Batman Stock has exhibited a standard deviation in share returns of 0.5, whereas Superman Stock has exhibited a standard deviation of 0.6. The correlation coefficient between the share returns is 0.5. What is the variance of a portfolio composed of 70 per cent Batman and 30 per cent Superman?
A) 0.1549
B) 0.2179
C) 0.4668
D) 0.5500

Question

Quizplus · Accepted Answer

First, we need to calculate the expected return of the portfolio:

Expected return = (0.7 * expected return of Batman) + (0.3 * expected return of Superman)

Next, we need to calculate the variance of the portfolio using the formula:

Variance of portfolio = (0.7^2 * variance of Batman) + (0.3^2 * variance of Superman) + (2 * 0.7 * 0.3 * covariance between Batman and Superman)

Covariance between Batman and Superman = correlation coefficient * standard deviation of Batman * standard deviation of Superman

Covariance between Batman and Superman = 0.5 * 0.5 * 0.6 = 0.15

Expected return of Batman = 0.08 (assumed)
Expected return of Superman = 0.12 (assumed)

Expected return of portfolio = (0.7 * 0.08) + (0.3 * 0.12) = 0.092

Variance of portfolio = (0.7^2 * 0.5^2) + (0.3^2 * 0.6^2) + (2 * 0.7 * 0.3 * 0.15) = 0.2179

Therefore, the answer is B - 0.2179.

Batman Stock Has Exhibited a Standard Deviation in Share Returns