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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 4.1%. The probability distribution of the risky funds is as follows: Expected Return Standard Deviation 338 Stock fund (S) Bond fund (B) 25 The correlation between the fund returns is 0.16. 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.) Portfolio invested in the stock Portfolio invested in the bond Expected return Standard deviation

Answer 1

Cofculation of proportions wn weightage of stock fund ton- Gy? covariance ' y = Bond fund. na stock fund 622 +67-2 Canariance = (25) ² 132 Covariance (33)+(25)? 2 X132 Ecar (0.7) = 8 x6nxby. = 493 - 16 X 33x25 T 132 - 493 1450 - 99 1089 +625-264 wy = (1.34) = 0.66 Expected return of risky - (118.34 + 8x portfolio Standard denation of nsky - Twt) 2 x variance + 2 wt. x wtx Covariance = √ (134) ² (33) ²4 (166) ²x (25) 2x134X.66 134 + 8x ,66) =(3174 +5.28) 29.02 wt) 2x variance t2 portfolio - x 132 = 1158x 1089 +0.4956X625+59 242 1125.89 +272125+59,242 = 457.38 = 21.39