systemic risk for financial institutions of major
TRANSCRIPT
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Systemic risk for financial institutions of major petroleum-based economies: The role of oil
-Complementary Material-
Ahmed Khalifa
College of Business and Economics, Qatar University, Doha, Qatar Email: [email protected]
Massimiliano Caporin
Department of Statistical Sciences, Università degli Studi di Padova, Italy Email: [email protected]
Michele Costola*
SAFE, Goethe University Frankfurt, Germany Email: [email protected]
Shawkat Hammoudeh
Lebow College of Business, Drexel University, Philadelphia, PA., United States; and Energy and Sustainable Development, Montpellier Business School
Email: [email protected]
Abstract To complete the analysis executed in the paper, we consider here different approaches and other measures for estimating the systemic risk of the GCC financial institutions and the role of oil. JEL Classification: C22, C58, G01, G17, G20, G21, G32 Keywords: Systemic risk, risk measurement, VaR, ΔCoVaR, oil, financial institutions, petroleum-based economies
*Corresponding author: (M. Costola). Tel. (+49) 69 798 34505.
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Appendix A: List of Companies
We report in Table A1 the number of financial companies according to the industry group for
each country and then the list of financial companies considered in the sample.
Banks Diversified Insurance Real Estate Investment Total
Abu Dhabi 12 2 17 4 0 35 Bahrain 9 2 4 3 1 19
Dubai 5 3 10 5 4 27 Kuwait 11 17 7 39 20 94 Oman 8 12 6 2 5 33 Qatar 9 2 5 4 3 23 Saudi 12 0 33 8 5 58 GCC 66 38 82 65 38 289
Table A1. Number of financial institutions according to the industry group for each country and the GCC region.
List of the considered financial companies
Abu Dhabi 49 INOVEST BI Real Estate 1 FAB UH Banks 50 BKIC BI Insurance 2 ADCB UH Banks 51 BNH BI Insurance 3 ALDAR UH Real Estate 52 ESTERAD BI Investment Companies 4 ADIB UH Banks 53 CPARK BI Real Estate 5 UNB UH Banks 54 SOLID BI Insurance 6 RAKBANK UH Banks Dubai 7 NBF UH Banks 55 EMIRATES UH Banks 8 NBQ UH Banks 56 EMAAR UH Real Estate 9 WAHA UH Diversified Finan Serv 57 DIB UH Banks
10 INVESTB UH Banks 58 EMAARMLS UH Real Estate 11 NBS UH Banks 59 MASQ UH Banks 12 AWNIC UH Insurance 60 DAMAC UH Real Estate 13 UAB UH Banks 61 CBD UH Banks 14 BOS UH Banks 62 DFM UH Diversified Finan Serv 15 ESHRAQ UH Real Estate 63 AMANAT UH Investment Companies 16 ADNIC UH Insurance 64 UPP UH Real Estate 17 RAKPROP UH Real Estate 65 DEYAAR UH Real Estate 18 CBI UH Banks 66 AJMANBAN UH Banks 19 EIC UH Insurance 67 SHUAA UH Investment Companies 20 ALAIN UH Insurance 68 SALAMA UH Insurance 21 ABNIC UH Insurance 69 AMLAK UH Diversified Finan Serv 22 FH UH Diversified Finan Serv 70 OIC UH Insurance 23 UNION UH Insurance 71 ALRAMZ UH Investment Companies 24 TKFL UH Insurance 72 GGICO UH Investment Companies 25 SICO UH Insurance 73 ASCANA UH Insurance 26 DHAFRA UH Insurance 74 DNIR UH Insurance
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27 RAKNIC UH Insurance 75 DIN UH Insurance 28 FIDELITY UH Insurance 76 SFWAMUBA UH Diversified Finan Serv 29 AFNIC UH Insurance 77 ORIENT UH Insurance 30 METHAQ UH Insurance 78 NGI UH Insurance 31 AKIC UH Insurance 79 TAKAFULE UH Insurance 32 SG UH Real Estate 80 AMAN UH Insurance 33 IH UH Insurance 81 DARTAKAF UH Insurance 34 GCIC UH Insurance Kuwait 35 WATANIA UH Insurance 82 NBK KK Banks
Bahrain 83 KFH KK Banks 36 AUB BI Banks 84 BOUBYAN KK Banks 37 GFH BI Diversified Finan Serv 85 CBK KK Banks 38 ABC BI Banks 86 GBK KK Banks 39 NBB BI Banks 87 BURG KK Banks 40 BBK BI Banks 88 MABANEE KK Real Estate 41 BARKA BI Banks 89 ALMUTAHE KK Banks 42 ITHMR BI Banks 90 ABK KK Banks 43 SALAM BI Banks 91 KPROJ KK Investment Companies 44 BISB BI Banks 92 ALAFCO KK Diversified Finan Serv 45 BCFC BI Diversified Finan Serv 93 WARBABAN KK Banks 46 SEEF BI Real Estate 94 KIB KK Banks 47 ARIG BI Insurance 95 SRE KK Real Estate 48 KHCB BI Banks 96 ALTIJARI KK Real Estate 97 TAM KK Real Estate 147 MASSALEH KK Real Estate 98 ALIMTIAZ KK Investment Companies 148 REMAL KK Real Estate 99 GINS KK Insurance 149 ALMADINA KK Investment Companies
