Estimating the Fama-French three-factor model

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 growth stocks are characterized by a low ratio.

Please see the See also section for a reference to how the factors are calculated.

The model can be represented as follows:

Or in its simpler form:

Here, E(r_i) denotes the expected return on asset i, r_f is the risk-free rate (such as a government bond), and α is the intercept. The reason for including...