A nonparametric approach for estimating betas: the smoothed rolling estimator

Abstract

In this study an alternative nonparametric estimator to the Fama and MacBeth approach for the Capital Asset Pricing Model (CAPM) estimation is proposed. Betas and risk premiums are estimated simultaneously in order to increase the explanatory power of the proxy for betas. A data-driven method is proposed for selecting the smoothness degrees, which are directly related to the subsample sizes. Based on this relation, the traditional estimator is obtained as a particular case. Contrary to the results obtained in other studies our empirical evidence for Spanish market data is favourable to the CAPM.

Acknowledgements

Financial aid from G. C. 9/UPV 00038.321-13631/2001, Ministerio de Educación y Ciencia (SEJ-2005-05549/ECON) and from FBBVA (1/BBVA00038.16421/2004) is gratefully acknowledged.

Notes

¹ Similar nonparametric asymptotic results are obtained by Cline and Hart (1991) for density estimation, Müller (1992) for regression and Chen and Liu (1993) for autoregressive models.

² For the American stock market Chen et al. (1986) or Ferson and Harvey (1991), among others, obtain similar contrary results.