100 TAMINV KK Investment Companies 150 ALSALAM KK Investment Companies 101 NRE KK Real Estate 151 INVESTOR KK Real Estate 102 FACIL KK Diversified Finan Serv 152 KMEFIC KK Diversified Finan Serv 103 AINS KK Insurance 153 EKTTITAB KK Investment Companies 104 URC KK Real Estate 154 ALAMAN KK Investment Companies 105 KINV KK Investment Companies 155 TAMEERK KK Real Estate 106 NINV KK Diversified Finan Serv 156 AMAR KK Diversified Finan Serv 107 KINS KK Insurance 157 ALMAL KK Investment Companies 108 MAZAYA KK Real Estate 158 SANAM KK Real Estate 109 MARKAZ KK Diversified Finan Serv 159 FTI KK Insurance 110 KRE KK Real Estate 160 ALAQARIA KK Real Estate 111 MUNSHAAT KK Real Estate 161 AJWAN KK Real Estate 112 FIRSTDUB KK Real Estate 162 BIIHC KK Investment Companies 113 KPPC KK Investment Companies 163 MENA KK Real Estate 114 MADAR KK Investment Companies 164 GFC KK Investment Companies 115 KFOUC KK Investment Companies 165 MASAKEN KK Real Estate 116 KBT KK Real Estate 166 IRC KK Real Estate 117 INJAZZAT KK Real Estate 167 MARAKEZ KK Real Estate 118 AREEC KK Real Estate 168 ALMUDON KK Real Estate 119 SOKOUK KK Real Estate 169 WETHAQ KK Insurance 120 AAYAN KK Diversified Finan Serv 170 EFFECT KK Real Estate 121 AAYANRE KK Real Estate 171 TAMKEEN KK Investment Companies 122 JIYAD KK Diversified Finan Serv 172 EXCH KK Investment Companies 123 ALOLA KK Diversified Finan Serv 173 KUWAITRE KK Insurance 124 ASIYA KK Diversified Finan Serv 174 THURAYA KK Real Estate 125 REAM KK Real Estate 175 ARGAN KK Real Estate 126 SECH KK Investment Companies Oman
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127 NOOR KK Diversified Finan Serv 176 BKMB OM Banks 128 ARZAN KK Diversified Finan Serv 177 BKDB OM Banks 129 TIJARA KK Real Estate 178 NBOB OM Banks 130 ARKAN KK Real Estate 179 OMVS OM Diversified Finan Serv 131 ABYAAR KK Real Estate 180 BKSB OM Banks 132 COAST KK Investment Companies 181 HBMO OM Banks 133 BAYANINV KK Investment Companies 182 ABOB OM Banks 134 KAMCO KK Diversified Finan Serv 183 BKNZ OM Banks 135 KFIC KK Diversified Finan Serv 184 BKIZ OM Banks 136 IFA KK Diversified Finan Serv 185 AOFS OM Diversified Finan Serv 137 ERESCO KK Real Estate 186 DIDI OM Investment Companies 138 ARABREC KK Real Estate 187 NFCI OM Diversified Finan Serv 139 UNICAP KK Diversified Finan Serv 188 UFCI OM Diversified Finan Serv 140 AQAR KK Real Estate 189 OUIS OM Insurance 141 NIH KK Investment Companies 190 MFCI OM Diversified Finan Serv 142 MANAZEL KK Real Estate 191 TFCI OM Diversified Finan Serv 143 WINS KK Insurance 192 GFIC OM Diversified Finan Serv 144 OSOUL KK Banks 193 AMAT OM Insurance 145 AMWAL KK Diversified Finan Serv 194 OEIO OM Investment Companies 146 MUNTAZAH KK Real Estate 195 DICS OM Insurance 196 GISI OM Diversified Finan Serv 244 BJAZ AB Banks 197 SAHS OM Real Estate 245 SIIG AB Investment Companies 198 VISN OM Insurance 246 ALARKAN AB Real Estate 199 TAOI OM Insurance 247 BUPA AB Insurance 200 FSCI OM Diversified Finan Serv 248 EMAAR AB Real Estate 201 NRED OM Real Estate 249 TAWUNIYA AB Insurance 202 MCTI OM Insurance 250 TIRECO AB Real Estate 203 SIHC OM Investment Companies 251 KEC AB Real Estate 204 AMII OM Investment Companies 252 SRECO AB Real Estate 205 FINC OM Diversified Finan Serv 253 ARCCI AB Insurance 206 DBIH OM Investment Companies 254 ALCO AB Investment Companies 207 NSCI OM Diversified Finan Serv 255 ALALAMIY AB Insurance 208 SISC OM Diversified Finan Serv 256 BATIC AB Investment Companies
Qatar 257 ALANDALU AB Real Estate 209 QNBK QD Banks 258 WALAA AB Insurance 210 QIBK QD Banks 259 AXA AB Insurance 211 ERES QD Real Estate 260 MUSHREIT AB REITS 212 MARK QD Banks 261 MEDGULF AB Insurance 213 CBQK QD Banks 262 SABBT AB Insurance 214 BRES QD Real Estate 263 JAZTAKAF AB Insurance 215 QATI QD Insurance 264 TRDUNION AB Insurance 216 QIIK QD Banks 265 SAIC AB Investment Companies 217 DHBK QD Banks 266 SARCO AB Investment Companies 218 ABQK QD Banks 267 MALATH AB Insurance 219 UDCD QD Real Estate 268 SAUDIRE AB Insurance 220 KCBK QD Banks 269 AICC AB Insurance 221 QGRI QD Insurance 270 SHIELD AB Insurance 222 MRDS QD Real Estate 271 BURUJ AB Insurance 223 QFBQ QD Banks 272 ALINMATO AB Insurance 224 QISI QD Insurance 273 UCA AB Insurance 225 DOHI QD Insurance 274 ALLIANZ AB Insurance 226 SIIS QD Investment Companies 275 SAGR AB Insurance 227 IGRD QD Investment Companies 276 WATAN AB Insurance
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228 DBIS QD Diversified Finan Serv 277 ATC AB Insurance 229 AKHI QD Insurance 278 SOLIDARI AB Insurance 230 QOIS QD Investment Companies 279 SALAMA AB Insurance 231 IHGS QD Diversified Finan Serv 280 ACIG AB Insurance
Saudi 281 ACE AB Insurance 232 RJHI AB Banks 282 SAICO AB Insurance 233 NCB AB Banks 283 METLIFE AB Insurance 234 SAMBA AB Banks 284 GGCI AB Insurance 235 RIBL AB Banks 285 AMANA AB Insurance 236 SABB AB Banks 286 GULFUNI AB Insurance 237 BSFR AB Banks 287 ENAYA AB Insurance 238 ARNB AB Banks 288 ALAHLIA AB Insurance 239 JOMAR AB Real Estate 289 SINDIAN AB Insurance 240 ALINMA AB Banks 241 ALAWWAL AB Banks 242 ALBI AB Banks 243 SIBC AB Banks
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Appendix B.
