Fama–French three-factor model

Fama–French three-factor model The Fama–French three-factor model is an asset pricing model developed to explain cross-sectional differences in stock returns by adding size and value risk factors to the market factor. It was introduced by Eugene Fama and Kenneth French to extend the Capital Asset Pricing Model and has been influential in academic research and institutional portfolio management.

Overview

The model was proposed by Eugene Fama and Kenneth French as an empirical improvement on the Capital Asset Pricing Model after examining data from the New York Stock Exchange, the American Stock Exchange, and the NASDAQ Stock Market. Fama and French built on prior work by William Sharpe, John Lintner, and researchers associated with the Cowles Commission and the University of Chicago to address anomalies such as the size effect and the value premium. The publication in the Journal of Finance brought attention from scholars at institutions like Harvard University, Massachusetts Institute of Technology, and University of California, Berkeley, and practitioners at firms including Barclays, Goldman Sachs, and Vanguard.

Model formulation

The three-factor specification augments the market excess return with two additional portfolios constructed from firm characteristics studied by Fama and French. The model regresses portfolio or asset returns on the excess return of a market portfolio—often proxied by the CRSP value-weighted index—and on two factor returns: SMB (Small Minus Big) capturing the size premium and HML (High Minus Low) capturing the value premium. Estimation typically uses time-series regression techniques popularized in work at Wharton School and London School of Economics, and diagnostics employ statistics from the Royal Statistical Society tradition and software from SAS Institute, StataCorp, and R Project.

Empirical evidence and tests

Empirical validation was conducted using long-run datasets from sources such as Center for Research in Security Prices (CRSP), Compustat, and historic listings on the New York Stock Exchange. Subsequent tests by researchers at University of Chicago Booth School of Business, Columbia Business School, Stanford University, and Princeton University examined robustness across countries including studies on London Stock Exchange, Tokyo Stock Exchange, Toronto Stock Exchange, Deutsche Börse, and emerging markets covered by the World Bank. Cross-sectional asset pricing tests and time-series tests applied methodologies from Robert Engle and Clive Granger for volatility and cointegration, while critiques used techniques from Eugene F. Fama’s critics and supporters at National Bureau of Economic Research conferences. Large-scale replications by groups at University of Pennsylvania and New York University Stern School of Business analyzed factor persistence, turnover, and transaction costs with data from Bloomberg LP and Thomson Reuters.

Applications and extensions

The three-factor model influenced portfolio construction at BlackRock, PIMCO, and State Street Corporation and spurred academic extensions such as the Carhart four-factor model adding a momentum factor associated with Mark Carhart. Researchers at Harvard Business School and MIT Sloan School of Management proposed five-factor and six-factor variants; these include factors studied by Robert Novy-Marx, Cliff Asness, and Ravi Jagannathan. The model underpins smart-beta products at firms like iShares and strategies at Dimensional Fund Advisors, and is used in performance attribution at Morgan Stanley and J.P. Morgan Chase as well as risk management at Federal Reserve Bank research teams and central banking seminars hosted by the International Monetary Fund.

Limitations and criticisms

Critics from Nobel Memorial Prize in Economic Sciences laureate commentators and scholars at London Business School and Bocconi University have pointed to omitted variables, data-snooping, and the role of accounting-based definitions used in HML. Debates at forums including the American Finance Association annual meeting and papers circulated via the National Bureau of Economic Research highlight alternative explanations such as behavioral hypotheses advanced by researchers at University of Chicago Booth School of Business and macroeconomic risk channels studied by Christopher Sims and Thomas Sargent. Implementation issues—transaction costs, capacity, and survivorship bias—were emphasized by analysts at Morningstar and audit teams at Ernst & Young, while international tests by teams at the Bank for International Settlements and Organisation for Economic Co-operation and Development have shown varying efficacy across markets.

Category:Asset pricing models