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 .
The total duration of drawdowns is shown to provide an 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 the bias of moment-based Sharpe ratio estimators and the tail exponent of the distribution of heavy-tailed price returns. The heterogeneity of tail exponents at any given time among assets implies that our new methods yields significantly different asset rankings than moment-based methods, especially in periods large volatility. This is fully confirmed by using 20 years of historical data on 3449 liquid US equities .
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be an
provide an moment-free, unbiased,
R
. Its properties are distribution-dependent: the expected total drawdown duration is smaller for
both for Gaussian and
R
returns than for Gaussian ones. As a consequence, in leptokurtic market conditions, the new estimator yields smaller Sharpe ratios than
price returns. We then use this quantity to infer an analytic expression of the the bias of
R
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
Sharpe ratio estimators and the tail exponent of the distribution of heavy-tailed price returns. The heterogeneity of tail exponents at any given time among assets implies that our new methods yields significantly different asset rankings than moment-based methods, especially in periods large volatility. This is fully confirmed by using 20 years of historical data on 3449 liquid US equities