296 Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no. 4

Transcription

1 JEL Classificaion: C32, F31, G11 Keywords: Emerging Easern Europe, sock and currency markes, porfolio, VaR Effeciveness of Porfolio Diversificaion and he Dynamic Relaionship beween Sock and Currency Markes in he Emerging Easern European and Russian Markes Yen-Hsien LEE Deparmen of Finance, Chung Yuan Chrisian Universiy, Chung Li, Taiwan Hao FANG Deparmen of Asses and Propery Managemen, Hwa Hsia Insiue of Technology, Taipei, Taiwan corresponding auhor Wei-Fan SU Deparmen of Finance, Chung Yuan Chrisian Universiy, Chung Li, Taiwan Absrac This sudy invesigaes volailiy spillovers and he dynamic relaionship beween he sock and currency markes in he Czech Republic, Poland, Hungary and Russia using four mulivariae GARCH models. We analyze he opimal weighs and he effeciveness of diversificaion for sock-currency porfolio holdings wih respec o he following poins. Firs, he empirical resuls show ha he dynamic condiional correlaion model wih spillovers (DCC-S) generally yields he mos effecive diversificaion model, which implies ha DCC-S can significanly improve he effeciveness of diversificaion. Second, we also provide he resuls of a Value a Risk analysis o deermine he amoun of capial reserves ha invesors should se aside o cover poenial exreme losses when invesing in a currency-sock porfolio. Third, our consideraion of he ime-varying weighing rend finds ha weighing generally increases when economic evens occur, excep for in Russia, whose economic policies are considered o be unique. We find significan dynamic correlaion in all of he counries considered in our analysis. Finally, we apply he uni roo es for boh ime-varying correlaions and weighings and find ha he variables are saionary a heir levels. 1. Inroducion Sudies relaed o linkages beween sock and currency markes mosly focus on developed markes (Yang and Doong, 2004; Francis e al., 2006). Alhough here is some lieraure ha discusses such linkages regarding emerging markes (Tai, 2007; Morales, 2008; and Yang and Chang, 2008), here remains a gap in he research wih respec o his field. In paricular, he emerging Easern European and Russian markes have gradually received increased aenion from foreign invesors in he pas decade. However, here are only a limied number of sudies invesigaing he linkages beween he emerging sock and currency markes in Easern Europe and Russia (Ulku and Demirci, 2012). We are aware of only four papers ha empirically demonsrae he relaionship beween emerging sock and currency markes in Easern Europe and Russia, i.e., Grambovas (2003), Savarek (2005), Fedorova and Saleem (2010) and Tudor (2012). 1 According o he World Invesmen Repor 2012, foreign direc invesmen (FDI) in he Easern European and Russian markes has risen sharply in he las decade. The summary saisics of FDI in hese counries are shown in Table 1A of he Appendix. The rapid increases in FDI and he relaively few 296 Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no. 4

