Dynamics of market correlations: Taxonomy and portfolio analysis

TLDR

The asset tree represents stock correlations by mapping each stock to a node and defining distances as a function of the correlation matrix. The study investigates how the asset tree’s structure evolves over time to capture the financial market taxonomy. The authors define a mean occupation layer based on the central vertex of the tree and analyze its dependence on the moving‑window size. During market crashes the asset tree collapses topologically, reflected by a low mean occupation layer, while its scale‑free degree distribution changes between normal and crash periods; the tree’s core structure remains stable over time and Markowitz portfolio assets occupy outer leaves.

Abstract

The time dependence of the recently introduced minimum spanning tree description of correlations between stocks, called the "asset tree" has been studied in order to reflect the financial market taxonomy. The nodes of the tree are identified with stocks and the distance between them is a unique function of the corresponding element of the correlation matrix. By using the concept of a central vertex, chosen as the most strongly connected node of the tree, an important characteristic is defined by the mean occupation layer. During crashes, due to the strong global correlation in the market, the tree shrinks topologically, and this is shown by a low value of the mean occupation layer. The tree seems to have a scale-free structure where the scaling exponent of the degree distribution is different for "business as usual" and "crash" periods. The basic structure of the tree topology is very robust with respect to time. We also point out that the diversification aspect of portfolio optimization results in the fact that the assets of the classic Markowitz portfolio are always located on the outer leaves of the tree. Technical aspects such as the window size dependence of the investigated quantities are also discussed.