Quantitative Economics

Journal Of The Econometric Society

Edited by: Stéphane Bonhomme • Print ISSN: 1759-7323 • Online ISSN: 1759-7331

Quantitative Economics: Jul, 2024, Volume 15, Issue 3

Changes in the Span of Systematic Risk Exposures

https://doi.org/10.3982/QE2330
p. 817-847

Yuan Liao, Viktor Todorov

We develop a test for deciding whether the linear spaces spanned by the factor exposures of a large cross‐section of assets toward latent systematic risk factors at two distinct points in time are the same. The test uses a panel of asset returns in local windows around the two time points. The asymptotic setup is of joint type: the number of assets and the number of return observations per asset increase asymptotically while the length of both time windows shrinks. We estimate the factor exposures, up to rotation, over the two periods using classical principal component analysis and evaluate their projection discrepancy, which is rotation invariant. This projection discrepancy is then centered with one between factor exposures computed over a partition of the pooled return data into odd and even increments. We derive the limit distribution of the statistic under the null hypothesis and develop an easy‐to‐implement bootstrap for constructing the critical region of the test. The test is applied to intraday financial data to determine whether the linear span of assets' systematic risk exposures differ during a trading day or after a release of important economic information.


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Supplemental Material

Supplement to "Changes in the Span of Systematic Risk Exposures"

Yuan Liao and Viktor Todorov

This Appendix contains the proofs of all theoretical results in the paper.

Supplement to "Changes in the Span of Systematic Risk Exposures"

Yuan Liao and Viktor Todorov

The replication package for this paper is available at https://doi.org/10.5281/zenodo.10685063. The authors were granted an exemption to publish their data because either access to the data is restricted or the authors do not have the right to republish them. However, the authors included in the package a simulated or synthetic dataset that allows running their codes. The Journal checked the synthetic/simulated data and the codes for their ability to generate all tables and figures in the paper and approved online appendices. However, the synthetic/simulated data are not designed to reproduce the same results. Given the highly demanding nature of the algorithms, the reproducibility checks were run on a simplified version of the code, which is also available in the replication package.