An Entropic Factor Model for Robust Portfolio Replication
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.
Related
- Estimation-Robust Minimum-Variance Portfolio Allocation Under Factor-Loading Uncertainty
- A splitting proximal method in portfolio optimization with entropic value-at-risk
- Sparsity Regularized and Robust Mean Variance Portfolio Selection Under Ellipsoidal Uncertainty
- Constrained Mean Variance Portfolio Selection under Reflected Factor Dynamics: Stochastic Riccati Equations, Neumann Problems,and a Deep Solver
- Mean-Variance Portfolio Selection: Statistical Properties and Distributionally Robust Optimization
BibTeX
@misc{arratia2026entropic,
title = {{An Entropic Factor Model for Robust Portfolio Replication}},
author = {Argimiro Arratia and Henryk Gzyl},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03552},
eprint = {2609.03552},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03552},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - An Entropic Factor Model for Robust Portfolio Replication
AU - Argimiro Arratia
AU - Henryk Gzyl
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03552
UR - https://arxiv.org/abs/2609.03552
AB - 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.
ER -