Network analysis of financial networks

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Network analysis of the Italian Stock Market

G. Rotundo Department of economics and management,

University of Tuscia,Viterbo, Italy

Galway, July 12nd, 2012MP0801 Annual meeting

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References

G. Rotundo, "Centrality Measures in Shareholding Networks". In: "Use of RiskAnalysis in Computer-Aided Persuasion", Edited by Ekrem Duman, Amir Atiya, NATO Science for Peace and Security Series - E: Human and Societal Dynamics, Volume 88 (2011), pp. 12 - 28. ISBN 978-1-60750-827-4 (print) ISBN 978-1-60750-828-1 (online).

G. Rotundo, A. M. D'Arcangelis, "Ownership and control in shareholding networks", Journal of Economic Interaction and Coordination, ISSN 1860-711X, Volume 5, Issue 2 (2010), 191-219.

G. Rotundo, A. M. D'Arcangelis, "Network analysis of ownership and control structure in the Italian Stock market", Advances and Applications in Statistical Sciences, ISSN 0974-68119, Special Issue Vol. 2, Issue 2 (2010), 255-274.

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outline:

• Targets• Data sets and Network building• Control, ownership, and wealth• Control through the board of directors

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Companies in the Stock Market buy shares of other Companies in the Stock Market, so adding dependency among firms.

• shareholding networks

Targets: understanding the dependence among companies and the outcome for

• Ownership

• Control

• board interlocksBoard of Directors are not disjoint. Companies create ties

though common Board members.

Through the analysis of

Using methods proper of

• Complex networks, operations research.

Is diversification of shareholdings in companies portfolios a good proxy for the relevance of the company on the market with respect to ownership and control of other companies?

Detecting coalitions and oligopolies through portfolio diversification.

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outline:


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The data sets/1: shareholding matrix• Companies traded on the Italian Stock Market (Borsa

Italiana) – 247 companies: shareholders and shareholding– 65 financial, 109 industrial, and 73 services companies – May 2008

• Data source: AIDA, CONSOB, BANKSCOPE (data on banks), ISIS (data on insurance companies)

• Threshold also below 2%• Data excluded: shareholdings via mutual funds (~0.01)

The data sets/2: board of directorsFor the same companies.

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Kout= 1 Kout=2 Kout= 3

A link is drawn from company i to company j if i holds shares of jOut-degree kout = number of links exiting from the node =portfolio diversification

i i ij1j1

j1

j2

j2

j3Direction opposite of

D. Garlaschelli, S. Battiston, M. Castri, V.D.P. Servedio, G. Caldarelli, The scale-free topology of market investments (2005) Physica A 350 (2005) 491-499

But the same of A. Chapelle, A. Szafarz, Controlling firms through the majority voting rule, Physica A 355 (2005) 509-529

The data sets/3: shareholding network building

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•The nodes of the network represent companies

•A link is drawn from company i to company j if

i holds shares of j

(the reversal direction of the one used in Garlaschelli et al.)

•The weight sij of the link is the percentage of shares of j holden by i. (the direction is the opposite of Garlaschelli et al., but the same of Simeone et al.).

Given cj= capitalization of j:

•Portfolio wealth vi= j sij cj=total wealth of portfolio of i

i

j

sij

Adding weight to edges

i

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Small connected components

Giant (weakly) connected component

(101 nodes)

232 connected components: most isolated nodes and

A strongly connected component inside the giant connected component (12 nodes) is the only responsible of cycles.

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The giant (weakly) connected component

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•isolated nodes: in financial sector: 12; industrial: 77; services: 41•1-connected nodes: in financial sector: 27; industrial: 52; services: 29.•Most connected nodes:

name N. of different assets in their portfolio

insurance

banks

'ASSICURAZIONI GENERALI ' 19 'ALLEANZA' 15 'INTESA SANPAOLO' 15 'FONDIARIA - SAI SPA' 13 'MILANO' 10 'MEDIOBANCA' 9 'BCA GENERALI' 7 'BANCA MPS' 6 'AZIMUT' 4 'BANCA POPOLARE' 4

Hypothesis testing:Scale-free networks: P(kout) k-

Detecting P(kout)

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13

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Comparison present analysis (MIB2008) Garlaschelli et al.

(MIB2002)• 247 assets• 56% of traded companies invest in

other traded companies

• Very close to power law

many companies decreased their diversification.

• 240 assets• 0.56 of traded companies invest

in other traded companies• No power law

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assortativity

Assortativity is a well known quantity that measures the tendency of high connected nodes to be connected with other high connected nodes.

The assortativity on the entire dataset gives 0.1659. This means that there is a weak tendency to form a high connected group

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outline:


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Example: a controls x through

a chain of majorities

51%

51%

51%

51%

51%

a

c

d

e

f

x

DIRECT CONTROL

Ownership>50%

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DIRECT CONTROL

The chains of control are very short.

(a)

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IFIPRIV was born to finance IFIL to be the financial part of car producer FIAT and football team JUVENTUS

Example:

The chains of control are very short.

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A

B C

D

30%

20%

40%30%

60%20%

20%

Which is the percentage of shares of D holden by A?

