Volatility Threshold Dynamic Conditional Correlations: Implications for International Portfolio Diversification

Transcription

1 Volailiy Threshold Dynamic Condiional Correlaions: Implicaions for Inernaional Porfolio Diversificaion Maria Kasch-Harouounian * February 005 Firs version Absrac In his paper we exend he Dynamic Condiional Correlaion mulivariae GARCH specificaion o invesigae how he correlaions beween he single pairs of he asses in our sysem behave in volaile markes. Our approach allows o idenify asse pairs he correlaions of which are less sensiive o exreme volailiy values associaed wih bear markes. In his conex he paper also discusses he possible porfolio diversificaion benefis. JEL classificaion: C50, C51, F37, G11, G15 Keywords: Dynamic condiional correlaions, Volailiy hreshold, Inernaional diversificaion benefis. * Universiy of Bonn, BWL I, Adenauerallee 4-4, Bonn, Germany, Phone , Fax , mkasch@uni-bonn.de.

2 1 Inroducion The seminal sudies by Grubel (1968), Levy and Sarna (1970), Lessard (1973) and Solnik (1974) laid he ground for considerable academic research advocaing he benefis of inernaional diversificaion on he basis of he low correlaion beween naional sock markes. However, he recen empirical evidence indicaes ha over he las decade he correlaions of he major securiy markes have increased significanly, by his srongly reducing he benefis of diversificaion among hese markes. On he oher hand a range of new markes has emerged, expanding he opporuniy se of invesors, and hereby offering new sources for he diversificaion of porfolio risk. A srand of lieraure on inernaional porfolio diversificaion has invesigaed he quesion wheher he benefis of diversificaion are presen when hey are needed mos, i.e. in imes of exreme marke volailiy, ofen associaed wih bear markes. 1 Evidence from capial marke hisory suggess ha poor marke performance was associaed wih an increase in inernaional correlaions. Goezmann, Li and Rouwenhors (00) cie he chairman of he Alliance Trus Company, reflecing on he Crash of 199: "Trus companies...have reckoned ha by a wide spreading of heir invesmen risk, a sable revenue posiion could be mainained, as i was no o be expeced ha all he world would go wrong a he same ime. Bu he unexpeced has happened, and every par of he civilized world is in rouble..." A range of sudies has inerpreed covariance asymmery wihin he framework of a paricular generalized auoregressive condiional heeroscedasiciy model, where he asymmery is defined o be an increase in condiional covariance or correlaion resuling from pas negaive shocks o reurn processes. Specifically, Cho and Engle (000), Bekaer and Wu (000), 1 See e.g. Lin, Engle and Io (1994), Erb, Harvey and Viskana (1994), Longin and Solnik (1995), Karolyi and Sulz (1996), Solnik, Bourcrelle, and Le Fur (1996), De Sanis and Gerard (1997), Ramchmand and Susmel (1998), Ang and Bekaer (1999), Das and Uppal (1999), Longin and Solnik (001), and Ang and Chen (00).

3 Kroner and Ng (1998), and Conrad e al. (1991) examine he covariance asymmery of domesic sock porfolios, and Capiello, Engle and Sheppard (004) invesigae he correlaion asymmery of inernaional equiy and bond reurns, using mulivariae asymmeric GARCH models. In his paper we exend he mulivariae GARCH Dynamic Condiional Correlaion (DCC) model of Engle (00) and is generalizaion by Capiello, Engle and Sheppard (004) o invesigae he relaionship beween he correlaion and he volailiies of he underlying asses. The hypohesis he exended model ess for is wheher high volailiy values (exceeding some prespecified hreshold) of he asses, implied by he model, are associaed wih an increase in heir correlaion values. The resuling specificaion could be inerpreed as asymmeric in he level of volailiy. The idenificaion of asse pairs he correlaions of which do no increase in volaile markes associaed wih bear markes, under ceeris paribus condiions, could be useful for leveraging he benefis of porfolio diversificaion. To demonsrae pracical relevance of our model we employ a sample of naional sock indices from markes heerogeneous in he level of heir developmen and inegraion ino inernaional securiies markes. While here is a considerable body of research invesigaing he Asian and Lain American emerging sock markes, he ransiion markes of Cenral Europe have seen much less aenion so far. Our sample includes he sock indices from he hree larges ransiion sock markes of Cenral Europe: Hungary, Poland and he Czech Republic. We conduc wo separae analysis, inernaional and regional European. In he inernaional par we consider he mixed sample of he ransiion indices wih he U.S. and European composie indices, while for he regional par we analyse a sample of he ransiion indices wih he major European marke indices. We sar from invesigaion of he volailiy and correlaion dynamics of he considered markes over he las decade. Some ineresing paerns in heir reacion o global evens appear. The response of he ransiion markes o hese evens, as expeced, is no always 3

4 similar o ha of he developed markes. The empirical resuls of he applicaion of he exended DCC model o our sample delivers srong evidence ha over he considered ime period he urbulen markes were associaed wih increases in he correlaions of he developed markes. For he cross-correlaions of he ransiion markes wih he res of he markes we do no observe a similar paern. This poenially makes hem aracive arges for he porfolio diversificaion of inernaional invesors. The paper is organized as follows. Secion sars from he descripion of he daa employed in his sudy. Secion 3 presens he base mulivariae GARCH models and analyses he empirical resuls. Secion 4 proposes an exension of he base models considered in secion 3 and presens he corresponding empirical resuls. Secion 5 summarises our findings. Daa descripion The empirical par of his paper concenraes on he invesigaion of he ime-varying correlaion dynamics of inernaional sock markes over he las decade. To make our analysis richer, our sample includes markes heerogeneous in he level of heir developmen, boh maure and emerging sock markes. This allows us o es hypohesis for differen marke environmens. The emerging markes chosen for his sudy are he hree larges ransiion sock markes of Cenral Europe: Hungary, Poland and he Czech Republic. In he regional European par of he analysis, he following six sock marke indices are considered: German 30, French CAC40, Briish FTSE100, Hungarian 30, Polish 0 and Czech PX50. For he inernaional par, we consider S&P500 and he European blue chip sock composie STOXX50 from he developed world, as well as he same ransiion markes indices employed for he regional analysis. The choice of he specific ransiion indices among oher indices available for hese markes is primarily based on he fac ha hose are he naional blue chip indices available for he longes ime period. These indices are published by he naional sock exchanges of he considered counries. All indices are observed a weekly frequency and are US dollar-denominaed. The 4

