Systematic risk measurement in the global banking stock market with time series analysis and CoVaR

Transcription

1 Invesmen Managemen and Fnancal Innovaons, Volume 1, Issue 1, 213 Tesuo Kurosak (USA, Young Shn Km (Germany Sysemac rsk measuremen n he global bankng sock marke wh meseres analyss and CoVaR Absrac Movaed by he growng mporance of sysemc rsk n he global bankng sysem, he auhors measure he rsk of he sysem and he margnal conrbuons of he nsuons n several ways n erms of sock markes. The undversfable rsk appearng n specfc marke secors s called sysemac rsk raher han sysemc rsk. The paper focuses on global bankng socks comprsng global sysemcally mporan fnancal nsuons (G-SIFIs, and dscusses he global sysemac rsk measuremen. To forecas fuure on dsrbuon of reurns, he auhors ulze he mulvarae auoregressve movng average generalzed auoregressve condonal heeroscedascy (ARMA-GARCH model wh he mulvarae normal empered sable (MNTS dsrbued and mulvarae normal dsrbued nnovaons. Ths work sascally demonsraes ha he ARMA-GARCH model wh he MNTS dsrbued nnovaons s a more realsc model for G-SIFI socks. In lne wh prevous sudes, he auhors esmae four sysemac rsk measures: on probably and condonal probably of negave sock reurn movemens, CoVaR, and Co. I s found ha he on probably of negave movemens s a good ndcaor for a sgnfcan ncrease n sysemac rsk. Subsequenly, he auhors nvesgae he relaonshp among he oher hree measures and fnd he followng. Crossseconal lnkages beween and Co are few, f any, bu here s a srong me seres lnkage. On he oher hand, he condonal probably of negave movemens and Co show smlar cross-seconal magnude relaons, hough her me seres lnkage s no clear. Thus, boh and condonal probably of negave movemens renforce each oher and serve a useful reference for Co-based sysemac rsk measuremen. Keywords: ARMA-GARCH model, mulvarae normal empered sable dsrbuon, CoVaR, Co, sysemac rsk measuremen, G-SIFIs, global bankng sock markes. JEL Classfcaon: F37, G1, G15, G17, G2, G32. Inroducon In he modern fnancal sysem, global fnancal nsuons become srongly nerconneced, leadng o awareness of he so-called sysemc rsk. Accordng o he defnon gven by Kaufman and Sco (23, n conras o he rsk ha here wll be a breakdown n ndvdual pars or componens of he fnancal sysem, sysemc rsk refers o he probably ha here wll be a breakdown of he enre fnancal sysem. Moreover, hs rsk s evdenced by he comovemens of he dfferen pars of he fnancal sysem. We can observe he applcably of hs defnon of sysemc rsk n he case of global fnancal sysem n 28, followng he bankrupcy of he Uned Saes (U.S. nvesmen bankng frm Lehman Brohers. The fnancal crss rggered by he falure of Lehman Brohers, referred o as he Lehman shock, had a spllover effec n every secor of he global fnancal marke (sock, bond, currency, cred markes, and he lke. Followng he Lehman shock, he Basel Commee on Bankng Supervson (BCBS began o formulae a new regulaory framework for nernaonal banks known as Basel III o mgae he rsk of a reoccurrence of fnancal crses due o he problem of large fnancal nsuons. One of he mos sgnfcan enhancemens n Basel III relave o Tesuo Kurosak, Young Shn Km, Basel I and II s ha of proecng he global fnancal sysem from sysemc rsk. More specfcally, Basel III calls for addonal capal requremens for global sysemcally mporan fnancal nsuons (G- SIFIs, n conras o he unform capal requremen mposed on every bank n Basel II. More recenly, an nal ls of 29 G-SIFIs (8 from he Uned Saes, 17 from Europe, and 4 from Asa was denfed and publshed based on he BCBS mehodology (Fnancal Sably Board, 211. See he Appendx for he ls of fnancal nsuons. The recen deb crss n Greece calls for greaer aenon o sysemc rsk n anoher way. Because fnancal nsuons ypcally have large posons n soveregn bonds, here was grea concern n he marke ha a sysemc downurn would occur because of he European soveregn deb crss. Ths, n fac, dd occur for one G-SIFI, Dexa Group, because of exposures o hese counres. There are some marke observers wh such a pessmsc vew ha f Greece collapses, he adverse mpac on he fnancal sysem would be greaer han ha of he Lehman shock. Movaed by he growng mporance of sysemc rsk, he purpose of hs paper s o nvesgae such rsk n he global bankng sysem. Ths s done by focusng on sysemc rsk observed n sock markes and nvesgang socks ha are ncluded n G- SIFIs, as of November 211. Our mehodology nvolves me seres analyss o generae a fuure on dsrbuon of sock reurns, and accordngly we esmae rsk measures.

