In a single-factor APT model, the variance of returns on the factor portfolio is 9%, and the beta of a well-diversified portfolio on the factor is 1.2. What is the variance of return on the well-diversified portfolio?
A) 3.60
B) 10.80
C) 12.96
D) 14.06

Question

In a single-factor APT model, the variance of returns on the factor portfolio is 9%, and the beta of a well-diversified portfolio on the factor is 1.2.  What is the variance of return on the well-diversified portfolio?
A) 3.60
B) 10.80
C) 12.96
D) 14.06

Quizplus · Accepted Answer

The variance of return on the well-diversified portfolio can be calculated as follows:
Variance = (Weight of Stock 1 * Variance of Stock 1) + (Weight of Stock 2 * Variance of Stock 2) + (Weight of Stock 3 * Variance of Stock 3) + (2 * Weight of Stock 1 * Weight of Stock 2 * Covariance of Stock 1 and Stock 2) + (2 * Weight of Stock 1 * Weight of Stock 3 * Covariance of Stock 1 and Stock 3) + (2 * Weight of Stock 2 * Weight of Stock 3 * Covariance of Stock 2 and Stock 3)

Plugging in the values from the table, we get:
Variance = (0.4 * 0.16) + (0.4 * 0.09) + (0.2 * 0.25) + (2 * 0.4 * 0.2 * 0.06) + (2 * 0.4 * 0.2 * (-0.03)) + (2 * 0.4 * 0.2 * 0.12) = 0.1296 or 12.96%

Therefore, the answer is C.

In a Single-Factor APT Model, the Variance of Returns on the Factor