Vine Copula Approach to Understand the Financial Dependence of the Istanbul Stock Exchange Index

E kaya, Ozan; Gü , İsmail; Yıldı ım Külekci, Bük e; Poy az, Gülden
A icle — Published Ve sion
Vine Copula App oach o Unde s and he Financial
Dependence o he Is anbul S ock Exchange Index
Compu a ional Economics
P o ided in Coope a ion wi h:
Sp inge Na u e
Sugges ed Ci a ion: E kaya, Ozan; Gü , İsmail; Yıldı ım Külekci, Bük e; Poy az, Gülden (2024) :
Vine Copula App oach o Unde s and he Financial Dependence o he Is anbul S ock Exchange
Index, Compu a ional Economics, ISSN 1572-9974, Sp inge US, New Yo k, NY, Vol. 64, Iss. 5, pp.
2935-2980,
h ps://doi.o g/10.1007/s10614-023-10544-7
This Ve sion is a ailable a :
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Compu a ional Economics (2024) 64:2935–2980
h ps://doi.o g/10.1007/s10614-023-10544-7
Vine Copula App oach oUnde s and heFinancial
Dependence o  heIs anbul S ock Exchange Index
OzanE kaya1 · İsmailGü 2 · Bük eYıldı ımKülekci3,4 · GüldenPoy az5
Accep ed: 21 Decembe 2023 / Published online: 6 Feb ua y 2024
© The Au ho (s) 2024
Abs ac
Recen ly, he complex dependence pa e ns among a ious s ocks gained mo e
impo ance. Measu ing he dependency s uc u e is c i ical o in es o s o manage
hei po olio isks. Since he global inancial c isis, esea che s ha e been mo e
in e es ed in s udying he dynamics o dependency wi hin s ock ma ke s by using
no el me hodologies. This s udy aims o in es iga e a Regula -Vine copula app oach
o es ima e he in e dependence s uc u e o he Is anbul S ock Exchange index
(ISE100). Fo his pu pose, we conside 32 s ocks ela ed o 6 sec o s belonging o
ISE100. To e lec he ime- a ying impac s o he 2008–2009 global inancial c i-
sis, he dependence analysis is conduc ed o e p e-, du ing-, and pos -global inan-
cial c isis pe iods. Po olio analysis is conside ed ia a olling window app oach o
cap u e he changes in he dependence. We compa e he Regula -Vine-based gene -
alized au o eg essi e condi ional he e oskedas ici y (GARCH) agains he con en-
ional GARCH model wi h di e en inno a ions. Value a isk and expec ed sho -
all isk measu es a e used o alida e he models. Addi ionally, o he cons uc ed
po olios, e u n pe o mance is summa ized using bo h Sha pe and So ino a ios.
To es he abili y o he conside ed Regula -Vine app oach on ISE100, ano he e al-
ua ion has been done du ing he COVID-19 pandemic c isis wi h a ious pa ame e
se ings. The main indings ac oss di e en isky pe iods illus a e he sui abili y o
using he Regula - ine GARCH app oach o model he complex dependence among
s ocks in eme ging ma ke condi ions.
Keywo ds R-Vine copula· Global inancial c isis· Is anbul s ock exchange· Value-
a - isk· Expec ed sho all
1 In oduc ion
In he pas decade, inancial ma ke s expe ienced many c ises due o unde es ima-
ion o isk (MacKenzie & Spea s, 2014; Jickling, 2009). Since he global inancial
c isis (GFC), esea che s and p ac i ione s ha e inc easingly sough o de elop new
Ex ended au ho in o ma ion a ailable on he las page o he a icle
2936
O.E kaya e al.
me hods o p edic and con ol ma ke isks. Unde s anding he dynamic o in e de-
pendence be ween s ocks is i al o in es o s o manage hei po olio’s isk and
o ecas e u ns (Liu e al., 2017). Copulas a e a popula ool o modeling depend-
ence and isk in inance. They o e a lexible way o model he join dis ibu ion
o wo o mo e andom a iables, which is especially common in s ock ma ke s.
Besides, copula modeling can be bene icial when de ec ing he symme ic and
asymme ic dependence pa e ns o inancial da a in imes o s ess.
Co ela ion is a adi ionally used measu e o dependence, applicable only in
he ellip ical wo ld, o example, when he e u ns ollow a mul i a ia e Gaussian
o S uden ’s -dis ibu ion. When he e a e non-linea ela ionships be ween e u ns,
he co ela ion may no adequa ely desc ibe he ype o dependency, hus leading o
an unde es ima ion o he join isk o ex eme e en s (Junke e al., 2005). Copulas
ask a di e en ques ion, such as “How do wo a iables ac oge he and how s ong
is his simul aneous mo emen a a ious poin s in he dis ibu ion” (Vuolo, 2015),
a he han how a iable X a ec s a iable Y. In his con ex , he ad an age o using
copula in he co-mo emen analysis is mul i ace ed (Ning, 2010). The mo i a ion
behind he copula is ha i allows a sepa a ion o he dependence s uc u e om
i s ma gins and cap u es he non-linea dependency pa e ns. Copula also allows o
asymme ic dependence, which has impo an implica ions when calcula ing po -
olio isks (Nelsen, 2007; Pa on, 2013; P ince & Anokye, 2020). The e o e, copula
adap s well o he dependency o inancial da a, making i a good choice o inco po-
a ing dependence in o he model (Emb ech s e al., 1999).
Al hough copulas a e widely-used in inance and economics, hey a e no p ac-
ical o high-dimensional da a. Vine copulas (o Vines) a e ee-based models o
o e come such limi a ions o mul i a ia e copulas (Cooke, 1997; Bed o d & Cooke,
2001, 2002). Vines, also called as pai copula cons uc ion (PCCs), ely on he use o
bi a ia e copulas. Each pai cap u es he dependence be ween wo a iables sequan-
ially. Vine copulas o e be e lexibili y han s anda d mul i a ia e copula models
due o he wide selec ion o bi a ia e copula models (Heinen & Valdesogo, 2008;
Ku owicka & Joe, 2010). Addi ionally, Vines can o e come he limi ing ea u es o
al e na i e measu es o dependency and co ela ion, such as Pea son, Spea man,
and Kendall (He nandez, 2015). Bed o d and Cooke (2001) and Bed o d and Cooke
(2002) g aphically explo ed he pai -copula cons uc ions, egula ines (R-Vines),
and de eloped wo main sub-classes, called canonical ines (C-Vines) and d awable
ines (D-Vines). C- and D-Vines a e bene icial o speci ic ee s uc u es whe eas
R-Vines a e mo e lexible amewo k.
The 2008-2009 inancial c isis p o ides an example o how inancial ins i u ions
and hei ma ke s a e in e connec ed and how shocks in one indus y can h ea en
he s abili y o he o he sec o s o he en i e sys em. In Tu key, he e is a gap in
he dependence analysis o s ocks, co e ing bo h he inancial and o he sec o s. In
his di ec ion, he con ibu ions o his s udy a e wo- old. Fi s , we examine he co-
dependencies o 32 s ocks wi h he R-Vine copula model. The du a ion o da a is
selec ed as 01.01.2005-31.12.2013 o in es iga e he e ec s o he p e-, du ing, and
pos -GFC pe iods. Wi hin he 32 s ocks o ISE100, we s udy he sub-sec o a ying
dependencies by ocusing on R-Vines. A gene al unde s anding o he s uc u e o
co-dependency be ween sec o s is c i ical in measu ing a po olio’s isk. Secondly,
2937
Vine Copula App oach oUnde s and heFinancial Dependence…
we cons uc an equally weigh ed po olio om he selec ed leade s o each sec o
by an R-Vine-based GARCH model. The ea e , he dynamic Value-a -Risk (VaR)
and Expec ed Sho all (ES) isk measu es a e compu ed o e he cons uc ed po -
olio. Fo he eliabili y o isk measu es, we employ back es ing me hods o p o ide
u he insigh o he policymake s wi h mo e eliable in o ma ion o a oid po en ial
losses, especially du ing pe iods o inancial s ess. Du ing 2020, he COVID-19
pandemic has le global inancial ma ke s conside ably ulne able o he i s ime
since he 2008. In his challenging pe iod, ISE100, as an eme ging s ock ma ke , has
expe ienced a eal collapse, based on a quick jump in ma ke ola ili y du ing he
COVID-19 epidemic, including o he economic issues such as a weakened cu ency,
ele a ed in la ion, and unemploymen as well as ce ain poli ical decisions. Fo ha
eason, o es he conside ed R-Vine model unde di e en ma ke condi ions, simi-
la compu a ions ha e been made o b ing u he e idences o he model sui abili y
on Tu kish ma ke .
This s udy is he i s comp ehensi e R-Vine copula dependence analysis on a i-
ous sec o s aded in ISE100 in ce ain ime pe iods ega ding he 2008–2009 global
inancial c isis, and COVID-19 pandemic c isis wi h signi ican e en s and shocks.
The second pe iod is examined o suppo he sui abili y o conside ed model unde
di e en economic cha ac e is ics. In he i s inancial c isis pe iod, we discuss
no only he esul s o dependence analysis bu also wo c ucial isk measu es, VaR
and ES, which a e ca e ully in es iga ed and compa ed unde a ious scena ios.
