Fama french model

LINK_POOL:

• "Capital Asset Pricing Model"
• "Risk-Free Rate"
• "Market Risk Premium"
• "Beta"
• "Market Capitalization"
• "Value Investing"
• "Growth Stocks"
• "Small-Cap Stocks"
• "Large-Cap Stocks"
• "Portfolio Management"
• "Asset Allocation"
• "Regression Analysis"
• "Systematic Risk"
• "Factor Investing"
• "Diversification"

What Is the Fama-French Model?

The Fama-French model is an asset pricing model that expands upon the traditional Capital Asset Pricing Model (CAPM) by incorporating additional factors beyond just market risk. Developed within the realm of quantitative finance and portfolio theory, the Fama-French model aims to provide a more comprehensive explanation for observed stock returns by accounting for the tendencies of certain types of stocks to outperform the broader market⁶⁵, ⁶⁶.

Specifically, the Fama-French model, often referred to as the three-factor model, considers three factors: the overall market's excess return, the outperformance of small-cap stocks compared to large-cap stocks, and the outperformance of value stocks (those with high book-to-market ratios) over growth stocks (those with low book-to-market ratios)⁶³, ⁶⁴. This model is essentially the result of econometric regression analysis of historical stock prices, seeking to capture systematic risk exposures that influence returns.

History and Origin

The Fama-French model was developed by Nobel laureate Eugene Fama and his colleague Kenneth French. Their seminal work, published in 1992, introduced the three-factor model as an extension of the CAPM⁶². Prior to their research, the CAPM, which uses only a single factor (beta) to compare a portfolio's returns with the market, was the predominant asset pricing model.

Fama and French, both former professors at the University of Chicago Booth School of Business, observed through their research that value stocks consistently outperformed growth stocks, and small-cap stocks tended to outperform large-cap stocks. These observations led them to develop their three-factor model, which aimed to better measure market returns by incorporating these size and value risk factors⁶¹. In 1993, they published "Common Risk Factors in the Returns on Stocks and Bonds," a paper that proposed their three-factor model, providing a framework for understanding why certain stocks and fund managers tended to outperform others⁶⁰. Kenneth French maintains an extensive library of economic data, including the Fama-French factors, which is publicly available for download⁵⁸, ⁵⁹.

Key Takeaways

• The Fama-French model expands on the CAPM by adding size and value factors to explain stock returns.⁵⁷
• It posits that small-cap stocks and value stocks tend to outperform the broader market over the long term.⁵⁶
• The model can explain a significant portion of the return in a diversified stock portfolio, often cited as over 90%.⁵⁵
• Investors can use the Fama-French model for risk assessment, portfolio management, and performance evaluation.⁵³, ⁵⁴
• Extensions to the original three-factor model, such as the five-factor model, have been developed to include additional factors like profitability and investment.⁵²

Formula and Calculation

The Fama-French three-factor model calculates the expected return of a portfolio or stock using the following formula:

Where:

• (E(R_i)) = Expected return of the stock or portfolio (i)
• (R_f) = Risk-Free Rate⁵¹
• (R_m) = Expected return on the overall market portfolio
• (R_m - R_f) = Market Risk Premium, representing the excess return of the market over the risk-free rate⁵⁰
• (SMB) = "Small Minus Big," the size factor. This represents the historical excess returns of small-cap companies over large-cap companies.⁴⁹
• (HML) = "High Minus Low," the value factor. This represents the historical excess returns of value stocks (high book-to-market ratio) over growth stocks (low book-to-market ratio).⁴⁸
• (\beta_m), (\beta_s), (\beta_h) = Factor sensitivities (Beta coefficients) to the market, size, and value factors, respectively. These are determined through regression analysis.⁴⁷
• (\alpha) = Alpha, the stock-specific intercept or residual return not explained by the model's factors.⁴⁶

The factor data for SMB and HML can be obtained from Kenneth French's Data Library, which provides historical data on these factors⁴⁴, ⁴⁵.

