# Sharpe ratio

## Description

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.

This formula calculates the Sharpe ratio.

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.

Use in finance

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.

Sharpe ratios, along with Treynor ratios and Jensen’s alphas, are often used to rank the performance of portfolio or mutual fund managers.

Related formulas## Variables

S_{a} | Sharpe ratio (dimensionless) |

R_{a} | asset return (dimensionless) |

R_{b} | risk free rate (dimensionless) |

σ_{a} | standard deviation of the asset excess return (dimensionless) |