Timescale betas and the cross section of equity returns: Framework, application, and implications for interpreting the Fama-French factors

Abstract

We show that standard beta pricing models quantify an asset's systematic risk as a weighted combination of a number of different timescale betas. Given this, we develop a wavelet-based framework that examines the cross-sectional pricing implications of isolating these timescale betas. An empirical application to the Fama-French model reveals that the model's well-known empirical success is largely due to the beta components associated with a timescale just short of a business cycle (i.e., wavelet scale 3). This implies that any viable explanation for the success of the Fama-French model that has been applied to the Fama-French factors should apply particularly to the scale 3 components of the factors. We find that a risk-based explanation conforms closely to this implication.