Are Three Matrices All You Need To Beat the Market? Observable Matrix Dynamics for Portfolio Optimization

Battle Count: 50

Highly relevant to quantitative trading. The paper presents a complete, implementable portfolio optimization framework using only market data (prices, volumes, market caps). It demonstrates out-of-sample outperformance of the S&P 500 on two non-overlapping test periods with Sharpe ratios of 1.06 and 1.32-1.44 net of transaction costs. The framework is deliberately simple (no neural networks, no matrix inversion, no forward-looking signals), uses standard mathematical software, and provides explicit hyperparameters. The information-theoretic diagnostics (entropy production, transfer entropy) offer interpretable tools for signal selection and market state monitoring. The regime-timed blend of long-only and market-neutral sleeves is directly applicable to systematic equity strategies. The paper also provides extensive ablation studies on fundamentals, spectral signals, and volume, which are valuable for practitioners evaluating signal sources.

Moderate complexity. The framework is deliberately simple in concept (three matrices, two Markov chains, rank-bucketing) but involves multiple interacting components: distance matrix computation, two conditioned Markov chains with covariates, maximum likelihood estimation of transition intensities, transfer entropy computation, portfolio construction with two sleeves, regime timing, no-trade bands, residual-distance diversification, and a convex insurance overlay. The paper explicitly avoids neural networks, matrix inversion, and advanced numerical optimization. The discrete rank-bucketing simplifies estimation to plug-in counts. However, the full pipeline with all components, walk-forward refitting, hyperparameter calibration, and the various overlays requires careful implementation. The paper states no advanced numerical optimization beyond standard mathematical software is required.

The paper provides detailed mathematical formulations, explicit hyperparameter tables, and describes the full pipeline. Code and analysis scripts are stated to be available at a GitHub repository (https://github.com/ighalp/omd_portfolio), but the repository is currently private. Data sources (CRSP, Compustat, Yahoo Finance) are standard but require paid subscriptions. The methodology is fully specified with equations, making independent reimplementation feasible for a skilled quantitative researcher. The paper notes all calculations were performed by Claude Code with Opus 4.8 as an AI assistant under author supervision.