Fama-French three-factor model
Encyclopedia
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.
The traditional asset pricing model, known formally as the Capital Asset Pricing Model, CAPM, uses only one variable, beta, 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 stock
s have tended to do better than the market as a whole: (i) small caps
and (ii) stocks with a high book-to-market ratio (BtM, customarily called value stocks, contrasted with growth stock
s). They then added two factors to CAPM to reflect a portfolio's exposure to these two classes:
Here r is the portfolio's rate of return,
is the risk-free return rate, and 
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. 
stands for "small (market capitalization) minus big" and 
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
and 
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). 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.
Portfolio management
Portfolio Management may refer to:* Investment management, handled by a portfolio manager* IT Program management* IT portfolio management* Project management* Project portfolio management...
the Fama-French three factor model is a model designed by Eugene Fama
Eugene Fama
Eugene Francis "Gene" Fama is an American economist, known for his work on portfolio theory and asset pricing, both theoretical and empirical. He is currently Robert R...
and Kenneth French
Kenneth French
Kenneth Ronald "Ken" French is the Carl E. and Catherine M. Heidt Professor of Finance at the Tuck School of Business, Dartmouth College. He has previously been a faculty member at MIT, the Yale School of Management, and the University of Chicago Booth School of Business...
to describe stock returns.
The traditional asset pricing model, known formally as the Capital Asset Pricing Model, CAPM, uses only one variable, beta, to describe the returns of a portfolio
Portfolio (finance)
Portfolio is a financial term denoting a collection of investments held by an investment company, hedge fund, financial institution or individual.-Definition:The term portfolio refers to any collection of financial assets such as stocks, bonds and cash...
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 stock
Stock
The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...
s have tended to do better than the market as a whole: (i) small caps
Market capitalization
Market capitalization is a measurement of the value of the ownership interest that shareholders hold in a business enterprise. It is equal to the share price times the number of shares outstanding of a publicly traded company...
and (ii) stocks with a high book-to-market ratio (BtM, customarily called value stocks, contrasted with growth stock
Growth stock
In finance, a growth stock is a stockof a company that generates substantial and sustainable positive cash flow and whose revenues and earnings are expected to increase at a faster rate than the average company within the same industry...
s). They then added two factors to CAPM to reflect a portfolio's exposure to these two classes:
Here r is the portfolio's rate of return,
is the risk-free return rate, and 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. stands for "small (market capitalization) minus big" and 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
and 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). 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.See also
- Carhart four-factor model (1997) - extension of the Fama-French model, containing an additional momentum factor (MOM), which is long prior-month winners and short prior-month losers
- The Dimensions of Stock Returns: Videos, paintings, charts and data explaining the Fama French Five Factor Model, which includes the two factor model for bonds.