2 sudies on his issue indicae ha furher research on he Easern European and Russian markes is required. Thus, his sudy examines he currency and sock markes in Russia and Easern Europe (as represened by such markes in Poland, Hungary and he Czech Republic) in a seing of regional influences. Invesors allocae funds beween currency and sock o diversify porfolio asse risk. Thus, he opimum weighs of a porfolio are an imporan issue; he correlaion beween sock and currency is also imporan because he opimum weighs are esimaed by his correlaion. Wih respec o he porfolio, correlaion is hus an imporan facor in porfolio opimizaion and asse allocaion. In general, correlaion in his conex has been widely discussed in he lieraure (Ghosh e al., 1996; Conover e al., 2002; Coer and Sevenson, 2006; Huang and Zhong, 2006; and Case e al., 2012). However, none of hese sudies analyzed he correlaions beween socks and currencies. A review of he lieraure indicaes ha more sudies are needed because here has been insufficien focus on he correlaion beween he sock and currency markes. This sudy will examine he correlaions beween he sock and currency markes of Easern Europe and Russia wih a focus on heir dynamic relaionship, porfolio diversificaion and heir opimum weighs. In our invesigaion of he porfolio, we firs noe ha a more flexible porfolio can be more effecively diversified. Previous sudies have used various mehods o invesigae he dynamic relaionship beween he sock and exchange markes. Grambovas (2003), Savarek (2005) and Tudor (2012) used he Granger causaliy es o examine he relaionship beween he exchange rae and sock markes in emerging markes in Europe and Russia. Fedorova and Saleem (2010) used a bivariae GARCH model o find a significan linkage beween he sock and currency markes in Hungary, he Czech Republic and Russia, bu no in Poland. However, we focus on analyzing he condiional volailiy and covariance across he markes dynamically over ime. The dynamic condiional correlaion (DCC) GARCH model, which provides a imevarying correlaion in volailiy among he markes, is a more appropriae model o capure he dynamic relaionship and o consruc a porfolio. In addiion, compared o he consan condiional correlaion (CCC) GARCH model, he DCC GARCH model enables he condiional correlaion in volailiy beween he markes o vary over ime. The DCC model developed by Engle (2002) provides a srong framework for analyzing dynamic condiional correlaion and has been used in recenly published papers (e.g., Huang and Zhong, 2006; Hassan and Malik, 2007; Agnolucci, 2009; Kang e al., 2009; Chang e al., 2011; and Arouri e al., 2011). For example, Hassan and Malik (2007), Agnolucci (2009), and Kang e al. (2009) have each shown ha he model saisfacorily capures he condiional volailiy and he dynamics of volailiy ineracion. Furhermore, Chang e al. (2011) used a mulivariae DCC model o analyze he condiional correlaions in he volailiies of Asian rubber spo and 1 Using he Granger causaliy es, Grambovas (2003) empirically finds ha here is a srong linkage beween foreign exchange and sock markes in Greece and Hungary bu no in he Czech Republic. Savarek (2005) uses he Granger causaliy es based on a vecor auoregressive (VAR) sysem o find ha he sock marke is no efficienly affeced wih respec o exchange rae forecasing in he EU-member counries and vice versa. Fedorova and Saleem (2010) use a bivariae GARCH model by Engle and Kroner (1995) o demonsrae ha here is a direc linkage beween sock markes and currency markes in Hungary, he Czech Republic and Russia, bu no in Poland. Tudor (2012) uses he Granger causaliy es o find ha changes in he exchange rae have a significan effec on sock markes in Brazil and Russia. Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no

3 fuures prices, and Arouri e al. (2011) applied he DCC model o analyze spillovers beween oil prices and sock secor reurns. Because he DCC model has been used in many dynamic condiional correlaion sudies, we apply his model o analyze he dynamic relaionship beween he sock and currency markes in Easern Europe and Russia. Shocks in a marke may affec he volailiy no only in ha marke bu also in relaed markes. Accordingly, volailiy spillovers among differen asses receive considerable aenion when porfolio managers are consrucing porfolios and assigning opimum porfolio weighs. In recen sudies, he GARCH specificaion has been he mos popular approach for evaluaing volailiy spillovers across relaed markes. Lin and Tamvakis (2001) and Milunovich and Thorp (2006) found ha volailiy spillovers were widely prominen across energy and financial markes. Fedorova and Saleem (2010) applied he GARCH model o analyze volailiy spillovers beween he sock and currency markes and found a direc link beween hese markes. Arouri e al. (2011) found evidence of significan volailiy spillovers beween oil and sock secor reurns. Sadorsky (2012) analyzed volailiy spillovers beween oil prices and he sock prices of clean energy companies and echnology companies and consruced opimal porfolios of hese wo marke asses. Because he above-menioned lieraure has rarely addressed volailiy spillovers when invesigaing he correlaion beween sock and currency markes, we analyze such volailiy spillovers in his sudy and consruc sock-currency porfolios in accordance wih such analysis. The lieraure on Value a Risk (VaR) includes many sudies aimed a calculaing VaR for sock indices, currencies and commodiy asses (Brooks and Persand, 2002; Gio and Lauren, 2003; Huang and Lin, 2004; Chan e al., 2007; Fan e al., 2008; and Hung e al., 2008). Similarly, his sudy also provides he resuls of VaR analyses o deermine he amoun of capial reserves ha invesors should se aside o cover poenial exreme losses when invesing in currency-sock porfolios. Moreover, we apply he Augmened Dickey-Fuller (ADF) and Phillips-Perron (PP) uni roo ess for boh ime-varying correlaions and weighings, and we find ha boh variables are saionary a heir levels. Our empirical sudy significanly conribues o his field of research and fills a gap in he lieraure on he dynamic relaionship beween socks and currencies in Easern Europe and Russia. We find ha he DCC model wih spillovers (DCC-S) provides he bes diversificaion effeciveness for all pairs of sock-currency porfolios. Moreover, we provide he VaR resuls using DCC-S for he Easern European and Russian markes. We also find ha he ime-varying weighings generally increase when economic evens occur, excep in Russia because of is unique economic policies. This case is more noiceable during he period of he European deb crisis. We furher find ha he weighings decline during he economic boom in 2009 ha followed he subprime crisis. Finally, we find ha boh ime-varying correlaions and weighings are saionary a heir levels for boh he ADF and PP uni roo ess. Our empirical resuls have imporan policy implicaions for he four counries considered. 2. Mehodology This sudy applies CCC and DCC models wih spillovers o esimae he porfolio diversificaion and opimum weighs beween sock and currency in emerging 298 Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no. 4

