A New Look to Three-Factor Fama-French Regression Model using Sample Innovations

Abstract: The Fama-French model is widely used in assessing the portfolio's performance compared to market returns. In Fama-French models, all factors are time-series data. The cross-sectional data are slightly different from the time series data. A distinct problem with time-series regressions is that R-squared in time series regressions is usually very high, especially compared with typical R-squared for cross-sectional data. The high value of R-squared may cause misinterpretation that the regression model fits the observed data well, and the variance in the dependent variable is explained well by the independent variables. Thus, to do regression analysis, and overcome with the serial dependence and volatility clustering, we use standard econometrics time series models to derive sample innovations. In this study, we revisit and validate the Fama-French models in two different ways: using the factors and asset returns in the Fama-French model and considering the sample innovations in the Fama-French model instead of studying the factors. Comparing the two methods considered in this study, we suggest the Fama-French model should be considered with heavy tail distributions as the tail behavior is relevant in Fama-French models, including financial data, and the QQ plot does not validate that the choice of the normal distribution as the theoretical distribution for the noise in the model.