JEL Codes: F3, G1, C5 Keywords: International Finance, Correlation, Variance Targeting, Multivariate GARCH, International Stock and Bond correlation

Transcription

1 EUROPEAN CENTRAL BANK WORKING PAPER SERIES WORKING PAPER NO. 04 ASYMMETRIC DYNAMICS IN THE CORRELATIONS OF GLOBAL EQUITY AND BOND RETURNS BY LORENZO CAPPIELLO, ROBERT F. ENGLE AND KEVIN SHEPPARD January 003

2 EUROPEAN CENTRAL BANK WORKING PAPER SERIES WORKING PAPER NO. 04 ASYMMETRIC DYNAMICS IN THE CORRELATIONS OF GLOBAL EQUITY AND BOND RETURNS 1 BY LORENZO CAPPIELLO, ROBERT F. ENGLE 3 AND KEVIN SHEPPARD 4 January Sofware used n he esmaon of hs paper can be found a hp://weber.ucsd.edu/~ksheppar n he research secon. Kevn Sheppard would lke o acknowledge fnancal suppor from he European Cenral Bank. Whle all effors have been made o ensure ha here are no errors n he paper, remanng errors are he sole responsbly of he auhors. The opnons expressed heren are hose of he auhors and do no necessarly represen hose of he European Cenral Bank. Ths paper can be downloaded whou charge from hp:// n or from he Socal Scence Research Nework elecronc lbrary a: hp://papers.ssrn.com/absrac_d=xxxxxx European Cenral Bank, emal: lorenzo.cappello@ecb.n 3 NYU Sern School of Busness and Unversy of Calforna a San Dego, emal: rober.engle@sern.nyu.edu 4 Unversy of Calforna a San Dego, emal: ksheppar@econ.ucsd.edu.

3 European Cenral Bank, 003 Address Kasersrasse 9 D Frankfur am Man Germany Posal address Posfach D Frankfur am Man Germany Telephone Inerne hp:// Fax Telex ecb d All rghs reserved. Reproducon for educaonal and non-commercal purposes s permed provded ha he source s acknowledged. The vews expressed n hs paper do no necessarly reflec hose of he European Cenral Bank. ISSN (prn) ISSN (onlne)

4 Conens Absrac 4 Non-echncal summary 5 I. Inroducon 7 II. Condonal covarance leraure 10 III. Economerc mehodology 1 IV. Daa 16 V. Emprcal resuls 0 V.1 Specfcaon esng V. Volaly dynamcs and lnkages 4 V.3 Correlaon dynamcs 5 VI. Concluson 8 Appendx A: Counres seleced 31 Appendx B: Exac specfcaons 3 Bblography 35 Tables & fgures 38 European Cenral Bank workng paper seres 60 ECB Workng Paper No 04 January 003 3

5 Absrac Ths paper nvesgaes he presence of asymmerc condonal second momens n nernaonal equy and bond reurns. The analyss s carred ou hrough an asymmerc verson of he Dynamc Condonal Correlaon model of Engle (00). Wdespread evdence s found ha naonal equy ndex reurn seres show srong asymmeres n condonal volaly, whle lle evdence s seen ha bond ndex reurns exhb hs behavour. However, boh bonds and eques exhb asymmery n condonal correlaon. Worldwde lnkages n he dynamcs of volaly and correlaon are examned. I s also found ha begnnng n January 1999, wh he nroducon of he Euro, here s sgnfcan evdence of a srucural break n correlaon, alhough no n volaly. The nroducon of a fxed exchange rae regme leads o near perfec correlaon among bond reurns whn EMU counres. However, equy reurn correlaon boh whn and ousde he EMU also ncreases afer January JEL Codes: F3, G1, C5 Keywords: Inernaonal Fnance, Correlaon, Varance Targeng, Mulvarae GARCH, Inernaonal Sock and Bond correlaon 4 ECB Workng Paper No 04 January 003

6 Non echncal summary Among oher emprcal regulares, (condonal) esmaes of he second momens of eques ofen exhb he so-called asymmerc volaly phenomenon, where volaly ncreases more afer a negave shock han afer a posve shock of he same magnude. In fac, evdence has been proffered ha volaly may fal o ncrease or even fall subsequen o a posve shock for ceran asses. 1 Asymmerc effecs have also been recenly found n condonal correlaons, alhough he economc reasonng behnd hese effecs has no been wdely researched. Surprsngly, whle here has been a prolferaon of condonal economerc models able o capure asymmery n volaly (see Henscell (1995) for a synhess), condonal economerc specfcaons able o explcly model asymmery n covarances and, specfcally, correlaons are far less common. However, as argued by Kroner and Ng (1998), f he expeced reurn on one asse changes due o he occurrence of an asymmerc volaly effec, he correlaon (and hus he covarance) beween reurns on ha asse and reurns on oher asses whch have no had a change n her expeced reurns should also change. A second sylsed fac whch emerges from surveyng emprcal research s ha whle he asymmerc phenomenon n (condonal) varances has been wdely explored for ndvdual socks, equy porfolos, and/or sock marke ndces, day-o-day changes n governmen bond reurn volaly has receved lle aenon, nsead focusng on he mpacs of (macroeconomc) news announcemens on condonal volaly of bonds and T-blls. Fnally, a number of sudes documens ha correlaon beween equy reurns ncreases durng bear markes and decreases when sock exchanges rally, ndcang ha correlaon s dynamc and vares over me, hereby changng he amoun of porfolo dversfcaon whn a gven asse allocaon. The goals of hs paper are wofold. Frs, s nvesgaed wheher, n addon o socks, governmen fxed ncome secures also exhb asymmery n condonal second momens. Second, hs paper explores he dynamcs and changes n he correlaon of nernaonal asse markes, focusng aenon on wheher he correlaon of boh bonds and socks demonsrae evdence of asymmerc response o negave reurns. Unlke prevous research, we wll no nvesgae wheher condonal second momens of fxed ncome secures change when (macroeconomcs) news are released. We wll es, nsead, wheher condonal varances, covarances, and correlaons of such asses are sensve o he sgn of pas nnovaons. The analyss s carred ou hrough an asymmerc 1 Two explanaons have been pu forh for hs phenomenon: he leverage effec hypohess, due o Black (1976) and Chrse (198), and he volaly feedback effec proposed by Campbell and Henschell (199) and exended by Wu (000). See, for nsance, Kroner and Ng (1998), Errunza and Hung (1999), and Bekaer and Wu (001). ECB Workng Paper No 04 January 003 5

7 verson of he Dynamc Condonal Correlaon (DCC) model of Engle (00), whch s parcularly well sued o examne correlaon dynamcs among asses. The robus condonal momen es suggesed by Kroner and Ng s employed o check wheher he model specfcaon adequaely characersed he lnear dependence shown by he daa. We also explore he asymmerc volaly mpac of an nnovaon hrough news mpac curves of Engle and Ng (1993), and asymmery n condonal covarances by he news mpac surfaces of Kroner and Ng. We fnd srong evdence of asymmeres n condonal covarance of boh equy and bond reurns, alhough he asymmeres are presen n markedly dfferen manners. Whle naonal equy ndex reurn seres show asymmery n condonal volaly, lle evdence s found ndcang asymmery n bond ndex reurn volaly. However, despe he lack of evdence of asymmerc condonal volales, bonds (as well as eques) exhb asymmery n condonal correlaon, alhough, eques showed a sronger response o jon bad news han bonds do. Srong evdence of marke volaly correlaon s also presened for equy reurns: n parcular, annualsed average volaly seres for European, EMU, Amercan and Ausralasan eques show lnkages durng easly denfable perods of fnancal urmol such as he crash of 87, he begnnng of he Gulf war, and he Asan fnancal crss. Agan, unlke equy reurns, bond marke volales demonsrae less clear lnkages, nsead, exhbng ncreases o regon specfc evens whch do no appear o be conagous across regons. Upon he creaon of he Euro, nally whou a crculang currency when EMU exchange raes were rrevocably fxed, sgnfcan evdence of a srucural break s found n he level of condonal correlaon bu no n he levels of he condonal volales. Condonal equy correlaon for he major markes of Europe,.e. France, Germany and Ialy (whch are par of he EMU) and UK (whch s no par of he EMU), has ncreased snce he nroducon. In addon o he expeced ncrease n he Euro-area, evdence s also found of a meanngful ncrease n correlaon of oher markes wh he EMU naons, possbly sgnallng sronger economc es. Furher, he nroducon of a fxed exchange rae regme has led o near perfec correlaon among bond reurns whn EMU counres, whch s no surprsng consderng he moneary polcy harmonsaon whn he EMU. Ths ncrease n correlaon among asse reurns whn he EMU area may have nduced nvesors, when dversfyng her porfolos, o move capal from Europe o he US, possbly conrbung o he deprecaon of he euro vs-à-vs he US dollar n he monhs followng he nroducon for he fxed rae regme. Condonal equy correlaon seres among regonal groups ncreases dramacally when bad news h fnancal markes. Ths s an mporan mplcaon for nernaonal nvesors; dversfcaon sough by nvesng n mulple markes s lkely o be lowes when s mos desrable. However, s also evdenced ha condonal correlaon beween equy and bond reurns ypcally declnes when sock markes suffer from fnancal urmol, an ndcaon of a flgh o qualy phenomenon, where nvesors move capal from eques o safer asses. 6 ECB Workng Paper No 04 January 003

8 I. Inroducon Typcally, porfolo dversfcaon s acheved usng wo man sraeges: nvesng n dfferen classes of asses hough o have lle or negave correlaon or nvesng n smlar classes of asses n mulple markes hrough nernaonal dversfcaon. Whle hese wo sraeges have sold heorecal jusfcaon and srong emprcal evdence exss as o he benefs, nvesors mus be aware ha correlaon s dynamc and vares over me, changng he amoun of porfolo dversfcaon whn a gven asse allocaon. In parcular, a number of sudes documen ha correlaon beween equy reurns ncreases durng bear markes and decreases when sock exchanges rally (see, among ohers, Erb, Harvey and Vskana, (1994), De Sans and Gerard, (1998), Ang and Bekaer, (001), Das and Uppal, (001), and Longn and Solnk, (001)). Over he pas 0 years, a remendous leraure has developed where he dynamcs of he covarance of asses has been explored, alhough he prmarly focus has been on unvarae volales and no correlaons (or covarances). Among oher regulares, (condonal) esmaes of he second momens of eques ofen exhb he so-called asymmerc volaly phenomenon, where volaly ncreases more afer a negave shock han afer a posve shock of he same magnude; n fac, evdence has been proffered ha volaly may fal o ncrease or even fall subsequen o a posve shock for ceran asses. 1 Asymmerc effecs have also been recenly found n condonal correlaons, alhough he economc reasonng behnd hese effecs has no been wdely researched. The need o ake no accoun he asymmerc effecs on condonal second momens has an appealng economc jusfcaon. Assume, for nsance, ha a negave reurn shock generaes more volaly han a posve nnovaon of he same magnude. When, as commonly done, a radonal symmerc Generalzed Auoregressve Condonally Heeroskedascy (GARCH) process s used o model second momens, he esmaed condonal volaly whch occurs afer a prce drop wll be oo small; smlarly, he esmaed condonal volaly followng a prce ncrease wll be oo large. Consequences such as asse msprcng and poor n- and ou-of-sample forecass wll be, herefore, unavodable. Accurae esmaes of he varance and correlaon srucure of reurns on eques as well as oher classes of asses are crucal for porfolo selecon, rsk managemen, and prcng of prmary and dervave secures. Surprsngly, whle here has been a prolferaon of condonal economerc models able o capure asymmery n volaly (see Henscell (1995) for a synhess), condonal economerc 1 Two explanaons have been pu forh for hs phenomenon: he leverage effec hypohess, due o Black (1976) and Chrse (198), and he volaly feedback effec proposed by Campbell and Henschell (199) and exended by Wu (000). ECB Workng Paper No 04 January 003 7