5 employed sample covers he period from he las week of April 1994 o he firs week of June 004, consiuing he oal of 58 reurn observaions. The use of weekly daa is preferred because daily daa could suffer from fricions in he markes especially in he case of ransiion markes. Addiionally, for he inernaional analysis, he use of daily daa would induce noise due o ime-zone differences in he counries analysed. All daa is obained from Daasream. Table 1 presens some descripive saisics for he indices. Inser Table 1 here All series show he ypical non-normaliy of financial ime series. Excess kurosis and negaive skewness are especially pronounced in he case of he Hungarian. All series wih excepion of STOXX50 display negaive skewness. The Ljung-Box saisics sugges auocorrelaion in he reurn levels of S&P500 and only. The squared reurns, on he oher hand, are highly auocorrelaed, which can be aken as evidence of ARCH effecs in he considered series. Inser Table here Table shows uncondiional correlaions of he reurns. The correlaions of 30, CAC40 and FTSE100 wih STOXX50 are, non-surprisingly, very high, parially explained by he fac ha a par of he componen socks of he German, French and Briish indices are also he componens of STOXX50. These are followed by he correlaion beween 30 wih CAC40 (0.80), FTSE100 wih CAC40 (0.73), and STOXX50 wih S&P500 (0.70). The correlaions of he considered individual developed European marke indices wih he U.S. marke are somewha lower (around 0.64). The regional European impac on he ransiion sock markes is clearly sronger han ha from he U.S., as he correlaions of hese markes wih S&P500 is significanly lower han wih he European indices. Finally, he correlaions beween he ransiion markes range from 0.41 for he Polish and Czech indices o 0.53 for he Hungarian and Polish indices. I is also ineresing o noe ha he correlaions beween he ransiion indices are higher han he correlaion of hese indices wih he res of he markes considered. 5

6 3 Dynamic Condiional Correlaions 3.1 The models Mulivariae modeling of he second momens of asse reurns plays an imporan role in many differen areas of financial managemen, like he assessmen of Value-a-Risk and oher risk measures esimaes, porfolio allocaion and asse pricing. I is now widely acceped ha wih he changes in marke condiions he volailiies and correlaions of asses change over ime as well. The las wo decades have produced a range of sudies modeling he ime-varying behavior of correlaions and covariances beween financial asses. The problems associaed wih he esimaion of he mulivariae GARCH models, relaed o he radeoff beween heir generaliy and he number of parameers o be esimaed as well as he considerable resricions on he parameers necessary for posiive definieness of he covariance marix, are well known. Bollerslev (1990) inroduced a new class of mulivariae GARCH models, he so-called Condiional Correlaion models. The specificaion of he condiional covariance marix for his class of models is implemened in a hierarchical way. Firs, volailiy for each individual series is esimaed using a univariae GARCH specificaion, hen, based on he resuling sandardized residuals, one models he condiional correlaion marix. The Consan Condiional Correlaion (CCC) model by Bollerslev (1990) ensures he feasibiliy of he model esimaion also in large dimensions and posiive definieness of he covariance marix simply requiring each univariae condiional variance o be posiive and he consan marix of condiional correlaions o be posiive definie. Due o is compuaional simpliciy, he CCC model is widely used in empirical applicaions. A range of sudies (like e.g. Bera and Kim (1996), Tsui and Yu (1999) and Tse (000)) find, however, ha he assumpion of consan condiional correlaion can be oo resricive. For he recen review of he exising mulivariae GARCH models see e.g. Bauwens e al. (003). 6

7 Engle (00) proposed a generalisaion of he CCC model of Bollerslev, he Dynamic Condiional Correlaion (DCC) model. 3 The new specificaion preserves he ease of he esimaion of he Bollerslev's model, bu allows ime variaion of he condiional correlaion marix. In Engle's model one fis o each asse reurn an appropriae univariae GARCH model (he models can differ from asse o asse) and hen sandardizes he reurns by he esimaed GARCH condiional sandard deviaions. The sandardized reurn vecor is hen used o model he correlaion dynamics. The model esimaion is performed hrough n + 1 numerical opimizaions, each involving only a few parameers, regardless of he size of n (number of asses in he sysem). Consider an n -variae condiionally normal reurn process r wih mean zero 4 and covariance marix H : r F 1 N(0, H) (1) H = DRD () { ii, } D = diag h (3) ε = D r (4) 1 where hii, s could e.g. be hough of as univariae GARCH models, ε i s are sandardized residuals wih mean zero and variance one, and R { ρ ij, } = is he ime-varying condiional correlaion marix of reurns. R corresponds o he condiional covariance marix of he sandardized residuals 5, i.e. ρ (, ), = E 1 ε ε. ij i j 3 For an alernaive generalizaion of he CCC model see Tse and Tsui (00). Addiionally, Pelleier (004) proposed a regime swiching model for dynamic correlaions, which can be seen as a midpoin beween he CCC model of Bollerslev (1990) and he DCC model of Engle (00), where he correlaions change every period. 4 ri s can be eiher mean zero or he residuals of a filered ime series. In he empirical par of his paper he daa were no filered oher han simple demeaning. 5 E 1,, 1( ) ( rir ) hii hjj E εε j i j ρij, = = = E 1( εε i j). E ( r ) E r h h E ( ε ) E ε ( ) ( ) 1 i 1 j ii, jj, 1 i 1 j 7

