The Sharpe Ratio and Coefficient of Variation are both risk$-$adjusted performance measures, but they

account for risk differently.

The Sharpe Ratio measures excess return per unit of total risk $($standard deviation$)$:

Sharpe Ratio $=($Portfolio Return $-$ Risk$-$Free Rate$)/$ Portfolio Standard Deviation

The Coefficient of Variation measures risk relative to the expected return:

Coefficient of Variation $=$ Standard Deviation $/$ Expected Return

Question:

Investment Fund X had an annualized return of $12\%$ with a standard deviation of $18\%.$ The risk$-$free rate

was $3\%.$

Calculate and compare the Sharpe Ratio and Coefficient of Variation for Fund X$.$

a$)$ Sharpe $=0\mathrm{.}5,$ CV $=0\mathrm{.}67,$ Sharpe is lower

b$)$ Sharpe $=0\mathrm{.}5,$ CV $=1\mathrm{.}5,$ Sharpe is higher

c$)$ Sharpe $=0\mathrm{.}75,$ CV $=0\mathrm{.}67,$ Sharpe is higher

d$)$ Sharpe $=0\mathrm{.}75,$ CV $=1\mathrm{.}5,$ Sharpe is lower