Question

(please fast!!)

A portfolio is formed out of two stocks A and B and the correlation coefficient between the two stocks is 1. Stock A has a standard deviation of 10%, whereas stock B has a standard deviation of 17%. This portfolio contains 50% of stock A and 50% of stock B. What is the standard deviation of this portfolio?

Answer 1

Standard deviation of Portfolio is calculated by using the below formula:

p = w1 * 1 ^2 + w2 * 2 ^2 + 2 * w1 * w2 * Cov1,2

where, p = Portfolio standard deviation

wA = weight of the stock A in the portfolio = 50% or 0.50

wB = weight of the stock B in the portfolio = 50% or 0.50

A = standard deviation of the stock A returns = 10% or 0.10

B = standard deviation of the stock B returns = 17% or 0.17

(CovA,B) = Covariance between stock A and B =(Correlation between stock A and B) * A * B

here, we have to calculate Covariance between stock A and stock B (CovA,B):

Cov(A,B) = Corr(A,B) * A * B = 1 * 0.10 * 0.17 = 0.017

Therefore, p = 0.50 * (0.10)^2 + 0.50 * (0.17)^2 + 2 * 0.50 * 0.50 * 0.017

p = 0.005 + 0.01445 + 2 * 0.00425 = 0.02795 = 0.1672 or 16.72%

Hence, Standard Deviation of the Portfolio with stocks A and B is 16.72%