Aquaman Stock has exhibited a standard deviation in share returns of 0.7, whereas Green Lantern Stock has exhibited a standard deviation of 0.8. The correlation coefficient between the share returns is 0.1. What is the standard deviation of a portfolio composed of 70 per cent Aquaman and 30 per cent Green Lantern?
A) 0.32122
B) 0.54562
C) 0.56676
D) 0.75000

Question

Quizplus · Accepted Answer

The formula to calculate the portfolio standard deviation is as follows:

Portfolio Standard Deviation = [(weight of stock A x standard deviation of stock A)^2 + (weight of stock B x standard deviation of stock B)^2 + 2 x (weight of stock A x weight of stock B x standard deviation of stock A x standard deviation of stock B x correlation coefficient)^0.5]

Using the given data, we can calculate the standard deviation of the portfolio as follows:

Portfolio Standard Deviation = [(0.7 x 0.7 x 0.7) + (0.8 x 0.8 x 0.3) + 2 x (0.7 x 0.8 x 0.1))^0.5 = 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 Share Returns