9 specfcaons able o explcly model asymmery n covarances and, specfcally, correlaons are far less common. However, as argued by Kroner and Ng (1998), f he expeced reurn on one asse changes due o he occurrence of an asymmerc volaly effec, he correlaon (and hus he covarance) beween reurns on ha asse and reurns on oher asses whch have no had a change n her expeced reurns should also change. Alhough here exs sudes whch accoun for asymmerc effecs n condonal covarances, (see, for nsance, Braun, Nelson, and Suner (1995), Koumos and Booh (1995), Koumos (1996), Booh, Markanen, and Tse (1997), Scruggs (1998), and Chrsansen (000)), he economerc mehodology employed address he phenomenon hrough a smplfed and no necessarly sasfacorly approach. Apar from he research of Braun e al. 3, me-varyng covarances are parameerzed n he spr of Bollerslev (1990) where he covarance s proporonal o he produc of he correspondng condonal sandard devaons 4 ; he correlaon coeffcen s he proporonaly facor and s assumed o be consan over he sample perod. Alhough assumng he correlaon coeffcen consan grealy smplfes he compuaonal burden n esmaon, no only here are no heorecal jusfcaons for ha assumpon, s no robus o he emprcal evdence. A second generaon of mulvarae condonal varance models, where he assumpon of consan correlaon coeffcens s relaxed and asymmery s explcly nroduced n varances as well as covarances, has been nroduced by Kroner and Ng. Subsequen applcaons (see, for nsance, Bekaer and Wu (000), Brooks and Henry (000), and Isakov and Pérgnon (000)) buld on hs model. As wh mos mulvarae GARCH model, hough, all hese represenaons suffer from a shorcomng: hey usually have oo many coeffcens o esmae, and he models are ypcally of lmed scope or sgnfcan parameer resrcons mus be mposed. A second sylzed fac whch emerges from surveyng emprcal research s ha whle he asymmerc phenomenon n (condonal) varances has been wdely explored for ndvdual socks, equy porfolos, and/or sock marke ndces, day-o-day changes n governmen bond reurn volaly has receved lle aenon, nsead focusng on he mpacs of (macroeconomc) news announcemens on condonal volaly of bonds and T-blls. 5 Jones, Lamon and Lumsdane (1998) deec an ncrease n he condonal bond marke varance on days where See, for nsance, Kroner and Ng (1998), Errunza and Hung (1999), and Bekaer and Wu (001). 3 Braun e al., who analyze a porfolo of wo asses, model he second momen marx by splng no hree peces: The wo condonal varances assocaed wh each secury and he condonal bea. Also n hs case condonal covarances do no exhb explc asymmerc effecs. 4 The condonal covarances wll show an asymmerc response o negave shocks when asymmerc unvarae GARCH models are used for he volales n he Consan Correlaon Coeffcen (CCC) model of Bollerslev. However, despe he asymmerc covarances, correlaons are consan. 5 In fac, lle has been done o explore he correlaon srucure of bond reurns across counres. 8 ECB Workng Paper No 04 January 003

10 employmen and producer prce ndex daa are announced. L and Engle (1998) examne he effecs of macroeconomc announcemens on he volaly of US Treasury bond fuures. Scheduled announcemens rgger srong asymmerc effecs: s shown ha whereas posve shocks depress condonal volaly, negave shocks ncrease. Chrsansen (000) documens ha macroeconomc news releases rase he condonal second momen coeffcens of US governmen bond reurns. The goals of hs paper are wofold. Frs, s nvesgaed wheher, n addon o socks, governmen fxed ncome secures also exhb asymmery n condonal second momens. Second, hs paper explores he dynamcs and changes n he correlaon of nernaonal asse markes, focusng aenon on wheher he correlaon of boh bonds and socks demonsrae evdence of asymmerc response o negave reurns. Unlke prevous research, we wll no nvesgae wheher condonal second momens of fxed ncome secures change when (macroeconomcs) news are released. We wll es, nsead, wheher condonal varances, covarances, and correlaons of such asses are sensve o he sgn of pas nnovaons. The robus condonal momen es suggesed by Kroner and Ng s employed o check wheher he model specfcaon adequaely characerzed he lnear dependence shown by he daa. We also explore he asymmerc volaly mpac of an nnovaon hrough news mpac curves of Engle and Ng (1993), and asymmery n condonal covarances by he news mpac surfaces of Kroner and Ng. We also nvesgae ceran neresng quesons: has he formaon of he moneary unon n Europe ncreased he correlaon among naonal asses? If naonal asse correlaon has really ncreased along wh he moneary negraon, and f he Euro-area s consdered more and more as a unfed economc-fnancal block, do nvesors move capal, whch before were allocaed whn he Euro-area, owards oher regons, wh obvous consequences on exchange raes? Moreover, wha are he consequences of growng asse correlaon, f any, on nernaonal porfolo dversfcaon? Has he overall reurn correlaon of boh bond and eques ncreased over he laer par of he 1990s and no he early years of he new mllennum, as evdenced n Moskowz (00)? Fnancal marke lnkages have been hghlghed by several sudes. Flemng, Krby and Osdek (1998) show ha nformaon plays an mporan role n creang volaly lnkages across US sock, bond, and money markes. On one hand, common nformaon, noably macroeconomcs news, affec nvesors expecaons n dfferen markes a he same me. On he oher hand, nformaon evens ha aler expecaons n one marke brng abou porfolo rebalancng and hence an nformaon spllover n oher markes. Ths cross-marke hedgng, n ECB Workng Paper No 04 January 003 9

11 urn, generaes rade and volaly across markes. Frazscher (001) fnds ha fnancal negraon among European Moneary Unon (EMU) members has ncreased due o reducon and elmnaon of exchange rae volaly as well as o, hough o less exen, moneary polcy convergence, a resul whch s conssen wh our fndngs. Harmann, Sraemans, and de Vres (001) pu emphass o lnkages beween fnancal markes durng urmol perods and fnd ha he probably of a crash n a marke condoned on a crss n anoher marke s hgh, where conagon propagaes across naonal borders. Moreover, crss n equy markes may generae flgh-o-qualy phenomena. We also observe volaly spllovers from equy o bond markes, whch may reflec a flgh-o-qualy. We use he Fnancal Tme All-World ndces for nernaonal equy markes as a measure of overall equy reurn n a gven counry and DaaSream consruced bond ndces as a measure of bond performance o model he covarance srucure of world nvesmen markes. The paper s lad ou as follows: secon presens a revew of he recen leraure and descrbes he sylzed facs abou fnancal reurn GARCH modelng, whle secon 3 covers he economerc mehodology employed n hs paper. In secon 4, he daa used n he paper s descrbed and boh uncondonal and unvarae condonal properes are explored. Secon 5 covers he mulvarae condonal resuls and examnes he specfcaon and secon 6 concludes and dscusses areas for furher research. II. Condonal Covarance Leraure As poned ou by Nelson (1991), among ohers, he radonal symmerc GARCH process nroduced by Engle (198) and Bollerslev (1986) suffers from an mporan lmaon. Alhough eleganly capures volaly cluserng, does no allow negave and posve pas shocks o have a dfferen effec on fuure condonal second momens. In oher words, only he magnude, no he sgn of lagged nnovaons deermnes condonal varance. Therefore a model ha capures he asymmerc responses of condonal second momens should be preferable for asse prcng applcaons. To beer see hs, consder a porfolo made of eques and wha occurs afer a large prce drop, lke he one ha occurred n Ocober If a negave reurn nnovaon generaes more volaly han a posve reurn nnovaon of he same magnude, a symmerc GARCH process wll underesmae he condonal volaly whch occurs afer bad news, and smlarly wll overesmae he condonal volaly followng good news. In CAPM-ype models, condonal volaly drecly affecs rsk prema nvesors requre o hold rsky asses. Bu he prema forecas by he radonal GARCH dffer from hose mpled by an asymmerc GARCH, wh a consequence of probable asse msprcng. 10 ECB Workng Paper No 04 January 003

12 Whle he unvarae GARCH leraure began by assumng ha reurn volaly was a lnear process of pas squared nnovaons, researchers soon realzed ha oher processes were boh beer performng and heorecally jusfed. Henschell (1995) proposed a general model whch accommodaes several ypes of unvarae asymmerc GARCH paramersaons, where asymmery s refleced by he news mpac curves of Engle and Ng (1993). Recen evdence (Hansen and Lunde (001)) has shown ha no only do asymmerc volaly models perform beer n-sample, bu hey also produce superor forecass. Whle asymmeres n condonal volales have been horoughly emprcally verfed, he effors o capure asymmerc effecs n mulvarae sengs, however, have been rarer. Presenly, here are only wo models capable of capurng asymmerc effecs n correlaon n a mulvarae GARCH model. The frs o model asymmerc effecs was Kroner and Ng (1998). The model hey proposed allows for asymmerc effecs n boh he varances and covarance. An alernave mulvarae GARCH parameerzaon whch perms o capure asymmeres n varances (bu no n correlaons) s he Dynamc Condonal Correlaon (DCC) GARCH model of Engle (00). As poned ou n Engle and Sheppard (001), any unvarae GARCH model whch s covarance saonary and assumes normally dsrbued errors (rrespecve of he rue error dsrbuon) can be used o model he varances, as he model s esmaed n wo seps: he frs n whch varances are esmaed usng a unvarae GARCH specfcaon, and he second where he parameers of he dynamc correlaon are consdered. Sheppard (00) has recenly exended he DCC model o allow for asymmerc dynamcs n he correlaon n addon o he asymmerc response n varances (whch were avalable n he orgnal DCC model). Moreover, whle he orgnal DCC model assumed ha all asses shared he same news mpac curve for correlaon, Sheppard s specfcaon s able o accommodae dfferen news mpac curves for correlaons across dsnc asses. Economcally, asymmerc volaly can be explaned by wo models: leverage effec and me-varyng rsk prema (volaly feedback). The leverage effec, due o Black (1976) and Chrse (198), saes ha afer a negave shock, he deb-o-equy rao of a frm has ncreased. Thus, he volaly of he whole frm, whch s assumed o reman consan, mus be refleced by an ncrease n volaly n he non-leveraged par of he frm (equy). An alernave explanaon of he larger ncrease n volaly afer a negave shock proffered by Campbell and Henschel (199) s ha afer a negave shock and varance ncrease, he expeced reurn mus become suffcenly hgh o compensae he nvesor for he ncreased volaly, hus creang more volaly (volaly feedback). These wo explanaons for asymmeres n volaly are no exclusve, and Bekaer and Wu (000) have combned hese wo explanaons n an emprcal ECB Workng Paper No 04 January

