Asset Trees and Asset Graphs in Financial Markets

Abstract

This paper introduces a new methodology for constructing a network of\ncompanies called a dynamic asset graph. This is similar to the dynamic asset\ntree studied recently, as both are based on correlations between asset returns.\nHowever, the new modified methodology does not, in general, lead to a tree but\na graph, or several graphs that need not be inter-connected. The asset tree,\ndue to the minimum spanning tree criterion, is forced to ``accept'' edge\nlengths that are far less optimal (longer) than the asset graph, thus resulting\nin higher overall length for the tree. The same criterion also causes asset\ntrees to be more fragile in structure when measured by the single-step survival\nratio. Over longer time periods, in the beginning the asset graph decays more\nslowly than the asset tree, but in the long-run the situation is reversed. The\nvertex degree distributions indicate that the possible scale free behavior of\nthe asset graph is not as evident as it is in the case of the asset tree.\n