Frequency Dependent Risk

51 Pages Posted: 26 Oct 2018

See all articles by Andreas Neuhierl

Andreas Neuhierl

University of Notre Dame - Department of Finance

Rasmus Tangsgaard Varneskov

Copenhagen Business School - Department of Finance; Nordea Bank AB - Nordea Asset Management

Date Written: October 3, 2018


This paper provides a new nonparametric framework for studying the dynamics of the state vector and its associated risk prices. Specifically, in a general setting where the SDF decomposes into permanent and transitory components, we analyze their contribution to the unconditional asset return premium using frequency domain techniques. We show analytically that the co-spectrum between returns and the SDF only displays frequency dependencies through its transitory components, that is, through the state vector. Moreover, we demonstrate that state vector dynamics and its risk prices can be uncovered by studying (transformations of) the covariance between (portfolios of) asset returns. We introduce two new frequency risk measures. We apply our framework to study frequency risk in the full cross-section of US stocks, utilizing the market, value, size and momentum factors as baseline portfolios to construct the risk measures. Our analysis uncovers the existence of, at least, two significantly priced low-frequency risk factors, one of which commands a large positive risk premium of 6% per year. Moreover, we document, at least, one high-frequency component in the state vector that is significantly priced. Importantly, we show that these frequency dependent risk factors are unspanned by a battery of appraised risk factors and characteristics. Our analysis demonstrates that multiple state vector components with varying persistence and risk prices are needed to be consistent with the cross-section. Throughout, we contrast our findings with the implications of the long-run risk model, the dynamic disaster model as well as a regime-switching CCAPM, providing new analytical results for such models.

Keywords: Asset Pricing, Factor Models, Nonparametric Measures, Spectral Analysis

JEL Classification: C1, G1, G11, G12

Suggested Citation

Neuhierl, Andreas and Varneskov, Rasmus Tangsgaard, Frequency Dependent Risk (October 3, 2018). Available at SSRN: or

Andreas Neuhierl (Contact Author)

University of Notre Dame - Department of Finance ( email )

P.O. Box 399
Notre Dame, IN 46556-0399
United States

Rasmus Tangsgaard Varneskov

Copenhagen Business School - Department of Finance ( email )

A4.17 Solbjerg Plads 3
Copenhagen, Frederiksberg 2000

Nordea Bank AB - Nordea Asset Management ( email )

PO Box 850
Copenhagen, 0900

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