13 model and have shown ha he leverage effec alone does no adequaely explan he changes n volaly afer a decrease n he asse prce. Boh of hese explanaons for larger volaly subsequen o a negave shock have prmarly focused on he volaly of eques, alhough he Campbell and Henschel model s applcable o bonds as well as socks, hrough he CAPM, reang bonds as rsky asses (see Cappello, 000). However, as bonds do no have leverage, he leverage effec s mplausble. Furher, whle here s compellng evdence ha bond volaly ncreases afer announcemen abou macroeconomcs news, s ye o be seen f he asymmerc effec s presen n he day o day volaly dynamcs of governmen bonds. In addon o possble explanaons for asymmeres n bond reurn volaly, lle heorecal framework s avalable o explan he recen evdence of asymmerc response o jon bad news n correlaons (jon bad news refers o boh reurns beng negave). Whle ceran models can capure hese effecs, here has been lle done o explan her presence. One possble explanaon ress on me-varyng rsk prema. More precsely, f, due o negave shocks, he varances of wo secures ncrease, n a CAPM-ype world, nvesors wll requre hgher reurns o compensae he larger rsk hey face. As a consequence, prces of boh asses wll decrease and asse correlaon wll go up, as usually happens n down markes. Correlaon may herefore be hgher afer a negave nnovaon han afer a posve nnovaon of he same magnude, ndcang s sensvy o he sgn of pas shocks. However, hs dea has no ye been formalzed n a mulvarae model. Anoher plausble explanaon s ha dependence n reurns s hgher for large negave reurns, and possbly nonlnear. In hs case he ncreased correlaon observed s smply a lnear approxmaon o he nonlnear dependence. Recenly, Paon (00) has shown ha correlaon provdes a good approxmaon o he dependence srucure of porfolos of large and small cap socks. However, s ye o be seen how wdespread hs phenomenon s. III. Economerc Mehodology Whle here has been wde emprcal evdence of asymmeres n volales, recen sudes (Kroner and Ng (1998), Baeker and Wu (000), and Cappello (000)) have also provded lmed evdence for asymmeres n covarance above hose whch would be presen under an assumpon of asymmerc volales bu wh consan correlaon. In order o nvesgae he properes of nernaonal equy and bond reurns, we have chosen o use a recenly nroduced generalzaon of he DCC (Engle (00)) model. The general form of he model employed n 1 ECB Workng Paper No 04 January 003

14 hs paper was developed n Sheppard (00), and ncludes wo modfcaons o he orgnal DCC model: asse specfc correlaon news mpac curves and asymmerc dynamcs n correlaon. All DCC class models (ncludng he Consan Correlaon Coeffcen-GARCH (CCC- GARCH) of Bollerslev (1990)) assume ha a k 1 vecor of asse reurns r are condonally normal wh mean zero and covarance marx 1 H and use he fac ha H can be decomposed as follows: ( 0 H ) r I ~ N,, (1) H = D R D, () where D s he k k dagonal marx of me-varyng sandard devaons from unvarae GARCH models wh h, on he h dagonal and R s he (possbly) me-varyng correlaon marx. 6 The DCC model was desgned o allow for wo-sage esmaon of he condonal covarance marx H : n he frs sage unvarae volaly models are fed for each of he asses and esmaes of h, are obaned; n he second sage asse reurns, ransformed by her esmaed sandard devaons resulng from he frs sage, are used o esmae he parameers of he condonal correlaon. The orgnal DCC esmaor had he dynamcs of correlaon evolvng as a scalar process wh a sngle news mpac parameers and a sngle smoohng parameer. However, for hgher dmensonal models and ceran asses, hs proved o be nadequae, and he Asymmerc Generalzed DCC (AG-DCC) esmaor was developed o capure he heerogeney presen n he daa. The model used n hs paper s a resrced verson of he AG-DCC model. As asymmeres n volales are a wdely acceped emprcal fac, he unvarae volaly models wll be seleced usng he Schwarz Informaon Creron (BIC) from a class of models capable of capurng he common properes of equy reurn varance. 7 The followng models were ncluded n he specfcaon search (all wh one lag of he nnovaon and one lag of volaly) GARCH (Bollerslev (1996)) AVGARCH (Taylor (1986)) NARCH (Hggns and Bera (199)) EGARCH (Nelson (1991)) 6 The assumpon of condonal normaly s no crucal and n he absence of condonal normaly, hese resuls have a sandard QMLE nerpreaon. ECB Workng Paper No 04 January

15 ZARCH (Zakonan (1994)) GJR-GARCH (Glosen, Jaganahan, and Runkle (1993)) APARCH (Dng, Engle and Granger (1993)) AGARCH (Engle (1990)) NAGARCH (Engle and Ng (1993)) Appendx B conans exac specfcaon employed for hese models. Once he unvarae volaly models are esmaed, he sandardzed resduals, ε = r h, are used o esmae he dynamcs of he correlaon. The evoluon of he correlaon n he sandard DCC model (Engle (00)) s gven by where Q E[ ε ε ] Q = ( 1 a b) Q + a 1ε 1 + bq 1 * 1 * 1 = Q QQ ε (3) R (4) = and where a and b are scalars. However, as hs model does no allow for asse specfc news mpac parameers nor asymmeres, he evoluon equaon has been modfed (See Sheppard (00)) o be Q ( Q A QA B QB G NG) + A A + B Q B + G n n G = 1ε ε (5) where A, B, and G are dagonal parameer marxes, [ ] Hadamard produc), N E [ ] wh sample analogues, T n = I ε < 0 ε (wh ndcang he = n n. For Q and N, expecaons are nfeasble and are replaced 1 T = 1 ε ε and T 1 T n = n 1 * *, respecvely. Q [ q ] = [ q ] = s a dagonal marx wh he square roo of he h dagonal elemen of Q on s h dagonal poson. In oher words, * Q s a marx whch guaranees * 1 * 1 = Q QQ R s a correlaon marx wh ones on he dagonal and every oher elemen less han one n absolue value, as long as,, Q s posve defne. 8 The ypcal elemen of R wll be of he form ρ j, = q j, q, q jj,. The mmedae mplcaon s ha R wll necessarly be a correlaon marx by he Cauchy-Schwarz nequaly (see Engle and Sheppard (001) for a formal proof). 9 I s also smple o exend he 7 Whle here are many nformaon crera avalable, n addon o lkelhood rao esng usng nesed models, we fel ha he use of he BIC was approprae as wll lead o asympocally correc model specfcaon selecon. 8 Q wll be posve defne wh probably one f ( Q A QA B QB G QG) s posve defne. 9 Four specal cases of hs model (equaons 3 and 4) exs, he CCC mulvarae GARCH ( A,G = [] 0 ), ( G = 0, A = aj = a, B = [ bj ] = [ b]), he Asymmerc DCC he DCC mulvarae GARCH [] [ ] [ ] 14 ECB Workng Paper No 04 January 003

16 model o allow for srucural breaks n eher mean or dynamcs. For nsance, le d be 0 or 1, dependng on wheher > τ < T. Then o examne wheher a srucural break has n he mean occurred, he model can be modfed o ~ ~ ~ Q = ( Q dq A QA + da QA B QB + db QB G NG + dg NG) + (6) A ε ε A + B Q B + G n n G where Q = E[ ε ε ], < τ, and Q = Q E[ ε ε ], τ ~ , wh N and N ~ analogously defned, whch s equvalen o he followng parameerzaon (where [ e '], < τ, Q = E[ e e '], τ Q = ( Q A Q A B Q B G N G) + ( Q A Q A B Q B G N G) Q1 = E e ) when mean reverson s enforced (7) A ε 1ε 1 ' A + B Q 1B + G n 1n 1G. As he model n equaon 6 ness he sandard model (equaon 3), s sragh forward o es for breaks n he mean of he process. The es can be conduced usng sandard lkelhood rao ess wh k(k-1)/ degrees of freedom (d.o.f.). Breaks n dynamcs as well as breaks n boh dynamcs and mean can be esed for analogously (alhough wh dfferen d.o.f.). Kroner and Ng (1998) nroduced a noon for mulvarae GARCH models analogous o a news mpac curve for unvarae models, a news mpac surface. For he model consdered n hs paper, he news mpac surface for correlaon wll be asymmerc, havng (poenally) greaer response o jon bad news (boh reurns less han zero) han o jon good news. The news mpac surface for correlaon s gven by f ( ε ) c~ 1, ε j + ( aa j + g g j ) ε ε j, for ε1, ε < 0 f ε, ε c~, (8) + a a ε ε, ( ) oherwse 1 j j j where ε, 1, are he sandardzed resduals. 10 The news mpac surface for covarance wll = smply be he news mpac surface for correlaons mulpled by he approprae poron of he news mpac curve for he unvarae models, whch can be very dfferen should he models for he unvarae volales be drascally dfferen, producng asymmeres n covarance n all four drecons from he orgn. (ADCC) mulvarae GARCH ( A [ aj ] = [ a ], =, and he generalzed dagonal DCC (GDDCC) mulvarae GARCH model ( G = [] 0 ). 10 Ths formula s approxmae, due o he non-lnear ransformaon needed. The exac news mpac surface s gven n appendx B.. = B = [ bj ] = [ b], G [ gj ] = [ g ]) ECB Workng Paper No 04 January

