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:

Expected Return (Left) Standard Deviation (Right)

Stock fund (S) 16% 45%

Bond fund (B) 7% 39%

The correlation between the fund returns is 0.0385. What is the Sharpe ratio of the best feasible CAL?

Answer 1

To calculate the weights, we use the below formula:

Ws = {(16-5.5)*39^2 - (7-5.5)*45*39*0.0385 }/ { (16-5.5)*39^2 + (7-5.5)*45^2 - (16-5.5+7-5.5)*45*39*0.0385}

Ws = 15,869.14875/ 18,197.19

Ws = 0.8721

Wb = 1-0.8721 = 0.1279

Expected return(Rp) = 0.8721*16% + 0.1279*7% = 14.85%\

Expected Std. deviation (Sp) = (0.8721^2*45^2 +0.1279^2*39^2 +2 *0.8721*0.1279*45*39*0.0385)^(1/2)

Expected Std. deviation (Sp) = 39.75%

Sharpe ratio of the best feasible CAL = (Rp-Rf)/Sp = (14.85% -5.5%)/39.75% = 0.2352

Sharpe ratio of the best feasible CAL = 0.2352