# Sharpe ratio

In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.

Since its revision by the original author, William Sharpe, in 1994, the ex-ante Sharpe ratio is defined as:

where ${\displaystyle R_{a}}$ is the asset return, ${\displaystyle R_{b}}$ is the risk free rate. ${\displaystyle E}$ is the expected value of the excess of the asset return over the benchmark return, and ${\displaystyle {\sigma _{a}}}$ is the standard deviation of the asset excess return.

The ex-post Sharpe ratio uses the same equation as the one above but with realized returns of the asset and benchmark rather than expected returns - see the second example below.

The Sharpe ratio is similar to the Information ratio but, whereas the Sharpe ratio is the 'excess' return of an asset over the return of a risk free asset divided by the variability or standard deviation of returns, the information ratio is the active return to the most relevant benchmark index divided by the standard deviation of the 'active' return or tracking error.

The Sharpe ratio characterizes how well the return of an asset compensates the investor for the risk taken. When comparing two assets versus a common benchmark, the one with a higher Sharpe ratio provides better return for the same risk (or, equivalently, the same return for lower risk). However, like any other mathematical model, it relies on the data being correct. Pyramid schemes with a long duration of operation would typically provide a high Sharpe ratio when derived from reported returns, but the inputs are false. When examining the investment performance of assets with smoothing of returns (such as with-profits funds) the Sharpe ratio should be derived from the performance of the underlying assets rather than the fund returns.

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