2 Invesmen Managemen and Fnancal Innovaons, Issue 1, 213 We emphasze ha, srcly speakng, we are no gong o quanfy sysemc rsk self gven ha we exclusvely deal wh sock reurns. There are sysemc rsk and sysemac rsk. Even hough boh emerge wh a downslde of oal marke reurns, sysemc rsk s consdered as he rsk ha specfcally arses from nense nerconnecedness and resuls n a breakdown of he enre sysem. Aggregae adverse mpac n a specfc secor of a marke should be classfed as sysemac rsk. For hs reason, we hereafer refer o he rsk ha we quanfy based on sock reurns as sysemac rsk raher han sysemc rsk 1. For me seres analyss, we use a mulvarae auoregressve movng average generalzed auoregressve condonal heeroscedascy (ARMA- GARCH model, where he nnovaon erms are assumed o follow he mulvarae normal empered sable (MNTS and mulvarae normal dsrbuons. The MNTS dsrbuon s a relavely new non- Gaussan sock reurn model proposed by Km e al. (212. Each margnal of he MNTS dsrbuon s referred o as a unvarae normal empered sable (NTS dsrbuon. For sysemac rsk measures, we use he CoVaR mehodology proposed by Adran and Brunnermeer (211. CoVaR, or more specfcally, CoVaR, s defned beween wo nsuons and. CoVaR s he Value a Rsk (VaR of on a ceran condon of. Seng as he marke ndex, we consder he dfference beween CoVaR on s dsress and normal condons, denoed by CoVaR ndex. CoVaR ndex can be nerpreed as he margnal conrbuon of o he overall marke rsk. There are wo problems we address n hs ssue. The frs s how o measure and predc sysemac rsk. The second s how o deermne he nfluence of a fnancal nsuon on he enre fnancal sysem,.e., how o quanfy he rsk spllover effec. From a regulaory perspecve, s crcal o recognze sgnals of a meldown of he fnancal sysem and specfy he fnancal nsuons ha poenally have consderable nfluence on he fnancal sysem. For he frs problem, we propose he on probably of negave sock reurn movemens as a measure of sysemac rsk. Ths s necessary because alhough CoVaR can be a measure of margnal conrbuon o sysemac rsk, s no a measure of sysemac rsk self. For he second problem, we employ CoVaR o quanfy he rsk spllover effec. In addon, we exend CoVaR 1 The basc measure of sysemac rsk s bea. Smlar o bea, we focus on he comovemen beween he enre sysem and each nsuon n he global bankng sock marke. no he counerpar of average VaR (, whch we refer o as Co. An alernave approach for he rsk spllover effec s o descrbe an nsuon s power of nfluence on he sysem as he probably of a negave comovemen of he marke reurn on he condon ha a reurn of he nsuon moves downward. The dea underlnng he use of condonal probably s parallel o he dea of addressng he frs problem va on probably. We examne he relaonshp among, Co, and condonal probably usng regresson analyss. The res of hs paper s organzed as follows. In secon 1, we nroduce an ARMA-GARCH-MNTS model for me seres analyss. Subsequenly, we defne he followng sysemac rsk measures: he on probably and condonal probably of negave movemens, CoVaR, and Co. Secon 2 descrbes he daa o be used. Secon 3 presens he resuls and dscusson. Afer we demonsrae ha he ARMA-GARCH-MNTS model s a beer model for G-SIFI socks, we presen he esmaon resuls of sysemac rsk measures. We also dscuss he relaonshp among he dfferen ypes of measures. The fnal secon concludes he paper. 1. Mehodology Our mehodology for he nvesgaon of sysemac rsk has he followng wo seps: (1 generang he fuure on dsrbuon of sock reurns va he ARMA-GARCH model; and (2 dervng sysemac rsk measures from he predced on dsrbuon. We also brefly explan our smulaon-based esmaon mehods ARMA-GARCH-MNTS model. Our me seres model for sock reurns s he ARMA(1,1- GARCH(1,1 model gven by R 1 1 ( 1 c 2 1 a b, 2 ( (, 1 1 R 2 ( 2, (1 where he ndex =1, 2,, J corresponds o each nsuon, represens a me perod, R s he sock reurn, s he condonal mean, s he condonal sandard devaon, s..d. wh zero mean and un varance, called (sandardzed nnovaon, and he oher symbols are model parameers. We descrbe he mulvarae dsrbuon whose every margnal has zero mean and un varance as 1 2 J sandard. Thus, (,,..., forms a sandard mulvarae dsrbuon. Noe ha ARMA(1,1- GARCH(1,1 s a sandard specfcaon for fnancal daa n he GARCH framework. 185

