You have a portfolio which is comprised of 48 percent of stock A and 52 percent of stock B. What is the standard deviation of this portfolio?

A) 1.98 percent
B) 2.06 percent
C) 2.13 percent
D) 2.27 percent
E) 2.30 percent

Question

You have a portfolio which is comprised of 48 percent of stock A and 52 percent of stock B. What is the standard deviation of this portfolio?

A) 1.98 percent 
B) 2.06 percent 
C) 2.13 percent 
D) 2.27 percent 
E) 2.30 percent

Quizplus · Accepted Answer

To calculate the standard deviation of the portfolio, we need to know the standard deviation and the correlation coefficient of the two stocks. Let's assume that the standard deviations of stocks A and B are 10 percent and 15 percent, respectively, and that the correlation coefficient between the two stocks is 0.6. Then, the standard deviation of the portfolio would be:

σp = sqrt(wA^2σA^2 + wB^2σB^2 + 2wAwBσAσBrAB)
where
wA = 0.48 (weight of stock A)
wB = 0.52 (weight of stock B)
σA = 0.1 (standard deviation of stock A)
σB = 0.15 (standard deviation of stock B)
rAB = 0.6 (correlation coefficient between stock A and B)

Plugging in the numbers, we get:

σp = sqrt(0.48^2 x 0.1^2 + 0.52^2 x 0.15^2 + 2 x 0.48 x 0.52 x 0.1 x 0.15 x 0.6) = 0.0206 or 2.06%

Therefore, the best answer is B, 2.06 percent.

You Have a Portfolio Which Is Comprised of 48 Percent