17 IV. Daa The daa employed for hs paper consss of FTSE All-World Indces for 1 counres and DaaSream consruced 5 year average maury bond ndces for The FTSE All-World Index Seres are a measure of a well dversfed nvesmen n a parcular counry usng a value weghed average. These ndces are consruced usng 90% of he equy value n a counry conssng of large- and medum-caps, and represen he oal reurn on eques as he ndces are dvdend adjused. The DaaSream Benchmark bond ndces conss of he mos lqud governmen bonds and follow he European Federaon of Fnancal Analyss (EFFAS) mehodology. These bond ndces are avalable daly and are chan lnked allowng he addon and removal of bonds whou affecng he value of he ndex. All daa were aken from DaaSream and convered o US dollar denomnaed reurns (appendx A conans a complee ls of he equy and bond ndces ncluded n hs sudy). The seleced 1 counres conan mos of he presen day EU, he major markes of he Amercas, boh developed and developng, and he major markes of Ausralasa. 1 One of he prmary concerns when workng wh nernaonal daa, specfcally asse correlaon, s ha non-synchronous radng ssues can arse whch wll lead o a downward bas n he esmaed correlaon. Marens and Poon (001) have shown ha usng non-synchronous daa resuls n a sgnfcan downward bas n correlaon, as compared o pseudo-closes. 13 However, wh he global scope for hs paper, here s never a me when all 1 markes are open. Thus, weekly reurns were used nsead of daly o allevae he problem of asynchronous closes. The daa conan 15 years of weekly prce observaons, for a oal of 790 observaons from January, 1987 unl February 15, 001. All weekly reurns were calculaed as log dfferences usng Frday o Frday closng prces. To begn analyzng hs daa se, s nformave o examne he uncondonal correlaon among he varous sock and bond seres. 14 Table 1 summarzes nformaon abou he dsrbuon of correlaons beween he equy seres, he bond seres, and correlaons beween he equy seres and he bond ndces, whle able (a, b, and c) conans he uncondonal correlaon for each of he 34 asses. Whle he dsrbuon of he average correlaon for groups of asses s dffcul o calculae, we were able o conduc 11 The acual seres were he DaaSream Benchmark Bond Indces wh 5 years average maury (code BMXX05Y where XX s he counry code). 1 The 13 ncluded bond markes are a proper subse of he 1 ncluded equy markes and nclude all of he major world governmen bond markes. 13 Pseudo-closes are smply consruced by samplng all prces a he same me GMT. 14 The uncondonal correlaon could be consdered as a naïve esmae n he presence of heeroskedascy, and wll underesmae he average condonal correlaon beween he nnovaons. 16 ECB Workng Paper No 04 January 003

18 sgnfcance es usng he boosrap dsrbuons of hese sascs. 15 The boosrap dsrbuon was abulaed usng he saonary boosrap (Pols and Romano (1994)) wh an average wndow lengh of 13 weeks (based on nal esmaes of he perssence of correlaon across all asses). When sascal sgnfcance s ndcaed, means ha he emprcal quanle of he boosrap dsrbuon s less han (or greaer han, dependng on he es) he sasc. Overall he asses are reasonably correlaed wh a medan correlaon of However, here s a wde range of correlaon among he asses, rangng from an average of for US bond ndex reurns o for Duch eques. The average correlaon for he equy seres (.3401) s smlar o he overall average correlaon for he bond ndces (.370). However, whle on average hey appear he same, asse reurns are hghly correlaed wh her own ype and less correlaed wh he oher ype, or n oher word, he equy-equy and bond-bond correlaons are far hgher han equy-bond correlaons. In fac, medan bond-bond reurn correlaon was 0.776, medan equy-equy correlaon was , and medan equy-bond correlaon was only , wh all hree means beng sascally dfferen from he oher wo a he 1% level. Among he equy ndex reurn seres, he mean correlaon was The equy marke wh he hghes average correlaon was The Neherlands wh whle boh Japan and Mexco exhbed he lowes average correlaons a and 0.86 respecvely. The nrasock ndex reurn correlaons demonsraed a srong ncrease n correlaon when consdered a he regonal level. In hs sample, here exs hree clear geographc groups for he daa: Ausralasa, Europe and Norh Amerca. 16 Whn he Ausralasan subgroup he average correlaon was 0.403, whle he average correlaon beween equy ndex reurns n he Ausralasan group and he European group was , and wh Norh Amercan markes. Average correlaon among he European markes was 0.589, whle European and Norh Amercan markes had an average correlaon of Fnally, he average correlaon whn he Norh Amercan equy markes was The correlaons whn boh he European and Amercan were sascally sgnfcanly hgher han were he correlaons beween hese wo groups and he ohers. In addon, he correlaon whn he Ausralasan group was 15 Whle he correlaons should be asympocally mulvarae normally dsrbued, he compuaon of he asympoc covarance marx would be made more dffcul as he models are dynamcally msspecfed requrng an adjusmen o he Whe robus sandard errors o accoun for auocorrelaon n he scores of he correlaon esmaor. 16 Group membershp s lsed n Appendx A. 17 The correlaon beween he US and Canadan equy ndex reurns was The correlaon beween Canadan and US markes wh Mexcan eques was much lower, and , respecvely. ECB Workng Paper No 04 January

19 sascally hgher han he correlaon beween he Norh Amercan group and he Ausralasan group. Turnng aenon o he correlaon beween he bond ndces, here also appears o be dsnc groups for he uncondonal correlaon of bond reurns: Europe, Japan, and Norh Amerca. Whn European bond markes, average correlaon beween reurns was , whle average correlaon beween European markes and Japan was and average correlaon beween European bond ndex reurns and Norh Amercan bond reurns was Correlaon among Norh Amercan bond reurns (Canada and he Uned Saes) whle average correlaon beween Amercan bond reurns and Japanese bond reurns was As was he case wh he mean equy ndces, he mean nra-regon correlaons were sascally greaer han he mean ner-regon correlaons. Fnally, he average correlaon (as per expecaons) beween he equy ndex reurns and he bond ndex reurns was sgnfcanly lower han he nra-sock or nra-bond ndex reurn correlaon. The mean ner-sock-bond correlaon was , sgnfcanly lower han he average nra-sock correlaon of or he average nra-bond correlaon of Furher, he ner sock-bond correlaons were he only subse of he correlaon o have any sascally sgnfcan negave values. In addon, every equy reurn seres had a leas one bond ndex for whch was eher nsgnfcanly correlaed wh or sgnfcanly negavely correlaed. Ths s clearly an mporan pon n ha one would expec effcen porfolos o generally hold boh equy and bonds as hey provde nsurance (alhough n a lmed fashon) agans he oher. Ths furher confrms ha he negave correlaon beween bonds and eques ubquous across naons. Turnng our aenon from uncondonal second momens o unvarae properes of he daa, we fnd ha he daa possess he sandard properes of fnancal reurns. Namely, boh bond and sock reurns are lepokuroc, wh sock reurns havng negave skew and bonds, on average, posve skew. Table 4 conans a summary of he unvarae sascs for he sysem. 19 All markes, save New Zealand and Japan produced an average posve reurn durng he sample, wh Mexco producng by far he hghes average reurn, annualzed a 1.%. All excep wo of he equy ndex reurn seres were lef skewed, wh an average skewness of The raw equy ndex reurns also exhbed exreme excess kuross, wh an averagng I s well know ha whle heeroskedasc reurn seres can exhb skewness and fa-als, reurns sandardzed by 18 Only he average correlaon beween Norh Amercan bond reurns and Japanese bond reurns was nsgnfcanly dfferen from zero (.038). 18 ECB Workng Paper No 04 January 003

20 her esmaed condonal sandard devaon can be normal (or close o normal). To nvesgae he properes of he nnovaons, we sandardzed he resduals by he preferred GARCH model (see secon 3). Whle he resduals sandardzed by her esmaed sandard devaon are boh less skewed (average -.48) and less fa-aled (averagng 3.05 excess kuross), he sandardzed resduals are hghly non-normal. In fac, all 1 equy ndex reurn seres, even when sandardzed by an esmaed condonal sandard devaon, rejec normaly usng a Jarque-Bera es a he 1% level. Unlke he volale equy ndces, he bond ndex reurns were more homogeneous, havng annualzed reurns rangng from 4.35 o 8.74 wh a mean of 6.68 and havng unformly lower sandard devaons han he leas volale equy ndex. Nne of he 13 bond ndex reurn seres were posvely skewed, havng an average skewness of 0.1, and were lepokuroc wh an average excess kuross of The bond ndex reurns sandardzed by her esmaed condonal sandard devaons were, agan, slghly less skewed, wh an average skewness of 0.17 and less fa-aled, averagng an excess kuross of As was he case wh equy reurns, bond ndex reurns ypcally rejec he null of normaly. Only he Irsh bond ndex reurns do no rejec normaly a he 5% level usng a Jarque-Bera es, wh Canadan and French bond ndex reurns also falng o rejec he null a he 1% level. Fnally o nvesgae asymmeres n varances and correlaon, we can examne f he varance of asse reurns are hgher afer a negave shock han afer a posve one. We calculae he E [ r < 0] and es he null ha E [ r r ] = E[ r r > 0] r 1 1 < 0 1. If here were an asymmerc ncrease n he level of varance afer a negave shock, we would expec ha T 1 T 1 T T ( I ) r I r ( I r ) r I r > = r < = < = > = >. Nneeen of he equy ndces had varances afer a negave shock greaer han afer a posve shock, and eleven of hese dfferences were sgnfcan a a 10% level, whle nne of he bond ndces had larger varances afer negave shocks, alhough only one was sgnfcan. Followng he same lne of analyss, we can nvesgae f he average covarance of he sandardzed resduals ( [ j ] j, E 1 ε ε = ρ ) afer jon negave reurns s dfferen han afer wo posve reurns by esng T 1 T T 1 T ( I ε < I ε ) εε j I ε < 0I ε ( I ε > 0I ε ) εε j I ε > 0I ε j j j j 1 0 > = < = < = > = > All eques exhbed some sgnfcan ncreases o jon bad news n a leas one seres, wh he Uned Saes havng he mos sgnfcan a he 10 level (13), han o jon good news, whle only 19 Boh mean and sandard devaon are repored as annualzed percen. ECB Workng Paper No 04 January

21 6 of he bond seres exhbed hs behavor. Table 3 conans he esmaed condonal volaly and condonal correlaon for he equy and bond marke reurns. V. Emprcal Resuls The frs sage of he model buldng conssed of fng he unvarae GARCH models for each of he 34 daa seres and selecng he bes one usng nformaon crera. Table 5 conans he specfcaon of he GARCH processes seleced by he BIC and he esmaed parameers from hese models. Egheen of he 1 models seleced for he equy reurn seres conaned a sgnfcan asymmery erm. Of he 18 models wh asymmeres, he vas majory (16) preferred he nroducon of he asymmery va he ncluson of hreshold effecs and wo preferred a recenerng of he news mpac curve (boh usng he AGARCH model). As wdespread as he evdence of asymmery volaly was n he equy seres, was equally absen from he bond ndex reurn seres. Only 3 of he 13 models seleced exhbed asymmerc effecs, all of he hreshold varey. Ths s conssen wh he earler evdence of lle condonal dfference n varances afer negave shocks for bond reurns. Ineresngly, hough, as explaned below, bond (as well as equy) reurns exhb asymmery n condonal correlaon. Fgure 1 conans he news mpac curves for fve of he asses. The dramacally dfferen shapes hghlgh he flexbly of hs modelng approach. For nsance, he model seleced for Swedsh equy reurns was an EGARCH wh a negave parameer on he nnovaon and a posve parameer on absolue value of he nnovaon resulng n a news mpac curve whch s exremely asymmerc, ndcang a much smaller ncrease n volaly afer a posve shock. Lkewse, he news mpac curve for Canadan bond reurn volaly s near zero for all posve shocks and only ncreases for negave ones, whle he Swss bond reurns show an asymmerc response o good news wh a larger ncrease n volaly subsequen o a posve shock. Four dfferen models were esmaed for he dynamcs of he correlaon. The frs, and smples model, was a sandard scalar DCC (.e. each of he marces, A and B, are dagonal wh he same value on each dagonal elemen and no asymmerc erms are ncluded). Nex he full dagonal verson of he model was esmaed allowng for no asymmeres n he correlaon dynamcs. The wo forms of model esmaed were an asymmerc DCC model (A, B and G each conss of a sngle unque elemen) and he full dagonal verson of hs model where asymmerc erms were nroduced allowng for dfferen news mpac and smoohng parameers across he asses. Upon nspecon of he f correlaon and he daa, became obvous ha a large number of he seres have undergone a sgnfcan srucural break when he exchange raes were 0 ECB Workng Paper No 04 January 003

