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 7%. The probability distribution of the risky funds is as follows: Expected Return Standard Deviation Stock fund (S) 18 % 35 % Bond fund (B) 15 20 The correlation between the fund returns is 0.12.

What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Answer 1

B18 X ✓ fi =((B7*B11)-(B8*B12)/((B7*B11)+(B8*B10)-(B7+B8)*B12) 18% 15% 35% 20% 0.12 7% 11% 8% 1 Expected return on stock fund [E(rs)] 2 Expected return on bond fund [E(rb)] 3 SD of stock fund (os) 4 SD of bond fund (ob) 5 Correlation between fund returns [r(sb)] 6 Risk free rate of return (RF) 7 Expected risk premium on stock fund [E(rps)] 8 Expected risk premium on bond fund [E(rpb)] 9 10 Variance of stock fund (os2) 11 Variance of bond fund (ob^2) 12 Covariance of stock and bond funds [COV(sb)] 13 (r(sb)xobxos) 14 15 Optimal risky portfolio variance (Ws) 16 (Portfolio invested in stock) 17 18 Portfolio invested in stock (Ws) 19 Portfolio invested in bond (Wb) 20 (1-Portfolio invested in stock) 21 22 Expected return on optimal risky portfolio (E(rp) 23 Expected return on optimal risky portfolio [E(rp)] 0.12 0.04 0.0084 [(ob^2)-COV(sb)]/[(os^2)+(ab^2)-2xCOV(sb)] 29.58% 70.42% Ers)<Ws+Erb)xWb 15.89% 24 25 SD of optimal risky portfolio (op) 26 SD of optimal risky portfolio (op) ((Ws)^2x(os^2)+(Wb)^2x(ob^2)+2xr(sb)xWsxWbx)^(12) 18.45% 27 28 Sharpe ratio 29 Sharpe ratio [E(rp)-Rf)]=op 0.4816

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