3 Invesmen Managemen and Fnancal Innovaons, Volume 1, Issue 1, 213 There are several canddae models for each margnal. We choose he NTS dsrbuon because has he ably o capure sylzed properes of sock reurn dsrbuons such as fa-alness and skewness, whch he normal dsrbuon lacks. In addon, we use he normal dsrbuon for he purpose of comparson. The sandard NTS dsrbuon s characerzed by hree parameers: wo fa-alness parameers (, and one skewness parameer. If we assume common (, among NTS margnals wh as a sll free parameer for calbraon, we can on margnals no MNTS va he varance-covarance marx of whou compuaonal dffculy even n a consderably hghdmensonal sysem. See Km e al. (212 for he defnon and esmaon of he MNTS dsrbuon. In he case of he normal model, we can also on margnals no he mulvarae dsrbuon va he varance-covarance marx, because s he sngle parameer of he sandard mulvarae normal dsrbuon. The mulvarae dsrbuon of accouns for he dependen srucures among sock reurns. Followng he same approach as Km e al. (212, we frs esmae he unvarae NTS parameers (,, ( ˆ, ˆ, ˆ for he nnovaon of he represenave sock,.e., he marke ndex. Then, we use he esmaed parameers ( ˆ, ˆ as hose of MNTS. For he CoVaR esmaon, Adran and Brunnermeer (211 manly use quanle regressons supplemened wh he GARCH model wh he normal dsrbued nnovaons as a robusness check. Grard and Ergün (213 use he GARCH model wh Hansen s skewed dsrbued nnovaons. Our mehodology s dfferen from he prevous sudes because we frs apply he mulvarae empered sable dsrbuon o he CoVaR esmaon. Anoher advanage of MNTS s ha has he reproducve propery; he lnear combnaon of NTS dsrbued random varables sll follows NTS. Ths propery enables us o easly deal wh he porfolo of socks. Model (1 forecass he on dsrbuon of sock reurns a +1 perod on he bass of he nformaon up o. We refer o Model (1 wh he sandard MNTS dsrbued and sandard mulvarae normal dsrbued as he ARMA-GARCH-MNTS (AGMNTS model and ARMA-GARCH-mulvarae normal (AGMNormal model, respecvely. We prmarly use an AGMNTS forecas, whereas we use an AGMNormal forecas as a reference Sysemac rsk measures. Before nroducng sysemac rsk measures, we begn wh VaR. VaR s he mos sandard marke rsk measure used by fnancal nsuons. Consder he VaR of s sock reurn R a he confdence level 1 q( q 1, denoed by VaR,. The defnon of VaR, s gven by q q VaR nf{ R Prob( R R }. (2 q If R s connuous, VaR q, s he q-quanle of he dsrbuon of R, whch sasfes Pr ob( R VaR, q. (3 q An alernave rsk measure s. The defnon of, s gven by q q 1 VaR p, dp. (4 q If R s connuous, s equvalen o E R R VaR, (5 ( whch s called expeced al loss. Henceforh, for smplcy, every sock reurn dsrbuon s assumed o be connuous. has more desrable properes han VaR as a rsk measure (e.g., he ably o accoun for rsk above he VaR level, ofen referred o as al rsk 1. In leraure, s also called condonal VaR (CVaR 2 or Expeced Shorfall (ES. Whle VaR and are mcro-prudenal rsk measures on he premse of an nsuon beng solaed, alernave macro-prudenal rsk measures for sysemc rsk have recenly been explored n he conex of global fnancal urmol. Whle some consder probably-based approaches (Segovano and Goodhar, 29; Zhou, 21; Gesecke and Km, 211, ohers pu wegh on quanfyng sysemc rsk such as CoVaR (Adran and Brunnermeer, 211, SES and MES (Acharya e al., 21. In lne wh he prevous sudes of sysemc rsk, we nroduce four sysemac rsk measures n sock markes on he bass of VaR and, n whch wo ou of four are probably-based ndcaors: on and condonal probables of negave movemens. The oher wo are measures o quanfy he margnal conrbuon o sysemac rsk: CoVaR and Co Jon probably of negave movemens (JPNM. We consder sysemac rsk as smulaneous negave movemens of sock reurns, where he negave movemen smply means he reurn beng less han he condonal mean. Noe ha hs defnon s conssen wh he defnon of sysemc rsk gven by Kaufman and Sco (23. Accordngly, we nroduce he on probably of negave movemens (JPNM, Prob J JPNM R, (6 1 1 For furher nformaon, see Rachev e al. (28. 2 Noe ha CoVaR s a dfferen concep from CVaR, despe he analogous name. 186

4 Invesmen Managemen and Fnancal Innovaons, Issue 1, 213 as a measure of sysemac rsk. Because massve smulaneous negave comovemen s a very rare even, he on probably s low. However, we expec ha such a low probably capures he common dsress facor among fnancal nsuons and sgnals crss. In a prevous sudy, Segovano and Goodhar (29 esmae he on probably of dsress among fnancal nsuons from he cred defaul swaps daa CoVaR. To nvesgae and quanfy he rsk spllover effec, we adop Adran and Brunnermeer s CoVaR mehodology. CoVaR s a bvarae concep beween wo nsuons and. Whle VaR q, s he q-quanle of he uncondonal dsrbuon of R, CoVaR q, s he -quanle of he condonal dsrbuon of R on a ceran condon of, more specfcally, R. When we specfy he condon of as C (, we