8 The DCC model of Engle (00) specifies he dynamics of he correlaion marix as follows: 1 1 ( ( )) ( ( )) R = diag Q Q diag Q (5) ' Q = (1 α β) Q+ α( εε ) + βq 1 (6) where Q is he uncondiional correlaion marix of ε. As a resul, he ypical elemen of R is of he form q ij, ρ ij, =. This normalizaion ensures ha all correlaion esimaes fall in qii, qjj, he [-1;1] inerval. The model is esimaed subjec o he uncondiional correlaion argeing consrain by which he long run correlaion marix is he sample correlaion marix. The specificaion is mean revering as long as α + β < 1. Noe, in case α and β are zero, one obains he CCC model by Bollerslev (1990). 6 A drawback of his specificaion is ha all he elemens of he condiional correlaion marix are resriced o have he same dynamics. Cappiello, Engle and Sheppard (004) propose he following generalizaion of he model 7, which allows he individual series specific news impac parameers: Q = ( Q AQA' BQB ') + A( ε ε ) A' + BQ B ' (7) ' where A and B are n n diagonal marices. As a resul, he dynamics of he individual elemens of he covariance marix Q is specified as follows: q = (1 αα ββ ) q + αα ε ε + ββ q (8) ij, i j i j ij i j i, 1 j, 1 i j ij, 1 Sufficien condiion for he covariance marix o be posiive definie is ha ( Q AQA' BQB') in (7) is posiive definie. Alhough his generalized model undoubly adds flexibiliy o Engle's specificaion, he number of parameers o be esimaed increases 6 Tesing for dynamic versus consan correlaion for he daa ha have ime-varying volailiies has proven in he lieraure o be a difficul problem. Some examples of such kind of ess are in Bera (1996) and Tse(1998). 7 The full Asymmeric Generalized DCC in Cappiello, Engle and Sheppard (004) includes addiionally a variable marix accouning for he asymmeric impac of he pas negaive shocks on he correlaion processes. 8

9 considerably. Alernaive aemps o generalize he sandard scalar DCC by Engle (00) can be found e.g. in Frances and Hafner (003) and Billio, Caporin and Gobbo (003). A nice feaure of condiional correlaion mulivariae GARCH models is ha hey allow for wo-sage esimaion. Specifically, he likelihood funcion of he DCC models oulined above can be wrien as a sum of a volailiy par and a correlaion par. Le he parameers of he volailiy par be denoed φ, and he addiional parameers of he correlaion par ψ. The esimaes of volailiy parameers can be found by replacing R in () by an ideniy marix of size n. The resuling firs sage log-likelihood funcion gives he sum of he log-likelihoods of individual volailiy equaions of n series in he sysem: 1 L n I D rd I D r T ' 1 1 v( φ) = log( π) log( n ) log( ) n = 1 T 1 ' = n log( π ) + log( D ) + rd r = 1 1 r = + + T n i nlog( π ) log( hi ) = 1 i= 1 hi 1 r = + + n T i Tlog( π ) log( hi ) i= 1 = 1 hi (9) The second sage log-likelihood is: 1 L n D R rd R D r T ' ( ˆ c ψ φ) = log( π) log( ) log( ) = 1 1 = T ' 1 n log( π) log( D ) log( R ) εr ε (10) = 1 Given he esimaes of he volailiy parameers, ˆ φ, he relevan par of L c, ha will influence he selecion of he correlaion parameers, ψ, is: 1 L R R (11) T * ' 1 ( ˆ c ψ φ) = log( ) ε ε + = 1 9

10 Engle and Sheppard (001), based on he resuls in Newey and McFadden (1994), demonsrae ha he wo-sep esimaion approach provides consisen, alhough no efficien, esimaes of he parameers of he model. We use his wo-sep esimaion procedure in he empirical par of he paper. 3. Univariae volailiy model choice and esimaes We sar from fiing he univariae volailiy models for each of he eigh series considered in his sudy. 8 The alernaive specificaions employed are he following GARCH models: Model name Specificaion GARCH h = α + α r + β h NARCH α h = α + α r + β h EGARCH r 1 r 1 ln( h ) = α0 + α1 / π + α + β1ln( h 1) h 1 h 1 GJR 1 if r h α0 α1r 1 αs 1 0 < = + + 1r 1+ β1h 1 wih S 1 = 0 oherwise AGARCH ( ) h = α + α r + α + β h NGARCH ( ) h = α + α r + α h + β h VGARCH ( ) h = α + α r / h + α + β h While GARCH and NARCH are symmeric 9, he res of he models allow for an asymmeric impac of he posiive and negaive news on he volailiy process. The asymmery is achieved eiher by allowing he slopes of negaive and posiive sides of he news impac curve, wih a 8 A similar approach is also employed in Cappiello, Engle and Sheppard (004). 9 Noe, as compared o GARCH, NARCH would imply a reduced response of volailiy o news if a <. 10

11 minimum a r 1 = 0, o differ (EGARCH and GJR), or he minimum of he news impac curve o be locaed a r 1 0 (AGARCH, NGARCH and VGARCH). 10 The resuls of he esimaion of he univariae volailiy models oulined above indicae evidence of an asymmeric impac of news on volailiy for all series in our sudy. For each of he series we selec a univariae volailiy specificaion based on he Schwarz Informaion Crierion. The seleced models and he corresponding parameer esimaes are presened in Table 3. As we see, while hree of employed indices prefer a model (NGARCH), implying recenering of he news impac curve a a posiive r 1, for he res we selec models (EGARCH and GJR), capuring he asymmery by allowing a seeper slope of he negaive side of he news impac curve compared o is posiive side. Inser Table 3 here Table 4 presens he cross-correlaions of he fied volailiy series, while figure 1 shows he developmen of he volailiies over he considered sample period. As expeced, he correlaions of he ransiion marke volailiies wih he developed marke series are much lower han hose beween he developed markes. From figure 1 i is clear ha he volailiies of he major markes comove, and reac o significan inernaional evens in a similar manner. 11 I is ineresing o noe ha while he reacion of he ransiion markes o he Russian defaul in Augus-Sepember 1998 was very srong, oher major inernaional evens like Sepember 11 or he new economy bubble burs did no have such a srong impac on hese markes. Inser Table 4 and Figure 1 here 10 For furher deails on he employed models and heir news impac curves see Engle and Ng (1993). 11 For he formal analysis of he cross counry volailiy comovemens, paricularly focusing on he periods of high volailiy, see e.g. Edwards and Susmel (001). 11

