Security Y has a total variance of 225. Its beta is 1.2 and the market variance is 100. The standard deviation of its random error term is
A) 6%.
B) 14%.
C) 3%.
D) 9%.

Question

Quizplus · Accepted Answer

The standard deviation of the random error term (unsystematic risk) can be calculated using the formula for the total variance of a security, which is the sum of systematic variance and unsystematic variance. Systematic variance can be found by squaring the beta and multiplying it by the market variance. Given that the total variance is 225, beta is 1.2, and market variance is 100, we first find the systematic variance: (1.2)^2 * 100 = 144. The unsystematic variance is the total variance minus the systematic variance: 225 - 144 = 81. The standard deviation is the square root of the variance, so the standard deviation of the random error term is sqrt(81) = 9%.

Security Y Has a Total Variance of 225