Investigating the Configurations in Cross-Shareholding: A Joint Copula-Entropy Approach.

Marcel Ausloos,Roy Cerqueti,Giulia Rotundo

doi:10.3390/e20020134

Marcel Ausloos, Roy Cerqueti + Show 1 more

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https://doi.org/10.3390/e20020134

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Abstract

The complex nature of the interlacement of economic actors is quite evident at the level of the Stock market, where any company may actually interact with the other companies buying and selling their shares. In this respect, the companies populating a Stock market, along with their connections, can be effectively modeled through a directed network, where the nodes represent the companies, and the links indicate the ownership. This paper deals with this theme and discusses the concentration of a market. A cross-shareholding matrix is considered, along with two key factors: the node out-degree distribution which represents the diversification of investments in terms of the number of involved companies, and the node in-degree distribution which reports the integration of a company due to the sales of its own shares to other companies. While diversification is widely explored in the literature, integration is most present in literature on contagions. This paper captures such quantities of interest in the two frameworks and studies the stochastic dependence of diversification and integration through a copula approach. We adopt entropies as measures for assessing the concentration in the market. The main question is to assess the dependence structure leading to a better description of the data or to market polarization (minimal entropy) or market fairness (maximal entropy). In so doing, we derive information on the way in which the in- and out-degrees should be connected in order to shape the market. The question is of interest to regulators bodies, as witnessed by specific alert threshold published on the US mergers guidelines for limiting the possibility of acquisitions and the prevalence of a single company on the market. Indeed, all countries and the EU have also rules or guidelines in order to limit concentrations, in a country or across borders, respectively. The calibration of copulas and model parameters on the basis of real data serves as an illustrative application of the theoretical proposal.

Highlights

The recent crises have evidenced the fragility of the financial system due to the growing interdependencies among many different organizations.In the context of network modeling applied to management organizations of industrial structures, usually nodes represent companies, while the links show the ownership, gathered in the cross-shareholding matrix
The present study offers to the regulatory bodies the possibility to monitor the rise of concentration by looking only to the network topology and to the stochastic dependence between in- and out-degree
We firstly present the definition of bivariate copula, which is crucial for the study

Summary

Introduction

The recent crises have evidenced the fragility of the financial system due to the growing interdependencies among many different organizations.In the context of network modeling applied to management organizations of industrial structures, usually nodes represent companies, while the links show the ownership, gathered in the cross-shareholding matrix. Many studies in literature mostly focused on the shape of the distribution of the node out-degree k out , because such results are linked to specific results on the resilience of the network [1,2,3,4,5]. Not many studies were done on the node in-degree k in distributions, where k in is the amount of (other) companies who bought some ownership of a specific company. The in-degree well represents the way in which each organization becomes more dependent on its counterparts, so it can be used to represent the integration of the company in the system ( for the concept of integration, refer to [6])

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