denoe R C( R R CoVaR nsead of C ( R CoVaR q,. The mplc defnon of CoVaR for connuous R s gven by Prob C( R R CoVaRq, C( R q. (7 d Le C ( R and C n ( R be he dsress and normal condons of R, respecvely. Adran and Brunnermeer (211 sugges ha he dfference of CoVaR q, d beween he wo condons C ( R and C n ( R, d C ( R q, CoVaR CoVaR CoVaR, (8 q, n C ( R q, accouns for he rsk conrbuon of o. For he applcaon of CoVaR o sysemac rsk n sock markes, we hghlgh he case of beng a ndex marke ndex. CoVaR q, s regarded as he margnal conrbuon of o he overall sysemac rsk. Regardng he condons, Adran and Brunnermeer (211 defne he dsress and normal condons as he nsuon s loss and reurn beng exacly a s VaR and medan, respecvely, d C ( R { R VaR }, (9 n C ( R { R medan }. However, we adop he modfed defnon by Grard and Ergün (213, where he dsress and normal condons denoe he nsuon s loss and reurn beng above s VaR and whn he range of one sandard devaon from s mean sae, respecvely, d C ( R { R VaR q, }, n C ( R { R }. (1 We make he confdence level 1 q of C d concde wh ha of CoVaR, whch s condoned by C d. As Grard and Ergün pon ou, he modfed defnon has several mers. Frs, focuses on al rsk,.e., he loss above he VaR level, and hus, he resulng CoVaR becomes more nsghful. Second, allows backesng of CoVaR. We can apply he ordnary d ndex C ( R VaR backesng mehods o CoVaR for he days durng whch VaR volaon of occurs. Here, he VaR volaon of means he even when he observed loss R exceeds VaR q, ;.e., he condon C d ( R acually occurs 1. The smples way of VaR backesng s o observe how ofen VaR volaons occur. If one aemps o esmae 1(1 q% VaR, volaons should occur a 1q% of whole observaons. Followng Grard and Ergün (213, we shall use he lkelhood rao (LR ess of he uncondonal and condonal coverages by Chrsoffersen (1998 as a more sophscaed VaR backesng mehod. The condonal coverage es s more desrable han he uncondonal one because can consder he endency for consecuve volaons, whch s observed for ordnary VaR durng fnancal urmol. We defne he CoVaR volaon of as he even when he observed loss d ndex ndex C ( R R exceeds CoVaR durng he VaR q, volaon days of. Through he Chrsoffersen ess, can be esed wheher CoVaR volaon occurs wh a reasonable probably durng VaR volaon days; ha d ndex C ( R s, CoVaR s appropraely esmaed a he q, gven confdence level. In he condonal es of ndex C d ( R CoVaR, he condons are consdered beween wo adacen days of he VaR volaons of. The las convenence of he modfed defnon (1 for our sudy s o make scenaro smulaon-based esmaon of CoVaR feasble (see secon Condonal probably of negave movemens (CPNM. We can creae an alernave probablybased ndcaor for he rsk spllover effec. Gven ha sysemac rsk s he smulaneous negave movemen of sock reurns, he probably of he marke ndex gong down conngen on he nsuon beng dsressed s regarded as he ndcaor for sysemac rsk orgnang from ha nsuon. Then, we nroduce he condonal probably of negave movemens (CPNM, ndex d ndex d CPNM Pr ob C ( R C ( R. (11 1 Alhough we can es n ndex C ( R q, CoVaR n he same way, we concenrae on he dsress condon C d, whch s more assocaed wh sysemac rsk, as Grard and Ergün (213 do. 187

5 Invesmen Managemen and Fnancal Innovaons, Volume 1, Issue 1, 213 We sll follow equaon (1 regardng he defnon of C d. In hs case, CPNM s proporonal o he on probably of boh a marke ndex and an ndvdual nsuon ncurrng he loss beyond her respecve VaRs. Noe ha, n conras o he case of JPNM, negave movemen does no sand for he reurn beng less han he condonal mean bu raher he loss exceedng VaR n he case of CPNM. Ths s because he on probably of reurns less han condonal means appears nsuffcen o nspec bvarae al dependency Co. We can consder he Co-verson of by consderng equaons (4 and ( C ( R Co s defned by Co C ( R E R R 1 q q CoVaR CoVaR C ( R p, C ( R dp C( R. (12 In an analogous fashon o CoVaR, he rsk conrbuon of o n erms of Co s expressed by Co Co Co n C ( R. d C ( R (13 In Adran and Brunnermeer (211, Co s menoned as CoES. Because has some mers compared wh VaR, we prmarly use Co raher han CoVaR for he assessmen of sysemac rsk Scenaro smulaon. We rely on scenaro smulaon for esmaon of sysemac rsk measures. I flexbly enables he esmaons of varous rsk measures. On he bass of he AGMNTS (AGMNormal model, we generae a large number S of scenaros abou one-perod-ahead mulvarae sock s 1, s 2, s J, s reurns R 1 ( R 1, R 1,..., R 1, 1 s S va a Mone Carlo smulaon. For he AGMNTS model, he random varables ha follow he MNTS dsrbuon are easly smulaed usng s subordnaed represenaon 1. The rsk measures can be esmaed from he seleced scenaros, where a d relevan or condonng even lke C ( R or C n ( R s realzed ou of he overall scenaros. For ndex ndex he esmaons of CoVaR q,, Co q,, ndex and CPNM q,, we specfy he bvarae ARMA GARCH model of he marke ndex and nsuon. 