Question

# A pension fund manager is considering three mutual funds. The first is a stock fund, the...

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 4.5%. The probability distribution of the risky funds is as follows:

 Expected Return Standard Deviation Stock fund (S) 15% 35% Bond fund (B) 6 29

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.)

 Portfolio invested in the stock % Portfolio invested in the bond % Expected return % Standard deviation %

Cov(Rs,Rb) = correlation coefficient * SDs * SDb

= 0.15 x 35 x 29 = 152.25

Ws = [{(ERs - Rf)*SDb2} - {(ERb - Rf)*Cov(Rs,Rb)}] / [{(ERs - Rf)*SDb2} + {(ERb - Rf)*SDs2}]

= [{(15 - 4.5)*(29)2} - {(6 - 4.5)*152.25}] / [{(15 - 4.5)*(29)2} - {(6 - 4.5)*(35)2}]

= [8,830.50 - 228.375] / [8,830.50 + 1,837.50] = 8,602.125 / 10,668.00 = 0.8063, or 80.63%

So, Portfolio invested in the stock = 80.63%

Wb = 1 - Ws = 1 - 0.8063 = 0.1937, or 19.37%

So, Portfolio invested in the bond = 19.37%

Expected return = (Ws * ERs) + (Wb * ERb)

= (0.8063 * 15%) + (0.1937 * 6%] = 12.10% + 1.16% = 13.26%

So, Expected return = 13.26%

S.D. = [(SDs2 * Ws2) + (SDb2 * Wb2) + (2*Ws*Wb*Cov(Rs,Rb)]1/2

= [(352 * 0.80632) + (292 * 0.19372) + (2 * 0.8063 * 0.1937 * 152.25)]1/2

= [796.49 + 31.54 + 47.55]1/2 = [875.58]1/2 = 29.59%

So, Standard Deviation = 29.59%

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