Conference Paper Identifying Volatility Signals from TimeVarying Simultaneous Stock Market Interaction


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1 econsor Der OpenAccessPublikaionsserver der ZBW LeibnizInformaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Srohsal, Till; Weber, Enzo Conference Paper Idenifying Volailiy Signals from TimeVarying Simulaneous Sock Marke Ineracion Beiräge zur Jahresagung des Vereins für Socialpoliik 2013: Webewerbspoliik und Regulierung in einer globalen Wirschafsordnung  Session: Inernaional Financial Markes, No. G21V3 Provided in Cooperaion wih: Verein für Socialpoliik / German Economic Associaion Suggesed Ciaion: Srohsal, Till; Weber, Enzo (2013) : Idenifying Volailiy Signals from Time Varying Simulaneous Sock Marke Ineracion, Beiräge zur Jahresagung des Vereins für Socialpoliik 2013: Webewerbspoliik und Regulierung in einer globalen Wirschafsordnung  Session: Inernaional Financial Markes, No. G21V3 This Version is available a: hp://hdl.handle.ne/10419/79903 Nuzungsbedingungen: Die ZBW räum Ihnen als Nuzerin/Nuzer das unengelliche, räumlich unbeschränke und zeilich auf die Dauer des Schuzrechs beschränke einfache Rech ein, das ausgewähle Werk im Rahmen der uner hp:// nachzulesenden vollsändigen Nuzungsbedingungen zu vervielfäligen, mi denen die Nuzerin/der Nuzer sich durch die erse Nuzung einversanden erklär. Terms of use: The ZBW grans you, he user, he nonexclusive righ o use he seleced work free of charge, erriorially unresriced and wihin he ime limi of he erm of he propery righs according o he erms specified a hp:// By he firs use of he seleced work he user agrees and declares o comply wih hese erms of use. zbw LeibnizInformaionszenrum Wirschaf Leibniz Informaion Cenre for Economics
2 Idenifying Volailiy Signals from TimeVarying Simulaneous Sock Marke Ineracion 1 Till Srohsal 2 Deparmen of Economics Free Universiy Berlin Enzo Weber 3 Deparmen of Economics and Economerics Universiy of Regensburg Absrac In he academic lieraure, he economic inerpreaion of sock marke volailiy is inherenly ambivalen, being considered an indicaor of eiher informaion flow or uncerainy. We show in a sylized model economy ha boh views sugges volailiydependen crossmarke spillovers. If higher volailiy in one marke leads o higher (lower) reacions in anoher marke, volailiy reflecs informaion (uncerainy). We inroduce a simulaneous imevarying coefficien model, where srucural ARCHype variances serve wo purposes: governing he ime variaion of spillovers and ensuring saisical idenificaion. The model is applied o daa of US and furher sock markes. Indeed, we find srong nonlinear, volailiydependen effecs. Keywords: Informaion, Uncerainy, Spillover, Simulaneous Equaions, Idenificaion JEL classificaion: G15, C32 1 We are graeful for commens and suggesions received from Jorien Korver, Helmu Lükepohl, Dieer Nauz, Sven Schreiber, Lars Winkelmann as well as paricipans of he 66h European Meeing of he Economeric Sociey in Málaga. Of course, all remaining errors are our own. Financial suppor by he Deusche Forschungsgemeinschaf (DFG) hrough CRC 649 Economic Risk is graefully acknowledged. 2 Free Universiy Berlin, Deparmen of Economics, Insiue of Saisics & Economerics, D Berlin, Germany, phone: +49 (0) Universiy of Regensburg, Deparmen of Economics and Economerics, D Regensburg, Germany, phone: +49 (0) , fax: +49 (0) , and Insiue for Employmen Research (IAB), OseuropaInsiu Regensburg.
3 1 Inroducion The presen sudy proposes a flexible economeric approach o examine he economic inerpreaion of volailiy in financial markes. Firsly, we pinpoin wo fundamenal undersandings of volailiy ha have emerged from he financial lieraure during he las decades. On he one hand, he fac ha prices vary is inerpreed as a sign of informaion flow. On he oher hand, high variabiliy is ofen seen as a mirror image of pronounced uncerainy in he marke. Boh views sugges volailiydependen sock marke ineracion, albei in differen direcions, and we aim a shedding ligh on he inheren ambivalence. In a simple economic framework, we show ha higher volailiy in one marke should lead o higher (lower) reacions in anoher marke if volailiy reflecs informaion (uncerainy). To he bes of our knowledge, hese wo views of volailiy have never been explicily conrased and empirically examined. Secondly, we propose a sraegy o infer he dominaing signal of reurn variabiliy from he daa: we analyse differen reacions of invesors o observed reurns, depending on he prevailing level of volailiy. As our economeric framework, we inroduce a simulaneous imevarying coefficien model, where ime variaion is a funcion of ARCHype variances. The analysis is based on daily daa of major sock indexes from he Americas, Ausralia and he Asian region. Le us firs provide some background concerning he wo signals of volailiy we pu up for discussion and review some lieraure we see conneced o our line of reasoning. From one poin of view, volailiy is ofen associaed wih uncerainy or risk. Considering he global financial crisis for insance, fuure marke developmens are highly uncerain. In he public discussion, he image of labile and disoriened financial markes prevails. Inuiively, he exensive sock marke volailiy is ofen inerpreed as he reflecion of his uncerainy. In he presen sudy his concep of volailiy shall be summarized as 1
