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A pension fund manager is considering three mutual funds
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 30%. The probability distributions of the risky funds are:
| Expected Return | Standard Deviation | |
| Stock fund (S) | 12% | 41% |
| Bond fund (B) | 5% | 30% |
The correlation between the fund returns is 0.18. What is the expected return and standard deviation of the optimal risky portfolio?
Expert Solution
Calculating the variance of stock fund and bond fund
Variance of stock fund=(Standard deviation of stock fund)2=(0.41)2=0.1681Variance of bond fund=(Standard deviation of bond fund)2=(0.30)2=0.009Variance of stock fund=(Standard deviation of stock fund)2=(0.41)2=0.1681Variance of bond fund=(Standard deviation of bond fund)2=(0.30)2=0.009
Calculating the Covariance of stock fund and bond fund
Covariance of stock and bond funds = Correlation×Standard deviation of bond fund ×Standard deviation of stock fund=0.18×0.30×0.41=0.02214Covariance of stock and bond funds = Correlation×Standard deviation of bond fund ×Standard deviation of stock fund=0.18×0.30×0.41=0.02214
Calculating the portfolio investment in stock fund and bond fund
Portfolio investment in stock fund (WS)=Bond variance - CovarianceStock variance + Bond variance - (2×Covariance)=0.009−0.022140.1681+0.009−(2×0.02214)=0.09893Portfolio investment in bond fund (WB)=1−Portfolio investment in stock fund=1−0.09893=0.9010Portfolio investment in stock fund (WS)=Bond variance - CovarianceStock variance + Bond variance - (2×Covariance)=0.009−0.022140.1681+0.009−(2×0.02214)=0.09893Portfolio investment in bond fund (WB)=1−Portfolio investment in stock fund=1−0.09893=0.9010
Calculating the expected return
Expected return =((Expected return of stock×Weight of stock ) + (Expected return of bond×Weight of bond))=((12%×0.09893)+(5%×0.9010))=0.0569Expected return =((Expected return of stock×Weight of stock ) + (Expected return of bond×Weight of bond))=((12%×0.09893)+(5%×0.9010))=0.0569
Calculating the Standard Deviation
Standard deviation=√(WS)2×Stock variance+(WB)2∗Bond variance + 2×Correlation×Covariance =√(0.09893)2×0.1681+(0.9010)2×0.02214+2×0.18×0.02214=0.1661
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