Das khan, Hossein; Gha neh, Nase Shams
A icle
De e mina ion o sys emically impo an companies wi h
c oss-sha eholding ne wo k analysis: A case s udy om an
eme ging ma ke
In e na ional Jou nal o Financial S udies
P o ided in Coope a ion wi h:
MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel
Sugges ed Ci a ion: Das khan, Hossein; Gha neh, Nase Shams (2016) : De e mina ion o sys emically
impo an companies wi h c oss-sha eholding ne wo k analysis: A case s udy om an eme ging
ma ke , In e na ional Jou nal o Financial S udies, ISSN 2227-7072, MDPI, Basel, Vol. 4, Iss. 3, pp.
1-17,
h ps://doi.o g/10.3390/ij s4030013
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In e na ional Jou nal o
Financial S udies
A icle
De e mina ion o Sys emically Impo an Companies
wi h C oss-Sha eholding Ne wo k Analysis: A Case
S udy om an Eme ging Ma ke
Hossein Das khan and Nase Shams Gha neh *
Depa men o Indus ial Enginee ing and Managemen Sys ems, Ami Kabi Uni e si y o Technology,
Ha ez S ., Teh an 15916-34311, I an; [email p o ec ed]
*Co espondence: [email p o ec ed]; Tel.: +98-216-454-5363
Academic Edi o : Nicholas Ape gis
Recei ed: 11 Feb ua y 2016; Accep ed: 17 June 2016; Published: 24 June 2016
Abs ac :
Sys emic isk e en s cons i u e an impo an issue in cu en inancial sys ems. A leading
cou se o ac ion used o mi iga e such e en s is iden i ica ion o sys emically impo an agen s in o de
o implemen he p uden ial policies in a inancial sys em. In his pape , a bi-le el c oss-sha eholding
ne wo k o he s ock ma ke is conside ed acco ding o di ec and in eg a ed owne ship s uc u e.
Fu he mo e, di e en sys emic isk indices a e applied o iden i y sys emically impo an companies
in an ea ly wa ning sys em. Resul s o applica ion o hese indices on c oss-sha eholding da a om
Teh an S ock Exchange show ha in eg a ed ne wo k indices p oduce mo e eliable esul s. Mo eo e ,
esul s o s a is ical analysis o he ne wo ks indica ed he exis ence o scale- ee cha ac e is ics in he
TSE c oss-sha eholding ne wo k.
Keywo ds: inance; ne wo k heo y; sys emic isk; c oss-sha eholding; cen ali y measu es
JEL: C6; E44; G10; G18; G32
1. In oduc ion
Sys emic isk is ela ed o in e -connec ion and co ela ion o di e en pa s o a ma ke .
In sys emic isk e en s, a inancial c isis occu s when an ini ial ailu e is ansmi ed o he whole
ma ke [
1
]. Acco dingly, con ol and mi iga ion o sys emic isk is an impo an conside a ion in he
inancial ma ke s. In e ms o sys emic isk, companies a e di e en in he ex en o hei con ibu ions
o he sys emic e en s. In many coun ies, sys emically impo an companies a e iden i ied by inancial
egula o y bodies and hese au ho i ies apply he p uden ial policies in he inancial sys ems. In he
ecen sys emic isk s udies [
1
–
3
], size, in e connec edness and he co ela ion o companies a e
in oduced as he main ac o s o sys emic isk. Some s udies ha e claimed ha la ge size companies
a e mo e ulne able o sys emic isk and in oduced he “ oo big o ail” no ion. In he o he s udies,
In e connec edness and co ela ion ha e a huge impac on he companies’ exposu e o each o he by
causal and balance shee ela ions and co-mo emen o companies o e he same ime pe iod [3].
In ecen yea s, ne wo k heo y has been widely applied o analysis o inancial sys emic isk and
inancial c isis [
4
,
5
]. Financial ne wo k s udies can be ca ego ized in o h ee main g oups. In he i s
g oup, con agion heo y is applied o inancial sys ems in o de o simula e he beha io o a inancial
sys em unde di e en ne wo k se ups [
6
]. The ocus o he second g oup is on he co ela ion-based
ne wo ks and he analysis o he s uc u e o a inancial ma ke in di e en ime pe iods [
7
,
8
]. Mos
esea ch in he ield alls in o he hi d g oup ha analyzes he s uc u e o in e -bank deb ne wo ks in
di e en coun ies and p oposes a ious p uden ial policies o mi iga e inancial sys emic isk and i s
associa ed cos s [
9
–
12
]. In his ype o s udies, in e -bank deb ne wo ks a e in oduced as scale- ee
In . J. Financial S ud. 2016,4, 13; doi:10.3390/ij s4030013 www.mdpi.com/jou nal/ij s
In . J. Financial S ud. 2016,4, 13 2 o 17
ne wo ks ha also ha e he “small wo ld” cha ac e is ics. These inancial ne wo ks a e also “ obus o
agile”, which means ha hey ope a e as a isk sha ing mechanism o inc ease s abili y o a inancial
sys em a he p e-c isis pe iod. Con e sely, in e connec edness would se e as a shock p opaga ion
mechanism du ing a c isis pe iod and would hus inc ease he p obabili y o sys em ailu e [1].
E en hough c oss-sha eholding ne wo ks a e one o he main ypes o inancial ne wo ks,
applica ion o c oss-sha eholding ne wo ks in he analysis o inancial sys emic isk has sca cely
been epo ed. In o he wo ds, mos sys emic isk publica ions ha e analyzed in e connec edness
in in e -bank deb ne wo ks. An excep ion is he s udy o Peco a and Spel a [
1
], which epo s
use o he c oss-sha eholding ne wo k o Eu opean banks o analyze sys emic isk. Because o
he limi ed a ailabili y o in o ma ion on bila e al exposu e be ween di e en companies, such as
in e -bank deb s, c oss-sha eholding da a could be applied as an app op ia e p oxy o in o ma ion
on in e connec edness. In addi ion o sys emic isk analysis in banking sys ems, applica ion o
c oss-sha eholding in o ma ion makes sys emic isk analysis o be possible o o he companies in a
inancial ma ke . Al hough a c oss-sha eholding ne wo k could ha e an impo an ole o main ain he
s abili y in a inancial sys em, no pa icula analysis has applied he s ock ma ke c oss-sha eholding
ne wo k o analyze sys emic isk.
In his pape , he c oss-sha eholding ne wo k o he s ock ma ke is applied as a bi-le el ne wo k.
A bi-le el c oss-sha eholding ne wo k means ha he ne wo k con ains companies lis ed in he s ock
ma ke as well as ex e nal sha eholde s o companies and he sha eholde ’s sha eholde s and hei
ela ionships. Fo his pu pose, he eme ging ma ke o Teh an S ock Exchange (TSE) was conside ed
o analysis ( he ecen cancella ion o in e na ional sanc ions has s imula ed he in e es s om bo h
in e nal and ex e nal in es o s). Based on he a ailable c oss-sha eholding in o ma ion, he di ec and
in eg a ed c oss-sha eholding ne wo k o TSE is ep esen ed and di e en sys emic isk indices a e
applied and s a is ically app aised. Mo eo e , he mos sys emically impo an companies and sec o s
a e de e mined in acco d o di e en indices.
Resul s show ha he c oss-sha eholding ne wo k is a good p oxy o analysis o
in e connec edness and sys emic isk in inancial ma ke s. Conside a ion o in eg a ed owne ship
in a c oss-sha eholding ne wo k leads o a mo e eliable ne wo k and be e unde s anding o he
sys emic isk impo ance o di e en companies. Mo eo e , esul s o s a is ical analysis o hese
ne wo ks show ha c oss-sha eholding ne wo k o TSE has a powe -law dis ibu ion. The powe -law
dis ibu ion ampli ies he hypo hesis ha he ne wo k can be “ obus ye agile” and is e ile o c isis
in he case o sys emic isk e en s.
