The beta of an active portfolio is 1.45. The standard deviation of the returns on the market index is 22%. The nonsystematic variance of the active portfolio is 0.03. The standard deviation of the returns on the active portfolio is
A) 36.30%.
B) 5.84%.
C) 19.60%.
D) 24.17%.
E) 26.0%.

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 calculated as (Beta^2 * Market Variance). Given that Beta = 1.45 and the standard deviation of the market is 22%, the market variance is (0.22)^2 = 0.0484. Therefore, the systematic variance = (1.45)^2 * 0.0484 = 0.10197. The nonsystematic variance is given as 0.03. The total variance of the portfolio = 0.10197 + 0.03 = 0.13197. The standard deviation is the square root of the total variance, which is sqrt(0.13197) = 0.363, or 36.3% when expressed as a percentage.

The Beta of an Active Portfolio Is 1