Moment-Free Sharpe Ratio Estimation from Total Drawdown Durations

The total duration of drawdowns is shown to be an efficient and robust estimator of Sharpe ratios. Its properties are distribution-dependent: the expected total drawdown duration is smaller for heavy-tailed returns than for Gaussian ones. As a consequence, in leptokurtic market conditions, the new estimator yields smaller Sharpe ratios than moment-based estimators, which implies that the standard estimator overestimates the information content of prices when the return distribution has heavy tails. Accordingly, using the standard estimator for taking trend-following decisions enhances large price fluctuations