Standard bootstrap resamples observations with replacement to estimate sampling distributions. For financial returns it has to be applied carefully.
The naive i.i.d. bootstrap fails for time series because returns are serially correlated (especially in volatility). Two fixes:
- Block bootstrap: resample blocks of consecutive observations to preserve short-range dependence. Block length is a tuning knob.
- Stationary bootstrap: blocks have random geometric lengths, smoothing the discontinuities at block boundaries.
Common applications include confidence intervals for Sharpe ratios, drawdown statistics, and trading-strategy performance. The bootstrap is also useful for backtest sensitivity — randomly subsample your history and re-fit to see how stable the results are.
Limits: the bootstrap can't extrapolate beyond the observed data. If your sample contains no -sigma days, your bootstrap will never produce one. Combine bootstrap with parametric tail models for full risk analysis.