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FinanceFama–French 3-Factor Model
Extends CAPM with size (SMB) and value (HML) factors.
Fama and French found that small-cap and high book-to-market (value) stocks earn returns CAPM can't explain. Regressing a fund's excess returns on the three factors reveals its true style tilts and whether any alpha survives.
Formula / theory
R − R_f = α + β·(R_m − R_f) + s·SMB + h·HML + ε
In Python
import statsmodels.api as sm X = sm.add_constant(factors[["Mkt_RF", "SMB", "HML"]]) fit = sm.OLS(excess_ret, X).fit() print(fit.params) # alpha + factor loadings