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Shareholding Networks Stefano Battiston

Shareholding Networks Stefano Battiston Lab. de Physique Statistique Ecole Normale Supérieure, Paris. June 9th, Exystence Thematic Institute, Budapest. Coevolution and Self-Organization

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Shareholding Networks Stefano Battiston

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  1. Shareholding Networks Stefano Battiston Lab. de Physique Statistique Ecole Normale Supérieure, Paris June 9th, Exystence Thematic Institute, Budapest

  2. Coevolution and Self-Organization in Dynamical Networks Funded by IST department - EU commission • COSIN is a FET project (Future and Emergent Technologies) • Information Technologies Networks as a novel ‘natural phenomenon’ : • measuring, modeling, shaping the evolution • 2 Computer Science Labs. + 4 Statistical Physics Labs. to address: • Social Networks (G.Weisbuch, ENS Paris) • Technological Networks (A.Vespignani, Paris Sud) • Congestion (A.Diaz Guilera, Univ. Barcelona) • Massive Webgraphs (S.Leonardi, La sapienza,Rome) • Networks Visualization (D.Wagner, Univ.Konstanz) S.Battiston, Exystence T.I., Budapest, June 9th 2004

  3. Overview • Motivations : the role of firm networks. • About real and reshuffled board networks: degree, clustering and assortativity. • Shareholding networks: extracting the network backbone from local quantities. • Work plan: designing models of firm network dynamics. S.Battiston, Exystence T.I., Budapest, June 9th 2004

  4. Motivations S.Battiston, Exystence T.I., Budapest, June 9th 2004

  5. Socio-economic Network Data Sets (1998-2004) • Collaborations: scientists and movie actors (Newman et al., Barabasi et al.,... ) • Collaborations: corporate board directors (Davis et al., Newman et al., Battiston et al.,…) • Asset return correlations (Kertész and coll., Mantegna and coll.,... ) • Shareholding networks (Stark and Vedres, Battiston et al. 2003 ) • The World Trade Web (WTW) (Serrano and Boguna 2003) • Energy suppliers. (Amaral et al. 1999,…) • Internet and WWW (Barabasi and Albert, Pastor-Satorras and Vespignani,…) • Airports (Barrat et al. 2004, Amaral and coll.) S.Battiston, Exystence T.I., Budapest, June 9th 2004

  6. Large Corporations are connected in networks: • Board and Director Network: some directors serve on several boards • Company and Investor Network: some investors own shares of several companies S.Battiston, Exystence T.I., Budapest, June 9th 2004

  7. Boards and directors, example I S.Battiston, Exystence T.I., Budapest, June 9th 2004

  8. Boards and directors, example II S.Battiston, Exystence T.I., Budapest, June 9th 2004

  9. Three degrees away from Parmalat S.Battiston, Exystence T.I., Budapest, June 9th 2004

  10. S.Battiston, Exystence T.I., Budapest, June 9th 2004

  11. Who decides what? (or why Board-Directors Networks are important) Uncertain Future • What is the Network Topology?[Battiston and Catanzaro2004] Boards and Directors Social Influence ‘Herd’ Behavior • Can a minority drive thedecision of a board?[Battiston, Bonabeau, Weisbuch 2003] DecisionMaking Dynamics • When do several boardsconverge to making the samedecision?[Battiston,Weisbuch, Bonabeau. 2003] Consensus on a another decision Consensus: the ‘Best’ Decision S.Battiston, Exystence T.I., Budapest, June 9th 2004

  12. Who owns whom? (or why Shareholding Networks are important) • Can we classify control networks in stock markets based on global properties? • What can be inferred about financial agents’ behavior? • [Garlaschelli, Battiston, Caldarelli 2004] [Caldarelli, Battiston, Garlaschelli 2003] Large Investors Indirect Control Capital Control • Is there a subset of ‘superholders’controlling the market • How do they share out the market among themselves? • [Battiston 2004] • [Battiston, Garlaschelli, Caldarelli 2004] Failure Cascades Democratic Corporate Control S.Battiston, Exystence T.I., Budapest, June 9th 2004

  13. Social bipartite networks: deviations from random bipartite graphs S.Battiston, Exystence T.I., Budapest, June 9th 2004

  14. Reshuffling under constraints • Keep the number of directors • per board • Keep the number of boards • per director S.Battiston, Exystence T.I., Budapest, June 9th 2004

  15. Board-Director Nets in US: real versus reshuffled Boards Dir. S.Battiston, Exystence T.I., Budapest, June 9th 2004

  16. Board-Director Nets in Italy: real versus reshuffled Boards Dir. S.Battiston, Exystence T.I., Budapest, June 9th 2004