4 Easern European and Russian markes. For each pair of sock and currency reurns, he condiional means are given by: where S R and v v S C S S = θs, 0 + θs,n -n + α S,m -m n= 1 m= 1 (1) R R R + e v v C S C C = θc,0 + θc,n n + αc,m -m ε n= 1 m= 1 (2) R R R + 1/2 ε = H η (3) C R are he reurns on socks and he currency exchange raes, respecively. The formula for he reurn is ( S C ε, ε ) p R = ln. p is he daily closing price, and p 1 ε = We derive condiional means of he sock and currency reurns from a VaR sysem o produce he erms in he se of equaions (1) and (2). In oher words, he second erm in equaion (2) denoes he impac of he lag sock reurns on he curren currency reurns, and ha in equaion (1) denoes he impac of he lag currency reurns on he curren sock reurns. The hird erm in equaion (2) denoes he impac of he lag currency reurns on he curren currency reurns, and ha in he equaion (1) means he impac of lag sock reurns on he curren sock reurns. This sudy used he Bayesian informaion crierion (BIC) o deermine he opimal 1/2 lag lengh of he AR erm in equaions (1) and (2). H is a (2 2) symmeric S C posiive definie marix and ( ) ' ( η ) 0 and ( ) E = η = η, η is he vecor of i.i.d. random errors wih N Var η = I. The mos well-known and commonly used specificaions are he CCC model by Bollerslev (1990) and he DCC model by Engle (2002). The CCC model wih volailiy spillovers and asymmery (hereinafer referred o as CCC-S) is defined as H = DPD (4) where diag (, ) S C = h h D and P = ( ij ) ρ is he (2 2) marix conaining he consan condiional correlaions, ij ρ wih 1, ( ) ρ ii = i = S, C. 2 The condiional variances and covariance are given by ( ) ( ) p 2 q p S S S C 2 S + αs,i ε i + βs, j j + αs,k ε k i= 1 j= 1 k = 1 (5) h = C h ( ) ( ) p 2 q p C C C S 2 C + αc,i ε-i + βc, j - j + αc,k ε-k i= 1 j= 1 k = 1 (6) h = C h 2 Bollerslev (1990) shows ha a posiive sign is no necessary for he ARCH and GARCH coefficiens o obain a posiive definie marix P. Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no

5 SC S C ρsc h h h = (7) C S SC where h, h, and h are he condiional volailiy of he currency marke, he condiional volailiy of he sock marke, and he condiional covariance beween currency and sock reurns a ime, respecively. The DCC model remedies he resricive assumpion of he consan condiional correlaion by allowing he condiional correlaion marix o vary over ime. In oher words, ( diag ( )) ( diag ( )) 1/2 = 1/2 P Q Q Q (8) ij where he (2 2) symmeric posiive definie marix = ( ) ( ) ' Q q is given by Q = 1 α + β Q + α η η + βq (9) In equaion (9), α and β are non-negaive scalars such ha α + β <1, Q is he (2 2) marix of uncondiional correlaions of he sandardized errors η. The condiional variances are specified as being similar o hose of he CCC model. 3 The condiional volailiies from CCC-S and DCC-S are used o consruc opimal porfolio weighs according o Kroner and Ng (1998). The opimal holding weigh is given by under he condiion S SC h - h w = (10) h C - SC S 2 h +h 0, if w < 0 w = w, if 0 w 1 1, if w > 1 In consrucing porfolio weighs beween wo asses, (11) w is he weigh of SC he sock index asse in a one-dollar sock-currency porfolio a ime, h is S he condiional covariance beween sock and currency asses, and h is he condiional variance of he sock asse. The weigh of he sock asse is 1 w. Moreover, by esimaing he ime-varying weigh of DCC-S for he four counries in our sample period, including economic evens, we can idenify wheher he weighing increases when economic evens occur. The effeciveness of diversificaion (DE) across consruced porfolios can be evaluaed by examining he realized hedging errors, which are deermined as Varundiversified Vardiversified DE = (12) Varundiversified 3 DCC-S reduces o a DCC model when seing α = α = 0. The DCC model reduces o a CCC model when seing α = β =0. S,k O,k 300 Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no. 4

