Explaining mispricing with Fama–French factors: new evidence from the multiscaling approach

Abstract

This article examines the Capital Asset Pricing Model (CAPM) over different frequencies utilizing a recently developed multiscaling method: wavelet analysis. Our empirical analysis shows that the risk factors are more relevant at the lower frequencies than at the higher frequencies in the traditional CAPM. In addition, the overreaction-related mispricing hypothesis explains the size effect but not the value premium. After incorporating the two risk factors (Small Minus Big (SMB) and High Minus Low (HML)), our empirical findings support the positive relationship between market risk and mean returns for big stocks, but not small stocks.

Acknowledgement

The authors are pleased to acknowledge the support of the Australian Research Council, grant number DP0557172.

Notes

¹ While Connor and Rossiter (2005) present this argument for the specific case of commodity markets, it is also applicable to most financial markets, and especially stock markets.

² The data are obtained directly from Ken French's homepage, which we gratefully acknowledge.

³ Intuitively, a small j or a low resolution level can capture smooth components of the signal, while a large j or a high resolution level can capture variable components of the signal (Lee and Hong, 2001).

⁴ Note that this version of MRA provides an important feature, which is not available to the original DWT. For instance, in contrast to the DWT, the MODWT details and smooths are associated with zero phase filters, thus making it easy to line up features in an MRA with the original time series meaningfully. For more detail, see Percival and Walden (2000) and In and Kim (2006).

⁵ In addition, we apply the method of Gençay et al. (2003) to examine the multiscale beta. However, the resulting betas are qualitatively similar. Therefore, we report the time series regression results. In this case, the constant terms could be not significantly different from zero in all time scales, due to the property of wavelet coefficients. To generate asymptotically valid SEs, in this and all remaining regressions estimated later in this article, we report heteroscedasticity adjusted SEs using Newey and West's (1987) method to insure the variance–covariance matrix is positive definite.