4 he uncerainy hypohesis. Regarding he pricing of asses, i seems naural ha invesors expec o be compensaed for bearing uncerainy in heir porfolios. In fac, in academia he undersanding of volailiy as risk long plays an imporan role wih a prominen example given by he µσuiliy funcion and he CAPM. Originaing from Engle e al.(1987), financial economericians ranslaed his idea ino he varianceinmean model (see also Bali and Engle 2010 and he references herein). Anoher example for volailiy proxying uncerainy is given by ineracions beween oupu or inflaion uncerainy and he condiional means of hese variables (e.g. Grier and Perry 2000). In a furher srand of lieraure, numerous sudies analyze how uncerainy abou exchange rae movemens affecs rade volume and foreign direc invesmen, e.g. Cushman (1985), Chowdhury (1993) and Kiyoa and Uraa (2004). For insance, volailiy migh negaively impac he size of rade flows if exchange rae uncerainy renders rade less profiable for risk averse agens. On he oher hand, we will refer o he view of volailiy being a measure of informaion flow inensiy as he informaion hypohesis. Some represenaives of he lieraure who elaborae on he volailiyinformaion link are Clark (1973), Epps and Epps (1976) and Ross (1989). Overall, he idea is ha no moivaion for furher rading would exis in a siuaion where all prices have seled a heir equilibrium values. Thus, volailiy would be zero in absence of relevan news. If, however, addiional informaion becomes available, price adjusmens will generae flucuaions unil a new equilibrium is reached. Of course, in realiy, shocks are oo frequen o allow convenional asse prices o ever sele a some consan consensus value, and percepion and handling of informaion boh represen more complicaed processes han assumed in sylized model economies. Noneheless, he line of reasoning exemplifies how volailiy is conneced o informaion arrival. The informaion conen of price movemens is normally no observable. This is likely 2
5 o be one of he main reasons why informaion flow was conneced o volailiy in he firs place. By he same oken, a srand of lieraure examined rading volume as an observable variable ha is a leas parly driven by he informaion arrival process; see Tauchen and Pis (1983), Harris (1987), Lamoureux and Lasrapes (1990), Foser and Viswanahan (1993, 1995) and Gagnon and Karolyi (2009). Cerainly, volume canno explain volailiy, in he sense of an exogenous variable. Insead, boh are affeced simulaneously by he laen informaion process. Moreover, many rades are unlikely o be linked o informaion arrival, such as in he cases of liquidiy managemen (e.g. Andersen 1996), sraegic rading under asymmeric informaion (e.g. Kyle 1985) or differences of opinions on he inerpreaion of signals (e.g. Kim and Verrecchia 1991). Aemps have been made o proxy informaion arrival direcly by, for example, cenral bank decisions, macroeconomic news or firmspecific announcemens. For sudies of corresponding volailiy effecs, see e.g. Andersen and Bollerslev (1998) or Kalev e al. (2004). Noneheless, even if imporan insighs ino news effecs could be gained, such direc observable measures canno represen more han a fracion of he universe of informaion arriving in financial markes. Above all, hey hardly capure privae informaion, which is a major facor behind volailiy (French and Roll 1986). Our disinc hypoheses serve o fix ideas concerning he characer of volailiy. Naurally, hey are no muually exclusive. Raher, exploring he signal of volailiy amouns o asking which effec predominaes. In fac, his calls for a mechanism connecing he laen variables informaion and uncerainy o a measure ha is esimable from he daa. In he presen approach, we propose leing he reacion of marke paricipans decide he characer of volailiy insead of leaving his ask up o he economerician. Specifically, we make use of he inensiy by which shocks feed ino acual marke prices, hereby connecing a high inensiy o high informaion conen, as furher explained below. However, given a single observed ime series, idenifying he size of he shocks 3
6 hemselves (i.e., volailiy) and he size of heir impac on he price separaely, proves evidenly impossible. We approach his problem by exending he informaion se o he mulivariae case. In paricular, we examine he inensiy of spillover beween wo differen markes. Logically, while shocks can be idenified in he source marke, ransmission inensiy is measured in he arge marke. In case observed price changes in he source marke are inerpreed as highly informaive (uncerain) signals by he arge marke, he laer will incorporae a relaively large (small) fracion of he innovaion ino is own price. We illusrae his principle in a sylized model economy, based on signal exracion by raional agens. Overall, high volailiy in he arge marke associaed wih high spillover inensiy would suppor he informaion hypohesis, while evidence for he uncerainy hypohesis would follow from an inverse linkage. Economerically, we measure his nonlinear effec in a imevarying coefficien model governed by he (auoregressive) condiional variance of he source marke, i.e., we uilize ime variaion in volailiy o idenify is impac on ransmission inensiy. Such an empirical sraegy has no ye been considered in he lieraure. Our concep does no aim a explaining he mere fac ha markes are inerconneced, e.g. by rade, policy coordinaion or common shocks. Raher, we exploi he exising ineracion for esimaing he spillover inensiy and is link o volailiy. Furhermore, he a priori division ino source and arge markes is an arificial one. In realiy, once one inroduces spillover effecs, one mus ake a sance on how o resolve endogeneiy. Our model seup will generally allow for bidirecional ransmission beween he US and he second counry of ineres. Idenificaion is achieved by making use of he heeroskedasiciy in he daa, which can be exploied o uniquely pin down he srucure of simulaneous sysems; compare Senana and Fiorenini (2001) or Rigobon (2003). Therefore, boh he direcion and he size of spillovers can be deermined empirically. These consideraions 4