12 3.3 Condiional correlaion esimaes On he basis of he individual sandardized residual series, obained as a resul of he esimaion of he univariae volailiy models, he dynamics of he condiional correlaion marix is parameerised as a scalar DCC in (6) and as a generalized DCC (GDCC) in (7) above. We conduc wo ypes of analysis, inernaional and regional European. In he inernaional par we model he correlaion dynamics of hree ransiion marke indices wih he S&P500 and STOXX50, while in he regional par wih hree European indices, 30, CAC40 and FTSE100. The esimaion resuls are presened in able 5 for he inernaional and in able 6 for he regional analysis. Inser Tables 5 and 6 here The las rows of ables 5 and 6 provide likelihood raio ess beween he sandard DCC and is generalized version. 1 The es saisic for he inernaional analysis canno rejec he null hypohesis of he scalar DCC. In he regional case he scalar DCC is rejeced in favour of he GDCC. The plos of he resuling condiional correlaion series are presened in Figure. 13 The firs imporan feaure we observe is ha correlaions of all developed marke indices have increased since mid-nineies. I is especially pronounced for he correlaion beween French and German indices, which is obviously influenced by he fixing of he exchange raes in We observe a sharp drop of he correlaions of FTSE100 wih 30 and CAC40 in he firs par of 000. This drop is presen for some oher marke pairs as well. Anoher regulariliy is ha Asian-Russian crisis around 1998 has lead o a swing in he inernaional correlaions for almos all counry pairs, including ransiion markes. Some oher ineresing hing o noe is ha he las par of our sample is characerized by a seady increase in he 1 The -saisics of he parameer funcions for he GDCC model are calculaed using he dela mehod. 13 Given ha for he regional European resuls he rejecion rae of he scalar DCC agains GDCC is no very high, and he shapes of he chars of condiional correlaions for hese wo specificaions differ only marginally, Figure presens regional correlaions implied by he scalar DCC (similar o he inernaional case). 1

13 correlaions of ransiion markes wih he res of he indices. This may be due o an anicipaion of he accession of hese counries o he European Union in May 004. Inser Figure here 3.4 Volailiy versus correlaion: Some empirical regulariies Figure 3 presens he scaer plos of he condiional correlaion series agains he volailiy of he underlying markes. The ineresing regulariy we noe is ha for he correlaions beween developed markes exreme volailiy values are associaed wih high correlaion values as well, while for he ransiion markes his paern is no as pronounced (boh for he correlaions beween ransiion markes and heir correlaions wih developed markes). The high correlaion values associaed wih he exreme volailiy in he underlying markes would make inernaional diversificaion benefis disappear, a leas parially, in imes when hey are required mos. For he invesors who diversify inernaionally, i would be beneficial o idenify markes he correlaions of which are less sensiive o exreme values of he volailiies in hese markes. This, ceeris paribus, could provide some proecion in urbulen marke imes. Inser Figure 3 here 4 Volailiy Threshold Dynamic Condiional Correlaions 4.1 The models The varying relaionship beween high volailiy and correlaion values of he differen asse pairs in he porfolio, if presen bu ignored, could have serious consequences for porfolio hedging effeciveness. The empirical regulariies idenified by observing he scaer plos sugges an exension of he DCC model considered in he previous secion. Given he hisorical daa for he asses under ineres up o ime period 1, wihin he wo-sep 13

14 esimaion framework, he invesor produces a volailiy esimae for ime period for each of he series in he sysem. Because he parameers of he volailiy models are deermined exclusively in he firs-sep, he fied volailiy series could be considered as given for he second correlaion sep of esimaion. The exension of he DCC model we propose ess he hypohesis wheher high volailiy values (exceeding a specific hreshold) of he underlying asses are associaed wih an increase in heir correlaion values. An invesor rearranging his porfolio would be graeful o idenify asses for which his associaion does no hold, as, oher hings being equal, one could consider hose asses as poenially aracive arges for porfolio diversificaion. Le V be a dummy variables marix wih elemens defined as: v ij, 1 if hi, > fhi( k) or h j, > fh j( k) = 0 oherwise (1) where fhi ( k ) is he k -h fracile of he volailiy series h i. One could now exend he DCC and GDCC models in (6) and (7) in he following way: Q = (1 α β) Q γv + αε ( ε ) + βq + γv (13) ' Q = ( Q AQA' BQB' ΓVΓ ') + A( ε ε ) A' + BQ B' +ΓVΓ ' (14) ' where V = E[ V ], and A, B and Γ are n n diagonal marices. For he GDCC specificaion he dynamics of he individual elemens of he covariance marix Q would hen be specified as: q = (1 αα ββ ) q γγ v + αα ε ε + ββ q + γγ v (15) ij, i j i j ij i j ij i j i, 1 j, 1 i j ij, 1 i j ij, Sufficien condiion for he covariance marix, Q, o be posiive definie is ha ( Q AQA' BQB' ΓVΓ ') in (14) is posiive definie. In case he aim of he empirical analysis is o idenify heerogeneiy in he response of he markes o he volailiy values exceeding some hresholds, i is more suiable o consider a 14

