Changes in the Span of Systematic Risk Exposures

Speaker: Viktor Todorov (Northwestern University)

We develop a test for deciding whether the linear spaces spanned by the factor exposures of a large cross-section of assets towards 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.

Learning the Stochastic Discount Factor

Speaker: Xinghua Zheng (Hong Kong University of Science and Technology)

The two square root laws of market impact and the role of sophisticated market participants

Speaker: Mathieu Rosenbaum (École Polytechnique)

The goal of this work is to disentangle the roles of volume and participation rate in the price response of the market to a sequence of orders. To do so, we use an approach where price dynamics are derived from the order flow via no arbitrage constraints and make connections with the rough volatility paradigm. We also introduce in the model sophisticated market participants having superior abilities to analyse market dynamics. Our results lead to two square root laws of market impact, with respect to executed volume and with respect to participation rate.

Control and Inference via Filtering for Partially-observed Markov Processes with Application to Ultra-high Frequency Data

Speaker: Yong Zeng (National Science Foundation)

In this talk, we present the stochastic control and statistical inference for a class of partially observed Markov processes with point process observations, which well fit the two features of time-stamped asset transaction price data. To solve the related mean-variance portfolio selection problem, which is non-Markovian, we first establish a separation principle, which divides the filtering and the control problems. Building upon the result of nonlinear filtering with counting process observations, we solve the control problem by employing the stochastic maximum principle for control with forward-backward SDEs, explicitly obtaining the efficient frontier, and derive the optimal strategy based on the filtering estimators. We also present recent results on the statistical inference for a partially observed Merton’s jump-diffusion process.

Statistics of high-frequency data with limit order microstructure noise

Speaker: Markus Bibinger (University of Würzburg)

We propose statistical methods to infer characteristics of a semi-martingale efficient log-price process in a boundary model with one-sided microstructure noise for high-frequency prices of limit orders. We develop methods to estimate and test for jumps and to estimate the volatility. Local minima of best ask quotes, and local maxima of best bid quotes, are the key statistics our inference is based on. We highlight differences to the established approach of using local averages of mid quotes with a standard market microstructure noise model. One main contribution is a Gumbel test for price jumps. Convergence rates are shown to be faster than under standard market microstructure noise, which also allows the identification of smaller jumps. A simulation study sheds light on the finite-sample properties of our statistics and draws a comparison to the popular test by Lee and Mykland for standard market microstructure noise. We apply the methods in an empirical example of intra-daily limit order book data.

The Fine Structure of Volatility Dynamics

Speaker: Carsten Chong (Hong Kong University of Science and Technology)

We develop a nonparametric test for deciding whether volatility of an asset follows a standard semimartingale process, with paths of finite quadratic variation, or a rough process with paths of infinite quadratic variation. The test utilizes the fact that volatility is rough if and only if volatility increments are negatively autocorrelated at high frequencies. It is based on the sample autocovariance of increments of spot volatility estimates computed from high- frequency asset return data. By showing a feasible CLT for this statistic under the null hypothesis of semimartingale volatility paths, we construct a test with fixed asymptotic size and an asymptotic power equal to one. The test is derived under very general conditions for the data-generating process. In particular, it is robust to jumps with arbitrary activity and to the presence of market microstructure noise. In an application of the test to SPY high-frequency data, we find evidence for rough volatility.

The Price of Money: The Reserves Convertibility Premium over the Term Structure

Speaker: Kjell Nyborg (University of Zürich)

Central bank money provides utility by serving as means of exchange for virtually all transactions in the economy. Central banks issue reserves (money) to banks in exchange for assets such as government bonds. If additional reserves have value to a bank, an asset’s degree of convertibility into reserves can affect its price. We show the existence of a government bond reserves convertibility premium, which tapers off at longer maturities. The degree of convertibility is priced, but heterogeneously so. Our findings have implications for our understanding of reserves, liquidity premia, the term structure of interest rates, and central bank collateral policy.

Jump Risk Premiums in Cryptocurrency Returns

Speaker: Suzanne Lee (Georgia Institute of Technology)

This study investigates how jumps are systematically priced in cryptocurrency markets. Leveraging intraday data from individual cryptocurrencies, we find that cryptocurrencies more sensitive to positive market jumps tend to exhibit lower expected returns. This negative premium is not fully explained by coskewness effects. Rather, this finding results from the attraction of trading activity towards high positive jump beta cryptocurrencies, indicating that cryptocurrency investors have nonmonotonic preferences. Investors with short positions on cryptocurrencies can hedge against unexpected price increases with high positive jump beta cryptocurrencies. The significant impact of positive tails on cross-sectional pricing distinguishes cryptocurrencies from traditional assets.

Co-jump networks, mixed membership and beyond

Speaker: Yingying Li (Hong Kong Institute of Science and Technology)

This talk will be based on two recent works about stock co-jump networks. We propose a Degree-Corrected Block Model with Dependent Multivariate Poisson edges (DCBM-DMP) to study stock co-jump dependency. Both pure memberships and mixed memberships are studied. We provide algorithms and statistical properties to support the estimation of the community structure. Such communities exhibit different features than GICS.  We further demonstrate the economic significance of these networks. 

Non-Linear Time Series Models and Machine Learning

Speaker: Nour Meddahi (Toulouse School of Economics)

We recently observed the irruption and rapid development of machine learning (ML) methods in econometrics and statistics, especially for forecasting purposes. For instance, ML methods have been recently used in several studies for forecasting economic and financial variables like assets returns (Gu, Kelly, and Xiu, 2020), stock and bond returns (Bianchi, Buchner, and Tamoni, 2021), volatility (Patton and Simsek, 2023), inflation (Medeiros, Vasconcelos, Veiga, and Zilberman, 2021), and macroeconomic variables (Goulet Coulombe, 2021; Goulet Coulombe, Leroux, Stevanovic, and Surprenant, 2022). An important common conclusion of these studies is that ML methods are successful in forecasting because they account for non-linearities that popular time series models do not. The first goal of the paper is to highlight the non-linearities that ML methods capture and connect them with traditional non-linear time series modeling. The second goal of the paper is to modify some traditional non-linear time series model by including insights from the ML literature. Applications to the Euro-US dollar exchange rate and the SP500 index are provided.