Paper: arXiv 2603.04441

Authors: Amine Boukardagha

Abstract

We propose an explainable regime-aware portfolio construction framework based on a strictly causal Wasserstein Hidden Markov Model. The model combines rolling Gaussian HMM inference with predictive model-order selection and template-based identity tracking using the 2-Wasserstein distance between Gaussian components. This allows regime complexity to adapt dynamically while preserving stable economic interpretation. Regime probabilities are embedded into a transaction-cost-aware mean-variance optimization framework and evaluated on a diversified daily cross-asset universe. Relative to equal-weight and SPX buy-and-hold benchmarks, the Wasserstein HMM achieves materially higher risk-adjusted performance with Sharpe ratios of 2.18 versus 1.59 and 1.18 and substantially lower maximum drawdown of negative 5.43 percent versus negative 14.62 percent for SPX. During the early 2025 equity selloff labeled Liberation Day, the strategy dynamically reduced equity exposure and shifted toward defensive assets, mitigating peak-to-trough losses. Compared to a nonparametric KNN conditional-moment estimator using the same features and optimization layer, the parametric regime model produces materially lower turnover and smoother weight evolution. The results demonstrate that regime inference stability, particularly identity preservation and adaptive complexity control, is a first-order determinant of portfolio drawdown and implementation robustness in daily asset allocation.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative combination of 2-Wasserstein optimal transport distance and Gaussian HMMs to solve regime label-switching and order selection issues in dynamic portfolio allocation. It features a rigorous, causality-strict empirical evaluation on cross-asset data spanning 2005–2026, demonstrating clear outperformance and significantly reduced turnover compared to non-parametric baselines.

Research Flowchart

  flowchart TD
    A["Research Goal: Explainable Regime-Aware Investing Strategy"] --> B["Data Inputs: Diversified Daily Cross-Asset Universe Features"]
    B --> C["Causal Wasserstein HMM: Adaptive Complexity & Template Identity Tracking"]
    C --> D["Transaction-Cost-Aware Mean-Variance Portfolio Optimization"]
    D --> E["Key Findings: Sharpe Ratio 2.18 vs SPX 1.18 & Max Drawdown -5.43% vs -14.62%"]
    D --> F["Stress Outcome: Smooth Weight Shifts to Defensive Assets During Early 2025 Selloff"]