### Sharpe Ratio

The Sharpe Ratio (SR) indicates how well the return of an asset compensates the investor for the risks taken. \begin{equation} \text{Sharpe Ratio} = \frac{E(r)-r_f}{\sigma} \end{equation}

- \(E(r)\)
- expected return
- \(r_f\)
- risk free rate of return
- \(\sigma\)
- standard deviation of asset returns (square root of variance)

An intraday version of the ratio could be reduced further by setting a risk-free rate equal to zero: \begin{equation} \text{Sharpe Ratio}_{\text{intraday}} = \frac{E(r)}{\sigma} \end{equation} This risk-adjusted measure was developed by Nobel Laureate William Sharpe. The Sharpe ratio performs particularly well when returns are distributed normally. This means that distribution of returns is completely described by its mean and volatility.

When returns are skewed, have non-zero kurtosis or other anomalies, Sharpe ratio might fail to capture such abnormal risks. Modified Sharpe Ratio could be used in case investment risks go beyond simple standard deviation.