Question

stock A has a standard deviation of 40% per year and stock B has a standard deviation of 10% per year. The correlation between stock A and stock B is .15 You have a portfoluo of these two stocks wherein stock B has a portfolio weight of 60%. What is your portfolio standard deviation?

Answer 1

Standard Deviation of the Portfolio

Weight of Stock A (wA) = 0.40

Weight of Stock B (wB) = 0.60

Standard Deviation of Stock A (σA) = 0.40

Standard Deviation of Stock B (σB) = 0.10

CorrAB = 0.15

Portfolio Standard Deviation = [(wA² * σA²) + (wB² * σB²) + (2* wA * σA * wB * σB * CorrAB)]^1/2

= [(0.40² * 0.40²) + (0.60² * 0.10²) + (2 * 0.40 * 0.40 * 0.60 * 0.10 * 0.15)] ^1/2

= [0.0256 + 0.0036 + 0.0288]^1/2

= [0.0580] ^1/2

= 0.2408 or

= 24.08%

“Hence, the Standard Deviation of the Portfolio would be 24.08%”