7 on simulaneiy apply o markes wih overlapping rading hours, like in he Americas. For models of he US and he major Asian or Ausralian sock indexes, he spillover direcion is given by he sequence of ime, since hese markes rade wih subsanial ime shifs. Consequenly, idenificaion problems are alleviaed in his seing. Our firs major resul is ha in all counries under invesigaion spillover inensiy significanly depends on volailiy. As regards he informaion conen of volailiy, our resuls ell ha i crucially depends on he combinaion of sender and receiver of volailiy signals. For indusrial counries, he informaion hypohesis holds. As for emerging economies, however, he uncerainy hypohesis prevails in heir relaions o he US. The res of he paper proceeds as follows. The nex secion presens a sylized model of sock marke reurns and derives he esable hypoheses. Secion 3 inroduces he economeric model and discusses idenificaion issues and he esimaion procedure. Secion 4 applies he mehodology o daily reurns of major sock indexes from he Americas, Ausralia and he Asian region. The las secion concludes. 2 Volailiy Signals in a Sylized Model Economy 2.1 The Marke Paricipan: Signal Exracion Problem Firs we illusrae he idea of he signal of volailiy in a sylized model economy. This should help fix ideas on how sock marke ineracion could depend on reurn variabiliy. Moreover, he naure of his inerdependence should reveal he characer of volailiy, i.e., i should indicae wheher volailiy in one marke means informaion or uncerainy (noise) o he oher. A prominen model from he lieraure, which can be used for his purpose, was considered by King and Wadhwani (1990). We adop his framework o 5
8 demonsrae ha in a signal exracion conex, he prevailing characer of volailiy can be idenified from he opimal reacion of invesors o observed reurns. For he presen purpose, i is sufficien o consider wo sock markes where price changes are associaed wih he arrival of relevan informaion and wih noise, i.e., uncerainy. The firs consiss wo pars: direcly observed informaion and a reacion o informaion ha is no fully observed in ha marke bu only in he oher: y 1 = ι 1 + α 12 E[ι 2 I 1 ]+ν 1 (1) y 2 = α 21 E[ι 1 I 2 ]+ι 2 + ν 2. (2) Sock reurns are given by y, informaion is denoed by ι, ν refers o noise and E[ I j ] represens he expecaions operaor condiional on he informaion observed in marke j a ime. When invesors form expecaions, say in marke 1, hey face a simple signal exracion problem, since all hey can observe from marke 2 is he conemporaneous price change. In order o exrac he signal from he par of he price movemen in marke 2 ha is no simply due o informaion in marke 1, agens in marke 1 have o find β 1 in E[ι 2 I 1 ]=β 1 (y 2 α 21 E[ι 1 I 2 ]). (3) The soluion o (3) is given by he minimumvariance esimaor: β 1 = Var[ι 2 ] Var[ι 2 ]+Var[ν 2 ]. (4) Evidenly, β 1 becomes ime varying, i.e., β 1, in case volailiy of eiher ι 2 or ν 2 changes over ime. 6
9 Of course, agens in marke 2 follow an analogous raionale. Using (3) and (4) o subsiue for he condiional expecaions in (1) and (2) yields he following simulaneous equaions sysem of sock reurns: y 1 = A 12 y 2 + ε 1 (5) y 2 = A 21 y 1 + ε 2, (6) wherehespillovercoefficiensaregivenby A 12 = α 12 β 1 and A 21 = α 21 β 2.Theshocks resul as ε 1 =(1 α 12 α 21 β 1 β 2 )(ι 1 + ν 1 ) and ε 2 =(1 α 12 α 21 β 1 β 2 )(ι 2 + ν 2 ). In our applicaion, we will choose he US as he firs counry and swich beween several oher sock markes in y 2. Logically,he model will change according o he choice of he second counry. In addiion o he second equaion, his concerns also (1). Apar from he spillover, he pariioning of he reurn shock ino informaion and noise, and hus also β and A, depend on he perspecive of he second counry. In order o keep he noaion simple, we wrie down model (1)(2) only for a given se of counries. 2.2 The Economerician: Tesable Hypoheses Following he reasoning from above, he conemporaneous impac from one marke o he oher depends on he variances of boh signal (informaion) and noise (uncerainy). However, assuming he model in (5) and (6) is idenified, he economerician can only esimae he variance of ε. Taking he ypical imevarying naure of financial ime series volailiy ino accoun, we denoe he condiional variance of ε by Var[ε I 1 ]=h and le he spillover coefficiens depend on he variances by A i j = f i j (h j ) i, j=1,2 and i j. (7) 7
10 In view of (4), f i j h j > 0 would imply ha Var[ι j I 1 ] dominaes he dynamics of marke volailiy, i.e., is rae of change is higher han he one of Var[ν j I 1 ]. This would favor he informaion hypohesis. On he conrary, f i j h j < 0 would represen evidence for he uncerainy hypohesis. The exac funcional form of f( ) is no clear, he more so he α i j from (1) and (2) migh also vary over ime. As discussed in deail in he nex secion, we approximae f( ) on an empirical basis. So far, we summarize he following wo esable hypoheses: Informaion Hypohesis: The spillover inensiy A i j in (5) and (6) depends posiively on he level of volailiy in he respecive oher marke, i.e., A i j h j > 0. Uncerainy Hypohesis: The spillover inensiy A i j in (5) and (6) depends negaively on he level of volailiy in he respecive oher marke, i.e., A i j h j < 0. 3 Empirical Approach: Measuring Invesors Reacion o Observed Reurns 3.1 Simulaneous Model and Idenificaion In order o explore he signal of volailiy, we firs discuss our simulaneous model seup. The considered sock reurns are colleced in he ndimensional vecor y. The daa generaing process is approximaed by he following simulaneous sysem: Ay = µ + ε, (8) 8
