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 rate of 8%. The probability distribution of the risky funds is as follows: Expected Return 19% Standard Deviation 31% 23 Stock fund (S) Bond fund (B) 14 The correlation between the fund returns is 0.10. a-1. What are the investment proportions in the minimum-variance portfolio of the two risky funds. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Portfolio invested in the stock Portfolio invested in the bond a-2. What is the expected value and standard deviation of its rate of return? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Rate of Return Expected return Standard deviation

Answer 1

B15 X ✓ fc =(B8-B9)/(B8+B7-2*B9) 19% 14% 31% 23% 0.1000 А 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) 11 12 Minimum portfolio variance (Ws) = 13 (Portfolio invested in stock) 14 0.0961 0.0529 0.0071 [(ob^2)-COV(sb)]/[(os^2)+(ob^2)-2xCOV(sb)] 15 Portfolio invested in stock (Ws) 0.3397 0.6603 16 Portfolio invested in bond (Wb) 17 (1-Portfolio invested in stock) 18 19 Expected return on minimum variance portfolio Expected return on minimum E(rs)<Ws+E(rb)xWb 20 variance portfolio 0.1570 21 ((Ws)^2x(os^2)+(Wb)^2x(ob^2)+2xr(sb)xWsxWb)^(1:2) 22 SD of minimum variance portfolio SD of minimum variance 23 portfolio 0.1933

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