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Probabilistic Sharpe ratio

The probability that a strategy's true Sharpe ratio exceeds some benchmark, given the observed Sharpe, the sample length, and the return distribution's shape.

Instead of reporting Sharpe equal to 1.2, report the probability that the true value is above zero, or above 0.5. On 250 daily observations an observed Sharpe of 1.2 might give only a 78% probability of being above zero once skew and kurtosis are accounted for.

Sample length does most of the work. The standard error of an annualised Sharpe is roughly the square root of 1 over the number of years, adjusted for higher moments. One year of data and a Sharpe of 1.0 is barely distinguishable from zero; five years and 1.0 is a real claim.

Negative skewness and high kurtosis both reduce the probability for the same observed Sharpe, which correctly penalises strategies like naked option selling that look smooth until they do not.

Related: deflated-sharpe-ratio, sharpe-ratio

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