Modelling Financial Markets Comovements During Crises: A Dynamic Multi-Factor Approach.

Modelling Financial Markes Comovemens During Crises: A Dynamic Muli-Facor Approach. Marin Belvisi, Riccardo Pianei, Giovanni Urga February 24, 2014 We wish o hank paricipans in he Finance Research Workshops a Cass Business School (London, 8 Ocober 2012), in paricular A. Beber and K. Phylakis, in he Fifh Ialian Congress of Economerics and Empirical Economics (Genova, 16 18 January 2013), in he Third Carlo Giannini PhD Workshop in Economerics (Bergamo, 15 March 2013), in paricular M. Berocchi, L. Khalaf and E. Rossi, in he CREATES Seminar (Aarhus, 4 April 2013), in paricular D. Krisensen, N. Haldrup, A. Lunde, and Timo Terasvira, in he Seminari di Diparimeno Banca e Finanza of Universià Caolica del Sacro Cuore (Milan, 13 December 2013), in paricular C. Bellavie Pellegrini, for useful discussions and valuable commens. Special hanks o Eric Hillebrand and Riccardo Borghi for very useful discussions and insighful commens on a previous version of he paper. The usual disclaimer applies. Riccardo Pianei acknowledges financial suppor from he Cenre for Economeric Analisis a Cass and he EAMOR Docoral Programme a Bergamo Universiy. KNG Securiies, London (UK). Universiy of Bergamo (Ialy). Corresponding auhor: Cass Business School, Ciy Universiy London, 106 Bunhill Row, London EC1Y 8TZ (UK) and Universiy of Bergamo (Ialy) Tel.+/44/(0)20/70408698, Fax.+/44/(0)20/70408881, g.urga@ciy.ac.uk 1

Modelling Financial Markes Comovemens During Crises: A Dynamic Muli-Facor Approach Absrac We propose a novel dynamic facor model o characerise comovemens beween reurns on securiies from differen asse classes from differen counries. We apply a global-classcounry laen facor model and allow ime-varying loadings using Kalman Filer. We are able o separae conagion (asse exposure driven) and excess inerdipendence (facor volailiy driven). Using daa from 1999 o 2012, we find evidence of conagion from he US sock marke during he 2007-09 financial crisis, and of excess inerdependence during he European deb crisis from May-2010 onwards. Neiher conagion nor excess inerdependence is found when he average measure of model implied comovemens is used, as consequence some securiies display diverging repricing dynamics during crisis periods. JEL: C3, C5, G1. Keywords: Dynamic Facor Models, Comovemens, Conagion, Excess Inerdependence, Kalman Filer, Auomerics. 2

1 Inroducion The sudy of financial marke comovemens is of paramoun imporance for is implicaions in boh heoreical and applied economics and finance. The pracical relevance of a horough undersanding of he mechanisms governing marke correlaions lies in he benefis ha his induces in he processes of asse allocaion and risk managemen. In paricular, recen crisis episodes have shifed he focus of he lieraure on he characerizaion of financial marke comovemens during periods of financial disress. Mos of he crises ha have hi he financial markes in he pas decades are he resul of he propagaion of a shock which originally broke ou in a specific marke. This phenomenon has been exensively explored in he lieraure and has led o he use of he erm conagion o denoe he siuaion in which a crisis originaed in a specific marke infecs oher inerconneced markes. For a review of he conribuions a he hear of he lieraure on conagion see he papers by Karolyi (2003), Dungey e al. (2005) and Billio and Caporin (2010). A well-documened phenomenon linked o a siuaion of conagion is an increase of he observed correlaions amongs he affeced markes. The origins of his empirical evidence race back o he conribuions of King and Wadhwani (1990), Engle e al. (1990), and Bekaer and Hodrick (1992). Longin and Solnik (2001) and, in paricular, he influenial paper by Forbes and Rigobon (2002), criicize he common pracice o idenify periods of conagion using esing procedures based on marke correlaions. Forbes and Rigobon (2002) show ha he presence of heeroscedasiciy biases his ype of esing procedure, leading o over-accepance of he hypohesis of he presence of conagion. Bae e al. (2003), Pesaran and Pick (2007) and Fry e al. (2010) propose esing procedures robus o he presence of heeroscedasiciy. In his paper we ake a differen sand. We propose a modelling framework which allows o conras a siuaion of conagion, in he Forbes and Rigobon (2002) sense, as opposed o he case in which excess inerdependence in financial markes is riggered by spiking marke volailiy. Conagion is no longer hough as correlaion in excess of wha implied by an economic model (as in Bekaer e al. 2005 and Bekaer e al. 2012), i insead 3

corresponds o a specific marke siuaion enailing a persisen change in financial linkages beween markes. On he conrary, condiional heeroscedasicy of financial ime series does no display rending behaviour (Schwer, 1989 and Brand e al., 2010), hus a rise in correlaions caused by excess volailiy has only a emporary effec. This feaure is in line wih he lieraure on marke inegraion (Bekaer e al. 2009), which explores he degree of inerconnecedness of markes hrough ime, borrowing from Forbes and Rigobon s (2002) analysis he fac ha excess inerdependence, riggered by volailiy, migh lead o spurious idenificaion of cases of marke inegraion. In his paper, we bring ogeher he lieraure on conagion wih he lieraure on marke inegraion in ha we associae a siuaion of conagion o a prolonged episode of marke disress alering he funcioning of he financial sysem. On he conrary, a siuaion of excess inerdependence is a shor lasing phenomenon. Being able o disinguish beween conagion and excess inerdependence has a crucial informaion conen as o how a crisis develops and spreads ou. We sudy comovemens amongs financial markes during crises, boh in a muli-counry and a muli-asse class perspecive, conribuing o he exan empirical lieraure on inernaional and inra asse class shock spillovers. We analyse sock, bond and FX comovemens in US, Euro Area, UK, Japan and Emerging Counries, providing an exensive coverage of he global financial markes. Mos of he conribuions o he lieraure on comovemens enail single asse classes, wih he vas majoriy focusing on sock and bond markes (see iner alia Driessen e al., 2003, Bekaer e al., 2009 and Baele e al., 2010). There is a srand of lieraure embracing a genuine muli-counry and muli-asse-classes approach in he sudy of shock spillovers. Dungey and Marin (2007) propose an empirical model o measure spillovers from FX o equiy markes o invesigae he breakdown in correlaions observed during he 1997 Asian financial crisis. Ehrmann e al. (2011) analyse he financial ransmission mechanism across differen asse classes (FX, equiies and bonds) in he US and he Euro Area, using a simulaneous srucural model. The main conribuion of his paper is wofold. Firs, we propose a dynamic facor model which allows o es for he presence of comovemens (excess inerdependence versus 4

conagion) in a muli-asse and muli-counry framework. Since he seminal works of Ross (1976) and Fama and French (1993), mulifacor models for asse reurns have been he main ool for sudying and characerizing comovemens. Moreover, our model is specified wih dynamic facor loadings, o accommodae ime-dependen exposures of he single asses o he differen shocks. This allows us o disenangle he differen sources of comovemens beween financial markes, and o analyse heir dynamics during financial crisis periods. Second, we repor an empirical applicaion using a sample period which encompasses boh he 2007-09 crisis as well as he curren sovereign deb crisis: his is an ineresing laboraory o use he proposed framework o explore financial marke comovemens during crisis periods. The empirical analysis suggess ineresing findings. The global facor is he mos pervasive of he considered facors, while he asse class facor is he mos persisen and he counry facor is negligible in our muliple asse framework. We find evidence of conagion semming from he US sock marke during he 2007-09 financial crisis and presence of excess inerdependence during he spreading of he European deb crisis from mid-2010 onwards. Any conagion or excess inerdependence effec disappears a he overall average level, because of ha some of he considered asses display diverging repricing dynamics during crisis periods. The remainder of he paper is organized as follows. Secion 2 inroduces he daa. In Secion 3, we presen our dynamic muli-facor model. Secion 4 repors he relevan empirical resuls regarding he relevance of global-asse-counry facors and he indenificaion of he siuaion of conagion and he case of excess inerdependence in financial asses. Secion 5 concludes. 2 Daa We analyse comovemens of equiy indices, foreign exchange raes, money marke insrumens, corporae and governmen bonds in US, Euro Area, UK, Japan and Emerging Counries. Following he lieraure, o minimise he impac of nonsynchronous rading across 5

differen markes, we base our sudy on weekly daa, spanning from 1 January 1999 o 14 March 2012, yielding o 690 weekly observaions. The saring dae coincides wih he adopion of he Euro, being he Euro Area one of he key geographical areas considered in he analysis. The sample offers he possibiliy o explore a variey of differen marke scenarios. The mos noable facs are he speculaion driven marke growh of lae-1990, he financial and economic slowdown of early 2000 s, he burs of he markes during he mid-2000, he financial urmoil of he period 2007-2009 and he following slow recovery, sill pervaded by a big deal of uncerainy, promped by he sovereign deb crisis in Europe and US beween 2010 and 2012. This allows us o pick up from an in-sample analysis which are he disincive feaures of marke comovemens during crisis periods. Deails on he ime series used in his paper are repored in Table 1. The daa sources are Daasream and Bloomberg. We embrace he MSCI definiion of Emerging Markes and we selec he 5 mos relevan counries in erm of size of heir economy, according o he ranking based on he real annual GDP provided by he World Bank. Thus we selec Brazil, India, China, Russia and Turkey as Emerging Counries. We exclude from he analysis money and reasury markes for Japan and Emerging Marke, as he series were affeced by excess noise caused by measuremen errors. We consider he US dollar as he numeraire: all he series are US dollar denominaed and he US dollar is he base rae for he FX pairs in he daase. In wha follows, we consider simple weekly percenage reurns for Equiy Indices, Bond Indices and Foreign Exchange Raes, whereas weekly firs differences are considered for Money Marke and Govermen Raes series. In Table 2, we repor some descripive saisics of he variables. [Tables 1-2 abou here] The mos remarkable facs are he exreme values which were recorded in correspondence of he 2008-2009 crisis period. This is paricularly eviden for sock markes and for shor erm raes, whereas along he counry specrum, he mos hi were Emerging Markes. All series exhibi he ypical characerisic of non normaliy wih high asymmery and kurosis. 6

