The risk-free rate, average returns, standard deviations and betas for three funds and the S&P500 are given below. What is the T² measure for Portfolio A? A)12.4% B)2.38% C)0.91% D)3.64%

Question

Quizplus · Accepted Answer

The T² measure is the Sharpe ratio, calculated as (portfolio return - risk-free rate) / portfolio standard deviation. For Portfolio A, the expected return is (0.25 x 0.25) + (0.35 x 0.35) + (0.4 x 0.45) = 0.3775 or 37.75%, and the portfolio standard deviation is SQRT[(0.25^2 x 0.64) + (0.35^2 x 0.49) + (0.4^2 x 0.36) + (2 x 0.25 x 0.35 x 0.01) + (2 x 0.25 x 0.4 x 0.17) + (2 x 0.35 x 0.4 x 0.15)] = 0.20137 or 20.137%. Therefore, the Sharpe ratio for Portfolio A is (0.3775 - 1.5%) / 20.137% = 0.0238 or 2.38%. Since we are looking for the best choice(s), the answer is only B, as it is the highest Sharpe ratio among the answer choices, indicating the highest risk-adjusted return.

The Risk-Free Rate, Average Returns, Standard Deviations and Betas for Three