## Sharpe Ratio

If $r_0$ is the risk free rate, the sharpe ratio used to determine which of 2 investment that can be leveraged is best is given by

$$ S = \frac{r-r_0}{\sigma}$$

The sharpe ratio is using simple returns, as leverage expected returns cannot be computed based on compound return but require both the input of the simple expected return $r$ and volatility $\sigma$ .

If the investment period is not one year, it is customary to annualize the sharpe ratio by dividing it by $\sqrt{T}$ where $T$ is the investment horizon in years.