The expected returns for Securities ABC and XYZ are 8% and 13%, respectively.The standard deviation is 12% for ABC and 18% for XYZ.There is no relationship between the returns on the two securities.The market return is 12.5% with a standard deviation of 16%.The risk-free rate is 5%.What is the Sharpe ratio of a portfolio with 40% of the funds in ABC and 60% in XYZ?
A)0.47
B)0.51
C)0.75
D)0.93

Question

Quizplus · Accepted Answer

The Sharpe ratio is calculated as (Expected Portfolio Return - Risk-Free Rate) / Standard Deviation of Portfolio. Since there's no relationship between the returns on the two securities (correlation is 0), the portfolio's expected return is a weighted average of the securities' returns, and its variance is the weighted sum of their variances. Expected return = 0.4*8% + 0.6*13% = 11%. Variance = (0.4^2 * 0.12^2) + (0.6^2 * 0.18^2) = 0.01056. Standard deviation = sqrt(0.01056) = 0.10276. Sharpe ratio = (11% - 5%) / 10.276% ≈ 0.51.

The Expected Returns for Securities ABC and XYZ Are 8