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AssessingthecontributionofsubindexestosystemicriskontheWarsawStockExchange...
13
Letevent
(
()
r
st
beequaltoValueatRiskatthelevelα,thedifferencebetween
theCoVaRatlevelalphaandCoVaRcomputedinmedianstateisdenotedasΔCoVaR
(Benoitetal.2013):
Δ
CoVaR
st
(
α
)
=
CoVaR
mr
t
|
st
=
VaR
st
()
α
-
CoaR
V
mr
t
|
st
=
median(
r
st
)
.
(5)
IntheliteratureonecanfindmanymethodstocomputeΔCoVaR.Ourapproachis
basedontheDCCmodelofBrownlessandEngle(2012)alongwithbivariatecopulas.
GivenValue-at-Riskofsubindexreturn(undertheinformation
F
t-1
availableup
totimet-1)
Pr
(
st
<
VaR
st
(
α
)
F
t
-
1
)
=
α
,Benoitetal.(2013)showedthatΔCoVaRcanbe
expressedas:
Δ
CoVaR
st
(
α
)
=
γ
st
f
L
VaR
st
(
α
)
-
VaR
st
(.
05
)
1
J
(6)
with
γ
st
=
ρ
st
h
mt
/
h
st
,whereρ
stisaconditionalcorrelationbetweenmarketandsu-
bindexreturns.
Tocompleteourconsiderationsweapplythemodelabovetopairsofsubindexes.
Inourspecificationwereplacethemainindex(marketorsystem)withsubindexand
consider(AdrianandBrunnermeier2016):
Δ
CoVaR
t
ji
|
(
α
)CoVaR
=
t
jr
|
it
=
VaR
it
(
α
)
-
CoVaR
t
jr
|
it
=
med
ian(
r
it
)
(7)
given
Pr
(
it
<
VaR
it
(
α
)
F
t
-
1
)
=
α
.Fromthisdefinition
Δ
CoVaR
ji
|
denotesthepartofriskof
j-thsectorthatcanbeattributedtoi-thsector.
4.Thedata
CurrentlytheWarsawStockExchangecalculatesadozensectoralindexes.The
mostrecentofthemisWIG-GAMES,whichhasbeencalculatedsinceMarch18,2019.
Forthisreasonweconsidertheclosingpricesof15sectoralindexesintheperiodfrom
March18,2019toMarch19,2021whichgives620dailyobservations.Inaddition,we
addtoourdatasettheclosingpricesofthelargestindexfromtheWarsawStockEx-
change-WIG.Onthebasisofthisinformationwecomputelogarithmicreturns(multi-
pliedby100)andbasicsummarystatistics,whicharepresentedinTable1.
Table1.Summarystatisticsoflogarithmicreturns
Index
WIG
WIG-banking
Mean
s.d.
Kurtosis
Skewness
-0.0018
1.4070
19.1036
-1.6542
-0.0611
2.0275
12.5919
-0.7957