B.1 The non-parametric quantile test (Jeong et al., 2012)
Let us define {"#}#∈& as the company/system returns and {'#}#∈& as the oil price or oil
volatility, and denote the lagged (#)* ≡ ,"#)*, … , "#)/0, 1#)* ≡ ('#)*, … , '#)3) and 5#)* ≡
("#)*, … , "#)6, '#)*, … , '#)3), respectively, with lags 7 and 8 being greater than one. The
distributions of "# conditional on 1#)* is defined as 9:;|=;>?("#|1#)*). For @ ∈ (0,1), the @-th
quantile of "# conditional on 5#)* or (#)* is CD(5#)*) ≡ CD("#|5#)*) and CD((#)*) ≡
CD("#|(#)*), respectively. Following Jeong et al. (2012), we can say that '# does not cause "# (oil
returns/volatility do/does not cause company/system) in its @-th quantile if CD(5#)*) = CD((#)*).
Therefore, the system of hypotheses that is to be tested is
GHI: KL9:;|M;>?(CD((#)*)|5#)*) = @N = 1,H*: KL9:;|M;>?(CD((#)*)|5#)*) = @N < 1.
The test statistic proposed by Jeong et al. (2012) is equal to
QR& =1
S(S − 1)ℎVWWXY
5#)* − 5#)Zℎ
[Z\#
&
#]*
^#̃^Z̃, (`. 1)
where a = 7 + 8 and X(∙) is the kernel function with bandwidth ℎ and ^#̃ = d{:;efgh(i;>?)}>h
where CgD is the estimated quantile.
B.2 The Hit Test by Engle and Manganelli (2004)
As stated by Engle and Manganelli (2004), the probability of exceeding the VaR should
not be dependent on the past information in each period. Consequently, the VaR estimate should
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be a filtered signal from potentially correlated and heteroskedastic time series to an independent
sequence of indicator functions denoted by Hjk#Z:Z|l and defined as
Hjk#Z:Z|l = m,n# < opqrs#,t
Z:Z|l0 − u, (`. 2)
where n# is the return at time k of a given institution, while u is the probability for the selected
quantile. Under the correct model’s specification, Hjk#Z:Z|l has a zero-mean and is uncorrelated
with its own lags and with those of opqrs#,tZ:Z|l. Therefore, we collect those explanatory variables
as the covariates (1#) and check if Hjk#Z:Z|l is orthogonal to 1#.
The Dynamic Quantile (DQ) test statistic is
wC =HjkxZ:Z|l1(1x1))*1xyl#z{z||
Su(1 − u)~~�,nrÄÅ(1)0, (`. 3)
which is distributed as a ~�, with degrees of freedom equal to the rank of 1.
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Appendix C. Granger-Causality Network-based Risk Measures
We consider the Granger causality test between the oil returns and the financial institutions’
returns, following the lines of Billio et al. (2012) that build on the Granger’s causality test
(Granger, 1980). In this second testing procedure, to summarize our findings, we introduce
network diagrams of the linear Granger-causality relationships in 2006, 2009, and 2016, where we
highlight the role of oil returns in the Granger causality–based networks and how such a role
changes over time. This further confirms that oil price returns have a relevant impact on financial
markets in the GCC countries. Therefore, we read these elements as supporting the potential
improvements we might obtain, in terms of systemic risk measurement and monitoring, by
introducing oil price returns in the evaluation of systemic risk measures.
To analyse the systemic risk through the financial linkages and the system connectedness,
we consider network-based risk measures. In this regard, Billio et al. (2012) propose Granger
causality on asset returns to extract the underlying network. Generally, a network is defined as a
set of nodes q# = {1,2, … , Ä#} and directed arcs (linkages) between nodes (financial institutions).
Note that the nodes’ number is time-varying, as the number of companies might change over time,
for several reasons. The network at time t can be represented through an Ä# −dimensional
adjacency matrix, É#, with the element rlÑ# being equal to 1 if there is an edge from institution j
directed to institution Ö with j, Ö ∈ q#, and 0 otherwise. The matrix É# is estimated using a pairwise
Granger causality approach to detect the direction and propagation of the relationships among the
institutions.