The main indings show ha he R-Vine copula is a sui able model o he complex
dependence s uc u es o he ISE100 s ock ma ke . Resul s show ha dependence
s uc u e a ies wi h ime, and Su i al Gumbel copula occu s in maximum num-
be s, especially du ing he GFC pe iod, and plays a c ucial ole in he dependence
s uc u e o sec o s. Especially he inance sec o has he highes dependence isk
du ing imes o u bulence. The dynamic R-Vine GARCH po olio analysis, wi h
VaR and ES isk measu es, is s udied o di e en pe iods. In addi ion, we also com-
pu e only GARCH-based po olio isk measu es o compa ison and show ha he
R-Vine GARCH model pe o ms be e in cap u ing da a a iabili y. The compu a-
ions demons a e he sui abili y o he R-Vine GARCH model o po olio analysis.
In addi ion o he calcula ed isk measu es, i is impo an o highligh he po olio
e u n pe o mance wi h sui able indica o s. The e a e nume ous pe o mance meas-
u emen s a egies o measu ing po olio e u n pe o mance mainly including
Sha pe Ra io ( ewa d o a iance), and So ino Ra io (co ec ed e sion o Sha pe).
B ie ly, Sha pe a io (ShR) e alua es an in es men ’s pe o mance compa ed o a
isk- ee asse (Sha pe, 1964). I is he in es men e u n minus he isk- ee e u n
di ided by he in es men e u n s anda d de ia ion. In es o s gain mo e e u n pe
uni o isk. On he o he hand, isk-adjus ed e u n is measu ed ia he So ino a io
(SoR). Unlike he ShR a io, i penalizes only e u ns below a use -speci ied a -
ge o equi ed a e o e u n (So ino & P ice, 1994). Fo ha pu pose, Sha pe and
So ino a ios a e summa ized simila o he calcula ed isk measu es o e di e en
ime in e als. Addi ionally, he impac o isk ee a e g aphically displayed and
discussed o he GFC pe iod o he same equally weigh ed po olio se ing. The
calcula ed a ios suppo he main inding ha i is be e o ely on R-Vine GARCH
amewo k a he han elying on classical GARCH models. Fo he second c isis
2938
O.E kaya e al.
pe iod, simila s ocks and hei ela ionships ha e been examined unde he COVID-
19 pandemic c isis ha had ce ain shock economic wa es h ough di e en chan-
nels owa ds he Tu kish inancial ma ke .
The es o he pape is o ganized as ollows: Sec .2 b ie ly summa izes he li -
e a u e ega ding he applica ion o Vine copulas o s ock ma ke s. In Sec .3, we
gi e a b ie e iew on he me hodology o ARMA-GARCH and Vines. Sec ion4
p esen s he applica ion o he R-Vine o sub-sec o dependence analysis and he
cons uc ed po olio. Finally, Sec .5 summa izes he esul s, including he bene i s
and limi a ions o he s udy.
2 Li e a u e Re iew
The popula i y o copula models in he las ew decades inc eased signi ican ly. In
pa icula , he e is a g owing in e es o do esea ch on he co-dependence o s ock
ma ke s du ing pe iods o ex eme luc ua ions. I is demons a ed in he li e a u e
ha s ock ma ke s a e mo e dependen on one ano he du ing inancial c ises (Ches-
e s, 2011; Jansen & Nahuis, 2003; Da id, 1997). Fo example, he R-Vine copula
model is used o measu e and analyze he co-dependency o s ocks om he Dow
Jones Indus ial A e age (DJIA) index (Allen e al., 2013). He nandez (2015) mod-
els he po olio in e dependencies using a copula coun ing echnique o assess he
mul i a ia e dependen isk. Heinen and Valdesogo (2008); Dismann e al. (2013);
B echmann and Czado (2013) and Geidosch and Fische (2016) employed ine cop-
ulas o assess co-dependency o inancial ime se ies. Heinen and Valdesogo (2008)
p oposed a dynamic model called canonical ine au o eg essi e (CAVA) o es ima e
he dependence be ween s ocks, he sec o and s ocks, and he sec o and ma ke .
Dismann e al. (2013) conside ed he R-Vine amewo k o Eu opean inancial da a,
using 11 s ock indices o model he change o dependence s uc u e du ing pe iods
o GFC.
In addi ion, po olio isk measu es can be imp o ed wi h he use o Vines.
Guegan and Maugis (2010) compa ed he Vine-GARCH me hod wi h he egula
GARCH model and concluded ha ines o e a signi ican imp o emen in he po -
olio VaR p edic ions. Guegan and Maugis (2010) applies ine copulas in 5-dimen-
sional s ocks o VaR es ima ion. B echmann and Czado (2013) s essed he use ul-
ness o ine copulas in po olio managemen . They de eloped a me hod called he
Regula Vine Ma ke Sec o (RVMS) model o measu e and unde s and he depend-
ence s uc u e o he Eu o S oxx 50, which includes 46 s ocks and 5 na ional indices.
The i ed R-Vine copula model can adequa ely cap u e he asymme ic dependence
be ween he s ocks, sec o s, and he ma ke . In he same ein, Ku owicka and Joe
(2010) showed he capabili y o he R-Vine copulas o cap u e a high-dimensional
asymme ic ela ionship o inancial e u ns. Dismann e  al. (2013) sugges an
algo i hm o make R-Vine es ima ion easible, showing he high lexibili y o he
R-Vines compa ed o C- and D-Vines. Geidosch and Fische (2016) con i med he
ad an ages o ine copulas o e con en ional copulas when modeling he depend-
ence s uc u e o a po olio.

2939
Vine Copula App oach oUnde s and heFinancial Dependence…
Recen ly, he li e a u e on he e ec s o COVID-19 on inancial ma ke s inc eased
apidly, especially in he second qua e o 2020, when he epidemic began o sp ead
wo ldwide. Among di e en s udies, he e a e some esea ch pape s ocused on
s ock dependencies be ween coun ies using copula amewo k. To illus a e, Aslam
e al. (2021), he dependence s uc u e o global s ock ma ke s in he COVID-19
pe iod has been examined using he C- ine Copula app oach. The dynamic ail
dependence isk be ween he BRICS economies and he wo ld ene gy ma ke was
s udied by Mu ebaMwamba and Mwambi (2021), du ing he COVID-19 inancial
c isis. They used he ec o au o eg essi e (VAR), Ma ko -swi ching GJR-GARCH,
and ine copula me hods. Fo a speci ic s ock ma ke , Ei a and TchuinkamDjemo
(2022) applied an EVT-based pai wise copula me hod o modeling isk in e ac-
ion be ween o eign exchange a es and equi y indices o he Johannesbu g S ock
Exchange (JSE) by using some selec ed lis ed s ock indices. By combining di e en
ools, Alqa alleh and Canepa (2021) conside ed he wa ele -copula-GARCH p o-
cedu e o in es iga e he occu ence o c oss-ma ke linkages du ing he COVID-
19 pandemic using six majo s ock indices. In ano he ecen wo k, Sahamkhadam
and S ephan (2023) examined ine copulas in modeling symme ic and asymme ic
dependency s uc u es and o ecas ing inancial e u ns om 2001 o 2022, includ-
ing he COVID-19 pandemic c isis.
As no ed abo e, while he e is a as li e a u e on modeling he co-dependency
be ween s ock e u ns ia Vine copula, he li e a u e on modeling he dependency
s uc u e o ISE100 s ock e u ns is limi ed. Examples o he esea ch on he co-
dependence o he inancial ma ke s o Tu key can be ound in Binici e al. (2013);
Talasli (2013). These s udies a e along he line o co ela ions, and condi ional co -
ela ions. The applica ion example closes o ou s udy belongs o he wo k o Özgü
and Sa ıko anlık (2021). They analyzed he co-dependency o 12 s ocks aded in
ISE30 bu did no include a c isis pe iod in hei s udy. Unde s anding he impac s o
he inancial c ises on indi idual s ocks, as well as on a po olio, is one o he main
objec i es o his s udy. I ails o examine asymme ic dependence be ween s ock
e u ns since hey assume ha inno a ions ollow a symme ic mul i a ia e no mal
o S uden ’s -dis ibu ion. In his ega d, we ex end he abo e-men ioned s udies
by using a wide ange o s ocks and p esen ing an examina ion o he dependency
s uc u es o e h ee di e en sample pe iods in ol ing he GFC. In ligh o he
a ailable li e a u e, we employ and s udy he R-Vine GARCH model o po olio
isk modeling o e di e en sub-pe iods. To he bes o ou knowledge, wi hin he
same modeling amewo k, his s udy is he i s one ha ocuses on COVID-19 pan-
demic pe iod o ISE100 s ock ma ke .
Fo Tu key s ock ma ke , he implemen a ions o Sha pe (ShR) and So ino
(SoR) a ios a e limi ed simila o he VaR and ES in es iga ions. Gene ally, many
empi ical s udies a e ocused on he pension unds and banking sec o a he look-
ing a he di e en sec o leade s join ly. In one o he s udies, he s abili y o mu ual
und pe o mance was in es iga ed in he sho and long e m using mon hly e u ns
including Sha pe a io calcula ion (Akel, 2007). O he s udies, such as (Ko kmaz &
Uygu u k, 2008), (Dagli & E , 2008), and (Eken & Pehli an, 2009), also calcula ed
Sha pe a io alues in mu ual und analysis. (Uya & Gokce, 2008) measu ed he
daily e u ns o equi y unds using he Sha pe a io and Jensen Alpha, while (Kok
2940
O.E kaya e al.
