Eur. Phys. J. B 73, 59-68 (2010)
https://doi.org/10.1140/epjb/e2009-00419-5

Equity trees and graphs via information theory

Centre for Research in Complex Systems, Charles Sturt University, Australia, and Centre for the Mind, The University of Sydney, Sydney, Australia

Corresponding authors: mharre@csu.edu.au tbossomaier@csu.edu.au

Received: 2 March 2009
Revised: 23 October 2009
Published online: 8 December 2009

Abstract

We investigate the similarities and differences between two measures of the relationship between equities traded in financial markets. Our measures are the correlation coefficients and the mutual information. In the context of financial markets correlation coefficients are well established whereas mutual information has not previously been as well studied despite its theoretically appealing properties. We show that asset trees which are derived from either the correlation coefficients or the mutual information have a mixture of both similarities and differences at the individual equity level and at the macroscopic level. We then extend our consideration from trees to graphs using the “genus 0” condition recently introduced in order to study the networks of equities.