A fund manager is considering three mutual funds. The 1st is a stock fund, the 2nd is a long-term government and corporate bond fund (investment grade), and the third is a T-bill money market fund that yields a sure rate of 3.00%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 12.00% 41.00% Bond fund (B) 5.00% 30.00% The correlation between the fund returns is 0.0667. What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds

Expected return is: 7.37% and the Standard deviation is: 24.96%

Explanation:

Correlation between fund S&B=0,0667

Standard Deviation of Fund S=41%

Standard Deviation of Fund (B) = 30%

E (R) of Stock Fund S=12%

E (R) of Stock Fund B=5%

Covariance between the funds = Standard Deviation of Fund (B) * Standard Deviation of Fund S * correlation between these funds

Cov = 0.41 * 0.30 * 0.0667 = 0.008204

Now minimum variance portfolio is found by applying:

W min (S) = (SDB) ^2-Cov (B, S) / ((SDS) ^2 + (SDB) ^2-2Cov (B, S)

W min (S) = 0.338431

W min (B) = 1-0.338431=0.661569

1) E (r) min = 0.338431 * 12% + 0.661569 * 5% = 7.37%

2) Standard Deviation:

SD Min = (Ws^2XSDs^2+Wb^2XSDb^2+2XWsWb*Cov (s, B) ^1/2

SDmin = (0.338431^2 * 0.41^2 + 0.661569^2 * 0.3^2 + 2 * 0.338431 * 0.661569 * 0.008204) ^1/2

SDmin=24.96%