15 version of he model where he diagonal elemens of marix Γ are allowed o vary. On he oher hand, he resricions on he GARCH dynamics of he condiional correlaions (he scalar version) in some cases could be well jusifiable, leading o a more parsimonious specificaion and/or making he model esimaion feasible also in large dimensions. 14 The version of he model in (14), which resrics he GARCH dynamics bu allows differen volailiy impacs on he correlaions of differen asse pairs, could be specified by resricing he diagonal elemens of he parameer marix A and B, for each of he marices, o be idenical. The expression in (15) hen becomes: q = (1 α β ) q v + α ε ε + β q + v (16) ij, ij i j ij i, 1 j, 1 ij, 1 i j ij, In he res we refer o he specificaion in (15) as he Volailiy Threshold GDCC (VT-GDCC), and o he specificaion in (16) as he Volailiy Threshold DCC (VT-DCC). As emphasized in he inroducion o his paper, a range of sudies have idenified ha he correlaions beween asses increase for downside moves, especially for exreme downside moves, raher han for upside moves. Below we propose a modificaion of he model in (14) which would consider he case of exreme volailiy associaed wih bear markes. 15 In he framework of he DCC model his could e.g. be defined as he case when he fied volailiy for he period exceeds he pre-specified hreshold and a he same ime he observed reurn a ime 1 is negaive (which is equivalen o he corresponding sandardized residual being negaive). To inegrae his feaure in our specificaion, one could redefine he dummy variables marix, V, as follows: v ij, ( if hi, fhi( k) and εi, 1 0 ) or ( hj, fhj( k) and ε j, 1 0) 1 = > < > < 0 oherwise (17) 14 As is shown in Engle and Sheppard (001), he scalar DCC model leads o sub-opimal porfolio selecion in case of many asses (like 0 or 30) as i assumes he same ype GARCH dynamics for all he asse-specific condiional correlaions. This assumpion becomes, however, increasingly more likely o be saisfied in case of small number of asses. 15 In his conex, see Capiello, Engle and Sheppard (004), who provide an exension of he GDCC model in (7), he Asymmeric Generalized DCC, o accoun for he asymmeric impac of he sign of he pas innovaions on he curren correlaion values. 15

16 In he res we refer o he specificaions in (15) and (16), wih he elemens of he marix V defined as in (17), he Volailiy Threshold Asymmeric GDCC (VT-AGDCC) and Volailiy Threshold Asymmeric DCC (VT-ADCC), respecively. All he models described in his secion could be modified in such a way ha he correlaion values are condiioned on he observed pas reurn series only (bu no on he fied volailiy values). The idea similar o he specificaion wih he marix V defined in (1) would be o condiion he correlaion values on he pas squared reurns exceeding a pre-specified hreshold. To es he hypohesis similar o he specificaion wih he marix V defined in (17) one would condiion he correlaion values on he large (exceeding some hreshold) pas negaive reurns. 4.. Esimaion resuls Tables 7-10 presen he resuls of he esimaion of he Volailiy Threshold DCC models specified above. The models are esimaed for differen predefined volailiy hreshold levels: 50 percen, 75 percen, 90 percen and 95 percen fraciles. As we were ineresed in he analysis of he heerogeneous impac of volailiies on correlaions of differen asse pairs in our sample, we did no consider he scalar model in (13), and esimaed wo versions of he model in (14), specified in (15) and (16), respecively. The las rows in he ables repor he likelihood raio saisics, esing he resricions of he specificaion in (16) agains he unresriced model in (15). For mos of he cases he resriced specificaion is preferred o he unresriced one (perhaps wih excepion of VT-ADCC for he regional analysis in able 10, where, however, he rejecion rae is no very high). Therefore, for he sake of parsimony, we repor parameer esimaes for he specificaion in (16) only. Inser Tables 7 and 8 here 16

17 The resuls in ables 7 and 8, which are based on he model wih he elemens of he marix V defined in (1), deliver srong evidence ha he correlaions of he developed marke indices are significanly affeced by he volailiy in one of he markes or boh exceeding a predefined hreshold (he excepion is he 50 percen hreshold for he pair S&P500 and STOXX50). Differen o ha, he high volailiy values seem no o affec he correlaions of he ransiion markes wih heir developed counerpars on he one side, and he ransiion markes among each oher on he oher side. The excepion is he correlaion of he Polish 0 wih S&P500 for he volailiy hreshold of 95 percen for he inernaional analysis, and he correlaion of he Czech PX50 wih he European developed marke indices for he volailiy hreshold of 75 percen for he regional analysis. Inser Tables 9 and 10 here Tables 9 and 10 are based on he specificaion wih he marix V defined as in (17). The general endency of he esimaes for he specificaions in ables 7 and 8, on he one side, and ables 9 and 10, on he oher, o be similar mos probably indicaes ha he high volailiy values are predominanly associaed wih negaive reurns. The resuls in his secion reflec he general picure illusraed by he scaer plos in figure 3, and indicae ha ransiion markes, under ceeris paribus condiions, could poenially provide some proecion for inernaional invesors in urbulen marke periods. 5 Conclusions In his paper we invesigae he volailiy and correlaion dynamics of naional sock indices from markes heerogeneous in he level of heir developmen. We exend he mulivariae GARCH Dynamic Condiional Correlaion of Engle (00) o analyse he relaionship beween he correlaions on he one side and he volailiy of he underlying asses exceeding a predefined hreshold on he oher side. The empirical resuls indicae ha he correlaions of 17

18 he developed markes are significanly affeced by high volailiy levels (associaed wih bear markes), while high volailiy seems no o have a direc impac on he correlaions of he ransiion blue chip indices wih he res of he markes. This feaure could be poenially relevan for he inernaional porfolio diversificaion consideraions. 18

