A Sharper Sharpe III : MLEs
Note: This blog post previously analyzed Damien Challet's 'Sharper estimator' of the Signal-Noise Ratio. We found that this drawdown estimator seemed empirically to have lower MSE than the Cramér Rao Lower Bound when used to estimate the mean of some distributions, which was a warning that something was wrong. 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.