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? Round the answer to five decimal points.
A) 0.32122
B) 0.54562
C) 0.56676
D) 0.75000

Question

Quizplus · Accepted Answer

The formula for calculating the standard deviation of a portfolio composed of two assets is as follows:

σportfolio = √(w1^2σ1^2 + w2^2σ2^2 + 2w1w2σ1σ2ρ)

where
σ1 = the standard deviation of Asset 1
σ2 = the standard deviation of Asset 2
w1 = the weight of Asset 1 in the portfolio
w2 = the weight of Asset 2 in the portfolio
ρ = the correlation coefficient between the returns of Asset 1 and Asset 2

Plugging in the given values:

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

Therefore, the standard deviation of the portfolio is 0.56676, which is closest to option C (0.56676).

Aquaman Stock Has Exhibited a Standard Deviation in Stock Returns