What is the Fama and French Three-Factor Model? Insights and Application
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Summary:
The Fama and French Three-Factor Model, developed by Nobel laureates Eugene Fama and Kenneth French, enhances the traditional capital asset pricing model (CAPM) by introducing size and value risk factors. This model acknowledges that small-cap and value stocks tend to outperform the market and adjusts for this trend. By considering three factors – size, book-to-market values, and excess market returns – investors gain insights into portfolio returns. While there’s ongoing debate about market efficiency, this model helps long-term investors manage risk and make informed decisions. Fama and French later expanded it to a Five-Factor Model, incorporating additional factors like profitability and investment.
What is the Fama and French three factor model?
The Fama and French Three-Factor Model, often referred to as the Fama French Model, emerged in 1992 as an asset pricing model that builds upon the traditional capital asset pricing model (CAPM). This innovative model was developed by Nobel laureates Eugene Fama and his colleague Kenneth French. It aims to provide a more comprehensive framework for assessing investment strategies by incorporating additional risk factors.
Understanding the Fama and French three factor model
Eugene Fama and Kenneth French, former professors at the University of Chicago Booth School of Business, introduced this model to address the limitations of CAPM. They conducted extensive research and found that certain stocks consistently outperform the market. Specifically, value stocks, which are characterized by a low price relative to their book value, and small-cap stocks tend to yield higher returns compared to the broader market.
This model recognizes that value and small-cap stocks frequently outshine the market, and it adjusts for this trend. It incorporates three key factors:
- Size: This factor, known as small minus big (SMB), accounts for publicly traded companies with small market capitalizations that often generate higher returns than their larger counterparts.
- Value: High minus low (HML) represents value stocks with high book-to-market ratios. These stocks tend to outperform the market over time.
- Market Returns: This factor considers the portfolio’s return minus the risk-free rate of return, reflecting the overall market performance.
The ongoing debate in financial circles revolves around whether the consistent outperformance of these stocks is a result of market efficiency or inefficiency. Proponents of market efficiency argue that this outperformance is attributed to the higher risk and business uncertainty associated with value and small-cap stocks. In contrast, supporters of market inefficiency suggest that these stocks are often mispriced by market participants, leading to long-term excess returns as prices adjust.
The formula
The mathematical representation of the Fama and French Three-Factor Model is as follows:
R – R = α + β(R – R) + βSMB + βHML + ϵ
Where:
- R = Total return of a stock or portfolio i at time t
- R = Risk-free rate of return at time t
- R = Total market portfolio return at time t
- α = Expected excess return
- R – R = Excess return on the market portfolio (index)
- SMB = Size premium (small minus big)
- HML = Value premium (high minus low)
- β = Factor coefficients
Fama and French’s insights
Fama and French emphasized that investors should be prepared to withstand extra volatility and occasional underperformance in the short term. Their research, based on thousands of random stock portfolios, demonstrated that when size and value factors are combined with the beta factor, they can explain up to 95% of the return in a diversified stock portfolio.
With the ability to account for 95% of a portfolio’s return, investors can construct portfolios that align with their risk tolerance. Key drivers of expected returns include sensitivity to the market, size, and value stocks, as measured by the book-to-market ratio. Any additional expected return may be attributed to unpriced or unsystematic risk.
What does Fama and French three factor model mean for investors?
The Fama and French Three Factor Model underscore the importance of long-term investment horizons. Investors with a time horizon of 15 years or more may encounter short-term volatility and underperformance but are likely to be rewarded in the long run. By explaining a substantial portion of a diversified portfolio’s return, this model empowers investors to tailor their portfolios to achieve expected returns based on their risk profiles.
The primary determinants of expected returns according to this model are:
- Sensitivity to the overall market
- Sensitivity to the size of companies in the portfolio
- Sensitivity to value stocks, as indicated by the book-to-market ratio
Any additional expected return may be attributed to unpriced or unsystematic risks, which investors should carefully consider in their investment strategies.
What are the three factors of the model?
The Fama and French model relies on three core factors:
- Size (SMB): This factor accounts for publicly traded companies with small market capitalizations that tend to deliver higher returns compared to larger companies.
- Value (HML): High minus low (HML) represents value stocks with high book-to-market ratios, which historically outperform the broader market.
- Market Returns: This factor considers the portfolio’s return minus the risk-free rate of return, reflecting overall market performance.
What is the Fama and French five factor model?
In 2014, Fama and French expanded their model to incorporate five factors. In addition to the original three factors, the model introduced two additional components:
- Momentum: This factor accounts for the tendency of stocks with recent positive performance to continue performing well, while those with negative performance tend to lag.
- Profitability: Companies reporting higher futureearnings are expected to have higher returns in the stock market.
Furthermore, the fifth factor, known as “investment,” relates to the concept of a company’s internal investment and returns. It suggests that companies directing profits toward major growth projects may experience losses in the stock market.
Frequently asked questions
What is the primary purpose of the Fama and French Three-Factor Model?
The Fama and French Three-Factor Model aims to enhance traditional asset pricing models like CAPM by accounting for size and value risk factors. It provides a more comprehensive framework for evaluating investment strategies.
How do size and value factors affect portfolio returns in this model?
Size (SMB) and value (HML) factors consider the size of firms and their book-to-market values, respectively. Stocks with small market caps and high book-to-market ratios tend to outperform, impacting portfolio returns.
Is the Fama and French model widely accepted in the finance industry?
Yes, it’s widely recognized and used by financial professionals. However, there’s ongoing debate about market efficiency, with some experts favoring the Efficient Markets Hypothesis (EMH) and others emphasizing market inefficiency.
What is the mathematical formula for the Fama and French Three-Factor Model?
The formula is R – R = α + β(R – R) + βSMB + βHML + ϵ, where each component represents various factors influencing returns.
How should long-term investors use this model?
Long-term investors, with horizons of 15 years or more, can benefit from this model. It helps them manage short-term volatility and align portfolios with their risk profiles, emphasizing potential long-term rewards.
Key takeaways
- The Fama and French Three-Factor Model enhances CAPM by including size and value risk factors, providing a more comprehensive framework for assessing investments.
- Investors should consider their long-term investment horizon of 15 years or more when using this model, as it accounts for short-term volatility and emphasizes the potential for long-term rewards.
- The three core factors in the model are size (SMB), value (HML), and market returns, which collectively explain a significant portion of portfolio returns.
- In 2014, Fama and French expanded the model to a Five-Factor Model, introducing additional factors like momentum and profitability.
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