Sharpe Ratio

A Sharper Sharpe II : Skewed Distributions

Note: This blog post previously analyzed Damien Challet's 'Sharper estimator' of the Signal-Noise Ratio. The analysis used version 1.1 of the sharpeRratio, written by Challet. That version of the package contained a bug which severely biased the estimator, causing illusory improvements in the achieved standard error. Challet has fixed the package, which is now at version 1.2 (or later), and thus the analysis that was here can no longer be reproduced. We will perform an investigation of the fixed drawdown estimator, and link to it here.

A Sharper Sharpe

I recently discovered Damien Challet's paper on arxiv for computing the Sharpe ratio for fat-tailed returns distributions. The central observation is that you can create a statistic of a returns sample which is a function of the population Sharpe, what I call the 'Signal-Noise ratio'. (For example, the drawdown has this property, c.f. Rej et al., or Magdon-Ismail et al..) Challet's idea is to use the number of times a price level hits a new maximum (and a new minimum) as this statistic. Since the dependence of this statistic on the Signal Noise ratio, sample size, and population kurtosis is complicated, the inversion is performed by a spline.

One immediately notices that this function seems to be defined by the order of the returns, whereas the traditional, moment-based estimator that we call 'the' Sharpe ratio, is invariant to order. This fact is used in the suggested computation: the computation is repeated many times for permuted returns, which should give a better estimate of the Signal Noise ratio. Indeed, it appears that the drawdown-based computation is more efficient than the moment-based estimator, that is, it exhibits a lower standard error in practice.

Note: This blog post previously analyzed the standard error of the drawdown-based and the traditional moment-based estimators. The analysis used version 1.1 of the sharpeRratio, written by Damien Challet. That version of the package contained a bug which severely biased the estimator, causing illusory improvements in the achieved standard error. Challet has fixed the package, which is now at version 1.2 (or later), and thus the analysis that was here can no longer be reproduced. We will perform an investigation of the fixed drawdown estimator, and link to it here.