Fama french models: Meaning, Criticisms & Real-World Uses

What Is Fama French Models?

The Fama French models are a series of asset pricing models that expand upon earlier frameworks, such as the Capital Asset Pricing Model (CAPM), to explain stock returns. Developed within the broader category of portfolio theory and asset pricing, these models propose that a stock's expected return is influenced by factors beyond just its market risk. The most well-known is the Fama French three-factor model, which identifies three primary factors driving expected returns: the overall market's excess return, a size premium, and a value premium. The Fama French models aim to provide a more comprehensive explanation for observed stock market behavior, particularly the historical outperformance of small-cap and value stocks⁴⁹.

History and Origin

The Fama French models originated from the empirical observations of Eugene Fama and Kenneth French, then professors at the University of Chicago Booth School of Business. Their seminal work in the early 1990s challenged the prevailing single-factor CAPM, which suggested that only a stock's sensitivity to market movements (beta) explained its excess return. Fama and French noted that small-capitalization (small-cap) stocks and value stocks (those with high book-to-market ratios) consistently outperformed the broader market, a phenomenon not fully captured by CAPM⁴⁷, ⁴⁸.

Their research led to the development of the Fama French three-factor model in 1992 and 1993, formally published in academic journals⁴⁶. This model incorporated factors for size and value alongside the traditional market factor. Eugene Fama's broader contributions to the empirical analysis of asset prices, including his work on market efficiency, were recognized when he shared the Nobel Memorial Prize in Economic Sciences in 2013.⁴⁵

Key Takeaways

The Fama French models are multi-factor asset pricing models that expand on the CAPM.
The three-factor model incorporates market risk, a size factor (Small Minus Big or SMB), and a value factor (High Minus Low or HML) to explain stock returns.
SMB accounts for the historical tendency of small-cap stocks to outperform large-cap stocks.
HML accounts for the historical tendency of value stocks (high book-to-market ratio) to outperform growth stocks (low book-to-market ratio).
Later extensions, such as the Fama French five-factor model, introduced additional factors like profitability and investment.

Formula and Calculation

The most commonly used iteration, the Fama French three-factor model, is expressed by the following formula:

E(R_i) - R_f = \beta_1(R_m - R_f) + \beta_2(SMB) + \beta_3(HML) + \alpha_i

Where:

(E(R_i)) = The expected return of asset (i).
(R_f) = The risk-free rate, often represented by the return on short-term government securities⁴³, ⁴⁴.
((R_m - R_f)) = The market risk premium, which is the expected return of the market portfolio minus the risk-free rate.
(SMB) (Small Minus Big) = The size premium, representing the historical excess return of small-cap stocks over large-cap stocks. This factor is constructed by taking the average return of small-cap portfolios and subtracting the average return of large-cap portfolios⁴¹, ⁴².
(HML) (High Minus Low) = The value premium, representing the historical excess return of value stocks (high book-to-market ratios) over growth stocks (low book-to-market ratios). This factor is constructed by taking the average return of high book-to-market portfolios and subtracting the average return of low book-to-market portfolios³⁹, ⁴⁰.
(\beta_1, \beta_2, \beta_3) = The sensitivities (or factor loadings) of the asset's return to the respective factors. These are derived through regression analysis ³⁷, ³⁸.
(\alpha_i) (alpha) = The asset's abnormal return not explained by the model's factors³⁵, ³⁶.

Data for the SMB, HML, and other Fama French factors are publicly available from sources like Kenneth French's Data Library.³⁴

Interpreting the Fama French Models

Interpreting the Fama French models involves understanding the significance of each factor's coefficient (beta) and the model's overall explanatory power. A positive (\beta_1) indicates the asset's positive correlation with the overall market. A positive (\beta_2) (SMB coefficient) suggests that the asset tends to perform well when small-cap stocks outperform large-cap stocks, implying a higher exposure to the size risk premium. Similarly, a positive (\beta_3) (HML coefficient) indicates the asset's sensitivity to the value premium, meaning it performs better when value stocks outperform growth stocks³², ³³.