Interpreting the Fama-French Model

Interpreting the Fama-French model involves understanding how the various factors contribute to a portfolio's or security's expected return. The beta coefficients ((\beta_m), (\beta_s), (\beta_h)) indicate the sensitivity of the asset's returns to each of the three factors.

• A positive (\beta_m) suggests the asset's returns generally move in the same direction as the overall market.
• A positive (\beta_s) indicates that the asset tends to perform better when small-cap stocks outperform large-cap stocks. This implies exposure to the size premium.⁴³
• A positive (\beta_h) suggests the asset has characteristics of value stocks and is likely to perform well when value stocks outperform growth stocks. This indicates exposure to the value premium.⁴²

By analyzing these sensitivities, investors can gain insight into the underlying drivers of a portfolio's returns beyond just its overall market exposure. For example, a portfolio with a high sensitivity to the size factor may be more vulnerable to fluctuations in the small-cap stock market⁴¹. The model helps to explain why certain portfolios have historically achieved higher or lower returns than what the CAPM might suggest, attributing these differences to exposures to size and value premiums⁴⁰.

Hypothetical Example

Imagine an investor wants to evaluate a diversified portfolio using the Fama-French model.

1. Gather Data:

   • Assume the historical monthly risk-free rate ((R_f)) is 0.05%.
   • The average monthly market risk premium ((R_m - R_f)) is 0.80%.
   • The average monthly SMB (Small Minus Big) factor is 0.30%.
   • The average monthly HML (High Minus Low) factor is 0.40%.
   • Through regression analysis of the portfolio's historical returns against these factors, the following sensitivities (betas) are determined:
     • (\beta_m) (market beta) = 1.1
     • (\beta_s) (SMB beta) = 0.6
     • (\beta_h) (HML beta) = 0.4
   • The alpha ((\alpha)) is found to be 0.02% (2 basis points).

2. Apply the Formula:
   (E(R_i) - R_f = \beta_m(R_m - R_f) + \beta_s(SMB) + \beta_h(HML) + \alpha)
   (E(R_i) - 0.0005 = 1.1(0.0080) + 0.6(0.0030) + 0.4(0.0040) + 0.0002)
   (E(R_i) - 0.0005 = 0.0088 + 0.0018 + 0.0016 + 0.0002)
   (E(R_i) - 0.0005 = 0.0124)
   (E(R_i) = 0.0124 + 0.0005)
   (E(R_i) = 0.0129)

3. Result:
   The expected monthly excess return for this portfolio is 1.24%, and the total expected monthly return is 1.29%. This indicates that, in addition to its exposure to the overall market, the portfolio's tilt towards small-cap and value stocks is contributing positively to its expected returns.

Practical Applications

The Fama-French model is a widely used tool in finance, particularly in portfolio management and asset pricing. Its applications span various areas of investment analysis and strategy:

• Performance Evaluation: Analysts use the Fama-French model to assess the performance of investment managers and portfolios. By attributing returns to the three factors, it becomes possible to determine whether outperformance is due to genuine skill (alpha) or simply exposure to the market, size, or value factors. This helps in understanding the true sources of returns.³⁸, ³⁹
• Risk Assessment: The model helps portfolio managers dissect the components of risk more effectively. By quantifying exposures to the market, size, and value factors, investors can better understand the sources of risk in their portfolios. For instance, a high sensitivity to the size factor implies greater vulnerability to shifts in the small-cap market.³⁶, ³⁷
• Asset Allocation and Portfolio Construction: Investors can use the Fama-French model to tailor their asset allocation strategies. If an investor believes that small-cap stocks or value stocks will outperform, they can tilt their portfolio towards assets with higher sensitivities to the SMB and HML factors, respectively, to optimize their risk-return profile. This forms a basis for certain factor investing strategies.³⁴, ³⁵
• Arbitrage Opportunities: Hedge funds and quantitative analysts may utilize the Fama-French framework to identify potential arbitrage opportunities by comparing the model's predictions against actual market returns.³³
• Academic Research: The Fama-French model serves as a foundational framework for much academic research in finance, leading to further developments like the Fama-French Five-Factor Model, which includes profitability and investment factors.³²

