A pension fund manager is considering three mutual funds. The first is a stock f
ID: 2788337 • Letter: A
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 5.5%. The probability distributions of the risky funds are:
The correlation between the fund returns is 0.15.
a. What would be the investment proportions of your portfolio if you were limited to only the stock and bond funds and the portfolio has to yield an expected return of 12%?
b. Calculate the standard deviation of the portfolio which yields an expected return of 12%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Standard deviation %
Expected Return Standard Deviation Stock fund (S) 15 % 32 % Bond fund (B) 9 % 23 %Explanation / Answer
W(E) = WEIGHT OF EQUITY
W(D) = WEIGHT OF DEBT = 1 - W(E)
Expected return on the portfolio = R(E) * W(E) + R(D) * W(D) = 12% ( required by question)
15 * W(E) + 9 * W(D) = 12
15 * W(E) + 9 * ( 1 - W(E) ) = 12
6 * W(E) = 3
W(E) = 0.50..................... 50%...............final answer
W(D) = 0.50..................... 50% ...............final answer
Standard deviation = root over [ sd(E)2 * W(E)2 + sd(D)2 * W(D)2 + 2*sd(E)*sd(D)*r*W(E)*W(D)]
sd = standard deviation and r = correlation coefficient = 0.15 (given)
= Root over [ 1024 * 0.25 + 529 * 0.25 + 2 * 32 * 23 * 0.15 * 0.5 * 0.5 ]
= Root over [ 388.25 + 55.2 ] = 21.06%.............final answer
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