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

Battle Count: 71

The paper explicitly demonstrates that the Granger causality finding does NOT generate trading profits (strategy: -6.1% annual return, Sharpe -0.75, max drawdown -97.5%). The practical value is limited to risk monitoring: during detected crisis regimes, HML movements may provide ~9-day lead time for SMB risk management decisions. This is relevant for factor-based portfolio managers and risk managers but not for alpha generation or algorithmic trading strategies. The regime detection component (Student-t HMM) has independent value for crisis identification. The finding is more relevant to institutional risk management than to quantitative trading per se.

The methodology involves: (1) fitting a multivariate Student-t HMM with K=3 regimes using EM algorithm (moderate complexity, requires careful initialization and convergence monitoring); (2) extracting regime-specific subsamples with boundary handling; (3) conducting Granger causality tests (standard VAR-based F-tests) on 30 directed factor pairs per regime; (4) Bonferroni correction; (5) event-based validation across 6 historical episodes. The HMM fitting is the most complex component, requiring multivariate Student-t density evaluation and EM updates. Standard statistical software (R, Python with hmmlearn or custom implementations) can handle this. The Granger causality tests are straightforward. Overall, a skilled quantitative researcher could implement this in 2-4 weeks.

Data is publicly available from Kenneth French's data library (1990-2024, 8,817 trading days). Methodology is well-described with specific parameters (K=3, Student-t, Bonferroni correction at α=0.01/30). However, no code or GitHub repository is provided. The HMM implementation details (EM convergence criteria, initialization) are not fully specified. The factor pair selection (HML-SMB) was based on preliminary screening of all 30 pairs, which introduces researcher degrees of freedom.