3. 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 4.9%. The probability distributions of the risky funds are:

Stock fund (S)	10%	39%
Bond fund (B)	5%	33%

The correlation between the fund returns is 0.0030.

What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds?

Hint: Use the formula and parameters:

The parameters of the opportunity set of possible portfolios are:

E(r_S) = 10%, E(r_B) = 5%, S = 39%, _B = 33%, = 0.0030, r_f = 4.9%

The covariance between stocks and bonds is calculated as:

Cov(r_S, r_B) = _SB

wmin(S)	=	B2 Cov(rS, rB)
		S2 + B2 2Cov(rS, rB)

Variance for the min-var portfolio:

_Min = [w_S²_S² + w_B²_B² + 2w_Sw_B Cov(r_S, r_B)]^1/2