2. Li e a u e Re iew
E en hough mos inancial ne wo k s udies a e ca ego ized in o he h ee abo e-men ioned
g oups, only a ew s udies ha e epo ed on applica ion o c oss-sha eholding ne wo ks o analyze
owne ship s uc u e and con ol low [
13
]. The main ocus o hese s udies has been s a is ical analysis
o c oss-sha eholding ne wo ks and con ol low in di e en coun ies. Fo example, Ba is on and
Gla elde [
14
] applied he p inciples o ne wo k heo y in a c oss-sha eholding ne wo k o analyze
owne ship con ol s uc u e in he wo ld inancial sys em. Gla elde and his co-wo ke s showed
ha he c oss-sha eholding ne wo k has a bow- ie s uc u e. The bow- ie s uc u e is a co e-pe iphe y
s uc u e wi h a cen al pa known as s ongly connec ed componen (SGC) and wo inpu and
ou pu sec o s [
14
,
15
]. In ano he s udy, Ba is on [
16
] compa es he desc ip i e cha ac e is ics o
c oss-sha eholding ne wo ks in Milan, New Yo k and London s ock exchanges. Ma, Zhuang and
Li [
17
] analyzed mu ual in es men in he Shanghai S ock Exchange. A deg ee-equi alen measu e was
in oduced o weigh ed di ec ed c oss-sha eholding ne wo k and analysis o s a is ical cha ac e is ics
o he ne wo k in e ms o co po a e, sec o and p o ince was epo ed. In addi ion o he abo e, he e
ha e been se e al o he s udies on he applica ion o c oss-sha eholding ( o example, see [
18
–
21
]).
In conclusion, al hough li le s udies ha e been done on applica ion o c oss-sha eholding ne wo ks,
In . J. Financial S ud. 2016,4, 13 3 o 17
no speci ic pape has ye been published on applica ion o he c oss-sha eholding ne wo k o sys emic
isk analysis.
3. Da a and Me hodology
3.1. The Da ase
In his pape , he c oss-sha eholding ne wo k o he Teh an s ock exchange, as an eme ging
ma ke , is applied. The sha eholding da a om 386 lis ed companies o he yea s 2013–2015 was
ex ac ed om he Teh an S ock Exchange da ase [
22
]. Because many lis ed companies had a small
amoun o ma ke alue, he da ase was limi ed o he sha eholding da a o 118 lis ed companies ha
ha e mo e han 0.1 pe cen sha e o he o al ma ke alue. The missing da a o he c oss-sha eholding
s uc u e a e di ec ly ex ac ed om he annual epo s o he companies. A gene al summa y o
he companies, indus ial sec o s and hei ma ke sha e is ep esen ed in Table 1. As shown in
Table 1, hese companies a e ca ego ized in o 27 di e en sec o s. The comple ed lis o he companies
and sec o s has been ep esen ed in Appendix A. Fo he sake o simplici y, he da ase consis s o
sha eholde s which ha e mo e han one pe cen o he lis ed companies. Mo eo e , as a signi ican
numbe o lis ed companies had ex e nal sha eholde s, he da ase con ained sha eholde s’ da a and
hei sha eholde ’s sha eholde in a bi-le el ne wo k.
Table 1. Gene al summa y o he selec ed da ase .
Row Sec o Numbe o
Companies
Ma ke
Sha e (%) Row Sec o Numbe o
Companies
Ma ke
Sha e (%)
1 Oil & Gas D illing 1 0.37 15 Re ailing 1 0.13
2 Me al Mining 5 4.99 16 Cemen 5 0.8
3 Oil P oduc s 11 10.63 17 Tou ism 1 0.2
4 Tie & Plas ic 2 0.34 18 In es men Co. 8 1.7
5 Me als 11 10.13 19 Banking 16 10.86
6 Me al P oduc s 1 0.19 20 Leasing 1 0.13
7Machines and
Equipmen 1 0.12 21 T anspo a ion 3 1.63
8 Elec onic Machines 2 0.43 22
Telecommunica ion
2 6.58
9 Ca P oduc ion 6 2.26 23 Insu ance Co. 4 0.47
10 Indus ial Holdings 4 6.65 24 Housing 3 0.39
11 Elec ici y Supply 1 0.24 25 Compu e & IT 2 1.06
12 Food P oduc ion 2 0.53 26 Enginee ing
Se ices 1 2
13 Medicine 7 1.34 27 Ex e nal
Sha eholde s 13 -
14 Pe ochemical 17 27.34
3.2. Me hodology
3.2.1. Ne wo k No a ion
A ne wo k is a se o ela ed nodes. In g aph heo y, ne wo ks a e ep esen ed as a se o e ices
and edges. Gene ally, a ne wo k N = (V, E) is ep esen ed as a se o e ices V and edges E, which
he se o edges can be shown as an adjacency ma ix. The ma ix elemen s
`Aij˘
show he exis ence
o a ela ion be ween he nodes iand jand each elemen can be 0 o 1. I he e is a ela ion be ween i
and j,
Aij
is 1 and 0 o he wise. I he ne wo k is an indi ec ne wo k, he adjacency ma ix is symme ic.
In weigh ed ne wo ks, Aij “wij.
The numbe o edges o each node iis called he deg ee o node iand is ep esen ed as
di
.
Fo di ec ed ne wo ks, he e is a di e ence be ween inpu and ou pu a cs. The numbe o inpu
and ou pu a cs o each node iis known as
din
i
and
dou
i
, espec i ely. As owne ship ela ions in
c oss-sha eholding ne wo ks a e asymme ic, hese c oss-sha eholding ne wo ks a e ep esen ed as a
weigh ed di ec ed ne wo k.
In . J. Financial S ud. 2016,4, 13 4 o 17
In addi ion o he abo e-men ioned no a ions, o each node in ne wo k N, he e a e alues such
as
i
ha ep esen an in insic alue o a node and a e no ele an o he s uc u e o a ne wo k.
In a c oss-sha eholding ne wo k,
i
could be he ma ke alue o he ope a ional e enue o each
company. A simple ep esen a ion o a c oss-sha eholding ne wo k as a weigh ed di ec ed ne wo k is
ep esen ed in Figu e 1.
In . J. Financial S ud. 2016, 4, 13 4 o 18
In addi ion o he abo e-men ioned no a ions, o each node in ne wo k N, he e a e alues
such as  ha ep esen an in insic alue o a node and a e no ele an o he s uc u e o a
ne wo k. In a c oss-sha eholding ne wo k,  could be he ma ke alue o he ope a ional e enue
o each company. A simple ep esen a ion o a c oss-sha eholding ne wo k as a weigh ed di ec ed
ne wo k is ep esen ed in Figu e 1.
j
w
ij
Figu e 1. Rep esen a ion o a c oss-sha eholding ne wo k as a weigh ed di ec ed ne wo k.
3.2.2. Ne wo ks Based Sys emic Risk Indices
One o he main challenges o ne wo k analysis o many esea che s is how o de e mine he
impo ance o each node a he han o he s in a ne wo k. In he li e a u e ela ed o sys emic isk, he
impo ance o nodes can be desc ibed as he con ibu ion o nodes in occu ence o a sys emic isk
e en . Fo his pu pose, he e a e many measu es men ioned in ne wo k li e a u e [23–25] e med as
“cen ali y measu es”. The wo main cen ali y measu es ha a e widely de eloped in he li e a u e
o ne wo k heo y a e he deg ee measu e and he eigen ec o o eedback-based cen ali y measu e.
Deg ee Cen ali y Measu e: The deg ee o each node in a c oss-sha eholding ne wo k is he
numbe o companies wi h an owne ship ela ion wi h he node. d
, as he ou -deg ee o node i, is
he numbe o companies ha a e sha eholde s o i. Con e sely, d
 as he in-deg ee o node i, is he
numbe o companies belonging o he in es men po olio o company i. The e o e, i could be
no ed ha d
 is a p oxy o he le el o in eg a ion o company i in he o he companies and d
 is
he deg ee o po olio di e si ica ion o company i.
Mic o-in es o s a e excluded in he es ima ion o d
 and d
 o each company. E en hough
his migh cause a bias in d
 and d
 es ima ion, bu because his is he case o es ima ion o all
companies, he bias e ec could be igno ed a he compa a i e analysis o companies.
In addi ion, i  ep esen s he ma ke alue o company i, P is in oduced as he po olio
alue o company i and conside ed as a sys emic isk index in [19].
P= w



