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

Chorok Lee

TL;DR

The paper investigates whether predictive structure among equity factors changes across market regimes. It uses a Student-$t$ Hidden Markov Model to identify crisis, elevated, and normal regimes and applies Granger causality tests within each regime, finding that the Value factor HML Granger-causes the Size factor SMB with a 9-day lead during crisis regimes (p ≈ $1.89 \times 10^{-5}$) across five of six historical stress episodes, while normal regimes show no such link. Although the lead time bears potential for risk monitoring, the relationship does not translate into tradable profits, underscoring that Granger causality reflects temporal precedence rather than structural causality or alpha. The authors emphasize the results as a regime-dependent predictive pattern, propose a plausible but unverified deleveraging mechanism, and discuss limitations related to regime labeling and sample size, while demonstrating the method’s usefulness for monitoring and risk management. Overall, the study advances understanding of how factor dynamics shift with regime and offers a framework for regime-aware risk assessment rather than static, cross-sectional risk models.

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.

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

TL;DR

The paper investigates whether predictive structure among equity factors changes across market regimes. It uses a Student- Hidden Markov Model to identify crisis, elevated, and normal regimes and applies Granger causality tests within each regime, finding that the Value factor HML Granger-causes the Size factor SMB with a 9-day lead during crisis regimes (p ≈ ) across five of six historical stress episodes, while normal regimes show no such link. Although the lead time bears potential for risk monitoring, the relationship does not translate into tradable profits, underscoring that Granger causality reflects temporal precedence rather than structural causality or alpha. The authors emphasize the results as a regime-dependent predictive pattern, propose a plausible but unverified deleveraging mechanism, and discuss limitations related to regime labeling and sample size, while demonstrating the method’s usefulness for monitoring and risk management. Overall, the study advances understanding of how factor dynamics shift with regime and offers a framework for regime-aware risk assessment rather than static, cross-sectional risk models.

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.
Paper Structure (22 sections, 1 equation, 1 figure, 6 tables)

This paper contains 22 sections, 1 equation, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. Our Findings
  3. Contributions
  4. Related Work
  5. Methodology
  6. Data
  7. Student-$t$ Hidden Markov Model
  8. Sample Overlap Consideration
  9. Per-Regime Granger Causality
  10. Factor Pair Selection
  11. Results
  12. Regime Characteristics
  13. Gaussian vs. Student-$t$ Comparison
  14. Main Result: Regime-Dependent Predictive Structure
  15. Hypothesized Economic Mechanism
  16. ...and 7 more sections

Figures (1)

  • Figure 1: Regime assignments over sample period (1990--2024). Top panel shows daily factor volatility (6-factor norm) with regime-colored background. Bottom panel shows regime classifications. Vertical dashed lines mark major stress events. Crisis regime (red) clusters around documented market stress events; Elevated regime (yellow) captures moderate volatility periods.