The price series are ploed in Figure 1. The downurn a he end of he year 2008 is immediaely apparen and common o all he considered series. [Figure 1 abou here] We propose a dynamic facor model wih muliple sources of shocks, a global, asse class and counry level. In order o validae his approach, a firs preliminary correlaion analysis is underaken. Table 3 repors he in-sample correlaion of he modelled variables. We observe high correlaion inra asse class groups. Paricularly remarkable are he cases of equiy and reasury raes, wih correlaions in he 70-80% range. We observe subsanial correlaion even wihin counries, in paricular here is evidence of high inerconnecion beween corporae bonds and FX markes a counry level: Euro Area (91.3%), Japan (83.6%) and UK (83.3%). Hence, here is evidence for he presence of boh an asse class and a counry effec. However, he asse class effec seems o be sysemaically more pervasive han he counry one. [Table 3 abou here] 3 A Dynamic Muli-Facor Model In his secion, we presen he modelling framework we propose. The main novely of he paper is he formulaion and he esimaion of a dynamic muli-facor model which allows o es for he presence of conagion in he Forbes and Rigobon (2002) sense versus he presence of volailiy riggered episodes of excess inerdependence on financial markes. Conagion is no longer hough as correlaion in excess of wha implied by an economic model (as in Bekaer e al. 2005 and Bekaer e al.2012), i insead corresponds o a specific marke siuaion, ha he framework proposed in his paper is able o capure, enailing a persisen change in financial linkages beween markes Building on he sandard laen facor finance lieraure (Ross, 1976; Fama and French 1992), le R i,j represen he weekly reurn for he asse belonging o asse class i = 1,..., I 7

and couny j = 1,..., J a ime. The general represenaion of he model is as follows: R i,j = E[R i,j ] + F i,j β i,j + ɛ i,j (1) β i,j = diag(1 φ i,j )β i,j + diag(φ i,j )β i,j 1 + ψ i,j Z 1 + u i,j (2) where E[R i,j ] is he expeced reurn for asse class i in counry j a ime, β i,j is a vecor of dynamic facor loadings, mapping from he zero-mean facors F i,j We enerain he possibiliy ha he facors F i,j o he single asse reurns. are heeroscedasic, ha is E[F i,j F i,j ] = Σ F i,j,, where Σ F i,j, is he ime-varying covariance marix of he facors. ɛ i,j o be whie noise and independen of F i,j is assumed. β i,j is he long-run value of β i,j, φ i,j and ψ i,j are 3-dimensional vecors of parameers o be esimaed, {u i,j } =1,...,T are independen and normally disribued. We assume u i,j o be independen of ɛ i,j. diag( ) is he diagonal operaor, ransforming a vecor ino a diagonal marix. Z is a condiional variable conrolling for period of marke disress. Following Dungey and Marin (2007), differen sources of shocks are considered, a global, asse class and counry level, in a laen facor framework. A firs facor, denoed as G, is designed o capure he shocks which are common o all financial asses modelled, whereas A i is he asse class specific facor for asse class i = 1,..., I and he counry facor C j is he counry specific facor for couny j = 1,..., J a ime. We denoe F i,j [G A i C j ] and, correspondingly, for he facor loading we specify β i,j [γ i,j δ i,j λ i,j ]. The full model is a muli-facor model wih dynamic facor loadings and heeroscedasic facors. This model seing allows us o explore and characerize dynamically he comovemens among he considered asses. On he one hand, ime-dependen exposures o differen shocks le us disenangle dynamically he differen sources of comovemen beween financial markes, namely disinguishing among shocks spreading a a global level, a he asse class or raher a he counry level. On he oher hand, he presence of ime-varying exposures o common facors enables us o es for he presence of conagion, conrolling a he same ime for excess inerdependence induced by heeroscedasiciy in he facors. In he follow- 8

ing secions, we explore he feaures of he model and use i o characerize financial marke comovemens during crisis. In Secion 3.1, we describe he esimaion of he facors F i,j, whereas he esimaion of Z 1 is presened in Secion 3.2. 3.1 Facor Esimaion The facors F i,j are esimaed by means of principal componen analysis (PCA). The choice of PCA is dicaed by model simpliciy and inerpreabiliy, ye providing consisen esimaes of he laen facors 1. The global facor G is exraced using he enire se of variables considered, whereas he oher wo facors, asse class (A) and he counry specific (C) are exraced from he differen asse class and counry groups, respecively. In his seing, he number of variables from which he facors are exraced, say K, is fixed and small, whils he number of observaions T is large. 3.1.1 Global facor (G). Le us firs consider he global facor G. demeaned reurns as r i,j R i,j In order o esimae i, we define he series of he E[R i,j ] and we sack hem ino he marix r. We hen consisenly esimae he variance-covariance marix of r, say Σ r, via maximum likelihood, as ˆΣ r 1 (T 1) r r (3) Le (l k, w k ) be he eigencouples referred o he covariance marix Σ r, wih k = 1,..., K, such ha l 1 l 2... l K. We esimae (l k, w k ) by exracing he eigenvalue-eigenvecor couples from he esimaed covariance marix of he reurns ˆΣ r, denoed as (ˆl k, ŵ k ). The esimae Ĝ of he common facor G is given by he principal componen exraced 1 In he facor model lieraure, consisency of he facor esimaion is a well esablished resul for he case in which he facor loading is sable. In his paper, we make use of he limiing heory developed by Sock and Wason (1998, 2002 and 2009) and Baes e al. (2013) for he case of insabiliy of he facor loading, suggesing ha facors are consisenly esimaed using principal componens. 9

using he marix ˆΣ r, ha is: Ĝ = rŵ 1 (4) Ĝ is a consisen esimaor of he facor G. Indeed, from he sandpoin ha ˆΣ r is a consisen esimaor of Σ r, we claim ha, as a direc consequence of he invariance propery for maximum likelihood esimaors, he esimaed eigencouples (ˆl k, ŵ k ) consisenly esimae (l k, w k ). See Anderson (2003). 3.1.2 Asse class (A) and counry specific (C) facors. Following he same procedure used for he esimaion of global facor, in order o esimae he asse class and he counry specific facors A i and C j (wih i = 1,..., I and j = 1,..., J) respecively, we define r i [r i,j ] j=1,...,j and r j [r i,j ] i=1,...,i as he marices of reurns referred o asse class i and counry j, respecively. Denoe as Σ r i and Σ r j he corresponding covariance marix and le ŵ i 1 and ŵ j 1 be he eigenvecors corresponding o he larges eigenvalues of he esimaes ˆΣ r i and ˆΣ r j. The esimaes of he asse class and he counry specific facors Âi and Ĉj are hen given by: Â i = r i ŵ i 1 (5) Ĉ j = r j ŵ j 1 (6) As we use demeaned reurns, he exraced facors will have zero mean by consrucion. For he sake of model inerpreabiliy, we orhogonalize he facors, so ha he hree groups of facors are muually independen. The preliminary correlaion analysis presened in Secion 2 suggess ha he asse class facors are more pervasive han he counry ones. So, we firs orhogonalize he asse class facors wih respec o he global facor. Then, we orhogonalize he counry facors wih respec o he asse class and he global facors. This ensures for insance ha he US facor is independen of he global facor and of he equiy facor. The orhogonalizaion process, however, is no carried ou wihin he groups 10

of facors, so hen he equiy facor migh have a nonzero correlaion wih he bond facor, and so he US facor wih he EU facor. In he empirical secion we repor below, we show ha our resuls are robus o he case in which one orhogonalizes he counry facors wih he global one and hen he asse class facors wih respec o he ohers. 3.2 Facor Loading Specificaion and Esimaion In our specificaion (2), Z 1 is a conrol facor exraced from pure exogenous variables and i is supposed o measure marke nervousness and accouns for poenial increase in he facor loading during marke disress periods. We ge an esimae Ẑ 1 of Z 1 via he principal componen exraced from he VIX, which is widely recognized as indicaor of marke senimen, he TED spread and he Libor-OIS spread for Europe, which measure he perceived credi risk in he sysem. Widening spreads corresponds o a lack of confidence in lending money on he inerbank marke over shor-erm mauriies, ogeher wih a fligh o securiy in he form of overnigh deposis a he lender of las resor. Thus, he specificaion of (2) for he facor loadings β i,j is now β i,j = diag(1 φ i,j )β i,j + diag(φ i,j )β i,j 1 + ψ i,j Ẑ 1 + u i,j (7) The condiional ime-varying facor loading specificaion 2 (7) emphasizes ha β i,j ends o is long-run value β i,j while following an auoregressive ype of process of order one wih a purely exogenous variable Z. Being Z a zero-mean variable, β i,j can indeed be inerpreed as he long-run value for β i,j. Specificaion (7) ness wo special cases. Firs, a saic specificaion of he form: β i,j β i,j, i = 1,..., I, j = 1,..., J (8) 2 Specificaion (7) is wihin he class of he so-called condiional ime-varying facor loading approach (see Bekaer e al., 2009), where he facor loadings are assumed o follow a srucural dynamic equaion (see for insance Baele e al., 2010) of he form β i,j β(f 1, X )where {F } =1,...,T is he informaion flow and X is a se of condiional variables 11