For each pair of the financial institutions, by using a given data sample, we estimate the
following model to test for the existence of Granger causality,
nl# =W8**Ünl#)Ü +V
Ü]*
W8*�ÜnÑ#)Ü +V
Ü]*
^l#, (o. 1)
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nÑ# =W8�*Ünl#)Ü +V
Ü]*
W8��ÜnÑ#)Ü +V
Ü]*Ñ̂#. (o. 2)
j ≠ Ö, ∀j, Ö = 1,… , Ä#, where a is the maximum lag (selected according to the BIC criterion), and
^l# and Ñ̂# are uncorrelated white noise processes. The test for Granger causality from nÑ# to nl#
corresponds to the evaluation of the null hypothesis, HI: 8*�Ü = 0, â = 1,2, …a. That is, all
coefficients linking nÑ# to nl# in the first equation are jointly equal to zero. If we reject the null, we
will have evidence suggesting the presence of causality. In a similar way, we can design a test for
Granger causality from nl# to nÑ#. We denote causality from nÑ# to nl# as Ö →ã j, while we useÖ ↛ã j,
if causality is not detected. Building on these two tests, we might observe four cases:
• ifÖ →ã j and j ↛ã Ö, then nÑ# causes nl# and, therefore, we set rÑl# = 1 and rlÑ# = 0;
• if Ö ↛ã j and j →ã Ö, then nl# causes nÑ# and,, therefore, we set rlÑ# = 1 and rÑl# = 0;
• if Ö →ã jand j →ã Ö, then there is a feedback relationship, whereby nl# causes nÑ# and vice
versa. Therefore, we set rlÑ# = rÑl# = 1;
• if Ö ↛ã j and j ↛ã Ö, there is no causality among the two financial institutions and,
therefore, we set rlÑ# = rÑl# = 0.
Building on the adjacency matrix A, we can design summary measures that have a systemic
risk interpretation. The first is the In-Out degree measure, mçl#, defined as
mçl# = WrlÑ# +
é;
Ñ]*
WrÑl#,
é;
Ñ]*
(o. 3)
k = 1,… , S, which indicates the total number of in and out connections involving a financial
institution. We also consider the Dynamic Causality Index, proposed by Billio et al. (2012), which
is a measure of the network density defined as
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wom# = ,2Ä#(Ä# − 1)0)*WWrlÑ#
é;
Ñ]*
,
é;
l]*
(o. 4)
k = 1,… , S. When ∆wom# > 0, there is an increase in the interconnectedness of the system, and
vice versa. For our analysis, we also test the Granger causality between institution j and oil (O),
nl# =W8**Ünl#)Ü +V
Ü]*
W8*�Üní#)Ü +V
Ü]*
^l#, (o. 5)
ní# =W8�*Ünl#)Ü +V
Ü]*
W8��Üní#)Ü +V
Ü]*Ñ̂#, (o. 6)
and we compute the Out-degree measure for oil, çïSíñó#, which is
çïSíñó# =WríñóÑ#,
é;
Ñ]*
(o. 7)
k = 1,… , S. This measure allows us to detect the oil causality to the considered financial
institutions.
We apply the same methodology, again using the rolling window approach, with the usual
bandwidth of 104 observations. Figure C.1 reports the dynamic causality index (DCI) of the GCC
financial network. The index clearly shows a great impact of the 2006 endogenous financial crisis
on the system connectedness but also displays a peak during the global financial crisis and the
decline of oil prices started in mid-2015 and culminated in February 2016.
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Figure C.1. The Dynamic Causality Index of the GCC financial network over time. Notes: An increase in the index signifies an increase in the interconnectedness of the system.
Figure C.2. The Oil Out-degree measure of the GCC financial network over time. Notes: This measure allows one to detect the causality from oil to the financial institutions, which peaked in July 2008 and March 2016.
Figure C.2 shows the Oil Out-degree among the GCC financial institutions, which is the number
of connections of a node to other nodes, that is, for oil vs other institutions. The graphical evidence
confirms the role of oil as one of the main drivers in the 2008 global financial crisis for the GCC
countries. The financial crises had a direct impact on the financial markets, a subsequent real effect
that impacted on oil, but the oil movement further increased the effects of the crises on the GCC
markets. On the contrary, Figure C.2 shows the irrelevance of oil during the 2006 endogenous
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crisis. Interestingly, the Oil Out-degree measure shows another local peak at the beginning of 2013.
One possible explanation could be the effect of growth in the production of shale oil, which showed
its fastest growth between 2013 and 2014, and the simultaneous drop in consumption in advanced
economies in 2013. This is also coherent with the evolution of the dynamic causality index in
Figure C.1, over the most recent years. In fact, we observe an overall increase in the index between
2013 and 2014. Lately, we observe an increase of the Oil Out-degree measure in correspondence
of the drop in oil prices started in mid-2014 and culminated in March 2016. For the sake of
completeness, we report in Figure C.3 the In-Out degree for both the GCC financial network and
each individual country. The measure reports the total connections (In and Out) from each node to
the others. We include in those figures the 95% density interval (the grey area) and the cross-
sectional mean (the solid blue line). It is worth noting the increase in the cross-sectional mean
during the subprime financial crisis is particularly visible in Bahrain, Oman, and Qatar. This
suggests that, during the financial crises, the connections among the financial companies in the
GCC markets tend to increase; this is in line with the systemic impact of the crises on the financial
institutions in the area. The same considerations apply to the drop in oil prices started in mid-2014.
