Fama–French three-factor model

Fama–French three-factor model
Name	Fama–French three-factor model
Type	Asset pricing model
Field	Financial economics
Inventor	Eugene Fama, Kenneth French
Year	1992
Journal	The Journal of Finance

Fama–French three-factor model is a foundational asset pricing model in financial economics developed by Eugene Fama and Kenneth French. It extends the capital asset pricing model by adding two additional factors to explain stock returns. The model has become a standard benchmark in empirical finance for evaluating portfolio performance and understanding systematic risk.

Overview

The model was introduced in a seminal 1992 paper published in The Journal of Finance. It was developed in response to empirical anomalies that the capital asset pricing model could not explain, such as the size effect and the value effect. The research built upon earlier work by Rolf Banz and Sanjoy Basu, among others. The University of Chicago Booth School of Business has been a central hub for this research, which significantly advanced the field of empirical asset pricing.

Model specification

The model expresses a stock's excess return over the risk-free rate as a linear function of three factors. The first factor is the excess return of a broad market portfolio, identical to the capital asset pricing model. The second factor, SMB (Small Minus Big), is the difference in returns between portfolios of small and large market capitalization stocks. The third factor, HML (High Minus Low), is the difference in returns between portfolios of stocks with high and low book-to-market ratios. The model is estimated using time-series regression on historical data, often sourced from CRSP and Compustat.

Empirical evidence

Extensive testing, primarily on U.S. stock market data from the NYSE, AMEX, and NASDAQ, has shown the model explains a large portion of the variation in stock returns. The original studies by Fama and French covered decades of data from CRSP. The value premium and size premium have been observed in many international markets, though their persistence and magnitude vary. Research from institutions like the National Bureau of Economic Research has documented these effects across different time periods and geographies.

Extensions and related models

The success of the three-factor model led to the development of multi-factor models. The most prominent extension is the Fama–French five-factor model, which adds factors for profitability and investment. Other influential models include the Carhart four-factor model, which adds a momentum factor, and the q-factor model developed by Lu Zhang. Research at Harvard University and the Massachusetts Institute of Technology has contributed to this expanding literature on factor investing.

Criticisms and limitations

Critics, such as Richard Roll and Stephen Ross, argue the factors are not theoretically grounded but are empirically discovered risk factors. Some studies suggest the size premium has diminished or disappeared since its discovery. Behavioral economists like Robert Shiller propose alternative explanations based on investor psychology and market inefficiency. There is also debate about data mining and whether the factors represent systematic risk or behavioral biases.

Applications

The model is widely used in performance attribution to evaluate mutual fund and hedge fund managers. It forms the basis for many smart beta and factor investing strategies offered by firms like Dimensional Fund Advisors and BlackRock. In corporate finance, it is used to estimate cost of equity capital. The factors are also central to academic research published in journals like The Review of Financial Studies and Journal of Financial Economics.

Category:Financial economics Category:Financial models Category:Eugene Fama