where we assume ha he exposure of all modelled variables o he differen groups of facors are kep consan hrough ime. A second nesed case is a ime-varying facor loading specificaion β i,j = diag(1 φ i,j )β i,j + diag(φ i,j )β i,j 1 + u i,j (9) where i is assumed ha no exogenous variables ener in he daa generaing process of he beas. In Bekaer e al. (2009), he dynamics of he beas is specified using subsamples of fixed lengh via a rolling window esimaion, so ha he facor loadings are consan wihin pools of observaions wih he facor loadings having he following specificaion: β i,j,s s = 1,..., S where β i,j,s is he saic facor loading esimae referred o subsample s, while S is he number of subsamples considered. Auhors pariion he sample in semesers and re-esimae he model every six monhs. However, he rolling windows esimaion is based on changing subsamples of he daa and i may no reflec ime-variaion fairly well especially in small samples as also poined ou, amongs ohers, by Benarjee, Lumsdaine and Sock (1992). Thus, in our paper we esimae specificaion (9) using Kalman Filer maximum likelihood esimaion o avoid boh issues on poenial inconsisency of he esimaes obained using sub-samples and any arbirary choice abou he ineria, he subsample lengh, as o which facor loadings evolve hrough ime. β i,j To summarise, our proposed dynamic muli-facor model is: R i,j = E[R i,j ] + i,j ˆF β i,j + ɛ i,j (10) β i,j = diag(1 φ i,j )β i,j + diag(φ i,j )β i,j 1 + ψ i,j Ẑ 1 + u i,j (11) OLS gives consisen esimaes of (10) when using specificaion (8), corresponding o he saic case, which we consider he baseline. When considering he alernaive specificaions (7) and (9), we allow ha he facor loadings show evidence of conagion eiher in a condiioned way (ψ i,j 0) or in an uncondiioned way (ψ i,j = 0), according o he specified 12

conrol variable. In hese oher wo cases, consisen esimaes are obained by applying he Kalman filer. The models are nesed and hus, he sandard likelihood raio es can be employed for model selecion. 3.3 Heeroscedasic Facors We se up our modelling framework so ha we can disinguish beween spikes in comovemens due o increasing exposures o common risk facors from he case in which spikes are riggered by excess volailiy in he common facors. For his reason, besides allowing for dynamic facor exposures, we allow for heeroscedasic facors. We model heeroscedasiciy using Engle s (2002) Dynamic Condiional Correlaions (DCC) model of order (1,1), and employing a GARCH(1,1) for he marginal condiional volailiy processes wih normal innovaions. The exen ha he hree groups of facors are muually independen by consrucion grealy simplifies he esimaion. For he case of he global facor G, a univariae GARCH(1,1) wih normal innovaion is employed o esimae ime-varying volailiy. For he asse class and he counry facors, we apply he Engle s DCC model separaely on A and C, defined by sacking he facors ino marices as follows: A [A i ] i=1,...,i and C [C j ] j=1,...,j. We obain consisen esimaes of he ime-varying covariance marices of he facors, esimaing he DCC model via quasi-maximum likelihood esimaion. 3.4 Financial Markes Comovemens: Conagion versus Excess Inerdependence From he dynamic facor model inroduced above, we can derive he ime-varying covariance beween pairs of financial asses. To simplifying he noaion, le us inroduce he one-o-one mapping n n(i, j), wih which we idenify asse n (n = 1,..., N), belonging o asse class i and counry j. Given he independence beween he facors F and he error erm ɛ, from (1) i follows ha he 13

covariance beween asse n 1 and asse n 2 a ime is given by: cov (R n 1, R n 2 ) = E[β n 1 F n 1 F n 2 β n 2 ] + E[ɛ n 1 ɛ n 2 ] (12) The firs erm on he righ hand side is wha is generally referred o as model implied covariance, whereas he second is called residual covariance. The empirical counerpar of (12) is given by: cov ˆ (R n 1, R n 2 ) = ˆβ n 1 ˆΣ n 1,n 2 F, ˆβ n 2 + ˆΣ n 1,n 2 ɛ, (13) which we rewrie for convenience, as: cov ˆ n1,n 2, = cov ˆ F n 1,n 2, + cov ˆ ɛ n 1,n 2, (14) Correspondingly, define he quaniies variances. We provide he esimaes of corr ˆ F n 1,n 2, and corr ˆ ɛ n 1,n 2, dividing by he appropriae corr ˆ ɛ n 1,n 2, via he DCC framework. We deliberaely do no adjus he residuals of he model by heeroscedasicy and/or serial correlaion, which are insead reaed as genuine feaures of he daa. We denoe he model implied variance of he n-h marke by var ˆ n,, which is defined as var ˆ n, cov ˆ n,n,. During period of financial disress, soaring empirical covariances are in general observed. Eq. (13) shows ha he covariance beween R n 1 and R n 2 can rise hrough hree differen channels: an increase in he facor loadings β, an increase in he covariance of he facors Σ F,, and an increase residual covariance Σ ɛ,. Bekaer e al. (2005) and he relaed lieraure idenify conagion as he comovemen beween financial markes in excess of wha implied by an economic model. In his view, conagion is associaed wih spiking residual covariance beween markes, which refers o he second erm on he righ-hand side of boh Eq. (13) and Eq. (14). In our modelling se-up, we ake a differen sand. Consisenly wih he case brough by Forbes and Rigobon (2002, pp. 2230-1), conagion is hough as an episode of financial disress characerized by increasing inerlinkages beween markes. This exen finds is model equivalen in a surge in he facor loadings β. On he conrary, spiking 14

volailiy in he facor condiional covariances is associaed wih excess inerdependence. We formalize his noion in Definiion 1 (conagion) and Definiion 2 (excess inerdependence) below. Following Bekaer e al. (2009), we consider he average measure of model implied comovemens: Γ F 1 N(N 1)/2 N N n 1 =1 n 2 >n 1 corr ˆ F n 1,n 2, (15) and similarly we define Γ ɛ as he residual comovemen measure. In order o characerize financial marke comovemens, we may assume ha he residual covariance cov ˆ ɛ n 1,n 2, is negligible and focus our aenion on he model implied covariance cov ˆ F n 1,n 2,. There are wo sources hrough which he covariance beween wo markes can surge: an increase in he facor loadings β, and/or increase in he facor volailiies Σ F,. In oher words, assuming ha our model fully capures he correlaions beween asses (E[ɛ n 1 ɛ n 2 ] = 0), he possible sources of a surge in he comovemens are eiher soaring facor volailiies or increasing exposures o he facors. We label he former effec as conagion, whereas we call he laer excess inerdependence. We can ge furher insighs ino he covariance decomposiion oulined in (12), by recalling ha he facors F i,j (12), i follows ha: = [G A i C j ] are by consrucion muually independen. Thus, from cov (R n 1, R n 2 ) = E[γ n 1 G G γ n 2 ] + E[δ n 1 A i 1 A i 2 δ n 2 ] + E[λ n 1 C j 1 C j 2 λ n 2 ] + E[ɛ n 1 ɛ n 2 ] (16) wih empirical counerpar of he form: cov (R n 1, R n 2 ) = ˆγ n 1 ˆΣ n 1,n 2 G, ˆγ n 2 + ˆδ n 1 ˆΣ n 1,n 2 2 A, ˆδn + ˆλ n 1 ˆΣ n 1,n 2 C, ˆλ n 2 + ˆΣ n 1,n 2 ɛ, (17) which for convenience we wrie as: cov ˆ n1,n 2, = cov ˆ G n 1,n 2, + cov ˆ A n 1,n 2, + cov ˆ C n 1,n 2, + cov ˆ ɛ n 1,n 2, (18) 15

Our model framework has he advanage ha i allows o discriminae among comovemens due o global, asse class or counry specific shocks. We define a measure of comovemen promped by he global facor as: Γ G 1 N(N 1)/2 N N n 1 =1 n 2 >n 1 corr ˆ G n 1,n 2, (19) where: corr ˆ G n 1,n 2, cov ˆ G n 1,n 2, var ˆ F n 1,var ˆ F n 2, (20) and can be seen as he par of he correlaion beween markes n 1 and n 2, due o he common dependence on he global facor. In he same manner, we define Γ A and Γ C as he measures of comovemens promped by asse class and counry facors, respecively. By consrucion we have: Γ F Γ G + Γ A + Γ C. We decline he same Γ-measures of comovemens also a he asse class and counry level. Le I i be he se of indices from he sequence n = 1,..., N referred o markes belonging o he asse class i, and J j be he indices referred o markes in counry j, ha is: I i = { n n = n(i, j); j = 1,..., J } J j = { n n = n(i, j); i = 1,..., I } (21) (22) The model implied comovemen measure for asse class i is given by: Γ i 1 I i ( I i 1) /2 and in he same manner for counry j, we have: Γ j 1 J j ( J j 1) /2 n 1 I i n 2 I i n 2 >n 1 n 1 J j n 2 J j n 2 >n 1 corr ˆ F n 1,n 2, (23) corr ˆ F n 1,n 2, (24) 16

