Paper: arXiv 2602.03325

Authors: T. Di Matteo, L. Riso, M. G. Zoia

Abstract

This paper proposes a machine learning-based framework for asset selection and portfolio construction, termed the Best-Path Algorithm Sparse Graphical Model (BPASGM). The method extends the Best-Path Algorithm (BPA) by mapping linear and non-linear dependencies among a large set of financial assets into a sparse graphical model satisfying a structural Markov property. Based on this representation, BPASGM performs a dependence-driven screening that removes positively or redundantly connected assets, isolating subsets that are conditionally independent or negatively correlated. This step is designed to enhance diversification and reduce estimation error in high-dimensional portfolio settings. Portfolio optimization is then conducted on the selected subset using standard mean-variance techniques. BPASGM does not aim to improve the theoretical mean-variance optimum under known population parameters, but rather to enhance realized performance in finite samples, where sample-based Markowitz portfolios are highly sensitive to estimation error. Monte Carlo simulations show that BPASGM-based portfolios achieve more stable risk-return profiles, lower realized volatility, and superior risk-adjusted performance compared to standard mean-variance portfolios. Empirical results for U.S. equities, global stock indices, and foreign exchange rates over 1990-2025 confirm these findings and demonstrate a substantial reduction in portfolio cardinality. Overall, BPASGM offers a statistically grounded and computationally efficient framework that integrates sparse graphical modeling with portfolio theory for dependence-aware asset selection.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.0/10 (capped from 7.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong combination of information-theoretic graphical modeling and practical portfolio construction. It addresses a real-world quantitative challenge (estimation error in high dimensions) through rigorous Monte Carlo simulations and extensive empirical validation across multiple asset classes over a 35-year period.

Research Flowchart

  flowchart TD
    A[Research Goal: Reduce estimation error & enhance diversification in portfolio construction] --> B[Data Inputs: US Equities, Global Indices & FX Rates 1990-2025]
    B --> C[BPASGM: Map asset dependencies into Sparse Graphical Model]
    C --> D[Dependence-Driven Screening: Remove redundant assets using Best-Path Algorithm]
    D --> E[Portfolio Optimization: Apply Mean-Variance to selected subset]
    E --> F[Validation: Conduct Monte Carlo Simulations & Empirical Testing]
    F --> G[Outcomes: Reduced cardinality, lower volatility & superior risk-adjusted returns]

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3 of 108 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.