6 where he variances of he diversificaion porfolio ( Var diversified ) are obained from he variance of he reurn on he sock-currency porfolios, whereas he variance of he undiversified porfolio ( Var undiversified ) is he variance of he reurn on he porfolio of socks. A higher DE raio denoes greaer diversificaion effeciveness in erms of he porfolio s variance reducion, which hus implies ha he associaed invesmen mehod can be considered a beer diversificaion sraegy. This sudy uses VaR o compare he effeciveness of he porfolios while aking ino consideraion he correlaion and porfolios wihou considering he correlaion o predic risk. The porfolio VaR is defined as VaR = Z σ W p * p (( ) ( ) ) S C SC 2 1 * 2 2 = Z w h + w h + w w h W (13) * where VaR p, Z, σ p and W are he porfolio VaR, normal disribuion, asse volailiy and he amoun invesed, respecively. 3. Empirical Resuls 3.1 Daa This sudy employs daily currency exchange raes and sock index prices for he hree emerging Easern European and Russian markes: he Czech Republic, Hungary, Poland and Russia. All currency exchange rae daa are obained from he Daasream daabase. The sample period exends from January 2001 o December 2011 and consiss of 3,130 observaions. In addiion, his sudy defines economic evens as he 9/11 erroris aacks in Sepember 2001, he dollar crisis in he final quarer of 2004, he subprime crisis from he middle of 2007 o he end of 2008, and he European deb crisis during 2010 and We also collec he corresponding prices from he following sock indices from he Daasream daabase: he PX 50 index for he Czech Republic, he BUX index for Hungary, he WIG20 index for Poland and he RTS index for Russia. 4 This sudy provides informaion on rading hours in he respecive sock and currency markes for he four counries in Panel A of Table 2A in he Appendix. The opening and closing hours of sock and currency markes for hese counries are shown in Panel B of Table 2A. Alhough here are non-overlapping opening and closing hours for he sock and currency markes in Panel B, we find ha he raio of non-overlapping hours is low excep in Russia. However, because he economy in Russia is dominaed by domesic demand, he higher non-overlapping raio beween he sock and currency markes has less impac on he invesing weigh of he sockcurrency porfolio han i would in oher counries. 4 The PX 50 index, raded on he Prague Sock Exchange, is an index of major socks on he Czech marke. The BUX index is a capializaion-weighed index adjused for free floa and is he main index of he Budapes Sock Exchange. The WIG20 index is a sock marke index of he weny larges companies on he Warsaw Sock Exchange in Poland. The RTS (Russian Trading Sysem) index, raded on he Moscow Exchange, is he benchmark index used o measure he Russian equiies marke. Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no

7 Table 1 Summary Saisics (Annualizing Reurns) Iems Czech Republic Hungary Poland Russia Panel A: Sock index reurns Mean 8.471% 8.204% % % Sd. Dev Maximum % % % % Minimum % % % % Skewness 1.419* ** Kurosis 4.636* ** Jarque-Bera 4.916* ** Panel B: Currency reurns Mean 5.865% 1.682% 2.964% 1.063% Sd. Dev Maximum 8.827% % % % Minimum % % % 8.928% Skewness Kurosis Jarque-Bera Noe: ** and *** denoe significance a he 5% and 1% levels, respecively. 3.2 Empirical Resuls Table 1 shows descripive saisics for he annualizing reurn series. In erms of sock markes (Panel A), Russia has he highes reurns (21.024) and Hungary has he lowes (8.204). Russia exhibis he highes volailiy (57.417) in he sock markes and he Czech Republic exhibis he lowes volailiy (33.358). In he currency markes (Panel B), Russia has he highes reurns (1.063). The wors performance regarding currency is ha of he Czech Republic ( 5.865). Hungary exhibis he highes volailiy (12.077) in he currency marke and Russia has he lowes volailiy (8.049). This sudy finds ha he reurn series of sock markes in he Czech Republic and Russia exhibi significan levels of skewness and kurosis. The skewness is negaive for sock reurns, indicaing ha he sock reurns are flaer o he lef. The sock reurns in hese counries all exhibi lepokuric siuaions, which shows ha he probabiliy of exreme sock prices in hese counries is high. As a resul, he Jarque-Bera es saisics only rejec he null hypohesis of normaliy for he reurn series of sock markes in he Czech Republic and Russia. We use he ADF uni roo es o examine he null of a uni roo in sock indices and corresponding exchange raes for he four sampled counries. The resuls of he ADF uni roo es in Table 2 show ha sock indices and he corresponding exchange raes are all uni roos and ha he firs-order differences of hose are saionary. These resuls sugges ha sock indices and exchange raes are I (1) sequences in hese counries. Table 3 shows he resuls of he Ljung-Box Q ess for he sandardized residuals and sandardized residuals squared; here is no evidence of serial correlaion 302 Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no. 4