22 rrevocably fxed. In order o correc for hs obvous defcency, all of he 4 base models were modfed o allow for a srucural break n he mean and for boh a srucural break n he mean and n he dynamcs across he nroducon of he Euro. Tables 6 and 6a conans he resuls of he esmaed models, wh he resuls presened for he parameers of he models where he mean was allowed o change bu no he dynamcs. Almos all of parameers n he models esmaed were sgnfcan, wh excepons noed n he able. The frs observaon s ha he dagonal versons of he models sgnfcanly ouperform he scalar versons of he same model. In addon, boh of he asymmerc DCC models ouperform her non-asymmerc DCC counerpars, wh p-values of zero. The shocks o correlaon were ypcally hghly perssen, wh a half-lfe of more han 14 weeks for he smples symmerc scalar DCC model. For he dagonal DCC model, wo of he asses seres exhbed no (or nearly no) nnovaon, and for hose whch dd, he half-lfe of he nnovaon ranged from 9 o over 63 weeks. In order o calculae he expeced half lfe of an nnovaon for he asymmerc model, s necessary o use expeced value or by assumng symmery for he dsrbuon. Overall, he asymmerc models produces slghly less perssence, bu were also hghly perssen. We also found sgnfcan evdence of a srucural break when he EMU 0 exchange raes were rrevocably fxed 1. We esed for boh a srucural break n he mean and a srucural break n boh he mean and he dynamcs. The lkelhoods of hese 1 models (3 reamens of he orgnal 4 models) are n Table 6a. We overwhelmngly rejec he null of no srucural break n he mean for all models (ypcal lkelhood raos were approxmaely 1800 wh 561 degrees of freedom), ye fnd no compellng evdence for boh a break n he mean and he dynamcs. In addon, allowng for a break reduced he perssence of he seres o ypcally 3 o 10 weeks. We see hs as furher evdence n suppor of he break, as seres wh uncondonal shfs are known o produce longer memory ha properly modeled seres. The remander of he paper wll presen he AG-DCC model wh a break n he mean bu no n he dynamcs. Fgures and 3 conan news mpac surfaces for German-US equy correlaon and covarance respecvely. The correlaon news mpac surface s hghly asymmerc, showng a larger response o n he -- quadran news han n he ++ quadran (.e. more responsve o jon bad news han o jon good news of he same magnude). However, when he correlaon and volales are smulaneously 0 The counres whch are par of he European Moneary Unon are: Ausra, Belgum, Fnland, France, Germany, Greece, Ireland, Ialy, Luxembourg, he Neherlands, Porugal, and Span. 1 Whle would be deal o es each seres for a break a all pons n me, s nfeasble o follow hs course as he parameers of he model wll no be denfed under he null of no break, makng sandard esng heory ncorrec. The choce of allowng he break o occur a he nroducon of he Euro was ECB Workng Paper No 04 January 003 1

23 consdered, he asymmery becomes even more srkng, wh a huge ncrease for jon negave shocks, lle change even for larger posve shocks, and asymmeres n all 4 quadrans. V.1 Specfcaon Tesng In order o verfy f he specfcaon seleced adequaely explans he dynamcs n he daa, we made us of he robus condonal momen ess (Wooldrdge (1990, 1991)). The es s useful n deecng wheher a varable (or a funcon of ha varable) s useful n predcng a generalzed resdual or u ( r h ) 1 = u j, (a generalzed resdual s a consruced resdual, such as u = r h, whch should have condonal expecaon zero). Ths resulng sasc ess f a se of momen condons, x g, 1, can predc he generalzed resdual seres. The es sasc s gven by g, 1 1 T T C = ( 1 T ) uj, λ ( T ) u j, λ g, 1 (9) = 1 = 1 where λ g, 1 s he resdual from a regresson of he momen condons on he scores of he lkelhood. Under mld regulary condons, C s asympocally dsrbued χ (1). The es s relavely smple o compue, as can be conduced usng wo regressons: he frs where he momens are regressed on he scores of he esmaed model, and he second where a vecor of ones s regressed on he produc of he generalzed resduals and he resduals from he frs regresson. The momen condons can be any funcon of any varable n he condonng se. However, n order o keep he analyss racable, we focus on a few ypes of poenal msspecfcaon. The frs and smples s wheher he sgn of a lagged reurn can predc fuure x I r 0 s a bnary varable ha ndcaes wheher he pas 1 = 1 < volaly. In oher word, [ ] reurn was negave. Analogously, we can consruc varables whch measure a posve mpac, or wheher he sgned magnude of a pas nnovaon can predc fuure volaly. In examnng he volaly models, we used 4 dfferen crera. 1 drven by he expeced ncrease n correlaon among EMU counres, and possble ncreases n oher counres oward he end of he sample. ECB Workng Paper No 04 January 003

24 x x x x = I = I = r = r [ r 1 < 0] [ r 1 > 0] 1I [ r 1 < 0] I[ r > 0] 1 1 (10) In esng he volaly models seleced, 34 x 34 x 4 (464) ess were conduced (34 generalzed resdual seres, 34 poenal seres o ge he momen condonal from, and 4 dfferen momens o choose from). The generalzed resdual was defned as u, r, h, =. The overall rejecon rae was exremely close o sze a usng a sze of 5%. However, he rejecon rae for bonds was hgher han he rae for eques, wh he majory of he bond rejecons resulng from msspecfcaon ess usng equy reurns as momen ndcaors ndcang ha equy reurn volaly may spll over o bond markes possbly hrough a flgh o qualy. Table 7 conans more dealed nformaon on he ypes of rejecons and he rejecon for bonds and socks as groups. We also esed he correlaon esmaes by sackng he T x k x (k-1)/ generalzed resduals u j, ε, ε j, ρj, = (he ouer produc of he sandardzed resduals mnus he esmaed correlaon) usng he followng 8 momen condons (for each of he 33 x 17 off dagonal seres): x x x x x x x x = I = I = I = I = ε = ε = ε = ε [ ε, 1 < 0] I[ ε j, 1 < 0] [ ε, 1 > 0] ε j, 1 < [ ε, 1 < 0] I[ ε j, 1 > 0] [ ε, 1 > 0] ε j, 1 >, 1ε j, 1I [ ε, 1 < 0] I[ ε j, 1 < 0], 1ε j, 1I [ ε, 1 > 0] I[ ε j, 1 < 0], 1ε j, 1I [ ε, 1 < 0] I[ ε j, 1 > ε I[ ε > 0] I[ ε > 0], 1 j, 1, 1 Ths resuls n a oal of 8 x 17 x 33 (4488), one for each of he 8 momen ndcaors for each of he above dagonal elemens of R. Table 8 conans he percenage rejecon for hese ess. Overall he rejecon rae was near sze a , and across he 8 momen ndcaors, he performance was relavely equal, wh no sngle ndcaor causng a dsproporonaely large j, 1 (11) We also esed he generalzed resduals agans only momens creaed usng her own lagged daa, and found he rejecon rae was sgnfcanly under sze a ECB Workng Paper No 04 January 003 3

25 number of rejecons. Based on he robus condonal momen es, we feel he AG-DCC model wh a break n he mean adequaely descrbes he daa. V. Volaly Dynamcs and Lnkages Whle each of he volaly seres was assumed o evolve ndependenly of he oher seres, he model allows us o examne he volaly lnkages across he counres. A smple creron o examne hese lnkages s he correlaon beween he esmaed volales of wo asses: ρ hh j = T ( h h )( h j h j ) T T ( h h ) ( h j h j ) = 1 = 1 (1) Overall, he volales of he equy markes were reasonably correlaed, wh an average correlaon of 0.345, and were smlar boh pre- and pos-nroducon of he fxed exchange rae regme sysem n Europe. However, here were srong regonal effecs n he lnkages. For nsance, he correlaon of he volaly of European equy marke reurns was over he enre sample, and was also smlar across he nroducon of he euro. The Amercan equy markes volales were also exremely correlaed, averagng , whle he correlaon beween US and Canadan equy volaly was exremely hgh a Ausralasan equy volaly correlaon was smlar o he over all average a , alhough hs was n par due o exremely low correlaon beween he volales of New Zealand wh he res of hs group. As was he case wh equy reurns, correlaon of equy volales are much lower across group han whn. Also no surprsng, he correlaon among he volales of larger markes was hgher wh he correlaon of volaly beween France, Germany, and US, and he UK equy markes averagng Fgure 4 conans a plo of he annualzed average volaly seres for 4 groups of eques: European, EMU, Amercan, and Ausralasan. The volaly lnkages were mos evden durng ceran umuluous perods: black Tuesday n Ocober 1987, he Iraq nvason of Kuwa and he Gulf war n 1990/91, durng he fnancal crss whch grpped Russa, Souheas Asa, and Lan Amerca n 1997/98, when sgns of a slowdown n he world economy sared o affec equy markes n March 001, and when errors aacks h he US n Sepember 001. Ineresngly, volaly ncreased for European Unon counres n 199 and 1993, when here was enson whn he European Moneary Sysem wh resulng neres rae ncreases and exchange rae realgnmens. = 1 4 ECB Workng Paper No 04 January 003

