A pension fund manager is considering three mutual funds. The first is a stock f

Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a longterm 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: The correlation between the fund returns is 0.15. 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.)

Explanation / Answer

Solution:

The proportion of the optimal risky portfolio invested in the stock fund is given by: w S = [ E ( r S ) - r f ] × 2 B - [ E ( r B ) - r f ] × Cov ( r S ,r B ) [ E ( r S ) - r f ] × 2 B + [ E ( r B ) - r f ] × 2 S - [ E ( r S ) - r f + E ( r B ) - r f ] × Cov ( r S ,r B ) = [(0 . 12 - 0 . 06) × 0 . 01] - [(0 . 09 - 0 . 06) × 0 . 5 × 0 . 2 × 0 . 1] [(0 . 12 - 0 . 06) × 0 . 01] + [(0 . 09 - 0 . 06) × 0 . 04] - [(0 . 06 + 0 . 03) × 0 . 5 × 0 . 2 × 0 . 1] = 1 / 3 w B = 1 - 1 / 3 = 2 / 3 The mean and standard deviation of the optimal risky portfolio are: E ( r p ) = (1 / 3) × 0 . 12 + (2 / 3) × 0 . 09 = 0 . 1 = 10% p = [(1 / 3) 2 × 0 . 04 + (2 / 3) 2 × 0 . 01 + 2 × (1 / 3) × (2 / 3) × 0 . 5 × 0 . 2 × 0 . 1] 1 2 = 11 . 55%

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