Monday, February 05, 2007

Fama and French Three-Factor (Predictor) Model

CAPM uses a single factor, beta, to compare a portfolio with the market. Why use more factors (predictors)?

Fama and French started with the observation that two classes of stocks have tended to do better than the market as a whole: (1) small caps [SML] and (2) stocks with a high book-value-to-price ratio [HML]. When they tested their hypothesis, they found small companies and companies with high B/M ratios had higher rates of return than the average stock (just as they hypothesized). Somewhat surprising by their research, however, they found no relation between beta and return.

They added two additional factors (predictors) to CAPM to reflect a portfolio’s exposure to size and B/M. The three-factor model is as follows:

ri = rf + bi(MRP) + ci(SMB) + di(HML) + alpha

One thing that is interesting is that Fama and French still see high returns as a reward for taking on high risk. For example, if returns increase with B/M, then stocks with high B/M ratio must be more risky than low B/M. Why?

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