Nonparametric methods for estimating and testing for constant betas in asset pricing models

Abstract

In this article, we study the performance of a smoothing spline method in estimating and testing for constant betas in two well-known asset pricing models, the usual market model and the three-factor model. The spline estimator is computed taking into account the conditional heteroscedasticity of the errors. Using the right model and estimation procedure for the variance term plays a crucial role in gaining efficiency in beta estimators. A simulation study shows the good performance of our method; in all the scenarios simulated, it outperforms the benchmark rolling estimator. The method enables users to obtain confidence intervals and to test for the significance and constancy of betas. Finally, the method is applied to US data, comprising 25 portfolios formed based on size and the ratio of book equity to market equity. The results show that the time-variability of the betas plays an important role, mainly when sensitivity to the HML factor is considered.

Keywords:

• time-varying coefficients
• beta pricing models
• smoothing splines
• Fama–French three-factor model

JEL Classification:

• B23
• G12
• C14
• C12

Notes

¹ http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data Library.html.

² For a detailed explanation of the GAM method and its implementation in R, see Wood (2006).

³ The results of the ACF and PACF are not presented here for the sake of brevity, but are available from the authors upon request.

⁴ The results of the ACF and PACF are not presented here for the sake of brevity, but are available from the authors upon request.

Additional information

Funding

Financial support from Ministry of Education (MEC)[ECO2011-29268], the Basque Government [DEUI, IT-783-13 and IT-567-13] and the University of the Basque Country (UPV/EHU) [UFI 11/46 BETS] is gratefully acknowledged.