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 rate of 4%. The probability distribution of the risky funds is as follows: Expected Return 24% 12 Standard Deviation 30% Stock fund (S) Bond fund (B) 19 The correlation between the fund returns is 0.13. What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Sharpe ratio

Answer 1

Calculate the best feasible CAL as follows:

B A 1 2 3 Stock fund(s) 4. Bond fund(B) 5 Risk free rate 6 Correlation 7 Covariance Optimal risky Expected rate Standard deviation 24% 30% 12% 19% 4.00% 0.13 0.00741 8 9 Propotion in stock 10 Propotion in bond 11 Expected return 12 Standard deviation 13 Reward to volatility ratio 0.5368 0.4632 0.1844 0.1933 0.7471

Sharpe ratio is 0.7471.

Formulas:

Optimal risky Standard deviation 0.3 1 2 3 Stock fund(s) 4. Bond fund(B) 5 Risk free rate 6 Correlation 7 Covariance 0.19 Expected rate 0.24 0.12 0.04 0.13 =B6*C3*C4 T 8 9 Propotion in stock 10 Propotion in bond 11 Expected return 12 Standard deviation 13 Reward to volatility ratio =(((B3-B5)*C4^2)-((B4-B5) *B7))/(((B3-B5)*C4^2)+((B4-B5)*C312)-(B3-B5+B4-B5) *B7)) =1-B9 =(B9*B3)+(B10*B4) =((B9^2*C3^2)+(B10^2*C4^2)+(2*B9*B10*B7))^(1/2) =(B11-B5)/B12