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 4.6%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	16%	36%
Bond fund (B)	7%	30%

The correlation between the fund returns is 0.0800.

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.)

Answer 1

Weight of (S) = ((Standard Deviation of B)^2 -correlation * Standard Deviation of S * Standard Deviation of B)/((Standard Deviation of S)^2 + (Standard Deviation of B)^2 - 2 * correlation * Standard Deviation of S * Standard Deviation of B)
=((30%^2)-0.0800*36%*30%)/((36%^2)+(30%^2)-2*0.0800*36%*30%)=40.2135%
Weight of B =1-40.2135%=59.7865%

Expected Return of min variance portfolio =40.2135%*16%+59.7865%*7%=10.62% or 0.11
Standard Deviation = ((Weight of S * Standard Deviation of S)^2 + (weight of B * standard Deviation of B)^2 + 2* Weight of S * Standard Deviation of S * weight of B * standard Deviation of B * correlation)^0.5=((40.2135%*36%)^2+(59.7865*30%)^2+2*40.2135%*59.7865%*36%*30%*0.0800)^0.5=23.93% or 0.24