Question

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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 5.6%. The probability distributions of the risky funds are: Stock fund (S) Bond fund (B) Expected Return 17% 8% Standard Deviation 46% 40% The correlation between the fund returns is .0600. 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 15.42 % 38.99 %

Answer 1

Weight of (A) = ((Standard Deviation of B)^2 -correlation * Standard Deviation of A * Standard Deviation of B)/((Standard Deviation of A)^2 + (Standard Deviation of B)^2 - 2 * correlation * Standard Deviation of A * Standard Deviation of B)
=(40%)^2-0.06*46%*40%)/((46%)^2+(40%)^2-2*0.06*46%*40%) =42.6184%
Weight of B =1-42.6184% =57.3816%

Expected Return =Weight of A * Return of A + Weight of B * Return of B =42.6184%*17%+57.3816%*8% =11.84%

Standard Deviation = ((Weight of A * Standard Deviation of A)^2 + (weight of B * standard Deviation of B)^2 + 2* Weight of A * Standard Deviation of B * weight of A * standard Deviation of B * correlation)^0.5
=((42.6184%*46%)^2+(57.3816%*40%)^2+2*42.6184%*57.3816%*40%*46%*0.06)^0.5 =31.07%