Galway July 12 nd 2012 MP 0801 Annual

Galway, July 12 nd, 2012 MP 0801 Annual meeting Network analysis of the Italian Stock Market G. Rotundo Department of economics and management, University of Tuscia, Viterbo, Italy 1

References G. Rotundo, "Centrality Measures in Shareholding Networks". In: "Use of Risk Analysis 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 -711 X, 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. 2

Network analysis of the Italian Stock Market outline: • • Targets Data sets and Network building Control, ownership, and wealth Control through the board of directors 3

Targets: understanding the dependence among companies and the outcome for • Ownership 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? • Control Detecting coalitions and oligopolies through portfolio diversification. Through the analysis of • shareholding networks Companies in the Stock Market buy shares of other Companies in the Stock Market, so adding dependency among firms. • board interlocks Board of Directors are not disjoint. Companies create ties though common Board members. Using methods proper of 4 • Complex networks, operations research.

Network analysis of the Italian Stock Market outline: • • Targets Data sets and Network building Control, ownership, and wealth Control through the board of directors 5

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 directors For the same companies. 6

The data sets/3: shareholding network building A link is drawn from company i to company j if i holds shares of j Out-degree kout = number of links exiting from the node =portfolio diversification j 1 i j 1 Kout= 1 i Kout=2 i j 2 Kout= 3 j 2 j 3 Direction 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 7

Adding weight to edges • The nodes of the network represent companies i • A link is drawn from company i to company j if i holds shares of j sij 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. ). i Given cj= capitalization of j: • Portfolio wealth vi= j sij cj=total wealth of portfolio of i 8

232 connected components: most isolated nodes and Small connected components Giant (weakly) connected component (101 nodes) A strongly connected component inside the giant connected component (12 nodes) is the only responsible of cycles. 9

The giant (weakly) connected component 10

• 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 'ASSICURAZIONI GENERALI ' 'ALLEANZA' 'INTESA SANPAOLO' 'FONDIARIA - SAI SPA' 'MILANO' 'MEDIOBANCA' 'BCA GENERALI' 'BANCA MPS' 'AZIMUT' 'BANCA POPOLARE' N. of different assets in their portfolio 19 15 15 13 10 9 7 6 4 4 insurance banks Detecting P(kout) Hypothesis testing: Scale-free networks: 11 P(kout) k-

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Comparison present analysis (MIB 2008) Garlaschelli et al. (MIB 2002) • 247 assets • 240 assets • 56% of traded companies invest in • 0. 56 of traded companies inves other traded companies in other traded companies • Very close to power law • No power law many companies decreased their diversification. 14

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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 16

Network analysis of the Italian Stock Market outline: • • Targets Data sets and Network building Control, ownership, and wealth Control through the board of directors 17

DIRECT CONTROL Ownership>50% a 51% c 51% d 51% e Example: a controls x through a chain of majorities 51% f 51% x 18

DIRECT CONTROL (a) The chains of control are very short. 19

The chains of control are very short. Example: IFIPRIV was born to finance IFIL to be the financial part of car producer FIAT and football team JUVENTUS 20

DIRECT and INTEGRATED OWNERSHIP Which is the percentage of shares of D holden by A? A 20% 30% 60% B 20% 30% C 40% D 21 20%

Which is the percentage of shares of D holden by A? A 20% 30% 60% B 20% 30% C 40% D 22 20%+ 30%(60%)

Which is the percentage of shares of D holden by A? A 20% 30% 60% B 20% 30% C 40% D 23 20%+ 30%(60%)+40%(30%)

Which is the percentage of shares of D holden by A? A 20% 30% 60% B 20% 30% C 40% D 20%+ 30%(60%)+40%(30%)+40%(20%(60%))=54, 8% 24

Which is the percentage of shares of D holden by A? A 20% DIRECT OWNERSHIP 30% 60% B 20% 30% C 40% D 20%+ 30%(60%)+40%(30%)+40%(20%(60%))=54, 8% OWNERSHIP THROUGH INTERMEDIATES 25 INTEGRATED OWNERSHIP

INTEGRATED OWNERSHIP Which is the percentage of shares of D holden by A? A ownership= sum (of the products of all the weights) on all the paths from A to B REMARK: the presence of cycles is properly entering in the calculus of paths (cfr. Simeone et al, Chapelle et al) D REMARK: weights <<1, then long paths are very close to 0. 26

