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

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.