This study analyzes the empirical performance of the single factor Capital Asset Pricing Model (CAPM) and the multi-factor models using a broad cross-section and long time series stock portfolios and controlling for size factor. Further, this study compares the empirical fit of the CAPM and the multi-factor models controlling for size, BE/ME, and momentum factors.
To compare the empirical results of single factor CAPM, the Fama and French three-factor model, and the Carhart four-factor model this study uses monthly return of 10 decile portfolios from January, 2000 to December, 2008. Linear regression analysis is used for pre-diagnosis of models and the Hansen and Jagannathan (HJ) distance, which is widely used for diagnosis of asset pricing model, is employed to compare the empirical results among three models.
For CAPM size, book/market, momentum portfolios shows significant positive maker risk premium. In all portfolios, explanatory power has a range from 70% to 80%, suggesting that single factor explains portfolio returns relatively well. For three-factor model SMB and market risk premium have significant positive effect on portfolio risk premium, while HML doesn't have significant effect on portfolio risk premium. Explanatory power is improved relative to single factor CAPM. For four-factor model, SMB and market risk premium have significant positive effect on portfolio risk premium. Again, explanatory power is higher than single factor model.
The findings from HJ distance indicate that the CAPM yields better fit than three-factor model and four-factor model for the size portfolios and four-factor model shows better fit than three-factor model. For the book/market portfolios and the momentum portfolios, the multi-factor models also show worse fit than the CAPM and four-factor model yields better fit than three-factor model.
In sum, the findings of this study suggest that multi-factor models yield a worse fit than the single factor CAPM. The relative fit of three- factor model and four-factor model varies across control variables. Controlling size effect improves the empirical fit relative to controlling BE/ME and momentum effects.