Along wih he definiion of comovemen measures inroduced so far, we propose a modificaion of hem, o es for conagion versus excess inerdependence. In he case of Γ F, besides he definiion in (15), we consider also: where Γ F,ED Γ F,V D 1 N(N 1)/2 1 N(N 1)/2 N N n 1 =1 n 2 >n 1 N N n 1 =1 n 2 >n 1 corr ˆ F n 1,n 2,,ED (25) corr ˆ F n 1,n 2,,V D (26) corr ˆ F n 1,n 2,,ED and corr ˆ F n 1,n 2,,V D are he correlaion coeffi ciens respecively associaed wih he following covariances: cov ˆ F n 1,n 2,,ED ˆβ n 1 ˆΣ n 1,n 2 F ˆβ n 2 (27) cov ˆ F n 1,n 2,,V D ˆβ n 1 1,n 2 ˆΣn ˆβ n 2 F, (28) Γ F,ED differs from ΓF in he sense ha he correlaions used in is definiion are compued assuming consan facor volailiies. In his case, he dynamics of he correlaion beween wo markes is riggered by heir ime-varying exposures o common facors. We call his correlaion measure as exposure driven (ED). On he conrary, Γ F,V D is an average measure of comovemens riggered by facor volailiy only, while he exposures o he facors are kep consan according o heir ime series average. We call his ype of comovemens as volailiy driven (VD). We consider he same wo definiions for Γ G, Γ A and Γ C, as well as for Γ i and Γ j. The ools used in he analysis of he resuling ime series are based on he Impulse- Indicaor Sauraion (IIS) echnique implemened in Auomerics T M, as par of he sofware PcGive T M (Hendry and Krolzig, 2005, Doornik, 2009, Casle e al., 2011). Casle e al. (2012) show ha Auomerics IIS is able o deec muliple breaks in a ime series when he daes of breaks are unknown. Furhermore, Auhors demonsrae ha he IIS procedure ouperforms he sandard Bai and Perron (1998) procedure. In paricular, IIS is robus in 17

presence of ouliers close o he end and he sar of he sample 3. Following Casle e al. (2012), we look for srucural breaks in he generic Γ ( ) comovemen measures, by esimaing he regression: average Γ ( ) = µ + η (29) where µ is a consan and η is assumed o be whie noise. We hen saurae he above regression using he IIS procedure, which reains ino he model individual impulse-indicaors in he form of spike dummy variables, signalling he presence of insabiliies in he modelled series. These dummies occur in block beween he daes of he breaks. In line wih he procedure oulined in Casle e al. (2012), we group he dummy variables wih he same sign and similar magniudes ha occur sequenially o form segmens of dummies, whereas he impulse-indicaors which can no be grouped will be labelled as ouliers. We inerpre he segmens of spike dummies as a sep dummy for a paricular regime. We can now sae he following: Definiion 1 (Conagion). A siuaion of conagion is idenified when a segmen of dummy variables is deeced hrough he IIS procedure for he average comovemen measure Γ ( ),ED. Definiion 2 (Excess inerdependence). A siuaion of excess inerdependence is idenified when a segmen of dummy variables is deeced hrough he IIS procedure for he average comovemen measure Γ ( ),V D. We se a resricive significance level of 1%, which leads o a parsimonious specificaion, as shown in Casle e al. (2012). Secion 4.2 gives accoun of he resuls of he oulined mehodology applied o our daa. 3 The use of he IIS sraegy o idenify srucural breaks using a number of dummy variables has similariies o he conagion es proposed by Favero and Giavazzi (2002) 18

4 Empirical Resuls In his secion, we repor he esimaes of he dynamic muli-facor model formulaed in Secion 3. In paricular, in Secion 4.1 we repor he resuls of he esimaion of he facors and he specificaion of he facor loading, in Secions 4.2 he empirical analysis of marke comovemens, boh he esimaes of measures of marke comovemens (Secion 4.2.1) and he regime of conagion vs excess inerdependence we idenify in marke comovemens (Secion 4.2.2). 4.1 Facor Esimaes and Facor Loading Selecion We sar our empirical analysis by exracing he facors according o he mehodology oulined in Secion 3.1. We exrac he firs principal componen a a global, asse class and counry level from he esimae of he covariance marix of he demeaned reurn ime series. The facors have by consrucion zero mean. The exraced facors accoun in oal for 83.28% of he overall variance, hus explaining a subsanial amoun of he variaion of he considered reurn series. In paricular, he global facor exracs as much as he 37.27% of he overall variance, whereas he asse class and he counry facors accoun for a quoa in he 50 80% range of he variaion in he groups hey are exraced from. We hen orhogonalize he exraced facors, so ha he sysem ˆF i,j [Ĝ Â i Ĉ j ] wih i = 1,..., I and j = 1,..., J consiss of orhogonal facors. We firs orhogonalize each of he asse class facors wih respec o he global facor and hen orhogonalize he counry facors wih respec o boh he global and he asse class facors. In Secion 4.2, we show ha all our main resuls do no depend on he paricular way he orhogonalizaion is carried ou. To validae he inerpreaions we aached o he facors, we map he conribuions of he original variables ono he facors via linear correlaion analysis. The resul of his analysis is repored in Table 4. 19

[Table 4 abou here] We find ha he sock indices are he mos correlaed wih he global facors, wih correlaions in he 80%-90% range. This characerizes he global facor as he momenum facor. Such an inerpreaion seems reasonable in view of he fac ha he equiy asse class can be hough as he mos direc indicaor of he financial aciviy among he asse classes here considered. More generally, when we sor he differen markes by he magniude of heir correlaion wih he global facor, hey end o group by asse class, raher hen by counry, wih he Treasury and he FX marke figure in he 30%-50% range and he money marke and he corporae bond marke in he 0%-30% range. This again suppors he evidence ha he asse class effec is more pervasive han he counry effec. The exen ha he global facor conains par of he asse class effec, however, does no pollue he inerpreaion of he asse class facors, which remain posiively and srongly correlaed wih he variables which hey are exraced from, even afer he orhogonalizaion process. To es for excess inerdependence promped by changes in he volailiy of he facors, we enerain he possibiliy ha he facor ime series migh be characerized by volailiy clusering. In Table 5, we repor he Engle es for residual heeroscedasiciy ha suggess ha a he 1% confidence level his is indeed he case for 7 ou of he 11 esimaed facors. [Table 5 abou here] We fi he Engle s DCC model on he series of he esimaed facors o ge a ime-varying esimae of heir covariance marix. We esimae (10) via OLS when we use he saic formulaion (8) for he facor loading, while when he facor loadings are specified as in eiher he ime-varying (9) or he condiional ime-varying facor loading (7) model, we esimae (10) via he Kalman filer using maximum likelihood esimaion mehod. The models are nesed and hus he likelihood raio es can be employed for model selecion. The likelihood raio saisics are repored in Table 6. [Table 6 abou here] 20

The es srongly rejecs he saic alernaive in favour of he dynamic ones. The condiional ime-varying facor loading approach dominaes he ime-varying facor loading approach. Thus, here is evidence ha he fiing of he model improves when we conrol for marke nervousness by means of he conrol facor Z. 4.2 Financial Marke Comovemens Dynamics 4.2.1 Measures of comovemens We urn now o analyse he average measures of comovemens inroduced in Secion 3.4. We sar wih he comparison beween Γ F and Γ ɛ. The wo measures are ploed in Figure 2. [Figure 2 abou here] As i can be clearly seen, he residual componen is negligible hroughou he sample period and on average does no convey any informaion abou he dynamics of he comovemens of he considered markes. We observed only a small jump in he idiosyncraic componen in correspondence o he lae 2008, which has been considered by many he harshes period of he 2007-09 global financial crisis. The model-implied measure of average comovemens Γ F flucuaes around wha can be regarded as a consan long-run value of roughly 20%. This erraic behaviour does no allow us o idenify any peak in correlaion possibly associaed o crisis periods. During he period 2007-09 a slighly lower average correlaions seem o be observed insead. We give accoun of his fac in wha follows, by disaggregaing he model implied covariaion measure Γ F. We sar doing his by considering he decomposiion of he overall comovemen measure Γ F ino Γ G, Γ A and Γ C, which is presened in Figure 3. The global facor appears o be he mos pervasive of all he hree facors considered, shaping he dynamics of he average overall measure. The asse class facor is slighly less pervasive, bu i is he mos persisen of he hree, meaning ha is conribuion is more resilien o change over ime. This expresses he fac ha he characerisics which are common o he asse class conribue in 21

a consan proporion o he average overall marke correlaion. The leas imporan facor is he counry one, which is almos negligible. Thus, comovemens ypically propagae hrough wo channels: a global one, in a ime varying manner, and an asse class channel, according o a consan conribuion. [Figure 3 abou here] We consider robusness check of hese conclusions, by pursuing an alernaive sraegy in orhogonalizing he sysem of facors here considered. We firs orhogonalize he counry facor agains he global and hen he asse class one wih respec o he oher wo. Then we re-esimae he model and consruc he comovemen measures. Embracing his alernaive approach Figure 3 ges modified ino he Figure 4. The dynamics of he comovemens is similar. The decomposiion changes in favour of he global facor, which is even more pervasive han before. However, he counry conribuion is almos absen, even when he counry facors are exraced and orhogonalized wih prioriy, hus validaing our orhogonalizaion mehod. [Figure 4 abou here] 4.2.2 Tesing for Conagion versus Excess Inerdependence In his secion, we propose an empirical analysis of he comovemen measures inroduced above by esing for he presence of differen regimes in he resuling ime series by means of Auomerics. Figures 5-7 repor he ime series analysed. Tables 7-9 show he resul of his procedure applied o our daa. [Figures 5 7 abou here] [Tables 7 9 abou here] Le us sar wih he analysis of he resuls for Γ F, Γ F,ED and ΓF,V D as repored in Table 7. As previously noed for Figure 2, no surprisingly, we do no find any srucural clear paern in he IIS reained by Auomerics when applied o Γ F. We find ouliers only, insead. 22

