Frequency Dependent Risk

We provide a model-free framework for studying the dynamics of the state vector and its risk prices. Specifically, we derive a frequency domain decomposition of the unconditional asset return premium in a general setting with a log-affine stochastic discount factor (SDF). Importantly, we show that the co-spectrum between returns and the SDF only displays frequency dependencies through the state vector, and that its dynamics and risk prices can be infered from covariances between asset (portfolio) returns, i.e., from the cross-section. Empirically, we find low \textit{and} high-frequency state vector risk to be differentially priced for US equities