8 Table 2 Uni Roo Tes for Sock Indices and Exchange Raes for ADF Iems Level 1 s difference C C&T Non C C&T Non Panel A: Sock index Czech Republic 2.662* *** *** *** Hungary *** *** *** Poland *** *** *** Russia *** *** *** Panel B: Exchange rae Czech Republic 2.662* *** *** *** Hungary *** *** *** Poland *** *** *** Russia *** *** *** Noes: ** and *** denoe significance a he 5% and 1% levels, respecively. C, C&T and Non indicae ha he models have consan, consan and rend, and non-consan and no rend, respecively. Table 3 Ljung-Box Q Tess Counry Q(8) for sock Q(8) for currency Q 2 (8) for sock Q 2 (8) for currency Saisic p-value Saisic p -value Saisic p -value Saisic p -value Panel A: Q es for DCC-S model Czech Republic Hungary Poland Russia Panel B: Q es for DCC model Czech Republic Hungary Poland Russia Panel C: Q es for CCC-S model Czech Republic Hungary Poland Russia Panel D: Q es for CCC model Czech Republic Hungary Poland Russia Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no

9 Table 4 LM Saisics for he Consan Correlaions Tes Counry DCC-S DCC-E DCC Czech Republic *** *** *** Hungary *** *** *** Poland *** *** *** Russia *** *** *** Noe: : *** denoes significance a he 1% level. Table 5 The Appropriae Model and he Lag Lenghs of he Spillover Effecs Panel A: The appropriae model Counry DCC DCC-S DCC-EGARCH Czech Republic # Hungary # Poland # Russia # Panel B: The lag lenghs of he spillover effecs on DCC-S Counry P = 1,Q = 1 P = 1,Q = 2 P = 2,Q = 1 P = 2,Q = 2 Czech Republic # Hungary # Poland # Russia # Noe: # denoes he appropriae model for he reurn volailiy. a he 1% level for he DCC-S, DCC, CCC-S and CCC models. These resuls indicae ha he DCC-S, DCC, CCC-S and CCC models are all suiable when esimaing he opimal weighs for currency-sock porfolios. 5 We provide Tse s (2000) LM saisics for he consan correlaions in Table 4. All saisics from he DCC-S and DCC model significanly rejec he null hypohesis of consan correlaion. The resuls indicae ha he DCC-S and DCC models each demonsrae ime-varying correlaion. However, he resuls also indicae ha he imevarying correlaion is more suiable for he financial markes. This sudy used he BIC o deermine he appropriae model for reurn volailiies. The appropriae model for reurn volailiies deermined by BIC is he DCC-S model for all counries repored in Panel A of Table 5. In addiion, we use BIC o deermine he lag lenghs of spillover effecs in equaions (5) and (6), and P = 1, Q = 1 is appropriae for all counries repored in Panel B of Table 5. Table 6 provides furher proof and shows he resuls of he ess of he effeciveness of porfolio diversificaion and he opimal porfolio weighs during he enire period and during crisis periods. The resuls in Panels A and C in Table 6 show ha he porfolio sraegies involving currency and sock asses make i possible o considerably reduce porfolio risk (variance). We find ha he DCC model s diversi- 5 Our resuls for he opimal lag lengh of he AR erm are 1, 1, 3 and 2 in he Czech Republic, Hungary, Poland and Russia, respecively. 304 Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no. 4