However, when looking a Γ F,V D we find evidence of excess inerdependence, ha is excess average correlaion promped by he heeroscedasiciy of common facors, in correspondence of he mos severe period of he 2007-09 crisis, i.e. he las par of 2008, as well as in Augus 2011, when he sovereign deb crisis spread from he peripheral counries in Europe o he res of he coninen and ulimaely o he US. On he oher hand, we deec a significan negaive break in he conagion measure Γ F,ED from lae 2007 o he end of 2008, which offses he peak in Γ F,V D, so ha no peaks are deeced in ΓF, as shown before. When only facor exposures are concerned, we observe an average de-correlaion of more han 6%. We furher disaggregae he Γ-measures a he asse class and counry level. Along wih he deeced segmens, we observe a few ouliers. In he case of Γ F,ED, we find a couple of ouliers in proximiy of he Do-Com bubble burs, winessing de-correlaion on he marke. All he oher IIS idenified by Auomerics are in proximiy of he sar and he end of he sample, a fac observed also in Casle e al. (2012). We urn our aenion o Table 8 which repors he resuls referred o he single asse classes. For sock indices, we find evidence of conagion from Aug-07 o mid-09, wih correlaion significanly up by 5% from he average level of 79%. We also find evidence of excess inerdependence for hree less exended periods, in correspondence of he mos dramaic monhs of 2008 and 2009, as well as in May-2010 and from Aug-2011 on, wih a surge of 13-15% in he average correlaion. We associae he former exen o he firs EU inervenion in he Greece s bailou programme, which marked he riggering of he sovereign deb crisis in Europe. The second idenified period has already been epiomized as he momen in which he sovereign deb crisis spread across and ouside Europe. A he aggregae level, he 2007-09 crisis and he deb crisis remain he mos relevan episodes in erms of average marke correlaions. Deecing conagion and excess inerdependence in he sock markes during crisis is very much in line wih he mainsream lieraure on comovemens. For he oher asse classes, he same periods are deeced, bu mos of hem are associaed wih decreasing marke correlaions. This is paricularly eviden a he aggregae level for Corporae Bonds 23

(wih average slumps in correlaion as high as 41.34% in he las par of 2008) and Foreign Exchange (-39.93% in roughly he same period). This phenomenon is sill presen when we look for conagion and excess inerdependence. The de-correlaion observed in he case of foreign exchange raes is due o he conrasing effecs of he crisis on he single pairs. Because of he low coss relaed o a borrowing posiion in Yen, since he early 2000s, he Japanese currency has been, ogeher wih he US Dollar, he currency used by invesors o finance heir posiions in risky asses. The massive ouflow from he markes experienced in he lae 2000s, led o he unwinding of hese borrowing posiions, which fuelled a seady appreciaion of he Japanese currency. This resuls in a massive de-correlaion of he Yen agains he oher currencies. As par of he same phenomenon, he Japanese Corporae Bond marke, even hough i experienced a sharp capial ouflow during he firs period of he lae 2000s financial crisis, coninued o grow rapidly (see Shim, 2012), proving o be a safe haven during his period of generalized financial disress. This again riggered de-correlaion of he Japan marke wih he oher counries. See Figure 8 for a graphic comparison of he marke dynamics in hese periods. [Figure 8 abou here.] Similarly, he money markes are pervaded by comovemens shocks of alernae signs, especially a he aggregae level and when esing for excess inerdependence. The series here considered are indicaive of he saus of he counry inerbank markes as well as a proxy of he conduc of he moneary policy. The negaive breaks in comovemens reflec he asymmeries in he shocks on he inerbank markes and he differences in he reacions of he moneary policy o he spreading of he crisis. We deec a posiive sign a he aggregae level and a he volailiy driven level in correspondence o he join moneary policy inervenion in Ocober 2008 by he FED, he ECB, he Bank of England and he Bank of Japan ogeher wih oher 3 indusrialized counries Cenral Bank (Canada, Swizerland and Sweden). We find no breaks for Treasury raes a he aggregae level. We now move on o Table 9 and analyse he same average comovemen measures a he counry level. We find evidence of a peak in he overall comovemens in US during he 2007-24

09 crisis. In paricular here is srong evidence of conagion a he naional level characerized by an escalaion in he magniude of he breaks in correspondence o he worsening of he crisis in lae 2008. Similarly, in he oher counries, we observe peaks during financial crises. In paricular, in Europe we observe excess inerdependence for mos of he period beween 2008 and 2012. In he UK we observe posiive breaks in he correlaions a he aggregae level and a he volailiy driven level boh for he 2007-09 crisis and for he sovereign deb crisis. For Japan we observe he de-correlaion phenomenon described above, wih he sock marke correlaed wih he oher sock markes, while he naional currency was following a seady appreciaion pah. The firs evidence of conagion during he lae 2000 s economic and financial crisis was observed for equiy markes and he US, as early as in he Augus 2007, anicipaing he allime peak of he S&P500 in Ocober, epiomizing he beginning of he 2007-09 global financial crisis. This combined evidence is in line wih wha has been observed in realiy: he crisis originaed in he US, spread across he counry and hen propagaed o he global financial markes, affecing firs he global sock markes. On he conrary, here is evidence ha he sovereign deb crisis originaed in Europe was characerized by excess inerdependence, raher han as an example of conagion. Indeed, in his case he mos exended episode of excess inerdependence was recorded for equiy indices and for Europe. 5 Conclusions This paper sudied he deerminans of he comovemens (conagion vs excess inerdependence) beween differen financial markes, boh in a muli-counry and a muli-asse class perspecive. We proposed a dynamic facor model able o capure muliple sources of shocks, a global, asse class and counry level and use i o es for he presence of conagion versus excess inerdependence. The model is specified wih ime-varying facor loadings, o allow for ime-dependen exposures of he single asses o he differen shocks. We saisically validaed he supremacy of his model as compared o a sandard saic approach and an 25

alernaive dynamic approach. The framework is applied o daa covering 5 counries (US, Euro, UK, Japan, Emerging), 5 asse markes (corporae bond yields, equiy reurns, currency reurns relaive o he US, shor-erm money marke yields and long-erm Treasury yields) for a oal of 20 series. The daa are weekly beginning January 1999 and ending March 2012. The main findings of our empirical analysis can be summarized as follows. Firs, he global facor is he mos pervasive of he considered facors, shaping he dynamics of he comovemens of he considered financial markes. On he conrary, he asse class facor is he mos persisen hrough ime, suggesing ha he srucural commonaliies of markes belonging o he same asse class sysemaically conribues in a consan proporion o he average overall comovemens. In our muliple asse class framework, he counry facor is negligible. In a robusness check, we showed ha his resul does no depend on he order in which he sysem of facors is orhogonalized. Secondly, we find evidence of conagion semming from he US and he sock marke joinly in correspondence o he mos harsh period of he 2007-09 financial crisis. On he conrary, he currency and sovereign deb crisis originaed in Europe characerized for he presence of excess inerdependence from mid-2010 onwards. According o he lieraure on comovemens, his le us characerize he spillover effecs during he 2007-09 financial crisis as persisen, alering he srengh of he financial linkages worldwide. On he oher hand, he shock ransmission experienced during he recen deb crisis has so far o be undersood as emporarily, being promped by excess facor volailiies, which do no display rend in he long-erm. Finally, a he overall average level, we do no find any evidence of conagion or excess inerdependence. We like o inerpre his resul as follows. During he crises some of he securiies considered in he sudy, he Japanese currency and corporae bond marke in paricular, displayed a diverging dynamics as resul of he unwinding of carry posiions, buil o finance risky invesmens. 26

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ID variable Asse class Counry Name Source (Ticker) CorpBond/US Corporae Bond US BOFA ML US CORP Daasream (MLCORPM) CorpBond/EU " Euro Area BOFA ML EMU CORP Daasream (MLECEXP) CorpBond/UK " UK BOFA ML UK CORP Daasream (ML CAU$) CorpBond/JP " Japan BOFA ML JAP CORP Daasream (MLJPCP$) CorpBond/EM " Emerging Counries BOFA ML EMERG CORP Daasream (MLEMCB$) EqInd/US Equiy Indices US MSCI USA Daasream (MSUSAML) EqInd/EU " Euro Area MSCI EMU U$ Daasream (MSEMUI$) EqInd/UK " UK MSCI UK U$ Daasream (MSUTDK$) EqInd/JP " Japan MSCI JAPAN U$ Daasream (MSJPAN$) EqInd/EM " Emerging Counries MSCI EM U$ Daasream (MSEMKF$) FX/EU Foreign Exchange Euro Area FX Spo Rae Bloomberg (EURUSD Curncy) FX/UK " UK FX Spo Rae Bloomberg (GBPUSD Curncy) FX/JP " Japan FX Spo Rae Bloomberg (JPYUSD Curncy) FX/EM " Emerging Counries FX Spo Rae Bloomberg (BRLUSD, CNYUSD, INRUSD, RUBUSD, TRYUSD Curncy) MoneyMk/US Money Marke US 3 monh US Libor Bloomberg (US0003M Index) MoneyMk/EU " Euro Area 3 monh Euribor Bloomberg (EUR003M Index) MoneyMk/UK " UK 3 monh UK Libor Bloomberg (BP0003M Index) Tr/US Treasury US US Gov 10 Year Yield Bloomberg (USGG10YR Index) Tr/EU " Euro Area EU Gov 10 Year Yield Bloomberg (GECU10YR Index) Tr/UK " UK UK Gov 10 Year Yield Bloomberg (GUKG10 Index) Table 1: Lis of variables used in he empirical applicaion. We repor he acronyms used o idenify each variable (ID variable), he asse class and he counry o which hey belong, he name of he series, ogeher wih he daa provider and he icker for series idenificaion. 31