Kenneth French's data library is a key resource for practitioners and academics, providing the necessary factor data for applying the model.³⁰, ³¹

Limitations and Criticisms

While the Fama-French model significantly advanced asset pricing, it is not without limitations and has faced several criticisms:

• Empirical, Not Theoretical: A primary criticism is that the Fama-French model is largely empirical, based on observed historical patterns, and lacks a strong theoretical foundation comparable to the CAPM. Critics sometimes argue it might be a result of "data mining," fitting the model to historical data rather than stemming from a deep economic theory. However, some supportive theories are being explored.²⁹
• Factor Premiums Variability: The observed premiums for size and value factors are not always consistent and can vary over time and across different market conditions. There's ongoing debate about the consistency and persistence of these factor premiums, especially the small-cap and value premiums.²⁸
• Incomplete Explanation of Returns: Despite explaining a high percentage of diversified portfolio returns, the three-factor model does not capture all market anomalies. Notably, Fama and French themselves acknowledged its failure to fully explain momentum, where past winning stocks tend to continue outperforming and past losing stocks continue underperforming in the short term. This led to the development of other models, such as the Carhart four-factor model, which adds a momentum factor.²⁷
• Assumption of Linear Relationships: The model assumes a linear relationship between the factors and returns, which may not always hold true in complex financial markets. Research suggests that non-linear relationships might exist between the factors.²⁵, ²⁶
• Reliance on Historical Data: Like many financial models, the Fama-French model is based on historical data. As the saying goes, "past performance is not indicative of future results." The model's parameters are estimated using historical data, and future market dynamics may differ.²⁴
• Applicability Beyond US Markets: While the model has shown strong explanatory power in the US market, its applicability and the magnitude of its factors may differ in other international markets.²², ²³

Fama-French Model vs. Capital Asset Pricing Model

The Fama-French model and the Capital Asset Pricing Model (CAPM) are both widely used in asset pricing, but they differ significantly in their approach to explaining asset returns.

While the CAPM provides a straightforward method for estimating expected returns based solely on systematic risk, the Fama-French model offers a more comprehensive explanation by incorporating size and value factors that have empirically been shown to influence returns¹¹, ¹², ¹³. This increased explanatory power makes the Fama-French model generally considered more effective in predicting variations in excess returns.⁹, ¹⁰

FAQs

Q: What are the three factors in the Fama-French model?
A: The three factors are: the market risk premium (the excess return of the market over the risk-free rate), Small Minus Big (SMB), and High Minus Low (HML). SMB accounts for the tendency of small-cap stocks to outperform large-cap stocks, while HML accounts for the tendency of value stocks to outperform growth stocks.⁸

Q: Why was the Fama-French model developed?
A: The Fama-French model was developed because the traditional Capital Asset Pricing Model (CAPM) did not fully explain observed stock returns, particularly the empirical findings that small-cap and value stocks tended to outperform. Eugene Fama and Kenneth French introduced additional factors to better capture these phenomena.⁷

Q: How is the Fama-French model used by investors?
A: Investors use the Fama-French model for various purposes, including evaluating the performance of portfolio managers, understanding the sources of risk in their portfolios, and making more informed asset allocation decisions. It helps in assessing whether returns are due to market exposure or specific tilts towards size and value factors.⁴, ⁵, ⁶

Q: Is the Fama-French model still relevant today?
A: Yes, the Fama-French model remains highly relevant in modern finance. It is a cornerstone of academic research in factor investing and is widely used by institutional investors and financial analysts for portfolio analysis and management. While it has limitations and has seen extensions (like the five-factor model), its core insights continue to influence investment strategies.², ³

Q: What is the Fama-French five-factor model?
A: The Fama-French five-factor model is an extension of the original three-factor model. It adds two more factors: profitability (robust minus weak, RMW) and investment (conservative minus aggressive, CMA). These additional factors aim to further explain the cross-section of stock returns by considering a company's profitability and investment policies.¹