Definition
Since its revision by the original author in 1994, the ex-ante Sharpe ratio is defined as:
where is the asset return, is the return on a benchmark asset, such as the risk free rate of return or an index such as the S&P 500. is the expected value of the excess of the asset return over the benchmark return, and is the standard deviation of this expected 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.
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.
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