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 sure rate of 4.8%. The probability distributions of the risky funds are: Expected Return 18% Standard Deviation Stock fund (S) Bond fund (B) 38% 98 32% The correlation between the fund returns is .1313. Suppose now that your portfolio must yield an expected return of 15% and be efficient, that is, on the best feasible CAL. a. What is the standard deviation of your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Standard deviation b-1. What is the proportion invested in the T-bill fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Proportion invested in the T-bill fund

Answer 1

fr =((B26*B33)-(B27*B34))/((B26*B33)+(B27*B32)-(B26+B27)*B34) B40 A 26 Expected risk premium on stock fund [E(rps)] 27 Expected risk premium on bond fund [E(rpb)] 28 SD of stock risk premium (os) 29 SD of bond risk premium (ob) 30 Correlation between funds risk premiums [rp(sb)] 13.20% 4.20% 38.00% 32.00% 0.1313 31 32 Variance of stock fund (os^2) 33 Variance of bond fund (ob^2) 34 Covariance of stock and bond funds [COV(sb)] 35 (r(sb)xobxos) 0.14 0.10 0.0160 36 37 Optimal risky portfolio variance (Ws) [(ob^2)-COV(sb)]/[(os^2)+(ob^2)-2×COV(sb)] 38 (Portfolio invested in stock) 39 40 Portfolio invested in stock (Ws) 76.45% 41 Portfolio invested in bond (Wb) 23.55% 42 (1-Portfolio invested in stock) 43 44 Expected return on optimal risky portfolio [E(rp)] E(rs)xWs+E(rb)xWb| Expected return on optimal risky portfolio 45 [E(rp)] 15.88% 46 47 SD of optimal risky portfolio (op) 48 SD of optimal risky portfolio (op) ((Ws)^2x(os^2)+(Wb)^2x(ob^2)+2xr(sb)xWsxWbx)^(1÷2) 30.96% 49 50 All combined portfolios on the CAL will be combinations on P and the risk free.

fx =B54*B40 B57 A B 52 Targeted portfolio expected return [E(rc)] 15.00% 28.50% 53 Weight of risky assets in portfolio [Ws+Wb] [E(rp)-Rf]/[E(rpsb)-Rf] a) 7.95% 92.05% b-1)T-bill fund 54 Weight of risky assets in portfolio [Ws+Wb] Standard deviation of portfolio (op) 55 [Ws+Wb]x(op) 28.50% b-2) Stocks 70.37% Bonds 21.68% 56 57 Proportion of P in the stock fund [Ws+Wb]xWs 70.37% 58 Proportion of P in the bond fund [Ws+Wb]xWb 59 T Bills (1-Ws-Wb) 21.68% 7.95%

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