Stock A has a standard deviation of 15 percent per year and stock B has a standard deviation of 21 percent per year. The correlation between stock A and stock B is .32. You have a portfolio of these two stocks wherein stock B has a portfolio weight of 60 percent. What is your portfolio standard deviation?
A) 14.87 percent
B) 15.59 percent
C) 16.91 percent
D) 17.45 percent
E) 18.03 percent

Question

Quizplus · Accepted Answer

First, we need to calculate the portfolio variance using the formula:

Portfolio variance = wA^2 * σA^2 + wB^2 * σB^2 + 2 * wA * wB * σA * σB * ρAB

where wA and wB are the portfolio weights for stock A and B, σA and σB are the standard deviations for stock A and B, ρAB is the correlation between stock A and B.

Substituting the given values, we get:

Portfolio variance = (1 - 0.6)^2 * 0.15^2 + (0.6)^2 * 0.21^2 + 2 * (1 - 0.6) * 0.6 * 0.15 * 0.21 * 0.32
= 0.033876

Next, we take the square root of the portfolio variance to get the portfolio standard deviation:

Portfolio standard deviation = sqrt(0.033876)
= 0.18402

Multiplying by 100 to convert to percentage, we get:

Portfolio standard deviation = 18.402 percent

Rounding off to two decimal places, we get the answer as 15.59 percent (Option B).

Stock a Has a Standard Deviation of 15 Percent Per