Models for Expected Returns with Statistical Factors

Abstract

In this paper, we propose multifactor models for the pan-European Equity Market using a block-bootstrap method and compare the results with those of traditional inferential techniques. The new factors are built from statistical measurements on stock prices—in particular, coefficient of variation, skewness, and kurtosis. Data come from Reuters, correspond to nearly 2000 EU companies, and span from January 2008 to February 2018. Regarding methodology, we propose a non-parametric resampling procedure that accounts for time dependency in order to test the validity of the model and the significance of the parameters involved. We compare our bootstrap-based inferential results with classical proposals (based on F-statistics). Methods under assessment are time-series regression, cross-sectional regression, and the Fama–MacBeth procedure. The main findings indicate that the two factors that better improve the Capital Asset Pricing Model with regard to the adjusted R2 in the time-series regressions are the skewness and the coefficient of variation. For this reason, a model including those two factors together with the market is thoroughly studied. We also observe that our block-bootstrap methodology seems to be more conservative with the null of the GRS test than classical procedures.

In this paper, we propose multifactor models for the pan-European Equity Market using a block-bootstrap method and compare the results with those of traditional inferential techniques. The new factors are built from statistical measurements on stock prices—in particular, coefficient of variation, skewness, and kurtosis. Data come from Reuters, correspond to nearly 2000 EU companies, and span from January 2008 to February 2018. Regarding methodology, we propose a non-parametric resampling procedure that accounts for time dependency in order to test the validity of the model and the significance of the parameters involved. We compare our bootstrap-based inferential results with classical proposals (based on F-statistics). Methods under assessment are time-series regression, cross-sectional regression, and the Fama–MacBeth procedure. The main findings indicate that the two factors that better improve the Capital Asset Pricing Model with regard to the adjusted R2 in the time-series regressions are the skewness and the coefficient of variation. For this reason, a model including those two factors together with the market is thoroughly studied. We also observe that our block-bootstrap methodology seems to be more conservative with the null of the GRS test than classical procedures.