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

Shareholding Networks Stefano Battiston

Lab. de Physique Statistique

Ecole Normale Supérieure, Paris

June 9th, Exystence Thematic Institute, Budapest

http://cercor.oupjournals.org/content/vol11/issue2/cover.shtml

http://www.cordis.lu/ist/

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)

Coevolution and Self-Organization in Dynamical Networks Funded by IST department - EU commission

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

http://www.cordis.lu/ist/fethome.htm

http://www.cosin.org/





OverviewOverview

•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.



MotivationsMotivations



Socio-economic Network Data Sets Socio-economic Network Data Sets (1998-2004)(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.)



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



6.40445

6.93145

7.45846

7.98547

8.51247

9.03948

9.56648

10.0935

10.6205

11.1475

AbbeyNatl

ColgPalmo

Computactr

FinTimes

Manpower

Nokia

Pearson

Thomson

TWarnerBell DC

Burns T

Lescuyer G

Mark R

Ogden PJ

Scardino MM

Stevenson Of Coddenham HD

Boards and directors, example I



6.66371

7.32707

7.99043

8.65379

9.31714

9.9805

10.6439

11.3072

11.9706

12.6339

AirLiquide

At&T

Bp

CocaCola

Egg

GlaxoSK

ReedElsevier

Reuters

ShellTradingIntl

Siemens

Economist

TLC02 Unilever

Yahoo

Barzach M

Coombe JD

Culp LDavis CH

Fitzgerald NW

Garnier JP

Hogg CA

Job PJ

Kozel ER

Mcarthur JH

Mchenry D

Mendoza R

Olver RL

Prosser IM

Schmitz RH

Shapiro L

Wilson R

Yamada T

Boards and directors, example II



Three degrees away from Parmalat





Who decides what?

(or why Board-Directors Networks are important)

Boards and Directors

Decision Making Dynamics

Uncertain Future •What is the Network

Topology? [Battiston and Catanzaro 2004]

•Can a minority drive the decision of a board? [Battiston, Bonabeau, Weisbuch 2003]

•When do several boards converge to making the same decision? [Battiston,Weisbuch, Bonabeau. 2003]

Consensus: the ‘Best’ Decision

Social Influence‘Herd’ Behavior

Consensus on a another decision



Who owns whom?

(or why Shareholding Networks are important)

Large Investors

Capital Control

Indirect Control

•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]

•Is there a subset of ‘superholders’ controlling the market

•How do they share out the market among themselves?

[Battiston 2004]

[Battiston, Garlaschelli, Caldarelli 2004]

Democratic Corporate Control

Failure Cascades



Social bipartite networks: Social bipartite networks:

deviations from random bipartite graphsdeviations from random bipartite graphs



Reshuffling under constraints

•Keep the number of directors per board

•Keep the number of boards per director



Board-Director Nets in US: real versus reshuffled

Boards

Dir.



Board-Director Nets in Italy: real versus reshuffled

Boards

Dir.



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



Shareholding Networks: Shareholding Networks:

extracting the network backbone from local extracting the network backbone from local quantitiesquantities



Network Representation


Coloniale srl

Parmalat

50.6%


•MIB = Milan stock exchange market. Data from Banca Nazionale del lavoro.NS = 240 NH=698 N=868 Nreduced=121

•NASDAQ. Data from Lycos Finance.NS=3134 NH=2099 N=5209 Nreduced =337

•NYSE. New York stock exchange market. Data from Lycos Finance.NS=2427 NH=1915 N=4263 Nreduced =1118

Data Sets



The Milan Stock Exchange Market Network (MIB)



Portfolio Diversification



Invested Volume

Invested volume vi=j wij Cj ~ k

(to compare with the notion node of strength, Barrat et al. 2004)[Garlaschelli, Battiston, Caldarelli 2004]



Ownership Concentration



Control Indices Histograms Number of

effective holdersITALY

US markets

Number of controlled companies, ITALY

US markets


SI ~out degree

HI ~in degree



Control Indices SI, HI

Network Re-building

‘Superholder’

Network ‘Backbone’

(local quantities)

(global quantities)

From micro to macro quantities

‘Superholders’ controlling the market


MIB superholder network




MIB Supeholders (the first 30) NYSE Supeholders



Designing models of firm network dynamics



•Node Dynamics dxi/dt= jfij(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) )

x2

a12

a21

x1

xi>0, aij>0 : real numbersE: set of edges

Class of Models




http://www.cosin.org/


dxi/d(t) =jf(xi,xj,aij,aji) <<1

daij/dt=df(xi,xj,aij,aji)/daij (if (i,j) in E)

Nodes and Edge Dynamics on a Static Graph

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]


•Node Dynamics dxi/dt= jfij(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) )

x2

a12

a21

x1

xi>0, aij>0 : real numbersE: set of edges

Work Plan

• 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


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/ [email protected]


Documents

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