Portfolio-level Monte Carlo with correlated drawdowns

[MDUYN]

Context

The current multi-strategy comparison report handles correlated drawdowns partially:

• Computes a correlation matrix across strategy returns
• Overlays equity curves and drawdowns on a shared timeline
• Surfaces beat-rate vs. benchmarks (Buy & Hold, DCA, risk-free, custom)

This lets users see when strategies draw down together, but Monte Carlo / permutation testing today still runs at the individual strategy level. The result is per-strategy tail-risk distributions, not a portfolio-level tail-risk distribution.

Goal

Add a joint Monte Carlo mode that resamples the correlated return matrix of multiple strategies together, producing:

• Distribution of portfolio equity curves
• Distribution of portfolio max drawdown / CVaR / Calmar
• Probability of joint drawdown exceeding a user-defined threshold
• Confidence bands on portfolio metrics

Approaches to evaluate

1. Stationary block bootstrap on the joint return matrix (preserves serial correlation + cross-correlation)
2. Cholesky-decomposed shuffles of standardized returns (preserves linear cross-correlation, breaks serial)
3. Copula-based resampling (e.g. Gaussian / t-copula) — preserves dependency structure with arbitrary marginals
4. Hybrid: block bootstrap for serial structure + copula for cross-sectional dependence

Acceptance criteria

• New API on the multi-strategy comparison level (e.g. compare_strategies(..., monte_carlo=PortfolioMC(...)))
• At least one resampling method implemented end-to-end (stationary block bootstrap is the pragmatic starting point)
• Results integrated into the HTML report: portfolio equity fan chart, drawdown distribution, joint tail-risk metrics
• Documented assumptions and limitations of each method

Out of scope (separate issue)

• Regime-conditional resampling (volatility clustering) — tracked separately

Notes

Community feedback on the 1k-stars LinkedIn post suggested this is one of the most-requested capabilities for serious EA / multi-strategy portfolio work. Input on preferred resampling method is welcome.

[Whatsonyourmind]

Since the headline metric is joint drawdown probability, the method choice hinges on whether it preserves tail co-movement — and that's exactly where Cholesky and the Gaussian copula fail you. Both impose a single linear correlation and have asymptotic tail independence, so they'll systematically understate the chance of strategies crashing together. For a "P(joint DD > threshold)" number that's the worst place to lose fidelity.

Stationary block bootstrap is the right pragmatic default: resampling whole blocks of the joint return matrix preserves both serial structure and contemporaneous cross-correlation with no distributional assumption. The only knob is mean block length — Politis–White gives an automatic estimate per series; take the max across strategies so you don't under-block the most persistent one.

If you later want explicit tail dependence, a t-copula with low ν beats Gaussian since it has nonzero lower tail dependence λ_L. Worth reporting the realized empirical λ_L from the data as a calibration check on whichever method ships.