 (1)
whe e w is he pe cen o company j ha is owned by company i and  is he ma ke alue o
company j.
Since he c oss-sha eholding ne wo k is a weigh ed ne wo k, i is equi ed o conside he
weigh s in o de o calcula e cen ali y as well as sys emic isk impo ance o companies. In-deg ee
and ou -deg ee indices can also be p esen ed in weigh ed ne wo ks. Fo he i s ime, Newman [26]
in oduced he deg ee o each node in a weigh ed ne wo k as he s eng h o a node. Then, a mixed
index o cen ali y based on s eng h and deg ee o each node was in oduced by Opsahl and hei
co-wo ke s [27]. Al hough he li e a u e epo s ha such indices a e used widely, hey canno be
applied in his case because o he na u e o weigh s in c oss-sha eholding ne wo ks. The e o e in
his pape , he wo ep esen ed measu es o Ba is on ha e been applied o measu e weigh ed
Figu e 1. Rep esen a ion o a c oss-sha eholding ne wo k as a weigh ed di ec ed ne wo k.
3.2.2. Ne wo ks Based Sys emic Risk Indices
One o he main challenges o ne wo k analysis o many esea che s is how o de e mine he
impo ance o each node a he han o he s in a ne wo k. In he li e a u e ela ed o sys emic isk, he
impo ance o nodes can be desc ibed as he con ibu ion o nodes in occu ence o a sys emic isk
e en . Fo his pu pose, he e a e many measu es men ioned in ne wo k li e a u e [
23
–
25
] e med as
“cen ali y measu es”. The wo main cen ali y measu es ha a e widely de eloped in he li e a u e o
ne wo k heo y a e he deg ee measu e and he eigen ec o o eedback-based cen ali y measu e.
Deg ee Cen ali y Measu e: The deg ee o each node in a c oss-sha eholding ne wo k is he numbe
o companies wi h an owne ship ela ion wi h he node.
dou
i
, as he ou -deg ee o node i, is he numbe
o companies ha a e sha eholde s o i. Con e sely,
din
i
as he in-deg ee o node i, is he numbe o
companies belonging o he in es men po olio o company i. The e o e, i could be no ed ha
dou
i
is a p oxy o he le el o in eg a ion o company iin he o he companies and
din
i
is he deg ee o
po olio di e si ica ion o company i.
Mic o-in es o s a e excluded in he es ima ion o
dou
i
and
din
i
o each company. E en hough
his migh cause a bias in
dou
i
and
din
i
es ima ion, bu because his is he case o es ima ion o all
companies, he bias e ec could be igno ed a he compa a i e analysis o companies.
In addi ion, i
i
ep esen s he ma ke alue o company i,
Pi
is in oduced as he po olio alue
o company iand conside ed as a sys emic isk index in [19].
Pi“ÿjNeighbo s o iwij j(1)
whe e
wij
is he pe cen o company j ha is owned by company iand
j
is he ma ke alue o
company j.
Since he c oss-sha eholding ne wo k is a weigh ed ne wo k, i is equi ed o conside he weigh s
in o de o calcula e cen ali y as well as sys emic isk impo ance o companies. In-deg ee and
ou -deg ee indices can also be p esen ed in weigh ed ne wo ks. Fo he i s ime, Newman [
26
]
in oduced he deg ee o each node in a weigh ed ne wo k as he s eng h o a node. Then, a mixed
index o cen ali y based on s eng h and deg ee o each node was in oduced by Opsahl and hei
co-wo ke s [
27
]. Al hough he li e a u e epo s ha such indices a e used widely, hey canno be
applied in his case because o he na u e o weigh s in c oss-sha eholding ne wo ks. The e o e in his

