  The total duration of drawdowns is shown to provide a moment-free, unbiased,
efficient and robust estimator of Sharpe ratios both for Gaussian and
heavy-tailed price returns. We then use this quantity to infer an analytic
expression of the bias of moment-based Sharpe ratio estimators as a function of
the return distribution tail exponent. The heterogeneity of tail exponents at
any given time among assets implies that our new method yields significantly
different asset rankings than those of moment-based methods, especially in
periods large volatility. This is fully confirmed by using 20 years of
historical data on 3449 liquid US equities.
