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%.

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 (beta squared times market variance) and the nonsystematic variance. First, calculate the market variance (standard deviation squared): $22\% ^2 = 0.0484$ (or 4.84%). Then, calculate the systematic variance: $1.36^2 \times 0.0484 = 0.0893$ (or 8.93%). Add the nonsystematic variance: $0.0893 + 0.012 = 0.1013$ (or 10.13%). The standard deviation is the square root of the total variance: $\sqrt{0.1013} = 0.3181$ or 31.81%, which rounds to 31.86%.

The Beta of an Active Portfolio Is 1