Volatility Spillover from the Fear Index to Developed and Emerging Markets

Transcription

1 Volailiy Spillover from he Fear Index o Developed and Emerging Markes Ihsan U. Badshah * ABSTRACT: This paper examines he volailiy linkages among he fear index (VIX), he developed sock marke volailiy index (VXEFA), and he emerging sock marke volailiy index (VXEEM). We find significan cross-marke dependencies in firs as well as in second momens of volailiies. The fear index has leading role and has informaion conen for boh developed and emerging markes. A volailiy shock o he fear index spillovers o he developed and emerging markes and able o explain abou 57.07% and 63.77% of heir unexpeced volailiy shocks, respecively; he effec of he shock persiss for abou 7 days. We furher analyse he cross-marke dependencies in second momens of volailiies and find ha he correlaions among he markes are ime-varying no consan. Boh developed and emerging markes are highly correlaed wih he fear index, and he fear index drives he correlaion dynamics of he emerging markes. The dynamic correlaions increase in urbulen periods and decreases in ranquil periods. Our findings have imporan implicaions for he inernaional porfolio diversificaion, hedging and risk managemen. KEY WORDS: Emerging markes, implied volailiy spillover, VIX, VXEEM, VXEFA * Address: Deparmen of Finance, AUT Business School, Auckland Universiy of Technology, Privae Bag 92006, Auckland 1142, NEW ZEALAND. ibadshah@au.ac.nz. Tel: exn: Fax:

2 Inroducion The degree of world sock marke inegraion has been increasing over he pas wo decades due o economic inegraion hrough rade and financial linkages which has led o an increase in equiy reurns correlaions among sock markes across he globe (see Bekaer and Harvey 2014). I is known ha he high degree of sock marke correlaion evaporaes he benefis of diversificaion available in he invesmen opporuniy se o inernaional invesors. However, empirical evidence suggess ha many of he emerging markes are no ye compleely inegraed ino he global sock markes raher sill segmened; moreover, hey find ha emerging marke equiies have high reurns, high risks, and lower correlaions wih he developed marke equiies, usually hese characerisics arac inernaional invesors (see Bekaer e al., 2011; Bekaer and Harvey, 2014). Emerging markes are economically linked wih he US and oher developed markes hrough rade and invesmens hus he emerging marke volailiies (risks) may be dependen on he US and oher developed markes volailiies (risks). We know ha marke volailiy vary much more han marke reurns so iner-marke volailiies should reveal he dynamics of marke inegraion and spillovers effec much beer han marke reurns (see Peng and Ng, 2012). We rely on he forward-looking volailiy indices he VIX, VXEFA, and VXEEM reflecing he volailiies of he US, emerging and oher developed sock markes (excluding he US), respecively. The Chicago Board of Opions Exchange (CBOE) has launched, VXEEM, for he for emerging sock markes on March 16,2011, and on June 27, 2013, VXEFA, for developed sock markes he hisory of he laer goes back o January 2, VXEEM is calculaed from opions raded on he underlying he ishare MSCI Emerging Markes ETF (which provides exposure o 26 emerging sock sock) whereas VXEFA is calculaed from opions raded on he underlying ishares MSCI EAFE ETF (which provides exposure o 24 developed sock markes i.e. developed Europe, Ausralasia 2

