Sharpe Ratio

问题如下：

Abbott, an analyst from an investment company, recently collected some information on a portfolio’s performance over the year. The mean annual return of the portfolio is 12%, the stanard deviation of return is 15%, the portfolio beta is 1.5, and the risk free rate is 6%. Which of the following is most appropriate?

选项：

A.

The coefficient of variation is 0.80 and Sharpe ratio is 4.

B.

The coefficient of variation is 1.25 and Sharpe ratio is 0.8.

C.

The coefficient of variation is 1.25 and Sharpe ratio is 0.4.

解释：

Total risk per unit of return can be measured by coefficient of

$variation=\frac{S_x}{\overline X}\times100\%=\frac{15\%}{12\%}\times100\%=1.25$

The excess return per unit of risk can be measured by

$sharp\;ratio=\frac{R_p-R_f}{\sigma_p}=\frac{12\%-6\%}{15\%}=0.40$