Mean Sandard Deviaion Min Max Skewness Kurosis CorpBond/US 0.119% 0.748% -5.355% 3.171% -0.935 8.553 CorpBond/EU 0.103% 1.558% -5.815% 5.385% -0.194 3.512 CorpBond/UK 0.100% 1.612% -13.152% 5.628% -1.075 10.651 CorpBond/JP 0.092% 1.347% -5.356% 8.924% 0.572 6.755 CorpBond/EM 0.163% 0.826% -9.332% 3.724% -3.717 38.973 EqInd/US 0.014% 2.747% -20.116% 11.526% -0.748 8.850 EqInd/EU -0.011% 3.502% -26.679% 12.245% -1.073 9.576 EqInd/UK -0.009% 3.091% -27.618% 16.243% -1.249 14.920 EqInd/JP 0.009% 2.887% -16.402% 11.016% -0.258 4.823 EqInd/EM 0.184% 3.380% -22.564% 18.538% -0.775 8.889 FX/EU 0.017% 1.468% -6.048% 4.992% -0.213 3.831 FX/UK -0.009% 1.341% -8.348% 5.195% -0.588 6.546 FX/JP 0.050% 1.498% -6.027% 7.445% 0.253 4.304 FX/EM -0.142% 1.517% -17.401% 4.786% -2.961 29.634 MoneyMk/US -0.350% 3.814% -27.877% 21.137% -1.850 16.873 MoneyMk/EU -0.187% 2.087% -11.989% 15.021% -0.717 11.723 MoneyMk/UK -0.262% 2.091% -26.170% 8.374% -4.357 43.968 Tr/US -0.126% 3.596% -19.122% 12.110% -0.045 5.511 Tr/EU -0.116% 3.056% -17.838% 14.018% -0.353 6.476 Tr/UK -0.105% 2.805% -16.758% 11.153% -0.362 5.943 Table 2: Descripive saisics for he marke reurns. We repor summary saisics for he variable used in he empirical applicaion. The number repored refer o he enire sample, which consiss of weekly observaions from Jan-1999 o Mar-2012. 32

CorpBond/US CorpBond/EU CorpBond/UK CorpBond/JP CorpBond/EM EqInd/US EqInd/EU EqInd/UK EqInd/JP EqInd/EM FX/EU FX/UK FX/JP FX/EM MoneyMk/US MoneyMk/EU MoneyMk/UK Tr/US Tr/EU CorpBond/EU 0.393 CorpBond/UK 0.462 0.694 CorpBond/JP 0.264 0.312 0.171 CorpBond/EM 0.578 0.539 0.516 0.046 EqInd/US -0.041 0.087 0.080-0.260 0.207 EqInd/EU 0.004 0.411 0.288-0.161 0.351 0.785 EqInd/UK 0.028 0.326 0.403-0.229 0.329 0.764 0.884 EqInd/JP 0.145 0.238 0.208 0.129 0.272 0.405 0.480 0.444 EqInd/EM 0.044 0.286 0.272-0.211 0.448 0.693 0.785 0.755 0.545 FX/EU 0.178 0.913 0.566 0.232 0.402 0.126 0.435 0.333 0.217 0.291 FX/UK 0.162 0.616 0.833 0.060 0.358 0.156 0.373 0.502 0.251 0.336 0.642 FX/JP 0.181 0.295 0.138 0.836 0.054-0.226-0.112-0.177 0.269-0.140 0.262 0.101 FX/EM 0.079 0.349 0.296-0.151 0.356 0.434 0.548 0.522 0.244 0.593 0.338 0.328-0.094 MoneyMk/US -0.342-0.233-0.174-0.133-0.247-0.020-0.094-0.091-0.076-0.088-0.144-0.081-0.102-0.077 MoneyMk/EU -0.177-0.056 0.001-0.009-0.141 0.030 0.053 0.034 0.029-0.005 0.015 0.036-0.007-0.018 0.385 MoneyMk/UK -0.227-0.104-0.002-0.077-0.245 0.061-0.002 0.033-0.017-0.037-0.023 0.119-0.083-0.003 0.536 0.525 Tr/US -0.733-0.246-0.292-0.388-0.230 0.329 0.294 0.262 0.061 0.275-0.104-0.037-0.295 0.152 0.141 0.112 0.090 Tr/EU -0.548-0.171-0.280-0.310-0.152 0.297 0.337 0.276 0.114 0.277 0.045 0.040-0.219 0.167 0.105 0.152 0.118 0.731 Tr/UK -0.531-0.205-0.330-0.313-0.176 0.266 0.268 0.267 0.121 0.247-0.031 0.083-0.208 0.133 0.084 0.105 0.159 0.715 0.798 Table 3: Sample correlaions among he marke reurns. 33

Global Corp Bond EqInd FX Money Mk Tr US EU UK JP EM CorpBond/US -0.188 0.595 0.684 0.325-0.337-0.714-0.234 0.017 0.032 0.098 0.059 CorpBond/EU 0.237 0.884 0.350 0.822-0.211-0.472 0.028 0.150-0.120-0.039-0.044 CorpBond/UK 0.185 0.882 0.425 0.700-0.131-0.550 0.038-0.163 0.145 0.052-0.022 CorpBond/JP -0.300 0.450 0.279 0.402-0.128-0.245-0.106 0.107-0.027-0.129 0.015 CorpBond/EM 0.281 0.587 0.413 0.377-0.248-0.475-0.007-0.078-0.153 0.061 0.278 EqInd/US 0.816-0.072 0.248-0.146 0.004-0.214 0.138-0.029-0.035-0.136-0.167 EqInd/EU 0.907 0.193 0.275 0.127-0.066-0.284-0.008 0.263-0.024-0.129-0.156 EqInd/UK 0.875 0.206 0.290 0.119-0.057-0.307-0.016-0.011 0.312-0.118-0.188 EqInd/JP 0.541 0.177 0.350 0.096-0.063-0.288-0.143-0.181-0.101 0.624 0.036 EqInd/EM 0.854 0.143 0.289 0.078-0.072-0.290 0.009-0.177-0.167 0.016 0.422 FX/EU 0.313 0.730 0.167 0.830-0.117-0.293-0.012 0.226-0.114-0.078-0.099 FX/UK 0.373 0.683 0.133 0.720-0.032-0.260-0.061-0.185 0.328 0.027-0.092 FX/JP -0.205 0.379 0.226 0.441-0.104-0.186-0.089 0.044-0.024-0.026 0.022 FX/EM 0.557 0.225 0.122 0.421-0.061-0.222 0.119-0.131-0.169 0.088 0.212 MoneyMk/US -0.021-0.241-0.175-0.139 0.973 0.187 0.133-0.019-0.034-0.059 0.040 MoneyMk/EU 0.092-0.061-0.138-0.030 0.551 0.108-0.360 0.152-0.021 0.193-0.096 MoneyMk/UK 0.065-0.104-0.150-0.010 0.697 0.118-0.332-0.031 0.176 0.120-0.109 Tr/US 0.559-0.474-0.716-0.350 0.153 0.738 0.309-0.142-0.123-0.025 0.028 Tr/EU 0.577-0.403-0.700-0.224 0.130 0.708-0.229 0.248-0.045 0.016-0.025 Tr/UK 0.536-0.439-0.695-0.239 0.118 0.712-0.250-0.059 0.266 0.023-0.017 Table 4: Correlaions beween he marke reurns and he exraced facors. We repor he correlaion beween he facors and he marke reurns from which he facors are exraced. There are 20 series displayed in he rows and 11 facors (one global, 5 asse class and 5 counry facors), which are displayed in he columns. The numbers repored are in-sample linear correlaions. 34

FACTOR STAT Global 51.982 *** CorpBond 7.577 *** EqInd 0.458 FX 3.254 * MoneyMk 59.335 *** Tr 0.318 US 31.535 *** EU 21.421 *** UK 26.668 *** JP 3.386 * EM 25.878 *** Table 5: Engle es for residual heeroscedasiciy for he esimaed facors. We repor he resuls of he es for residual heeroscedasiciy for he 11 exraced facors (one global, 5 asse class and 5 counry facors). The firs columns repors he name of he facor, he second repors he es saisics in he Engle es for residual heeroscedasiciy. In he hird column, ***, ** and * indicae rejecion of he null of no ARCH effec a he 1%, 5% and 10% significance level, respecively. 35

Alernaive model Null model Time-varing facor loading Condiional ime-varying facor loading Saic facor loading 260142.36*** 261869.86*** Time-varing facor loading 1727.50*** Table 6: Likelihood raio es for he alernaive models. We repor he es saisics for he likelihood raio es comparing he proposed alernaive models. The es is employed o evaluae he null hypohesis ha he Null model provides a beer fi han he Alernaive model. The models refer o he following alernaive formulaion for he facor loadings: he saic facor loading in Eq. (??), he ime-varying facor loading in Eq. (??) and he condiional ime-varying facor loading in Eq. (??). *** indicaes rejecion of he null model a he 1% significance level. 36