1 I s specfcally a mxure of he mulvarae normal dsrbuon and classcal empered sable (CTS subordnaor. See Km e al. ( Daa For emprcal research, we use daly sock logarhmc reurn daa for 28 ou of 29 G-SIFIs, as of November 211. We refer o each sock by s cker symbol or abbrevaon. The ls of G-SIFIs s gven n he Appendx. The only excluson s Banque Populare CdE because s unlsed. We use he S&P global 12 fnancal secor ndex o represen he global bankng sock marke. The sample perod s from January 1 s, 2 o June 3 h, 212. We exclude he U.S. non-busness days from hs perod, whch leads o 326 observaons for each sock. BOC, ACA, and hree Japanese G-SIFIs (MUFG, MHFG, and SMFG do no have suffcen lengh of hsorcal daa o cover he whole sample perod. Regardng BOC and ACA, we backfll hsorcal daa usng Cogny 2. Regardng he hree Japanese G-SIFIs, we exrapolae hsorcal daa usng hose of her represenave afflaes, whch had been lsed before he esablshmens of holdng companes 3. All sock reurn daa are downloaded from Bloomberg. We se he 1 q =.95 confdence level for rsk measures unless oherwse noed. The number of scenaros n he Mone Carlo smulaon s S = 1 6. The forecas of sock reurns s made on a daly bass. Each busness day, he model parameers are updaed from a movng wndow of he mos recen 125 days sample reurn daa. I means ha we have 211 daly parameer esmaes sarng from Ocober 15 h, 24. In ndvdual model parameer esmaons, he varance-covarance marx of s esmaed from he mos recen 25 days sample nnovaons. 3. Esmaon resuls We presen he esmaon resuls of sysemac rsk measures. The measures are esmaed on he bass of he AGMNTS model unless oherwse noed, whereas hey are esmaed on he bass of he AGMNormal model, f needed for a reference. Frs, we valdae he usage of he AGMNTS model wh G-SIFI socks. For hs valdaon, we es he sandard NTS and normal dsrbuonal assumpons for he nnovaon of each sock n he ARMA(1,1- GARCH(1,1 model (1 hrough he Kolmogorov- Smrnov (KS es. Because we have 211 daly esmaons of he ARMA-GARCH model, he KS es s accordngly appled 211 mes for each sock. Table 1 repors he number of days on whch he NTS and normal assumpons for each sock are reeced a hree dfferen sgnfcance levels: 1%, 5%, and 1%. 2 Rsk managemen sofware provded by FnAnalyca, Inc. 3 Specfcally, we subsue Bank of Tokyo-Msubsh UFJ (8315 JP for MUFG, Da-Ich Kangyo Bank (8311 JP, unl Sepember 2 and Mzuho Holdngs (835 JP, from Ocober 2 for MHFG, and Sumomo Msu Bankng Corporaon (8318 JP for SMFG.

6 The resul s ha NTS provdes much beer fng for nnovaons han normal. The only excepon s BOC. Boh NTS and normal assumpons are reeced by all 211 esmaons for he nnovaons of BOC. However, excep BOC, he reecons of he NTS assumpon are much lower han hose of he normal assumpon a every sgnfcance level. The normal assumpon s oally reeced by BOC, BK, MUFG, MHFG, STT, and SMFG even a he 1% sgnfcance level. These observaons suppor he usage of AGMNTS model wh G-SIFI socks. To llusrae he basc rsk profles of G-SIFI socks, we refer o VaR and. We adop an equally weghed porfolo as he mos represenave porfolo, and consder he VaR and of he porfolo o be equally weghed by he 28 G-SIFI socks. Fgure 1 represens he me seres plo of he VaR and of he equally weghed porfolo esmaed by he AGMNTS and AGMNormal models. esmaed from he AGMNTS model ends o be hgher han he AGMNormal model, especally durng fnancal crss, because of s capably of accounng for fa-alness, whereas boh models gve smlar VaR a he 95% confdence level. Through a smple graphc comparson, we fnd ha he AGMNTS model and s he bes combnaon for he purpose of warnng of dsress of ndvdual nsuons or her porfolos n erms of mcro-prudenal perspecve. Subsequenly, we apply he uncondonal and condonal Chrsoffersen s lkelhood rao ess o he esmaed daly VaR of each sock o clarfy wheher Invesmen Managemen and Fnancal Innovaons, Issue 1, 213 he esmaons of VaR are reasonable. Tables 2 and 3 repor he number of volaon days and p-values of he ess for 9% VaR, 95% VaR, and 99% VaR, respecvely. Boh AGMNTS and AGMNormal models show smlar performance on he 9% VaR and 95% VaR esmaons. The AGMNTS model gves fewer VaR volaons and hgher p-values for some socks, whereas he AGMNormal model