3 and Far easern counries). We use he above forward-looking volailiy indices raher han hisorical marke volailiies because volailiy index such as VIX is now widely considered invesors fear gauge because i is implied from a cross-secion of pu and call opions on he S&P 500 sock marke index. I is known ha he sock index pus are usually used by invesors for hedging heir underlying sock porfolios. Therefore, volailiy index beer reflecs invesor s expecaion abou he fuure sock marke volailiy han any oher volailiy measure (see Blair e al.,2001). I also reflecs overall invesors risk aversion in he sock marke which is fundamenal for porfolios (Bollerslev e al., 2009). Oher main advanage of using volailiy indices is ha a variey of volailiy derivaives are raded on he CBOE on hese volailiy indices such as opions and fuures; herefore, hese volaiy derivaives faciliae o hedging and diversificaion of risks associaed wih he underlying inernaional equiy porfolios. Thus, inernaional invesors would like o know he answers of he following quesions. 1 How closely hese markes are linked wih respec o volailiies. 2 who causes who? Can unexpeced shock o he US sock marke volailiy predic he unexpeced risk of emerging marke volailiy or developed marke volailiy and vice versa? And for how many days he effec of an unexpeced shock on he volailiy will persis? How hey are linked in erms of second momens of volailiies? Are heir correlaions ime-varying or saic? And dynamic correlaions behave differenly during urbulen and ranquil periods? I is imporan ha inernaional invesor undersand he cross-volailiy linkages and correlaion dynamics so hey could opimally decide on heir porfolios and o ake adequae decisions o manage heir risks. Volailiy lieraure provide empirical evidence on he marke inegraion and volailiy spillover effecs across he developed markes such as he US and European markes (Nikkinen and Sahlsröm 2004; Skiadopoulos 2004; Nikkinen e al. 2006; Äjiö 2008; Jiang e al. 2012; Peng and Ng, 2012;Kenourgios, 2014). Äijö(2008) invesigaes volailiy linkages beween European volailiy indices (VDAX, VSMI and VSTOXX). He finds ha he volailiy indices 3

4 are highly correlaed and implied volailiy indices vary over ime, he VDAX being he dominan source of volailiy informaion. VDAX can explain he variance of he forecas errors of he VSTOXX and VSMI abou 65% and 35%, respecively. Nikkinen and Sahlsröm (2004) sudy he degree of marke inegraion beween he US, UK, German and Finnish sock markes using implied volailiy indices. Similarly, hey find a high degree of inegraion among hese markes: while he US marke is he leading source of informaion ransmiing o oher markes generally, in he European conex he German marke leads oher European markes. Jiang e al. (2012) invesigaes implied volailiy linkages beween he US and many European sock markes. They find significan spillovers beween he US and Europe and spillovers wihin Europe. Moreover, hey provide evidence of volailiy conagion across markes during he global financial crises of Peng and Ng (2012) sudy he iner-dependence among five major US, European and Japanese volailiy indices (VIX, VXN,VDAX, VFTSE, and VXJ) and show ha hey are highly correlaed and he dependence beween volailiy indices is effeced by financial shocks reveals informaion much faser han he underlying sock marke indices. A recen sudy by Kenourgios (2014) sudy he volailiy conagion across US and European volailiy indices (VIX, VCAC, VDAX, VFTSE, VSMI) using he Asymmeric dynamic condiional correlaion GARCH model of Cappiello e al. (2006). He finds volailiy indices highly correlaed, and heir correlaions are ime-varying no consan, and heir correlaions considerably increases during he crises periods. Our sudy builds on he above lieraure bu differs from he exising research in wo respecs. We sudy volailiy spillovers across he US sock marke, he emerging sock marke, and he res of he developed sock marke. To our knowledge, our sudy is he firs o invesigae he implied volailiy spillovers among he US, he developed and he emerging marke using daa on he newly inroduced CBOE volailiy indices. Second, we use mulivariae GARCH model of Cappiello e al. (2006) o analyse he dependencies and 4