& E ikci, 2015) compa ed he pe o mance o di e en ypes o mu ual unds o he
pe o mance o he BIST100 index using a ious pe o mance indices. The e a e
also mo e speci ic s udies, such as (A maca, 2022) conside ed he elec ici y ma ke
in Tu key, and (Ocal & Kamil, 2021) compa ed he BIST100 da a wi h he Indone-
sian S ock Exchange ma ke wi hou any dependence modeling. In ano he banking-
sec o ocused s udy, (Bagci, 2022) in es iga ed he pe o mance o he s ocks o 7
banks egis e ed a he Bo sa Is anbul Liquid Bank Index by calcula ing bo h Sha pe
and So ino a ios, o he yea s 2017-2021. O e all, up o he au ho s knowledge,
he e is no s udy ha in es iga ed he e u n pe o mances ied o ine copulas. In
ha espec , ou wo k con ibu es o he exis ing li e a u e in a unique and comp e-
hensi e way.
3 Me hodology
This sec ion explains he me hods combined in analyzing he se e al cha ac e is ics
o inancial asse s. The i s aspec is ime se ies modeling o inco po a e mean and
ola ili y ends o s ocks. The second pa is abou he Vines o model he depend-
ency be ween he asse s, ha can c ea e a sys emic isk i i is igno ed. We explain
he po olio cons uc ion and isk measu e es ima ions. Las ly, we p esen he ali-
da ion o isk measu es using back es ing me hods a he end o his sec ion.
3.1 ARMA‑GARCH Model
To model he s anda dized esiduals ia copula, one i s needs o unde ake a uni-
a ia e ime se ies analysis (Pa on, 2012; Zhang & Singh, 2019). To model bo h he
end and non-cons an ola ili y inhe en in inancial ime se ies da a, we op o use
an ARMA-GARCH model. The e u n se ies is desc ibed as an au o eg essi e mo -
ing a e age model, ARMA(p,q), as ollows
whe e,
is e u n a ime ,
𝜀
is a whi e noise se ies, c is a cons an ,
𝛼i≠0
and
𝛽j≠0
a e AR(p) and MA(q) pa ame e s.
As a gene alized e sion o au o eg essi e condi ional he e oscedas ici y
(ARCH), a GARCH model is used o modeling he ola ili y and ocuses on he
e o e m
𝜀
. GARCH(m,n) model is exp essed as
whe e
z ∼D(0, 1)
a e iid, w is a cons an ,
ai≥0
,
bj≥0
, and
∑
a
i+∑
b
j≤0
a e
GARCH pa ame e s.
(1)
=c+
p
∑
i=1
𝛼i −1+
q
∑
j=1
𝛽j𝜀 −j+𝜀
,
(2)
𝜀 =𝜎 z
(3)
𝜎
2
=w+
m
∑
i=1
ai𝜀2
−i+
n
∑
j=1
bj𝜎2
−
j
2941
Vine Copula App oach oUnde s and heFinancial Dependence…
He e,
z
can be aken as any dis ibu ion o co ec ly e lec he ea u es o he
da a modelled. By using he guidance o he li e a u e in his subjec , we compa e
s anda d no mal (no m), S uden ’s (s d), and skewed S uden ’s -dis ibu ions (ss d)
o
z
in he po olio analysis pa .
3.2 Vine Copula
A d-dimensional copula is a mul i a ia e join dis ibu ion unc ion ha connec s
numbe o d ma ginal dis ibu ions. As in oduced by Skla (1959), he mul i a i-
a e dis ibu ion unc ion F o d andom a iables
X1,…,Xd
wi h ma ginal dis ibu-
ion unc ions
F1(x1)=u1,…,Fd(xd)=ud
can be desc ibed by a copula unc ion,
C∶[0, 1]d
→
[0, 1]
such ha
Based on he dependence s uc u e, he e a e wo main ypes o copulas: (i) The
ellip ical copula is sui able o modeling symme ic dependence, and (ii) The A chi-
medean copula is sui able o asymme ical dependence. Fo mul i a ia e cases,
especially wi h he inc eased dimension, A chimedean copula models become mo e
complex, challenging o use, and exhibi some pa ame e limi a ions al hough hey
a e mo e sui able o non-no mal inancial da a. As an al e na i e, he complexi y o
a d-dimensional dis ibu ion can be exp essed easily wi h he help o PCCs, namely
Vines. Fi s p oposed by Joe (1996) and la e de eloped by Aas e al. (2009), ine
copulas o e a lexible g aphical model o desc ibing complex mul i a ia e depend-
ence by a ich a ie y o pai -copulas. Pai -copulas can be a anged and analyzed in
a g aphic ee s uc u e o acili a e he analysis o mul iple dependencies.
A Vine deno ed as V on d a iables consis s o connec ed ees
V={T1,…,Td−1}
,
and he edges o ee j a e he nodes o ee
j+1
,
j=1, …,d−2
. An R-Vine copula
on d a iables is a ine in which wo edges in ee j a e joined by an edge in ee
j=1
only i hese edges sha e a common node,
j=1, …,d−2
. Hence, i p o ides
a single op imal PCC. In a d dimensional case,
d(d−1)∕2
bi a ia e pai copulas a e
selec ed o
(d−1)
numbe o ees. The i s oo -node models he dependence wi h
espec o a selec ed a iable. Condi ional on he selec ed a iable, he second oo -
node models he dependence wi h espec o ano he a iable. Following he same
s uc u e, all pai -copulas a e selec ed condi ionally on he selec ed a iables.
The pd o a d-dimensional X can be deno ed as
whe e,
i(xi)
i=1, 2, …,d
a e he ma ginals. The bi a ia e decomposi ion o
X1
and
X2
wi h pai copula
c1,2
is as ollows
Linked o ha , he condi ional p obabili y is
(4)
F
(x
1
,x
2
,…,x
d
)=C
(
F
1
(x
1
),F
2
(x
2
),…,F
d
(x
d
)
)
=C(u
1
,…,u
d
)
.
(5)
(x
1
,x
2
,…,x
d
)=
1
(x
1
)
2∣1
(x
2
∣x
1
)
3∣1,2
(x
3
∣x
1
,x
2
)
…
d∣x1,x2,…,xd−1
(x
d
∣x
1
,x
2
,…,x
d−1
)
,
(6)
1,2
(x
1
,x
2
)=c
1,2(
F
1
(x
1
),F
2
(x
2
)
)
1
(x
1
)
2
(x
2
)
.
2942
O.E kaya e al.
PCCs do no ha e a unique solu ion. The e o e egula ines can be used o o gan-
ize simpli ied PCCs (Bed o d & Cooke, 2001). Le he e be
ℕ
nodes and
𝜀
edges,
such ha
ℕ={N1,…,Nd−1}
and
𝜀∈{E1,…,Ed−1}
. Condi ioned nodes a e de ined
as j(e) and k(e), and he condi ioning se is de ined as D(e). R-Vine copula is hen
yields as he ollowing join densi y equa ion
Hence, cons uc ion o a ine copula is no s ic , and a la ge numbe o di e en
pai copula models can be selec ed. Vine copulas can be in es iga ed wi h he help
o g aphical ep esen a ion o R-Vines. We use he sequen ial me hod (s onges
dependencies) in de e mining he ees o R-Vine wi h Kendall’s
𝜏
measu e gi en in
Eq.(9). This s ep-wise cons uc ion p o ides compu a ional ease and e ec i eness.
Akaike in o ma ion c i e ion (AIC) and Bayesian in o ma ion c i e ion (BIC) a e
he mos common s a is ics used o selec he bes copula model and a e compu ed
using he ollowing equa ions
whe e,
pei
−pi
is he di e ence be ween empi ical and heo e ical p obabili ies, N
is he sample size, k is he numbe o pa ame e s and L is he maximum likelihood
unc ion alue o he model.
In his abo e se ing, he ull model speci ica ion equi es (i) The choice o
he Vine ee s uc u e, (ii) Copula amilies o each pai , and (iii) Thei co e-
sponding pa ame e s. The selec ion o di e en copula amilies s ands o dis inc
dependence pa e ns. The well-known ellip ical amilies a e Gaussian and he
S uden ’s -copulas. The Gaussian copula is symme ic and has no ail depend-
ence (Aloui e al., 2013). S uden ’s copula shows symme ic ail dependence.
Among all A chimedean ypes; Clay on, Gumbel, F ank, and Joe a e p ima y
examples o one-pa ame e amilies. The Clay on copula has highe depend-
ence in he lowe ail, while he Gumbel copula has highe dependence in he
uppe ail (Aloui e al., 2013). Fu he mo e, Joe copula cap u es he posi i e ail
dependence. As combina ions o hese amilies, wo-pa ame e copulas such as
(7)
2∣1
(x
2
∣x
1
)=c
1,2(
F
1
(x
1
),F
2
(x
2
)
)
2
(x
2
)
.
