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

w_min(S)

=

_B²- Cov(r_S, r_B)

_S²+ _B²- 2Cov(r_S, r_B)

Variance for the min-var portfolio:

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