11 where µ represens a vecor of predicable componens such as lags or a consan erm and ε is a ndimensional vecor of srucural innovaions. The conemporaneous impacs are included in marix A wih diagonal elemens normalized o one. I is hese effecs ha model he spillovers beween reurns in he curren seing and ha we will allow o depend on volailiy laer on. Common shocks will be accommodaed by allowing for correlaion of ε, as explained below. The simulaneous specificaion (8) is no mean o ake a sance on fundamenal causaliy, in he sense ha an impulse say in marke j is necessarily he rue causal originof aspilloveromarke i. Ofcourse,onecanhinkofidiosyncraicevensinmarke j affecing marke i, based on economic linkages or psychological effecs. However, an impulse in marke j may well be iniiaed by some informaion ha is equally relevan for marke i, where invesors observe he signal from j. Then i would evidenly be he hirdpary origin of he informaion, and no marke j iself, which would underlie he impac on marke i. In summary, spillovers characerize signals in one sock index ha are incorporaed by oher markes, bu no necessarily based on acual bivariae causaliy. Saisically,model(8)asisandsisnoidenified:Inhemarix Awihanormalized diagonal, n(n 1) simulaneous impacs have o be esimaed, whereas he covariance marixof hereducedformresiduals A 1 ε deliversonly n(n 1)/2deerminingequaions due o is symmery. However, as for insance Senana and Fiorenini(2001) and Rigobon (2003) show, unobservable facor srucures like(8) become unique if heeroskedasiciy is presen in he sochasic componens. The idea is ha, alhough breaks in he srucural variances inroduce addiional unknowns (i.e., he variances in he new regime), hey shif he whole covariance marix in he reduced form, from which available informaion (i.e., variances and covariances) is doubled. Timevarying volailiy is a common feaure of financial variables, ofen modeled as ARCHype processes. Indeed, he approach 9
12 of Senana and Fiorenini (2001) subsumes he case of regime swiches jus as oher forms of heeroskedasiciy such as ARCH. Here, we follow Weber (2010), who specifies mulivariae EGARCH processes for he srucural shocks. Formalizing he model seup, firs denoe he condiional variances of he elemens in ε by Var(ε j Ω 1 )=h 2 j j=1,...,n, (9) where Ω 1 sands for he whole se of available informaion a ime 1. Furhermore, denoe he sandardized innovaions by ε j = ε j /h j j= 1,...,n. (10) EGARCH(1,1)processes are hen given by logh 2 j = c j + g j logh 2 j 1+ d j ( ε j 1 2/π)+ f j ε j 1 j=1,...,n, (11) where c j, g j, d j and f j represen he coefficiens. The erm 2/π serves o demean he absolue shock. In addiion, going beyond he pure magniude of shocks, he signed ε inroduce asymmeric volailiy effecs. The logarihmic formulaion ensures posiive variances wihou relying on parameric resricions. Common shocks are aken ino accoun via he srucural consan condiional correlaion (SCCC) approach of Weber (2010). The advanage of he SCCC model is o relax he uncorrelaedness assumpion for srucural shocks on he one hand bu o keep up he idenificaion of he simulaneous model achieved hrough heeroskedasiciy on he oher. The covariances of srucural shocks are recovered by he CCC specificaion Cov(ε i,ε j I 1 )=h i j = ρ i j h i h j i j, (12) 10
13 where ρ i j denoes he correlaion beween he ih and he jh innovaion. 4 This correlaion can be hough of as arising from he exposure of variables i and j o unobserved common facors. For markes wih nonoverlapping rading hours idenificaion problems are alleviaed. Naurally, a riangular coefficien marix A can be used. Even hough he index hen does no refer o he same ime for all variables, we keep he noaion for simpliciy purposes. 3.2 TimeVarying Coefficiens Up o his poin, he offdiagonal elemens of marix A in (8) imply spillovers beween he endogenous variables ha are proporional o he size of shocks wih proporionaliy facors consan over ime. While his represens he sandard in simulaneous sysems, he curren research quesion requires a more complex specificaion. Therefore, we develop a framework ha combines he heeroscedasic srucural model inroduced above wih a imevarying spillover specificaion. In order o discriminae beween he informaion and uncerainy hypoheses, we allow he ransmission inensiy o depend on source marke volailiy as derived in secion 2.2. Sricly speaking, A is subsiued by A in (8). The elemens A i j, i j, denoe he coefficiens of ransmission from variable j o i a ime. As a parsimonious funcional form, consider he linear specificaion of (7): A i j = a i j + b i j h j, (13) for all i, j. Here, he condiional sandard deviaion h j serves as he ransiion variable. Since A sands on he lef hand side, negaive values represen posiive ransmission. 4 We also considered he srucural dynamic condiional correlaion (SDCC) approach. However, empirical evidence was in favor of he SCCC model. 11
14 Therefore, a i j is expeced o be smaller han zero. Accordingly, a oneuni increase in source marke volailiy decreases spillover inensiy by b i j. Hence, from he above discussion i follows ha b i j < 0 would favor he informaion hypohesis, whereas prevalence of he uncerainy hypohesis requires b i j > 0. Alernaively, b i j = 0 would bring us back o he case of consan parameers. We noe ha his specificaion can be compared o he GARCHinmean model, where reurns are explained by heir own condiional variances. In our approach, he variance series is also employed for an ineracion effec wih he level. However, we allow he spillover in one mean equaion o depend on he condiional variance of anoher reurn. No case can be made, a priori, ha he ransiion funcion (13), i.e., he volailiy effec on spillover inensiy, is necessarily linear. While he advanage lies in parameric parsimony, he exac