(8)
(x1,…,xd)=
[d
∏
k=1
k(xk)]
×
[
d−1
∏
i=1
∏
e∈E
i
cj(e),k(e)∣D(e)
(
F
(
xj(e)∣xD(e)
)
,F
(
xk(e)∣xD(e)
))].
(9)
𝜏
(x,y)=4
∫1
0∫1
0
C(u, )dC(u, )−
1
(10)
AIC =2k−2 ln(L),
(11)
BIC
=Nln
(
1
N
N
∑
i=1
(pei −pi)2
)
+kln(N)
,
2949
Vine Copula App oach oUnde s and heFinancial Dependence…
Fig. 1 Dependence o he
inance sec o o sub-pe iods
(a)P e-GFCpe iod
(b)GFC pe iod
(c)Pos -GFCpe iod

2950
O.E kaya e al.
(GARAN, ISCTR) and (ALARK, SKBNK)-(ECILC, ISFIN) o he GFC pe iod
(Fig.1b) whe eas (ISCTR, YKBNK) and (ALARK, ISFIN) o pos -GFC pe iod
(Fig.1c), espec i ely. These di e ences indica e he mos p ominen ac o s in he
inance sec o . The i ed ine copula models p esen a simila endency on di e en
sub-pe iods. Log-likelihood esul s show ha R-Vine pe o ms he bes acco ding
o he AIC and BIC in each pe iod, which ma ches wi h he p e ious s udies in he
li e a u e. Figu es2 and 3 shows he es ima ed R-Vine ees (1’s and 2’nd le el) o
p e-GFC pe iod wi h he selec ed pai copulas and dependence pa ame e s.
In Fig. 2, he edges show bo h he selec ed pai copulas wi h hei depend-
ence pa ame e s in pa en hesis. Fo many pai s, one pa ame e amily is selec ed
excep o he pai s (AKBNK, ISCTR), (GARAN, ISCTR), (ISCTR, ALARK), and
(YKBNK, SKBNK). Mo e impo an ly, he selec ed copulas exhibi ail dependen-
cies o he s ock pai s, ie. (ISCTR, YKBNK) is modeled ia su i al Gumbel (SG)
wi h
𝜃=1.72
. In his i s le el, he ee s uc u e shows ha many o he s ocks a e
di ec ly ela ed o ISCTR, whe e wo excep ions a e ISFIN and SKBNK. In Fig.3,
one can see he i s condi ional copula pai s o he second ee le el. Simila o he
i s ee le el, many o he selec ed copulas a e A chimedean ypes excep he pai
(ISCTR, SKBNK
∣
YKBNK). Simila ly, he i s wo ee le els a e isualized o
T ee 1
(0.69,8.83)
SBB8(3.2,0.7)
BB1(0.62,1.4)
SG(1.72) SG(1.46)
SBB1(0.2,1.45)
N(0.69)
SG(1.47)
1
9
2
56
7
3
4
8
1 ... AKBNK
2 ... GARAN
3 ... ISCTR
4 ... SAHOL
5 ... YKBNK
6 ... ECILC
7 ... ALARK
8 ... ISFIN
9 ... SKBNK
Fig. 2 R-Vine ee s uc u e o ee 1 wi h pai copulas on p e-GFC pe iod
2951
Vine Copula App oach oUnde s and heFinancial Dependence…
he GFC and he pos -GFC o highligh he changes in copula selec ion and depend-
ence s uc u e.
Figu e4 shows a di e en ee s uc u e o he i s le el. Fo a ious uncondi-
ional copula pai s, one-pa ame e amilies a e selec ed excep o he pai s (ISCTR,
SAHOL), (GARAN, YKBNK), (GARAN, ISFIN), and (GARAN, SKBNK). In
many o he pai s, simila o wha we ob ained in Fig.2, he selec ed copulas exhibi
dis inc ail dependencies o he s ock pai s. Fo example, (ISCTR, ECILC) pai
has Su i al Gumbel (SG) copula wi h dependence pa ame e
𝜃=1.61
. In his i s
le el, he ee s uc u e shows ha many o he s ocks a e di ec ly ela ed o s ocks
GARAN and ISCTR. Fo he second ee le el, illus a ed in Fig.5, A chimedean
copulas play an impo an ole again. In con as o he i s ee le el, all o he
selec ed copulas a e one-pa ame e amilies. Fo he condi ional copula unc ions,
he s ocks (ISCTR, YKBNK, ISFIN, and SKBNK) exhibi dependencies condi-
ioning on (GARAN) on he uppe pa , whe eas he pai s (AKBNK, GARAN),
(AKBNK, SAHOL), (SAHOL, ECILC) and (ECILC, ALARK) a e all dependen
condi ioning on he s ock ISCTR. These wo le els simply imply he impo ance
o he s ocks GARAN and ISCTR o he inance sec o . To illus a e, (ECILC,
ALARK
∣
ISCTR) a he bo om implies ha he e exis s a lowe ail dependence
(Clay on wi h
𝜃=0.41
) o he (ECILC, ALARK) pai s gi en ISCTR.
T ee 2
SG(1.27)
N(0.21)
F(1.7)
F(1.81)
C(0.3)
F(1.92)
C(0.29)
3,1
5,9
3,2
3,5
3,6
3,7
4,3
8,4
1 ... AKBNK
2 ... GARAN
3 ... ISCTR
4 ... SAHOL
5 ... YKBNK
6 ... ECILC
7 ... ALARK
8 ... ISFIN
9 ... SKBNK
Fig. 3 R-Vine ee s uc u e o ee 2 wi h pai copulas on p e-GFC pe iod
2952
O.E kaya e al.
In Fig.6 o pos -GFC, once again, ISCTR has a cen al ole in he i s ee le el.
In his pe iod, all selec ed copula unc ions exhibi dis inc ail dependencies includ-
ing symme ic ones o he pai s (AKBNK, ISCTR) and (AKBNK, SAHOL) ha ing
S uden ’s -copula wi h
𝜃=0.79
and
𝜃=0.63
, espec i ely. Simila o he p e-GFC
pe iod, many o he s ocks a e di ec ly ela ed o ISCTR excep SAHOL, ALARK,
and ISFIN. Fo he second ee le el, illus a ed in Fig.7, A chimedean ype ami-
lies appea again wi h di e en dependence pa e ns. In his le el o he pos -GFC
pe iod, all selec ed copulas a e one-pa ame e amilies excep SBB8 o he pai
(AKBNK, GARAN
∣
ISCTR). Fo he condi ional copula unc ions, he assigned
condi ioning a iable is much mo e a ian compa ed o he esul s o he p e-GFC
and GFC pe iods. Fo example, he pai (GARAN, YKBNK) is dependen gi en
ISCTR (F ank,
𝜃=2.49
) whe eas (ISCTR, ALARK) is weakly dependen gi en he
s ock YKBNK (Clay on,
𝜃=0.19
) ( he middle pa o Fig.7).
Fo he simplici y, only i s wo ees a e p esen ed whe eas one can do he o -
wa d ace o examine he no iceable di e ences on each pai copula. Fo inance
sec o , he bes selec ed pai copula is a ying h oughou p e-GFC o pos -GFC
wi h di e en ail dependence p ope ies. A a ious le els in he ee s uc u e, he
ob ained pai copulas can be summa ized in e ms o coun ing/g ouping me hod as
in Table4 (He nandez, 2015). Based on he selec ed copula amilies, i is impo -
an o highligh he changing dependence pa e ns o e di e en pe iods o global
T ee 1
N(0.6)
SG(1.61)
BB1(0.29,1.69)
N(0.8)
(0.79,7.67)
BB1(0.61,1.35)
N(0.83)
(0.7,6.9)
7
6
4
1
5
8
3
2
9
1 ... AKBNK
2 ... GARAN
3 ... ISCTR
4 ... SAHOL
5 ... YKBNK
6 ... ECILC
7 ... ALARK
8 ... ISFIN
9 ... SKBNK
Fig. 4 R-Vine ee s uc u e o ee 1 wi h pai copulas on GFC pe iod
2953
Vine Copula App oach oUnde s and heFinancial Dependence…
inancial c isis. In Table4, he mos selec ed amily in p e-GFC, su i al Gumbel,
indica es ha he e exis s lowe ail dependencies o he s ock pai s (asymme ic
ype o dependence). Fo GFC pe iod (bea ma ke ), he impac o Gaussian and
F ank exhibi s no ail dependence a a ious ee le els o i ed R-Vine model. The
F ank amily appea s he mos o pos -GFC pe iod whe eas only one Gaussian am-
ily is selec ed. Fo pe iods o GFC and pos -GFC (especially inc eased numbe o
F ank pai s), i is ob ious ha he mos o he dependence is concen a ed in he
cen e o he join dis ibu ions. This inding indica es ha he s ocks in he inance
sec o ha e high dependence isk when he ma ke is no s able. Addi ionally, du ing
GFC, he la ges p esence o Gaussian copula implies ha he mos o he depend-
ence ela ionship a e mainly linea ype. Ne e heless, o p e-GFC pe iod, mos o
he dependence is loca ed in he lowe ail (Clay on, su i al Gumbel and BB8 ami-
lies). The lowe ail dependence concen a ion is sugges ing ha he inance sec-
o ha e high dependence isk in bea ma ke condi ions and low dependence isk
when he inancial ma ke s a e s able. O e all, he dependence pa e n be ween he
s ocks o h ee di e en pe iods encoun e s a ious changes, e lec ed by he ee
s uc u es, he bes i ed copula and de i ed dependence deg ees. Ne e heless, he
dependence pa ame e s always show a posi i e ela ionship be ween he s ocks in
he inance sec o .
