Question

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

Answer 1

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

Step-by-step 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%