In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment such as a security or portfolio compared to a risk-free asset, after adjusting for its risk. It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk. It was named after William F. Sharpe, who developed it in 1966. Definition Since its revision by the original author, William Sharpe, in 1994, the ex-ante Sharpe ratio is defined as: where is the asset return, is the risk-free return (such as a U.S. Treasury security). is the expected value of the excess of the asset return over the benchmark return, and 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 information ratio is a generalization of the Sharpe ratio that uses as benchmark some other, typically risky index rather than using risk-free returns. Use in finance The Sharpe ratio seeks to characterize how well the return of an asset compensates the investor for the risk taken. When comparing two assets, the one with a higher Sharpe ratio appears to provide better return for the same risk, which is usually attractive to investors. However, financial assets are often not normally distributed, so that standard deviation does not capture all aspects of risk. Ponzi schemes, for example, will have a high empirical Sharpe ratio until they fail. Similarly, a fund that sells low-strike put options will have a high empirical Sharpe ratio until one of those puts is exercised, creating a large loss. In both cases, the empirical standard deviation before failure gives no real indication of the size of the risk being run. Even in less extreme cases, a reliable empirical estimate of Sharpe ratio still requires the collection of return data over sufficient period for all aspects of the strategy returns to be observed. For example, data must be taken over decades if the algorithm sells an insurance that involves a high liability payout once every 5–10 years, and a high-frequency trading algorithm may only require