In . J. Financial S ud. 2016,4, 13 5 o 17
pape , he wo ep esen ed measu es o Ba is on ha e been applied o measu e weigh ed in-deg ee
and ou -deg ee measu es [
16
].
sj
, which is an in-deg ee equi alen cen ali y measu e, ep esen ed
as ollows:
sj“ˆřdin
j
i“1wij˙2
řdin
j
i“1wij2
(2)
whe e
sj
shows he numbe o inwa d a cs o he node j. In o he wo ds,
sj
calcula es he e ec i e
numbe o companies owned by company j. On he o he hand,
Hi
is in oduced as an equi alen
ou -deg ee measu e and desc ibed as ollows:
Hi“
kou
i
ÿ
j“1
hij (3)
hij which shows he amoun o con ol ha company jhas on company i, is calcula ed as ollows:
hij “w2
ij
řkin
j
l“1w2
lj
(4)
In o he wo ds,
hij
shows he impo ance o company iwi hin he companies ha belong o
company j.
Hi
measu es he o al impo ance o company i o companies ha ha e in es ed in
company iand acco dingly shows he e ec i e numbe o in es o s o company i.
Eigen Vec o Cen ali y Measu e: Eigen ec o cen ali y measu es a e based on he concep ha
impo ance o each node is ela ed o he impo ance o i s neighbo s. This concep leads o a se ies
o equa ions ha should be sol ed simul aneously. In a weigh ed di ec ed ne wo k, he Hubbell
measu e [
28
] is he mos amilia Eigen ec o measu e. In his measu e, each node could ha e
an in insic impo ance, such as
c0
and impo ance is ela ed o exis ing ela ions o o he nodes.
The ollowing ela ion shows he Hubbell index:
cH“AcH`c0(5)
whe e
cH
is he Hubbell cen ali y measu e and A is he adjacency ma ix o he ne wo k. The solu ion
o Equa ion (5) is ep esen ed as:
cH“ pI´Aq´1c0(6)
The abo e solu ion is ob ained, i he
pI´Aq
ma ix is in e ible o equi alen ly none o he
eigen alues o A is equal o 1. The e o e, choosing he pa ame e s
c0
and
cH
in a c oss-sha eholding
ne wo k, he Hubbell measu e could be used o de e mine companies ha a e sys emically impo an .
In his pape , ma ke alues and he in eg a ed ma ke alues a e chosen as c0and cH.
3.2.3. In eg a ed Ma ke Value and In eg a ed C oss-Sha eholding Ma ix
In his sec ion, cen ali y and impo ance o each company in a c oss-sha eholding ne wo k
is e alua ed based on in eg a ed owne ship o companies. Acco ding o B ioschi [
29
], in eg a ed
owne ship is de e mined by agg ega ed amoun s o di ec and indi ec owne ship o a sha eholde
on an asse . Figu e 2illus a es a simple compa ison o di ec and indi ec owne ship in a
c oss-sha eholding ne wo k.
In . J. Financial S ud. 2016,4, 13 6 o 17
In . J. Financial S ud. 2016, 4, 13 6 o 18
i
j
k
l
w
ij
w
jk
w
jl
wik
~
wil
~
Figu e 2. Rep esen a ion o di ec and indi ec owne ship in a c oss-sha eholding ne wo k.
As inancial agen s in a s ock ma ke can be ca ego ized in o lis ed companies and ex e nal
sha eholde s, he po olio alue o a lis ed company is calcula ed as Equa ion (7).
P=w