  17. Preliminary Conclusions on Constrained bipartite random graphs: • Fix: Nb boards, Nd directors, vector of boards size • random assignment: number of appointments per director follows a binomial distribution • in real data directors with more than 5 appointments are much more frequent • Fix: Nb boards, Nd directors, vector of boards size, vector of number of appointments of each director • deviations from random assignment: board degree distribution and assortativity S.Battiston, Exystence T.I., Budapest, June 9th 2004

  18. Shareholding Networks: • extracting the network backbone from local quantities S.Battiston, Exystence T.I., Budapest, June 9th 2004

  19. Coloniale srl 50.6% Parmalat Network Representation S.Battiston, Exystence T.I., Budapest, June 9th 2004

  20. Data Sets • MIB= Milan stock exchange market. Data from Banca Nazionale del lavoro. • NS= 240 NH=698N=868Nreduced=121 • NASDAQ. Data from Lycos Finance. • NS=3134 NH=2099N=5209 Nreduced=337 • NYSE. New York stock exchange market. Data from Lycos Finance. • NS=2427 NH=1915 N=4263Nreduced=1118 S.Battiston, Exystence T.I., Budapest, June 9th 2004

  21. The Milan Stock Exchange Market Network (MIB) S.Battiston, Exystence T.I., Budapest, June 9th 2004

  22. Portfolio Diversification S.Battiston, Exystence T.I., Budapest, June 9th 2004

  23. Invested Volume Invested volume vi=Sj wij Cj ~ kb (to compare with the notion node of strength, Barrat et al. 2004) [Garlaschelli, Battiston, Caldarelli 2004] S.Battiston, Exystence T.I., Budapest, June 9th 2004

  24. Ownership Concentration S.Battiston, Exystence T.I., Budapest, June 9th 2004

  25. Control Indices Histograms Number of effective holders ITALY SI ~out degree Number of controlled companies, ITALY US markets HI ~in degree US markets S.Battiston, Exystence T.I., Budapest, June 9th 2004

  26. From micro to macro quantities ‘Superholder’ Control Indices SI, HI (global quantities) Network ‘Backbone’ Network Re-building (local quantities) S.Battiston, Exystence T.I., Budapest, June 9th 2004

  27. ‘Superholders’ controlling the market S.Battiston, Exystence T.I., Budapest, June 9th 2004

  28. MIB superholder network

  29. S.Battiston, Exystence T.I., Budapest, June 9th 2004

  30. MIB Supeholders (the first 30) NYSE Supeholders S.Battiston, Exystence T.I., Budapest, June 9th 2004

  31. Designing models of firm network dynamics S.Battiston, Exystence T.I., Budapest, June 9th 2004

  32. x2 a12 a21 x1 Class of Models xi>0, aij>0 : real numbers E: set of edges • Node Dynamics dxi/dt= Sjfij(xi,xj,aij,aji) • Edge Dynamics daij/dt=gij(xi,xj,aij,aji) , (if (i,j) in E) • Edge Evolution P{(i,j) in E }= h(xi, xj,Top.Prop. ( i,j) ) S.Battiston, Exystence T.I., Budapest, June 9th 2004

  33. Nodes and Edge Dynamics on a Static Graph dxi/d(at) =Sjf(xi,xj,aij,aji) a<<1 daij/dt=df(xi,xj,aij,aji)/daij(if (i,j) in E) Ex. 1: f(xi,xj,aij,aji)= (aij – a2ij xi) xj An equilibrium a*={aij*(xi,xj)} exists for any x>0 and therefore for any network topology. Ex. 2: f(xi,xj,aij,aji)= (aij – a2ji xi) xj No equilibrium a* exists for any x>0 and therefore for any network topology. In general : the existence and the value of aij* depends on (xi,xj) Ex: subgraphs of nodes in a range of x values may reach an equilibrium. [Battiston and Weisbuch 2004] S.Battiston, Exystence T.I., Budapest, June 9th 2004

  34. x2 a12 a21 x1 Work Plan xi>0, aij>0 : real numbers E: set of edges • Node Dynamics dxi/dt= Sjfij(xi,xj,aij,aji) • Edge Dynamics daij/dt=gij(xi,xj,aij,aji) , (if (i,j) in E) • Edge Evolution P{(i,j) in E }= h(xi, xj,Top.Prop. ( i,j) ) • narrow down the class of functions f and h • constraints on aij ? • build models that can be tested on data of firm network over time S.Battiston, Exystence T.I., Budapest, June 9th 2004

  35. Conclusions • Board Networks: deviations from random bipartite networks with constraints • Shareholding networks: in-degree, out degree must be replaced with other local quantities. It turns out that these one allow to extract the backbone of the network • Open question: how to narrow down the class of models of firm network dynamics/evolution • References • All references are available at • http://www.lps.ens.fr/battiston/ • battiston@ens.fr S.Battiston, Exystence T.I., Budapest, June 9th 2004

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