Causality in the 5-factor Model of Stock Returns

Does the Fama-French 5-factor model of stock returns stand up to causality analyses? Do the factors cause the returns? In their December 2023 paper entitled “Re-Examination of Fama-French Factor Investing with Causal Inference Method”, Lingyi Gu, Ellen Zhang, Andrew Heinz, Jingxuan Liu, Tianyue Yao, Mohamed AlRemeithi and Zelei Luo construct causal graphs to analyze the relationship between future (next-month) stock return and each of the five factors in the model, which are:

1. Market – value-weighted market return minus the risk-free rate.
2. Size – return on small stocks minus the return on big stocks.
3. Value –  return on high book-to-market ratio stocks minus the return on low book-to-market ratio stocks.
4. Profitability – return on robust profitability stocks minus the return on weak profitability stocks.
5. Investment – return on conservative investment stocks minus the return on aggressive investment stocks.

They consider a constraint-based algorithm, a score-based algorithm and a functional model to estimate causality. For each approach, they evaluate the stability and strength of the causal relationships across different conditions by explore robustness to data loss or alterations. Their goal is to replicate initial conditions and datasets used in the 2015 paper that introduced the 5-factor model. Using monthly returns for a broad sample of U.S. common stocks and the five specified factors during July 1963 through December 2013, they find that:

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