Γ F Ouliers 26/02/1999-0.0583 **... 16/12/2011-0.0584 ** Consan 0.2230 *** Γ F,ED Segmens 17/08/2007-21/11/2008-0.0670 *** Ouliers 07/04/2000-0.0608 ** 30/06/2000-0.0607 ** 09/03/2001-0.0746 *** 25/11/2011-0.0646 *** 02/12/2011-0.0583 ** Consan 0.2282 *** Γ F,V D Segmens 31/10/2008-05/12/2008 0.0564 *** 12/08/2011-26/08/2011 0.0594 *** Ouliers 23/04/1999-0.0507 *** Consan 0.2320 *** Table 7: IIS resuls for he overall average comovemen measures. Γ F is he average comovemen measure a he overall level, defined as he mean of he model implied correlaions beween all he couples of asse considered. Γ F,ED (ΓF,V D ) considers he correlaions for he case in which facor exposures are allowed o vary wih ime (held a consan) and facor covariances are held a consan (allowed o vary wih ime). We repor he resuls of he sauraion of model in Eq. (29) by means of Auomerics. We repor he daes deeced via he IIS echnique, ogeher wih he esimaed coeffi ciens. Segmen refers o group of sequenial dummies wih he same size and similar magniude. Ouliers are dummies which can no be grouped. Consan refers o he consan erm µ in Eq. 29 (***, ** and * indicae significance of he coeffi cien a he 1%, 5% and 10% significance level, respecively). 37

Γ CorpBond Γ EqInd Γ F X Γ MoneyMk Γ T r X r Segm ens Segm ens Segm ens Segm ens O uliers 24/08/2007-26/09/2008-0.1614 *** 10/10/2008-27/03/2009 0.1664 *** 26/05/2006-04/08/2006-0.1623 *** 29/01/1999-20/04/2001-0.0748 *** 15/01/1999-0.4502 *** 03/10/2008-23/01/2009-0.4134 *** 12/08/2011-03/02/2012 0.1447 *** 16/03/2007-25/07/2008-0.1681 *** 14/03/2008-28/03/2008-0.9199 ***... 06/02/2009-04/06/2010-0.1867 *** O uliers 19/09/2008-15/05/2009-0.3993 *** 11/04/2008-19/09/2008-0.0650 *** 16/12/2011-0.7062 *** 12/08/2011-03/02/2012-0.3610 *** 01/01/1999 0.1596 *** 12/08/2011-27/01/2012-0.2528 *** 26/09/2008-14/11/2008 0.0521 ** Consan 0.8238 *** O uliers 18/02/2000-0.1695 *** O uliers 06/02/2009-22/01/2010-0.1794 *** 22/01/1999-0.1643 *** 24/03/2000-0.1718 *** 22/01/1999-0.1107 ** 07/05/2010-28/05/2010 0.0525 ** 21/04/2000-0.1535 *** Consan 0.7408 *** 07/04/2000-0.1149 *** 15/04/2011-29/07/2011-0.1010 *** 28/09/2001-0.1812 *** 09/03/2001-0.1756 *** 12/08/2011-19/08/2011-1.2057 *** 05/10/2001-0.1859 *** 28/09/2001-0.1433 *** 11/11/2011-27/01/2012-0.1060 *** 12/10/2001-0.1343 *** 21/05/2004-0.1340 *** O uliers Consan 0.8557 *** 24/07/2009-0.1781 *** 28/09/2001 0.0570 ** 21/05/2010-0.1111 ** 16/11/2001 0.0550 ** Consan 0.7481 *** 22/11/2002-0.1174 *** 21/02/2003-0.0593 ** 28/03/2003-0.1570 *** 04/04/2003-0.0613 ** 27/06/2003-1.2632 *** 01/02/2008 0.0524 ** 29/02/2008-0.0606 ** 05/12/2008-0.3098 *** 26/12/2008 0.0502 ** 02/07/2010-0.0835 *** 03/09/2010 0.0522 ** 26/11/2010-0.0771 *** 14/01/2011-0.0900 *** Consan 0.9421 *** Γ CorpBond,ED Γ EqInd,ED Γ F X Γ MoneyMk,ED X,ED Segm ens Segm ens Segm ens Segm ens O uliers 24/08/2007-05/09/2008-0.0805 *** 24/08/2007-15/05/2009 0.0448 *** 19/03/1999-09/07/1999-0.1037 *** 08/11/2002-29/11/2002-0.0623 *** 08/01/1999-0.1247 ** 19/09/2008-03/04/2009-0.1858 *** O uliers 20/05/2005-19/09/2008-0.1385 *** 14/02/2003-20/06/2003-0.0190 ***... 10/04/2009-18/09/2009-0.0686 *** 01/01/1999 0.1132 *** 26/09/2008-02/01/2009-0.2525 *** 17/08/2007-01/02/2008-0.0207 *** 16/12/2011-0.7230 *** 12/08/2011-23/12/2011-0.0628 *** 26/03/1999 0.0267 *** 09/01/2009-15/05/2009-0.1326 *** 14/03/2008-21/03/2008-1.3015 *** Consan 0.8304 *** O uliers 18/06/1999 0.0387 *** 12/08/2011-25/11/2011-0.1176 *** 04/04/2008-24/04/2009-0.0313 *** 22/01/1999-0.0803 *** 02/03/2001-0.0931 *** O uliers 05/06/2009-27/11/2009-0.0204 *** 22/10/1999-0.0574 *** 28/09/2001-0.0413 *** 22/01/1999-0.0871 ** 14/05/2010-29/07/2011-0.0311 *** 21/04/2000-0.0419 *** 05/10/2001-0.0386 *** 14/01/2000-0.1109 *** 12/08/2011-19/08/2011-1.2619 *** 15/09/2000 0.0415 *** 15/03/2002 0.0367 *** 07/04/2000-0.1090 *** 26/08/2011-16/12/2011-0.0321 *** 10/11/2000 0.0403 *** 09/03/2007-0.0312 *** 09/03/2001-0.2604 *** O uliers 08/12/2000 0.0493 *** 17/07/2009-0.0435 *** 16/03/2001 0.1068 *** 18/06/1999-0.0142 *** 05/01/2001 0.0440 *** 14/08/2009-0.0267 *** Consan 0.7349 *** 30/07/1999-0.0134 *** 02/08/2002-0.0440 *** 12/03/2010-0.0257 *** 17/09/1999 0.0157 *** 01/08/2003 0.0403 *** 14/05/2010-0.0460 *** 08/10/1999-0.0175 *** Consan 0.8276 *** 21/05/2010-0.0336 *** 12/01/2001-0.0233 *** 20/08/2010 0.0271 *** 10/08/2001-0.0259 *** 08/04/2011-0.0345 *** 28/12/2001-0.0165 *** 15/04/2011-0.0522 *** 08/02/2002-0.0148 *** 26/08/2011 0.0293 *** 27/06/2003-1.2770 *** 23/09/2011 0.0290 *** 28/03/2008-0.2650 *** 11/11/2011 0.0305 *** 01/05/2009-1.0106 *** Consan 0.7860 *** 29/05/2009-0.2165 *** Consan 0.9720 *** Γ T,ED r Γ CorpBond,V D Γ EqInd,V D Γ F X Γ MoneyMk,V X D,V D Segm ens Segm ens Segm ens Segm ens Segm ens 28/09/2001-26/10/2001-0.1392 *** 18/02/2000-14/04/2000-0.1367 *** 28/09/2001-02/11/2001-0.1156 *** 29/01/1999-30/04/1999-0.0511 ** 01/10/1999-05/05/2000-0.0650 *** 23/12/2005-27/01/2006 0.0485 * 12/09/2008-13/03/2009 0.1491 *** 01/04/2005-15/04/2005 0.0495 * 17/12/1999-10/03/2000-0.0891 *** 06/12/2002-21/03/2003-0.0536 *** 24/08/2007-28/09/2007-0.1147 *** 14/05/2010-28/05/2010 0.1366 *** 19/09/2008-04/12/2009-0.1399 *** 26/09/2008-16/01/2009 0.0540 ** 31/10/2008-07/11/2008 0.0571 *** 17/10/2008-31/07/2009-0.1823 *** 12/08/2011-10/02/2012 0.1347 *** 14/05/2010-16/07/2010-0.0955 *** 06/02/2009-20/03/2009-0.1680 *** 17/04/2009-11/09/2009-0.0502 *** 14/05/2010-11/06/2010-0.1108 *** Consan 0.7437 *** 15/07/2011-17/02/2012-0.1452 *** 22/05/2009-29/05/2009 0.0534 ** O uliers 08/07/2011-24/02/2012-0.1627 *** O uliers 17/07/2009-11/09/2009 0.0525 ** 29/01/1999-0.0454 ** O uliers 14/05/1999-0.0794 *** 16/10/2009-20/11/2009-0.0697 *** 12/08/2011 0.0545 *** 21/04/2000-0.0857 *** 18/10/2002-0.1335 *** 07/05/2010-03/09/2010 0.0541 ** Consan 0.8791 *** 04/07/2003 0.0503 * 25/10/2002-0.0899 *** O uliers 12/12/2003 0.0499 * 30/07/2004 0.0523 * 15/10/1999 0.0491 ** 30/09/2005 0.0513 * Consan 0.7604 *** 19/09/2008-0.0521 ** 15/02/2008-0.0854 *** 19/06/2009-0.0690 *** Consan 0.8623 *** 08/01/2010-0.0504 ** 26/11/2010-0.0522 ** 11/11/2011-0.0583 ** 06/01/2012-0.0865 *** 13/01/2012-0.1019 *** Consan 0.9401 *** Γ T,V r D Table 8: IIS resuls for he average comovemens measures a he asse class level. Γ CorpBond is he average comovemen measure wihin he corporae bond marke, defined as he mean of he model implied correlaions beween all he couples of securiies in he corporae bond asse class. Γ EqInd, Γ F X, Γ MoneyMk and Γ T r are analogously defined for he oher asse classes. Exposure-driven (mid-panel) and volailiy-driven (boom panel) comovemen measures consider he correlaions for he case in which facor exposures are allowed o vary wih ime (held a consan) and facor covariances are held a consan (allowed o vary wih ime). Refer o he capion of Tab. 7 for a legend of he resuls of he esimaion. 38

