An Entropic Factor Model for Robust Portfolio Replication
To address the instability and over-leveraging of traditional variance-minimizing models in portfolio replication, this paper proposes a two-stage information-theoretic Entropic Factor Model (EFM). It employs Fermi-Dirac entropy directly on constraint sets and replaces statistical assumptions with data-driven empirical bounds, enhancing robustness, especially under market shocks.
01 ABSTRACT
The paper introduces the Entropic Factor Model (EFM) for robust portfolio replication. The model first estimates parameters by entropy minimization within empirical bounds, then determines optimal weights using the same entropic approach. Through five numerical experiments (including tracking, multi-asset synthesis, and stress tests), the authors compare EFM with Ordinary Least Squares (OLS). Results show that EFM outperforms OLS in annualized turnover and net-of-fees returns, and during the COVID-19 crash and data corruption, EFM defensively reduces allocation to compromised assets, acting as a probabilistic circuit breaker.
02 KEY FINDINGS
- Proposes a two-stage Entropic Factor Model (EFM) using Fermi-Dirac entropy for both parameter estimation and weight optimization.
- EFM uses data-driven empirical bounds, reducing reliance on statistical assumptions and enhancing robustness.
- In five numerical experiments, EFM outperforms OLS in annualized turnover and net-of-fees returns.
- Under extreme market conditions, EFM automatically decreases allocations to affected assets, acting like a circuit breaker.
- The method generalizes to various portfolio replication tasks, including multi-asset synthesis.
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