For a one-factor model, an analyst finds the variance of the factor is 6 and the variance of the random error is 10. If the total variance for the security is 106, its sensitivity to the factor is
A) 2.
B) 5.
C) 6.
D) 4.

Question

For a one-factor model, an analyst finds the variance of the factor is 6 and the variance of the random error is 10.	If the total variance for the security is 106, its sensitivity to the factor is
A) 2.
B) 5.
C) 6.
D) 4.

Quizplus · Accepted Answer

The sensitivity to the factor, often denoted as beta (β), can be calculated using the formula for the total variance in a one-factor model: Total Variance = (Beta^2 * Factor Variance) + Error Variance. Given the total variance (106), factor variance (6), and error variance (10), we can solve for Beta: 106 = (Beta^2 * 6) + 10. Subtracting 10 from both sides gives 96 = Beta^2 * 6. Dividing both sides by 6 gives Beta^2 = 16. Taking the square root of both sides gives Beta = 4.

For a One-Factor Model, an Analyst Finds the Variance of the Factor