Fama French ModelEdit
The Fama-French model is a foundational framework in empirical finance that expands on the classic capital asset pricing model (CAPM) by adding factors designed to capture systematic patterns in stock returns. Developed by Eugene Fama and Kenneth French in the early 1990s, the model aims to explain why some portfolios and stocks earn higher or lower returns than would be predicted by market exposure alone. By incorporating size and value effects, the model provides a more nuanced view of how risk and fundamental characteristics relate to expected returns. The core idea is that a few well-defined factors can account for a substantial portion of cross-sectional variation in stock returns and help investors and researchers differentiate between compensation for risk and apparent mispricing Eugene Fama Kenneth French.
The three-factor version of the model retains the market factor from CAPM and adds two more drivers: a size factor and a value factor. The empirical regularities it targets are the so-called size effect (smaller firms tend to outperform larger firms on average) and the value effect (companies with high book-to-market ratios tend to outperform those with low book-to-market ratios). These effects are captured by constructing portfolios that isolate the relevant characteristics and examining their average returns over time. The model’s structure can be described in terms of a regression that links an asset’s excess return to a small set of underlying factors, with each factor representing a source of systematic risk or risk-related payoff. The key factors are:
- Market factor: the excess return on the broad market portfolio, capturing overall market risk akin to the CAPM framework Capital asset pricing model.
- SMB (Small minus Big): the return difference between portfolios of small-cap stocks and large-cap stocks, designed to proxy the size effect.
- HML (High minus Low): the return difference between portfolios with high and low book-to-market ratios, designed to proxy the value effect. The high book-to-market (value) stocks are often contrasted with low book-to-market (growth) stocks.
Three-factor models are typically estimated by regressing the excess returns of portfolios or individual equities on these factors. When the factors are constructed from broad-sample portfolios rather than ad hoc constructs, this approach allows researchers and practitioners to decompose returns into exposures to market risk and the two additional systematic sources recognized by the model. The logic behind these factors rests on the idea that size and value characteristics are associated with risk exposures that investors demand to bear, or alternatively that they capture persistent mispricing that is corrected over time.
Model specification and factor construction
- The market factor mirrors the CAPM framework and is derived from the excess return on the market portfolio (the market return minus the risk-free rate) Cross-section of expected returns.
- SMB is formed by taking the average returns on small-cap portfolios and subtracting the returns on large-cap portfolios, thereby isolating the size dimension.
- HML is formed by the difference between returns on high book-to-market and low book-to-market portfolios, isolating the value dimension.
The three-factor model can be written in a stylized form as: Excess return of the asset = alpha + beta_market × (Market excess return) + beta_SMB × SMB + beta_HML × HML + error term.
This specification emphasizes betas (factor loadings) as the risk exposures that determine how much of each factor’s return the asset earns. The model’s explanatory power stems from the systematic regularities captured by SMB and HML, which were found to persist across many samples and time periods in the U.S. data and in other markets Eugene Fama Kenneth French Three-factor model.
Extensions and adaptations
- Five-factor model: In 2015, Fama and French expanded the framework to include profitability and investment characteristics, deriving two additional factors labeled RMW (robust minus weak profitability) and CMA (conservative minus aggressive investment). The five-factor model aims to explain a broader set of anomalies and to provide a more complete accounting of cross-sectional returns across a wider range of stocks and portfolios Five-factor model.
- Carhart model and momentum: Some practitioners combine the Fama-French factors with momentum to capture the persistent tendency of recent winners to continue outperforming in the short run. This leads to the Carhart four-factor model, which adds a momentum factor to the three-factor specification Momentum.
- Global and regional applications: Researchers have tested the model in many markets beyond the United States, with varying degrees of success. The strength and stability of SMB and HML premia can differ across regions and time, highlighting the importance of local market structure and data considerations in factor construction Asset pricing.
Evidence, interpretation, and debates
- Empirical performance: The three-factor model has been widely recognized for its ability to reduce unexplained average returns (alphas) for many portfolios and to attribute part of observed performance to well-documented risk and fundamental characteristics. For many portfolios, exposure to SMB and HML helps explain why small-cap and value stocks have delivered higher average returns compared with CAPM alone. These results have been influential in both academic research and practitioner circles, where the model informs benchmark design and risk management Capital asset pricing model Three-factor model.
- Risk-based vs mispricing explanations: A central debate concerns whether SMB and HML reflect true risk premia that investors require to bear certain kinds of risk (e.g., size-related risk, value-related risk) or whether they largely capture persistent mispricing or behavioral patterns that are not fully risk-based. The consensus leans toward a combination: some portion of the premia is plausibly risk-based, while other portions may reflect behavioral or structural market features. This nuanced view reflects ongoing research into the origins of the premia and the economic interpretation of the factors Efficient market hypothesis Value premium.
- Limitations and criticisms: Critics point out that factor definitions rely on historical samples and specific portfolio constructions, which can be sensitive to methodology and sample period. Some studies document time variation in factor premia or limited out-of-sample predictability, especially after accounting for trading costs and constraints faced by real-world investors. Others note that the model’s explanatory power can fade in certain markets or time periods, prompting refinements such as the five-factor framework or alternative factor sets Book-to-market ratio Size effect.
- Practical implications: For asset management, the Fama-French framework provides a structured way to decompose returns and to design factor-based strategies. It informs the construction of diversified portfolios, the interpretation of performance attribution, and the assessment of risk factors beyond simple market exposure. In academic settings, it serves as a benchmark against which new models and anomalies are assessed, including cross-sectional studies of expected returns Cross-section of expected returns.