The Sharpe ratio can be precisely computed from the total drawdown duration

What is it about?

The Sharpe ratio, also known as the signal ratio in signal processing, or the t-statistics, is an ubiquitous measure of performance (average price return) adjusted for risk (standard deviation). Regrettably, measuring the Sharpe ratio in the usual way, i.e., dividing the average by the standard deviation, does not work for financial price returns as they are not Gaussian. Some corrections have been proposed in the past. They require to compute the average of the third and fourth power of the price returns. Alas, these two quantities are extremely volatile and may diverge in the limit of very long time series. This paper instead proposes to infer the Sharpe ratio from the total drawdown duration, as it shows that there is a one-to-one correspondance between these two quantities. This leads to a more robust and moment-free estimator. In other words, by using time as a proxy, one computes the ratio of the first moment (the average) and a second moment (the standard deviation) of price returns without computing any moment.

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Why is it important?

Sharpe ratio is a fundamental performance measure in Finance. Yet, it is grossly unadapted to financial data and some of the proposed corrections are even less adapted. Thus this work provides a totally new way to estimate Sharpe ratios. A simple application shows that ranking assets according the new estimator and the plain one leads to totally different rankings, especially for the best assets.

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