funcional form of (7) should be deermined on an empirical basis. For insance, le us assume a siuaion wih a < 0 and evidence for he uncerainy hypohesis, say b > 0. A a cerain poin, a linear ransiion funcion could approach a negaive correlaion beween markes (i.e., wih a posiive lefhandside coefficien). Since such a consellaion appears raher implausible, he ransiion effec is likely o exhibi dampening nonlineariy for high volailiy values. Sill, if such realizaions are rare in he sample, (13) migh work well as approximaion of he ransiion funcion (7). As an alernaive specificaion, lieraure on smooh ransiion regression (STR) (e.g. Luukkonen e al. 1988) has adoped flexible funcions o grasp ime variaion in coefficiens. Specifically, consider A i j = a i j + α i j /(1+e γ i j(h j β i j ) ). (14) The exac form of he ransiion is deermined by he logisic funcion (1+e γ(h β) ) 1, 12
15 which is monoonically increasing 5 in h j and bounded beween zero and one. The slope parameer γ indicaes he speed or smoohness of ransiion: as γ, he logisic funcionapproachesheindicaorfuncion I(h j > c),i.e.,asinglehreshold.inconras, γ = 0 simply gives he linear case. The parameer β represens he locaion of he ransiion. In sum, he STRbased specificaion les he daa decide abou he shape of he volailiy effec on spillover size. Nonlinear funcional forms are one way of dealing wih large realizaions of he condiional sandard deviaion. Anoher sraighforward opion is given by ransforming he ransiion variable. While we use he sandard deviaion, aking logarihms as in (11), for insance, would furher dampen exreme volailiy spikes. While here is lile reason o believe ha a correc opion could be chosen on heoreical grounds, our resuls proved robus in his respec. A las commen concerns he esing of saisical significance of he ransiion variables in he STR seup. Luukkonen e al. (1988) show ha sraighforward hypoheses like α i j = 0 or γ i j = 0 are inappropriae because of he presence of unidenified nuisance parameers under he null. Insead, for esing purposes he funcions are approximaed by a Taylor series of a higher order, usually of order hree: A i j = a i j + b i j,1 h j + b i j,2 h 2 j+ b i j,3 h 3 j. (15) Here, sandard likelihood raio (LR) principles apply o he hypohesis b i j,1 = b i j,2 = b i j,3 = 0. Of course, linearizaion may adversely affec he power of he es. However, as Skalin (1998) poins ou, simulaionbased echniques would be exremely compuaionally demanding and boosrapping does no provide superior size and power properies. Therefore, we will rely on he LR es in he ransiion model (15). Furhermore, if 5 We hink of volailiy effecs on ransmission srengh being monoonous, even if hey are no necessarily linear. More involved STR funcions should hus no be required. 13
16 b i j,2 = b i j,3 = 0 bu b i j,1 0 is found, he ransiion funcion can be approximaed by he linear specificaion (13). Esimaion is based on (quasi) maximum likelihood. 4 Applicaion: The Signal of Inernaional Sock Marke Volailiy 4.1 Daa We examine a balanced sample from 1/1/1988 o 12/31/2010 of daily reurns on major sockindicesfromheus(s&p500)andasecondcounryofineres.fromheamericas we choose Canada (S&P/TSX 60), Argenina (TOTMKAR 6 ), Brazil (Bovespa Index) and Mexico (IPC) as examples for conemporaneous rading. The markes of Ausralia (S&P/ASX 50), Japan (Nikkei) Korea (KOSPI) and he Philippines (PSEi) are all locaed overseas from he US and represen markes wih nonoverlapping rading hours. Sock reurns are depiced in Figure 1. The ime variaion in volailiy appears very pronounced in all series. This is also saisically indicaed by significan auocorrelaion of squared reurns found in preliminary daa inspecion. The presence of heeroskedasiciy is of special imporance o our approach, as i allows esimaion of volailiy effecs on spillover inensiy. 4.2 Specificaion Tess The se of equaions o be esimaed consiss of bivariae simulaneous models wih condiional heeroskedasiciy for he US and a second counry of ineres. The empirical applicaion sars wih specifying he funcional form of he ransiion funcion by means 6 Due o daa availabiliy for Argenina we use he TOTMKAR provided by Daasream insead of he MERVAL, see hp://produc.daasream.com/navigaor/helpfiles/daaypedefi niions/en/3/dsgi oal marke daa.hm. 14
17 reurn reurn (a) USA reurn reurn (b) Canada reurn (c) Argenina reurn (d) Brazil reurn (e) Mexico reurn (f) Ausralia reurn (g) Japan (h) Korea (i) Philippines Figure 1: Daily Sock Reurns on (a) S&P 500, (b) S&P/TSX 60, (c) TOTMKAR, (d) Bovespa Index, (e) IPC, (f) S&P/ASX 50, (g) Nikkei, (h) KOSPI and (i) PSEi 15
18 of likelihood raio ess. The specificaion es procedure can be described as follows: Since sock marke rading hours in Canada and he US are exacly he same and hose in Argenina, Brazil and Mexico largely coincide wih he US, we allow for bidirecional simulaneous effecs. Idenificaion is achieved hrough he SCCC approach. In he Asian region and Ausralia, sock markes open afer hose in he US have closed so ha idenificaion issues are alleviaed due o his chronology. Hence, we only es for he funcional form of he ransiion funcion in one direcion. Firsly, we es he null of consan coefficiens agains linearly imevarying coefficiens in all counries. Secondly, he null of linear spillover in boh direcions is esed separaely agains he alernaive of nonlinear (STR) spillover. In view of he hird order Taylor approximaion his ranslaes ino esing wo linear resricions in (15) for each case: H 0 : b 12,2 = b 12,3 = 0 and H 0 : b 21,2 = b 21,3 = 0, respecively. Columns 2 and 3 of Table 1 include pvalues of LR specificaion ess corresponding o he null given in he firs row. Bold numbers reflec rejecion of he respecive null. Column 4 shows he final model specificaion. 