10 Table 6 Porfolio Diversificaion Effeciveness and Average Opimal Porfolio Weighs during he Enire Period and he Crisis Periods Counry DCC-S DCC CCC-S CCC Panel A: Porfolio diversificaion effeciveness (%) during he enire period Czech Republic Hungary Poland Russia Panel B: The average Opimal porfolio weighs during he enire period Czech Republic Hungary Poland Russia Panel C: Porfolio diversificaion effeciveness (%) during he crisis period Czech Republic Hungary Poland Russia Panel D: The average opimal porfolio weighs during he crisis periods Czech Republic Hungary Poland Russia Noes: Figures in bold denoe he highes diversificaion effeciveness in Panels A and C. The financial crisis period in Panels C and D denoes he subprime crisis period from he middle of 2007 o he end of ficaion effeciveness is greaer han ha of he CCC model boh across he enire period and during crisis periods. Furhermore, he DCC-S model provides he bes overall diversificaion effeciveness. When only he model ha provides he bes diversificaion effeciveness is considered (DCC-S), he diversificaion effeciveness ranges from 24.44% (Hungary) o 85.94% (Russia) during he enire period and from 23.82% (Hungary) o 87.20% (Russia) during crisis periods. The diversificaion effeciveness differs significanly across counries bu generally remains relaively sable across he models and across he periods. This resul is consisen for all cases and for all models considered. We show he average values of he realized opimal porfolio weighs in Panels B and D of Table 6. 6 The coefficiens indicae ha he average opimal weighs for he sock asses in he porfolios vary subsanially across markes bu are only slighly differen across he models used. The average opimal weighs of he sock asse suggesed by he DCC-S model for he Czech Republic, Hungary, Poland and Russia across he enire period are 70.20%, 69.68%, 57.69% and 94.89%, respec- 6 The opimal holding weigh is specified dynamically; herefore, his sudy provides an average opimal porfolio weigh. Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no

11 Figure 1 Czech Republic Weighing Tendency Figure 2 Hungary Weighing Tendency Figure 3 Poland Weighing Tendency Figure 4 Russia Weighing Tendency Noe: In he figures, 911 erroris aack occurs in Sepember 11, 2001, dollar crisis occurs in he final quarer 2004, subprime worries occur form in he middle of 2007 and las o he end of 2008, and he European deb crisis occurs during 2010 and ively. This resul suggess ha he average opimal allocaions for he Czech (Hungarian, Polish and Russian) sock marke in a one-dollar sock-currency porfolio in he enire period should be 70.2 (69.68, and 94.89) cens, wih he remaining (30.32, and 5.11) cens being invesed in he Czech (Hungarian, Polish and Russian) currency marke. Consequenly, he ime-varying weighed rends (esimaed by he DCC-S model) for he four counries in Figures 1 o 4 provide valuable informaion ha would enable inernaional invesors o effecively 306 Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no. 4

12 Table 7 Value a Risk Analysis Counry DCC-S DCC-S VaR (5%) VaR (1%) Czech Republic Hungary Poland Russia implemen heir opimal invesmen allocaion beween he sock and currency markes. To confirm he robusness of our resuls, his sudy compues hem during he financial crisis period ha is shown in Panels C and D of Table 6. 7 We find ha he endency of porfolio diversificaion effeciveness and average opimal porfolio weighs during he crisis period is similar wih ha during he enire period. Table 7 shows he mean 5% and 1% VaRs for he DCC-S currency-sock porfolios. The mean 5% VaRs in he differen markes are (he Czech Republic), (Hungary), (Poland) and (Russia). The mean 1% VaRs in he markes are (he Czech Republic), (Hungary), (Poland) and (Russia). Using he 5% VaRs as an example, hese figures indicae ha invesing in a en-million-dollar currency-sock porfolio in hese markes will resul in a loss of 92,528 dollars (he Czech Republic), 137,832 dollars (Hungary), 111,620 dollars (Poland) and 242,040 dollars (Russia). Similarly, he resuls from he 1% VaRs indicae ha invesing in a en-million-dollar currency-sock porfolio in hese markes will resul in a loss of 130,864 dollars (he Czech Republic), 194,952 dollars (Hungary), 157,866 dollars (Poland) and 342,322 dollars (Russia). The above findings sugges ha invesors should se aside an adequae amoun of capial reserves o cover poenial exreme losses when invesing in currency-sock porfolios. We display he ime-varying weighed rends (esimaed by DCC-S) for he four counries in Figures 1 o 4. We find ha weighing generally rises when economic evens occur, excep for Russia, whose economic policies are considered o be unique. This rend is paricularly apparen during he European deb crisis period. We also find ha weighing declines during he economic boom in 2009 following he subprime crisis, which indicaes ha foreign invesors prefer o hold local currency insead of invesing in socks when an economic crisis occurs and prefer o inves in socks when he economy is booming. Compared o he oher hree counries in Easern Europe, we see from Figures 1 o 4 ha he average level of sock-currency weigh in Russia is higher and he variance is lower, possibly because Russia ends o be more influenced by domesic demand han he oher hree counries. Domesic demand affecs he volailiy of a sock index more han i affecs he volailiy of he currency rae. Hence, he weigh of sock asses ha are owned by inernaional invesors is significanly higher han he weigh of currency asses. Furhermore, he sabiliy of sockcurrency weigh in Russia is higher han ha in he oher hree counries. 7 The financial crisis period in Panels C and D of Table 6 denoes he subprime crisis period from he middle of 2007 o he end of Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no

