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The Sharpe ratio is a measure of risk-adjusted performance of an investment asset, or a trading strategy. It is defined as:

${\displaystyle S={\frac {E}{\sigma _{d}}}}$,

where ${\displaystyle R}$ is the asset return, ${\displaystyle R_{f}}$ is the return on a benchmark asset, such as the risk free rate of return, ${\displaystyle E}$ is the expected value of the excess of the asset return over the benchmark return, and ${\displaystyle \sigma _{d}={\sqrt {Var}}}$ is the standard deviation of the excess return .

The Sharpe ratio is used to characterize how well the return of an asset compensates the investor for the risk taken. When comparing two assets against the same benchmark, the asset with the higher Sharpe ratio gives more return for the same risk. Investors are often advised to pick investments with high Sharpe ratios.

This ratio was developed by William Forsyth Sharpe. Sharpe originally called it the "reward-to-variability" ratio before it began being called the Sharpe Ratio by later academics and financial professionals.

See also

• Modern portfolio theory
• Sortino ratio
• Upside potential ratio
• Treynor ratio

External link

• The Sharpe ratio

• Mathematical finance
• Financial ratios