In their famous paper, Fama and French expanded the CAPM model by adding two additional factors explaining the excess returns of an asset or portfolio. The factors they considered are:
- The market factor (MKT): It measures the excess return of the market, analogical to the one in the CAPM.
- The size factor, SMB (Small Minus Big): It measures the excess return of stocks with a small market cap over those with a large market cap.
- The value factor, HML (High Minus Low): It measures the excess return of value stocks over growth stocks. Value stocks have a high book-to-market ratio, while the growth stocks are characterized by a low ratio.
The model can be represented as follows:
Or in its simpler form:
Here, E(ri) denotes the expected return on asset i, rf is the risk-free rate (such as a government bond), and α is the intercept. The reason for including the constant intercept is to make sure its value is equal to 0. This confirms that the three-factor model evaluates the relationship between the excess returns and the factors correctly.
Due to the popularity of this approach, these factors became collectively known as the Fama-French Factors, or the Three-Factor Model. They have been widely accepted in both academia and the industry as stock market benchmarks and they are often used to evaluate investment performance.
In this recipe, we estimate the three-factor model using 5 years (2014-2018) of monthly returns on Facebook.