Cross-Sectional Dispersion of Risk in Trading Time

52 Pages Posted: 30 Sep 2019 Last revised: 11 Jun 2023

Date Written: September 2019

Abstract

We study the temporal behavior of the cross-sectional distribution of assets' market exposure, or betas, using a large panel of high-frequency returns. The asymptotic setup has the sampling frequency of the returns increasing to infinity, while the time span of the data remains fixed, and the cross-sectional dimension is fixed or increasing. We derive a Central Limit Theorem (CLT) for the cross-sectional beta dispersion at a point in time, enabling us to test whether this quantity varies across the trading day. We further derive a functional CLT for the dispersion statistics, allowing us to test if the beta dispersion, as a function of time-of-day, changes across days. We extend this further by developing inference techniques for the entire cross-sectional beta distribution at fixed points in time. We demonstrate, for constituents of the S&P 500 index, that the beta dispersion is elevated at the market open, gradually declines over the trading day, and is less than half the original value by the market close. The intraday beta dispersion pattern also changes over time and evolves differently on macroeconomic announcement days. Importantly, we find that the intraday variation in market betas is a source of priced risk.

Suggested Citation

Andersen, Torben G. and Thyrsgaard, Martin and Todorov, Viktor, Cross-Sectional Dispersion of Risk in Trading Time (September 2019). NBER Working Paper No. w26329, Available at SSRN: https://ssrn.com/abstract=3461498

Torben G. Andersen (Contact Author)

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
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Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Martin Thyrsgaard

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

Viktor Todorov

Independent ( email )

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