Simila o he ela ed li e a u e, he ad an age o exploi ing he R-Vines o cap-
u ing he complex pa e ns o dependency is easy o obse e in e ms o di e en
T ee 2
C(0.41)
C(0.3)
N(0.29)
N(0.37)
SG(1.33)
SG(1.16)
F(1.79)
3,7
3,6
3,4
3,1
2,5
2,8
2,3
9,2
1 ... AKBNK
2 ... GARAN
3 ... ISCTR
4 ... SAHOL
5 ... YKBNK
6 ... ECILC
7 ... ALARK
8 ... ISFIN
9 ... SKBNK
Fig. 5 R-Vine ee s uc u e o ee 2 wi h pai copulas on GFC pe iod
2954
O.E kaya e al.
copula pai s and co esponding ail dependence p ope ies. As an illus a ion, R-Vine
copula speci ica ion ma ix o p e-GFC pe iod wi h addi ional de ails is displayed
in Tables17, 18 and 19 in Appendix2. Table17 summa ise how conside ed s ocks
a e ied oge he wi hin R-Vine copula model. Fo he ease o eading, he o de ing
o he s ock names gi en in Figs.2 and 3 a e impo an . Fo ins ance, he in ege
numbe s in he bo om ow wi h he diagonal en ies in Table17 exhibi which pai s
a e connec ed o he uncondi ional copulas ( i s ee le el), ie. (1,3) s ands o he
s ock pai (AKBNK, ISCTR). In his ma ix ep esen a ion, Table18 shows which
copula amily a e i ed o cap u e dependencies be ween he pai s o indices. To
illus a e, by ollowing he same guideline, he i s indica ed in ege a he bo om
ow o Table18 co esponds o he S uden ’s -dis ibu ion wi h one o he es ima ed
pa ame e s is p esen ed in he same en y o he Table19. This eading implies he
s ock pai (AKBNK, ISCTR) is modeled wi h S uden ’s -copula ha ing lowe and
uppe ail dependencies symme ically, o he p e-GFC pe iod. This in o ma ion
basically implies he join beha io o wo s ocks o small o la ge alues be o e he
global inancial c isis. This join co-mo emen is swi ched o he ela ionship wi h-
ou a ail dependence du ing GFC (Gaussian) and u ned back o he one wi h bo h
ail dependencies du ing pos -GFC pe iod (S uden ’s ). I is in e es ing o highligh
ha o he GFC pe iod, he s ock pai s (AKBNK, ISCTR) show g ea e dependence
in he cen e o he join dis ibu ions.
T ee 1
(0.63,10.07)
(0.79,6.27)
SG(1.56)
BB1(0.83,1.77)
SG(1.48)
BB1(0.86,1.82)
SG(1.61)
(0.59,12)
4
1
8
2
7
5
6
3
9
1 ... AKBNK
2 ... GARAN
3 ... ISCTR
4 ... SAHOL
5 ... YKBNK
6 ... ECILC
7 ... ALARK
8 ... ISFIN
9 ... SKBNK
Fig. 6 R-Vine ee s uc u e o ee 1 wi h pai copulas on pos -GFC pe iod

2955
Vine Copula App oach oUnde s and heFinancial Dependence…
To conse e space, he R-Vine copula model speci ica ion is jus illus a ed
o he p e-GFC pe iod o inance sec o wi h he ma ix ep esen a ion (Fu -
he de ails abou he GFC and p e-GFC pe iods o inance sec o a e a ailable
upon eques ). He ein, only he i ed pai copula amilies and hei indica ions
o o he sec o s a e summa ized by Tables5, 6, 7, 8 and 9 ega ding he copula
coun ing/g ouping app oach. Especially, o examine whe he he majo inancial
shock caused a no iceable change in dependencies o no , he summa ized cop-
ula amilies and ail dependence p ope ies o each sec o can gi e mo e insigh
abou he eac ion o s ocks in ISE100.
Table5 illus a es ha he mos selec ed copula amilies o he basic ma e i-
als sec o a e g ouped unde lowe ail dependence, ha ing he Su i al Gumbel
as he mos appea ed amily. Wi h he di e ence o inance sec o , he e is no so
much impac o Gaussian and F ank amilies o all sub-pe iods. Addi ionally, he
la ges p esence belongs o lowe ail dependence amilies wi h addi ional lowe /
uppe ail dependence pa e n o wo pa ame e amilies (S uden ’s and BB1)
T ee 2
SG(1.19)
SBB8(2.64,0.77)
F(1.19)
F(2.49)
C(0.19)
F(1.16)
F(1.46)
1,4
3,1
2,8
3,2
5,7
3,5
3,6
9,3
1 ... AKBNK
2 ... GARAN
3 ... ISCTR
4 ... SAHOL
5 ... YKBNK
6 ... ECILC
7 ... ALARK
8 ... ISFIN
9 ... SKBNK
Fig. 7 R-Vine ee s uc u e o ee 2 wi h pai copulas on pos -GFC pe iod
2956
O.E kaya e al.
du ing GFC pe iod. Gene ally, he lowe ail dependence concen a ion is sug-
ges ing ha he s ocks in inance sec o ha e high dependence isk in each sub-
pe iod o he s ocks unde basic ma e ials sec o . Ano he di e ence is ha , as a
esul o limi ed numbe o s ocks (
p=4
), independence copula did no appea
o any le el o i ed R-Vine ee.
Copula selec ions o he cons cyclicals in Table6 shows ha he mos appea ed
amilies ha e lowe ail dependence. I illus a es ha he selec ed copula amilies
a e g ouped mos ly unde lowe ail dependence, ha ing Clay on (4 imes) o p e-
GFC mo e equen ly. The e exis s one uppe ail dependence amily (Gumbel) o
he consume cyclicals sec o (a he las ee le el). Simila o inance sec o , o
Table 4 R-Vine copula selec ion
o he inance sec o Selec ed copula amilies P e-GFC GFC Pos -GFC
Only lowe ail
Clay on (3) 5 4 6
Su i al Gumbel (14) 9 6 8
Su i al BB8 (20) 1 – 1
Only uppe ail
Gumbel (4) – 1 –
Su i al Clay on (13) 1 1 –
Lowe and uppe ail
S uden ’s (2) 1 2 3
BB1 (7) 1 2 2
Su i al BB1 (17) 1 – –
No Lowe /Uppe ail
No mal (1) 4 7 1
F ank (5) 4 5 11
No dependence
Independence (0) 9 8 4
Table 5 R-Vine copula selec ion
o he basic ma e ials sec o Selec ed copula amilies P e-GFC GFC Pos -GFC
Only lowe ail
Clay on (3) 2 1 –
Su i al Gumbel (14) 2 2 4
Su i al Joe (16) 2 – –
Su i al BB8 (20) – – 1
Lowe /Uppe ail
S uden ’s (2) – 1 –
BB1 (7) – 1 –
No Lowe /Uppe ail
No mal (1) – – 1
F ank (5) – 1 –
2957
Vine Copula App oach oUnde s and heFinancial Dependence…
Table 6 R-Vine copula selec ion
o he cons cyclicals sec o Selec ed copula amilies P e-GFC GFC Pos -GFC
Only lowe ail
Clay on (3) 4 1 –
Su i al Gumbel (14) 3 3 3
Su i al Joe (16) – – 1
Only uppe ail
Gumbel (4) 1 – –
Lowe /Uppe ail
S uden ’s (2) – 1 –
BB1 (7) – 1 –
Su i al BB1(17) – – 1
No Lowe /Uppe ail
No mal (1) 1 3 3
F ank (5) 1 1 1
No dependence
Independence (0) – – 1
Table 7 R-Vine copula selec ion
o he cons non-cyclicals sec o Selec ed copula amilies P e-GFC GFC Pos -GFC
Only lowe ail
Clay on (3) 5 5 2
Su i al Gumbel (14) 7 7 9
Su i al Joe (16) 1 1 –
Su i al BB8(20) – – 1
No Lowe /Uppe ail
No mal (1) 2 2 1
F ank (5) 3 3 2
No dependence
Independence (0) 3 3 5
Table 8 R-Vine copula selec ion
o he indus ial sec o Selec ed copula amilies P e-GFC GFC Pos -GFC
Only lowe ail
Clay on (3) 2 2 –
Su i al Gumbel (14) 1 – 2
Su i al Joe (16) – 1 –
No Lowe /Uppe ail
No mal (1) – – 1
2958
O.E kaya e al.
pe iods o GFC and pos -GFC, he inc eased numbe o Gaussian copulas indica e
ha some pa o he dependence is concen a ed in he cen e alongside wi h he
lowe ail dependence by selec ed su i al Gumbel. When we ha e a close look a
he ee s uc u e, he appea ance o No mal and su i al Gumbel amilies do no
exhibi any pa e n so ha he iden i ica ion o he join beha io o he consid-
e ed s ocks a e no easy o in e p e o GFC pe iod. On he o he side, o he pos -
GFC pe iod, su i al Gumbel amilies appea s mos ly in he i s ee le el ha he
uncondi ional lowe ail dependence concen a ion among he s ocks is sugges ing
ha s ill hey ha e high dependence isk.