7 To menion one example, in he case of he US and Canada (second row), we find evidence in favor of linear spillover on he US (no rejecing he null in column 2) and nonlinear spillover on Canada (rejecing he null in column 3). During esimaion we se µ consan, as auocorrelaion of reurns is mosly very close o zero. Resuls urn ou o be insensiive o he inclusion of lagged erms in (8). Furhermore, sandardized squared residuals appear free from auocorrelaion. Thus, we can be confiden ha our parsimonious EGARCH(1,1) specificaion is sufficien o capure he ime variaion in he volailiy series. 7 In wo cases we do no follow he oucome of he specificaion ess, namely he Argeninian and Brazilian spillover on he US. Even hough saisically nonlinear effecs are indicaed by he pvalues, we resric he spillover o zero. A closer analysis of hese wo cases revealed ha he smooh ransiion funcion acually serves as a dummy o capure only very few ouliers a he beginning of our sample while he spillover on he US is oherwise consan and close o zero (beween 1% and 2%). 16
19 H 0 : linear on US H 0 : linear on X signal X H 1 : STR on US H 1 : STR on X final model specificaion coefficien esimaes of pvalues for df=2 pvalues for df=2 volailiy Canada linear on US a 12 = 0 b 12 = 0.45 informaion STR on Canada a 21 = 9.16 α 21 = 9.46 γ 21 = 9.47 β 21 = 0.19 informaion Ausralia 0.25 no spillover on US  linear on Ausralia a 21 = 0.35 b 21 = 0.08 informaion Japan 0.04 no spillover on US  STR on Japan a 21 = 0.28 α 21 = 0.18 γ 21 = β 21 = 0.34 informaion Korea 0.00 no spillover on US  STR on Korea a 21 = 0.20 α 21 = 0.22 γ 21 = β 21 = 0.40 informaion 17 Argenina no spillover on US  STR on Argenina a 21 = α 21 = γ 21 = 5.74 β 21 = 0.40 uncerainy Brazil no spillover on US  STR on Brazil a 21 = α 21 = γ 21 = 5.58 β 21 = 0.56 uncerainy Mexico STR on US a 12 = 0 α 12 = 0.04 γ 12 = β 12 = 0.64 informaion linear on Mexico a 21 = 0.78 b 21 = 0.10 uncerainy Philippines 0.00 no spillover on US  STR on Philippines a 21 = 0.45 α 21 = 0.16 γ 21 = β 21 = 0.72 uncerainy Noes: Columns 2 and 3 repor pvalues of likelihood raio ess of he indicaed null hypoheses wih degrees of freedom equal o df. Bold numbers reflec he rejecion of he null. In Argenina and Brazil, we resriced he spillover on US o zero even hough es saisics poin o nonlinear spillovers; see also foonoe 7, page 13. The final specificaion of he funcional form for he imevarying spillover is found in column 4. Columns 5 o 8 show he esimaed coefficiens. The las column liss he signal for marke i ha emerges from volailiy in marke j. Linear or STR specificaions of he ransiion funcion refer o A i j = a i j + b i j h j and A i j = a i j + α i j /(1+e γ i j(h j β i j ) ) of he simulaneous model: ( ) 1 A12 y A 21 1 = ε. Table 1: Specificaion Tess and Esimaion Resuls
20 4.3 Resuls The firs major resul is ha we find evidence for imevarying spillover coefficiens in all counries under invesigaion. In paricular, LR ess (no presened in Table 1) of consan agains linearly imevarying spillover resul in pvalues of (Canada), (Ausralia), (Mexico), (Argenina), (Brazil), (Japan), (Korea) and 0.031(Philippines). Tha is, for all counries es resuls sugges he rejecion of consan parameers. Esimaed coefficiens are presened in columns 5 o 8 of Table 1. The hypohesis favored by our evidence is lised in he las column. The resuls can be divided ino wo groups. Firs, he informaion hypohesis prevails in Ausralia, Canada, Japan and Korea as US volailiy increases he fracion of US shocks ha feed ino sock prices of hese counries. The same holds for Canadian volailiy, signaling informaion for US raders. Second, Argeninian, Brazilian, Mexican and Philippine sock markes seem o undersand US volailiy as uncerainy since higher volailiy leads o a reducion of spillover inensiy in hese markes. Considering he opposie direcion, we find he informaion hypohesis o dominae in he US wih respec o Mexican volailiy. However, he small effec from Mexico on he US is economically of minor imporance. The ransiion funcions of hese markes are ploed in Figures 2 o 9 (righ hand side) ogeher wih he spillover inensiies (lef hand side). We obain he following resuls. Evidence for he Informaion Hypoheses in Indusrial Economies  In Canada, he effec of US volailiy is quie pronounced, indicaed by a seep ransiion funcion. This resuls in a ransmission ha varies beween 10% in imes of low and approximaely 30% in imes of high volailiy. 18
21  The informaion signaling effec of Canadian volailiy is also subsanial. I produces an even higher spillover variaion on he US bu, of course, wih a lower mean.  In Ausralia he informaion signaling US volailiy leads o spillover inensiy beween roughly 36% and 43%. The spike owards he end of he sample resuling from high US volailiy during he crisis drives up ransmission srengh o 50%.  Transiion funcions in Japan and Korea are boh srongly increasing in a range of low volailiy. Spillover inensiy increases for higher levels of volailiy by up o 20 percenage poins. Evidence for he Uncerainy Hypoheses in Emerging Economies  The ransiion funcions and spillover inensiy for Argenina and Brazil are of similar shape. In Argenina, however, ransmission srengh varies around a lower level (70%) han in Brazil (80%). US volailiy srongly reduces spillover inensiy and is hus inerpreed as signaling uncerainy. In boh cases, he variance of domesic shocks is high compared o he US, and also o Ausralia and Canada. Thus, despie high spillover, domesic shocks represen a major facor of reurn variaion in Argenina and Brazil.  Analogously, ransmission srengh akes values beween 60% and 76% in Mexico wih an average of 73% and US volailiy having a negaive impac. On he conrary, in he US, Mexican volailiy increases spillover. Ye, economically he effec flucuaing beween zero and a few percen appears o be of secondary imporance.  The conemporaneous impac from he US on he Philippines equals abou 45% during imes of low volailiy. When volailiy approaches 1, spillover srongly decreases and falls below 30%. 19
