Question

hightlight the answer please

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 4.5%. The probability distribution of the risky funds is as follows: Standard Deviation Stock fund (S) Bond fund (B) Expected Return 155 356 29 The correlation between the fund returns is 0.15. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places. Omit the "%" sign in your response.) 17.52 Portfolio invested in the stock Portfolio invested in the bond Expected return Standard deviation

Answer 1

Calculate the proportion, expected return as follows:

А В C Optimal risky Expected rate Standard deviation 1 2 3 Stock fund(S) 4 Bond fund(B) 15% 35% 6% 29% 5 Risk free rate 4.50% 6 Correlation 0.15 7 Covariance 0.015225 8 9 Propotion in stock 10 Propotion in bond 11 Expected return 97.30% 2.70% 14.76% 34.18% 12 Standard deviation

Formulas:

А В Optimal risky 1 Standard deviation Expected rate 2 3 Stock fund(S) 0.15 0.35 4 Bond fund(B) 0.06 0.29 5 Risk free rate 0.045 0.15 6 Correlation -В6*С3*С4 7 Covariance Е(В3-B5)*C4^2)-(В4-B5)*B7)/(В3-B5)*С4^2)+(В4-B5)*СЗ^2)-(В3-B5+B4-B5)*B7)) -1 - B9 9 Propotion in stock 10 Propotion in bond 11 Expected return Е[B9*вз)+(В10*В4) =((B9^2*C3^2)+(B10^2*C4^2)+(2*B9*B10*B7))^(1/2) 12 Standard deviation 13 Reward to volatility ratio=(B11-B5)/B12