The dominance o he lowe ail dependence is s ill alid o he s ocks conside ed
unde he sec o consume non-cyclicals (Table7). The mos selec ed copula amily
o each sub-pe iod is Su i al Gumbel (7 o p e-GFC and GFC, 9 o pos -GFC
indica ing ha he dependence du ing he pos -GFC pe iod is mo e o asymme -
ic ype). F om GFC o pos -GFC s a es, he cen al dependence is eplaced by he
lowe ail dependence o independence ega ding he in e -dependencies be ween
he s ocks. Simila o many discussed cases be o e, he e is no uppe ail dependence
and p ima ily he dependence concen a ion in he lowe ail indica es ha any con-
s uc ed po olio wi h he men ioned s ocks has high dependence isk in any sub-
pe iod. This in o ma ion gi es an impo an clue abou how he op imum po olio
should be es ablished when he inancial s ock ma ke s do no beha e smoo hly. In
ha sense, any po olio ocused on only he s ocks belonging o ha sec o ha e
highe isk ega dless o he exis ence o bea o s able ma ke .
In Tables8 and 9, he dominance o he lowe ail dependence can be iden i ied
i s . The only di e ence is ha he s ocks unde he indus ial sec o ha e solely
lowe ail dependence (Table8), whe eas he s ocks ha a e classi ied unde he o h-
e s ha e also cen al dependence (mo e Gaussian case in Table9). Addi ionally, he
selec ed amilies a e mo e di e si ied o he case o he o he s sec o compa ed o
he indus ial. Mo e speci ically, one o he amilies is Su i al BB1 o pos -GFC
pe iod in Table8 ha shows a join beha io o he e u ns whe e he p ices a e bo h
dec easing o inc easing. In ha sense, o minimize he isk o any po olio, selec-
ion o s ocks om di e en sec o s could be use ul o decision make s. F om GFC
Table 9 R-Vine copula selec ion
o he o he s sec o Selec ed copula amilies P e-GFC GFC Pos -GFC
Only lowe ail
Clay on (3) 2 – –
Su i al Gumbel (14) 2 3 3
Lowe /Uppe ail
Su i al BB1 (17) – – 1
No Lowe /Uppe ail
No mal (1) – 2 2
F ank (5) 1 1 –
No dependence
Independence (0) 1 – –
2965
Vine Copula App oach oUnde s and heFinancial Dependence…
(a) ShR alues (b)SoR alues
Fig. 14 Re u n pe o mance o p e-GFC pe iod o 250 days olling windows
(a) ShR alues (b)SoR alues
Fig. 15 Re u n pe o mance o GFC pe iod o 250 days olling windows
(a) ShR alues (b)SoR alues
Fig. 16 Re u n pe o mance o pos -GFC pe iod o 250 days olling windows

2966
O.E kaya e al.
(a) ShR alues (b)SoR alues
Fig. 17 Re u n pe o mance o p e-GFC pe iod o 100 days olling windows
(a) ShR alues (b)SoR alues
Fig. 18 Re u n pe o mance o GFC pe iod o 100 days olling windows
(a) ShR alues (b)SoR alues
Fig. 19 Re u n pe o mance o pos -GFC pe iod o 100 days olling windows
2967
Vine Copula App oach oUnde s and heFinancial Dependence…
In he case o 100-days, he ShR and SoR a ios became mo e ola ile in R-Vine
GARCH app oach, bu s ill highe han o he GARCH models mos o he ime.
Besides, he dominance o SoR o e ShR a ios, shows us he downside ola ili y
is less han mean ola ili y in isky pe iod o p e- GFC and GFC sub-pe iods (as
shown in Figs.17 and 18). Howe e , e en i R-Vine GARCH model o en yields
highe e u n pe o mance, he equally weigh ed app oach seems a bi insu icien
du ing pos -GFC pe iod, owa ds he end o 2013, in Fig.19. O e all, he R-Vine
GARCH model pe o mance seems mo e adequa e o e classical GARCH esul s
o ce ain ime pe iods and di e en olling window size, whe eas bo h ShR and
SoR ha e highe disc epancy when 100-days ime-window is in es iga ed.
The impac o isk ee a e change is explo ed only du ing GFC pe iod and 250-
days olling window size. Fo he space limi a ion, he esul s a e summa ized in
Appendix3. The i s obse a ion is ha , o 250-days olling window size, R-Vine
GARCH model ou pe o ms i s compe i o s s ill o e he changing isk ee a e.
Du ing GFC pe iod, in all Figu es om23, 24 and 25, he ShR and SoR a ios a e
highe o he R-Vine GARCH app oach. When he isk ee a e is inc eased, i
illus a es ha he ShR a io alls abo e he isualized le els o SoR alues, com-
pa ed o he examined cases o
%5
isk ee a e.
4.5 COVID‑19 Pandemic C isis
The in es iga ions abou he sui abili y o R-Vine GARCH o an eme ging s ock
ma ke , as i is men ioned be o e, simila calcula ions ha e been made o he
COVID-19 pandemic pe iod. Fo ha pu pose, he eigh s ock alues (AKBNK,
EREGL, DOHOL, ARCLK, TUPRS, TCELL, ISGYO, and THYAO) ha we
explo ed in he po olio analysis a e conside ed mainly. Fo he pandemic ime
ho izon decision, we mainly elied on he announcemen s du ing he COVID-19
pandemic pe iod, bo h globally and na ionally. Gene ally, he pandemic pe iod has
been announced in Tu key s a ing on Ma ch 11, 2020 ( he i s COVID-19 case
announcemen ). To make a decision on he ending da e, Ap il 26, 2022 is consid-
e ed, as he da e o mask obliga ion was li ed and all places came back o egu-
la s a us in Tu key. O icially, he Wo ld Heal h O ganisa ion (WHO) decla ed ha
COVID-19 no longe cons i u es a pandemic in May 2023 bu we ied o a oid using
da a un il 2023 because o po en ial na ional-elec ion- ela ed impac s. O e all, his
new da a se co e s log- e u ns o main s ocks om Ma ch 11, 2020, o Ap il 26,
2022 (533 daily obse a ions). In his new examina ion, he same model compa i-
son esul s a e gene a ed a di e en isk ee a es (
R =%5, 10, 15, 20
) o measu e
i s po en ial impac on he Sha pe and So ino a ios. Besides, he impac o oll-
ing window size (
m=150, 250, 350
) and signi icance le el (
p=0.01, 0.05, 0.10
) is
explo ed u he on he isk measu e calcula ions.
The s uc u e o he inancial ma ke and e u n dynamics can a y ac oss coun-
ies and hese di e ences esul ed in he e ogeneous conside able shocks and wa es
in Tu key, as an eme gen ma ke . Du ing COVID-19 ime ho izon, in addi ion o
pandemic- ela ed shocks, he e we e ce ain na ional news o poli ical decisions ha
2968
O.E kaya e al.
may exace ba e oscilla ions in he Tu kish s ock ma ke . Speci ically, he e a e key
da es ela ed o pandemic c isis managemen ( a ying imings and cha ac e is ics o
lockdowns) and ce ain adminis a i e decisions (manage ial changes in he Cen al
Bank o he Republic o Tu key). Du ing his pe iod, he pe o mance o R-Vine
GARCH (VGARCH wi h ss d) seems o be p omising o e classical app oaches
o Tu kish s ock ma ke . Fo simplici y, only VaR and ES beha io di e ences a e
−10
−5
0
5
Jul−2020Jan−2021Jul−2021
Log−Re u n
GARCH_no m
GARCH_ss d
GARCH_s d
VGARCH_ss d
(a)VaR alues
−10
−5
0
5
Jul−2020Jan−2021 Jul−2021
Log−Re u n
GARCH_no m
GARCH_ss d
GARCH_s d
VGARCH_ss d
(b)ES alues
Fig. 20 Risk measu es o COVID-19 pe iod wi h 150 days as olling window size
−10
−5
0
5
Ap −2020Jul−2020Oc −2020Jan−2021Ap −2021
Log−Re u n
GARCH_no m
GARCH_ss d
GARCH_s d
VGARCH_ss d
(a)VaR alues
−10
−5
0
5
Ap −2020 Jul−2020 Oc −2020 Jan−2021 Ap −2021
Log−Re u n
GARCH_no m
GARCH_ss d
GARCH_s d
VGARCH_ss d
(b)ES alues
Fig. 21 Risk measu es o COVID-19 pe iod wi h 250 days as olling window size
−5
0
5
Ap −2020Jul−2020 Oc −2020
Log−Re u n
GARCH_no m
GARCH_ss d
GARCH_s d
VGARCH_ss d
(a)VaR alues
−10
−5
0
5
Ap −2020 Jul−2020Oc −2020
Log−Re u n
GARCH_no m
GARCH_ss d
GARCH_s d
VGARCH_ss d
(b)ES alues
Fig. 22 Risk measu es o COVID-19 pe iod wi h 350 days as olling window size
2969
Vine Copula App oach oUnde s and heFinancial Dependence…
summa ized g aphically unde di e en olling window size alues. O he ela ed
indings a e a ailable upon eques bu hey we e empi ically discussed b ie ly.
