Nonlinear intraday trading invariance in the Russian stock market

Annals of Operations Research. 2025. Vol. 352. P. 441–469.

Teplova T., Gurov S.

Using high-frequency transaction-level data for liquid Russian stocks, we empirically reveal a joint nonlinear relationship between the average trade size, log-return variance per transaction, trading volume, and the asset price level described by the Intraday Trading Invariance hypothesis. The relationship is also confirmed during stock market crashes. We show that the invariance principle explains a significant fraction of the endogenous variation between market activity variables at the intraday and daily levels. Moreover, our tests strongly reject the mixture of distributions hypotheses that assume linear relationships between log-return variance and transaction intensity variables such as trading volume or the number of transactions. We demonstrate that the increase in the ruble risk transferred by one bet per unit of business time was accompanied by the rise in the average spread cost. Different aggregation schemes are used to mitigate the impact of errors-in-variables effects. Following the predictions of the Information Flow Invariance hypothesis, we also study the relationship between trading activity and the information process approximated by either the flows of news articles or Google relative search volumes of Russian stocks over the 2018–2021 period. The evidence suggests that a sharp increase in the number of retail investors who entered the Moscow Exchange in 2020 entailed a higher synchronization between trading activity and search queries in Google since February 2020, in contrast to the arrival rates of news articles. The changes are driven by the increasing influence of the trading behavior of individual investors using Google Search rather than professional news services as the main source of information.

Keywords: ликвидность, инвариантность, нелинейность, liquidity, market microstructure, микроструктура рынка, non-linearity, invariance, trade size, Transaction data, объем торгов, данные о транзакциях

Publication based on the results of: Models and methods for identifying patterns in global and national financial markets (2025)