1. value: 10.00 points Problem 6-9 A pension fund manager is considering three m
ID: 2714706 • Letter: 1
Question
1.
value:
10.00 points
Problem 6-9
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 5.5%. The probability distribution of the risky funds is as follows:
Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places. Omit the "%" sign in your response.)
rev: 11_21_2013_QC_39542
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 5.5%. The probability distribution of the risky funds is as follows:
Explanation / Answer
The parameters of the opportunity set are:
The parameters of the opportunity set are:
E(rS) = 16%, E(rB) = 7%, S = 45%, B = 39%, = 0.15, rf = 5.5% From the standard deviations and the correlation coefficient we generate the covariance matrix [note that Cov(rS, rB) = SB]: Bonds Stocks Bonds 0.1521 0.026325 Stocks 0.026325 0.2025 The optimal risky portfolio proportions are: wB = [E(rB) rf ]S2 [E(rS) rf ]BSBS [E(rB) rf ]S2 + [E(rS) rf ]B2 [E(rB) rf + E(rS) rf ]BSBS wB = (((0.07 0.055) × 0.2025) (0.16 0.055) × (0.026325)) (((0.07 0.055) × 0.2025) + (0.16 0.055) × 0.1521) ((0.07 0.055 + 0.16 0.055) × 0.026325) = 0.017249 = 1.72% wS = 1 wB wS = 1 0.01724 = 0.98276 = 98.27% The mean and standard deviation of the optimal risky portfolio are: E(r) = wB × E(rB) wS × E(rS) = (0.01724 × 0.07) + (0.98276 × 0.16) = 0.1584 = 15.84% SD(r) = [wS2S2 + wB2B2 + 2wSwB Cov(rS, rB)]1/2 = [(0.982762 × 0.452) + (0.017242 × 0.392) + (2 × 0.98276 × 0.01724 × 0.026325))]1/2 = 0.4433 = 44.33%.Related Questions
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