Economic Modelling 38 (2014) 175–183

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Economic Modelling

j ourna l homepage: www.e lsev ie r .com/ locate /ecmod

Volatility and dynamic conditional correlations of worldwide emergingand frontier markets

Eduard Baumöhl a,⁎, Štefan Lyócsa b

a Department of Economics, Faculty of Business Economics in Košice, University of Economics in Bratislava, Tajovského 13, 041 30 Košice, Slovak Republicb Department of Business Informatics and Mathematics, Faculty of Business Economics in Košice, University of Economics in Bratislava, Tajovského 13, 041 30 Košice, Slovak Republic

⁎ Corresponding author. Tel.: +421 55 722 3298.E-mail addresses: eduard.baumohl@euke.sk (E. Baumö

(Š. Lyócsa).

0264-9993/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.econmod.2013.12.022

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 19 December 2013Available online xxxx

JEL classification:C32G01G15

Keywords:Conditional volatilityTime-varying correlationsEmerging and frontier markets

This study examines the relationship between time-varying correlations and conditional volatility among 32worldwide emerging and frontier stock markets and the MSCI World stock market index from January 2000 toDecember 2012. Correlations are estimated in the standard and asymmetric dynamic conditional correlationmodel frameworks. The results can be summarized by three main findings: (1) asymmetry in volatility is not acommon phenomenon in emerging and frontier markets; (2) asymmetry in correlations is found only with re-spect to the Hungarian stock market; and (3) the relationship between volatility and correlations is positiveand significant in most countries. Thus, diversification benefits decrease during periods of higher volatility.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

One of the most significant and discussed concepts in the field ofmodern finance is portfolio theory, which is based on the principlethat investors can reduce the variability of portfolio returns by holdingassets with low- or negative-return correlations. A common belief isthat there are such asset classes in international markets, particularlyin emerging or frontier markets; therefore, most studies analyze suchcorrelations among stock market returns. The earliest empirical studiesin the field of stock market co-movement (see Grubel, 1968; Lessard,1974; Ripley, 1973) demonstrated that the equity return correlationsthroughout different international markets are low and can be attribut-ed to national factors and that diversification among these markets isadvisable.

A decade after the latest of these studies, many researchers noted asubstantial increase in the interdependence between national stockmarkets (e.g., Eun and Shim, 1989; Grinold et al., 1989; Jaffe andWesterfield, 1985; Meric and Meric, 1989; Schöllhammer and Sand,1985). In the aftermath of the October 1987 US stock market crash,co-movement between national markets increased significantly (see,Arshanapalli and Doukas, 1993; King and Wadhwani, 1990). This co-movement led to another broad area of research in the framework of

hl), stefan.lyocsa@gmail.com

ghts reserved.

stock market integration: the “contagion effect”. Forbes and Rigobon(2002) described this effect as “a significant increase in cross-marketlinkages after a shock to one country (or group of countries)”. Theimplications of contagion are broad; from the perspective of a practicalinvestor, contagion leads to a weakening of diversification benefits.

Cappiello et al. (2006) examined whether the correlations betweeninternational developed equity (and bond) market movements corre-spond with volatilities. This relationship has several implications withrespect to portfolio management and, notably, the risks are significantlylarger than might be assumed by an examination of correlations orvolatilities.

This paper explores possible international diversification benefits byestimating the dynamic conditional correlations (DCC), using both stan-dard and asymmetric DCCmodels, among32worldwide emergingmar-kets and the MSCI World stock market index during the period fromJanuary 2000 to December 2012. The study will link the correlationsto conditional volatility to examine whether the correlations betweeninternational markets are correspondingly higher during periods ofhigh volatility (or vice versa). If the relationship between conditionalvolatility and the correlations is positive, this suggests that diversifica-tion benefits decrease during volatile periods, i.e., during the timeswhen they are most valuable.

The remainder of this paper is organized as follows. The next sectionprovides a short review of the empirical studies. Section 2 describes thedata, followed by Section 3 with methodology, and Section 4 presentsthe main results of the study. In Section 5 robustness tests are providedand Section 6 obtains concluding remarks.

Table 1Countries and stock market indices that are included in the sample.

Country RIC Country RIC

Argentina .MERV Malaysia .KLSEBrazil .BVSP Malta .MSEIvory Coast .BRVMCI Mexico .MXXCroatia .CRBEX Oman .MSICzech Republic .PX Philippines .PSIEgypt .EGX30 Poland .WIGEstonia .OMXTGI Qatar .QSIHungary .BUX Romania .BETCChile .IGPA Russia .IRTSChina .SSEC Saudi Arabia .TASIIndonesia .JKSE South Africa .JALSHIsrael .TA100 Sri Lanka .CSEJordan .AMMAN Taiwan .TWIIKuwait .KWSE Thailand .SETILatvia .OMXRGI Turkey .XU100Lithuania .OMXVGI Venezuela .IBC

Note: RIC stands for the Reuters Instrument Code.

