Fama-French Five-Factor Model

Definition

The Fama-French five-factor model explains the cross-section of average stock returns with five factors — market, size, value, profitability, and investment — extending the 1993 three-factor model by adding profitability (RMW) and investment (CMA) factors (Fama-French 2015). It is an empirical factor model of expected returns: an asset's excess return is a linear combination of factor exposures.

Key Ideas

• The regression. $R_{it}-R_{Ft}=a_i+b_i(R_{Mt}-R_{Ft})+s_i\,\mathrm{SMB}_t+h_i\,\mathrm{HML}_t+r_i\,\mathrm{RMW}_t+c_i\,\mathrm{CMA}_t+e_{it}$.
• The five factors.
  • Mkt−RF — market excess return.
  • SMB (Small Minus Big) — the size premium.
  • HML (High Minus Low book-to-market) — the value premium.
  • RMW (Robust Minus Weak) — return spread between high- and low-profitability firms.
  • CMA (Conservative Minus Aggressive) — return spread between low- and high-investment firms.
• Valuation-theory motivation. The dividend-discount / Miller-Modigliani (1961) identity implies that, holding book-to-market fixed, higher expected profitability raises expected return and higher expected investment lowers it — which is what RMW and CMA proxy.
• Zero-intercept hypothesis. If the five exposures capture all variation in expected returns, every intercept $a_i=0$; this is tested jointly with the GRS (Gibbons-Ross-Shanken) statistic, and interpreted via a mean-variance-efficient tangency-portfolio argument (Huberman-Kandel 1987).
• HML becomes redundant. In their sample, once RMW and CMA are added, the value factor (HML) is redundant for describing average returns — its information is absorbed by profitability and investment.

Why It Matters

• The workhorse benchmark. Fama-French factors are the default controls for "risk-adjusting" returns and the benchmark any new anomaly must beat — the practical embodiment of the joint-hypothesis view that expected returns are compensation for factor exposures.
• Data infrastructure. The FF factor and portfolio datasets (e.g. FF48, FF100) are standard test assets, used across the portfolio literature (e.g. sparse Markowitz and estimation-risk work).
• Set the stage for the factor zoo. Adding two factors and finding one (HML) redundant crystallized the question of how many factors are real — the problem the later factor-zoo literature attacks.

Open Questions

• Main empirical failure: the model does not capture the low average returns of small stocks that behave like firms investing heavily despite low profitability.
• Whether RMW/CMA are risk factors or reflect mispricing (the recurring risk-vs-behavioral debate).
• How the five factors relate to competing models (q-factor model of Hou-Xue-Zhang; characteristic vs covariance explanations) — and which of the proliferating candidate factors add real explanatory power.

Related

• Factor Model
• Efficient Market Hypothesis
• Capital Asset Pricing Model
• Sparse Portfolio Selection
• Fama-French (2015) A Five-Factor Asset Pricing Model
• Eugene F. Fama
• Kenneth R. French
• Factor Zoo
• Machine Learning in Asset Pricing