The beta of an active portfolio is .80. The standard deviation of the returns on the market index is 25%. The nonsystematic variance of the active portfolio is 0.03. The standard deviation of the returns on the active portfolio is
A) 28.32%.
B) 26.46%.
C) 24.62%.
D) 22.17%.
E) 20.08%.

Question

Quizplus · Accepted Answer

The standard deviation of the returns on the active portfolio can be calculated using the formula for the total variance of a portfolio, which is the sum of the systematic variance and the nonsystematic variance. The systematic variance can be found by squaring the portfolio's beta and multiplying it by the variance of the market. Given that the beta is 0.80 and the standard deviation of the market is 25% (or 0.25 when expressed as a decimal), the variance of the market is 0.25^2 = 0.0625. Therefore, the systematic variance is 0.80^2 * 0.0625 = 0.04. Adding the nonsystematic variance of 0.03 gives a total variance of 0.07. The standard deviation is the square root of the variance, so sqrt(0.07) = 0.2646 or 26.46%.

The Beta of an Active Portfolio Is