The beta of an active portfolio is 1.36. The standard deviation of the returns on the market index is 22%. The nonsystematic variance of the active portfolio is 1.2%. The standard deviation of the returns on the active portfolio is
A) 3.19%.
B) 31.86%.
C) 42.00%.
D) 27.57%.
E) 2.86%.

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 systematic variance and nonsystematic variance. 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 1.36 and the standard deviation of the market is 22%, the variance of the market is 22%^2 = 0.0484. Therefore, the systematic variance is 1.36^2 * 0.0484. The nonsystematic variance is given as 1.2%, or 0.012 in decimal form. Adding these together gives the total variance, and taking the square root of this sum gives the standard deviation of the portfolio's returns. Calculating this yields a standard deviation of approximately 31.86%.

The Beta of an Active Portfolio Is 1