19 REFERENCES Ang, A., and G. Bekaer, 1999, Inernaional asse allocaion wih ime-varying correlaions, Working Paper, Sanford Universiy. Ang, A., and J. Chen, 00, Asymmeric correlaions of equiy porfolios, Journal of Financial Economics 63, Bauwens L., S. Lauren, and J.V.K. Rombous, 003, Mulivariae GARCH models: A survey, CORE Discussion Paper 003/31. Bekaer, G., and G. Wu, 000, Asymmeric volailiy and risk in equiy markes, Review of Financial Sudies 13, 1-4. Bera, A. K., and S. Kim, 1996, Tesing consancy of correlaion wih an applicaion o inernaional equiy reurns, Working Paper , Universiy of Illinois, Urbana- Champaign. Billio, M., M. Caporin, and M. Gobbo, 003, Block Dynamic Condiional Correlaion mulivariae GARCH models, Working Paper 03.03, GRETA. Bollerslev, T., 1990, Modeling he coherence in shor run nominal exchange raes: A mulivariae Generalized ARCH model, Review of Economics and Saisics 7, Capiello L., R. F. Engle, and K. Sheppard, 004, Asymmeric dynamics in he correlaions of global equiy and bond markes, Working Paper, ECB. Cho, Y. H., and R.F. Engle, 000, Time-varying beas and asymmeric effecs of news: empirical analysis of blue chip socks, Working Paper, NBER. Conrad, J., Gulekin, M., and G. Kaul, 1991, Asymmeric predicabiliy for he condiional variances, Review of Financial Sudies 4, Das, S. R., and R. Uppal, 1999, The effec of sysemic risk on inernaional porfolio choice, Working Paper, Harvard Universiy. De Sanis, G., and B. Gerard, 1997, Inernaional asse pricing and porfolio diversificaion wih ime-varying risk, Journal of Finance 5, Edwards, S., and R. Susmel, 001, Volailiydependence and conagion in emerging equiy markes, Working Paper 8506, NBER. Engle, R. F., 00, Dynamic Condiional Correlaion - A simple class of mulivariae GARCH models, Journal of Business and Economic Sudies 0, Engle, R. F., and V. Ng, 1993, Measuring and esing he impac of news on volailiy, Journal of Finance 48, Engle, R. F., and K. Sheppard, 001, Theoreical and empirical properies of Dynamic Condiional Correlaion mulivariae GARCH, UCSD Working Paper

20 Erb, C. B., C. E. Harvey, and T. E. Viskana, 1994, Forecasing Inernaional Correlaion, Financial Analys Journal 50, Franses, P.H and C. Hafner, 003, A Generalized Dynamic Condiional Correlaion Model for Many Asse Reurns, Working Paper, Erasmus Universiy Roerdam. Goezmann, W. N., L. Li, and K. G. Rouwenhors, 00, Long-erm global marke correlaions, Yale ICF Working Paper Grubel, H. G., 1968, Inernaionally diversified porfolios, American Economic Review 68, Karolyi, G. A., and R. M. Sulz, 1996, Why do markes move ogeher? An invesigaion of U.S.-Japan sock reurn comovemen, Journal of Finance 51, Kroner, K. F., and V. K. Ng, 1998, Modeling asymmeric comovemens os asse reurns, Review of Financial Sudies 11, Lessard, D. R., 1973, Inernaional porfolio diversificaion mulivariae analysis for a group of Lain American counries, Journal of Finance 8, Levy, H., and M. Sarna, 1970, Inernaional diversificaion of invesmen porfolios, American Economic Review, Lin, W. L., R. F. Engle, and T. Io, 1994, Do bulls and bears move across borders? Inernaional ransmission of sock reurns and volailiy, The Review of Financial Sudies 7, Longin, F., and B. Solnik, 1995, Is he correlaion in inernaional equiy reurns consan: ?, Journal of Inernaional Money and Finance 14, 3-6. Longin, F., and B. Solnik, 001, Exreme Correlaions of Inernaional Equiy Markes, Journal of Finance 56, Newey, W. K., and D. McFadden, 1994, Large sample esimaion and hypohesis esing, in Handbook of Economerics, vol. 4, Elsevier Norh Holland. Pelleier, D., 004, Regime Swiching for Dynamic Correlaions, Journal of Economerics, forhcoming. Ramchmand, L., and R. Susmel, 1998, Volailiy and cross correlaion across major sock markes, Journal of Empirical Finance 5, Solnik, B., 1974, Why no o diversify inernaionally raher han domesically?, Financial Analyss Journal 30, Solnik, B., C. Bourcrelle, and Y. Le Fur, 1996, Inernaional marke correlaion and volailiy, Financial Analys Journal 5, Tse, Y. K., 000, A es for consan correlaions in a mulivariae GARCH model, Journal of Economerics 98,

21 Tse, Y., and A. Tsui, 00, A mulivariae GARCH model wih ime-varying correlaions, Journal of Business and Economic Saisics 0, Tsui, A. K., and Yu, Q., 1999, Consan condiional correlaion in a bivariae GARCH model: Evidence from he sock marke in China, Mahemaics and Compuers in Simulaion 48,

22 Table 1. Summary Saisics SP500 STOXX50 30 CAC40 FT PX50 Mean e-05 Max Min Sandard Dev Skewness Kurosis JB LB(6) LBS(6) Noes: JB is Jarque-Bera es saisic, disribued χ. LB(6) and LBS(6) are Ljung-Box es saisics wih 6 lags for reurn levels and reurn squares, respecively, disribued χ 6. The upper 1 and 5 percenile poins of he χ disribuion are 9.1 and 5.99, respecively. The upper 1 and 5 percenile poins of he χ 6 disribuion are and 1.59, respecively. Table. Uncondiional cross-correlaions STOXX50 30 CAC40 FTSE PX50 SP STOXX CAC FTSE

