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 T­bill 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 .15. What is the expected return and standard deviation for the minimum­variance portfolio of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Please do this problem by hand so i understand each step. I am particularily confused with COV(Rs ,Rb )

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

Explanation / Answer

A minimum variance portfolio (MVP) is a portfolio at which the standard deviation (or variance) of the portfolio is the minimum.

E(R) = w1 x R1 + w1 x R2

Std. Dev. = [(w1 x SD1)^2 + (w2 x SD2)^2 + (2 x w1 x w2 x SD1 x SD2 x corr12)]^(1/2)

here, w - weight of funds, R - Returns of the funds, SD - Std. Dev. and corr12 is the correlation between two funds.

Now, we need to find w1 = 1 - w2 such that the standard deviation is the lowest.

Using excel solver, we get the above weight at which the portfolio has the lowest variance.

w1 = 31.42% and w2 = 68.58%

Returns S.D. Weights S 15% 32% 31% B 9% 23% 69% MVP 10.9% 19.94% 0.15

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