()
 (7)
whe e w shows he pe cen o company j ha is owned by company i, Γ() is he se o neighbo s
o company i and  is he ma ke alue o company j. The ma ix ep esen a ion o Equa ion (7)
could be ep esen ed as ollows:
P=WV (8)
whe eP shows ec o o po olio alues, W is an n × n adjacency ma ix,V is he ec o o ma ke
alues and n is he numbe o lis ed companies. Con e sely as he main ex e nal sha eholde s o he
lis ed companies a e conside ed in his s udy, he po olio alue o an ex e nal sha eholde k (P,)
is ep esen ed as ollows:
P, =d
و=1,2,…, (9)
whe e m is he numbe o ex e nal sha eholde s, P, ep esen s ma ke alues o he lis ed
companies and d is he owne ship ac ion o ex e nal sha eholde k on he lis ed companies. The
ma ix ep esen a ion o he alue o ex e nal sha eholde s po olio is de e mined om Equa ion (10).
P =d
(10)
When he c oss-sha eholding ne wo k is shown as a combina ion o ex e nal sha eholde s and
lis ed companies, he ollowing ma ix A is ep esen ed:
A=W0
󰇍

d0
󰇍

 (11)
whe e 0
󰇍

is a ze o ma ix and A is a (m + n) × (m + n) ma ix. Acco dingly, he in eg a ed ma ke
alue o each company could be calcula ed as a combina ion o in insic alues and amoun s o
in e connec edness as ollows:
V =AV +V (12)
whe e V and V show in insic ma ke alues and he in eg a ed ma ke alues o companies,
espec i ely. The solu ion o Equa ion (13) is as ollows:
V =(I−A)V (13)
The V, as he in eg a ed alues o companies could be applied as a sys emic isk index ha
shows impo ance in e ms o sys emic isk. I in he Equa ion (6), he c=V and V=c, i is
ob ious ha he V is a kind o Hubbell cen ali y measu e.
Figu e 2. Rep esen a ion o di ec and indi ec owne ship in a c oss-sha eholding ne wo k.
As inancial agen s in a s ock ma ke can be ca ego ized in o lis ed companies and ex e nal
sha eholde s, he po olio alue o a lis ed company is calcula ed as Equa ion (7).
Pi“ÿ
jeΓpiq
wij j(7)
whe e
wij
shows he pe cen o company j ha is owned by company i,
Γpiq
is he se o neighbo s o
company iand
j
is he ma ke alue o company j. The ma ix ep esen a ion o Equa ion (7) could be
ep esen ed as ollows:
P“WV (8)
whe e
P
shows ec o o po olio alues,
W
is an n
ˆ
nadjacency ma ix,
V
is he ec o o ma ke
alues and nis he numbe o lis ed companies. Con e sely as he main ex e nal sha eholde s o he
lis ed companies a e conside ed in his s udy, he po olio alue o an ex e nal sha eholde k
`Pk,ex ˘
is
ep esen ed as ollows:
Pk,ex “dk
In . J. Financial S ud. 2016, 4, 13 6 o 18
i
j
k
l
w
ij
w
jk
w
jl
wik
~
wil
~
Figu e 2. Rep esen a ion o di ec and indi ec owne ship in a c oss-sha eholding ne wo k.
As inancial agen s in a s ock ma ke can be ca ego ized in o lis ed companies and ex e nal
sha eholde s, he po olio alue o a lis ed company is calcula ed as Equa ion (7).
P=w

()
 (7)
whe e w shows he pe cen o company j ha is owned by company i, Γ() is he se o neighbo s
o company i and  is he ma ke alue o company j. The ma ix ep esen a ion o Equa ion (7)
could be ep esen ed as ollows:
P=WV (8)
whe eP shows ec o o po olio alues, W is an n × n adjacency ma ix,V is he ec o o ma ke
alues and n is he numbe o lis ed companies. Con e sely as he main ex e nal sha eholde s o he
lis ed companies a e conside ed in his s udy, he po olio alue o an ex e nal sha eholde k (P,)
is ep esen ed as ollows:
P, =d
و=1,2,…, (9)
whe e m is he numbe o ex e nal sha eholde s, P, ep esen s ma ke alues o he lis ed
companies and d is he owne ship ac ion o ex e nal sha eholde k on he lis ed companies. The
ma ix ep esen a ion o he alue o ex e nal sha eholde s po olio is de e mined om Equa ion (10).
P =d
(10)
When he c oss-sha eholding ne wo k is shown as a combina ion o ex e nal sha eholde s and
lis ed companies, he ollowing ma ix A is ep esen ed:
A=W0
󰇍

