Fama–French three-factor model
In asset pricing and portfolio management the Fama–French three-factor model is a model designed by Eugene Fama and Kenneth French to describe stock returns. Fama and French were professors at the University of Chicago Booth School of Business, where Fama still resides. The three factors are company size, company price-to-book ratio, and market risk.
The traditional asset pricing model, known formally as the capital asset pricing model (CAPM) uses only one variable to describe the returns of a portfolio or stock with the returns of the market as a whole. In contrast, the Fama–French model uses three variables. Fama and French started with the observation that two classes of have tended to do better than the market as a whole: (i) small caps and (ii) stocks with a high Book-to-market ratio (B/P, customarily called , contrasted with ). They then added two factors to CAPM to reflect a portfolio's exposure to these two classes:
Here r is the portfolio's expected rate of return, Rf is the risk-free return rate, and Km is the return of the market portfolio. The "three factor" β is analogous to the classical β but not equal to it, since there are now two additional factors to do some of the work. SMB stands for "Small [market capitalization] Minus Big" and HML for "High [book-to-market ratio] Minus Low"; they 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 (BtM ranking, Cap ranking) and available historical market data. Historical values may be accessed on Kenneth French's web page.
Moreover, once SMB and HML are defined, the corresponding coefficients bs and bv are determined by linear regressions and can take negative values as well as positive values. The Fama–French three-factor model explains over 90% of the diversified portfolios returns, compared with the average 70% given by the CAPM (within sample). They find positive returns from small size as well as value factors, high book-to-market ratio and related ratios. Examining β and size, they find that higher returns, small size, and higher β are all correlated. They then test returns for β, controlling for size, and find no relationship. Assuming stocks are first partitioned by size the predictive power of β then disappears. They discuss whether β can be saved and the Sharpe-Lintner-Black model resuscitated by mistakes in their analysis, and find it unlikely.
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