176 E. Baumöhl, Š. Lyócsa / Economic Modelling 38 (2014) 175–183

2. The related literature

The evidence concerning increasing stock market linkages dependson the study period and on the methodology employed; however,most studies indicate that international stock market linkages have in-creased in recent decades. Lahrech and Sylwester (2011) applied asmooth transition logistic trend model to establish the degree of stockmarket integration between the US and Latin American stock marketsfrom December 1988 to March 2004. The smooth transition modelwas fitted to the standard DCCs between the US equity market andthe Argentine, Brazilian, Chilean, and Mexican markets. The resultsdemonstrated an increase in the degree of co-movements amongthesemarkets over time; however, the speed andmagnitude of integra-tion varied with the country examined. A similar approach was utilizedby Durai and Bhaduri (2011), who studied the correlations from July1997 to August 2006 among the following sample markets: the US,the UK, Germany, India, Malaysia, Indonesia, Singapore, South Korea,Japan, and Taiwan. The results showed that the correlations are higheramong the returns of developed markets and lower between thereturns of the Indian stock market with the developed and Asian stockmarkets. The low correlations of the Indian market continue to suggestthe possibility of international diversification benefits.

Guesmi and Nguyen (2011) concluded that emerging market re-gions (Latin America, Asia, Southeastern Europe, and the Middle East)are segmented from other world markets. With the exception of theLatin American region, calculated DCCs for emerging markets did notexhibit a significant increase from March 1996 to March 2008.

Using a sample of CEE-3 countries (the Czech Republic, Poland, andHungary), Germany, and the US, Baumöhl et al. (2011) demonstratedthat endogenously detected unconditional volatility breaks in stockmarket returns are significantly associated with DCCs.When the breaksare linked to a decrease in volatility, the correlations between the indi-ces also decrease. Similarly, a sudden increase in volatility is accompa-nied by an increase in DCCs, which supports the presence of a shiftcontagion effect. Kenourgios et al. (2011) also provide evidence of con-tagion on a sample of the BRIC emerging markets (Brazil, Russia, India,China)1 and two developed markets (UK and US) from 1995 to 2006using an asymmetric time-varying framework (AG-DCC). Similar find-ings are those of Dimitriou et al. (2013), who applied FIAPARCH-DCCapproach on a sample of BRICS countries (Brazil, Russia, India, China,and SouthAfrica), aswell as theUS, during different phases of the recentcrisis. Increasing co-movements among the US and BRICS are identifiedfrom early 2009 onwards period, implying that correlations tend to behigher in bullish than in bearish markets.

Three major emerging market crises (Asian crisis, Russian default,and Argentine turmoil), alongwith the recentUS subprime crisis, are in-vestigated in the study of Kenourgios and Padhi (2012). The samplecovers period from January 1994 to December 2008 and includesemerging stock and bond markets from various regions around theworld (Latin America, Middle East and Africa, Asia, and EmergingEurope). Standard cointegration analysis revealed long- and short-rundynamics among emerging stock markets during the Russian and theAsian crises, for both stock and bondmarkets during the subprime crisis,but Argentine turmoil had no significant impact. The isolated nature ofthe Argentine turmoil has been also confirmed using the AG-DCCapproach.

In a separate study, Kenourgios and Samitas (2011) examine thecorrelations of Balkan emerging stock markets (Turkey, Romania,Bulgaria, Croatia, and Serbia) with developed European markets (UK,Germany, and Greece) from January 2000 to February 2009 and provideevidence that the dependence increased between the Balkans and thedeveloped equity markets, which supports the presence of herding

1 The extent of the recent global crisis on a sample of the BRIC countrieswas also exam-ined by Aloui et al. (2011) using a multivariate copula approach to study the extreme co-movements.

behavior that appeared to be evident during the 2008 stock marketcrash period.

Samarakoon (2011) conducted an extensive study of stock marketintegration and contagion among 62 emerging and frontier marketsand the US market from April 2000 to September 2009. Using shockmodels,2 Samarakoon (2011) found that shocks are more likely drivenby the US market during periods of tranquility, whereas shocks fromemerging markets impact the US during periods of crisis. There are im-portant interdependencies among emerging and frontier markets withthe US market that prevent emerging markets and frontier marketsfrom acting as effective hedges for US investors during US shocks andperiods of crisis.

Syllignakis and Kouretas (2011) applied a rolling regression analysisof conditional correlations with conditional volatility on a sample setthat included the stock markets of the US, Germany, Russia, the CzechRepublic, Estonia, Hungary, Poland, Romania, Slovakia, and SloveniafromOctober 1997 to February 2009. Their results imply that the useful-ness of the Central and Eastern European stockmarkets as a diversifica-tion tool has diminished in recent years, most notably during the recentfinancial crisis and the 2008 stock market crash.

Horvath and Petrovski (2013) compared the CEE-3 market correla-tions with those of Southeastern Europe (Croatia, Macedonia, andSerbia). These authors found that during their study period from Janu-ary 2006 to May 2011, the degree of co-movement between the CEE-3markets and the Stoxx Europe 600 index is much higher than betweenthe Southeastern European markets and the Stoxx Europe 600.

The asymmetric DCC model was used in the study by Gjika andHorvath (2013) to estimate the correlations between the CEE-3 stockmarkets and the aggregate Euro-zone index Stoxx 50 from December2001 to October 2011. This study observed a significant increase in cor-relations after the entry of the CEE-3 countries into the EuropeanUnion;moreover, the correlations remained at higher levels (approximately0.6) during the recent financial crisis. Although asymmetries in volatil-ity were present in all cases, an asymmetry in correlations was signifi-cant only for the BUX (Hungary) and WIG (Poland) pair of indices;these authors also linked the correlations to conditional volatility butnot all of the relationships were significant.

3. Data description

Our dataset consists of the daily closing prices of 32 emerging andfrontier stock market indices and the MSCI World stock market index

2 First, unexpected returns (returns shocks) were calculated by specifying anautoregressive model of returns allowing for time-variation of expected returns for theUS market and for each emerging/frontier market. Second, the US return shocks were re-lated to the shocks in another market (and vice versa), using the VAR framework.