d0
󰇍

 (11)
whe e 0
󰇍

is a ze o ma ix and A is a (m + n) × (m + n) ma ix. Acco dingly, he in eg a ed ma ke
alue o each company could be calcula ed as a combina ion o in insic alues and amoun s o
in e connec edness as ollows:
V =AV +V (12)
whe e V and V show in insic ma ke alues and he in eg a ed ma ke alues o companies,
espec i ely. The solu ion o Equa ion (13) is as ollows:
V =(I−A)V (13)
The V, as he in eg a ed alues o companies could be applied as a sys emic isk index ha
shows impo ance in e ms o sys emic isk. I in he Equa ion (6), he c=V and V=c, i is
ob ious ha he V is a kind o Hubbell cen ali y measu e.
k“1, 2, . . . , m(9)
whe e mis he numbe o ex e nal sha eholde s,
Pk,ex
ep esen s ma ke alues o he lis ed companies
and
dk
is he owne ship ac ion o ex e nal sha eholde kon he lis ed companies. The ma ix
ep esen a ion o he alue o ex e nal sha eholde s po olio is de e mined om Equa ion (10).
Pex “d (10)
When he c oss-sha eholding ne wo k is shown as a combina ion o ex e nal sha eholde s and
lis ed companies, he ollowing ma ix A is ep esen ed:
AҬ
˝
WÑ
0
dÑ
0˛
‚(11)
whe e
Ñ
0
is a ze o ma ix and A is a (m+n)
ˆ
(m+n) ma ix. Acco dingly, he in eg a ed ma ke
alue o each company could be calcula ed as a combina ion o in insic alues and amoun s o
in e connec edness as ollows:
Vin “AVin `V (12)
In . J. Financial S ud. 2016,4, 13 7 o 17
whe e
V
and
Vin
show in insic ma ke alues and he in eg a ed ma ke alues o companies,
espec i ely. The solu ion o Equa ion (13) is as ollows:
Vin “ pI´Aq´1V (13)
The
Vin
, as he in eg a ed alues o companies could be applied as a sys emic isk index ha
shows impo ance in e ms o sys emic isk. I in he Equa ion (6), he
cH“Vin
and
V“c0
, i is
ob ious ha he Vin is a kind o Hubbell cen ali y measu e.
Howe e , he in eg a ed owne ship ma ix can also be ep esen ed as ollows:
Ain “Ain A`A (14)
whe e
Ain
conside s all di ec and indi ec pa hs o calcula e amoun s o in eg a ed owne ship.
Fo example, he in eg a ed pe cen o company j ha is owned by company iis ep esen ed as ollows:
ain
ij “aij `ÿ
k
aikain
kj (15)
The solu ion o he Equa ion (14) is as ollows:
Ain “ pI´Aq´1A (16)
Acco ding o he abo e-men ioned equa ions, i is possible o each a dual ela ion o each
company as he Equa ion (17), whe e each side o he equa ion shows he in eg a ed po olio alues
o companies.
Ain V“AVin “Pin (17)
The
Pin
, which is a complemen o he po olio alue indices (
Pi
), can been used as ano he
sys emic isk index.
4. Resul s and Analysis
4.1. Di ec C oss-Sha eholding Ne wo k
Using ne wo k heo y and Pajek so wa e, a ep esen a ion o c oss-sha eholding ne wo k o
companies lis ed on he Teh an S ock Exchange is shown in Figu e 3. As i is ob ious, nodes a e
ep esen a i e o lis ed companies and ex e nal sha eholde s. Acco ding o he sec o classi ica ion
o TSE, he conside ed companies a e ca ego ized acco ding o 27 di e en sec o s dis inguished by
colo s. As can be seen in Figu e 3, he e a e some companies and ex e nal sha eholde s ha ha e
mo e owne ship ela ions wi h he o he agen s. The size o node (Figu e 3) ep esen s he amoun
o a node’s deg ee, whe e he “go e nmen ”, “Tamin o ganiza ion” and he “na ional pension und”
anked highes wi h 40, 31 and 27 a cs, espec i ely.
Al hough i is no possible o ecognize he gene al s uc u e o he TSE c oss-sha eholding
ne wo k, he exis ence o a bunch o nodes wi h many in-deg ee and ou -deg ee as well as some nodes
wi h only inwa d a cs and ou wa d a cs shows ha he exis ence o a bow- ie s uc u e in he TSE
is likely.
Table 2 ep esen s a summa y o he s a is ical analysis o he di ec c oss-sha eholding ne wo k
and he ele an sys emic isk indices in he company and sec o le el. As shown in Table 2, he e was
no signi ican di e ence be ween he op i e companies o deg ee, in-deg ee,
sj
and
Pi
in he di ec
c oss-sha eholding ne wo k; howe e , he di e ence o hese indices is mo e e iden in he lowe
o de companies. Excep o di e ence in he o de o companies, he only a ia ion was acco ding o
exis ence o “Adala Sha es” in he op i e companies based on
sj
and
Pi
, which indica es ha e en
hough he “Adala Sha es” has only a ew ela ions wi h he o he companies, i has a signi ican sha e
in i s own companies. Sec o analysis shows some di e ences be ween he ou indices.
In . J. Financial S ud. 2016,4, 13 8 o 17
In . J. Financial S ud. 2016, 4, 13 8 o 18
Figu e 3. Rep esen a ion o c oss-sha eholding ne wo k o Teh an S ock Exchange. The size o nodes
is ela ed o he deg ee o each node and he deg ee is he sum o in-deg ee and ou -deg ee o nodes.
Table 2. Compa ison o di e en sys emic isk indices o di ec ne wo k in he Teh an S ock
Exchange.
Deg ee In-Deg ee Ou -Deg ee
Min. Deg ee 0 Min. In-Deg ee 0 Min. Ou -Deg ee 0
Max. Deg ee 40 Max. In-Deg ee 40 Max. Ou -Deg ee 8
A g. Deg ee 5.88 A g. In-Deg ee 2.94 A g. Ou -Deg ee 2.94
