When i.i.d. resampling flatters a drawdown estimate

Question

A quant estimates a confidence interval for a strategy's worst peak-to-trough drawdown by bootstrapping: she resamples the daily returns with replacement (each day drawn independently), re-stitches them into a synthetic path, measures the drawdown, and repeats thousands of times. The resulting interval says the worst drawdown should be mild. In live trading the strategy suffers a drawdown far outside that interval.

Explain what went wrong with the resampling scheme and what method would give an honest drawdown interval.

Accepted Answer

The core mistake: i.i.d. resampling destroys dependence. Drawing days independently with replacement assumes returns are independent and identically distributed. Real return series are not: they show volatility clustering (big moves bunch together) and short-run autocorrelation. Drawdown is a path-dependent statistic, it is driven precisely by runs of consecutive bad days. When you shuffle days independently, you scatter those bad days apart, so the synthetic paths almost never contain the long losing streaks that create severe drawdowns. The bootstrap therefore systematically understates dra…

When i.i.d. resampling flatters a drawdown estimate

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