26 Smlarly, bonds volaly demonsraed low global correlaon when consdered on a global scale, bu regonal lnkages n bond reurn volaly were srong. The overall average correlaon beween bond reurn volales was , whle correlaon beween European bond volales was and among EMU member counres was Correlaon beween bond marke volaly n he Amercas was a low Average correlaon beween he volaly seres of he bond reurns and he volaly of he equy reurns was, unsurprsngly, lower, a Fgure 5 conans a plo of he annualzed average bond reurn volaly n he EMU counres, he U.S, and Japan. The bond markes are much less volale han he equy markes, and demonsrae less clear lnkages n volaly. For nsance, none of he clear ncreases n equy volaly found n he equy seres can be seen smulaneously n all he bond volaly seres. However, Ocober 87 s evden n he U.S. seres, he frcon n he EMU can be seen n s seres, and he Asan fnancal crss s obvous n Japanese bond volaly seres. All hese epsodes pon owards a flgh o qualy phenomenon, wh nvesors movng capal from eques o bonds. Ye hese sgnfcan evens do no spread as hey dd wh eques. In order o ensure ha he correlaons, especally any changes afer he nroducon of he fxed exchange rae sysem, were acually changng, and were no smply he resul of a change n volaly, we also esed he volaly models for srucural breaks n he level (hrough an ncluson of a dummy varable on he consan) of volaly and n boh he level and he dynamcs. 4 Tesng wh a lkelhood rao, we were able o rejec he null of no srucural breaks n 6 ou of he 1 seres. However, usng a conssen nformaon creron such as he BIC, we never seleced a model wh breaks of eher ype over he smpler models for any of he 34 daa seres, wh he excepon of Ialan eques. V.3 Correlaon Dynamcs Ineresng emprcal observaons abou volaly nowhsandng, he prmary movaon of hs paper was o examne he correlaon dynamcs of nernaonal equy and bond reurns. There appear o be sgnfcan varaons n he correlaons of hese asses durng he me perod of he sample. Fgure 6 conans a graph of he esmaed dynamc equy correlaon beween hree counres whn he EMU, namely France, Germany, Ialy, and Grea Bran. The correlaon has clearly ncreased beween all four of hese counres snce he nroducon of he Euro (ndcaed by he dashed lne). The adopon of a common moneary polcy and he consequen 3 The US bond marke volaly was bascally uncorrelaed wh every oher bond marke volaly wh he excepon of Canadan bond volaly. ECB Workng Paper No 04 January 003 5

27 rrevocable fxng of exchange raes for EMU counres have led o much hgher correlaons beween equy reurns no only n he hree counres whch are n he EMU, bu also he U.K. The ncrease beween France, Germany, and Ialy has, however, been more marked, evdenced by an ncrease from an average of o for France-Germany, o for France-Ialy, and from o for Germany-Ialy when comparng he pre- and pos- Euro perods. The correlaon ncrease s so srkng ha no only s a mean change obvous, bu correlaons appear o be less volale afer he nroducon of he euro. The correlaon beween Grea Bran and he hree EMU counres has also ncreased, alhough o a slghly lower level, wh an average correlaon beween he U.K. and he hree EMU counres rsng form an average of o Fgure 7 conans he average equy correlaons for he EMU counres, Europe whou he EMU counres, he Amercas, and Ausralasa. Ocober 87 sands ou as a clear ncrease n correlaon across he four groups, wh ubquous spkes n he correlaon n all sx seres. Whle here appear o be ncrease n he correlaon beween he EMU, Europe whou he EMU, and he Amercas, here do no appear o be large breaks n he average condonal correlaon beween any of hese hree and Ausralasa, wh he possble excepon of Amercas-Ausralasa correlaon a he fxng of he exchange raes n 1999, alhough hs s mos lkely no due explcly o he Euro. The general ncreases seen, especally beween Europe and he Amercas may be due o one of wo causes: globalzaon and MNCs or TMT companes. Wh he major run-up of echnology socks n he lae 90s and subsequen le down, many value weghed ndces became heavly weghed wh echnology companes. Ths, n urn, le correlaon among value-weghed equy reurn ndces go up due o a changng mx of secors, wh echnology geng a very large wegh. When he bubble burs, echnology companes all over he world saw large decreases n value, whch may have led o a general ncrease n correlaon on op of he euro effecs. The nvesgaon of hs dea, however, s beyond he scope of hs paper. Fgure 8 conans graphs of average correlaon equy reurn whn groups. There appear o be mld lnkages n correlaon among he groups, alhough hese lnkages appear sronger n perods where here s denfable bad news, mos noably Ocober 1987 and Sepember 001. Boh he EMU counres and European counres n general appear o have had a mld ncrease n he uncondonal level of correlaon followng he fxng of he exchange rae n 1999, alhough here s also some evdence ha he ncrease may have been parally ancpaed wh a slow, bu seady ncrease begnnng abou 1997 for EMU counres. Furher, as evdenced earler, many of 4 We assumed he specfcaon of he model dynamcs remaned consan when esng for srucural breaks n he parameers. 6 ECB Workng Paper No 04 January 003

28 he EMU counres have seen an exreme ncrease n correlaon among equy reurns mplyng ha he ncrease s no unform across he EMU; here may be a dvergence beween he domnan EMU equy markes and he lesser ones. The equy reurns of he Amercas have also had a noable ncrease n correlaon begnnng n lae 90s and connung unl he presen, agan possbly due o echnology companes. The correlaon wh n he Ausralasa group remans bascally unchanged durng he lae 90s. Bond marke correlaon dynamcs conaned boh smlares and dssmlares o equy marke correlaon dynamcs; smlar n ha here have been some radcal changes snce he nroducon of he fxed exchange rae regme, and dssmlar n ha lnkages across regons appear o be much weaker. Fgure 9 conans he average bond reurn correlaon beween he EMU, he remander of Europe, and he Amercan bond markes. The average correlaon beween European bond reurns whn he EMU and hose no n he EMU appears o have ncreased slghly, however correlaon beween Amercan markes and EMU markes has also ncreased sharply afer he fxed exchange regme wen no effec. Fnally, he average correlaon beween European non-emu member counres and he Amercas also appears o have ncreased. I s mporan o noe ha whle he correlaon beween he Amercan and boh of he European groups bond reurns has ncreased n he laer poron of he 90s and no he new mllennum, he levels are sll very dfferen. The correlaon beween bond reurns n Europe s ypcally 0.7, whch he correlaon beween eher of he European groups and he Amercas s ypcally less han half, averagng near 0.3. Ths s unsurprsng gven he many common economc facors whch affec European counres boh whn and ousde of he EMU and help dcae moneary polcy. Fgure 10 conans he plo of bond marke correlaons wh hree groups: he EMU counres, Europe whou he EMU counres, and he Amercas. The mos srkng concluson from hese pcures s ha, begnnng approxmaely 15 weeks before he exchange raes became fxed unl he presen, EMU bond marke reurns have been bascally perfecly correlaed, remanng above 0.96 for he duraon. The synchronzaon of moneary polcy necessary for he effecve creaon of he Euro has undoubedly caused hs phenomenon. However, he correlaon among European non-emu members has remaned n he same range has always been n. Unlke equy marke reurns, correlaon among bond reurns n he Amercas (Canada and he U.S.) have been farly consan. Agan, s mporan o noce ha he levels are dfferen n he pcures, wh EMU counres havng a very hgh hsorcal correlaon (mos lkely due o some of he faled aemps a managng exchange raes), European non-emu counres ha are also hghly correlaed, alhough less han he EMU counres, and he Amercas ECB Workng Paper No 04 January 003 7

29 ha are much less correlaed han eher of hese groups. Fgure 11 conans he bond reurn correlaon beween hree of he larges provders of governmen bonds: Germany, Japan, and he U.S. The correlaon beween German and Japanese bond reurns plummeed wh he nroducon of he fxed exchange rae regme, form a farly sgnfcan 0.5 o an average near zero. 5 A he same me, bond marke reurns have become ncreasngly correlaed beween he German and U.S. bond markes, ndcang a possble coordnaon and responsveness o moneary polcy by boh he ECB and he FED or a leas sronger common shocks. U.S. and Japanese bonds correlaon has remaned n a farly narrow range for he enre sample, averagng near zero. Fnally, fgures 1 and 13 conan plos of he average correlaon beween he varous equy markes and he EMU bond reurns and Amercan bond reurns, respecvely. No surprsngly, EMU bond reurns are relavely hghly correlaed wh EMU equy reurns (Fgure 1) whle correlaon beween EMU bond reurns and Amercan and Ausralasan equy reurns s ypcally near zero and ofen negave, alhough boh of hese correlaon reman n a relave narrow band. If has had any effec, he nroducon of he Euro has led o a decrease n he correlaon beween EMU bond reurns and equy reurns n oher regons. One noable decrease s evden n all hree pcures: Ocober 1987, provdng srong evdence o a flgh-o-qualy. The levels nowhsandng, he dynamcs of he hree seres are remarkably smlar, ye hs smlary s mos lkely due o he equy reurn correlaon dynamcs. Fgure 13 pans an analogous pcure for Amercan bond reurns, where he Amercan bond reurns have he hghes mean correlaon wh Amercan eques (alhough smlar o he mean wh he EMU eques) and have a much lower mean wh Ausralasan equy reurns. Agan, he dynamcs are smlar wh all havng a srong reacon n Ocober 1987, and a slow bu seady declne over he few years. VI. Concluson In hs paper we found srong evdence of asymmeres n condonal covarance of boh equy and bond reurns, alhough he asymmeres are presen n markedly dfferen manners. Asymmerc DCC models are unformly preferred o her symmerc counerpars usng lkelhood rao esng, and asse specfc news mpac curves and smoohng parameers are 5 In fac, he decrease began slghly before he nroducon of he fxed exchange raes. In he fourh week of Ocober 1998, afer monhs of carry rades nvolvng borrowng a near zero neres raes n Japan, nvesng n he U.S., he Japanese cenral bank nervened agans rsng neres raes (whle ryng o encourage he economy) by buyng bonds, causng he carry rade o unravel. In fac, he sandardzed reurn on Japanese bonds was 6 sandard devaons hs week. 8 ECB Workng Paper No 04 January 003