Finally, Figure C.4 shows the network diagrams of the linear Granger-causality
relationships in 2006, 2009, and 2016, where we highlight the role of oil (blue node) in the
Granger-Network. The size of the nodes depends on the number of the IO (In-Out degree)
connections in each node. Clearly, the IO for oil changes in the three considered periods, showing
the highest number of connections during the global financial crisis (middle panel). Once again,
this highlights the effect of oil on the GCC financial system.
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(a) GCC Area
(b) Abu Dhabi
(c) Bahrain
(d) Dubai
(e) Kuwait
(f) Oman
(g) Qatar
(h) Saudi
Figure C.3. The 95% highest density region (grey area) by means of cross-sectional quantiles (2.5% and 97.5%, respectively) over the financial institutions and the cross-section median (solid blue line) of In-Out degree for the GCC area over time.
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Figure C.4. Network diagrams of the linear Granger-causality relationships. Notes: The relationships are statistically significant at the 5% level among the daily returns in 2006 (top), 2009 (middle), and 2016 (bottom). The red nodes represent the financial institutions, while the blue node is oil and the edge (grey lines) describes the financial linkages. The size of the dots depends on the number of the IO connections in each node. The network places the most relevant nodes in the centre, and the length of edges cannot be interpreted here. The figures report the biggest red node for the institutions in each period. These are 2006, Al Rajhi Bank (Bank, Saudi) and Taiba Holding Co (Real Estate, Kuwait); 2009, Esterad Investment Co BSC (Investment Company, Bahrain) and Mazaya (Real Estate, Kuwait); and 2016, Qatar Insurance Co SAQ (Insurance, Qatar) and Gulf General Investment Co (Investment Company, Saudi).
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Appendix D. CoVaR and MES estimates
As complementary results, we report the estimates for CoVaR and Marginal Expected
Shortfall (MES) proposed by Acharya et al. (2017). Like the ΔCoVaR included in the paper,
Figures B.1 report the 95% high density region (grey area) and the cross-section mean (solid blue
line) of CoVaR for both the entire GCC area and each country over time.
As additional analysis, we report the Marginal Expected Shortfall (MES). The MES is a
measure of systemic risk, which assesses the expected losses in case the market faces a tail event.
It is defined as the expected value of the returns of the institution when the market is experiencing
losses. This state is identified when the return of the reference asset Xm,t (usually the market) is
below a given quantile return qk and Xi,t is the return of a given institution. That is, for k = 0.05,
ôöõl = ö(1l|1V < uú%). (w. 1)
The intuition behind MES is that, if the institution is linked to a systemic event, its conditional
returns should highlight such a link. This measure is successful in capturing systemic relations if
calculated on returns (Löeffler and Raupach, 2013).
Figure D.2 reports the 95% high density region (grey area) and the cross-section mean
(solid blue line) of the MES for the GCC area as a whole and for each individual country over
time.
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(a) GCC Area
(b) Abu Dhabi
(c) Bahrain
(d) Dubai
(e) Kuwait
(f) Oman
(g) Qatar
(h) Saudi
Figure D.1. The 95% highest density region (grey area) by means of cross-sectional quantiles (2.5% and 97.5%, respectively) over the financial institutions and the cross-section median (solid blue line) of CoVaR for the GCC area over time.
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(a) GCC Area
(b) Abu Dhabi
(c) Bahrain
(d) Dubai
(e) Kuwait
(f) Oman
(g) Qatar
(h) Saudi
Figure D.2. The 95% highest density region (grey area) by means of cross-sectional quantiles (2.5% and 97.5%, respectively) over the financial institutions and the cross-section median (solid blue line) of MES for the GCC area over time.
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Appendix E: SRisk (Systemic risk)
Brownlees and Engle (2016) define the Capital Shortfall (CS) of firm i on day t as
oõl# = ÅÉl# −ûl# = Å(wl# +ûl#) −ûl#, (ö. 1)
where ûl# is the market value of equity, wl# is the book value of debt, and Él# is the value of assets.
Å is the prudential capital fraction, usually set to 8%.
The systemic risk event is defined as a market decline below a threshold C, over a time
horizon (h). We set C equal to 10%, as in Brownlees and Engle (2016) and h equal to 4 which is
approximately 1 month at weekly frequency (22 days in Brownlees and Engle, 2012).
Therefore,
õsmõXl# = ö#(oõl#ü†|sV#ü*ü† < o),
= Åö#(wl#ü†|sV#ü*ü† < o) − (1 − Å)ö#(ûl#ü†|sV#ü*ü† < o), (ö. 2)
where sV#ü*ü† is the arithmetic multi-period market return, assuming that, in the case of a
systemic event, the debt cannot be renegotiated, Åö#(wl#ü†|sV#ü*ü† < o) = wl#.
It follows that,
õsmõXl# = ûl#[Å¢q£l# − (1 − Å)¢sôöõl# − 1], (ö. 3)
where ¢q£l# is the leverage ratio (wl#+ûl#)/ûl# and ¢sôöõl# = ö#(sl#ü*:#ü†|sV#ü*ü† < o).
We report the LGV in Figure C.1. õsmõXl# is a function of the size of the firm, the degree of
leverage, and the expected equity depreciation conditional on a market distress. The LRMES is
obtained by using a GARCH-DCC model (Bollerslev, 1986; Engle, 2002).
