Chebychev–Grübler–Kutzbach criterion: Difference between revisions

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In [[asset pricing]] and [[Investment management|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 (finance)|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) [[Market capitalization|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:<ref name="FamaFrench1993">{{Cite doi|10.1016/0304-405X(93)90023-5}}</ref>
:<math>r=R_f+\beta_3(K_m-R_f)+b_s\cdot\mathit{SMB}+b_v\cdot\mathit{HML}+\alpha</math>


Here r is the portfolio's expected rate of return, ''R''<sub>''f''</sub> is the risk-free return rate, and ''K''<sub>''m''</sub> 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 "'''S'''mall [market capitalization] '''M'''inus '''B'''ig" and ''HML'' for "'''H'''igh [book-to-market ratio] '''M'''inus '''L'''ow"; 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 [http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html Kenneth French's web page].
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Moreover, once SMB and HML are defined, the corresponding coefficients ''b''<sub>''s''</sub> and ''b''<sub>''v''</sub> 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.<ref>{{Cite doi|10.1111/j.1540-6261.1992.tb04398.x}}</ref>
 
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.<ref>{{Cite doi|10.1093/rfs/15.3.783}}</ref> Therefore, updated risk factors are available for other stock markets in the world, including the [http://xfi.exeter.ac.uk/researchandpublications/portfoliosandfactors/disclaimer.php United Kingdom], [http://www.fm.wi.tum.de/en/research/data Germany] and [http://www.ammannsteiner.ch/ 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.<ref name="FamaFrench2012">{{Cite doi|10.1016/j.jfineco.2012.05.011}}</ref> The global and local risk factors may also be accessed on [http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 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.<ref>{{cite doi|10.1111/jifm.12005}}</ref>
 
==See also==
* [[Returns-based style analysis]], a model that uses style indices rather than market factors
* [[Carhart four-factor model]] (1997)<ref>{{Cite doi|10.1111/j.1540-6261.1997.tb03808.x}}</ref> — 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: [http://www.ifa.com/articles/dimensions_of_stock_and_bond_returns Videos, paintings, charts and data explaining the Fama–French Five Factor Model, which includes the two factor model for bonds. ]
 
==References==
{{Reflist}}
 
{{DEFAULTSORT:Fama-French Three-Factor Model}}
[[Category:Finance theories]]
[[Category:Financial economics]]
[[Category:Portfolio theories]]

Latest revision as of 11:51, 23 December 2014


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