13 Table 8 Uni Roo Tess for Correlaion and Weighing Level Counry ADF PP Panel A: correlaion Czech Republic ** * Hungary *** *** Poland *** *** Russia *** *** Panel B: weighing Czech Republic *** *** Hungary *** *** Poland *** *** Russia *** *** Noe: *, **, and *** denoe significance a he 10%, 5%, and 1% levels, respecively. The resuls of he uni roo ess in Table 8 show he four counries correlaion series and weighed series esimaed by he DCC-S model. All of he variables are saionary a heir levels for boh he ADF and PP uni roo ess. Therefore, all he variables are inegraed on order zero I(0). Conversely, he ime-varying correlaions and weighings are no displayed in he random-walk sae, which indicaes ha he ime-varying correlaions and weighings are predicable and can be esimaed. 4. Conclusions The main objecive of his sudy is o discuss he exen of volailiy spillovers, porfolio diversificaion and dynamic relaionships beween he sock and currency markes in Easern Europe (he Czech Republic, Hungary and Poland) and in Russia using DCC and CCC models. The empirical resuls show ha he DCC-S model is preferred over he oher models, alhough he DCC model is a close second in model choice. The condiional volailiies from he DCC model can be used o esimae he effeciveness of diversificaion. Our resuls peraining o diversificaion effeciveness show ha he DCC-S model generally provides he bes diversificaion effeciveness in all pairs of sockcurrency markes. Moreover, he coefficiens show ha he opimal weighs for he sock index asses in he diversificaion porfolios vary subsanially across markes, bu hey are only slighly differen across he models used. This sudy also provides VaR resuls for he DCC-S model a he 5% and 1% levels o deermine he amoun of capial reserves ha invesors should se aside o cover poenial exreme losses when invesing in currency-sock porfolios. Furhermore, his sudy also presens he relevan ime-varying weighed rends and finds ha weighings generally rise when economic evens occur, excep in Russia because of is unique economic policies. This rend is paricularly noiceable during he European deb crisis period. We also perform Tse s (2000) LM es and find significan dynamic correlaion in all of he counries we consider. Finally, we apply he ADF and 308 Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no. 4

14 PP uni roo ess for boh he ime-varying correlaions and weighings and find ha boh variables are saionary a heir levels. In conclusion, he relaionship beween he sock and currency asses in hese markes should be considered dynamic, and he ime-varying weigh of he wo asses is valuable informaion ha helps improve he performance of a porfolio ha is well diversified beween sock and currency asses. This informaion also allows inernaional invesors o diversify he sock marke s risk more effecively. APPENDIX Table 1A FDI in Easern European and Russian Counries Iems Panel A Increasing rae of FDI (from 2000 o 2011) Panel B FDI socks in 2000 (million US dollars) FDI socks in 2011 (million US dollars) Czech Republic Hungary Poland Russia 478% 269% 477% 1300% 21,644 22,870 34,227 32, ,245 84, , ,474 Noes: The percenage in Panel A denoes he increasing rae of he amoun of FDI from 2000 o 2011 in hese counries. The FDI socks in Panel B is according o he world Invesmen Repor 2012 of he Unied Naions Conference on Trade and Developmen (UNCTAD). Table 2A Trading Hours Panel A: Trading hours Sock marke Currency marke Czech Republic Hungary Poland Russia Panel B: Opening and closing hours Czech Republic 9:30 16:00 09:30 18:00 Hungary 8:00 16:37 09:00 17:00 Poland 9:00 16:35 09:00 17:00 Russia 10:30 18:00 07:00 15:00 Noe: In he figures, 911 erroris aack occurs in Sepember 11, 2001, dollar crisis occurs in he final quarer 2004, subprime worries occur form in he middle of 2007 and las o he end of 2008, and he European deb crisis occurs during 2010 and Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no

