Bootstrap simulation

Bootstrap simulation, formalised by Efron (1979), generates synthetic return paths by sampling from the historical record with replacement. Unlike Monte Carlo under Geometric Brownian Motion, bootstrap inherits the empirical distribution — including fat tails, skew, and the actual observed kurtosis — without any parametric assumption.

The two flavours

• ·Simple bootstrap: draw single observations independently. Preserves marginal distribution but destroys serial correlation (volatility clusters, momentum, mean reversion).
• ·Block bootstrap: draw contiguous blocks of length k. Preserves serial structure on the timescale of k periods. Block length is a hyperparameter — typically 5 to 21 days for daily returns.

Bootstrap vs Monte Carlo (GBM)

• ·Tail honesty: bootstrap reproduces empirical CVaR. GBM understates it for fat-tailed assets.
• ·Forward range: bootstrap cannot generate events worse than the worst historical event. GBM can — but only because it assumes a parametric tail that may itself be wrong.
• ·Speed: identical at 10,000 paths.

How MEDGE Capital uses bootstrap

Block bootstrap is on the MEDGE Monte Carlo roadmap as an alternative to GBM for users whose backtest window includes a tail-rich regime (2008, 2020). The current Monte Carlo report uses GBM; bootstrap CVaR is computed historically and reported alongside.