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Fama-French 3- and 5-Factor Model

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Dan Buckley
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Written By
Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.
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Updated
Mar 22, 2024

The Fama-French three-factor model is a statistical model formulated in 1992 by Eugene Fama and Kenneth French, both then colleagues at the University of Chicago Booth School of Business.

Eugene Fama, a 2013 Nobel Memorial Prize in Economic Sciences laureate, designed this model to help predict and understand stock returns.

The three factors in this model include:

  • (1) market excess return
  • (2) the outperformance of small versus big companies, and
  • (3) the outperformance of high book/market versus low book/market companies

The 5-factor model includes:

  • (4) RMW (Robust Minus Weak), which measures the difference in returns between firms with high operating profitability and those with low operating profitability, and
  • (5) CMA (Conservative Minus Aggressive), which compares the returns of firms that invest conservatively versus those that invest aggressively

 

Key Takeaways – Fama-French 3- and 5-Factor Model

  • The Fama-French three-factor model, formulated by Eugene Fama and Kenneth French, helps predict and understand stock returns by considering market excess return, the outperformance of small-cap stocks, and the outperformance of high book-to-market ratio stocks.
  • There is ongoing debate about the last two factors of the model, primarily due to their variability and potential impact on the overall outcome.
  • Some argue that the small-cap premium and value premium may not be consistent across all market conditions.
  • The Fama-French five-factor model expands upon the three-factor model by adding profitability and investment factors.
  • While the five-factor model improves the explanatory power of stock returns, concerns have been raised about its measurement of profitability and its applicability to markets outside the US. The inclusion of a momentum factor is also a subject of debate.

 

The Fama-French Model’s Factors

Factor one, the market excess return, encapsulates the idea that investing in the stock market as a whole should yield higher returns than investing in a risk-free instrument, like a government bond.

The second factor acknowledges that smaller firms tend to outperform larger ones.

This factor reflects the risk inherent in investing in these smaller firms, which are more volatile and may not have as stable a financial history as larger, established corporations.

The third factor concerns the ratio between a company’s book value and its market value.

The model posits that companies with a high book-to-market ratio tend to outperform those with a low ratio, even when accounting for other risks.

 

Critiques and Debates

However, these last two factors are the subject of debate.

Some researchers argue that the small-cap premium may not be as consistent as the model suggests, and the value premium may not apply in all market conditions.

Despite these critiques, the Fama-French three-factor model has stood as a significant development in finance, helping traders/investors better understand and predict stock returns.

 

Evolution to the Fama-French 5-Factor Model

Addition of New Factors

In 2014, Fama and French expanded their model to include two more factors: profitability and investment.

The profitability factor, known as RMW (Robust Minus Weak), measures the difference in returns between firms with high operating profitability and those with low operating profitability.

The investment factor, or CMA (Conservative Minus Aggressive), compares the returns of firms that invest conservatively versus those that invest aggressively.

Impact on Previous Factors

In the US from 1963 to 2013, the addition of these two factors rendered the high minus low (HML) factor redundant.

The time series of HML returns were fully explained by the other four factors, most notably the CMA, which had a 0.7 correlation with HML.

Addressing Concerns

These portfolios’ returns covary positively with SMB (Small Minus Big) and negatively with RMW (Robust Minus Weak) and CMA (Conservative Minus Aggressive), resulting in a large negative five-factor alpha.

However, despite these concerns, the five-factor model has been shown to improve the explanatory power of the returns of stocks relative to the three-factor model.

 

Critiques and Considerations

Momentum Factor

Although a momentum factor wasn’t initially included in the model, some experts, such as Cliff Asness, former Ph.D. student of Eugene Fama and co-founder of AQR Capital, have argued for its place in the financial world.

Asness posits that the momentum of a stock – the speed at which its price is changing – can have a significant effect on its return, and therefore should be considered in any comprehensive asset pricing model.

Questions about Profitability Measurement

Some criticisms have also been raised about how Fama and French measure profitability.

For instance, Foye (2018) tested the five-factor model in the UK and voiced concerns.

Foye questions the way Fama and French measure profitability and points out that the five-factor model fails to offer a convincing asset pricing model for the UK.

