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:

	Expected Return		Standard Deviation
Stock fund (S)	15 %		32%
Bond fund (B)	9 %		23%

The correlation between the fund returns is 0.15.

1. 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%?

Investment Proportions
Stocks	%
Bonds	%

b. Calculate the standard deviation of the portfolio which yields an expected return of 12%.

Standard deviation             %

Answer 1

a.

Let W be the proportion of the stock.

(1-W) be the proportion of the bond.

Rs = Expected return of the stock.

Rb = Expected return of the bond.

Calculate proportion as follows:

Expected return = (W*Rs) + ((1-W)*Rb)

12% = (W*15%) + ((1-W)*9%)

12% = 15%W+ 9% - 9%W

W = 3% / 6%

W = 50%.

W be the proportion of the stock = 50%

(1-W) be the proportion of the bond = (1-50%) = 50%

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b.

Calculate the standard deviation as follows:

Standard deviation = ((50%*32)^2 + (50% * 23%)^2 + 2*50%*50%*32*23*0.15)^(1/2)

= (2.56% + 1.3225% + 4.4345%)^(1/2)

= 21.06%

Therefore, the standard deviation is 21.06%.