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 4.4%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	14%	34%
Bond fund (B)	5%	28%

The correlation between the fund returns is 0.0214.

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

Variance of the stock fund = standard deviation^2
= 0.34^2
= 0.1156

Variance of bond fund = standard deviation^2
= 0.28^2
= 0.0784

Covariance of stock and bond funs = Correlation * standard deviation of stock fund * standard deviation of bond fund
= 0.0214 * 0.34 * 0.28
= 0.00203728

Portfolio invested in stock = (Bond's variance - covariance) / (stock's variance + bond's variance - 2 * covariance)
= (0.0784 - 0.00203728) / (0.1156 + 0.0784 - 2 * 0.00203728)
= 0.07636272 / 0.18992544
= 40.21%

Portfolio invested in Bond = 1 - 40.21% = 59.79%

Expected return on minimum variance portfolio = (Expected return on stock fund * weight of stock) + (expected return on bond fund * weight of bond)
= (14% * 40.21%) + (5% * 59.79%)
= 5.6288 + 2.9897%
= 8.62%

Expected return on minimum variance portfolio = 8.62%

Standard deviation of minimum variance portfolio = ((Weight of stock^2 * stock variance) + (weight of bond^2 * bond variance) + (2 * correlation * covariance))^(1/2)
= ((0.4021^2 * 0.1156) + (0.5979^2 * 0.0784) + (2 * 0.0214 * 0.00203728))^(1/2)
= (0.018686999 + 0.028026777 + 0.000087195584)^(1/2)
= 0.046800971^(1/2)
= 21.63%

Standard deviation of minimum variance portfolio = 21.63%

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