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 0.0667. What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Answer 1

	Stock Fund=Asset 1,Bond Fund=Asset 2
	Return of asset1=R1=12%
	Return of asset2=R2=5%
	Standard deviation of asset 1=S1=41%
	Standard deviation of asset 2=S2=30%
	Correlation of asset 1 and 2=Corr(1,2)=0.0667
	Covariance(1,2)=Corr(1,2)*S1*S2=0.0667*41*30	82.041
	Portfolio Return
	w1*R1+w2*R2=w1*12+w2*5			……..Equation (1)
	Portfolio Variance=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov(1,2)
	Portfolio Variance=(w1^2)*(41^2)+(w2^2)*(30^2)+2*w1*w2*82.041
	Portfolio Variance=(w1^2)*1681+(w2^2)*900+w1*w2*164.082……………Equation (2)
	Portfolio Standard Deviation=Square root of Variance
	Sharp ratio=(Portfolio Return-Risk free rate)/(Portfolio Standard Deviation)
	Risk Free Rate=	3%
	Highest possible Reward to Volatility: Highest Sharp ratio will give Highest possible Reward to Volatility: Portfolio Expected   Return 10.25 % Portfolio Standard Deviation 32.13 % SharpRatio 0.22561948 w1=0.75, w2=0.25 Best Possible CAL STOCK FUND 75% BOND FUND 25%