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A Novel approach to portfolio construction

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

TL;DR

BPASGM introduces a dependence-aware asset selection framework that extends the Best-Path Algorithm to build a sparse directed graphical model, enabling pruning of redundant or positively dependent assets before standard mean-variance optimization. By re-estimating portfolio moments on the selected subset and exploiting time-varying dependence through simulations and empirical data, BPASGM yields more stable risk-return profiles, lower realized volatility, and improved risk-adjusted performance in finite samples. The approach reshapes the efficient frontier through diversification-driven screening rather than altering the underlying optimization problem, and it is demonstrated via Monte Carlo tests and an empirical application spanning US equities, international indices, and FX markets from 1990–2025. The method is computationally efficient, interpretable, and adaptable to alternative risk measures, providing a practical bridge between sparse graphical modeling and robust portfolio construction.

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.

A Novel approach to portfolio construction

TL;DR

BPASGM introduces a dependence-aware asset selection framework that extends the Best-Path Algorithm to build a sparse directed graphical model, enabling pruning of redundant or positively dependent assets before standard mean-variance optimization. By re-estimating portfolio moments on the selected subset and exploiting time-varying dependence through simulations and empirical data, BPASGM yields more stable risk-return profiles, lower realized volatility, and improved risk-adjusted performance in finite samples. The approach reshapes the efficient frontier through diversification-driven screening rather than altering the underlying optimization problem, and it is demonstrated via Monte Carlo tests and an empirical application spanning US equities, international indices, and FX markets from 1990–2025. The method is computationally efficient, interpretable, and adaptable to alternative risk measures, providing a practical bridge between sparse graphical modeling and robust portfolio construction.

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.
Paper Structure (19 sections, 1 theorem, 52 equations, 26 figures, 2 tables)

This paper contains 19 sections, 1 theorem, 52 equations, 26 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Best Path Algorithm for Sparse Graphical Models
  3. Overview of the BPASGM procedure and its extension over BPA
  4. The Network Construction through the generalization of the BPA
  5. The detection of links via the matrix $Theta$
  6. From BPASGM to optimal asset selection
  7. BPASGM at work: a simulation study
  8. Properties of the Efficient Frontier
  9. Assessment of the characteristics of a portfolio composed of stocks selected by BPASGM.
  10. An Empirical Application of the BPASGM
  11. The Network of dependencies brought to the fore by BPASGM
  12. Optimal asset selection
  13. Properties of optimal portfolios
  14. Conclusions
  15. Best Path Algorithm
  16. ...and 4 more sections

Key Result

Lemma 2.1

Let $X_i$ be a node of the BPASGM, $\bm{X}_{{ps}_{i}}$ its optimal set of predictors and $\bm{X} / \{ \bm{X}_{{ps}_{i}}\}$ the set of all variables not included in $\bm{X}_{{ps}_{i}}$ Then, it can be proved that the following property holds:

Figures (26)

  • Figure 1: Example of Network build via BPASGM
  • Figure 2: Representation of $\bm{D}$ matrix starting from the Network in figure \ref{['figEXMP']}
  • Figure 3: Representation of $\bm{U}$ matrix starting from the Network in figure \ref{['figEXMP']}
  • Figure 4: Representation of $\bm{S}$ matrix starting from the Network in figure \ref{['figEXMP']}
  • Figure 6: Representation of $\widetilde{\bm{\Theta}}_{s.u}$, resulting from Step 2, starting from the Network in figure \ref{['figEXMP']} with $X_7$ (in orange) selected starting asset
  • ...and 21 more figures

Theorems & Definitions (2)

  • Lemma 2.1: Markov-Properties
  • proof