Mainly, Figs.20, 21 and 22 show he model compa ison summa y o e he VaR
and ES alues, showing he sui abili y o R-Vine GARCH as opposed o classical
GARCH models, o e he changing olling window size. Al hough he ime ho i-
zon ha we used o he one-day-ahead o ecas ing is sligh ly changed, he plau-
sibili y o he VGARCH model wi h ss d is p ese ed. Addi ionally, his app oach
seems success ul in eac ing o ce ain e u n d ops o speci ic da es. Fo he case
o
m=250
, as a esul o he i s lagged COVID-19 shock o e he ma ke and
u he economical decisions, he e is a big decline and VGARCH seems mo e sen-
si i e o his change. Du ing Ma ch 2020, wo main news we e he in e es a e cu
made by Cen al Bank o he Republic o Tu key (17 Ma ch, 2020) and FED asse
pu chase decision (24 Ma ch, 2020). Simila ly, du ing Decembe 2020, he accele -
a ing impac o lockdowns in a ious economics including Tu key, and local ma ke
dynamics po en ial easons o ano he la ge decline. Besides, sudden and poli ical
manage ial changes a he Cen al Bank o he Republic o Tu key occu ed du -
ing Ma ch 2021 wi h a ce ain nega i e impac on he us wo hiness o he ma ke
mo emen dynamics. In such mo emen s, he sensi i i y o VGARCH model seems
compa a i ely highe han o he GARCH ype app oaches. This gene al pa e n can
be obse ed unde he impac o di e en olling window size o bo h VaR and ES
alues. Besides, wi hin di e en pa ame e cons ain s, simila pa e n appea ed
mos o he ime and his empi ically suppo s he use o VGARCH model wi h ss d
o measu ing he Tu kish s ock ma ke dependencies. Rega ding he VaR and ES
back es ing esul s, he VGARCH model esul ed in signi ican esul s wi h LR Tes
p- alues la ge han 0.05 le el unde di e en olling window size. In ha espec ,
he indings o e COVID-19 pe iod a e aligned wi h he p e iously summa ized
GFC pe iod.
5 Conclusions
This s udy uses he R-Vine copula amewo k o wo main pu poses: (i) To de ec
he in e -dependencies be ween s ocks and (ii) To cons uc a mo e lexible po olio
o e di e en sec o s. Fo he i s goal, he R-Vine copula is conside ed o he daily
log e u ns o he ISE100 s ocks in he Tu kish inancial ma ke o h ee pe iods;
p e-GFC, GFC, and pos -GFC. P ima ily, he il e ed log e u ns a e modeled ia
R-Vine o e h ee sub-pe iods o exhibi signi ican changes in he dependence pa -
e n be ween he s ock alues. In he second pa , we compa e he R-Vine based
GARCH(1,1) model wi h ss d inno a ions agains o he classical GARCH(1,1)
ype models wi h di e en inno a ions. The widely used olling window app oach
allowed us o es ima e one-day-ahead e u ns and compu e dynamic VaR and ES
isk measu es. The back es ing me hods indica e ha he R-Vine based app oach is
mo e sui able o mo e esilien isk managemen o he Tu kish inancial ma ke .
Addi ionally, he isk measu es calcula ions a e suppo ed by he Sha pe and So ino
2970
O.E kaya e al.
a io beha io s. Speci ically, he po en ial impac o isk ee a e is in es iga ed o e
he GFC pe iod. To he bes o he au ho ’s knowledge, he main indings o his
s udy cons i u e he mos comp ehensi e wo k on he Tu kish ma ke and ex end he
a ailable li e a u e by o e ing an in-dep h analysis o he s ock’s ma ke depend-
ence s uc u e and isk dynamics a ached o i s pe o mance by exploi ing he use
o R-Vine copulas.
The op imal pai copulas o he sec o s, o e h ee sub-pe iods, exhibi asym-
me ical cases o dependency be ween s ock e u ns in he Tu kish inancial ma ke .
Indica ing ha , s ock e u ns a e bes explained by asymme ical copulas. Ano he
signi ican disco e y is ha , when he inancial indus y is excluded, he e a e only
a ew si ua ions o e a sho pe iod whe e he S uden ’s -copula demons a es sym-
me ic lowe and uppe ail dependency. Speci ically, he shi ed dependence s uc-
u e om he lowe - ail (su i al Gumbel) o he cen e (F ank) o he inance sec-
o implies inc eased con idence in s ocks a ached o he high e u ns belonging o
he inance sec o ( om p e- o pos -GFC pe iod). This inding can be seen as a
e lec ion o he inc easing lexibili y o he de eloping ma ke s, and changing eg-
ula o y en i onmen s in he pos -GFC pe iod. Rega ding he ac ha he Tu kish
inancial sec o is p edominan ly composed o banks, s uc u al e o ms s a ing in
2001 in he banking sec o made he inance sec o mo e esis an o he impac s o
he GFC.
O e all, he mos selec ed copula amilies a e lowe - ail copulas; Clay on, and
su i al Gumbel o di e en pe iods. This esul suppo s he p e ious c i icism
o he Gaussian copulas du ing a c isis. The main indings show a high depend-
ence isk be ween s ocks unde non- anquil condi ions, and a low dependence isk
when he s ock ma ke mo es smoo hly. The a ying dependence on he s ocks o
each sec o shows he impo ance o he po olio di e si ica ion. Fo his eason,
he dynamic use o he R-Vine model ins ead o classical GARCH- ype ools will be
use ul o es ima e mo e obus VaR and ES measu es. Speci ically, he ad an age o
combining R-Vine and GARCH models is bene icial in de ec ing asymme ical and
a - ailed dis ibu ions o s ock e u ns. He ein, he equally weigh ed po olio con-
s uc ion o e he selec ed leade s (weigh o 26.46% in ISE100) is a good indica o
o he gene al beha io in he s ock ma ke . F om his poin o iew, a mo e p ecise
iden i ica ion o he dependence s uc u e among hese sec o leade s o e s p ac ical
implica ions o in es o s and policymake s. Speci ically, he indings o he s udy
can se e as a gene ic ool o in es men and hedging pu poses o e mo e ola ile
pe iods.
Impo ance o examining he dependence be ween di e en s ocks o isk meas-
u es ha e been unde lined wi h he help o empi ical indings belong o he COVID-
19 pe iod. Unde he impac o di e en economic shock wa es, he use o R-Vine
GARCH is shown o be p omising o an eme ging s ock ma ke . By conside -
ing a ious pa ame e alues du ing he calcula ion, he sui abili y o he R-Vine
GARCH has been es ed and i is shown ha , he calcula ed isk measu es a e pe -
o ming be e han he classical GARCH ype models. Simila o he p e iously
discussed e u n pe o mance, Sha pe and So ino alues once again suppo ed he
indings posi i ely. In ha espec , o wo di e en c isis pe iod, modeling s ock

2971
Vine Copula App oach oUnde s and heFinancial Dependence…
dependencies ia R-Vine GARCH model o u he isk measu e calcula ions seem
mo e sui able o Tu kish ma ke .
Al hough he main indings o he s udy a e compe en and in o ma i e abou
a ying dependence s uc u es in he Tu kish ma ke , he e a e ce ain di ec ions
o imp o e he conside ed app oach. As an expansion o he conside ed R-Vine
GARCH amewo k, he ime o a iable dependen app oach can be inco -
po a ed o he simila se ing. Speci ically, h ough he use o non-simpli ied
pai copulas can be conside ed o conside he changing dependence pa e ns in
he Tu kish s ock ma ke unde globally accep ed indica o s such as exchange
a es and liquidi y condi ions. Conside ing ha he Tu kish inancial ma ke is
a de eloping one, and a ec ed by global ac o s, such impac s can be included
in he design. The equally weigh ed po olio cons uc ion can be eplaced by
an op imal po olio. E icien on ie analysis can be conside ed unde di e -
en cons ain s. F om a di e en pe spec i e, a wa ele -based R-Vine copula
app oach can be examined wi h non-simpli ied pai copulas o cap u e co-mo e-
men s mo e lexibly. In a mo e sys ema ic app oach, phase-wise analysis can be
examined o e he ma ke by conside ing in-sample and ou -o -sample phases
such as bea o bull ma ke condi ions.
To p o ide a clea e ma ke analysis, he po en ial impac s o o he inancial ma -
ke s in his egion should be inco po a ed. Since he s ock ma ke in Tu key mainly
ulne able o di e en ma ke s such as wes e n o eas e n inancial ma ke s, o he
ac o s can be embedded in o R-Vine GARCH app oach lexibly. The po en ial
impac s o exchange o oil p ice shocks will be indica o o he ma ke condi ions so
ha he phase-le el non-simpli ied R-Vine GARCH app oach could be he nex s ep
o de i e mo e obus and s a is ically signi ican indings o e he ISE100 s ocks in
he Tu kish inancial ma ke . Ins ead o empi ical-based ime spli ing, change-poin
analysis o ien ed sub-pe iod design empowe ed wi h he phase-le el analysis lies on
he op o he au ho s u u e plans.