15 REFERENCES Agnolucci P (2009): Volailiy in crude oil fuures: A comparison of he predicive abiliy of GARCH and implied volailiy models. Energy Economics, 31: Arouri MEH, Jouini J, Nguyen DK (2011): Volailiy spillovers beween oil prices and sock secor reurns: Implicaions for porfolio managemen. Journal of Inernaional Money and Finance, 30: Bollerslev T (1990): Modelling he coherence in shor-run nominal exchange raes: A mulivariae generalized ARCH model. Review of Economics and Saisics, 72: Brooks C, Persand G (2002): Model choice and value-a-risk performance. Financial Analyss Journal, 58(5): Case B, Yang Y, Yildirim Y (2012): Dynamic correlaions among asse classes REIT. Journal of Real Esae Finance and Economics, 44: Chan NH, Deng SJ, Peng L, Xia Z (2007): Inerval esimaion of value-a-risk based on GARCH models wih heavy-ailed innovaions. Journal of Economerics, 137(2): Chang CL, Khamkaew T, Tansucha R, McAleer M (2011): Modelling condiional correlaions in he volailiy of Asian rubber spo and fuures reurns. Mahemaics and Compuers in Simulaion, 81: Conover CM, Friday HS, Sirmans GS (2002): Diversificaion benefis from foreign real esae invesmens. Journal of Real Esae Porfolio Managemen, 8(1): Coer J, Sevenson S (2006): Mulivariae modeling of daily REIT volailiy. Journal of Real Esae Finance and Economics, 32(3): Engle RF (2002): Dynamic condiional correlaion A simple class of mulivariae GARCH models. Journal of Business and Economic Saisics, 20: Engle R, Kroner K (1995): Mulivariae simulaneous GARCH. Economeric Theory, 11: Fan Y, Zhang YJ, Tsai HT, Wei YM (2008): Esimaing Value-a-Risk of crude oil price and is spillover effec using he GED-GARCH approach. Energy Economics, 30: Fedorova E, Saleem K (2010): Volailiy Spillovers beween Sock and Currency Markes: Evidence from Emerging Easern Europe. Finance a úvěr-czech Journal of Economics and Finance, 60: Francis B, Hasan I, Huner D (2006): Dynamic relaions beween inernaional equiy and currency markes: The role of currency order flow. Journal of Business, 79(1): Ghosh C, Miles M, Sirmans CF (1996): Are REITs socks? Real Esae Finance, 13: Gio P, Lauren S (2003): Value-a-Risk for long and shor rading posiions. Journal of Applied Economerics, 18: Grambovas C (2003): Exchange rae volailiy and equiy markes: Evidence from he Czech Republic, Greece, and Hungary. Easern European Economics: 41: Hassan H, Malik F (2007): Mulivariae GARCH model of secor volailiy ransmission. Quarerly Review of Economics and Finance, 47: Huang YC, Lin BJ (2004): Value-a-risk analysis for Taiwan sock index fuures: fa ails and condiional asymmeries in reurn innovaions. Review of Quaniaive Finance and Accouning, 22: Hung JC, Lee MC, Liu HC (2008): Esimaion of value-a-risk for energy commodiies via fa-ailed GARCH models. Energy Economics, 30: Kang SH, Kang SM, Yoon SM (2009): Forecasing volailiy of crude oil markes. Energy Economics, 31: Kroner KF, Ng VK (1998): Modelling asymmeric co movemens of asse reurns. Review of Financial Sudies, 11: Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no. 4

16 Lin S, Tamvakis M (2001): Spillover effecs in energy fuures markes. Energy Economics, 23: Milunovich G, Thorp S (2006): Valuing volailiy spillover. Global Finance Journal, 17:1 22. Morales L (2008): Volailiy spillovers beween equiy and currency markes: Evidence from major Lain American counries. Cuadernos de Economia, 45: Sadorsky P (2012): Correlaions and volailiy spillovers beween oil prices and he sock prices of clean energy and echnology companies. Energy Economics, 34: Savárek D (2005): Sock Prices and exchange raes in he EU and he USA: Evidence of heir muual ineracion. Finance a úvěr-czech Journal of Economics and Finance, 55: Tai C (2007): Marke inegraion and conagion: Evidence from Asian emerging sock and foreign exchange markes. Emerging Markes Review, 8: Tse YK (2000): A es for consan correlaions in a mulivariae GARCH model. Journal of Economerics, 98(1): Ülkü N, Demirci E (2012): Join dynamics of foreign exchange and sock markes in emerging Europe. Journal of Inernaional Financial Markes, Insiuions and Money, 22(1): Yang S, Doong S (2004): Price and volailiy spillovers beween sock prices and exchange raes: Empirical evidence from he G-7 counries. Inernaional Journal of Business and Economics, 3: Yang Y, Chang C (2008): A double-hreshold GARCH model of sock marke and currency shocks on sock reurns. Mahemaics and Compuers in Simulaion, 79: Yang J, Zhou Y, Leung WK (2012): Asymmeric correlaion and volailiy dynamics among sock, bond and securiized real esae markes. Journal of Real Esae Finance and Economics, 45: Finance a úvěr-czech Journal of Economics and Finance, 64, 2014, no