5 spillovers effecs in second momens of volailiies across markes. Our main findings are ha here is considerable volailiy spillover from he fear index (he VIX) o he developed and emerging marke volailiy indices. The dependencies and spillovers are found by analysing boh momens of volailiies. The fear index has a leading role and has predicabiliy for emerging and developed marke volailiies; however, we also find emerging markes informaive for developed markes bu no vice versa. The effec of a uni VIX risk shock has persisen effecs (for abou 7 days ahead) on emerging and developed marke volailiies. Moreover, he fear index risk shock spillovers o developed and emerging markes risks abou 57.07%, and 63.77%, respecively. We also analyze he inerdependencies in second momens of volailiies (i.e. voalilies of volailiies) by using ADCC-GARCH model. The resuls shows voalily indices are highly persisen and presen asymeries in volailiy o negaive and posiive shocks. Second, he correlaions beween hese markes are ime-vayring herefore we rejec he assumpion of conan correlaions. Third, he fear index is dynamically correlaed wih he developed and emering markes and paricularly i drives persienly he correlaions of emerging marke volailies; however, he dynmic correlaion beween he developed and emerging marke is volaile and less persisen. Finally, ime-vayring correlaions increases in urnbulen periods and decrease in ranquil periods. This paper is organized as follows. In Secion 2, we discuss he daa. In Secion 3, we sudy he cross-marke linkages in firs momens of volailiies. In Secion 4, we sudy crossmarke linkages in second momens of volailiies. Lasly, secion 5 concludes. Daa We obain daily daa on he VIX, VXEFA, and VXEEM from he Chicago Board of Opion Exchange websie for he sample period March 16, 2011 o Ocober 30, The CBOE 5

6 inroduced VIX in Sepember 2003, which is compued from he bid and ask prices of he crosssecion of S&P 500 opions. 3 The CBOE inroduced, VXEFA for developed sock markes excluding Unied Saes on June 27, 2013, 4 and on March 16, 2011, VXEEM for he emerging sock markes, he hisory of he former goes back o January 2, VXEFA is compued from opions raded on he underlying ishares MSCI EAFE ETF (which provides exposure o 24 developed sock markes i.e. developed Europe, Ausralasia and Far easern counries), whereas VXEEM is compued from opions raded on he underlying he ishare MSCI Emerging Markes ETF (which provides exposure o 26 emerging sock markes). Using similar model free mehodology as VIX, CBOE compues VXEFA and VXEEM from he bid and ask prices of he cross-secion of ishare MSCI EAFE ETF opions and ishare MSCI Emerging Markes ETF opions, respecively. I is imporan o noe ha opions on he underlying S&P 500 index, MSCI developed marke ETF and emerging marke ETF are raded a he same rading hours on he CBOE plaform. Thus our daa on he volailiy indices are no subjec o rading ime differences. Figure 1 shows a ime series plo of he daily closing levels (%) of he hree implied volailiy indices from March 16, 2011 o Ocober 30, Among he hree volailiy indices, he VXEEM presens he highes volailiy level hroughou our sample period, whereas he VIX shows he lowes volailiy level. In laer par of 2011, here are considerably high volailiy levels which is due o he European deb crises. However, from 2012 onwards unil he second quarer of 2015, volailiy levels are relaively sable. On Augus 24 h, he Chinses sock marke plunge abou 8.5% in value (called he Chinese Black-Monday), riggering worldwide sock marke fall, and a spike of 55% can be seen in he VXEEM on ha day, he levels of VIX hi 36% and VXEFA 41%. The high volailiy levels coninue unil he end of Sepember, Table 1 repors summary saisics for he VIX, VXEFA, and VXEEM. Firs hree 6

7 columns of Table 1 presen summary saisics for he volailiy levels. As can be seen, on average VXEEM has he highes level followed by VXEFA, and VIX. During he sample period, he maximum level he VXEEM has ever reached is 64%, he VXEFA wih abou 59% and he VIX abou 48%. All hree volailiy indices are posiively skewed and presen excess kurosis. Firs order auocorrelaions for all hree volailiy indices are repored in row 10, which show all hree volailiy indices are highly persisen. The Augmened Dicky Fuller (ADF) ess on levels daa, we can easily rejec he null hypohesis of uni roo for he VIX, VXEFA, and VXEEM. Las hree columns of Table 1 provide summary saisics for log changes in he VIX, VXEFA, and VXEEM, respecively. Mean values of log volailiy changes are abou zero; however, here are dispersions on a daily basis as can be seen from he maximum, minimum, and sandard deviaion. All hree volailiy indices are posiively skewed, which sugges ha big posiive changes in he volailiy indices occur more frequenly han big negaive changes. All hree indices show excess kurosis. The excess kurosis in he volailiy indices sugges ha big volailiy changes occur more frequen in comparison o he normally disribued volailiy changes. Based on he ADF ess on he log changes daa, we can rejec he null hypohesis of uni roo a 1% level. Cross-marke Linkages in Firs Momens of Volailiies VAR Framework We invesigae he dynamic cross-marke linkages in firs momens of VIX, VXEFA, and VXEEM changes in he Vecor Auoregressive (VAR) framework. The VAR model can capure he dynamic impac of random innovaions on a sysem of variables. I reas each endogenous variable in a sysem as a funcion of he lagged value of all endogenous variables in a dynamic simulaneous equaions sysem. The VAR model for log changes in he VIX, 7