22 spillover spillover on US 0.3 on Canada 0.3 on Canada on US h 1, h 2 (a) Spillover (b) Transiion Funcion Figure 2: Spillover and Transiion Funcion for Canada and he US spillover spillover h 1 (a) Spillover (b) Transiion Funcion Figure 3: Spillover and Transiion Funcion for Ausralia 20
23 spillover spillover h 1 (a) Spillover (b) Transiion Funcion Figure 4: Spillover and Transiion Funcion for Japan spillover spillover h 1 (a) Spillover (b) Transiion Funcion Figure 5: Spillover and Transiion Funcion for Korea 21
24 spillover spillover h 1 (a) Spillover (b) Transiion Funcion Figure 6: Spillover and Transiion Funcion for Argenina spillover spillover h 1 (a) Spillover (b) Transiion Funcion Figure 7: Spillover and Transiion Funcion for Brazil 22
25 spillover spillover 0.76 on Mexico 0.76 on Mexico on US on US h 1, h 2 (a) Spillover (b) Transiion Funcion Figure 8: Spillover and Transiion Funcion for Mexico and he US spillover spillover h 1 (a) Spillover (b) Transiion Funcion Figure 9: Spillover and Transiion Funcion for he Philippines 23
26 Inerpreing he Sock Marke Evidence Reurning o he discussion a he beginning of he paper, he answer o he quesion wheher volailiy predominanly signals informaion or uncerainy is  lierally  in he eye of he beholder. On he one hand, idenifying shocks in he source marke and measuring heir impac on ransmission inensiy in he arge marke renders idenificaion and esimaion possible. On he oher hand, his implies one paricular combinaion of sender and receiver of volailiy signals in each model. The differences in he resuls across counries show ha his combinaion is crucial. The generally high level of US spillover on he counries under invesigaion indicaes he imporan role of US sock marke developmens as a major poin of reference. However, even hough he sender of volailiy remains he same in all cases, in imes of high volailiy his imporance decreases for some receivers, whereas for ohers i increases. An inuiion for hese resuls migh be found in he inerconnecion and commonaliies of each counry and he US. Specifically, facors such as rade, policy coordinaion or insiuional similariies migh be one reason for he indusrial counries Ausralia, Canada, Japan and Korea o predominanly idenify informaion from sock marke flucuaions in he US. The US signal bears highly relevan and wellundersood informaion ha ouweighs he uncerainy, and, is priced insananeously. By conras, he reducion of spillover inensiy o he emerging economies Argenina, Brazil, Mexico and he Philippines in imes of rising US volailiy may be explained in he ligh of dissimilariies, for insance, in he insiuional, legal and regulaory framework and relaive poliical and economic insabiliy. The informaion conen in US price changes becomes less visible during urbulen imes, which are perceived as propagaing uncerainy insead. 24
27 4.4 Crisis, Correlaion and Coefficiens During urbulen imes, such as he ongoing global financial crisis, sock marke comovemen is commonly perceived o be more pronounced. Indeed, spliing he presen sample in a pre and poslehman period wih break dae 9/15/2008 reveals a subsanial increase in he empirical reurn correlaion beween each counry and he US. Ye, a he same ime, our previous resuls showed decreasing spillover inensiy in some markes (Argenina, Brazil, Mexico and he Philippines). Even hough we already specified a ime varying coefficien model, hese findings sugges ha he volailiy effec on he ransmission srengh migh exhibi a srucural break. So far, our approach implicily assumed ha eiher he informaion or he uncerainy hypoheses predominaes over he whole sample period. Therefore, we pursue his issue furher wih emphasis on a precrisis and a crisis sample. I is also well known, however, ha a rise in correlaion beween wo variables migh very well simply be riggered by an increased variance of he explanaory variable. Forbes and Rigobon(2002), for insance, documen his crucial role of volailiy changes ha can resul in biased esimaes of correlaion coefficiens. For he presen daa we evaluaed his effec in a small simulaion sudy. Denoing US reurns by x and hose of he oher counry by y, we simulaed y = βx + ε for he pre and poslehman period wih parameers according o our empirical esimaes from he above models. Thereby, he following rule of humb was used: We se β o he average spillover inensiy and drew ε and x from normal disribuions wih zero mean and Var(ε ) and Var(x ) equal o he average ARCH variances  before and afer 9/15/2008, respecively. Wih his paramerizaion we were able o reproduce he sharp rise in reurn correlaion during he crisis period. Thus, he increasing US volailiy urned ou o be he major driving force behind he rising correlaions wih Argenina, Brazil, Mexico and 25