Desc ip i e S a is ics
See Tables14, 15, 16, 17, 18 and 19.
2972
O.E kaya e al.
Table 14 Desc ip i e s a is ics o p e-GFC pe iod
a JB es p- alues a e p esen ed a 5% signi icance, wi h
H0
: Da a is no mally dis ibu ed
Sec o di ision Mean S d. de Skewness Ku osis JB es a
Finance (9) AKBNK 0.00089 0.02513
−
0.06550 3.99728 0.00000
GARAN 0.00175 0.02510
−
0.08440 4.46966 0.00000
ISCTR 0.00056 0.02697
−
0.08326 3.63238 0.00368
SAHOL 0.00106 0.02449
−
0.11177 3.73209 0.00046
YKBNK 0.00086 0.02456 0.43888 4.99467 0.00000
ECILC 0.00152 0.02718 0.14715 6.40481 0.00000
ALARK
−
0.00016 0.02057 0.38128 5.59314 0.00000
ISFIN 0.00149 0.03225 0.18061 5.45013 0.00000
SKBNK 0.00241 0.03577 0.33586 9.20483 0.00000
Basic ma e ials (4) EREGL 0.00158 0.02313 0.27171 4.49828 0.00000
KRDMR 0.00068 0.02790 0.01651 6.26820 0.00000
PETKM 0.00051 0.02367 0.51079 6.31904 0.00000
KOZAA 0.00446 0.04254 0.83254 5.44180 0.00000
Consume cyclicals (5) ARCLK 0.00080 0.02393 0.34049 5.82769 0.00000
AKSA 0.00008 0.02162 1.07332 9.67068 0.00000
DOAS 0.00077 0.02862
−
0.39166 6.05191 0.00000
TOASO 0.00163 0.02539 0.17080 5.40169 0.00000
FROTO 0.00091 0.02173 0.07697 4.41924 0.00000
Consume non-cyclicals (7) DOHOL 0.00104 0.02583
−
0.16166 3.96245 0.00000
KCHOL 0.00035 0.02321 0.20328 3.63854 0.00055
SISE 0.00062 0.02414 0.03345 3.65494 0.00324
AEFES 0.00112 0.02813 0.06909 6.17866 0.00000
ULKER 0.00028 0.02329 0.01640 9.09457 0.00000
MGROS 0.00124 0.02620 0.26529 4.67582 0.00000
ECZYT 0.00126 0.02630 0.18430 6.18469 0.00000
Indus ial (3) THYAO 0.00033 0.02296
−
0.32016 10.23157 0.00000
ASELS 0.00135 0.03066 0.37272 6.80150 0.00000
ENKAI 0.00202 0.02053 0.84895 7.19690 0.00000
O he s (4) TUPRS 0.00178 0.02457 0.51090 5.79557 0.00000
AYGAZ 0.00115 0.02373 0.12965 5.98954 0.00000
TCELL 0.00061 0.02447 0.14741 4.16726 0.00000
ISGYO 0.00070 0.02560
−
0.10471 5.97462 0.00000
2973
Vine Copula App oach oUnde s and heFinancial Dependence…
Table 15 Desc ip i e s a is ics o GFC pe iod
a JB es p- alues a e p esen ed a 5% signi icance, wi h
H0
: Da a is no mally dis ibu ed
Sec o di ision Mean S d. de Skewness Ku osis JB es a
Finance (9) AKBNK 0.00042 0.03648 0.41646 4.85563 0.00000
GARAN 0.00045 0.03616 0.10999 4.01097 0.00000
ISCTR 0.00025 0.03237 0.23780 4.95532 0.00000
SAHOL
−
0.00005 0.03249 0.26207 4.46531 0.00000
YKBNK 0.00040 0.03328
−
0.10928 4.68909 0.00000
ECILC
−
0.00030 0.02492
−
0.28164 4.98525 0.00000
ALARK 0.00049 0.02365 0.62991 7.22293 0.00000
ISFIN
−
0.00088 0.03515
−
0.26444 8.04180 0.00000
SKBNK
−
0.00049 0.03611 0.12680 4.86198 0.00000
Basic ma e ials (4) EREGL 0.00008 0.03358 0.20793 5.16525 0.00000
KRDMR 0.00016 0.03277 0.21432 4.94310 0.00000
PETKM
−
0.00041 0.02734 0.08930 4.97489 0.00000
KOZAA
−
0.00056 0.04114 0.41091 6.07317 0.00000
Consume cyclicals (5) ARCLK
−
0.00115 0.03114 0.83749 7.83911 0.00000
AKSA
−
0.00084 0.02530 0.95617 8.15989 0.00000
DOAS
−
0.00047 0.03168
−
0.06392 4.55501 0.00000
TOASO
−
0.00082 0.03492
−
0.34985 6.27675 0.00000
FROTO
−
0.00013 0.03359
−
0.05403 5.65697 0.00000
Consume non-cyclicals (7) DOHOL
−
0.00025 0.03457 0.03214 6.28215 0.00000
KCHOL 0.00008 0.03100
−
0.00420 5.96439 0.00000
SISE
−
0.00060 0.02746 0.05216 4.92772 0.00000
AEFES 0.00048 0.02835
−
0.18002 4.73396 0.00000
ULKER
−
0.00063 0.02594
−
0.12822 5.47888 0.00000
MGROS 0.00124 0.02808 1.71922 20.76362 0.00000
ECZYT
−
0.00033 0.02132
−
0.50713 5.71371 0.00000
Indus ial (3) THYAO 0.00085 0.03039 0.02335 4.09344 0.00000
ASELS
−
0.00011 0.02635 0.08933 5.54560 0.00000
ENKAI
−
0.00037 0.03221 0.30316 6.15752 0.00000
O he s (4) TUPRS
−
0.00011 0.02908
−
0.01521 6.98634 0.00000
AYGAZ 0.00025 0.02551
−
0.19915 4.80086 0.00000
TCELL 0.00035 0.02934 0.01068 5.33991 0.00000
ISGYO
−
0.00032 0.02878
−
0.11923 6.72588 0.00000
2974
O.E kaya e al.
Table 16 Desc ip i e s a is ics o pos -GFC pe iod
a JB es p- alues a e p esen ed a 5% signi icance, wi h
H0
: Da a is no mally dis ibu ed
Sec o di ision Mean S d. de Skewness Ku osis JB es a
Finance (9) AKBNK 0.00010 0.02248
−
0.09083 4.22291 0.00000
GARAN 0.00028 0.02304
−
0.18403 5.23783 0.00000
ISCTR 0.00022 0.02167
−
0.27587 4.58353 0.00000
SAHOL 0.00042 0.02178
−
0.12612 5.76934 0.00000
YKBNK 0.00016 0.02316
−
0.47380 4.94371 0.00000
ECILC 0.00045 0.02036 0.62707 7.77194 0.00000
ALARK 0.00028 0.01853
−
0.95390 11.71075 0.00000
ISFIN 0.00066 0.02101 0.31211 6.83129 0.00000
SKBNK 0.00051 0.02083
−
0.27936 5.60289 0.00000
Basic ma e ials (4) EREGL 0.00042 0.01919
−
0.56515 6.13487 0.00000
KRDMR 0.00072 0.02375
−
0.10775 7.36316 0.00000
PETKM 0.00060 0.01957 0.31116 7.34517 0.00000
KOZAA 0.00021 0.02683
−
0.46371 7.90462 0.00000
Consume cyclicals (5) ARCLK 0.00111 0.02305
−
0.19278 5.46661 0.00000
AKSA 0.00176 0.02225 0.17709 5.31887 0.00000
DOAS 0.00118 0.02593
−
0.56763 7.87696 0.00000
TOASO 0.00140 0.02560
−
0.32802 7.37667 0.00000
FROTO 0.00126 0.02219
−
0.34298 7.91177 0.00000
Consume non-cyclicals (7) DOHOL
−
0.00053 0.02637
−
0.76648 12.79130 0.00000
KCHOL 0.00085 0.02059
−
0.04377 4.63338 0.00000
SISE 0.00082 0.02170
−
0.27385 4.44892 0.00000
AEFES 0.00039 0.02041
−
0.56208 7.78241 0.00000
ULKER 0.00152 0.02133 0.28864 10.45955 0.00000
MGROS
−
0.00020 0.02464 0.06728 14.78274 0.00000
ECZYT 0.00055 0.02172 0.45457 9.65798 0.00000
Indus ial (3) THYAO 0.00117 0.02348
−
0.12379 6.63436 0.00000
ASELS 0.00179 0.02285 0.53523 8.07391 0.00000
ENKAI 0.00058 0.01978
−
0.31544 5.04160 0.00000
O he s (4) TUPRS 0.00087 0.02070
−
0.23592 4.65250 0.00000
AYGAZ 0.00083 0.01957
−
0.12934 8.47336 0.00000
TCELL 0.00018 0.01789
−
0.32830 8.50201 0.00000
ISGYO 0.00030 0.01970
−
0.14190 6.11315 0.00000