Regime-Dependent Predictive Structure Between Equity Factors: Evidence from Granger Causality

Paper: arXiv 2601.10732

Authors: Chorok Lee

Abstract

We document regime-dependent predictive structure between equity factors using 35 years of Fama-French data (1990-2024). We find that Value (HML) Granger-causes Size (SMB) during crisis regimes (p < 1e-4, 9-day lag) but not during normal conditions, validating across 5 of 6 historical stress events (2008, 2011, 2015, 2018, 2020). Regimes are identified via a Student-t HMM, which detects moderate crises such as 2011 (69%) that Gaussian models miss entirely (0%). Although the relationship does not yield trading profits, the 9-day lead time may support risk management decisions. We note that Granger causality implies temporal precedence, not structural causality, and that common drivers could explain the pattern; our economic interpretation is a hypothesis rather than a verified mechanism.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong empirical investigation into regime-dependent factor predictability using a Student-t HMM and Granger causality tests over 35 years of data. It excels in intellectual honesty by clearly distinguishing predictive precedence from causal mechanism and demonstrating that the statistical finding does not yield trading alpha.

Research Flowchart

  flowchart TD
    A[Research Goal: Detect Regime-Dependent Factor Predictability] --> B[Data Input: 35 Years Fama-French Data 1990-2024]
    B --> C[Regime Identification: Student-t HMM vs Gaussian HMM]
    C --> D[Granger Causality Testing Across Regimes]
    D --> E[Key Outcome: Value Granger-causes Size in Crises 9-Day Lag]
    E --> F[Validation & Application: Validated in 5/6 Crises for Risk Management]