The R-squared value of a Fama French model regression indicates how much of an asset's return variability is explained by the model's factors. The Fama French three-factor model typically explains a higher percentage of diversified portfolio returns (often over 90%) compared to the CAPM (around 70%), making it a more robust tool for explaining historical returns³⁰, ³¹. A significant positive alpha suggests that the asset has generated returns in excess of what would be expected given its exposure to the Fama French factors. Conversely, a negative alpha indicates underperformance.

Hypothetical Example

Consider an investor, Sarah, who is evaluating the historical performance of a particular equity fund. She decides to use the Fama French three-factor model to understand its return drivers.

Sarah gathers the following hypothetical monthly data:

Fund's Excess Return: 1.2%
Market Risk Premium ((R_m - R_f)): 0.8%
SMB Factor: 0.3%
HML Factor: 0.5%

After running a regression of the fund's historical excess returns against the market risk premium, SMB, and HML factors, Sarah obtains the following coefficients:

(\beta_1) (Market Beta): 1.1
(\beta_2) (SMB Sensitivity): 0.6
(\beta_3) (HML Sensitivity): 0.4
(\alpha_i) (Alpha): 0.1%

Plugging these values into the Fama French formula:
(1.2% = 1.1(0.8%) + 0.6(0.3%) + 0.4(0.5%) + 0.1%)
(1.2% = 0.88% + 0.18% + 0.20% + 0.1%)
(1.2% = 1.26%) (due to rounding, a slight difference may occur)

This indicates that, based on its exposure to market risk, small-cap stocks, and value stocks, the model predicts a return of approximately 1.16% ((0.88% + 0.18% + 0.20%)). The fund's actual excess return was 1.2%, meaning it generated an additional 0.1% (alpha) that the Fama French factors did not explain. This positive alpha suggests the fund slightly outperformed what would be expected given its factor exposures, perhaps due to active management or other uncaptured factors²⁹.

Practical Applications

The Fama French models are widely applied in financial analysis and portfolio management for several key purposes:

Performance Attribution: Investment managers use Fama French models to analyze the sources of a portfolio's returns. By breaking down returns into contributions from market, size, and value factors, managers can determine whether outperformance or underperformance is due to skill (positive or negative alpha) or simply exposure to these common risk factors²⁷, ²⁸.
Portfolio Construction: Investors can intentionally tilt their portfolios towards certain factors if they believe those factors will generate higher returns in the future. For example, if an investor expects small-cap value stocks to outperform, they might construct a portfolio with higher exposure to the SMB and HML factors²⁶.
Risk Assessment: The factor sensitivities (betas) derived from the Fama French models provide a more nuanced understanding of a portfolio's risk exposures than a single market beta. This helps investors identify and manage specific factor risks within their portfolios²⁵.
Cost of Capital Estimation: Companies and analysts use the Fama French model to estimate the cost of equity capital more accurately, especially for firms with significant size or value characteristics²⁴.
Academic Research: The Fama French models remain a cornerstone of academic research in financial economics, serving as a benchmark for testing new asset pricing theories and identifying additional factors that might explain returns. Kenneth French's Data Library provides comprehensive historical data for these factors, facilitating ongoing research.²³

Limitations and Criticisms

Despite their widespread acceptance and improved explanatory power over single-factor models, the Fama French models face several limitations and criticisms:

