Fama-French, momentum, quality — the empirical canon

Fama and French's 1992 paper documented systematic deviations from CAPM along three dimensions: size, book-to-market, and (later) momentum. The 3-factor and 5-factor extensions to CAPM have become the empirical workhorse of cross-sectional asset pricing, the benchmark every quant strategy is judged against, and the foundation of the smart-beta industry.

The Fama-French 3-factor model

R_i - r_f = α_i + β_i,M (R_M - r_f) + β_i,SMB SMB + β_i,HML HML + ε_i

• Market: R_M - r_f, the CAPM excess market return.
• SMB (Small Minus Big): return of small-cap minus large-cap portfolios. Captures the 'size effect'.
• HML (High Minus Low): return of high-B/M minus low-B/M portfolios. Captures the 'value effect'.

All three factors are themselves long-short portfolios. Time-series regressions on these three identify the three β's; cross-sectional regressions identify the corresponding risk premia.

Empirical fact: size and value premia

• Long-run US size premium: ~2-3% per year. Concentrated in the very smallest deciles.
• Long-run US value premium: ~3-4% per year. Stronger pre-1990, weaker since.
• Both premia have been highly variable: long drawdowns (value's 2010-2020 underperformance) common.

Momentum (Carhart 1997)

Add MOM = past 12-month return minus most-recent month

Stocks that performed well over the past 6-12 months tend to continue doing well over the next 1-12 months. The momentum premium is roughly 6-8%/year over long horizons in US data (and similarly internationally), with catastrophic crashes about once a decade (e.g., spring 2009). Adding MOM gives the 4-factor Carhart model — the standard hedge-fund-evaluation benchmark.

Fama-French 5-factor (2015)

Adds two more factors:

• RMW (Robust Minus Weak): profitability factor. Long high-profit, short low-profit.
• CMA (Conservative Minus Aggressive): investment factor. Long low-investment firms, short high-investment.

Adding these makes HML largely redundant — the value factor's power was partially capturing profitability/investment effects.

Q-factor model (Hou-Xue-Zhang 2015)

Alternative 4-factor model: market, size, investment, profitability — derived from the neoclassical q-theory of investment. Often outperforms FF5 in horse-race comparisons. The take-away: there is no single 'true' multi-factor model; multiple specifications fit comparably well.

Survival in the replication wars

Harvey-Liu-Zhu (2016): of ~300 published 'anomalies' in finance, most don't survive multiple-testing correction. The robust survivors:

• Market: universally accepted (modulo magnitude).
• Size and value: contested. Smaller post-2000 than before.
• Momentum: replicates across time and geography; the most robust empirical regularity in finance.
• Quality / profitability: replicates.
• Low-volatility: replicates.
• Most published anomalies fail rigorous out-of-sample tests.

The smart-beta industry

ETFs and index products targeting size, value, momentum, quality, and low-vol exposures have grown to > $1T globally. The empirical premia justify these products under reasonable assumptions, but live tracking has often disappointed: post-publication decay of value and size premia is one of the most replicated findings in empirical asset pricing.

African / EM factor models

FF-style factor structures have been documented in many EM equity markets including South Africa, Kenya, Nigeria. Premia are noisier (shorter samples, fewer stocks), often statistically insignificant at single-country level, but consistent in sign with US findings. Pooled EM studies find robust value and momentum effects.