Realized betas and the cross-section of expected returns

Abstract

What explains the cross section of expected returns for the 25 size/value Fama–French (FF) portfolios? It is found that modelling time-varying betas is important to explain the cross section of expected returns, as well as to comply with the time series restriction on Jensen-alpha. Support for a modified version of the conditional Jagannathan and Wang's (1996) Capital Asset Pricing Model (CAPM) is found, where implementation is carried out in the realized beta framework proposed in this article. About 63% of the cross-sectional variability of the expected returns for the 25 FF size and value sorted portfolios is then found to be explained by this parsimonious two-variable model.

Acknowledgement

The author is grateful to A. Beltratti for very constructive comments.

Notes

¹ See Campbell and Vuolteenaho (2004) for an account of the initial empirical literature.

² See for instance, Lobato and Savin (1998), Martens et al. (2004), Beltratti and Morana (2006) and Baillie and Morana (2007). See also Baillie (1996) for an introduction to long memory processes.

³ Bollerslev and Zhang (2003) also consider a multivariate case. Yet, by assuming orthogonality of the factors, the realized betas have been computed using the standard bivariate formulas.

⁴ This is proved by noting that and and that using also the continuous mapping theorem.

⁵ See Barndorff-Nielsen and Shephard (2002) for additional details on the asymptotic properties of the realized regression estimator.

⁶ These findings are not peculiar to the smallest portfolio of the first FF class of portfolios plotted in Figs 1 and 2, but hold for all of the estimated betas. Details are available upon request from the author.

⁷ Detailed results are not reported for reasons of space.

⁸ The JW approach has been implemented as in Jagannathan and Wang (1996), but using the default spread innovation only as a proxy for the conditional market risk premium.

⁹ The analysis has also been carried out using the GLS estimator, with and without Shanken's errors-in-variables correction for the SEs, as well as by using the nonorthogonalized residuals. Similar results have been obtained in both cases and are available from the author upon request.