Fama-French Three-Factor Model

The Fama–French three-factor model is a model designed by Eugene Fama and Kenneth French to describe stock returns . Like CAPM and the Arbitrage Pricing Theory, the Fama-French three-factor model is a linear model that relates structural factors to the expected return of an asset. Unlike those two models, however, the Fama-French model has three specific and defined factors.

Eugene Fama Winning an Award

Eugene Fama (left) designed the Fama-French model with Kenneth French.

The result is the following model:

$r=R_f+\beta_3(K_m-R_f)+b_s\cdot\mathit{SMB}+b_v\cdot\mathit{HML}+\alpha$

The Fama-French model tries to explain the return of a stock (r) through the risk free rate (R_f), the market return (K_m), and small market capitalization minus big (SMB), and high book-to-market ratio minus low (HML). Beta, b_s, and b_v are coefficients, and alpha is an error term.

Both SMB and HML measure the historic excess returns of small caps over big caps and of value stocks over growth stocks. These factors are calculated with combinations of portfolios composed by ranked stocks and available historical market data, and are listed online for easy reference.

Research shows that SMB and HML, are country specific, meaning that they must be calculated for the specific country and market in which the company is located and listed. That is not to say that global factors are not influential in determining the return of an asset, but rather, that for a three-factor model, the return of an equity is better explained using local factors.

Though it is more complex than CAPM, the Fama-French model has been shown to be a better at explaining the returns of a diversified portfolio: CAPM explains 70% of returns on average, while the Fama-French model explains 90% on average.