23 Table 3. Univariae volailiy model choice Index Model SP500 EGARCH (-.4975) Parameer esimaes α 0 α 1 β 1 α (3.9988) ( ) (-.3413) STOXX50 EGARCH (-.3893) 0.48 (4.85) 0.96 (60.717) ( ) 30 EGARCH (-.6399) (4.349) ( ) ( ) CAC40 GJR 8.86e-04 (1.7334) (0.1087) ( ) (.4389) FTSE100 NGARCH 6.51e-04 (3.3940) (5.4103) ( ) (-5.405) 30 NGARCH 04 (.4748) 0.31 (.0873) (.6514) (-.4854) 0 NGARCH 9.6e-04 (.5461) (.9765) (4.0095) (-.163) PX50 EGARCH ( ) (3.353) ( ) ( ) Noes: This able gives he quasi-maximum likelihood esimaes of he seleced univariae volailiy models. -saisics are given in parenheses. Table 4. GARCH volailiy correlaions STOXX50 30 CAC40 FTSE PX50 SP STOXX CAC FTSE

24 Figure 1. GARCH volailiy Sep Sep Asian-Russ. crisis New economy bubble burs Asian-Russ. crisis New economy bubble burs VSP VSTOXX Asian-Russ. crisis Sep. 11 Sep New economy bubble burs Asian-Russ. crisis New economy bubble burs Asian-Russ. crisis Sep. 11 New economy bubble burs V30 VCAC40 VFTSE Asian-Russ. crisis Asian-Russ. crisis Asian-Russ. crisis V30 V0 VPX50 4

25 Table 5. DCC condiional correlaion esimaes: inernaional analysis DCC α (3.1183) β ( ) GDCC α α SP SP STOXX (3.819) α α (1.901) α α SP (1.9569) α α SP PX (1.805) α α STOXX (1.9408) α α 0.00 STOXX (1.956) α α STOXX PX (1.8675) α α (1.3994) α α 0.09 PX (1.3770) α α PX (1.4379) β β SP SP STOXX ( ) β β SP (1.6476) β β SP PX ( ) β β STOXX (6.470) β β STOXX (1.6471) β β STOXX PX ( ) β β (6.90) β β PX (1.6480) β β PX (1.6038) β β (6.1848) L DCC L GDCC LR 8.34 Noes: This able gives he quasi-maximum likelihood esimaes of DCC model in (6) and GDCC model in (7) for he inernaional par of analysis. -saisics are given in parenheses. -saisics of he parameer funcions for GDCC model are calculaed using he dela mehod. LR is likelihood raio es saisic of GDCC agains DCC specificaion, disribued χ 8. The upper 1 and 5 percenile poins of he disribuion are 0.09 and 15.51, respecively. χ 8 5

26 Table 6. DCC condiional correlaion esimaes: regional analysis DCC α (7.7099) β ( ) GDCC α α CAC FTSE (3.631) α α (.8775) α α (1.6855) α α (1.4986) α α PX (1.8745) α α CAC FTSE (3.3854) α α CAC (1.7486) α α CAC (1.610) α α CAC PX (1.9606) α α FTSE (1.8903) α α FTSE (1.4443) α α FTSE PX (1.9331) α α 0 (1.1135) α α PX (1.306) α α PX (1.1599) β β CAC FTSE (1.199) β β (1.848) β β (.736) β β PX (16.779) β β CAC FTSE (14.847) β β CAC (3.67) β β CAC (4.5071) β β CAC PX ( ) β β FTSE (15.351) β β FTSE (8.7756) β β FTSE PX (17.180) β β (15.811) β β PX ( ) β β PX ( ) β β (11.563) L DCC L GDCC LR Noes: This able gives he quasi-maximum likelihood esimaes of DCC model in (6) and GDCC model in (7) for he regional par of analysis. -saisics are given in parenheses. -saisics of he parameer funcions for GDCC model are calculaed using he dela mehod. LR is likelihood raio es saisic of GDCC agains DCC specificaion, disribued disribuion are 3.1 and 18.31, respecively. χ 10. The upper 1 and 5 percenile poins of he χ 10 6

27 Figure. Condiional correlaions CORR_SP_STOXX CORR_SP_ CORR_SP_ CORR_SP_PX CORR_STOXX_ CORR_STOXX_ CORR_STOXX_PX CORR 7

28 CORR CORR PX CORR CAC CORR FTSE CORR CORR PX CORR CORR_CAC_FTSE 8

29 CORR_CAC_ CORR_CAC_PX CORR_CAC_ CORR_FTSE_ CORR_FTSE_ CORR_FTSE_PX 9

30 Figure 3. Volailiy versus correlaions VSP VSTOXX.00 VSP CORR_SP_STOXX CORR_SP_STOXX CORR_SP_ V VSP V CORR_SP_ CORR_SP_ CORR_SP_ VSP VPX VSTOXX CORR_SP_PX CORR_SP_PX CORR_STOXX_ V VSTOXX V CORR_STOXX_ CORR_STOXX_ CORR_STOXX_ VSTOXX VPX V CORR_STOXX_PX CORR_STOXX_PX CORR 30

31 V.006 V VPX CORR.005 CORR PX.007 CORR PX V.006 VPX V CORR PX.007 CORR PX.004 CORR CAC VCAC V VFTSE CORR CAC.036 CORR FTSE.007 CORR FTSE V.003 V V CORR.007 CORR.005 CORR V.006 V.003 VPX CORR CORR PX CORR PX 31

32 VCAC VFTSE VCAC CORR_CAC_FTSE.0036 CORR_CAC_FTSE.010 CORR_CAC_ V VCAC V CORR_CAC_.005 CORR_CAC_.004 CORR_CAC_ VCAC VPX VFTSE CORR_CAC_PX.004 CORR_CAC_PX.010 CORR_FTSE_ V VFTSE V CORR_FTSE_.005 CORR_FTSE_ CORR_FTSE_.000 VFTSE VPX CORR_FTSE_PX CORR_FTSE_PX 3

