Contact Information
Finance Department
Northwestern University
2210 Campus Dr
Evanston, IL 60208
Phone: 847-387-2798
email: martin.thyrsgaard@kellogg.northwestern.edu
Personal Site: sites.google.com/view/mthyrsgaard
Employment
Postdoctoral Fellow, Kellogg School of Management, Northwestern University, 2019-present
Education
Ph.D., Economics, Aarhus University, 2019
MSc., Quantitative Economics, Aarhus University, 2017
BSc., Economics and Management, Aarhus University, 2014
Primary Fields of Specialization
Asset Pricing, Market Microstructure, Applied and Theoretical Econometrics
Curriculum Vitae
Job Market Paper
Recalcitrant Betas: Intraday Variation in the Cross-Sectional Dispersion of Systematic Risk (Revise and Resubmit at Quantitative Economics), joint work with Torben G. Andersen & Viktor Todorov
Download Job Market Paper (PDF)
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 returns increasing to infinity, while the time span of the data remains fixed, and the cross-sectional dimension of the panel is either fixed or increasing. We derive functional limit results for the cross-sectional distribution of betas evolving over time. We demonstrate, for constituents of the S&P 500 market index, that the dispersion in betas is elevated at the market open and gradually declines over the trading day. This intraday pattern varies significantly over time and reacts to information shocks such as clustered earning announcements and releases of macroeconomic news. We find that earnings news increase beta dispersion while FOMC announcements have the opposite effect on market betas.
Publications
We develop a nonparametric test for whether return volatility exhibits time-varying intraday periodicity using a long time series of high-frequency data. Our null hypothesis, commonly adopted in work on volatility modeling, is that volatility follows a stationary process combined with a constant time-of-day periodic component. We construct time-of-day volatility estimates and studentize the high-frequency returns with these periodic components. If the intraday periodicity is invariant, then the distribution of the studentized returns should be identical across the trading day. Consequently, the test compares the empirical characteristic function of the studentized returns across the trading day. The limit distribution of the test depends on the error in recovering volatility from discrete return data and the empirical process error associated with estimating volatility moments through their sample counterparts. Critical values are computed via easy-to-implement simulation. In an empirical application to S&P 500 index returns, we find strong evidence for variation in the intraday volatility pattern driven in part by the current level of volatility. When volatility is elevated, the period preceding the market close constitutes a significantly higher fraction of the total daily integrated volatility than during low volatility regimes.
We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF) – inferred from noisy high-frequency data – is consistent as the mesh of the observation grid goes to zero. In a double-asymptotic framework, with time also increasing to infinity, the REDF converges to the cumulative distribution function of volatility, if it exists. We exploit these results to construct some new goodness-of-fit tests for stochastic volatility models. In a Monte Carlo study, the REDF is found to be accurate over the entire support of volatility. This leads to goodness-of-fit tests that are both correctly sized and relatively powerful against common alternatives. In an empirical application, we recover the REDF from stock market high-frequency data. We inspect the goodness-of-fit of several two-parameter marginal distributions that are inherent in standard stochastic volatility models. The inverse Gaussian offers the best overall description of random equity variation, but the fit is less than perfect. This suggests an extra parameter (as available in, e.g., the generalized inverse Gaussian) is required to model stochastic variance.
Other Research Papers
Optimal Sequential Treatment Allocation (Submitted), with Anders Bredahl Kock
In treatment allocation problems the individuals to be treated often arrive sequentially. We study a problem in which the policy maker is not only interested in the expected cumulative welfare but is also concerned about the uncertainty/risk of the treatment outcomes. A sequential treatment policy, which attains near minimax optimal regret, is studied with and without covariates. We also demonstrate that the expected number of suboptimal treatments only grows slowly in the number of treatments. Finally, we study a setting where outcomes are observed only with delay. Simulations illustrate the theoretical results.
This paper provides empirical evidence on predictable shifts in the degree of bond return predictability. Bond returns are predictable in high (low) economic activity (uncertainty) states, which suggests that the expectations hypothesis of the term structure holds periodically. These state-dependencies in predictability, established by introducing a new multivariate test for equal conditional predictive ability, can be used in real-time to improve out-of-sample bond risk premia estimates and investors’ economic utility through a novel dynamic forecast combination scheme. Dynamically combined forecasts exhibit strong countercyclical behavior and peak during recessions. The empirical findings are consistent with the predictions of a non-linear term structure model.
Intraday Periodicity in Cross-Market Trading
I study cross-market trading activities by high-frequency traders (HFTs). To assess whether they systematically change their behavior over the trading day, I develop a test for determining for intraday periodicity. Technological innovations and changes in market accessibility have reshaped the cross-market trading landscape over time, thus the series of interest display structural breaks and other forms of non-stationary. The proposed test is fully non-parametric and can accommodate these features. I derive the associated limit theory, and show the validity of a bootstrap procedure. The newly developed method is then used to study cross-market trading between the E-mini S&P 500 futures and the SPDR S&P 500 ETF, which are two of the most liquid exchange traded assets. I find that cross-market trading activity by HFTs increases systematically over the trading day and drops sharply just before close.
Beta Risk and Expected Returns, with Torben G. Andersen and Viktor Todorov
Cross-Sectional Dispersion of Volume – a New Perspective on Two-Fund Separation
Teaching
Lecturer, Investment and Finance, Aarhus University, 2018
Teaching Assistant, Investment and Finance, Aarhus University, 2016
Guest Lecturer, Mathematical Economics II, Aarhus University, 2015
References
Prof. Torben G. Andersen
Prof. Viktor Todorov
Prof. Kim Chirstensen (Advisor)