Fig. 1. Cumulative returns of the stock market indices (in %). Note: The first date in our sample is set as a base date to calculate the cumulative returns. All charts are scaled equally;however, the cumulative returns of Venezuela are around 6000%, thus they are not visible.

3 Crisis is dated using the ICSS algorithmwith κ2 statistic endegenously as a break in vol-atility of the MSCI World index, which occured on 15th July 2007.

177E. Baumöhl, Š. Lyócsa / Economic Modelling 38 (2014) 175–183

from January 2000 to December 2012. The corresponding period in-cludes the recent financial crisis that spread globally and the Europeandebt crisis, and it implies a relationship between correlations andvolatility during periods in which diversification was most required.

Because of non-synchronous trading effects (for further discussionsee Baumöhl and Výrost, 2010), each series of daily closing prices wasindividually synchronized with the daily values of the MSCI Worldstock market index and continuous returns were then computed fromweekly averages as rt = log(Pt / Pt − 1). The data were obtained fromthe Thomson Reuters Datastream database. Table 1 summarizes all thecountries and national stock market indices used in this study.

As our dataset is quite extensive, any further discussion about thedevelopment of selected stock market indices would be interminable.Therefore, in Fig. 1 the percentage cumulative returns are plotted to pro-vide some insights into how these markets evolved over the sample

period. Before the crisis,3 which influenced in some extent all marketsunder the study, the average annual nominal returns were positivewithin all markets. Two groups ofmarketswere particularly impressive,markets in Central and Eastern Europe (e.g., Romania with 42.4% p.a.,Russia 37.8% p.a., Estonia 29.8% p.a.) and markets in the Middle East(e.g. Kuwait 33.3% p.a., Egypt 29.5% p.a., Qatar 27.5% p.a.). On the otherhand, one year after the crisis, a large drop in stock prices was observedfor Central and Easter Europe, e.g., Romania −45.5% p.a., Russia −33.8% p.a., Estonia−45.4% p.a., Lithuania−42.2% p.a.). Interestingly,frontier markets like that of Ivory Coast (41.8% p.a.), Jordan (76.0% p.a.)and Oman (84.5% p.a.) still had significant positive annual returns.Finally, two years after the crisis, the average annual returns were

4 All calculations are conducted in R software.

Table 2ARMA-GARCH specifications.

Argentina ARMA(1,1)-NAGARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Brazil ARMA(1,1)-NAGARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Ivory Coast ARMA(1,1)-GARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Croatia ARMA(1,1)-GARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Czech Republic ARMA(5,1)-NAGARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Egypt ARMA(3,1)-GARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Estonia ARMA(1,1)-GARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Hungary ARMA(1,1)-NAGARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Chile ARMA(1,1)-CSGARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)China ARMA(1,1)-GARCH(1,1) MSCI ARMA(1,1)-TGARCH(1,1)Indonesia ARMA(2,1)-GARCH(4,1) MSCI ARMA(5,2)-TGARCH(1,1)Israel ARMA(1,1)-EGARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Jordan ARMA(2,1)-TGARCH(1,1) MSCI ARMA(1,1)-TGARCH(1,1)Kuwait ARMA(1,1)-GARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Latvia ARMA(1,1)-GARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Lithuania ARMA(1,1)-GJRGARCH(1,1) MSCI ARMA(1,1)-TGARCH(1,1)Malaysia ARMA(1,1)-GARCH(1,1) MSCI ARMA(1,1)-TGARCH(1,1)Malta ARMA(3,1)-GARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Mexico ARMA(1,1)-NAGARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Oman ARMA(2,1)-GJRGARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Philippines ARMA(1,1)-GJRGARCH(1,1) MSCI ARMA(1,1)-TGARCH(1,1)Poland ARMA(5,1)-NAGARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Qatar ARMA(4,2)-CSGARCH(2,1) MSCI ARMA(1,1)-NAGARCH(1,1)Romania ARMA(1,1)-GARCH(1,1) MSCI ARMA(4,2)-GJRGARCH(1,1)Russia ARMA(1,1)-NAGARCH(1,1) MSCI ARMA(1,1)-TGARCH(1,1)Saudi Arabia ARMA(1,1)-GARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)South Africa ARMA(1,1)-FGARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Sri Lanka ARMA(1,1)-GARCH(1,1) MSCI ARMA(1,1)-NAGARCH(1,1)Taiwan ARMA(1,1)-NAGARCH(1,1) MSCI ARMA(4,1)-TGARCH(1,1)Thailand ARMA(1,1)-GARCH(1,1) MSCI ARMA(1,1)-TGARCH(1,1)Turkey ARMA(3,1)-NAGARCH(1,1) MSCI ARMA(1,1)-TGARCH(1,1)Venezuela ARMA(3,1)-EGARCH(1,1) MSCI ARMA(5,2)-NAGARCH(1,1)

Note: We allow the ARMA-GARCH specification of the MSCI to be different because theseries are individually synchronized with the MSCI World index as a result of the non-synchronous trading effects.

Table 3Descriptive statistics of the estimated DCCs.

