Dynamics of competition between collectivity and noise in the stock market

TL;DR

This paper analyzes the time-dependent correlation structure of the DAX stock market, revealing how collective behaviors and noise fluctuate during market drawdowns and ups, impacting information entropy.

Contribution

It provides a detailed empirical analysis of the correlation matrix dynamics in the stock market, highlighting the interplay between collectivity and noise during market fluctuations.

Findings

Draw downs are linked to a dominant collective eigenstate reducing noise.

Draw ups involve more uniform eigenstate participation, increasing entropy.

Correlation structures exhibit nontrivial time dependence.

Abstract

Detailed study of the financial empirical correlation matrix of the 30 companies comprised by DAX within the period of the last 11 years, using the time-window of 30 trading days, is presented. This allows to clearly identify a nontrivial time-dependence of the resulting correlations. In addition, as a rule, the draw downs are always accompanied by a sizable separation of one strong collective eigenstate of the correlation matrix which, at the same time, reduces the variance of the noise states. The opposite applies to draw ups. In this case the dynamics spreads more uniformly over the eigenstates which results in an increase of the total information entropy.