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Cliometrics of world stock markets evolving networks

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Abstract

This article crosses two fields: financial cliometrics and networks graphs. The results illustrate that the field of application of operations research methods on graphs is very broad. We assess how the web of global stock markets linkages has changed over 1960–2018. We compute minimum spanning trees and hierarchical trees using six institutional sub-periods, and document the long term evolution of network patterns using different network metrics. Then we analyse the time dynamics of linkages, focusing on the most connected nodes. Finally, we analyse the effect of the network structure on system resilience. We highlight two main contributions of network graphs and operations research methods to financial cliometrics. First, we highlight a long term evolution of stock market network patterns from a monostar to a multistar network. This structural shift is associated to a greater connectivity of the hubs, leading to less resilience of the system. The sharp decrease in local path lengths strengthens this effect. Our second major outcome is that network graphs provide a methodological corpus to explain the role of path dependence in financial history. This is particularly true to explain the persistent centrality of a small number of hubs of world stock markets networks.

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Data availability

Title: Data for: Evolving structures of world stock markets 1960–2018: a complex networks analysis. Repository: Mendeley Data. https://data.mendeley.com/datasets/9g38dvf6xp/draft?a=65a288a5-228d-495e-bc35-f53b69e377e0

Notes

  1. The terms of “node” and “vertex” are often used interchangeably.

  2. This definition, provided in the context of the so-called travelling salesman problem, is not the first. It is usual to cite the works of Kruskal (1956) and Prim (1957) as the early sources, with several apparently independent sources in Europe in the early twentieth century (Graham & Hell, 1985).

  3. For example, Gower and Ross (1969) show that “when two points are linked at level d (say) in the dendrogram [or hierarchical tree], no segment joining the same two points in the minimum spanning tree can be longer than d units [...]. This relationship between the minimum spanning tree construction and SLCA [single linkage cluster analysis] shows that SLCA is very similar to the taxonomic method of Florek et al. (1951) (p. 58)”. The method of Florek et al. (1951) is one of the first minimum spanning tree construction algorithms.

  4. It has to be noted that measures of density, as it is common in the literature on interbank markets flows networks, are not suitable for price networks (Newman, 2003).

  5. The detailed composition of the sample is a follows. 1960–1971: Austria, Australia, Canada, Switzerland, Germany, Finland, France, UK, Ireland, Italy, Japan, NL, Sweden, USA, S. Africa. 1971–1982: Austria, Australia, Canada, Switzerland, Germany, Finland, France, UK, Ireland, Italy, Japan, NL, NZ, Sweden, USA, S. Africa. 1982–1992: Austria, Australia, Canada, Switzerland, Germany, Finland, France, UK, Ireland, Israel, India, Italy, Japan, Mexico, NL, NZ, Sweden,USA, S. Africa. 1992–2002: Austria, Australia, Belgium, Brazil, Canada, Switzerland, Chile, Germany, Denmark, Spain, Finland, France, UK, Greece, Ireland, Israel, India, Italy, Japan, Korea, Mexico, NL, Norway, NZ, Sweden, USA, S. Africa. 2002–2009 and 2009–2018: Austria, Australia, Belgium, Brazil, Canada, Switzerland, Chile, China, Cz. Rep., Germany, Denmark, Spain, Finland, France, UK, Greece, Ireland, Israel, India, Italy, Japan, Korea, Luxembourg, Mexico, NL, Norway, NZ, Poland, Russia, Sweden, USA, S. Africa.

  6. “Cross-correlations matrices are intrisically limited by the fact that they assume temporally stationary and linearly interdependent time series. Clearly, both assumptions are, in general, violated in real financial markets and many other complex systems; Nonetheless, cross-correlations are still the most widely used quantity”.

  7. The Kruskal algorithm and Prims algorithms are the most commonly used algorithms in the computation of the MST. The Kruskal algorithm consists of (i) sorting distances within the complete distance matrix in a non-decreasing ordrer; (ii) choosing the lowest distance and putting an edge in the graph if the addition does not make a cycle with previously put edges, and (iii) repeat step (ii) till the graph is connected. The Prim algorithm consists in (ii) choosing arbitrarily a node, (ii) choosing the lowest cost (lowest distance) going from this node and putting an edge in the graph if the addition does not make a cycle with previously put edges, (iii) treat the nodes which already belong to the tree as one single node and repeat step (ii) till the graph is connected. For more details see Kruskal (1956) and Prim (1957) .

  8. Interestingly, the structure of equity market networks can also depend on granularity. Thus, the existence of regional stock exchanges, for example, in the United Kingdom, France or the United States during the study period means that indices considered here as individual nodes are at the most disaggregated level the hubs of domestic networks that are themselves star-shaped. Although the issue of regional exchanges is outside the scope of this study, it is important to keep in mind that the disappearance or consolidation of regional exchanges may also affect the resilience of international equity market networks.

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. LEAD, Université de Toulon, Toulon, France

    Cécile Bastidon

  2. LED, Université Paris 8, Saint-Denis, France

    Antoine Parent

  3. OFCE-Sciences Po, Paris, France

    Antoine Parent

  4. CAC-IXXI, ENS Lyon, Lyon, France

    Cécile Bastidon & Antoine Parent

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  1. Cécile Bastidon
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The authors wish to thank Patrice Abry, Marcel Ausloos, Michael Bordo, Pierre Borgnat, Damien Challet, Jérome Creel, Philippe De Peretti, Steven Durlauf, Max Gillman, Pablo Jensen, Alan Kirman, Diego Garlaschelli, Hayette Gatfaoui, Gilles le Garrec, Paul Hubert, Francesco Magris, Rosario Mantegna, Xavier Ragot, Leonidas Sandoval, Henri Sterdyniak, Vincent Touzé, Jorgen Vitting Andersen, and the anonymous referees for their remarks and suggestions. We also thank for their comments on earlier versions the participants in Econophysics 2018 (Palermo, 10–12 Sept 2018), the OFCE Seminar (Paris, 17 Oct. 2018), and the European Public Choice Society 2019 (Hebrew University of Jerusalem, Jerusalem, 1–4 Apr. 2019). Finally we thank Dylan Milligan, Han Soo Kim et Soyoung Jeon for their carefull copyediting.

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Bastidon, C., Parent, A. Cliometrics of world stock markets evolving networks. Ann Oper Res 332, 23–53 (2024). https://doi.org/10.1007/s10479-022-04564-z

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