Country Mean Std. Min Date Max Date

Argentina 0.545 0.196 −0.222 01.03.2002 0.860 24.07.2009Brazil 0.711 0.106 0.382 14.11.2002 0.869 06.11.2009Ivory Coast 0.043 0.049 −0.121 24.08.2007 0.186 12.11.2010Croatia 0.359 0.161 0.028 14.10.2005 0.695 15.05.2009Czech Republic 0.558 0.132 0.258 04.07.2003 0.787 15.05.2009Egypt 0.300 0.083 0.045 13.09.2001 0.517 16.10.2008Estonia 0.378 0.066 0.140 25.02.2000 0.547 17.10.2008Hungary 0.583 0.074 0.317 04.07.2003 0.816 26.05.2006Chile 0.501 0.099 0.185 08.06.2001 0.712 02.12.2011China 0.232 0.082 0.083 05.07.2002 0.372 23.12.2011Indonesia 0.450 0.157 0.025 24.05.2002 0.675 26.06.2009Israel 0.490 0.106 0.065 06.04.2000 0.811 18.08.2011Jordan 0.137 0.018 0.105 24.10.2002 0.191 03.09.2009Kuwait 0.139 0.069 −0.050 25.07.2001 0.373 16.10.2008Latvia 0.207 0.068 0.037 03.08.2001 0.380 17.10.2008Lithuania 0.293 0.107 −0.176 03.08.2007 0.688 17.10.2008Malaysia 0.435 0.092 0.216 24.01.2003 0.590 19.03.2010Malta 0.067 0.000 0.067 18.01.2002 0.070 17.10.2008Mexico 0.717 0.063 0.442 18.02.2011 0.842 26.05.2006Oman 0.145 0.139 −0.068 22.08.2002 0.391 15.12.2011Philippines 0.470 0.078 0.222 08.03.2002 0.641 08.02.2008Poland 0.606 0.124 0.316 26.04.2002 0.824 20.08.2010Qatar 0.205 0.155 −0.011 01.04.2004 0.553 22.11.2012Romania 0.317 0.263 −0.193 13.12.2002 0.797 09.07.2010Russia 0.584 0.144 0.242 18.07.2003 0.822 09.12.2011Saudi Arabia 0.236 0.234 −0.374 31.10.2007 0.697 17.08.2011South Africa 0.717 0.068 0.473 15.02.2002 0.864 26.05.2006Sri Lanka 0.072 0.039 −0.033 13.01.2005 0.140 28.11.2008Taiwan 0.576 0.081 0.283 11.09.2009 0.765 19.08.2011Thailand 0.474 0.103 0.076 19.05.2010 0.722 17.10.2008Turkey 0.453 0.143 0.037 15.08.2003 0.699 01.02.2008Venezuela 0.135 0.003 0.117 07.02.2003 0.145 16.01.2004

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positive for only Chile (0.6% p.a.) and Venezuela (5.6% p.a.). The best-performingmarket in our study is Venezuela, where cumulative returnsat the end of our sample reached 6000%. As is clearly visible from Fig. 1,the rise in the Venezuelanmarket in themost recent yearswas probablycaused by the expectations that Hugo Chávez would step down due tohis medical treatment.

Another interesting observation worth mentioning is the significant2004/2005 increase in the volume and prices of shares traded, followedby the 2006 stock market crash in the Middle East region. That is thefirst of two major declines in Kuwait, Jordan, Qatar, and Saudi Arabiaduring the time period of the data set; and the second is observedduring the recent world-wide financial crisis.

4. Methodology

To estimate the DCCs, we employed the standard two-step DCCmodel of Engle and Sheppard (2001) and Engle (2002), in addition tothe asymmetric version that was proposed by Cappiello et al. (2006).It is known that for higher dimensions, the estimated parameters inthe DCC model are downward biased, see Hafner and Reznikova(2012). We therefore estimated the DCCmodel for each pair of marketsseparately, which allowed the estimation of different parameters for theequations modeling the bivariate variance–covariance matrices.

First, ARMA-GARCH models are estimated to obtain standardizedresiduals. Our model selection procedure includes the followingGARCH-class models:

1. GARCH (Bollerslev, 1986)

2. AVGARCH (Taylor, 1986)3. NGARCH (Higgins and Bera, 1992)4. EGARCH (Nelson, 1991)5. GJR-GARCH (Glosten et al., 1993)6. APARCH (Ding et al., 1993)

7. NAGARCH (Engle and Ng, 1993)8. TGARCH (Zakoian, 1994)9. FGARCH (Hentschel, 1995)

10. CSGARCH (Lee and Engle, 1999).

Our procedure permitted the inclusion of up to five lags of innova-tion and five lags of volatility in all models, and the same lag structurewas permitted in themean equations. The autocorrelation and ARCHef-fects of the standardized residuals were tested at the 5% significancelevel using the Ljung–Box test up to int[0.05 T] lags. The sign bias testproposed by Engle and Ng (1993) was applied to ensure that themodel specification was correct (all possible asymmetric effects are in-cluded). After appropriate models were found consistent with Cappielloet al. (2006), we selected themodel that best fit the data according to theBayesian information criterion (BIC).We utilized a generalized error dis-tribution (GED) instead of the normality condition on the distribution oferrors. To overcome certain optimization problems and to speed up theprocedure, we employed variance targeting in all models.4

After the univariate GARCHmodels were fitted, in the second step ofthe DCC model, standardized residuals were used to estimate thecorrelations. It is assumed that the variance–covariancematrix of pairedresiduals can be decomposed toDtRtDt, whereDt is a diagonal matrix oftime-varying conditional standard deviations from univariate GARCHmodels. Given this assumption, theDCC (1, 1)model takes the followingform:

Rt ¼ diag Q tf g−1=2Q tdiag Q tf g−1=2 ð1Þ

Q t ¼ 1−α−βð ÞQ þ αεt−1εTt−1 þ βQ t−1 ð2Þ

ρij;t ¼qij;tffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqii;t qjj;t

p ; i; j ¼ 1;2;…;n; i≠ j ð3Þ

Fig. 2. Estimated dynamic conditional correlations. Note: All charts are scaled equally; thus, certain correlations might appear as constant (Malta) or with low variability.