DIRECT CONTROL a WARNING: ownership (biggest shareholding) is different from control 51% Example: c a controls x through a chain of majorities 51% But a owns only 3, 45% of x Much less than b (5%) d 51% e 3, 45% b 5% 51% f 51% x 27

Comparison between direct control and integrated ownership 28

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wealth 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 shareholding v=capitalization wealth=A*v 30

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 31

Is diversification of shareholdings in companies portfolios a good proxy Questions: 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? Target: to build the shareholding network and calculate the correlation among quantities measuring portfolio diversification, ownership and control. Portfolio diversification capitalization Portfolio diversification Out-degree wealth Network structure control wealth ownership 0. 7006 control 0. 6751 Positively Correlated ownership Out-degree 0. 3469 capitalization Network structure Of course highly correlated The companies that most diversify their portfolio are also the ones with highest wealth invested. 32

Target: to build the shareholding network and to calculate the correlation among quantities measuring portfolio diversification, ownership and control. Portfolio diversification capitalization Portfolio diversification Out-degree wealth Network structure ownership control Out-degree wealth ownership control 0. 3469 0. 7006 0. 1446 0. 15476 0. 6751 capitalization Network structure 0. 5696 0. 818 0. 2029 0. 3650 Also companies having small capitalization own other firms. Also companies having small capitalization control other firms. 0. 7370 33

Target: to build the shareholding network and to calculate the correlation among quantities measuring portfolio diversification, ownership and control. Portfolio diversification capitalization Portfolio diversification Out-degree wealth Network structure ownership control Out-degree wealth ownership control 0. 3469 capitalization Network structure 0. 7006 0. 1446 0. 15476 0. 6751 0. 5696 0. 818 0. 2029 0. 3650 Many companies with a few links own other ones. 0. 7370 Due to companies having the only role to be the financial part of other company. 34

Example: Agnelli family IFIPRIV was born to finance IFIL to be the financial part of car producer FIAT and football team JUVENTUS Chains of control are short (maximum length=2) 35

Portfolio diversification capitalization Portfolio diversification Out-degree wealth Network structure Out-degree wealth ownership control 0. 3469 0. 7006 0. 1446 0. 15476 0. 6751 0. 5696 0. 818 0. 2029 Out-degree is relevant for capitalization ownership much more than the total wealth Network structure 0. 3650 ownership control THE QUESTION THE ANSWER Out-degree is relevant for control much more than the total wealth 0. 7370 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? On the data set portfolio diversification is neither a necessary nor a sufficient 36 condition for ownership/control

Network analysis of the Italian Stock Market outline: • • Targets Data sets and Network building Control, ownership, and wealth Control through the board of directors 37

Corporate Board of Directors network Nodes=companies Out-degree kout = number of links exiting from the node Companies i and j are connected if they have at least one Director in common N. Common directors/N. directors in j j i N. Common directors/N. directors in i 38

Corporate Board of Directors network. Isolated nodes are not shown 39

Board size Mean 10, 25 Standard deviation 3, 569 Maximum 24 Minimum 3 Directorships per Director Mean 1, 190 Standard deviation 0, 585 Fraction of directors sitting in n boards 1 2 207 (8, 12%) 3 65 (2, 55%) 4 33 (1, 29%) 5 11 (0, 43%) 6 • • • 2232 (87, 56%) 1 (0, 04%) Board Diameter 8 Assortativity 0. 05 shareholding 9 0. 86 40

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Corporate Board Empirical analyses (connectivity, assortativity, ownership, control) g =0. 9689 (0. 8068, 1. 131) g = 0. 4693 (0. 3903, 0. 5482) g =1. 2717 (1. 2139, 1. 3296) g = 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 42

Companies having large board could control companies with small board 43

Overlap with the shareholding network 44

New information on the control of the market Direct control may be achieved through direct ownership and board control. 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. Integrated control reports the control through controlled intermediaries (using the matrix of effective control instead of 45 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 48

Conclusions: on the Italian Stock Market • Short chains of control • Management through Boards Work in progress: • Market concentration 49

Thanks to MP 0801 and Long life to COST! 50