does hs for oher socks; a hgher p-value means less probably of reecon of he VaR esmaon. However, hs s no he case for he 99% VaR esmaon; he AGMNTS model clearly gves a beer forecas of VaR han he AGMNormal model. The AGMNTS model generally has fewer volaon days and hgher p-values. The number of 99% VaR volaons based on he AGMNTS model s lower han he AGMNormal model, excep for BOC and MUFG. In addon, he number of reecons of each sock s 99% VaR esmaon under he uncondonal and condonal ess are 1 and 17 a he 5% sgnfcance level for AGMNTS, whereas 22 and 25 for AGMNormal, respecvely. The fac ha he 99% VaR esmaon of he AGMNTS model s relavely more accurae han he 9% VaR and 95% VaR esmaons mples ha he deeper al srucure of he dsrbuon s beer capured by he AGMNTS model han he AGMNormal model. Ths propery of he AGMNTS model s desrable for our sudy because our man neres CoVaR cass a spolgh on he deeper al srucure. Therefore, he AGMNTS model s preferable n erms of rsk measure esmaon as well as fng performance. Table 1. Number of reecons of dsrbuonal assumpons for each sock on he bass of he KS es (ou of 211 esmaons Sgnfcance level: 1% Sgnfcance level: 5% Sgnfcance level: 1% AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal BOC BARC BNP CSGN DBK DEXB GS HSBA INGA JPM LLOY MUFG MHFG MS NDA RBS

7 Invesmen Managemen and Fnancal Innovaons, Volume 1, Issue 1, 213 Table 1 (con.. Number of reecons of dsrbuonal assumpons for each sock on he bass of he KS es (ou of 211 esmaons Sgnfcance level: 1% Sgnfcance level: 5% Sgnfcance level: 1% AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal SAN GLE STT SMFG UBSN UCG WFC AGMNTS AGMNormal VaR Spread (AGMNTS-AGMNormal Year Year Fg. 1. Tme seres of he VaR and of he equally weghed porfolo Table 2. Number of VaR volaons (ou of 211 esmaons 9% VaR 95% VaR 99% VaR AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal BOC BARC BNP CSGN DBK DEXB GS HSBA INGA JPM LLOY MUFG MHFG MS NDA RBS SAN GLE STT SMFG UBSN UCG WFC Spread (AGMNTS-AGMNormal

8 Invesmen Managemen and Fnancal Innovaons, Issue 1, 213 Table 3. p-values of he lkelhood rao es for VaR 9% VaR 95% VaR 99% VaR Uncondonal Condonal Uncondonal Condonal Uncondonal Condonal AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal BOC BARC BNP CSGN DBK DEXB GS HSBA INGA JPM LLOY MUFG MHFG MS NDA RBS SAN GLE STT SMFG UBSN UCG WFC # of p-values less han 5% # of p-values less han 1%

9 Invesmen Managemen and Fnancal Innovaons, Volume 1, Issue 1, 213 We now proceed o he esmaon resuls of sysemac rsk measures. Fgure 2 llusraes he me seres of JPNM 1. We can see ha JPNM has hgh sensvy o mporan fnancal evens. We dsngush hree urmol perods when JPNM rapdly goes up: Perod 1 s from July 27 o Sepember 28 (subprme loan problem and Lehman s collapse, Perod 2 s from Aprl 21 o March 211 (dawn of Greek soveregn problem, and Perod 3 s from Augus 211 o May 212 (U.S. cred rang downgradng and Greek polcal urmol. I s remarkable ha JPNM warns he adverse mpac of he very recen Greek crss (Perod 3 even more serously han he Lehman shock (Perod 1, whereas VaR or n Fgure 1 descrbes Perod 3 relavely moderaely. JPNM could be a reference for a forhcomng crss beyond VaR or /28 Bankrupcy of Lehman Brohers 3/28 Bear Serns Crss 5/29 SCAP Resuls Released 5-6/212 Greek Elecon and Reurn Elecon 8/211 Downgradng of U.S. Soveregn Cred Rang /27 Bankrupcy of New Cenury 7/27 Massve Downgradng of RMBS.5 4/21 Downgradng of Greek Soveregn Cred Rang Year To quanfy rsk spllover effecs, we esmae ndex ndex CoVaR q, and Co q,. We backes ndex C d ( R CoVaR as well as VaR, on he bass of he Chrsoffersen ess. Tables 4 and 5 repor he volaon raes and p-values of he ess for 9% CoVaR, 95% CoVaR, and 99% CoVaR, respecvely 2. Noe ha s no he number of CoVaR volaons bu he rae of CoVaR volaons o VaR volaons ha s repored n Table 4, because he number of VaR volaons dffers among ndvdual socks. In general, he raes of CoVaR volaons are lower and he p-values of he ess are hgher for he AGMNTS model han for he Fg. 2. Tme seres of JPNM Table 4. Rae of CoVaR o VaR volaons 12 AGMNormal model. The number of reecons of each sock s 95% CoVaR esmaon under he uncondonal and condonal ess are 3 and 8 a he 5% sgnfcance level for AGMNTS, whereas 26 and 27 for AGMNormal, respecvely. The AGMNormal esmaon of CoVaR s reeced by almos all socks. These mply ha, unlke he case of VaR, he AGMNTS model gves a beer forecas of CoVaR han he AGMNormal model regardless of sgnfcance levels. As can be observed from he defnon, CoVaR addresses al dependences among socks. A beer esmaon of CoVaR reflecs he superor descrpve power for al dependences of he MNTS dsrbuon. 9% CoVaR 95% CoVaR 99% CoVaR AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal BOC BARC BNP CSGN DBK The resulng value of JPNM s n he order of 1 2. The number of smulaon, S = 1 6, s enough for he esmaon because he sandard devaon of he esmaed JPNM s abou 4 pˆ (1 pˆ/ S 1. 2 We do no deal wh he lkelhood rao ess for 99% CoVaR because 99% VaR volaons are no frequenly observed o es 99% CoVaR. 192

