A pension fund manager is considering three mutual funds. The first is a stock f
ID: 2788674 • Letter: A
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 5.5%. The probability distributions of the risky funds are:
The correlation between the fund returns is .15.
What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
Sharpe ratio
Expected Return Standard Deviation Stock fund (S) 15% 32% Bond fund (B) 9% 23%Explanation / Answer
Expected Standard Return deviation Stock fund (S) 15% 32% Bond fumd(B) 9% 23% Expected Return of the portfolio=Ws*Rs+Wb*Rb Ws=Weight of Stock fund in the portfolio Wb=Weight of Bond fund in the portfolio Rs=Return of stock fund(in percent)= 15 Rb=Return of bond fund(in percent)= 9 Portfolio Variance=(Ws^2)*(Ss^2)+(Wb^2)*(Sb^2)+2Ws*Wb*Cov(s,b) Ss=Standard deviation of stock fund(in percent)= 32 Sb=Standard deviation of Bond fund(in percent)= 23 Cov(s,b)=Covariance of return of stock fund and bond fund Cov(s,b)=Corr(s,b)*Ss*Sb Corr(s,b)=Correlation coefficient of return of Stock fund and Bond fund= 0.15 Con(s,b)=0.15*32*23= 110.4 Portfolio Variance=(Ws^2)*(Ss^2)+(Wb^2)*(Sb^2)+2Ws*Wb*110.4 Portfolio Variance=(Ws^2)*(32^2)+(Wb^2)*(23^2)+Ws*Wb*220.8 Portfolio Standard deviation=Square Root (Portfolio Variance) Sharp Ratio=(Expectedportfolio return)-(risk free return)/(Portfolio standard deviation) Sharp Ratio=(Expectedportfolio return-5.5)/(Portfolio standard deviation) CALCULATION OF SHARP RATIO FOR DIFFERENT ALLOCATIONS IN STOCK FUND AND BOND FUND (15*Ws+9*Wb) Ws Wb Rp Vp Sp=(Vp^0.5) SR=(Rp-5.5)/Sp Weight of Wright of Expected Portfolio Portfolio SHARP Stock fund Bond fund portfolio return Variance Std. Deviation RATIO 0 1 9 529 23 0.152173913 0.1 0.9 9.6 458.602 21.41499475 0.191454635 0.2 0.8 10.2 414.848 20.36781775 0.230756189 0.3 0.7 10.8 397.738 19.94336983 0.26575248 0.4 0.6 11.4 407.272 20.18098115 0.292354468 0.5 0.5 12 443.45 21.05825254 0.308667587 0.6 0.4 12.6 506.272 22.50048888 0.315548699 0.648 0.352 12.888 545.8905088 23.36429988 0.316208919 0.65 0.35 12.9 547.6745 23.40244645 0.316206257 0.7 0.3 13.2 595.738 24.40774467 0.315473638 0.8 0.2 13.8 711.848 26.68047976 0.311088859 0.9 0.1 14.4 854.602 29.23357659 0.304444445 1 0 15 1024 32 0.296875 SHARP RATIO FOR BEST FEASIBLE CAL 0.316208919 Allocation to Stock Fund 0.648 Allocation to Bond Fund 0.352
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