DIRECT and INTEGRATED OWNERSHIP

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A

B C

D

30%

20%

40%30%

60%20%

20%+ 30%(60%)


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A

B C

D

30%

20%

40%30%

60%20%

20%+ 30%(60%)+40%(30%)


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A

B C

D

30%

20%

40%30%

60%20%

20%+ 30%(60%)+40%(30%)+40%(20%(60%))=54,8%


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A

B C

D

30%

20%

40%30%

60%20%

20%+ 30%(60%)+40%(30%)+40%(20%(60%))=54,8%

OWNERSHIP THROUGH INTERMEDIATES

DIRECT

OWNERSHIP


INTEGRATED OWNERSHIP

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A

D

ownership=

sum (of the products of all the weights) on all the paths from A to B

REMARK: weights <<1, then long paths are very close to 0.


INTEGRATED OWNERSHIP

REMARK: the presence of cycles is properly entering in the calculus of paths (cfr. Simeone et al, Chapelle et al)

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WARNING: ownership (biggest shareholding) is different from control

Example: a controls x through a chain

of majoritiesBut a owns only 3,45% of xMuch less than b (5%)

51%

51%

51%

51%

51%

5%

a

b

c

d

e

f

x

3,45%

DIRECT CONTROL

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Comparison between direct control and integrated ownership

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wealthwealth of company i invested in the other companies in

the dataset

= j (the shares of j that i holds) * (capitalization of j)

A=matrix of shareholdingv=capitalization

wealth=A*v

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Questions:Is diversification of shareholdings in companies portfolios a good proxy for the relevance of the company on the market with respect to ownership and control of other companies?

Are the most wealthy companies buying more shares of the others just because of the higher level of wealth?

Answers:Correlation analysis among node degree, wealth, ownership, control

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Target: to build the shareholding network and calculate the correlation among quantities measuring portfolio diversification, ownership and control.

Portfolio diversification Network structure

capitalization Out-degree wealth ownership control

capitalization 0.3469 0.7006

Portfolio diversification

Out-degree 0.6751

wealth

Network structure ownership

control

Positively

CorrelatedOf course highly correlated

The companies that most diversify their portfolio are also the ones with highest wealth invested.

Questions:Is diversification of shareholdings in companies portfolios a good proxy for the relevance of the company on the market with respect to ownership and control of other companies?

Are the most wealthy companies buying more shares of the others just because of the higher level of wealth?

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Target: to build the shareholding network and to calculate the correlation among quantities measuring portfolio diversification, ownership and control.



capitalization 0.3469 0.7006 0.1446 0.15476


Out-degree 0.6751 0.5696 0.818

wealth 0.2029 0.3650

Network structure ownership 0.7370

control

Also companies having small capitalization own other firms.

Also companies having small capitalization control other firms.

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Target: to build the shareholding network and to calculate the correlation among quantities measuring portfolio diversification, ownership and control.



capitalization 0.3469 0.7006 0.1446 0.15476


Out-degree 0.6751 0.5696 0.818

wealth 0.2029 0.3650


control

Many companies with a few links own other ones.

Due to companies having the only role to be the financial part of other company.

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IFIPRIV was born to finance IFIL to be the financial part of car producer FIAT and football team JUVENTUS

Example: Agnelli family

Chains of control are short (maximum length=2)

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capitalization 0.3469 0.7006 0.1446 0.15476


Out-degree 0.6751 0.5696 0.818

wealth 0.2029 0.3650


control

Out-degree is relevant for ownership much more than the total wealth

Out-degree is relevant for control much more than the total wealth

Is diversification of shareholdings in companies portfolios a good proxy for the relevance

of the company on the market with respect to ownership and control of other companies?

THE QUESTION

THE ANSWER On the data set portfolio diversification is neither a necessary nor a sufficient condition for ownership/control

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outline:


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i

j

N.Common directors/N.directors in j

N.Common directors/N.directors in i

Corporate Board of Directors network

Out-degree kout = number of links exiting from the nodeNodes=companies

Companies i and j are connected if they have at least one Director in common

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Corporate Board of Directors network. Isolated nodes are not shown

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Board sizeMean 10,25

Standard deviation 3,569Maximum 24Minimum 3

Directorships per DirectorMean 1,190

Standard deviation 0,585Fraction of directors sitting in n boards

1 2232 (87,56%)2 207 (8,12%)3 65 (2,55%)4 33 (1,29%)5 11 (0,43%)6 1 (0,04%)

• Board shareholding• Diameter 8 9• Assortativity 0.05 0.86

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( )p k k

=0.9689 (0.8068,1.131)

1( )P k k

=1.2717 (1.2139,1.3296)

( ) kp k e

= 0.4693 (0.3903, 0.5482)

( ) kP k e ( ) kP k e

= 0.7143 (0.6806, 0.748).

The Jarque-Bera test accepts the hypothesis of Gaussianity of residuals in all cases. Confidence intervals do not overlap:hypotheses rejected

Fast decay

Corporate BoardEmpirical analyses (connectivity, assortativity, ownership, control)

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Companies having large board could control companies with small board

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Overlap with the shareholding network

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Integrated ownership was introduced for ownership in shareholding network, but it counts votes: the approach can be repeated considering effective control, that is obtained by applying the majorization rule to the matrix of voting rights, i.e. formalizing the expropriation faced by the minority shareholders.

New information on the control of the market

Direct control may be achieved through direct ownership and board control.

Integrated control reports the control through controlled intermediaries (using the matrix of effective control instead of the original shareholding matrix).

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In the Italian market:Although Chain of control are short

Hidden relationships are relevant Social relationships are relevant

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Conclusions: on the Italian Stock Market

• Short chains of control

• Management through Boards

Work in progress:

• Market concentration

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Thanks to MP0801

and

Long life to COST!

Network analysis of financial networks

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