The Fama-French Three-Factor Model

The Fama-French Three-Factor Model

🔥 The traditional asset pricing model, Capital Asset Pricing Model (CAPM), is a model which was developed in the 1960s and suggests that the expected return on an asset can be calculated based on its BETA (beta measures the asset’s sensitivity to movements in the overall market portfolio). It has been used by investors, analysts as well as managers over the years to make investment decisions. As can be depicted, the traditional asset pricing model uses only one variable to compare the returns of a portfolio or stock with the returns of the market as a whole. Hence, in 1992, Fama and French added two other factors namely size and value factors to the CAPM.

Background of Fama-French Three-Factor Model

According to Research Foundation of the Institute of Chartered Financial Analysts (1994), factor models are statistical models that attempt to explain complex phenomena using a small number of underlying causes or factors. The Fama and French Three-Factor Model (the Fama French Model) is an asset pricing model developed in 1992 that expands on the CAPM by adding SIZE and VALUE factors to the market risk factor in CAPM. The model is claimed to have been developed using an econometric regression of historical stock prices.
Fama and French found empirical evidence that a size and value premium exist in stock returns. They started observing that two classes of stocks, smaller companies and those with higher book-to-market ratios (value stocks) have tended to perform much better than the market as a whole, based on a new model that includes these additional 2 factors.
According to Fama and French’s research, the three factor model explains over 90% of the diversified portfolios returns, compared with the average 70% given by the CAPM (within their sample). They found positive returns from small size as well as value factors, like a high book-to-market ratio and related ratios.
Although there is academic debate about the size and value factors being applicable and relevant, the Fama-French model has become a widely used tool in finance for explaining stock returns and evaluating portfolio performance (Christoph, 2015).

Calculating the Fama-French Model. Formula

As stated, the 3 factors of the model are: the SIZE of firms, BOOK-TO-MARKET VALUES, and EXCESS RETURN ON THE MARKET.
In other words, the three factors used are small minus big (SMB), high minus low (HML), and the portfolio's return less the risk-free rate of return. SMB accounts for publicly traded companies with small market caps that generate higher returns, while HML accounts for value stocks with high book-to-market ratios that generate higher returns in comparison to the market.

The formula of Fama-French Model:

Rit − Rft = αit + β1(RMt−Rft) + β2SMBt + β3HMLt + ϵit

Where:
Rit = total return of a stock or portfolio i at time t
Rft = risk free rate of return at time t
RMt = total market portfolio return at time t
Rit−Rft = expected excess return
RMt−Rft = excess return on the market portfolio (index)
SMBt = size premium (small minus big) - The difference each month between the average returns of three small stock portfolios and three big stock portfolios.
HMLt = value premium (high minus low) - The difference each month between the average returns of two high book-to-market equity portfolios and two low book-to-market equity portfolios.
β1,2,3 = factor coefficients

Benefits of Fama-French Model

The additional 2 factors (size and value) address major anomalies and empirical regularities in stock returns better than the single factor CAPM
It helps to explain differences in average returns across stocks based on market cap and valuation ratios.
Enables investors to refine asset pricing and build diversified portfolios that target size and value premiums through calculating expected returns and exposure to risk.

Drawbacks of Fama-French Model

Researchers are of the view that the factors have unstable and time-varying premiums and their performance tends to come in long cycles, underperforming for years before rebounding.
Compared to the CAPM, the Fama-French model is obviously more complex, which may pose challenges in interpretation and implementation for some users.
The model is based on historical realized returns, which may not represent expected returns going forward. The size and value premiums may be sample-specific.

Application of Fama-French Model

According to the Journal of Finance (1988), the three factor model can be applied for:

Estimating the cost of equity capital for firms and portfolios.
Constructing diversified portfolios and smart beta strategies targeting premiums related to size, value, and other factors (strategic asset allocation)
Estimating factor risk premiums and constructing optimized portfolios based on exposures to priced risk factors.
Evaluating the performance of investment strategies or portfolios through comparing actual returns to those predicted by the model, analysts, advisors and managers can assess the effectiveness of their investment decisions and identify areas for improvement.

To sum up, the Fama and French model can be a useful model to add to your strategies as it factors in two additional factors (size and value) as opposed to the CAPM which focuses on only one factor. This will allow you, investment analysts and managers to make more informed decisions when making investment based on a diversified factors. In your quest to apply the model, do not disregard some of its drawbacks which may hinder the effectiveness of the model such the complexity that comes with the model and that it is based on historical data which is not a representation of the future results. Nonetheless, Christoph (2015) claims that the model is a widely used tool by those in finance for explaining stock returns and evaluating portfolio performance.

References
1. Lohrmann, Christoph. "Comparison of the CAPM, the Fama-French Three Factor Model and Modifications". Germany, GRIN Verlag, 2015.
2. Eugene F. Fama and Kenneth R. French. "Multifactor Explanations of Asset Pricing Anomalies." The Journal of Finance, Volume 51, No. 1, 1996, Pages 55-84.
3. Eugene F. Fama and Kenneth R. French. "Value versus Growth: The International Evidence." The Journal of Finance, Volume 53, No. 6, 1988, Pages 1975-1999.
4. "A Practitioner's Guide to Factor Models". (1994). United States: Research Foundation of the Institute of Chartered Financial Analysts.