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 3.0%. 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 .0667.

What is the reward-to-volatility ratio of the best feasible CAL? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Reward-to-volatility ratio ???

Explanation / Answer

For minimum portfolio variance , the weights of assets are as follows:                                                          

W(X) = [V(Y) - C(XY)]/[V(X)+V(Y)-2C(XY)] = 0.0667/(0.41^2+0.30^2-2*0.0667)=0.534

So W(Y)=1-0.534=0.466

So Reward=0.534*12+0.466*5=8.73%

Variance of the portfolio=V(Portfolio)=V(X) * (Weight X ^2 ) + V(Y) * (Weight Y ^2) + 2*Weight X*Weight Y*SD(X)*SD(Y)*Correlation Coefficient C(XY)=(0.41^2)*(0.534^2)+(0.3^2)(0.466^2)+2*0.534*0.466*0.41*0.30*0.0667=0.071

Standard Deviation=(0.071)^(1/2)=0.266 or 26.6%

So Reward-to-volatility ratio =8.73/26.6=0.328

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