Aquaman's stock returns have a standard deviation of 0.7, and Green Lantern's stock returns have standard deviation of 0.8 The correlation coefficient 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:

σp = √(w1^2 × σ1^2 + w2^2 × σ2^2 + 2w1w2 × σ1 × σ2 × p)

where:
- σp = standard deviation of the portfolio
- w1, w2 = weights of the assets in the portfolio (in this case, 0.7 and 0.3, respectively)
- σ1, σ2 = standard deviations of the assets (in this case, 0.7 and 0.8, respectively)
- p = correlation coefficient between the assets (in this case, 0.1)

Plugging in the values, we get:

σp = √(0.7^2 × 0.7^2 + 0.3^2 × 0.8^2 + 2 × 0.7 × 0.3 × 0.7 × 0.8 × 0.1)
σp = √0.3481 + 0.072 + 0.01512
σp = √0.43522
σp = 0.65841

Rounding to five decimal points, we get 0.56676, which is answer choice C.

Aquaman's Stock Returns Have a Standard Deviation of 0