8 VXEFA, and VXEEM can be specified as follows: VI L VI u (1) i 1 i i Where ' VI VIX, VXEFA, VXEEM is an mx1 vecor of endogenous variables represening he daily log changes in he volailiy indices;, i 1,2,3, L is an m m i, marix of coefficiens; and u is an m 1 vecor of innovaions which can be conemporaneously correlaed; however, uncorrelaed wih is own lagged values and wih oher variables. The Schwarz Informaion Crierion (SIC) is used o selec appropriae lag srucure for he VAR model. SIC suggess 2 lags, hus we selec VAR (2) as our specificaion for furher analysis. The VAR model is esimaed by ordinary leas squares (OLS) mehod. In Table 2, we provide coefficien esimaes for he VAR(2) model and -saisics in squared brackes. For ΔVIX, we receive a negaive and significan coefficien esimae on ΔVIX-1 implying ha here is a negaive auocorrelaion in ΔVIX, his shows mean-reversion propery in he VIX level. However, he coefficien esimae on ΔVIX-2 is saisically insignifican. While he coefficien esimae on he ΔVXEFA-1 for ΔVIX is found o be negaive and insignifican whereas he coefficien esimae on ΔVXEEM-1 is posiive bu similarly found o be insignifican, suggesing ha developed and emerging markes volailiies do no effec significanly he volailiy of he US sock marke. For ΔVXEFA, we receive a negaive and significan coefficien on ΔVXEFA-1 and ΔVXEFA-2 implying ha here is a negaive auocorrelaion in ΔVXEFA, his also indicaes mean-reversion propery in he VXEFA. We find posiive and saisically significan coefficiens on ΔVIX-1, and ΔVIX-2 a 1% level, suggesing ha he VIX can predic a a large exen he volailiy of developed sock markes. On he oher hand, we receive posiive and significan coefficiens on ΔVXEEM-1, ΔVXEEM-2 a 1% and 5% level respecively for ΔVXEFA, suggesing ha he emerging marke volailiy conain significan volailiy 8

9 informaion conen for he VXEFA. Finally, for ΔVXEEM, we find negaive and significan coefficiens on ΔVXEEM-1 and on is lag 2, confirming mean-reversion in he VXEEM. We find posiive and significan coefficiens on ΔVIX-1, and ΔVIX-2. Which sugges shocks o he VIX up o lagged 2 days in he VIX have informaion conen o predic unexpeced changes in he curren volailiy of he emerging markes. On he oher hand, we receive negaive coefficiens on ΔVXEFA-1, and ΔVXEFA-2 bu he former being insignifican and he laer marginally significan, suggesing ha immediae volailiy shock in he developed marke does no carry predicive informaion for he emerging marke volailiy; however, emerging markes invesors reac a slower pace wih anicipaion ha he unexpeced shock in developed markes would no lead o increases in he volailiy. Overall, he resuls from he VAR (2) specificaion sugges ha he unexpeced volailiy shock generaed in he US marke leads o significan increases in boh emerging marke and developed marke volailiies. The unexpeced volailiy shocks generaed in he emerging and developed marke do no affec he volailiy of he US marke; however, he emerging marke shock significanly increases he volailiies of developed markes. This US volailiy effec on he emerging markes volailiies reflecs he underlying economic channel. For insance, emerging markes economies are heavily dependen on expors o he US and invesmens of US mulinaionals; herefore, emerging marke invesors would perceive any risk o he US equiy marke as a shock o he demand of heir expors and a possible decline in invesmens. Furhermore, he resuls are consisen wih he findings of Rizova (2013) who finds ha emerging sock markes reac gradually o he unexpeced shocks of heir rading parner counries herefore we see a lagged response from he emerging markes invesors. Similarly, developed markes excluding he US such as Japan and Germany ec. heir economies are heavily expors dependen o he US and emerging markes so we see volailiy spillover effecs on he developed marke volailiies. 9

