Microstructure under the Microscope: Tools to Survive and Thrive in the Age of (Too Much) Information

Abstract

In this age of (too much) information, it is imperative to uncover nuggets of knowledge (signal) from buckets of nonsense (noise). To aid in this effort to extract meaning from chaos and gain a better understanding of the relationships between financial variables, we summarize the application of Kashyap’s 2016 theoretical results to microstructure studies. The central concept rests on a novel methodology based on the marriage between the Bhattacharyya distance, a measure of similarity across distributions, and the Johnson Lindenstrauss lemma, a technique for dimension reduction, providing us with a simple yet powerful tool that allows comparisons between datasets representing any two distributions. We provide an empirical illustration using prices, volumes, and volatilities across seven countries and three continents. The degree to which different markets or subgroups of securities have different measures of their corresponding distributions tells us the extent to which they are different. This can aid investors who are looking for diversification or looking for more of the same thing.