Chebychev–Grübler–Kutzbach criterion

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.

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 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 (BtM, customarily called value stocks, contrasted with growth stocks). They then added two factors to CAPM to reflect a portfolio's exposure to these two classes:

$r=R_f+{\beta }_3(K_m-R_f)+b_s\cdot \mathit{S}\mathit{M}\mathit{B}+b_v\cdot \mathit{H}\mathit{M}\mathit{L}+\alpha$

Here r is the portfolio's expected rate of return, R_f is the risk-free return rate, and K_m is the return of the whole stock market. 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 b_s and b_v 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.

Griffin shows that the Fama and French factors are country specific and concludes that the local factors provide a better explanation of time-series variation in stock returns than the global factors. Therefore, updated risk factors are available for other stock markets in the world, including the United Kingdom, Germany and Switzerland. Eugene Fama and Kenneth French recently analysed models with local and global risk factors for four regions (North America, Europe, Japan and Asia Pacific) and conclude that local factors work better than global factors for regional portfolios. The global and local risk factors may also be accessed on Kenneth French's web page.

A number of studies have reported that when the Fama–French model is applied to emerging markets the book-to-market factor retains its explanatory ability but the market value of equity factor performs poorly. In a recent paper, Foye, Mramor and Pahor (2013) propose an alternative three factor model that replaces the market value of equity component with a term that acts as a proxy for accounting manipulation.

See also

• Returns-based style analysis, a model that uses style indices rather than market factors
• 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.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.