Spectral factor models

We represent risk factors as sums of orthogonal components capturing fluctuations with cycles of different length. The representation leads to novel spectral factor models in which systematic risk is allowed—without being forced—to vary across frequencies. Frequency-specific systematic risk is captured by a notion of spectral beta. We show that traditional factor models restrict the spectral betas to be constant across frequencies. The restriction can hide horizon-specific pricing effects that spectral factor models are designed to reveal. We illustrate how the methods may lead to economically meaningful dimensionality reduction in the factor space.