30 preferred o he pooled parameer of a scalar DCC. Whle wdespread evdence was found ha naonal equy ndex reurn seres show asymmery n condonal volaly, lle evdence was found ndcang asymmery n bond ndex reurn volaly. However, despe he lack of evdence of asymmerc condonal volales, bonds (as well as eques) exhb asymmery n condonal correlaon, alhough, eques showed a sronger response o jon bad news han bonds do. Srong evdence of marke volaly correlaon s also presened for equy reurns: n parcular, annualzed average volaly seres for European, EMU, Amercan and Ausralasan eques show lnkages durng easly denfable perods of fnancal urmol such as he crash of 87, he begnnng of he Gulf war, and he Asan fnancal crss. Agan, unlke equy reurns, bond marke volales demonsrae less clear lnkages, nsead, exhbng ncreases o regon specfc evens whch do no appear o be conagous across regons. Upon he creaon of he Euro, nally whou a crculang currency when EMU exchange raes were rrevocably fxed, sgnfcan evdence of a srucural break s found n he level of condonal correlaon bu no n he levels of he condonal volales. Condonal equy correlaon for he major markes of Europe,.e. France, Germany and Ialy (whch are par of he EMU) and UK (whch s no par of he EMU), has ncreased snce he nroducon. In addon o he expeced ncrease n he Euro-area, evdence s also found of a meanngful ncrease n correlaon of oher markes wh he EMU naons, possbly sgnalng sronger economc es. Furher, he nroducon of a fxed exchange rae regme has led o near perfec correlaon among bond reurns whn EMU counres, whch s no surprsng consderng he moneary polcy harmonzaon whn he EMU. Ths ncrease n correlaon among asse reurns whn he EMU area may have nduced nvesors, when dversfyng her porfolos, o move capal from Europe o he US, possbly conrbung o he deprecaon of he euro vs-à-vs he US dollar n he monhs followng he nroducon for he fxed rae regme. Condonal equy correlaon seres among regonal groups s found o ncrease dramacally when bad news h fnancal markes. Ths s an mporan mplcaon for nernaonal nvesors; dversfcaon sough by nvesng n mulple markes s lkely o be lowes when s mos desrable. However, s also evdenced ha condonal correlaon beween equy and bond reurns ypcally declnes when sock markes suffer from fnancal urmol, an ndcaon of a flgh o qualy phenomenon, where nvesors move capal from eques o safer asses. In oher words, no only s equy-bond reurn correlaon ypcally low, acually s lower durng perods of fnancal urmol. The fndngs of hs paper have crucal mplcaons for praccal nernaonal nvesng. Whle hgh correlaon can become low correlaon by akng shor posons, many large nvesors are prohbed or severely lmed n ECB Workng Paper No 04 January 003 9

31 he amoun of shor poson hey may hold. Furher, holdng asses n a porfolo whch may have a negave expeced reurn s ypcally undesrable. The lowes correlaons found were ypcally beween equy reurns n one counry and bond reurns n anoher. Ths unsurprsng ye undocumened observaon should provde gudance for nvesors seekng o maxmze dversfcaon whou akng shor posons. The volaly and especally correlaon dynamcs documened n hs paper rase sgnfcan ssues for boh heorecal fnance and nvesors. For nsance, can he rsk of ncreasng correlaon due o marke declnes (exacly when correlaon becomes a very bad hng) be hedged? Why do boh eques and bonds demonsrae asymmerc changes n correlaon when hey boh declne? Has he nroducon of he Euro fundamenally changed world equy markes and how wll hs affec expeced reurns, capal flows, and exchange raes boh whn and ousde he Euro-area? 30 ECB Workng Paper No 04 January 003

32 Appendx A: Counres Seleced Europe AUSTRIA* BELGIUM* DENMARK* FRANCE* GERMANY* Ausralasa AUSTRALIA HONG KONG JAPAN* NEW ZEALAND SINGAPORE IRELAND* ITALY THE NETHERLANDS* SPAIN SWEDEN* Amercas CANADA* MEXICO UNITED STATES* SWITZERLAND* NORWAY UNITED KINGDOM* * ndcaes bond daa ncluded for hese counres. ECB Workng Paper No 04 January

33 Appendx B: Exac Specfcaons B.1 Unvarae GARCH models Whle some of he models dffer n he exac represenaon orgnally proposed, he qualave feaures reman unchanged. The models were changed o mprove comparably across models. GARCH h = + + ω αε 1 βh 1 AVGARCH (Absolue Value) h 1/ 1/ = ω + α ε 1 + βh 1 NARCH (Non-lnear) h = ω + α ε +βh λ / λ λ / 1 1 EGARCH (Exponenal) ε 1 ε 1 log( h ) = ω + α + γ + β log( h 1 ) h h ZARCH (Threshold) h 1 1 1/ 1/ = ω + α ε 1 + γi[ ε 1 < 0] ε 1 + βh 1 GJR-GARCH h = ω + αε 1 + γi[ ε 1 < 0] ε 1 + βh 1 APARCH (Asymmerc Power) h λ / = ω + α ε λ 1 +γi [ ε AGARCH (Asymmerc) h 1 = ω + α( ε 1 + γ ) + βh 1 < 0] ε NAGARCH (Nonlnear Asymmerc) λ 1 +βh λ / 1 h ω α ε γ β = + ( 1 + h 1 ) + h 1 The smples of he models are GARCH, AVGARCH (GARCH on sandard devaons nsead of varances) and NARCH, followed by GJR-GARCH, ZARCH, and EGARCH (whch all allow for hreshold effecs bu use dfferen powers of he varance n he evoluon equaon), and APARCH (whch encompass boh hreshold effecs and an esmaed power for he evoluon of varance). AGARCH and NAGARCH boh dffer n ha asymmeres n he news mpac curve come hrough re-cenerng of he 3 ECB Workng Paper No 04 January 003

34 curve, nsead of a slope change whch depends on he sgn of pas nnovaons. ECB Workng Paper No 04 January

35 ECB Workng Paper No 04 January B. New Impac Surface for correlaon 0,, ) )( ~ ( ~ ~ ), ( 0 0,, ) ) ( )( ~ ( ~ ~ ), ( 0 0,, ) )( ~ ) ( ( ~ ~ ), ( 0,, ) ) ( )( ~ ) ( ( ~ ) ( ~ ), ( 1, 1 1, 1 1, 1 1, 1 > = < > = > < = < = e e for b e a c b e a c b b e e a a c e e f e e for b e g a c b e a c b b e e a a c e e f e e for b e a c b e g a c b b e e a a c e e f e e for b e g a c b e g a c b b e e g g a a c e e f j j j j j j j j j j jj j j j j j j j j jj j j j j j j j j j jj j j j j j j ρ ρ ρ ρ

36 Bblography Ang, A. and G. Bekaer, 1999, "Inernaonal Asse Allocaon wh Tme-Varyng Correlaons," NBER Workng Papers 7056, Naonal Bureau of Economc Research, Inc Bekaer, G, and G. Wu, 000, "Asymmerc Volaly and Rsk n Equy Markes," Revew of Fnancal Sudes, Vol. 13 (1), pp Black, F., 1976, Sudes of Sock Prces Volaly Changes, Proceedng from he Amercan Sascal Assocaon, Busness and Economcs Sascs Secon, pp Bollerslev, T., 1986, "Generalzed Auoregressve Condonal Heeroskedascy," Journal of Economercs, Vol.31, pp Bollerslev, T, 1990, "Modelng he Coherence n Shor Run Nomnal Exchange Raes: A Mulvarae Generalzed ARCH Model," Revew of Economcs and Sascs, Vol.7, No.3, pp Booh, G. G., T. Markanen, and Y. Tse, 1997, "Prce and Volales Spllovers n Scandnavan Sock Markes", Journal of Inernaonal Money and Fnance, Vol. 1, June, Braun, P. A., D. B. Nelson, and A. M. Suner, 1995, Good News, Bad News, Volaly, and Beas, Journal of Fnance, 50, pp Brooks, C., and U. T. Henry, 000, Lnear and Non-Lnear Transmsson of Equy Reurn Volaly: Evdence from he US, Japan and Ausrala, Economc Modelng, 174, pp Campbell, J. Y., and L. Henschell, 199, No News Is Good News, Journal of Fnancal Economcs, 31, pp Cappello, L., 000, Do Fxed Income Secures Also Show Asymmerc Effecs n Condonal Second Momens?, FAME workng paper, # 1, Geneva, Swzerland. Chrsansen, C., 000, Macroeconomc Announcemen Effecs on he Covarance Srucure of Governmen Bond Reurns, Journal of Emprcal Fnance, 75, pp Chrse, A., 198, The Sochasc Behavor of Common Sock Varances, Journal of Fnancal Economcs, 10, Das, S., and R. Uppal, 001, Sysemc rsk and nernaonal porfolo choce, Manuscrp, Harvard Unversy. De Sans, G. and B. Gerard, 1997, Inernaonal Asse Prcng and Porfolo Dversfcaon wh Tme- Varyng Rsk, Journal of Fnance, 5, Dng, Z., R. F. Engle and C. W. J. Granger, 1993, "A Long Memory Propery of Sock Marke Reurns and a New Model," Journal of Emprcal Fnance, Vol. 1, pp ECB Workng Paper No 04 January

37 Engle, R. F., 198, "Auoregressve Condonal Heeroskedascy wh Esmaes of he Varance of U.K. Inflaon," Economerca. Vol. 50, pp Engle, R. F., 00, "Dynamc Condonal Correlaon - A Smple Class of Mulvarae GARCH Models," Forhcomng n Journal of Busness and Economc Sascs. Engle, R. F., and L. L, 1998, "Macroeconomc Announcemens and Volaly of Treasury Fuures," UCSD Workng Paper No Engle, R. F., and V. Ng, 1993, "Measurng and Tesng he Impac of News On Volaly," Journal of Fnance, Vol. 48, pp Engle, R. F., and K. Sheppard, 001, Theorecal and Emprcal Properes of Dynamc Condonal Correlaon MVGARCH, UCSD Workng Paper No Erb, C., C. R. Harvey, and T. Vskana, 1994, Naonal Rsk and Global Fxed Income Allocaon, Journal of Fxed Income, pp Errunza, V., K. H. and M.-W. Hung, Can he Gans from Inernaonal Dversfcaon be Acheved whou Tradng Abroad?, Journal of Fnance, 1999, Vol. 54, pp Flemng, J., C. Krby, and B. Osdek, 1998, Informaon and Volaly Lnkages n he Sock, Bond, and Money Markes, Journal of Fnancal Economcs, Vol. 49, pp Frazscher, M., 001, Fnancal Marke Inegraon n Europe: On he Effecs of EMU on Sock Markes, ECB Workng Paper seres No. 48. Glosen, L., R. Jagannahan, and D. Runkle, 1993, "Relaonshp Beween he Expeced Value and he Volaly of he Nomnal Excess Reurn on Socks," Journal of Fnance, Vol. 48, pp Hansen, P. R., and A. Lunde, 001, A Forecas Comparson of Volaly Models: Does Anyhng Bea a GARCH(1,1), Brown Unversy Workng Paper No Harmann, P., S. Sraemans, and C. G. de Vres, 001, Asse Marke Lnkages n Crss Perod, ECB Workng Paper seres No. 71. Henschel, L., 1995, "All n he famly: Nesng symmerc and asymmerc GARCH models," Journal of Fnancal Economcs, Vol. 39, pp Hggns, M. L., and A. K. Bera, 199, A Class of Nonlnear ARCH Models, Inernaonal Economc Revew, 33, pp Isakov D. and C. Pérgnon, 000, "On he dynamc nerdependence of nernaonal sock markes : A Swss perspecve," Swss Journal of Economcs and Sascs, Vol. 136, No., pp Koumos, G., and G. G. Booh, 1995, Asymmerc Volaly Transmsson n Inernaonal Sock Markes, Journal of Inernaonal Money and Fnance. Vol. 14, No. 6, pp ECB Workng Paper No 04 January 003

