}]^(1/2)

=

((0.66)^2*(33)^2 + (0.34)^2*(25)^2 + (2*0.5*0.5*0.1560*25*33))^(1/2)

=

24.72