Empirical, Not Theoretical: A primary critique is that the Fama French models are largely empirical, meaning they are based on observed patterns in historical data rather than derived from a pure theoretical foundation, unlike the CAPM²¹, ²². Critics sometimes accuse the model of "data mining," suggesting that the factors were identified after observing historical relationships, which might not hold consistently in the future²⁰.
Time-Varying Relationships: The relationships between factors and returns can be time-varying, meaning the factor sensitivities (betas) and even the premiums themselves might change over different economic cycles or periods¹⁸, ¹⁹.
Factor Redundancy and New Factors: As markets evolve and new anomalies are identified, the initial three factors might not fully capture all return drivers. Fama and French themselves extended the model to a five-factor model in 2015, adding profitability (Robust Minus Weak, RMW) and investment (Conservative Minus Aggressive, CMA) factors¹⁷. However, even these expanded models face critiques regarding the redundancy of certain factors in different markets and timeframes¹⁵, ¹⁶.
Assumptions: Like many financial models, the Fama French models assume market efficiency, implying that all available information is reflected in asset prices. While useful, real-world markets are not perfectly efficient and can be influenced by behavioral biases or irrational investor behavior¹³, ¹⁴.
Out-of-Sample Performance: While the models explain a high percentage of past returns, their predictive power for future returns can be debated, as past performance is not indicative of future results¹².

Fama French Models vs. Capital Asset Pricing Model (CAPM)

The Fama French models emerged as a significant refinement of the single-factor Capital Asset Pricing Model (CAPM), which was the dominant asset pricing theory for decades. The core distinction lies in the number of factors used to explain expected asset returns and, consequently, how risk and return are understood.

Feature	Capital Asset Pricing Model (CAPM)	Fama French Models (e.g., Three-Factor)
Factors	One factor: Market risk premium ((R_m - R_f))	Multiple factors: Market risk premium, Size (SMB), Value (HML)
Risk Definition	Assumes only systematic risk (market risk) is priced.	Argues that size and value are additional priced risk factors.
Explanatory Power	Explains approximately 70% of diversified portfolio returns.	Explains typically over 90% of diversified portfolio returns, a significant improvement.
Origin	Theoretical model based on equilibrium in financial markets.	Primarily empirical, based on observed patterns in historical data.
Focus	Determines expected return based on sensitivity to market movements (beta).	Determines expected return based on sensitivity to market, size, and value factors.

The Fama French models essentially address observed market anomalies that the CAPM could not explain, such as the persistent outperformance of small-cap and value stocks⁹, ¹⁰, ¹¹. While CAPM remains a foundational concept for understanding the relationship between risk and return, the Fama French models offer a more nuanced and empirically robust framework for analyzing asset prices and evaluating investment performance.⁸

FAQs

What are the main factors in the Fama French models?

The Fama French three-factor model includes three main factors: the market risk premium (the excess return of the market over the risk-free rate), the size factor (SMB, or Small Minus Big), and the value factor (HML, or High Minus Low). SMB captures the outperformance of small companies, while HML captures the outperformance of value-oriented companies⁷.

Why were the Fama French models developed?

The models were developed by Eugene Fama and Kenneth French to better explain the returns of stocks and portfolios. They observed that the traditional CAPM did not fully account for the consistent outperformance of small-cap and value stocks. By adding size and value as specific risk factors, the Fama French models aimed to provide a more complete explanation for these patterns⁶.

How do Fama French models differ from CAPM?

The primary difference is that the Fama French models incorporate additional factors beyond just market risk. While CAPM uses only the market's excess return to explain a stock's expected return, the Fama French three-factor model adds factors for company size (SMB) and value (HML). This makes the Fama French models generally more effective at explaining observed stock returns in diversified portfolios⁴, ⁵.

Can Fama French models predict future stock returns?

The Fama French models are primarily explanatory, meaning they are very good at describing why past returns occurred based on exposure to market, size, and value factors. While they provide a framework for understanding expected returns given these exposures, they do not guarantee or precisely predict future returns², ³. Market dynamics can change, and other factors not included in the models might influence future performance.

Are there other Fama French models beyond the three-factor model?

Yes, Fama and French have extended their original three-factor model. In 2015, they introduced the Fama French five-factor model, which added two new factors: profitability (RMW, Robust Minus Weak) and investment (CMA, Conservative Minus Aggressive)¹. These additional factors aim to further capture dimensions of equity returns.