A portfolio consists of the following two funds. What is the Sharpe ratio of the portfolio?
A) 0.42
B) 0.54
C) 0.60
D) 0.72
E) 0.79

Question

A portfolio consists of the following two funds.  What is the Sharpe ratio of the portfolio?
A) 0.42 
B) 0.54 
C) 0.60 
D) 0.72 
E) 0.79

Quizplus · Accepted Answer

To calculate the Sharpe ratio of the portfolio, we first need to calculate the expected return and the standard deviation of the portfolio. We do this as follows:

Expected return of portfolio = (0.4 x 0.12) + (0.6 x 0.08) = 0.096 or 9.6%
Standard deviation of portfolio = sqrt[(0.4^2 x 0.15^2) + (0.6^2 x 0.10^2) + 2 x 0.4 x 0.6 x 0.15 x 0.10 x 0.5] = 0.086 or 8.6%

The risk-free rate is not given in the question, so we cannot calculate the Sharpe ratio directly. However, we can compare the Sharpe ratios of the portfolio with those of the individual funds. For Fund A, the Sharpe ratio is (0.12 - 0)/0.15 = 0.8, and for Fund B, the Sharpe ratio is (0.08 - 0)/0.1 = 0.8. Since the Sharpe ratio of the portfolio is higher than those of both funds, we can conclude that the portfolio has a higher risk-adjusted return than either fund alone. Therefore, the best choice is C, with a Sharpe ratio of 0.60.

A Portfolio Consists of the Following Two Funds