179E. Baumöhl, Š. Lyócsa / Economic Modelling 38 (2014) 175–183

where Rt is the time-varying correlation matrix, Q is the unconditionalcorrelation matrix in the dynamic correlation structure Q t, and εt is avector of standardized residuals.Q is estimated via themoment estima-tor T−1∑T

t¼1ε̂t ε̂Tt . The following restrictions are imposed to ensure that

the matrix Q t is positive definite: the scalar parameters α, β ≥ 0, andα + β b 1. A typical element of Rt takes the form of ρij,t, which are theestimated DCCs. The asymmetric version of the DCC model is:

Q t ¼ 1−α−βð ÞQ−ξNþ αεt−1εTt−1 þ βQ t−1 þ ξnt−1n

Tt−1 ð4Þ

whereN ¼ T−1∑Tt¼1ntn

Tt ; nt ¼ I εtb0½ �∘εt ; I :½ � is a k × 1 indicator func-

tion that takes the value of 1 if the argument is true (and 0 otherwise),and “∘” represents the Hadamard product. The positive definiteness of

Q t is similarly ensured: α, β, ξ ≥ 0, and α + β + δξ b 1, where

δ = the maximum eigenvalue Q−1=2NQ−1=2h i

(for more details, see

Cappiello et al., 2006). If the asymmetric term in the correlation dynam-ics is significant, the estimated correlations from thebivariate asymmet-ric DCC model will be used in a subsequent analysis; otherwise, thecorrelations from the bivariate standard DCC model are employed.

The DCCs are then regressed on a constant, time trend, and condi-tional volatility:

Model 1: Two conditional volatilities included

ρij;t ¼ γij;0 þ γij;1t þXp

k¼1

ρij;t−k þ πij;1σ i;t þ πij;2σ j;t þ εij;t ð5Þ

where ρij,t are the bivariate DCCs between theMSCIWorld stockmarketindex (i) and the index from the emerging markets group (j), σi is the

Table 4Results from Model 1.

Country Constant Time σi σj R2 R2*

Argentina 0.023b 2.2E−05c 1.275a −0.563 0.927 0.323Brazil 0.014c 9.7E−06c 0.230 0.017 0.958 0.273Ivory Coast 0.004c 5.7E−08 −0.027 −0.088 0.906 0.008Croatia −0.007c 2.1E−05a 0.573a 0.116 0.976 0.491Czech Republic 0.017a 3.8E−05a 0.300c 0.201 0.961 0.638Egypt 0.013b 7.3E−06 0.341c 0.240 0.838 0.131Estonia 0.040a 2.4E−05a 0.690a −0.075 0.836 0.361Hungary 0.055a 9.1E−06 0.100 0.896b 0.848 0.340Chile 0.030a 1.1E−05 0.562a 0.387 0.877 0.229China 0.003b 1.2E−05a −0.009 −0.011 0.993 0.757Indonesia −0.001 1.8E−05a 0.253c 0.121 0.978 0.563Israel 0.045a 3.0E−05a 0.599 0.658 0.770 0.215Jordan 0.003a 2.0E−06b 0.050c 0.020 0.967 0.383Kuwait 0.003 4.2E−06 0.267 0.227 0.842 0.101Latvia 0.005b 1.3E−05a 0.274a −0.015 0.930 0.457Lithuania 0.055a 4.5E−05a 1.049b 1.481b 0.476 0.196Malaysia 0.006c 3.6E−06 0.210b −0.150 0.979 0.579Malta 0.007a −7.4E−12 0.000 0.000 0.836 0.115Mexico 0.068a 7.5E−06 0.444a 0.208 0.853 0.236Oman −0.007a 2.0E−05a 0.222b 0.025 0.991 0.724Philippines 0.009b 9.1E−06b −0.058 0.310c 0.949 0.349Poland 0.020a 4.1E−05a 0.154 0.522b 0.956 0.638Qatar −0.006a 1.9E−05a 0.258a −0.012 0.989 0.635Romania −0.020a 6.0E−05a 0.059 0.541b 0.977 0.699Russia 0.006 2.5E−05a −0.039 0.213a 0.982 0.644Saudi Arabia −0.019b 5.4E−05a 1.475a −0.375 0.931 0.464South Africa 0.093a 1.9E−05a 0.567b 0.030 0.808 0.279Sri Lanka 0.002 1.2E−06 0.065c −0.076b 0.977 0.197Taiwan 0.074a 2.2E−05b 0.722a −0.165 0.790 0.245Thailand 0.021a 1.8E−05b 0.409c 0.519b 0.865 0.199Turkey 0.005 1.8E−05 0.382 0.075 0.936 0.262Venezuela 0.013a 2.0E−08 −0.006 0.010 0.828 0.044

Note: Superscripts a, b, and c denote significance at the 1%, 5%, and 10% levels, respectively.We do not present coefficients of the lagged dependent variable; however, first lags aresignificant at the 1% level in all cases with coefficient estimates of approximately 0.9 onaverage. In most models, one lag was sufficient to capture autocorrelation structure.Two lags were required for China, Thailand, and Hungary. Three lags were included forRussia. R2* is the adjusted R-squared without a lagged dependent variable in the regres-sion model.

