Several multivariate linear models

As we mentioned at the beginning of the chapter, we could show several applications of multivariable linear models. The first one is a three-factor linear model. The general formula is quite similar to the one-factor linear model, shown here:

The definitions are the same as before. The only difference is that we have three independent variables instead of one. Our objective is to estimate four parameters, one intercept plus three coefficients:

For example, the equation of the famous Fama-French 3-factor model is given, where R_i is the stock i's return and R_m is the market return. SMB (Small Minus Big) is defined as the returns of the small portfolios minus the returns of the big portfolios and HML (High Minus Low) is the difference of returns of high book-to-market portfolios minus the returns of low book-to-market portfolios. (See the...