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Recalcitrant Betas: Intraday Variation in the Cross-Sectional Dispersion of Systematic Risk, Quantitative Economics


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 in nity, while the time span of the data remains fixed, and the cross-sectional dimension of the panel may be either fixed or increasing. We derive a fi nite-dimensional Central Limit Theorem for a measure of the cross-sectional beta dispersion at fi xed points in time, which can be used to test whether this quantity varies across the trading hours. We further derive a functional Central Limit Theorem for the dispersion statistics, enabling us to test whether the dispersion in betas, viewed as a function of the time within the trading day, changes across days. We further extend this analysis by developing inference techniques for the entire cross-sectional beta distribution at fi xed points in time. Applying the developed econometric tools, we demonstrate, for constituents of the S&P 500 market index, that the dispersion in betas is elevated at the market open, gradually declines over the trading day, and reaches a low around the market close, where the dispersion is less than half of its value at the market open. The shape of the intraday pattern in the dispersion of beta has changed over time and it evolves di fferently on days with pre-scheduled macroeconomic announcements. Importantly, we also fi nd that the intraday variation in market betas is a source of priced risk.




Torben Andersen, Martin Thyrsgaard, Viktor Todorov

Date Published



Andersen, Torben, Martin Thyrsgaard, and Viktor Todorov. 2021. Recalcitrant Betas: Intraday Variation in the Cross-Sectional Dispersion of Systematic Risk. Quantitative Economics. 12: 647–682.


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