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 4.1%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	11%	33%
Bond fund (B)	8%	25%

The correlation between the fund returns is 0.1560.

What is the Sharpe ratio of the best feasible CAL?

Answer 1

For best feasible CAL we need to calculated weights for Optimally Risky Portfolio

Weight of Stock =(E(r)of Stock-Rf)* b^2-(E(r) of Bond -Rf)* s* b*Correlation)/((Er of Stock-Rf)* b^2+(Er of Bond-Rf)* s^2-(E(R) of Stock -Rf)* b^2+(E(R) of bond -Rf)* s^2-(E(R) of Stock -Rf+E(R) of bond -Rf)* s* b*Correlation)
=((11%-4.1%)*25%^2-(8%-4.1%)*33%*25%*0.1560)/((11%-4.1%)*25%^2+(8%-4.1%)*33%^2-(11%-4.1%+8%-4.1%)*33%*25%*0.1560) =53.1487%
Weight of Bond =1-53.1487% =46.8513%

Expected Return =Weight of Stock*Return of Stock+Weight of Bond*Return of Bond =53.1487%*11%+46.8513%*8% =9.59%
Standard Deviation =((Weight of Stock*Standard Deviation of Stock)^2+(Weight of Bond*Standard Deviation of Bond)^2+2*Weight of Stock*Weight of Bond*Standard Deviation of Stock*Standard Deviation of Bond*Correlation)^0.5
=((53.1487%*33%)^2+(46.8513%*25%)^2+2*53.1487%*46.8513%*33%*25%*0.1560)^0.5 =22.56% or 0.2256

Sharpe ratio of best feasible CAL =(Expected return-Risk Free rate)/Standard Deviation
=(9.59% -4.1%)/22.56% =0.2434 or 0.24