AdvancedQuantitative MethodsPython

Run this module

cd "Quantitative Methods - Bootstrap"
python "bootstrap.py"

Bootstrap Resampling¶

The bootstrap estimates the sampling distribution of any statistic by resampling the observed data with replacement — no normality assumption required. It is the honest way to put confidence intervals around backtest metrics like Sharpe ratio, mean return, or maximum drawdown.

Functions¶

Function	Description
`iid_bootstrap(data, statistic, n_boot)`	Resample individual observations (assumes no serial dependence)
`block_bootstrap(data, statistic, block_size, n_boot)`	Resample contiguous blocks — preserves autocorrelation
`stationary_bootstrap(data, statistic, expected_block, n_boot)`	Politis–Romano: random geometric block lengths, circular wrap
`confidence_interval(estimates, alpha)`	Percentile confidence interval from bootstrap estimates

Key Concepts¶

Why bootstrap? Financial returns are fat-tailed and serially correlated, so parametric (normal-theory) confidence intervals are usually wrong. Resampling makes no distributional assumption.
i.i.d. vs. block: the i.i.d. bootstrap destroys time structure. For returns with autocorrelation or volatility clustering, use a block method so each resample preserves short-term dependence.
Stationary bootstrap: blocks of random (geometric) length with circular wrap-around guarantee the resampled series is stationary, avoiding the fixed-block boundary artefacts.
Percentile CI: take the 2.5th and 97.5th percentiles of the bootstrap estimates for a 95% interval.

Example¶

import numpy as np
from bootstrap import block_bootstrap, confidence_interval

returns = np.random.default_rng(0).normal(0.0005, 0.012, 504)
sharpe = lambda x: x.mean() / x.std(ddof=1) * np.sqrt(252)

est = block_bootstrap(returns, sharpe, block_size=20, n_boot=2000, seed=1)
print(confidence_interval(est))   # 95% CI for the annualised Sharpe

Practical Notes¶

A typical rule of thumb for the average block length is n^(1/3) for the stationary bootstrap.
Use n_boot >= 1000 for stable percentile intervals; 2000–10000 for tail statistics.
The bootstrap quantifies sampling uncertainty — it cannot rescue a backtest that suffers from look-ahead bias or overfitting.

Continue in Quantitative Methods¶

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