Top Fi e Nodes Deg ee Top Fi e Nodes In-Deg ee Top Fi e Nodes Ou -Deg ee
Go . 40 Go . 40 MADN 8
Tamin O g 31 Tamin O g 31 MS022 8
SA3A1 27 SA3A1 24 PK061 8
Oilcopen 23 Oilcopen 23 GD021 7
NIKX1 22 NIKX1 17 FO041 7
Top Fi e Sec o A g Deg ee Top Fi e Sec o A g In-Deg ee Top Fi e Sec o A g Ou -Deg ee
Indus ial Holdings 17.25 Indus ial Holdings 13.5 Me al Mining 5.6
Ex Sha eholde s 13 Ex Sha eholde s 13 Insu ance Co. 5.25
In es men Co. 10.125 In es men Co. 6.75 D illing 5
Me al Mining 8 Me al Mining 2.4 Cemen 4.4
Insu ance Co. 6 Bank 2 Basic Me als 4
  (Million Rials)
Min. 0 Min. 0 Min. 0
Max. 20.1 Max. 2.36 Max. 424,000,000
A g. 1.63 A g. 0.51 A g. 17,600,000
Top Fi e Nodes  Top Fi e Nodes Top Fi e Nodes  (Million Rials)
Go . 20.1 TORZ1 2.36 Adala Sha e 424,000,000
Adala Sha e 13.33 ARFZ1 2.03 Go . 354,000,000
Tamin O g 11.66 BDYZ1 2.02 Tamin O g 218,000,000
Oilcopen 9.75 SMAZ1 2.01 Oilcopen 142,000,000
SA3A1 8.78 KS121 2 SA3A1 115,000,000
Top Fi e Sec o A g.  Top Fi e Sec o A g  Top Fi e Sec o A g 
(Million Rials)
Ex . Sha eholde s 6.48 Insu ance Co. 1.29 Ex Sha eholde s 109,000,000
Figu e 3.
Rep esen a ion o c oss-sha eholding ne wo k o Teh an S ock Exchange. The size o nodes is
ela ed o he deg ee o each node and he deg ee is he sum o in-deg ee and ou -deg ee o nodes.
Table 2.
Compa ison o di e en sys emic isk indices o di ec ne wo k in he Teh an S ock Exchange.
Deg ee In-Deg ee Ou -Deg ee
Min. Deg ee 0 Min. In-Deg ee 0 Min. Ou -Deg ee 0
Max. Deg ee 40 Max. In-Deg ee 40
Max. Ou -Deg ee
8
A g. Deg ee 5.88 A g. In-Deg ee 2.94 A g. Ou -Deg ee 2.94
Top Fi e Nodes Deg ee Top Fi e Nodes In-Deg ee Top Fi e Nodes Ou -Deg ee
Go . 40 Go . 40 MADN 8
Tamin O g 31 Tamin O g 31 MS022 8
SA3A1 27 SA3A1 24 PK061 8
Oilcopen 23 Oilcopen 23 GD021 7
NIKX1 22 NIKX1 17 FO041 7
Top Fi e Sec o A g Deg ee Top Fi e Sec o A g In-Deg ee Top Fi e Sec o A g Ou -Deg ee
Indus ial
Holdings 17.25 Indus ial
Holdings 13.5 Me al Mining 5.6
Ex Sha eholde s 13 Ex Sha eholde s 13 Insu ance Co. 5.25
In es men Co. 10.125 In es men Co. 6.75 D illing 5
Me al Mining 8 Me al Mining 2.4 Cemen 4.4
Insu ance Co. 6 Bank 2 Basic Me als 4
sjHiPi(Million Rials)
Min. 0 Min. 0 Min. 0
Max. 20.1 Max. 2.36 Max. 424,000,000
A g. 1.63 A g. 0.51 A g. 17,600,000
Top Fi e Nodes sjTop Fi e Nodes HiTop Fi e Nodes Pi(Million Rials)
Go . 20.1 TORZ1 2.36 Adala Sha e 424,000,000
Adala Sha e 13.33 ARFZ1 2.03 Go . 354,000,000
Tamin O g 11.66 BDYZ1 2.02 Tamin O g 218,000,000
Oilcopen 9.75 SMAZ1 2.01 Oilcopen 142,000,000
SA3A1 8.78 KS121 2 SA3A1 115,000,000
Top Fi e Sec o A g. sjTop Fi e Sec o A g HiTop Fi e Sec o A g Pi
(Million Rials)
Ex . Sha eholde s
6.48 Insu ance Co. 1.29 Ex Sha eholde s 109,000,000
Ind. Holdings 6.22 Me al Mining 1.16 Ind. Holdings 72,100,000
In es men Co. 3.42 T anspo a ion 1.09
Telecommunica ion
54,400,000
Me al Mining 1.76 Elec ici y 1 Pe ochemical 13,100,000
Ca P oduc ion 1.65 Basic Me als 0.78 Me al Mining 11,100,000
In . J. Financial S ud. 2016,4, 13 15 o 17
Company Symbol Sec o Company Symbol Sec o
44
Omid In . Mng OIMC1 Ind. Holdings
110
Pa sian IPAR1 Insu ance Co.
45
Ba gh Mapna Co. BMAZ1 Elec ici y Supp.
111
Mella Insu . BMEX1 Insu ance co.
46
Behshah TS3A1 Food P od.
112
Pasa gad Insu . BIPZ1 Insu ance co.
47
Behshah Ind. SBEX1 Food P od.
113
Shahed In . SAHX1 Housing
48
Tamin Da oo DTIP1 Medicine
114
Housing In . MSKX1 Housing
49
Albo z In . ALBZ1 Medicine
115
In . Cons . BSTE1 Housing
50
Sobhan Pha m. DSOZ1 Medicine
116
In . Se ices INFX1 Compu e & IT
51
Os ah Pha m. DOSE1 Medicine
117
Pa sian E-Comme ce PRSX1 Compu e & IT
52
Razak Lab. DRZX1 Medicine
118
MAPNA MAPX1 Compu e & IT
53
Zah a i Pha . DZAX1 Medicine
119
Go e men Go
Ex . Sha eholde
54
Da oupakhsh DARO1 Medicine
120
Tamin O ganiza ion Tamin O g
Ex . Sha eholde
55
Tamin Pe o PT3A1 Pe ochemical
121
A my Pen. Fund Sa a
Ex . Sha eholde
56
I .In .Pe . IPTZ1 Pe ochemical
122
Adala Sha es Adasha e
Ex . Sha eholde
57
KhalijFa s PL081 Pe ochemical
123
Mos aza in Founda ion Mos ound
Ex . Sha eholde
58
Pa sianOil PA021 Pe ochemical
124
Oil Comp Pen. und Oilcopen
Ex . Sha eholde
59
Shazand Pe . PARK1 Pe ochemical
125
Tadbi In . Tadbi in
Ex . Sha eholde
60
Pa dis Pe . PRDZ1 Pe ochemical
126
Fa hangian In . Fa hin
Ex . Sha eholde
61
Paksho PASH1 Pe ochemical
127
Village Pen. Fund Villpen
Ex . Sha eholde
62
Kho asan Pe o PSKZ1 Pe ochemical
128
Foolad Pen. Fund Fooladpen
Ex . Sha eholde
63
Kha k Pe . PK061 Pe ochemical
129
Meh In . Co. Meh in
Ex . Sha eholde
64
I an Chem. Ind. SSIN1 Pe ochemical
130
Banks Pen Find Bankpen
Ex . Sha eholde
65
Jam Pe . PJMZ1 Pe ochemical
131
Meh eayande In .
Meh ayande Ex . Sha eholde
66
Ke man PK3A1 Pe ochemical
Appendix B. Appendix B: His og am and Cumula i e Dis ibu ion o Sys emic Risk Measu es
In . J. Financial S ud. 2016, 4, 13 16 o 18
Appendix B: His og am and Cumula i e Dis ibu ion o Sys emic Risk Measu es








