Question

Stock X has a standard deviation of return of 10%. Stock Y has a standard deviation of return of 20%. The correlation coefficient between stocks is 0.5. If you invest 60% of the funds in stock X and 40% in stock Y, what is the standard deviation of the portfolio?A. 10%B. 20%C. 1.48%D. 12.20%

Answer 1

Answer:

D. 12.20%

Explanation:

Stock X Weight = 0.60

Stock Y Weight = 0.40

sdX = 10%

sdY = 20%

Portfolio Variance = w2X*sd2(X) + w2X*sd2(Y) + 2*(wX)*(wY)*Cov(X, Y)

Where: wX and wY are portfolio weights, sd2(X) and sd2(Y) are variances and

Cov(X, Y) is the covariance

Correlation = 0.5

Cov(X, Y) = Correlation * sd(X) * sd(Y)

= 0.50 * 0.10 * 0.20

= 0.01

Portfolio Variance = 0.60^2 * 0.10^2 + 0.40^2 * 0.20^2 + 2 * 0.60 * 0.40 * 0.01

Portfolio Variance = 0.0036 + 0.0064 + 0.0048

Portfolio Variance = 0.0148

sd(P) = √Variance = 0.121655 = 12.20%