Answer:
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%