33 Table 7. Volailiy Threshold DCC: inernaional analysis 50% 75% 90% 95% α (5.9788) (5.803) (5.6149) (5.4494) β (7.1674) ( ) ( ) (88.545) γ SPγ STOXX (0.8597) (1.961) (.4799) (3.693) γ SPγ (1.1350) (-0.513) (-0.765) (-0.541) γ SPγ (1.403) (0.6814) (1.490) (.063) γ SPγ PX (1.1075) (-0.594) (-1.358) (-1.531) γ STOXXγ (1.013) ( ) ( ) ( ) γ STOXXγ (1.13) (0.6711) (1.3134) (1.8090) γ STOXXγ PX (1.0495) (-0.633) ( ) ( ) γ γ (1.3677) ( ) ( ) ( ) γ γ PX (1.110) (0.3598) (0.6579) (0.494) γγ PX (1.4453) ( ) (-1.315) ( ) L VT DCC LVT GDCC LR Noes: This able gives he quasi-maximum likelihood esimaes of VT-DCC model in (14) wih he resricions on he GARCH dynamics of he condiional correlaions, and he marix V defined as in (1). -saisics are given in parenheses. -saisics are calculaed using he dela mehod. LR is likelihood raio es saisic of VT-GDCC agains VT-DCC specificaion, disribued χ. The upper 1 and 5 percenile poins of he χ 8 disribuion are 0.09 and 15.51, respecively. 8 33

34 CAC CAC CAC CAC FTSE FTSE FTSE Table 8. Volailiy Threshold DCC: regional analysis 50% 75% 90% 95% α (5.8697) (5.0309) (6.938) (6.8836) β ( ) ( ) ( ) ( ) CAC (3.4165) (3.8353) (3.905) (.7911) FTSE (3.3095) (3.9613) (3.7319) (.8360) (1.467) (1.6508) (1.344) (0.8045) (0.457) ( v ( ) (0.778) PX (1.6058) (.1164) (1.4531) (0.7396) FTSE (.8114) (3.3691) (3.1801) (.3748) (1.531) ) (1.3000) (0.7853) (0.4779) ( ) ( ) (0.771) PX (1.6639) (.0895) (1.463) (0.7183) (1.5514) (1.6979) (1.3386) (0.8155) (0.4649) ( ) (-0.318) (0.7713) PX (1.553) (1.9764) (1.496) (0.7444) (0.4154) ( ) (-0.333) (0.5198) PX (1.03) (1.05) (0.945) (0.5361) PX (0.431) ( ) ( ) (0.5048) L VT VT DCC L GDCC LR Noes: This able gives he quasi-maximum likelihood esimaes of VT-DCC model in (14) wih he resricions on he GARCH dynamics of he condiional correlaions, and he marix V defined as in (1). -saisics are given in parenheses. -saisics are calculaed using he dela mehod. LR is likelihood raio es saisic of VT-GDCC agains VT-DCC specificaion, disribued χ. The upper 1 and 5 percenile poins of he χ 10 disribuion are 3.1 and 18.31, respecively

35 Table 9. Volailiy Threshold Asymmeric DCC: inernaional analysis 50% 75% 90% 95% α (5.8548) (6.140) (4.857) (4.55) β (9.695) (6.1097) ( ) ( ) γ SPγ STOXX (1.3886) (0.9844) (.6939) (3.105) γ SPγ (1.566) (1.3539) ( ) ( ) γ SPγ (.0795) (1.6569) (1.516) (1.7796) γ SPγ PX (1.506) (1.907) ( ) (-.039) γ STOXXγ (1.4384) (1.1497) (-0.671) ( ) γ STOXXγ (1.8807) (1.3374) (1.4787) (1.7875) γ STOXXγ PX (1.471) (1.1538) (-1.569) (-.3375) γ γ (1.6168) (1.6443) ( ) ( ) γ γ PX (1.300) (1.3036) (0.5731) (0.330) γγ PX (1.6854) (1.6164) (-1.394) (-1.737) L VT DCC LVT GDCC LR Noes: This able gives he quasi-maximum likelihood esimaes of VT-ADCC model in (14) wih he resricions on he GARCH dynamics of he condiional correlaions, and he marix V defined as in (17). -saisics are given in parenheses. -saisics are calculaed using he dela mehod. LR is likelihood raio es saisic of VT-GDCC agains VT-DCC specificaion, disribued χ. The upper 1 and 5 percenile poins of he χ 8 disribuion are 0.09 and 15.51, respecively. 8 35

36 CAC CAC CAC CAC FTSE FTSE FTSE Table 10. Volailiy Threshold Asymmeric DCC: regional analysis 50% 75% 90% 95% α (5.7776) (5.5377) (6.5093) (7.5531) β ( ) ( ) ( ) ( ) CAC (3.3683) (3.5847) (3.197) (1.9090) FTSE (3.0191) (3.3344) (3.356) (.3488) (1.3315) (1.7667) (1.4954) (0.340) e (0.4379) (0.71) ( ) (0.6645) PX (1.3800) (1.480) (0.861) (-1.343) FTSE (.6473) (3.1061) (3.3160) (.9305) (1.3879) (1.7340) (1.4146) (0.3394) (0.4484) (0.74) ( ) (0.6694) PX (1.4334) (1.494) (0.8604) (-1.677) (1.3537) (1.837) (1.588) (0.3434) (0.4371) (0.57) (-0.891) (0.6693) PX (1.314) (1.4180) (0.8648) (-1.078) (0.3894) (0.164) (-0.960) (0.930) PX (0.8878) (1.056) (0.7131) ( ) PX (0.4018) (0.1) ( ) ( ) L VT DCC LVT GDCC LR Noes: This able gives he quasi-maximum likelihood esimaes of VT-ADCC model in (14) wih he resricions on he GARCH dynamics of he condiional correlaions, and he marix V defined as in (17). -saisics are given in parenheses. -saisics are calculaed using he dela mehod. LR is likelihood raio es saisic of VT-GDCC agains VT-DCC specificaion, disribued χ. The upper 1 and 5 percenile poins of he χ 10 disribuion are 3.1 and 18.31, respecively