Batman Stock has exhibited a standard deviation in stock returns of 0.5, whereas Superman Stock has exhibited a standard deviation of 0.6. The correlation coefficient between the stock returns is 0.5. What is the variance of a portfolio composed of 70 percent Batman and 30 percent Superman?

Question

Quizplus · Accepted Answer

First, we need to calculate the portfolio's weighted average standard deviation using the formula:

portfolio standard deviation = sqrt(w1^2 * SD1^2 + w2^2 * SD2^2 + 2*w1*w2*r*SD1*SD2)

where:
w1 = 0.7 (weight of Batman stock)
SD1 = 0.5 (standard deviation of Batman stock)
w2 = 0.3 (weight of Superman stock)
SD2 = 0.6 (standard deviation of Superman stock)
r = 0.5 (correlation coefficient between the stock returns)

Plugging in the numbers, we get:

portfolio standard deviation = sqrt(0.7^2 * 0.5^2 + 0.3^2 * 0.6^2 + 2*0.7*0.3*0.5*0.5*0.6) = 0.4326

Next, we need to square the portfolio standard deviation to get the variance:

portfolio variance = 0.4326^2 = 0.1869

Finally, we need to adjust for the weights of the individual stocks to get the variance of the portfolio composition. Since we have 70% Batman and 30% Superman, we can calculate the variance as:

portfolio variance = 0.7^2 * 0.5^2 + 0.3^2 * 0.6^2 + 2*0.7*0.3*0.5*0.5*0.6 = 0.2179

Therefore, the answer is B) 0.2179.

Batman Stock Has Exhibited a Standard Deviation in Stock Returns