Fama-French three-factor model

In the portfolio management field, Eugene Fama and Kenneth French developed the highly successful Fama-French three factor model to describe market behavior.

CAPM uses a single factor, beta, to compare the excess returns of a portfolio with the excess returns of the market as a whole. But it oversimplifies the complex market. Fama and French started with the observation that two classes of stocks have tended to do better than the market as a whole: (i) small caps and (ii) stocks with a high book-to-market ratio (BM, customarily called value stocks; to be differentiated from growth stocks). They then added two factors to CAPM to reflect a portfolio's exposure to these two classes:Cite journal |last=Fama |first=Eugene F. |coauthors=French, Kenneth R. |year=1993 |title=Common Risk Factors in the Returns on Stocks and Bonds |journal=Journal of Financial Economics |volume=33 |issue=1 |pages=3–56 |url= |issn= |doi=10.1016/0304-405X(93)90023-5 ]

Here r is the portfolio's return rate, $R\_\{f\}$ is the risk-free return rate, and $K\_\{m\}$ is the return of the whole stock market. The "three factor" is analogous to the classical but not equal to it, since there are now two additional factors to do some of the work. SMB and HML stand for "small (market capitalization) minus big" and "high (book-to-price ratio) minus low"; they measure the historic excess returns of small caps over big caps and "value stocks" over "growth stocks". It is important to note that these factors are calculated with combinations of portfolios composed by ranked stocks (BM ranking, Cap ranking) and available historical market data. By the way, you may find their historical values in [http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html Kenneth French's web page] .

Moreover, 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. Intuitively, one would expect a portfolio of Big Caps to have a negative bs coefficient, a portfolio of value stocks to have a positive bv coefficient, etc. The Fama-French Three Factor model explains over 90% of the diversified portfolios returns, compared with the average 80% given by the CAPM. The signs of the coefficients suggested that small cap and value portfolios have higher expected returns—and arguably higher expected risk—than those of large cap and growth portfolios. [Cite journal |last=Fama |first=Eugene F. |coauthors=French, Kenneth R. |year=1992 |title=The Cross-Section of Expected Stock Returns |journal=Journal of Finance |volume=47 |issue=2 |pages=427–465 |url= |issn= |doi=10.2307/2329112 ]

The three factor model is gaining recognition in portfolio management. Morningstar.com classifies stocks and mutual funds based on these factors. Many studies show that the majority of actively managed mutual funds underperform broad indexes based on three factors if classified properly. This leads to more and more index funds and ETFs being offered based on the three factor model.

References