We report here the estimates of the SRISK (Figure E.2) using the rolling window approach in the
same manner used to estimate ΔCoVaR.
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Figure E.1. The 95% highest density region (grey area) by means of cross-sectional quantiles (2.5% and 97.5%,
respectively) over the financial institutions and the cross-section median (solid blue line) of financial leverage (LVG) for the GCC area over time.
Figure E.2. The SRISK measure of the GCC financial institutions over time.
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Appendix F. CoVaR estimates with volatilities
In this section, we repeat all the analysis included in the paper with the volatility
framework. Here, we perform the test by focusing on the 95% conditional quantile1 of the
institutions’ changes on volatilities (right tail) and detect the significance at the 5% level.
Regarding the non-parametric quantile causality test of Jeong ed al. (2012), Table F.1 reports the
frequency of the significant causality impact in the cross section of the GCC financial institutions.
Our findings show that the lagged oil volatility in 68.86% of the cases2 (last row) influences
the financial institution volatility are at the 95% quantile. The percentages show evidence of the
presence of quantile causality across the 289 financial institutions in the GCC countries. We find
that Dubai has the highest value for the impact of oil in causing the low quantiles of financial
institutions, 85.19% for the lagged return. The lowest corresponding values are for Saudi Arabia
(60.34%).
Table F.1. Non-parametric quantile causality test of Jeong et al. (2012).
Country #Inst ∆¶ßlÜ Abu Dhabi 35 82.86% Bahrain 19 63.16%
Dubai 27 85.19% Kuwait 94 67.02%
Oman 33 66.67% Qatar 23 65.22%
Saudi Arabia 58 60.34% GCC 289 68.86%
1 Given that changes on volatility have an opposite relationship with prices compared to returns, we focus on the right tail of the distribution at 95% quantile. 2 We stress that we compute these percentages over the cross-section of the companies included in the analysis.
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Notes: Percentage of the significant oil return (second column) causality impact for each country. The test focuses on the 5% conditional quantile of the institutions’ returns and detects significance at the 5% level. We highlight the impact of lagged oil returns (one single lag) and (contemporaneous) conditional variance of oil (as estimated from an APARCH model) on the returns (in a given quantile) of the GCC financial institutions.
Regarding the CoVaR analysis, we perform the analysis on two specific events which includes the
2006 GCC endogenous crisis and the 2008 global financial crisis, respectively. Table F.2 reports
the total significance of the HAR structure in the four specifications we consider. Even in the
volatility framework, the role of the individual financial institution, as measured by ®tZ:Z|l, is
highly significant for both crises’ samples, either including or excluding oil (Columns 1/6 and
7/14), with the percentages either closer to or higher than 70% for most of the GCC. Therefore,
the financial companies have a statistically significant systemic impact. If we compare the quantile
regression results at the median and at the 5% quantiles for the financial institutions, oil has also
in this case no impact in the median quantile (Columns 2-3/10-11) in both 2006 and 2009.
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Table F.2. Total significance of the estimated quantile coefficients for the financial institutions in October 2006 and January 2009.
i ii iii iv sys median quantile sys sys median quantile sys !"#$#|& '"&,) '"&,* '"&,) '"&,* !"#$#|& !"#$#|& '"#$#|&,) '"#$#|&,* '"&,) '"&,* '"&,) '"&,* !"#$#|& '"#$#|&,) '"#$#|&,* October 2006 # Inst GCC 68% 1% 0% 34% 33% 66% 62% 25% 26% 1% 0% 34% 33% 62% 25% 26% 110 Abu Dhabi 59% 0% 0% 47% 18% 53% 53% 24% 12% 0% 0% 47% 18% 53% 24% 12% 17 Bahrain 67% 11% 0% 56% 56% 78% 56% 0% 22% 11% 0% 56% 56% 56% 0% 22% 9 Dubai 70% 0% 0% 30% 20% 70% 50% 50% 0% 0% 0% 30% 20% 50% 50% 0% 10 Kuwait 66% 0% 0% 26% 39% 63% 68% 11% 16% 0% 0% 26% 39% 68% 11% 16% 38 Oman 69% 0% 0% 25% 31% 63% 44% 75% 81% 0% 0% 25% 31% 44% 75% 81% 16 Qatar 67% 0% 0% 17% 33% 67% 67% 0% 0% 0% 0% 17% 33% 67% 0% 0% 6 Saudi 86% 0% 0% 43% 29% 86% 86% 21% 43% 0% 0% 43% 29% 86% 21% 43% 14 January 2009 # Inst GCC 73% 1% 2% 21% 55% 72% 64% 12% 87% 1% 2% 21% 55% 64% 12% 87% 181 Abu Dhabi 74% 0% 0% 11% 44% 70% 67% 15% 85% 0% 0% 11% 44% 67% 15% 85% 27 Bahrain 65% 0% 0% 6% 24% 71% 35% 0% 100% 0% 0% 6% 24% 35% 0% 100% 17 Dubai 58% 0% 8% 17% 58% 58% 50% 8% 50% 0% 8% 17% 58% 50% 8% 50% 12 Kuwait 73% 2% 3% 26% 59% 68% 56% 8% 100% 2% 3% 26% 59% 56% 8% 100% 66 Oman 74% 0% 0% 30% 52% 78% 74% 11% 85% 0% 0% 30% 52% 74% 11% 85% 27 Qatar 73% 0% 7% 27% 80% 80% 80% 20% 73% 0% 7% 27% 80% 80% 20% 73% 15 Saudi 94% 0% 0% 18% 65% 88% 100% 35% 65% 0% 0% 18% 65% 100% 35% 65% 17
Notes: The ΔCoVaR estimation includes four variants: i) the No OIL in the state variables; ii) the OIL with an HAR structure in the financial institutions; iii) the OIL with an HAR structure in the financial system's equation; and iv) the oil in both equations. The aim is to evaluate the significance of the oil-related coefficients of the median and the left quantiles to measure the impact of oil as a source of systemic risk. We report the financial system equation (sys)’s quantile regression on the median (no stress state) and the quantile regression at 95% (+,-.,/0%2 ). The last column reports the number of institutions present in the considered sample.
