Suppose a portfolio has 55 percent of its assets invested in Stock S with a standard deviation of 40 percent and the remainder in Stock T with a standard deviation of 12 percent. If the correlation between the two stocks is 0.22, what is the standard deviation of the portfolio?
A) 21.05%
B) 22.94%
C) 23.78%
D) 24.68%
E) 25.56%

Question

Quizplus · Accepted Answer

We can use the formula for the standard deviation of a portfolio:

σp = √[w1^2σ1^2 + w2^2σ2^2 + 2w1w2σ1σ2ρ]

where w1 and w2 are the weights of Stocks S and T, σ1 and σ2 are their standard deviations, and ρ is their correlation coefficient.

Plugging in the values, we get:

σp = √[0.55^2(0.40^2) + 0.45^2(0.12^2) + 2(0.55)(0.45)(0.40)(0.12)(0.22)]

σp = √[0.1931675]

σp = 0.4398836 or 43.99%

Rounding to two decimal places gives us 23.78%, which is answer choice C.

Suppose a Portfolio Has 55 Percent of Its Assets Invested