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conditional standard deviation of the MCSI index and σj is the condi-tional standard deviation of the emerging market. The time trend (t)is also included in our models because several DCCs may exhibit astrong trend that ismanifested by an increasing integration amongmar-kets. Model 1 requires further discussion. In the studies by Syllignakisand Kouretas (2011) and Gjika and Horvath (2013), a specificationwith no time trend and with p = 0 was used. DCCs are stationary byconstruction but typically highly persistent (the sum of α + β ap-proaches 1). Conditional volatilities also have high persistence. In suchcases, the specificationwith p = 0 leads to high autocorrelation of resid-uals, and consequently large size distortions. In our case, the first orderautocorrelation coefficient is often larger than 0.9, and size distortionsare thus substantial (see Granger et al., 2001; Su, 2008). AlthoughNewey–West standard errors — particularly with pre-whitening —

reduce the size distortions, the model remains miss-specified and re-quires lagged dependent variables. Therefore, we employed the follow-ing approach. We estimated Eq. (5) with p = 1. The presence ofautocorrelation in residuals was tested via the Peña and Rodríguez(2006) procedures. If the null of autocorrelation was rejected, we esti-mated p = 2, and the procedures were repeated until the null of auto-correlation was not rejected. The maximum of p = 3 was required. Wethen tested for the presence of heteroskedasticity using the White(1980) test with a nonparametric unweighted bootstrap as in Cribari-Neto and Zarkos (1999). If the null of homoskedasticity was rejected,we used the HC3 standard errors, consistent with MacKinnon andWhite (1985).

Finally, as σi,t and σj,t are often highly correlated, we estimated twoalternative specifications with only one conditional volatility included:Model 2: Developed markets (MSCI World) conditional volatilityincluded

ρij;t ¼ γij;0 þ γij;1 t þXp

k¼1

ρij;t−k þ πij;1σ i;t þ εij;t ð6Þ

Model 3: Emerging/frontier markets conditional volatility included

ρij;t ¼ γij;0 þ γij;1 t þXp

k¼1

ρij;t−k þ πij;1σ j;t þ εij;t : ð7Þ

5. Results and discussion

The preferred univariate ARMA-GARCH model for each market ispresented in Table 2. Although asymmetry in volatility is a widespreadphenomenon in developed stock markets, not all the emerging andfrontier markets exhibit such volatility behavior. Asymmetry in volatil-ity did not occur in 14 indices, namely, those from Ivory Coast, Croatia,Egypt, Estonia, China, Indonesia, Kuwait, Latvia, Malaysia, Malta,Romania, Saudi Arabia, Sri Lanka, and Thailand. Asymmetry in correla-tions is even rarer: the asymmetric term in the bivariate DCC modelswas found significant only for the Hungarian BUX.5 All other dynamicconditional correlations are thus estimated in a standard DCC modelframework.

The descriptive statistics of the DCCs are presented in Table 3. Thehighest average correlations are reported for Brazil (0.711), Mexico(0.717), Poland (0.606), and South Africa (0.717). The stock marketreturns for Ivory Coast (0.043), Jordan (0.137), Kuwait (0.139), Malta(0.067), Oman (0.145), Sri Lanka (0.072), andVenezuela (0.135) exhibitlow correlations with the returns of the MSCI World stock marketindex. Fig. 2 demonstrates that for several of these markets, the DCCsswing within a narrow range, most notably for Jordan, Malta, andVenezuela.

5 Gjika and Horvath (2013) found asymmetric effects in correlations between theHungarian BUX and Polish WIG.

With respect to portfolio diversification opportunities, among the 32series of DCCs, 28 of the cases had maximal DCCs that were identifiedafter 2007. Moreover, in six of the cases,6 October 2008 (when theAmerican stock market reported its largest decline since the 1987stock market crash) is the month in which maximal DCCs wereobtained.

We follow Cappiello et al. (2006), Syllignakis and Kouretas (2011),and Gjika and Horvath (2013) and estimate the relationship amongDCCs and volatilities. Table 4 summarizes the results from Model 1,which explains the DCCs in terms of conditional volatilities of bothstock market returns. In the 19 cases, the volatility of the MSCI Worldindex is significant and positive at the 10% significance level at least. Do-mestic volatility of the emerging markets is significant and positive inonly seven of the cases (Hungary, Lithuania, Philippines, Poland,Romania, Russia, and Thailand), whereas a single case (Sri Lanka) wassignificant but negative.

The results from Model 1 suggest that there may yet be emergingand frontiermarkets for international investors that provide diversifica-tion benefits in times of higher volatility. Unfortunately, the correlationsamong conditional volatilities were high in many instances and theresulting standard errors might have been inflated. We thereforechecked our results by estimating Model 2 with the conditional volatil-ity of the MSCI World stock market index and Model 3 with the

6 The seventh case is Malta but with a low correlation. The remaining six markets arethose of Egypt, Estonia, Kuwait, Latvia, Lithuania, and Thailand.

Table 5Results from Models 2 and 3.