23
Even in the volatility framework, the most interesting finding comes from the results
associated with the estimation of the financial institutions’ Value-at-Risk. In Table F.2, Columns
4-5/12-13 show the fraction of cases where the weekly and monthly oil-related HAR components
are statistically significant. Here, the significance of the monthly components is higher with respect
to the weekly counterpart for the 2009 while in 2006 the two are very similar. Similarly, the
significance of the quantile regression at the 5% level for the system risk, !"#$%&,()*)|,, reported in
Columns 8-9/15-16 is higher for the monthly component in 2009.
In this regard, we analyse the impact of oil price movements on the financial institutions
by investigating the median of the significant estimated coefficients reported in Table F.3. The
impact of financial institutions on the market risk, as measured by -()*)|,, is positive for both the
2006 and 2009 samples, with the inclusion and exclusion of oil (Columns 1/6 and 7/14). The
magnitude of the coefficients for the entire GCC area is 0.23 (Columns 1 and 6) and 0.23 (Columns
7 and 14) in 2006. However, the mean of the quantile coefficients is higher, at 0.34 (Columns 1
and 6) and 0.35 (Columns 7 and 14) in 2009. The impact of the weekly component of oil, as
monitored by .(,,/, is almost entirely positive for the countries in 2006 (except for Oman) while is
almost entirely negative (except for Abu Dhabi). Conversely, the magnitude is opposite for the
monthly component .(,,0 in 2006 (negative, except for Kuwait) and 2009 (positive). This finding
may simply indicate a contribution to the reversion towards the equilibrium value.
24
Table F.3. Median of the significant estimated parameters for the financial institutions in October 2006 and January 2009.
i ii iii iv
sys median quantile sys sys median quantile sys
!"#$#|& '"&,) '"&,* '"&,) '"&,* !"#$#|& !"#$#|& '"#$#|&,) '"#$#|&,* '"&,) '"&,* '"&,) '"&,* !"#$#|& '"#$#|&,) '"#$#|&,*
October 2006 GCC 0.23 0.00 - 0.03 -0.05 0.23 0.23 0.02 -0.03 0.00 - 0.03 -0.05 0.23 0.02 -0.03 Abu Dhabi 0.24 - - 0.04 -0.08 0.26 0.17 -0.03 0.04 - - 0.04 -0.08 0.17 -0.03 0.04 Barhain 0.04 0.00 - 0.00 -0.05 0.03 0.02 - -0.01 0.00 - 0.00 -0.05 0.02 - -0.01 Dubai 0.16 - - 0.22 -0.28 0.16 0.15 0.05 - - - 0.22 -0.28 0.15 0.05 - Kuwait 0.21 - - 0.03 0.04 0.24 0.20 0.00 -0.03 - - 0.03 0.04 0.20 0.00 -0.03 Oman 0.08 - - -0.01 -0.02 0.09 0.10 0.02 -0.03 - - -0.01 -0.02 0.10 0.02 -0.03 Qatar 1.04 - - 0.65 -0.44 1.04 1.09 - - - - 0.65 -0.44 1.09 - - Saudi 0.81 - - 0.00 -0.17 0.81 0.78 0.08 -0.17 - - 0.00 -0.17 0.78 0.08 -0.17 January 2009 GCC 0.34 0.00 0.01 -0.03 0.20 0.35 0.35 -0.03 0.06 0.00 0.01 -0.03 0.20 0.35 -0.03 0.06 Abu Dhabi 0.09 - - 0.05 0.37 0.13 0.29 -0.02 0.16 - - 0.05 0.37 0.29 -0.02 0.16 Barhain 0.03 - - -0.02 0.05 0.04 0.02 - 0.01 - - -0.02 0.05 0.02 - 0.01 Dubai 0.34 - 0.00 -0.05 0.51 0.34 0.37 -0.09 0.22 - 0.00 -0.05 0.51 0.37 -0.09 0.22 Kuwait 0.22 0.00 0.01 -0.03 0.13 0.22 0.10 -0.01 0.05 0.00 0.01 -0.03 0.13 0.10 -0.01 0.05 Oman 0.82 - - -0.04 0.29 0.76 0.86 -0.01 0.18 - - -0.04 0.29 0.86 -0.01 0.18 Qatar 1.17 - 0.08 -0.06 0.18 1.17 1.46 -0.05 0.13 - 0.08 -0.06 0.18 1.46 -0.05 0.13 Saudi 0.82 - - -0.05 0.22 0.87 0.94 -0.05 0.12 - - -0.05 0.22 0.94 -0.05 0.12
Notes. The ΔCoVaR estimation includes four variants: i) the No OIL in the state variables; ii) the OIL with an HAR structure in the financial institution; iii) the OIL with an HAR structure in the system's equation; and iv) the Oil in both equations. The aim is to evaluate the significance of the oil-related coefficients in the median and left quantiles to measure the impact of oil as a source of systemic risk. We report the system equation (sys)’s quantile regression in the median (no stress state) and the quantile regression at the 95% level (+,-.,/0 ). Note: The symbol ‘-’ indicates that there are non-significant coefficients in all the estimates as reported in Table 2.
