Galway, July 12nd, 2012
MP0801 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 1860-711X, 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.
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
j1
j1
i
j1
Kout= 1
i
Kout=2
i
j2
j2
Kout= 3
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
7
Adding weight to edges
•The nodes of the network represent companies
i
•A link is drawn from company i to company j if
sij
j
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.).
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-
12
13
Comparison
present analysis (MIB2008)
Garlaschelli et al.
(MIB2002)
• 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
15
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%
Example:
a controls x through
a chain of
majorities
c
51%
d
51%
e
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%
20%
B
C
30%
40%
D
21
20%
Which is the percentage of shares of D holden by A?
A
20%
30%
60%
20%
B
C
30%
40%
D
22
20%+ 30%(60%)
Which is the percentage of shares of D holden by A?
A
20%
30%
60%
20%
B
C
30%
40%
D
23
20%+ 30%(60%)+40%(30%)
Which is the percentage of shares of D holden by A?
A
20%
30%
60%
20%
B
C
30%
40%
D
24
20%+ 30%(60%)+40%(30%)+40%(20%(60%))=54,8%
Which is the percentage of shares of D holden by A?
A
20%
30%
60%
DIRECT
OWNERSHIP
20%
B
C
30%
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
D
in the calculus of paths (cfr. Simeone et al, Chapelle et
al)
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%
b
5%
e
51%
3,45%
f
51%
x
27
Comparison between direct control and integrated ownership
28
29
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
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.
capitalization
capitalization
Portfolio
diversification
Out-degree
wealth
Portfolio diversification
Network structure
Out-degree
wealth
ownership
0.3469
0.7006
0.6751
Positively
Correlated
Network structure
ownership
control
control
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.
capitalization
capitalization
Portfolio
diversification
Out-degree
wealth
Network structure
ownership
control
Portfolio diversification
Network structure
Out-degree
wealth
ownership
control
0.3469
0.7006
0.1446
0.15476
0.6751
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.
capitalization
capitalization
Portfolio
diversification
Out-degree
wealth
Network structure
ownership
control
Portfolio diversification
Network structure
Out-degree
wealth
ownership
control
0.3469
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
Out-degree is relevant for
capitalization
ownership much more
than the total wealth
capitalization
Portfolio
diversification
Out-degree
wealth
Network structure
Portfolio diversification
Network structure
Out-degree
wealth
ownership
control
0.3469
0.7006
0.1446
0.15476
0.6751
0.5696
0.818
0.2029
0.3650
ownership
control
THE QUESTION
THE ANSWER
0.7370
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?
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
2232 (87,56%)
2
207 (8,12%)
3
65 (2,55%)
4
33 (1,29%)
5
11 (0,43%)
6
1 (0,04%)
Board
Diameter
8
Assortativity 0.05
shareholding
9
0.86
40
41
Corporate Board
Empirical analyses (connectivity, assortativity, ownership, control)
p(k )  k 
P(k )  k 1
 =0.9689 (0.8068,1.131)
P(k )  e  k
 =1.2717 (1.2139,1.3296)
P(k )  e  k
p (k )  e  k
 = 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
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).
46
47
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 MP0801
and
Long life to COST!
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