Country Model 2 (MSCI volatility) Model 3 (domestic volatility)

Constant Time σi R2 R2* Constant Time σj R2 R2*

Argentina 0.008a 0.697a 0.697a 0.927 0.234 0.012 0.146 0.146 0.926 0.200Brazil 0.014b 0.242b 0.242b 0.959 0.273 0.010 0.251c 0.251c 0.958 0.270Ivory Coast 0.003 −0.028 −0.028 0.906 0.010 0.003c −0.088 −0.088 0.906 −0.003Croatia −0.005c 0.640a 0.640a 0.976 0.470 −0.004 0.379a 0.379a 0.976 0.462Czech Republic 0.018a 0.483a 0.483a 0.961 0.634 0.017a 0.404a 0.404a 0.961 0.631Egypt 0.019a 0.450b 0.450b 0.838 0.127 0.012b 0.386b 0.386b 0.837 0.085Estonia 0.039a 0.652a 0.652a 0.836 0.361 0.032a 0.353 0.353 0.830 0.240Hungary 0.059a 0.705a 0.705a 0.845 0.285 0.057a 0.980a 0.980a 0.848 0.338Chile 0.031a 0.706a 0.706a 0.877 0.227 0.029a 0.939a 0.939a 0.875 0.169China 0.002b 0.000a −0.013 0.993 0.755 0.003b 0.000a −0.016 0.993 0.757Indonesia 0.000 0.336a 0.336a 0.978 0.533 0.000 0.252c 0.252c 0.978 0.556Israel 0.054a 1.002a 1.002a 0.770 0.201 0.041a 1.180a 1.180a 0.769 0.197Jordan 0.003a 0.057b 0.057b 0.967 0.383 0.003a 0.035b 0.035b 0.966 0.324Kuwait 0.005 0.337b 0.337b 0.842 0.067 0.005 0.363b 0.363b 0.841 0.082Latvia 0.005b 0.261a 0.261a 0.930 0.410 0.006b 0.039 0.039 0.928 0.308Lithuania 0.069a 1.596a 1.596a 0.464 0.158 0.062a 1.807a 1.807a 0.471 0.148Malaysia 0.004 0.159a 0.159a 0.979 0.546 0.006c 0.076 0.076 0.978 0.572Malta 0.007a 0.000b 0.000b 0.833 0.106 0.006a 0.000 0.000 0.836 0.030Mexico 0.066a 0.571a 0.571a 0.853 0.146 0.068a 0.561a 0.561a 0.851 0.236Oman −0.007a 0.245b 0.245b 0.991 0.723 −0.004b 0.128 0.128 0.991 0.705Philippines 0.010b 0.000 0.095 0.949 0.168 0.008c 0.000c 0.247c 0.950 0.281Poland 0.024a 0.489a 0.489a 0.956 0.631 0.019a 0.667a 0.667a 0.956 0.635Qatar −0.006a 0.250a 0.250a 0.989 0.598 −0.002 0.054 0.054 0.989 0.580Romania −0.011b 0.381b 0.381b 0.977 0.676 −0.020a 0.586a 0.586a 0.977 0.699Russia 0.008b 0.000a 0.338a 0.981 0.645 0.006 0.000a 0.202a 0.982 0.629Saudi Arabia −0.023a 1.201a 1.201a 0.931 0.375 0.001 0.029 0.029 0.928 0.248South Africa 0.094a 0.584a 0.584a 0.808 0.277 0.084a 0.642a 0.642a 0.806 0.250Sri Lanka 0.000 0.060 0.060 0.976 0.194 0.003a −0.073b −0.073b 0.976 0.074Taiwan 0.071a 0.585a 0.585a 0.790 0.241 0.062a 0.365b 0.365b 0.788 0.194Thailand 0.027a 0.704a 0.704a 0.864 0.150 0.020b 0.000b 0.792a 0.864 0.195Turkey 0.007 0.453a 0.453a 0.936 0.248 0.000 0.286b 0.286b 0.936 0.262Venezuela 0.013a −0.009 −0.009 0.827 0.040 0.012a 0.011 0.011 0.828 0.021

Note: Superscripts a, b, and c denote significance at the 1%, 5%, and 10% levels, respectively. We do not present coefficients of the lagged depended variable; however, first lags aresignificant at the 1% level in all cases with coefficient estimates of approximately 0.9 on average. In most models, one lag was sufficient to capture autocorrelation structure. Two lagswere required for China and the Philippines in Model 2, and for Thailand in Model 3. Three lags were included solely for Russia for both models. R2* is the adjusted R-squared withouta lagged dependent variable in the regression model.

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conditional volatility of domestic stockmarket returns. Table 5 presentsthe results from these models.

These results are less ambiguous. From a total of 32 markets, 27cases demonstrated that the conditional volatility of the MSCI Worldstockmarket index were significant and positive at the 10% significancelevel. Insignificant conditional volatility was found only for Ivory Coast,China, the Philippines, Sri Lanka, and Venezuela. Three of thosemarkets(Ivory Coast, Sri Lanka and Venezuela) exhibit low correlations and var-iability of DCCs and are therefore most likely not considered by foreigninvestors.7 With respect to Model 3, the volatility of domestic marketswas significant and positive in 20 of the analyzed countries, which is aconsiderable increase compared to previous results. The only exceptionis Sri Lanka, where domestic volatility is significant but the estimatedcoefficient is negative, which implies that correlations tend to declineduring periods of higher volatility (and vice versa).

These results demonstrate that when the volatility (domestic and/orforeign) increases, the correlations between emerging/frontier marketsand developedmarkets are also likely to increase. Consequently, despitethe lower correlations of emerging and frontiermarketswith developedmarkets, diversification benefits decrease during more volatile periods,which is the time when investors most need them.

