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 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 Stock fund 11% 33% (S) Bond fund (B) 8 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 portfollo. (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

B39 X ✓ fc =((B25*B32)-(B26*B33))/((B25*B32)+(B26*B31)-(B25+B26)*B33) Α 25 Expected risk premium on stock fund [E(rps)] 26 Expected risk premium on bond fund [E(rpb)] 27 SD of stock risk premium (os) 28 SD of bond risk premium (ob) 29 Correlation between funds risk premiums (rp(sb)] 6.9% 3.9% 33% 25% 0.16 30 0.11 0.06 0.0132 [(ob^2)-COV(sb)]/[(os^2)+(ob^2)-2xCOV(sb)] 31 Variance of stock fund (os^2) 32 Variance of bond fund (ob^2) 33 Covariance of stock and bond funds [COV(sb)] 34 (r(sb)xobxos) 35 36 Optimal risky portfolio variance (Ws) 37 (Portfolio invested in stock) 38 39 Portfolio invested in stock (Ws) 40 Portfolio invested in bond (wb) 41 (1-Portfolio invested in stock) 42 43 Expected return on optimal risky portfolio [E(rp)] Expected return on optimal risky 44 portfolio (E(rp)] 53.23% 46.77% E(rs)xWs+E(rb)xWb 9.60% 45 (Ws)^2x(os^2)+(Wb)^2x(ob^2)+2xr(sb)xWsxWbx)^(1-2) 46 SD of optimal risky portfolio (op) Standard deviation of optimal 47 risky portfolio (op) 22.61%

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