A Visit to the Spectral Zoo

with Bartosz Gebka and Georgios Xyngis, 2022. [Paper] [Internet Appendix] We present a unifying framework for cross-sectional asset pricing that includes frequency as a dimension of risk explicitly and with the right level of generality. In particular, we estimate the frequency-dependent risk loadings between a proposed factor and asset returns using generalized wavelet-based beta decompositions. Our approach includes time-scale and symmetric time-frequency transforms that are defined for any discrete-time wavelet family. We examine inference with a useless and a useful factor and provide recommendations for credible empirical analysis. Finally, we revisit the results in previous studies and show that robust evidence for the pricing of frequency-specific factors remains largely elusive.