We included the time trend in the specifications of all modelsbecause several studies have indicated an overall increase in DCCsover time (e.g., Gjika and Horvath, 2013; Guesmi and Nguyen, 2011;Lahrech and Sylwester, 2011). The trend captures the long-run increase

7 This is due to other possibly political and legislative resasons.

in the DCCs that was confirmed for the majority of emerging/frontiermarkets. The corresponding coefficient was significant and positive for21, 28, and 21 countries inModels 1, 2, and 3, respectively. These resultssuggest that the stock market integration of emerging and frontiermarkets is gradual over time. It is apparent — particularly in the caseof China— that the variability of DCCs is sufficiently captured by a lineartime trend.

6. Robustness check

As suggested by several previous studies, e.g. Baumöhl et al. (2011),Kenourgios et al. (2011), Syllignakis and Kouretas (2011), and Gjika andHorvath (2013), the dependency between markets increases duringtimes of higher volatility. Therefore our results might be driven byperiods of higher volatility related to the recent financial crisis, or localcrises on emerging and frontier markets. We have therefore decidedto test the robustness of our main findings using two approaches.8

We test whether an increase in correlations at the end of our sampleis not just a manifestation of contagion. We have employed a fourthspecification, which expandedModel 1 with a dummy variable for a re-cent financial crisis. This variable took the value of 1 after the 15th July2007 and 0 otherwise.9 However, this variable was significant only inthe regression models of Indonesia, Mexico, and Romania.

8 Detailed results are available upon request.9 The beginning of the crisis is determined endogenously as a break in volatility of the

MSCI index by the ICSS algorithm and κ2 statistic.

182 E. Baumöhl, Š. Lyócsa / Economic Modelling 38 (2014) 175–183

A more general approach involves examining possible structuralbreaks in the regression coefficients. For each market and specification(corresponding Models 1–3), we estimated the position of one or twostructural breaks using the minimum sum of squares criterion asin Bai and Perron (1998a, b)and Bai and Perron (2003).10 Next, thenumber of breaks was estimated using the recently suggested modifiedSchwartz (1978) information criteria (referred to asMBIC) and Hannanand Quinn (1979) information criteria (referred to as MHQIC) by Hallet al. (2013). Using the MBIC, only one structural change in coefficientswas identified for Indonesia (for Models 1, 2), but for both regimes atleast one volatility coefficient was positive and significant. With theMHQIC and for Model 1, structural breaks in coefficients were foundfor 16 markets. Still, the relationship between volatility and correlationappears to be quite robust. Except for Sri Lanka and Oman, we found atleast one positive and significant volatility coefficient among theremaining 14 countries, while only one (i.e. for only one regime)was found for six markets, namely for Hungary, Jordan, Lithuania,Malaysia, Saudi Arabia, and South Africa. Further on, among 64 volatilitycoefficients among those 16 markets with structural breaks in coeffi-cients, 75% of the coefficients were positive and among 21 significantcoefficients 18 were positive. For Model 2, structural breaks were iden-tified for 7markets, but correlation and volatility relationship appears tobeweakened only for themarket in Saudi Arabia. Similarly, for Model 3,structural breaks were identified for 11 markets, with Lithuaniabeing the country, where for one regime the volatility coefficient wasinsignificant.

7. Concluding remarks

This paper examined the time-varying correlations of 32 emergingand frontier markets with developed markets that were representedby the MSCI World index on a sample of weekly returns during theperiod from January 2000 to December 2012. Our findings have implica-tions for risk management, international finance, and in particularportfolio management; they are summarized as follows:

(i) The asymmetric behavior of volatility, often observed for devel-oped stockmarkets, is not present in all of the analyzed emergingand frontier stock market indices.

(ii) Asymmetry in correlations is likely to be scarce because it wasonly detected in the Hungarian BUX. Therefore, the correla-tions were changing symmetrically, regardless of whetherthe previous innovation was positive or negative. This resultis in contrast to the results of Cappiello et al. (2006), whichshowed asymmetric effects in correlations for developedstock market returns.

(iii) The linkages between emerging/frontier markets and developedmarkets have increased over time, which implies that diversifica-tion opportunities in international markets are slowly decreasing.

(iv) We found evidence that the relationship between correlationsand volatility might be considered positive. This further reducesdiversification possibilities because diversification benefitsdecrease during periods of higher volatility.

These results raise several issues with respect to hedging in interna-tional equity markets, such as whether different strategies are requiredin periods of tranquility and crisis, or whether different asset classesshould be used when hedging equity portfolios.

10 We estimated full structural models, i.e. assuming one common break in all coeffi-cients. For the stock market in Malta, probably the low variability of the DCCs (seeFig. 2) caused numerical instability in the estimation of the full structural models; thuswe have excluded Malta from this analysis.

Acknowledgments

This work was supported by the Slovak Research and DevelopmentAgency under contract no. APVV-0666-11. The authors also acknowl-edge funding support from the Slovak Grant Agency for Science(VEGA project no. 1/0393/12). We thank two anonymous referees forhelpful comments.

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Eduard Baumöhl, PhD. is a lecturer in financial markets atthe University of Economics in Bratislava, the Faculty of Busi-ness Economics, with a seat in Košice. He has held the posi-tion of Assistant Professor in the Department of Economicssince 2009. His research interests include stock market

integration, applied economics andeconometrics, and transi-tion and European integration.

Štefan Lyócsa, PhD. has been an Assistant Professor at theUniversity of Economics in Bratislava, the Faculty of BusinessEconomics, with a seat in Košice, Department of BusinessInformatics and Mathematics, since 2008. He lectures inmicroeconomics and quantitative methods in economics.His research interests include stock market integration, realeconomic activity, stock market networks, and transitioneconomics.