25
As a further comparison in Figures F.4 to F.6, we report the fraction of the statistically
significant estimated coefficients for the HAR, separately reporting the weekly (black line) and
monthly (blue line) components. The fraction of the statistically significant estimated coefficients
(over the total estimated coefficients), when considering the oil component in the financial
institutions’ median equation (Figure F.4) remains lower and flat for all the considered period,
with a mean in the period around zero for both the weekly and monthly components.
Figure F.4. Fraction of the significant estimated coefficients for the HAR weekly (black line) and monthly (blue line), considering the oil component in the financial institution median equation. Notes: Estimates are obtained using the rolling window approach, with a bandwidth of 104 observations (two years).
Figure F.5. Fraction of the significant estimated coefficients for the HAR weekly (black line) and monthly (blue line), considering the oil component in the financial institution quantile equation. Notes: Estimates are obtained using the rolling window approach, with a bandwidth of 104 observations (two years).
26
However, the fraction of statistically significant coefficients for the oil component in the financial
institution quantile equation at the 5% level (Figure F.5) shows that the mean in the period is
around 25% (weekly) and 30% (monthly). Moreover, the fraction of the components increases
during 2008, with a peak of around 15% (weekly) and 50% (monthly) of the significant estimated
coefficient at the beginning of 2009. Similarly, the fraction for the oil component in the system
equation (Figure F.6) shows patterns that have increased during 2008, with peaks around 30% for
the weekly component and 80% for the monthly component, at the beginning of 2009.
Figure F.6. Fraction of the significant estimated coefficients for the HAR weekly (black line) and monthly (blue line), considering the oil component in the system equation. Notes: Estimates are obtained using the rolling window approach, with a bandwidth of 104 observations (two years).
27
Finally, we test if there is an improvement in the CoVaR calculation with the inclusion of
oil, using the HAR structure by means of the Engle–Manganelli Dynamic Quantile (DQ) test
(2004).
Table F.4. Fraction of cases where the null hypothesis is accepted for the Dynamic Quantile test by Engle and Manganelli (2004).
OIL HAR Covariates i ii iii iv
Sample N. Inst not present Inst. Syst. Inst.+Syst 2006 107 47.66% 52.34% 45.79% 46.73% 2007 151 56.29% 60.26% 56.95% 56.29% 2008 177 32.77% 39.55% 29.38% 25.42% 2009 192 54.69% 58.85% 42.19% 36.46% 2010 224 75.00% 81.25% 70.09% 70.09% 2011 242 53.31% 57.02% 48.76% 46.69% 2012 249 41.37% 45.38% 39.36% 38.96% 2013 261 25.29% 29.50% 22.61% 20.69% 2014 266 23.31% 31.20% 21.43% 21.80% 2015 268 31.34% 33.96% 25.75% 19.78% 2016 274 43.43% 42.70% 38.69% 36.13% 2017 279 44.44% 51.61% 41.94% 40.86% 2018 284 38.03% 43.31% 36.62% 38.38%
All Sample 284 12.32% 14.79% 13.03% 13.03% Notes. The test is performed on the four variants for ΔCoVaR: i) the No OIL in the state variables; ii) the OIL with a HAR structure in financial institution; iii) the OIL with a HAR structure in system's equation; and iv) the Oil in both equations.
Table F.4 reports the fraction of cases in which we do not reject the null hypothesis of the
DQ test developed by Engle and Manganelli (2004), including the four variants for ΔCoVaR. The
results show that, for all the considered sample, the specification of the CoVaR using oil with the
HAR structure in the individual financial institution provides the highest ratio of no rejection
(14.79%) for the null hypothesis of the correct specification (Column ii). Looking at the sample in
each year, Model ii has the highest ratio in twelve out of the thirteen years (except for 2016) which
confirm the role of oil as a systemic risk driver.
28
Additional References
• Acharya, V. V., Pedersen, L. H., Philippon, T., & Richardson, M. (2017). Measuring systemic risk. Review of Financial Studies, 30(1), 2-47.
• Adrian, T., Brunnermeier, M. (2016). CoVaR. American Economic Review, 106(7): 1705-41.
• Billio, M., Getmansky, M., Lo, A. W., & Pelizzon, L. (2012). Econometric measures of connectedness and systemic risk in the finance and insurance sectors. Journal of Financial Economics, 104(3), 535-559.
• Brownlees, C., Engle, R. (2012). Volatility, correlation and tails for systemic risk measurement. Available at SSRN 1611229.
• Brownlees, C., Engle, R. (2016). SRISK: A Conditional Capital Shortfall Measure of Systemic Risk. Review of Financial Studies, 30 (1): 48-79.
• Engle, R. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics, 20(3), 339–350.
• Engle, R., Jondeau, E., & Rockinger, M. (2014). Systemic risk in Europe. Review of Finance, 19(1), 145-190.
• Granger, C. (1980). Testing for causality: a personal viewpoint. Journal of Economic Dynamics and control, 2, 329-352.