Question

Problem 7-8 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 (5) 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

Weight of stock fund S, in an optimally risky portfolio is given by:

Ers)-ro-E(TB) =r7]Cov(B,S) E{rB),rg]o%E(rs)-rE(rB),rg]Cou(B, S) E(rs)-r

where E(rS) = expected return of S = 24%; E(rB) = expected return of B = 12%

rf = risk-free rate = 4%; $\sigma _{S}$ = standard deviation of S = 30%; $\sigma _{B}$ = standard deviation of B = 19%

Cov(B,S) = covariance between B & S = Correlation(B,S)*$\sigma _{S}$*$\sigma _{B}$ = 0.13*30%*19% = 0.00741

Ws = {(24%-4%)*(19%^2) - (12%-4%)*0.00741}/{(24%-4%)*(19%^2) + (12%-4%)^(30%^2) - (24%-4%+12%-4%)*0.00741}

= 0.537

Weight of bond fund B (Wb) = 1-0.537 = 0.463

Expected return of the optimal risky portfolio = sum of weighted returns = (0.537*24%) + (0.463*12%) = 18.44%

Standard deviation = {(Ws*$\sigma _{S}$)^2 + (Wb*$\sigma _{B}$)^2 + (2*Ws*Wb*Cov(B,S)}^0.5

= {(0.537*30%)^2 + (0.463*12%)^2 + (2*0.537*0.463*0.00741)}^0.5 = 19.33%

Sharpe ratio of the best feasible CAL = (portfolio return - rf)/portfolio standard deviation

= (18.44%-4%)/19.33% = 0.7471 (Answer)