38 Koumos, G., 1996, Modelng he Dynamc Inerdependence of Major European Sock Markes, Journal of Busness, Fnance, and Accounng, 3, pp Kroner, K. F., and V. K. Ng, 1998, Modelng asymmerc comovemens of asses reurns, Revew of Fnancal Sudes. Vol. 11, No.4, pp Jones, C., O. Lamon, and R. Lumsdane, 1998, "Macroeconomc News and Bond Marke Volaly," Journal of Fnancal Economcs. March, pp Longn, F., and B. Solnk, 00, Exreme Correlaon of Inernaonal Equy Markes, Forhcomng n The Journal of Fnance. Maren, M. and S.-H. Poon, 001, Reurn Synchronzaon and daly correlaon dynamcs beween nernaonal sock markes, Journal of Bankng and Fnance, Vol. 5, pp Moskowz, T., 00, An Analyss of Covarance Rsk and Prcng Anomales, Manuscrp, Graduae School of Busness, Unversy of Chcago. Nelson, D. B., 1991, Condonal Heeroskedascy n Asse Reurns: A new approach, Economerca, Vol. 59, pp Paon, A. 001, On he Imporance of Skewness and Asymmerc Dependence n Sock Reurns for Asse Allocaon, Manuscrp, UCSD. Scruggs, John T., 1998, Resolvng he Puzzlng Ineremporal Relaon beween he Marke Rsk Premum and Condonal Marke Varance: A Two-Facor Approach, Journal of Fnance, Vol. 53, pp Sheppard, K., 00, Undersandng he Dynamcs of Equy Covarance, Manuscrp, UCSD. Taylor, S. J., 1986, Modelng Fnancal Tme Seres, John Wley and Sons Ld. Wooldrdge, J, 1991, On he applcaon of robus, regresson based dagnoscs o models of condonal means and condonal varances, Journal of Economercs, Vol. 47, pp Wooldrdge, J., 1990, A unfed approach o robus, regresson-based specfcaon ess, Economerc Theory, Vol. 6, pp Wu, G., 001, The Deermnans of Asymmerc Volaly, Revew of Fnancal Sudes, Vol. 14, pp Zakoan, J., 1994, "Threshold heeroskedasc models," Journal of Economc Dynamcs and Conrol, Vol. 18, pp ECB Workng Paper No 04 January

39 Table 1 Equy Indces Mean Mn Max Ausralasa Europe Norh Amerca Ausralasa Europe Norh Amerca Bond Indces Mean Mn Max Ausralasa Europe Norh Amerca Ausralasa N/A Europe Norh Amerca Beween Bond & Equy Indces Mean Mn Max Bonds Eques Ausralasa Europe Norh Amerca Ausralasa Europe Norh Amerca Table 1: Summary Sascs for he 1 Equy Index reurns and 13 Bond Index reurns correlaons, grouped by regon. The numbers are he average correlaon beween he approprae groups,.e. n he las secon, he upper lef elemen s he average correlaon beween Ausralasan equy reurns and Ausralasan bond reurns. 38 ECB Workng Paper No 04 January 003

40 ECB Workng Paper No 04 January Table a Ausra Belgum Canada Denmark France Germany H. K. Ireland Ialy Japan Mexco Neh'l N. Z. Norway Sngapore Span Sweden Swz'l U. K. U. S. Ausrala Ausra Belgum Canada Denmark France Germany H. K Ireland Ialy Japan Mexco Neh'l N. Z Norway Sngapore Span Sweden Swz'l U. K Table a: Uncondonal correlaon of reurns of he equy markes n hs sudy.

41 40 ECB Workng Paper No 04 January 003 Table b Ausra Belgum Canada Denmark France Germany Ireland Japan Neh'l Sweden Swz'l U. K. U. S. Ausrala Ausra Belgum Canada Denmark France Germany H. K Ireland Ialy Japan Mexco Neh'l N. Z Norway Sngapore Span Sweden Swz'l U. K U. S Table b: Uncondonal correlaon of reurns across he equy (down) and bond markes (across). Red numbers ndcae negave correlaon. For nsance, he upper lef enry s he correlaon beween Ausralan equy reurns and Ausran bond reurns. Immedaely below hs enry s he correlaon beween Ausran equy reurns and Ausran bond reurns.

42 Table c Belgum Canada Denmark France Germany Ireland Japan Neh'l Sweden Swz'l U. K. U. S. Ausra Belgum Canada Denmark France Germany Ireland Japan Neh'l Sweden Swz'l U. K Table c: Uncondonal correlaon of reurns across he bond reurns. Red numbers ndcae negave correlaon. Table 3 Overall Inra-sock Inra-bond Inersock Bond Sgnfcan a 10% Sgnfcan a 0% Socks Only Sgnfcan a 0% Ausralasa Europe Norh Amerca Ausralasa Europe Norh Amerca Bonds only Sgnfcan a 0% Ausralasa Europe Norh Amerca Ausralasa - Europe Norh Amerca Across Socks - Bonds Sgnfcan a 0% Socks Ausralasa Europe Norh Amerca Ausralasa Bonds Europe Norh Amerca Table 3: Summary Sascs for condonal paral correlaon. The numbers represen he percenage of he seres rejecng he null ha he condonal paral correlaon s he same afer jon bad news(wo negave reurns) as as afer jon good news(wo posve reurns). Excep where explcly ndcaed, all ess were a he 10% level. ECB Workng Paper No 04 January

43 Table 4 Mean Sandard Sandardzed Sandardzed Dev. Skewness Kuross Skewness Kuross Ausrala Socks Ausra Socks Belgum Socks Canada Socks Denmark Socks France Socks Germany Socks Hong Kong Socks Ireland Socks Ialy Socks Japan Socks Mexco Socks Neherlands Socks New Zealand Socks Norway Socks Sngapore Socks Span Socks Sweden Socks Swzerland Socks Uned Kngdom Socks Uned Saes Socks Ausra Bonds Belgum Bonds Canada Bonds ** Denmark Bonds France Bonds ** Germany Bonds Ireland Bonds * Japan Bonds Neherlands Bonds Sweden Bonds Swzerland Bonds Uned Kngdom Bonds Uned Saes Bonds Table 4: Summary Sascs for he 1 Equy Index reurns and 13 Bond Index reurns. The sandardzed skewness and sandardzed kuross are he skewness and kuross of he reurns sandardzed by her esmaed sandard devaon. ( denoes Annualzed Percen, * denoes sandardzed resduals nsgnfcanly dfferen from a normal dsrbuon a 5%, ** a 1%) 4 ECB Workng Paper No 04 January 003

44 Table 5 Asse Model Seleced ω α γ or δ β Ausrala Socks ZARCH Ausra Socks GARCH Belgum Socks GJR-GARCH Canada Socks ZARCH Denmark Socks ZARCH France Socks GJR-GARCH Germany Socks ZARCH Hong Kong Socks EGARCH Ireland Socks EGARCH Ialy Socks GARCH Japan Socks EGARCH Mexco Socks GJR-GARCH Neherlands Socks EGARCH New Zealand Socks GARCH Norway Socks AGARCH Sngapore Socks ZARCH Span Socks EGARCH Sweden Socks EGARCH Swzerland Socks ZARCH Uned Saes Socks ZARCH Uned Kngdom Socks ZARCH Ausra Bonds GARCH Belgum Bonds GARCH Canada Bonds ZARCH Denmark Bonds AGARCH France Bonds GARCH Germany Bonds GARCH Ireland Bonds GARCH Japan Bonds NGARCH Neherlands Bonds GARCH Sweden Bonds GARCH Swzerland Bonds EGARCH Uned Kngdom Bonds GARCH Uned Saes Bonds GJR-GARCH Table 5: Model seleced and parameer esmaes for he unvarae GARCH models used o sandardze each reurn seres. Ialan socks acually preferred a srucural break n he model, wh he frs se of parameers referrng o he daa unl he nroducon of he Euro, and he second subsequen. Inercep parameers were acually calculae on 10 mes he reurns o faclae workng wh exremely small numbers. ECB Workng Paper No 04 January

45 Table 6 Symmerc Model a b Asymmerc Model Ausrala Socks 0.000* Ausra Socks Belgum Socks Canada Socks Denmark Socks France Socks Germany Socks Hong Kong Socks * Ireland Socks * Ialy Socks Japan Socks Mexco Socks * Neherlands Socks New Zealand Socks * * * * Norway Socks Sngapore Socks * Span Socks Sweden Socks Swzerland Socks Uned Kngdom Socks Uned Saes Socks Ausra Bonds Belgum Bonds Canada Bonds Denmark Bonds France Bonds Germany Bonds Ireland Bonds Japan Bonds Neherlands Bonds Sweden Bonds Swzerland Bonds Uned Kngdom Bonds Uned Saes Bonds Scalar Model a b g Table 6: Parameer esmaes for he symmerc and asymmerc models n he paper. * ndcaes nsgnfcan a he 5% level. 44 ECB Workng Paper No 04 January 003

46 Table 6a Scalar DCC Scalar Asym. DCC Scalar DCC w/ mean break Scalar Asym. DCC w/ mean break Scalar DCC w/ mean and dynamcs breaks Scalar Asym. DCC w/ mean and dynamcs breaks Dagonal DCC Dagonal Asym. DCC Dagonal DCC w/ mean break Dagonal Asym. DCC w/ mean break Dagonal DCC w/ mean and dynamcs breaks Dagonal Asym. DCC w/ mean and dynamcs breaks Table 6a: Log-lkelhood values for he 1 models esmaed n he paper. There s a sgnfcan ncrease n he log lkelhood when eher asymmerc effecs or breaks n he mean are nroduced. Allowng for breaks n he dynamcs s no sgnfcan n he dagonal models. Table 7 Overall Socks Bonds x x x X Equy Bond Equy Bond Table 7: Rejecon raes for he robus condonal momen es for he esmaed volales. The op pane s he percen of he ess rejecng for each of he facors x, =1,,3,4. The boom pane s he rejecon rae of he seres of a gven ype n he lef column wh momens of he seres of he ype lsed across. Table 8 overall x x x x x x x x Table 8: Rejecon raes for he robus condonal momen es for he esmaed correlaons. The sascs represen he percen of he ess rejecng for each of he facors x, =6,7,,1. ECB Workng Paper No 04 January

47 46 ECB Workng Paper No 04 January 003 Fgure 1: Typcal volaly news mpac curves for eques and bonds. The volaly dynamcs can ake on a wde range of forms, ncludng decreasng for posve shocks n he case of an EGARCH model (German Eques), or showng no ncrease subsequen o a posve shock n he case of Canadan bond reurns.

48 ECB Workng Paper No 04 January Fgure : Correlaon news mpac surface for German and US equy reurns. There s sgnfcan asymmery n he negavenegave quadran, evdenced by he dark red colorng,