In this chapter, we looked at several applications of linear models, including CAPM, the Fama-French 3-factor linear model, the Fama-French-Carhart 4-factor linear model, and the Fama-French 5-factor linear model. Obviously, CAPM is the simplest one since it only involves a market index as the explanatory variable. One question remains though: which model is the best? In other words, how do we rank these models and how is their performance measured? When running linear regressions, the output will show both the R2 and adjusted R2. When comparing models with different numbers of independent variables, the adjusted R2 is a better measure since it is adjusted by the number of input variables. However, note we should not depend only on the adjusted R2 since this is in the sample measure. In other words, a higher adjusted R2 simply means that based...
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