Question

# A pension fund manager is considering three mutual funds. The first is a stock fund, the...

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 %

 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%

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