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 (and is a deviation risk measure), named after William F. Sharpe.

Definition

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

where R_a is the asset return, R_b is the return on a benchmark asset, such as the risk free rate of return or an index such as the S&P 500. E[R_a-R_b] is the expected value of the excess of the asset return over the benchmark return, and {\sigma} is the standard deviation of this excess return. This is often confused with the information ratio, in part because the newer definition of the Sharpe ratio matches the definition of information ratio within the field of finance. Outside of this field, information ratio is simply mean over the standard deviation of a series of measurements.

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