Fama-French three-factor model
Quantitative Finance glossary · Quantitative Finance
Definition
Extension of CAPM: R_i - r_f = α_i + β_i,MKT(R_m - r_f) + β_i,SMB,SMB + β_i,HML,HML + varepsilon_i, where SMB is small-minus-big (size) and HML is high-minus-low book-to-market (value). The five-factor extension (2015) adds RMW (robust-minus-weak profitability) and CMA (conservative-minus-aggressive investment), absorbing much of the value premium; Carhart (1997) prepended momentum (UMD).
Fama-French three-factor model in plain English
For decades the standard theory said a stock's extra return over safe bonds depends on just one thing: how much it swings along with the overall market. Fama and French noticed that wasn't enough — historically, small companies and cheap 'bargain' companies (high value relative to price) earned extra returns the old model couldn't explain, so they added two ingredients: SMB (small stocks minus big stocks) and HML (cheap 'value' stocks minus pricey 'growth' stocks). It's like explaining a runner's speed not only by the wind at their back (the market) but also by their build and training style — more factors, better prediction. Later versions bolted on even more ingredients (profitability, investment habits, and momentum) to explain returns more fully.
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