Question

A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 20%, while stock B has a standard deviation of return of 26%. Stock A comprises 60% of the portfolio, while stock B comprises 40% of the portfolio. If the variance of return on the portfolio is 0.035, the correlation coefficient between the returns on A and B is _________.

A .157

B.392

C.235

D.102

Answer 1

Weight of stock A in the portfolio = wA = 60%, Weight of stock B in the portfolio = wB = 40%

Standard deviation of stock A = σA = 20%, Standard deviation of stock B = σB = 26%

Correlation coefficient between stock A and stock B = ρ

Variance of the portfolio = σ2 = 0.035

Variance of the portfolio is calculated suing the formula:

σ2 = wA2*σA2 + wB2*σB2 + 2*ρ*wA*wB*σA*σB = 0.035

(60%)2*(20%)2 + (40%)2*(26%)2 + 2*ρ*60%*40%*20%*26% = 0.035

0.0144 + 0.010816 + 0.02496*ρ = 0.035

0.025216 + 0.02496*ρ = 0.035

0.02496*ρ = 0.035 - 0.025216

0.02496*ρ = 0.009784

ρ = 0.009784/0.02496 = 0.39198717948718 ~ 0.392 (Rounded to three decimals)

Answer -> 0.392 (Option B)