Simulating 5,000 Alternate Realities: Block Bootstrap Monte Carlo
Block bootstrap Monte Carlo with regime-conditioned resampling validating 0.08% breach probability across 5,000+ simulations.
Why Block Bootstrap Over Standard Monte Carlo
Standard Monte Carlo randomizes individual trade outcomes, destroying the serial correlation in the return series. If V7 tends to have winning streaks followed by losing streaks (regime-dependent performance), standard Monte Carlo would smooth this out and underestimate tail risk.
Block bootstrap preserves serial correlation by resampling blocks of consecutive trades rather than individual trades. S41 uses blocks of 20 trades (approximately one week of trading) drawn with replacement. This preserves intra-block correlation while generating diverse path combinations.
Regime-Conditioned Resampling
S41 goes further by conditioning the block selection on regime. Blocks from trending regimes are resampled with probability proportional to the fraction of time the market spends in trending regimes. This prevents scenarios where a simulated year consists entirely of trending blocks or entirely of ranging blocks, which would be unrealistic.
The regime conditioning uses the K-Means cluster assignments from S09. Each block is labeled with its dominant regime, and the resampling probability matches the historical regime distribution. This produces simulated paths that mirror the statistical properties of real trading more closely than unconditioned sampling.
What 5,000 Simulations Tell Us
The 5,000 simulated paths produce a distribution of drawdown outcomes. The 50th percentile max DD is 0.9% (most simulations are benign). The 95th percentile is 6.79%. The 99th percentile is 8.10%. The 99.9th percentile (breach territory) is 9.7%. The breach probability (paths exceeding 10%) is 0.08%.
These numbers provide confidence intervals around the backtest's single-path result of 1.49% max DD. The single path was fortunate (better than median) but not suspiciously so (within the 25th percentile of outcomes). This confirms that the backtest result is realistic and not the product of a lucky path through market history. The Monte Carlo validation is the ultimate honesty check: it says "even in the unluckiest plausible trading year, the system survives."