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, where Fama still resides. In 2013, Fama shared the Nobel Memorial Prize in Economic Sciences. The three factors are market risk, the outperformance of small versus big companies, and the outperformance of high book/market versus small book/market companies. However, the size and book/market ratio themselves are not in the model. For this reason, there is academic debate about the meaning of the last two factors.
Development
The traditional asset pricing model, known formally as the capital asset pricing model 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: small caps and stocks with a high book-to-market ratio. They then added two factors to CAPM to reflect a portfolio's exposure to these two classes: Here r is the portfolio's expected rate of return, Rf is the risk-free return rate, and Rm is the return of themarket portfolio. 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 Minus Big" and HML for "High 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 and available historical market data. Historical values may be accessed on . Moreover, once 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.
Discussion
The Fama–French three-factor model explains over 90% of the diversified portfolios returns, compared with the average 70% given by the CAPM. They find positive returns from small size as well as value factors, high book-to-market ratio and related ratios. Examining β and size, they find that higher returns, small size, and higher β are all correlated. They then test returns for β, controlling for size, and find no relationship. Assuming stocks are first partitioned by size the predictive power of β then disappears. They discuss whether β can be saved and the Sharpe-Lintner-Black model resuscitated by mistakes in their analysis, and find it unlikely. 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 , and . Eugene Fama and Kenneth French also analysed models with local and global risk factors for four developed market regions and conclude that local factors work better than global developed factors for regional portfolios. The global and local risk factors may also be accessed on . Finally, recent studies confirm the developed market results also for emerging markets. 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 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.
Fama–French five-factor model
In 2015, Fama and French extended the model, adding a further two factors -- profitability and investment. Defined analogously to the HML factor, the profitability factor is the difference between the returns of firms with robust and weak operating profitability; and the investment factor is the difference between the returns of firms that invest conservatively and firms that invest aggressively. In the US, adding these two factors makes the HML factors redundant since the time series of HML returns are completely explained by the other four factors. Whilst the model still fails the Gibbons, Ross & Shanken test, which tests whether the factors fully explain the expected returns of various portfolios, the test suggests that the five-factor model improves the explanatory power of the returns of stocks relative to the three-factor model. The failure to fully explain all portfolios tested is driven by the particularly poor performance of portfolios made up of small firms that invest a lot despite low profitability. If the model fully explains stock returns, the estimated alpha should be statistically indistinguishable from zero. Whilst a momentum factor wasn't included in the model since few portfolios had statistically significant loading on it, Cliff Asness, former PhD student of Eugene Fama and co-founder of AQR Capital has made the case for its inclusion.. Foye tested the five-factor model in the UK and raises some serious concerns. Firstly, he questions the way in which Fama and French measure profitability. Furthermore, he shows that the five-factor model is unable to offer a convincing asset pricing model for the UK..
