1. 1 Network analysis of the Italian Stock Market G. Rotundo Department of economics and management, University of Tuscia, Viterbo, Italy Galway, July 12nd, 2012 MP0801 Annual meeting

2. 2 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 1860-711X, 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.

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

4. 4 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 interlocks Board 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.

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

6. 6 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.

7. 7 Kout= 1Kout=2 Kout= 3 A link is drawn from company i to company j if i holds shares of j Out-degree k out = number of links exiting from the node =portfolio diversification i ii j1 j2 j3 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 The data sets/3: shareholding network building

8. 8 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 s ij 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 c j = capitalization of j: Portfolio wealth v i =  j s ij c j =total wealth of portfolio of i i j s ij Adding weight to edges i

9. 9 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.

10. 10 The giant (weakly) connected component

11. 11 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(k out )  k -  Detecting P(k out )

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14. 14 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

15. 15

16. 16 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

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

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

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

20. 20 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.

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

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

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

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

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

26. 26 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. Which is the percentage of shares of D holden by A? INTEGRATED OWNERSHIP REMARK: the presence of cycles is properly entering in the calculus of paths (cfr. Simeone et al, Chapelle et al)

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

28. 28 Comparison between direct control and integrated ownership

29. 29

30. 30 wealth 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

31. 31 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

32. 32 Target: to build the shareholding network and calculate the correlation among quantities measuring portfolio diversification, ownership and control. Portfolio diversificationNetwork structure capitalizationOut-degreewealthownershipcontrol capitalization 0.3469 0.7006 Portfolio diversification Out-degree 0.6751 wealth Network structure ownership control Positively Correlated Of 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?

33. 33 Target: to build the shareholding network and to calculate the correlation among quantities measuring portfolio diversification, ownership and control. Portfolio diversificationNetwork structure capitalizationOut-degreewealthownershipcontrol capitalization 0.3469 0.7006 0.14460.15476 Portfolio diversification Out-degree 0.67510.56960.818 wealth 0.20290.3650 Network structure ownership 0.7370 control Also companies having small capitalization own other firms. Also companies having small capitalization control other firms.

34. 34 Target: to build the shareholding network and to calculate the correlation among quantities measuring portfolio diversification, ownership and control. Portfolio diversificationNetwork structure capitalizationOut-degreewealthownershipcontrol capitalization 0.3469 0.7006 0.14460.15476 Portfolio diversification Out-degree 0.67510.56960.818 wealth 0.20290.3650 Network structure ownership 0.7370 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.

35. 35 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)

36. 36 Portfolio diversificationNetwork structure capitalizationOut-degreewealthownershipcontrol capitalization 0.3469 0.7006 0.14460.15476 Portfolio diversification Out-degree 0.67510.56960.818 wealth 0.20290.3650 Network structure ownership 0.7370 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

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

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

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

40. 40 Board size Mean10,25 Standard deviation3,569 Maximum24 Minimum3 Directorships per Director Mean1,190 Standard deviation0,585 Fraction of directors sitting in n boards 12232 (87,56%) 2207 (8,12%) 365 (2,55%) 433 (1,29%) 511 (0,43%) 61 (0,04%) Boardshareholding Diameter 89 Assortativity 0.05 0.86

41. 41

42. 42  =0.9689 (0.8068,1.131)  =1.2717 (1.2139,1.3296)  = 0.4693 (0.3903, 0.5482)  = 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 Board Empirical analyses (connectivity, assortativity, ownership, control)

43. 43 Companies having large board could control companies with small board

44. 44 Overlap with the shareholding network

45. 45 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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48. 48 In the Italian market: Although Chain of control are short Hidden relationships are relevant Social relationships are relevant

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

50. 50 Thanks to MP0801 and Long life to COST!