Further Concerns and Ongoing Debate

Beyond the lack of momentum, more concerns with the five-factor model have been raised, and the debate on the best asset pricing model has not yet been settled.

Regardless of these debates, the Fama-French models remain well-known and widely used in the finance industry, underpinning many investment strategies and serving as a tool for understanding the multifaceted dynamics of asset pricing.

Related

 

FAQs – Fama-French 3- and 5-Factor Model

What is the Fama-French Three-factor model?

The Fama French Three-factor model is a statistical model introduced by Eugene Fama and Kenneth French in 1992.

It aims to explain the returns on a company’s stock based on three factors:

  1. Market excess return
  2. Outperformance of small-cap stocks compared to large-cap stocks
  3. Outperformance of stocks with a high book-to-market ratio compared to those with a low book-to-market ratio

This model builds upon the Capital Asset Pricing Model (CAPM), adding two additional factors to better explain the variations in stock returns.

What is the Fama French Five-factor model?

The Fama French Five-factor model is an expansion of the Three-factor model introduced in 2014.

This model adds two more factors:

  1. Profitability, measured as the difference between the returns of firms with high and low operating profitability
  2. Investment, measured as the difference between the returns of firms that invest aggressively versus those that invest conservatively

These additional factors further refine the model’s predictive ability, but there’s ongoing academic debate over their significance and interpretation.

What is the significance of the Fama French models in portfolio management?

Both the Fama French Three-factor and Five-factor models are important in portfolio management and asset pricing.

They provide an empirical method to predict and analyze stock returns based on factors other than the market return alone.

These models help portfolio managers to identify the risk factors affecting the stocks in a portfolio and to adjust their strategies accordingly.

How do the Fama French models differ from the Capital Asset Pricing Model (CAPM)?

The Capital Asset Pricing Model (CAPM) calculates the expected return on an investment considering its systematic risk, represented by beta.

It states that the expected return on a security is equal to the risk-free rate plus beta times the market excess return.

The Fama French models extend the CAPM by including additional factors like size, value, profitability, and investment in explaining stock returns.

This makes these models potentially more accurate and informative than the CAPM.

Why is there a debate about the last two factors in the Fama French Five-factor model?

There is academic debate regarding the profitability and investment factors in the Five-factor model because these two factors can completely explain the high minus low (HML) returns, making the HML factor redundant.

There are also concerns about the correct measure of profitability and the overall applicability of the model to markets outside the US.

Although the Five-factor model improves the explanatory power of the returns of stocks relative to the Three-factor model, it fails to fully explain all portfolios.

For instance, portfolios comprising small firms that invest heavily despite low profitability perform poorly with this model.

Additionally, concerns have been raised about the model’s measurement of profitability and its ability to provide a convincing asset pricing model for markets like the UK.

What is the argument for including a momentum factor in the Fama French model?

Despite Fama and French not including a momentum factor in their model, Cliff Asness, a former Ph.D. student of Eugene Fama, has advocated for its inclusion.

Asness argues that momentum, or the tendency of rising stock prices to continue to rise in the near term, is a significant factor influencing stock returns and should therefore be accounted for in the model.

However, this proposition is still a topic of ongoing debate in the academic community.

What are the limitations of the Fama-French 3- and 5-Factor models?

Here are some key limitations of the Fama-French 3- and 5-factor models:

  • They are backward-looking models based on historical data. Future returns may not conform to the historical relationships identified.
  • The models assume a linear relationship between factors and returns. This may not always hold true.
  • The models were developed specifically for US equity markets. Applying them internationally or to other asset classes is questionable.
  • The factors are based on sorts on firm characteristics like size and book-to-market. The underlying drivers of the factors are not well understood.
  • The models do not perfectly explain returns. A large portion of returns remains unexplained.
  • Adding more factors does not necessarily lead to a better model. The 5-factor model has marginal explanatory power over the 3-factor model.
  • The models say nothing about the fundamental or intrinsic value of securities. They are statistical models capturing historical return patterns.
  • The factors have shown instability over time. Factor returns and risk premia are not constant and can disappear for long periods.

So, while useful, the Fama-French models have limitations as statistical models that may not reliably predict future returns or provide deep insights into the return generating process.

Investors/traders should be cautious about relying too heavily on these types of models for trading/investment decisions.