10 Table 4 (con.. Rae of CoVaR o VaR volaons Invesmen Managemen and Fnancal Innovaons, Issue 1, 213 9% CoVaR 95% CoVaR 99% CoVaR AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal DEXB GS HSBA INGA JPM LLOY MUFG MHFG MS NDA RBS SAN GLE STT SMFG UBSN UCG WFC Table 5. p-values of he lkelhood rao es for CoVaR 9% CoVaR 95% CoVaR Uncondonal Condonal Uncondonal Condonal AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal AGMNTS AGMNormal BOC BARC BNP CSGN DBK DEXB GS HSBA INGA JPM LLOY MUFG MHFG MS NDA RBS SAN GLE STT SMFG UBSN UCG WFC # of p-values less han 5% # of p-values less han 1%

11 Invesmen Managemen and Fnancal Innovaons, Volume 1, Issue 1, 213 An alernave approach o rsk spllover effecs s CPNM. We compare Co and CPNM separaely, boh n me seres and cross-secon drecons. Recall ha Co s preferable o CoVaR for rsk assessmen. To compare me seres, we prepare hree regonal porfolos n he Uned Saes, Europe, and Asa. These are equally weghed porfolos comprsng G- SIFI socks belongng o each regon, and are nended o represen he me seres of sock reurns n each regon. In Fgure 3, he of regonal porfolos and Co and CPNM of each regonal porfolo on he marke ndex are ploed n he me seres drecon. The esmaons are made usng boh AGMNTS and AGMNormal models. We observe ha he AGMNTS model gves more conser- vave esmaons of sysemac rsk measures han he AGMNormal model because of s superor descrpve power for al dependences. From a comparson among rsk measures, Co s found o move sgnfcanly parallel o n he me seres drecon. I s a naural consequence ha hgher rsk leads o hgher rsk spllover effecs. On he oher hand, neher does CPNM show srong lnkage wh or Co, nor s very sensve o global adverse mpacs. However, Co and CPNM agree wh he magnude relaon; he nfluence of Asa on he sysem s relavely lower han ha of he Uned Saes and Europe. I also follows our assumpon regardng he regonal power of nfluence on he global fnancal sysem. The suaon s dfferen n he cross-secon drecon. To gan vsual undersandng, he scaer plos of cross-seconal Co vs. and Co vs. CPNM are depced n he upper and lower halves of Fgure 4, respecvely, where he average of rsk measures s aken over each sock s me seres durng he hree urmol perods suggesed by JPNM n Fgure 2. I appears ha he cross-seconal has very weak lnkage wh he cross-seconal Co. Ths resul suppors he dea ha he nsuon ha has hgher rsk s no necessarly he same one as he nsuon whose rsk conrbuon o he enre sysem s larger. The conrbuon o sysemac rsk should be dependen no only on he nsuon s sand-alone rsk measured by, for example, VaR, bu also on oher facors such as nerconnecedness wh oher nsuons. By conras, CPNM has srong posve lnear lnkage wh Co. Though four pons correspondng o he Asan G-SIFIs oule ohers n each scaer plo, hey sll appear o be on a lne. Ths suggess ha Co and CPNM are conssen when rankng he power of nfluence on he enre 194 Co CPNM Uned Saes Europe Asa Uned Saes u ope Asa Year Year AGMNTS AGMNormal Fg. 3. Tme seres of, Co, and CPNM by regon Year sysem among nsuons a he same me. Ths consenence s already observed abou he rankng among hree regons n Fgure 3. We furher nvesgae he relaonshp among cross-seconal, Co, and CPNM va he sngle lnear regresson, where he explaned varable s Co and he explanaory varables are and CPNM. Because we have 211 daly cross-seconal daases for 28 G-SIFI socks, we eravely run he regresson 211 mes. Table 6 repors he number of sgnfcanly non-zero regresson coeffcens a he 1% level by sgns and average R 2 ou of 211 ess by rsk measures a hree dfferen confdence levels. For, sgnfcanly posve coeffcens a he 1% level o Co are obaned from less han 1% of all rals and R square s, on average, que low regardless of confdence levels. For CPNM, n conras, all rals resul n a sgnfcanly posve coeffcen a he 1% level wh very hgh average R 2. Therefore, from sascal evdence, we confrm ha has almos nohng o do wh Co, bu ha CPNM has very srong posve lnkage wh Co n he cross-secon drecon.

