Aquaman Stock has exhibited a standard deviation in stock returns of 0.7, whereas Green Lantern Stock has exhibited a standard deviation of 0.8. The correlation coefficient between the stock returns is 0.1. What is the standard deviation of a portfolio composed of 70 percent Aquaman and 30 percent Green Lantern?

Question

Quizplus · Accepted Answer

To find the standard deviation of a portfolio with two stocks, we use the formula:

σportfolio = √(w1^2σ1^2 + w2^2σ2^2 + 2w1w2ρσ1σ2)

where w1 and w2 are the weights of the two stocks in the portfolio, σ1 and σ2 are the standard deviations of the two stocks, ρ is the correlation coefficient between the two stocks.

Given:

w1 = 0.7, w2 = 0.3
σ1 = 0.7, σ2 = 0.8
ρ = 0.1

Substituting the values in the formula, we get:

σportfolio = √(0.7^2*(0.7)^2 + 0.3^2*(0.8)^2 + 2*0.7*0.3*0.1*0.7*0.8)
= √(0.34522)
= 0.56676

Therefore, the standard deviation of the portfolio is 0.56676, which corresponds to choice C.

Aquaman Stock Has Exhibited a Standard Deviation in Stock Returns