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 5.5%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	16%	45%
Bond fund (B)	7%	39%

The correlation between the fund returns is .0385.

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

From the standard deviations and the correlation coefficient we can generate the “covariance matrix”
	Bonds	Stock
Bonds	?^2 B	COV(B,S)= ?SBx ?S X ?B
Stock	COV(B,S)	?^2A
	Bonds	Stock
Bonds	1521	67.5675		0.00675675	covariance %
Stock	67.5675	2025
minimum variance weight
WSMin = ?^2 B - COV(B,S)/?^2 B + ?^2 S - 2Cov(B,S)
WSMin = (1521-67.5675)/(1521+2025 - 2 x 67.5675)	42.6118%	Weight Stock
WB min = 1- 42.61%	57.3882%	Weight Bond
Expected Return = 16% x 42.61% +7% x 57.38%	10.84%
Standard Deviation = [(0.4261)^2(0.45)^2+ (0.5738)^2(0.39)^2+ 2(0.4261)(0.5738)(.006757)]^1/2	30.03%