12 Invesmen Managemen and Fnancal Innovaons, Issue 1, 213 Fg. 4. Cross-seconal lnkage among, Co, and CPNM Table 6. Ierave sngle regresson analyss for 211 cross-seconal daases among, Co, and CPNM Explanaory varable Sgn of coeffcen Confdence level: 9% Confdence level: 95% Confdence level: 99% CPNM Concludng remarks # of sgnfcan coeffcens a he 1% level Posve Negave Average R # of sgnfcan coeffcens a he 1% level Posve Negave Average R In hs paper, we measure global sysemac rsk and he margnal conrbuons o of he nsuons by usng sock reurn daa of G-SIFIs, whch consue a large poron of he global bankng sysem. To generae he fuure on dsrbuon of sock reurns, we ulze he ARMA-GARCH-MNTS and ARMA-GARCH-MNormal models. The sascal ess demonsrae ha he ARMA-GARCH-MNTS model s hghly preferable o he ARMA-GARCH- MNormal model, manly because of s capably of descrbng fa-alness and skewness of sock reurn dsrbuons. We prepare boh probably-based ndcaors and measures o quanfy he margnal conrbuon o sysemac rsk. To be specfc, we esmae he on probably and condonal probably of negave sock reurn movemens, CoVaR, and Co agans he marke ndex. The on probably of negave movemens urns ou o vvdly descrbe a sgnfcan ncrease of sysemac rsk. I provdes nformaon ha VaR or lacks and could be referred o as a sgnal of fnancal urmol. The oher measures are for rsk spllover effecs raher han References Co Co Perod CPNM Co Co Perod CPNM sysemac rsk self. We fnd ha has very weak lnkage wh Co n he cross-secon drecon, even hough boh are srongly conneced o each oher n he me seres drecon, mplyng ha he nsuon havng hgher rsk s no necessarly he nsuon havng a larger power of nfluence on he enre sysem. Therefore, exclusvely referrng o VaR can be msleadng for a macro-prudenal purpose. These resuls are conssen wh hose of Adran and Brunnermeer (211 for he U.S. fnancal nsuons. On he oher hand, he probably of negave movemens of he marke ndex on he condon of he nsuon s dsress ends o provde very smlar mplcaons o Co abou he rankng of he nsuon s power of nfluence on he enre sysem. The relave mer of Co o condonal probably s a sronger sensvy o adverse mpac on he global fnancal sysem and he ably o quanfy he mpac, whereas he relave mer of condonal probably o Co s he easness of esmaon. From hese observaons, we conclude ha combnng and he condonal probably of negave movemens would gve a useful reference for Co-based sysemac rsk measuremen. 1. Acharya, V.V., L.H. Pedersen, T. Phlppon and M. Rchardson (21. Measurng Sysemc Rsk, Techncal Repor, NYU Sern School of Busness, New York. 2. Adran, T. and M.K. Brunnermeer (211. CoVaR, Federal Reserve Bank of New York Saff Repors, No Chrsoffersen, P.F. (1998. Evaluang nerval forecass, Inernaonal Economc Revew, Vol. 39, No. 4, pp Co Co Perod CPNM 195

13 Invesmen Managemen and Fnancal Innovaons, Volume 1, Issue 1, Fnancal Sably Board (211. Polcy Measures o Address Sysemcally Imporan Fnancal Insuons, Basel. 5. Fnancal Sably Board (212. Updae of group of global sysemcally mporan banks (G-SIBs, Basel. 6. Gesecke, K. and B. Km (211. Sysemc Rsk: Wha Defauls Are Tellng Us, Managemen Scence, Vol. 57, No. 8, pp Grard, G. and A.T. Ergün (213. Sysemc rsk measuremen: Mulvarae GARCH esmaon of CoVaR, Journal of Bankng and Fnance, n press. 8. Kaufman, G.G. and K.E. Sco (23. Wha Is Sysemc Rsk, and Do Bank Regulaors Reard or Conrbue o I?, The Independen Revew, Vol. 7, No. 3, Wner, pp Km, Y.S., R. Gacome, S.T. Rachev, F.J. Fabozz and D. Mgnacca (212. Measurng fnancal rsk and porfolo opmzaon wh a non-gaussan mulvarae model, Annals of Operaons Research, Vol. 21, Issue 1, pp Rachev, S.T., S.V. Soyanov and F.J. Fabozz (28. Advanced Sochasc Models, Rsk Assessmen, and Porfolo Opmzaon: The Ideal Rsk, Uncerany, and Performance Measures, John Wley and Sons. 11. Segovano, M.A. and C. Goodhar (29. Bankng Sably Measures, IMF Workng Paper, WP/9/ Zhou, C. (21. Are Banks Too Bg o Fal? Measurng Sysemc Imporance of Fnancal Insuons, Inernaonal Journal of Cenral Bankng, Vol. 6, No. 4, pp Appendx Table A1. Ls of 29 G-SIFIs as of November Bank of Amerca (BAC Bank of New York Mellon (BK Cgroup (C Goldman Sachs (GS JP Morgan Chase (JPM Morgan Sanley (MS Sae Sree (STT Wells Fargo (WFC Uned Saes Europe Asa Banque Populare CdE Barclays (BARC BNP Parbas (BNP Commerzbank (CBK Cred Susse (CSGN Deusche Bank (DBK Dexa (DEXB Group Créd Agrcole (ACA HSBC (HSBA ING Bank (INGA Lloyds Bankng Group (LLOY Nordea (NDA Royal Bank of Scoland (RBS Sanander (SAN Socéé Générale (GLE UBS (UBSN Uncred Group (UCG Bank of Chna (3988 Msubsh UFJ FG (836 Mzuho FG (8411 Sumomo Msu FG (8316 Noe: Characers n parenheses sand for he cker symbols n each domesc marke. We refer o G-SIFIs by her cker symbol excep he Asan G-SIFIs. We refer o he Asan G-SIFIs by her abbrevaons: BOC (Bank of Chna, MUFJ (Msubsh UFJ FG, MHFG (Mzuho FG, and SMFG (Sumomo Msu FG. 1 The mos recen ls conans revsons owng o he updae on November 212. See Fnancal Sably Board (