An Entropic Factor Model for Robust Portfolio Replication

Paper: arXiv 2609.03552

Authors: Argimiro Arratia, Henryk Gzyl

Abstract

Portfolio replication, or the construction of a tradable basket of assets to match the risk-return profile of a target benchmark, is fundamentally an ill-posed inverse problem. When restricted to a subset of available assets, classical variance-minimizing models often yield unstable, over-leveraged portfolios highly vulnerable to market shocks. We propose a unified, two-stage methodology rooted in information theory to achieve robust portfolio replication. First, we model the constituent asset returns against target factors, estimating parameters within data-driven empirical bounds via an entropy minimization principle. Second, using the same entropic approach, we determine the optimal weight replication. In both cases we use an entropy function of the Fermi-Dirac type defined directly on sets of constraints of the inverse problem. We validate this Entropic Factor Model (EFM) against standard Ordinary Least Squares (OLS) across five numerical experiments, including standard equity tracking, multi-asset synthesis, and severe stress-test scenarios. Empirical results demonstrate that the EFM consistently outperforms OLS in terms of annualized turnover and net-of-fees returns. Crucially, during the COVID-19 market crash and under severe idiosyncratic data corruption, the entropic framework acts as a probabilistic ``circuit breaker", defensively reducing capital allocation to compromised assets and providing a highly robust, risk-averse solution for generalized portfolio replication.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated approach using information theory and Fermi-Dirac entropy for portfolio replication. It validates this novel methodology with several empirical experiments, including stress tests, demonstrating strong performance against OLS. The combination of advanced mathematical derivations and robust empirical validation places it in the ‘Holy Grail’ quadrant.

Research Flowchart

  flowchart TD
    A[Research Goal: Robust Portfolio Replication] --> B{Problem: Ill-posed Inverse Problem};
    B --> C[Methodology: Two-Stage Entropic Factor Model (EFM)];
    C --> D{Stage 1: Factor Parameter Estimation via Entropy Minimization};
    C --> E{Stage 2: Optimal Weight Replication via Entropy Minimization};
    D -- Inputs --> F[Asset Returns, Target Factors, Empirical Bounds];
    E -- Inputs --> F;
    F --> G[Computational Process: Fermi-Dirac Entropy Function, Constraint Sets];
    G --> H[Outcomes: EFM vs OLS Comparison];
    H --> I{Key Findings: EFM Outperforms OLS (Turnover, Net-of-Fees Returns), Robust during Stress (COVID-19, Data Corruption)};

Cited References (19)

1. Optimizing index tracking: A Random Matrix Theory approach to portfolio selection (2025) — link
2. An Entropic Approach to Constrained Linear Regression (2025) — link
3. Index tracking using shapley additive explanations and one-dimensional pointwise convolutional autoencoders (2024) — link
4. How to Keep Your Portfolio Close in Risk and Diversification to a Desired Benchmark (2023) — link
5. Accurate solution of the Index Tracking problem with a hybrid simulated annealing algorithm — → 2303.13282
6. Constructing optimal sparse portfolios using regularization methods (2014) — link
7. Ill-Posed Inverse Problems in Economics (2013) — link
8. Optimal Portfolio Diversification Using the Maximum Entropy Principle (2008) — link

1 of 19 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.