Γ US Γ EU Γ UK Γ JP Γ EM Segmens Ouliers Segmens Segmens Ouliers 22/10/1999-29/10/1999 0.0576 *** 27/06/2008-0.2400 ** 11/02/2000-21/04/2000 0.1197 *** 08/10/1999-12/05/2000-0.2752 *** 22/01/1999 0.1323 *** 04/02/2000-18/02/2000 0.0643 *** 05/12/2008 0.2282 ** 04/07/2003-08/08/2003-0.1149 *** 17/08/2007-24/07/2009-0.3622 ***... 24/11/2000-22/12/2000 0.0516 *** 19/12/2008 0.2436 ** 10/10/2008-13/03/2009 0.1552 *** 21/05/2010-25/06/2010-0.2484 *** 09/12/2011 0.0618 ** 28/09/2001-02/11/2001-0.0532 *** 10/07/2009-0.2203 ** 12/08/2011-18/11/2011 0.1079 *** 12/08/2011-27/01/2012-0.3288 *** Consan 0.6248 *** 19/07/2002-27/09/2002 0.0568 *** 07/05/2010-0.2203 ** Ouliers Ouliers 24/08/2007-26/09/2008 0.0566 *** 07/01/2011-0.2155 ** 06/11/2009 0.1012 *** 30/05/2003 0.1582 * 03/10/2008-19/12/2008 0.1524 *** 29/07/2011 0.2320 ** 16/07/2010 0.1076 *** 16/06/2006-0.2002 ** 02/01/2009-16/07/2010 0.0545 *** 12/08/2011 0.2404 ** 03/12/2010-0.0992 *** Consan 0.3496 *** Ouliers 26/08/2011 0.2648 ** Consan 0.1988 *** 08/08/2003-0.0515 *** 21/10/2011 0.2253 ** Consan -0.1399 *** 18/11/2011 0.2779 *** 23/12/2011 0.2197 ** 06/01/2012 0.2225 ** Consan 0.1667 *** Γ US,ED,ED,ED,ED,ED Γ EU Γ UK Γ JP Γ EM Segmens Ouliers Ouliers Segmens Ouliers 06/08/1999-08/12/2000 0.0331 *** 13/08/1999-0.2253 ** 01/01/1999 0.0567 *** 27/08/1999-02/06/2000-0.2321 *** 22/01/1999 0.1545 *** 19/07/2002-11/10/2002 0.0291 *** 04/02/2000-0.2319 **... 17/08/2007-10/07/2009-0.3365 ***... 23/07/2004-14/04/2006-0.0147 * 03/03/2000-0.2266 ** 01/10/2010-0.0249 *** 12/08/2011-20/01/2012-0.2486 *** 21/10/2011 0.1071 *** 17/08/2007-05/09/2008 0.0436 *** 14/04/2000-0.2216 ** Consan 0.1989 *** Ouliers Consan 0.6273 *** 12/09/2008-30/01/2009 0.0766 *** 23/06/2000-0.2245 ** 12/03/2004 0.2703 *** 06/02/2009-17/07/2009 0.0447 *** 23/02/2001-0.2252 ** 04/02/2005 0.1355 * 12/08/2011-09/03/2012 0.0331 *** 07/06/2002-0.2163 ** 27/05/2005 0.1404 * Ouliers 11/10/2002-0.2222 ** 08/07/2005 0.1449 * 11/06/2010 0.0252 ** 07/03/2003-0.2263 ** Consan 0.3521 *** 03/12/2010 0.0275 *** 23/07/2004-0.2145 ** Consan -0.1457 *** 20/08/2004-0.2269 ** 08/04/2005-0.2288 ** Consan 0.1805 *** Γ US,V D,V D,V D,V D,V D Γ EU Γ UK Γ JP Γ EM Segmens Segmens Segmens Segmens Segmens 28/09/2001-19/10/2001-0.0484 *** 27/06/2003-08/08/2003-0.0716 ** 04/07/2003-08/08/2003-0.1111 *** 20/06/2003-27/02/2004 0.1288 *** 23/04/1999-04/06/1999 0.0683 *** 26/07/2002-20/09/2002 0.0451 *** 23/01/2004-01/10/2004-0.0565 * 17/10/2008-20/03/2009 0.1308 *** 17/10/2008-19/12/2008-0.1532 *** 30/07/1999-20/08/1999-0.0542 *** 20/06/2008-25/09/2009-0.0365 *** 17/10/2008-26/12/2008 0.1748 *** 06/11/2009-13/11/2009 0.0826 ** 19/11/2010-14/01/2011 0.1434 *** 26/01/2001-02/11/2001 0.0680 *** 19/11/2010-17/12/2010-0.0336 ** 02/01/2009-23/07/2010 0.1044 *** 02/07/2010-16/07/2010 0.0863 ** 12/08/2011-18/11/2011-0.1162 *** 05/07/2002-01/11/2002 0.0660 *** 19/08/2011-09/03/2012-0.0377 *** 08/07/2011-27/01/2012 0.1300 *** 12/08/2011-11/11/2011 0.1050 *** Consan 0.2815 *** 07/05/2004-21/05/2004 0.0519 *** Consan -0.1346 *** Ouliers Ouliers 24/08/2007-14/09/2007 0.0688 *** 31/08/2007 0.0796 ** 20/06/2008-0.0976 *** 18/04/2008-31/10/2008 0.0479 *** Consan 0.2112 *** 03/12/2010-0.0978 *** 12/08/2011-11/11/2011 0.0505 *** Consan 0.1994 *** Ouliers 29/09/2000 0.0593 *** Consan 0.6394 *** Table 9: IIS resuls for he average comovemens measures a he counry level. Γ US is he average comovemen measure wihin he US marke, defined as he mean of he model implied correlaions beween all he couples of securiies in he US group. Γ EU, Γ UK, Γ JP and Γ EM are analogously defined for he oher counries. Exposure-driven (mid-panel) and volailiydriven (boom panel) comovemen measures consider he correlaions for he case in which facor exposures are allowed o vary wih ime (held a consan) and facor covariances are held a consan (allowed o vary wih ime). Refer o he capion of Tab. 7 for a legend of he resuls of he esimaion. 39

40 Figure 1: Price daa used in he empirical applicaion. Asse classes are displayed in he rows, whereas counries are in he columns. We plo he weekly price series for he considered markes. Corporae bond, equiy indices and foreign exchange raes (op hree rows) are rebased using he firs available observaion. US foreign exchange is excluded from he analysis because is used as he numeraire. The oher missing series are no considered due o lack of daa.

41 Figure 2: Model implied versus residual average correlaion measures. Γ F is he average comovemen measure a he overall level, defined as he mean of he model implied correlaions beween all he couples of asse considered. Γ ɛ is he average residual comovemen measure, defined as he mean of he correlaions beween he error erm in he model for all he couples of asse considered.

42 Figure 3: Decomposiions of he overall average comovemens by source of he shock. Γ G, Γ A Γ C are he average measures of comovemen promped by he global, he asse class and he counry facor, respecively.

43 Figure 4: Robusness check of he decomposiion by source. Fig. 3 repors he decomposiions of he overall average comovemens by source of he shock, for he case in which he asse class facors are firs orhogonalized wih respec o he global facor and hen he counry facors are orhogonalized wih respec o he asse class and he global facors. Here we repor he same decomposiion for he case in which he counry facors are orhogonalized wih respec o he global facor and hen he asse class facors are orhogonalized wih respec o he ohers.

44 Figure 5: Average correlaion measures. Γ F (op panel) is he average comovemen measure a he overall level, defined as he mean of he model implied correlaions beween all he couples of asse considered. Γ F,ED -mid panel- (ΓF,V D -boom panel-) considers he correlaions for he case in which facor exposures are allowed o vary wih ime (held a consan) and facor covariances are held a consan (allowed o vary wih ime).

Figure 6: Average correlaion measures a he asse class level. Γ CorpBond is he average comovemen measure wihin he corporae bond marke, defined as he mean of he model implied correlaions beween all he couples of securiies in he corporae bond asse class. Γ EqInd, Γ F X, Γ MoneyMk and Γ T r are analogously defined for he oher asse classes. Exposure-driven (second column) and volailiy-driven (hird column) comovemen measures consider he correlaions for he case in which facor exposures are allowed o vary wih ime (held a consan) and facor covariances are held a consan (allowed o vary wih ime). 45

Figure 7: Average correlaion measures a he counry level. Γ US is he average comovemen measure wihin he US marke, defined as he mean of he model implied correlaions beween all he couples of securiies in he US group. Γ EU, Γ UK, Γ JP and Γ EM are analogously defined for he oher counries. Exposure-driven (second column) and volailiy-driven (hird column) comovemen measures consider he correlaions for he case in which facor exposures are allowed o vary wih ime (held a consan) and facor covariances are held a consan (allowed o vary wih ime). 46