28 he Philippines. A he same ime, his implies ha he ransiion funcions wih sable parameers are compaible wih he daa. Despie he increase in reurn correlaions, our approach is able o idenify wha we have ermed he uncerainy effec, i.e., spillover srengh decreases in volailiy. The reason is ha he variance changes, which affec he correlaion coefficiens, are explicily aken ino accoun in our model. 5 Conclusion The presen sudy moivaed volailiydependen simulaneous sock marke ineracion by discussing he fundamenal characer of volailiy, which we argue is inherenly ambivalen. Regarding he academic lieraure, volailiy is used o proxy wo differen laen variables: informaion and uncerainy. We summarize he firs view as he informaion hypohesis referring o sudies where volailiy is direcly relaed o informaion flow inensiy (see e.g. Ross 1989, Foser and Viswanahan 1993, 1995 or Kalev e al. 2004). The uncerainy hypohesis, on he oher hand, has is source in large srands of lieraure where volailiy is funcioning as an uncerainyproxy (see e.g Engle e al. 1987, Grier and Perry 2000, Chowdhury 1993 or Kiyoa and Uraa 2004). We propose an economeric approach ha consiss of a simulaneous equaions model wih imevarying parameers. The imevariaion of he spillover coefficien in one marke is driven by he volailiy of he oher. In his seing i is he effec of volailiy on he spillover srengh ha reflecs wheher he informaion hypohesis (posiive effec) or he uncerainy hypohesis (negaive effec) dominaes. Our main finding is ha sock marke ineracion depends significanly on volailiy in all counries under invesigaion. Evidence for he informaion hypohesis is found for he indusrial counries (Ausralia, Canada, Japan and Korea), whereas he daa of developing counries (Argenina, Brazil, Mexico and he Philippines) suppor he 26
29 uncerainy hypohesis. This paper reveals ha foreign volailiy plays a crucial role in he ineracion of sock markes. Thereby, he signal of volailiy differs subsanially across counries. We show ha, appar from he wellknown capabiliy of condiional variances o capure volailiy clusers and ensuring efficien esimaion, hey consiue a useful ool for furher purposes. Namely, condiional variances also help idenify simulaneous effecs and, especially, describe he imevarying naure of hese effecs in financial applicaions. References [1] Andersen, T.G. (1996): Reurn volailiy and rading volume: An informaion flow inerpreaion of sochasic volailiy. Journal of Finance, 51, [2] Andersen, T.G., T. Bollerslev (1998): Deusche MarkDollar volailiy: Inraday aciviy paerns, macroeconomic announcemens, and longer run dependencies. Journal of Finance, 53, [3] Bali, T.G., R.F. Engle (2010): The ineremporal capial asse pricing model wih dynamic condiional correlaions. Journal of Moneary Economics, 57, [4] Chowdhury, A.R. (1993): Does exchange rae volailiy depress rade flows? Evidence from errorcorrecion models. Review of Economics and Saisics, 75, [5] Clark, P.K. (1973): A subordinaed sochasic process model wih finie variance for speculaive prices. Economerica, 41, [6] Cushman, D.O. (1985): Real exchange rae risk, expecaions, and he level of direc invesmen. Review of Economics and Saisics, 67,
30 [7] Engle, R.F., D.M. Lilien, R.P. Robins (1987): Esimaing ime varying risk premia in he erm srucure: The ARCHM model. Economerica, 55, [8] Epps, T.W., M.L. Epps (1976): The sochasic dependence of securiy price changes and ransacion volumes: Implicaions for he mixureofdisribuions hypohesis. Economerica, 44, [9] Forbes, K.J., R. Rigobon (2002): No Conagion, Only Inerdependence: Measuring Sock Marke Comovemens. Journal of Finance, 57, [10] Foser, F.D., S. Viswanahan (1993): Variaions in rading volume, reurn volailiy and rading coss: Evidence on recen price formaion models. Journal of Finance, 48, [11] Foser, F.D., S. Viswanahan (1995): Can speculaive rading explain he volumevolailiy relaion? Journal of Business and Economic Saisics, 13, [12] French, K.R., R. Roll (1986): Sock reurn variances: The arrival of informaion and he reacion of raders. Journal of Financial Economics, 17, [13] Gagnon, L., G.A. Karolyi (2009): Informaion, rading volume, and inernaional sock reurn comovemens: Evidence from crosslised socks. Journal of Financial and Quaniaive Analysis, 44, [14] Grier, K.B., M.J. Perry (2000): The effecs of real and nominal uncerainy on inflaion and oupu growh: Some GARCHM evidence. Journal of Applied Economerics, 15, [15] Harris, L. (1987): Transacion daa ess of he mixure of disribuions hypohesis. Journal of Financial and Quaniaive Analysis, 22,
31 [16] Kalev, P.S., W.M. Liu, P.K. Pham, E. Jarnecic (2004): Public informaion arrival and volailiy of inraday sock reurns. Journal of Banking & Finance, 28, [17] Kim, O., R. Verrecchia (1991): Trading volume and price reacion o public announcemens. Journal of Accouning Research, 29, [18] King, M.A., S. Wadhwani (1990): Transmission of Volailiy beween Sock Markes. Review of Financial Sudies, 3, [19] Kiyoa, K., S. Uraa (2004): Exchange rae, exchange rae volailiy and foreign direc invesmen. The World Economy, 27, [20] Kyle, A. (1985): Coninuous aucions and insider rading. Economerica, 53, [21] Lamoureux, C.G., W.D. Lasrapes (1990): Heeroskedasiciy in sock reurn daa: Volume versus GARCH effecs. Journal of Finance, 45, [22] Luukkonen, R., P. Saikkonen, T. Teräsvira (1988): Tesing lineariy agains smooh ransiion auoregressive models. Biomerika, 75, [23] Rigobon, R. (2003): Idenificaion hrough heeroskedasiciy. Review of Economics and Saisics, 85, [24] Ross, S.A. (1989): Informaion and volailiy: he noarbirage maringale approach o iming and resoluion irrelevancy. Journal of Finance, 44, [25] Senana, E., G. Fiorenini (2001): Idenificaion, esimaion and esing of condiionally heeroskedasic facor models. Journal of Economerics, 102,
32 [26] Skalin, J. (1998): Tesing lineariy agains smooh ransiion auoregression using a parameric boosrap. SSE/EFI Working Paper in Economics and Finance 276, Sockholm School of Economics. [27] Tauchen, G.E., M. Pis (1983): The price variabiliyvolume relaionship on speculaive markes. Economerica, 51, [28] Weber, E. (2010): Srucural condiional correlaion. Journal of Financial Economerics, 8,
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