Bootstrapping Returns

Bootstrapping Returns

Bootstrapping is a resampling technique to estimate the sampling distribution of a statistic without making distributional assumptions. It is essential in finance for constructing confidence intervals on Sharpe ratios, means, and other metrics.

The procedure:

1. From a sample of $n$ values, draw $n$ values with replacement → bootstrap sample
2. Compute the statistic of interest on this bootstrap sample
3. Repeat $B$ times to get a bootstrap distribution
4. Use percentiles of this distribution for confidence intervals

Bootstrap confidence interval at level $\alpha$ (e.g., 0.05 for 95% CI):

• Lower bound: $\alpha/2$ percentile of bootstrap distribution
• Upper bound: $(1 - \alpha/2)$ percentile

Use random.choices(xs, k=len(xs)) for sampling with replacement.

Your Task

Implement:

• bootstrap_mean(xs, n_boot, seed) — list of bootstrap sample means
• bootstrap_ci(xs, n_boot, seed, alpha=0.05) — (lower, upper) confidence interval