Question

Question 1B (10 points) a. 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 Government money market fund (a proxy for the risk-free assets) that yields a rate of 8%. The probability distribution of the risky funds is as follows: Expected Return Stock fund (S) 20% Bond fund (B) 12% The correlation between the stock (S) and bond (B) fund returns is 0.2 Standard deviation 30% 15% Compute the investment proportions in the minimum-variance portfolio of the two risky funds, and the expected return and standard deviation of the portfolio given that the Government money market fund exists. Show all computations.

Answer 1

B15 X ✓ fi =(B8-B9)/(B8+B7-2*B9) B 20% 12% 30% 15% 0.2 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 7 Variance of stock fund (os^2) 8 Variance of bond fund (ob^2) 9 Covariance of stock and bond funds [COV(sb)] 10 (r(sb)xobxos) 0.0900 0.0225 0.0090 ds [COV(sb) 11 [(ob^2)-COV(sb)]/[(os^2)+(ob^2)-2xCOV(sb)] 12 Minimum portfolio variance (Ws) = 13 (Portfolio invested in stock) 14 15 Portfolio invested in stock (Ws) 16 Portfolio invested in bond (Wb) 17 (1-Portfolio invested in stock) 14.29% 85.71% _ 18 E(rs)xWs+E(rb)xWb 19 Expected return on minimum variance portfolio Expected return on minimum 20 variance portfolio 21 22 SD of minimum variance portfolio 23 SD of minimum variance portfolio 13.14% ((Ws)^2x(os^2)+(Wb)^2x(ob^2)+2xr(sb)xWsxWb)^(1-2) 14.34%

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