Appendix C: Complemen o Cumula i e Dis ibu ion o Sys emic Risk in Log-Log Scale
(

)
(

)
(



)
(


)
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
0
10
20
30
40
50
60
70
F equency Cumula i e % 1-CDF(%)
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
0
5
10
15
20
25
30
35
F equency Cumula i e % 1-CDF (%)
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
0
10
20
30
40
50
60
70
F equency Cumula i e % 1-CDF % 0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
0
5
10
15
20
25
30
35
40
45
F equency Cumula i e % 1-CDF %
-2.5
-2
-1.5
-1
-0.5
0
24.82
27.69
28.35
28.90
29.15
29.43
29.99
30.24
30.31
30.58
30.79
31.11
31.38
31.49
31.89
32.16
32.32
32.65
33.49
33.86
-6
-5
-4
-3
-2
-1
0
28.97
30.18
30.71
31.06
31.31
31.52
31.74
31.96
32.11
32.45
32.59
32.95
33.28
33.98
-6
-5
-4
-3
-2
-1
0
0.0
0.7
1.1
1.4
1.6
1.8
1.9
2.1
2.2
2.4
2.5
2.6
2.6
2.8
2.9
3.0
3.2
3.6
-6
-5
-4
-3
-2
-1
0
-1.39
-0.69
-0.29
0.00
0.22
0.41
0.56
0.69
0.81
0.92
=0.033 (0.000)
R-Squa e=0.887
p- alue=0.000
=0.083 (0.000)
R-Squa e=0.92
p
- alue=0.000
=0.194 (0.000)
R-Squa e=0.963
p- alue=0.000
=0.48 (0.000)
R-Squa e=0.944
p- alue=0.000

In . J. Financial S ud. 2016,4, 13 16 o 17
Appendix C. Appendix C: Complemen o Cumula i e Dis ibu ion o Sys emic Risk in
Log-Log Scale
In . J. Financial S ud. 2016, 4, 13 16 o 18
Appendix B: His og am and Cumula i e Dis ibu ion o Sys emic Risk Measu es








Appendix C: Complemen o Cumula i e Dis ibu ion o Sys emic Risk in Log-Log Scale
(

)
(

)
(



)
(


)
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
0
10
20
30
40
50
60
70
F equency Cumula i e % 1-CDF(%)
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
0
5
10
15
20
25
30
35
F equency Cumula i e % 1-CDF (%)
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
0
10
20
30
40
50
60
70
F equency Cumula i e % 1-CDF % 0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
0
5
10
15
20
25
30
35
40
45
F equency Cumula i e % 1-CDF %
-2.5
-2
-1.5
-1
-0.5
0
24.82
27.69
28.35
28.90
29.15
29.43
29.99
30.24
30.31
30.58
30.79
31.11
31.38
31.49
31.89
32.16
32.32
32.65
33.49
33.86
-6
-5
-4
-3
-2
-1
0
28.97
30.18
30.71
31.06
31.31
31.52
31.74
31.96
32.11
32.45
32.59
32.95
33.28
33.98
-6
-5
-4
-3
-2
-1
0
0.0
0.7
1.1
1.4
1.6
1.8
1.9
2.1
2.2
2.4
2.5
2.6
2.6
2.8
2.9
3.0
3.2
3.6
-6
-5
-4
-3
-2
-1
0
-1.39
-0.69
-0.29
0.00
0.22
0.41
0.56
0.69
0.81
0.92
=0.033 (0.000)
R-Squa e=0.887
p- alue=0.000
=0.083 (0.000)
R-Squa e=0.92
p
- alue=0.000
=0.194 (0.000)
R-Squa e=0.963
p- alue=0.000
=0.48 (0.000)
R-Squa e=0.944
p- alue=0.000
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