A pension fund manager is considering three mutual funds. The first is a stock f

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 5.7%. The probability distributions of the risky funds are:

The correlation between the fund returns is .0317.

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.)

Explanation / Answer

Return of Stock Fund=Rs=18% Return of Bond Fund=Rb=7% Standard deviation of Stock fund=Ss=47% Standard deviation of Bond Fund=Sb=41% Correlation between the fund returns=Corr(s,b)=0.0317 Covariance(s,b)=Corr(s,b)*Sa*Sb=0.0317*47*41= 61.0859 Ws=Weight of Stock Fund in the portfolio Wb=Weight of Bond fund in the portfolio Ws+Wb=1 Expected Portfolio Return=Rp Ws*18+Wb*7 Vp=Portfolio Variance=(Ws^2)*(47^2)+(Wb^2)*(41^2)+2*Ws*Wb*61.0859 Vp=2209(Ws^2)+1681*(Wb^2)+122.1718*Ws*Wb Sp=Portfolio Standard Deviation=Square root ofPortfolio Variance Ws Wb Rp=18Ws+7Wb Vp=2209(Ws^2)+1681*(Wb^2)+122.1718*Ws*Wb Sp= Square root Vp Weight of Stock Fund Weight of Bond Fund ExpectedPortfolio Return Portfolio variance Portfolio Standard Devuation 0 1 7 1681 41 0.1 0.9 8.1 1394.695462 37.34562 0.2 0.8 9.2 1183.747488 34.40563 0.3 0.7 10.3 1048.156078 32.37524 0.4 0.6 11.4 987.921232 31.43121 0.43 0.57 11.73 984.5453082 31.37746 0.5 0.5 12.5 1003.04295 31.67085 0.6 0.4 13.6 1093.521232 33.06843 0.7 0.3 14.7 1259.356078 35.48741 0.8 0.2 15.8 1500.547488 38.7369 0.9 0.1 16.9 1817.095462 42.6274 1 0 18 2209 47 Minimum Variance 984.5453 Expected Return of Minimum Variance Portfolio 11.73% Standard Deviation of Minimum Variance Portfolio 31.38%

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