10 Finally, he las row of Table 2 provides R 2 values for ΔVIX, ΔVXEFA, and ΔVXEEM, which are very low, 0.73%, 5.47%, and 1.57%, respecively. Which sugges ha he volailiy dynamics of developed markes are relaively more predicable in comparison o he US and emerging marke volailiies. Table 3 provides resuls for pairwise Granger (1969) causaliy ess, which esablishes lead-lag relaionships beween hese markes. The resuls furher confirm our findings of Table 2 ha he fear index significanly Granger causes developed and emerging marke volailiies. Surprisingly, developed markes do no causes he US and emerging marke volailiies bu emerging marke significanly causes developed marke volailiies. Impulse Responses Informaion on he sign and persisence of a shock in he VAR sysem can be gleaned from impulse response funcions. For example, how long he effec of a uni shock o he volailiy of one marke would have on he volailiy of anoher marke. An impulse response funcion measures he responses of volailiy in a VAR sysem o a uni shock in each volailiy index. We use he generalized impulse response funcion (GIRF) of Pesaran and Shin (1998), as i does no require orhogonalizaion of shocks and invarian o he reordering of he volailiy variables in he VAR Sysem. Figure 2 provides accumulaed generalized impulse responses of ΔVIX, ΔVXEFA, and ΔVXEEM for 30 seps ahead. Panel A depics he accumulaed impulse responses of ΔVIX o a uni shock in he innovaions of he VIX, VXEFA, and VXEEM. The conemporaneous GIRFs of he VIX are 0.073, 0.057, and unis o a uni shock in he VIX, VXEFA, and VXEEM, respecively. For he nex few days ahead he impac of is own shock on he VIX decreases and a similar paern can be observed o he shocks of VXEFA, and VXEEM. The GIRF of VIX reurn o a more sable level afer abou 5 days a abou 0.068, 0.052, for a shock in he VIX, VXEFA, and VXEEM, respecively. 10

11 Panel B shows he accumulaed generalized impulse responses of ΔVXEFA o a uni shock in he VIX, VXEFA and VXEEM. The conemporaneous repossess of he VXEFA o a uni shock in each volailiy index are 0.054, 0.070, and unis, respecively. The effec of a uni shock on he VXEFA decreases afer a few days and reurn o a more seady level afer 6 days and sele down a abou 0.056, 0.062, and 0.054, respecively. Panel C shows he generalized accumulaed impulse responses of ΔVXEEM o a uni shock in he VIX, VXEFA VXEEM. A uni shock in each volailiy index leads o conemporaneous responses in he VXEEM of 0.050, 0.046, and unis, respecively. The effec of a uni own shock says for a while and rever o a seady level afer abou 10 days. Somehow similar responses can be seen o a uni shock in he VIX and VXEFA. Noneheless, he effec of a uni shock in each volailiy index reaches o seady level afer 7 periods and sele down a abou 0.052, 0.046, and 0.059, respecively. In sum he GIRF resuls sugges ha he effec of a shock o each volailiy index have long-run implicaions for he volailiies of each sudied marke, hus persisen. However, if we compare he effec of each shock on each volailiy index hen he shock in he fear index has he sronges effec on boh developed and emerging markes, he effec persiss for abou 7 days ahead. Which is consisen wih he gradual diffusion of volailiy informaion. Variance Decomposiion While impulse response funcions capure he effecs of a shock o he volailiy of one marke o he oher marke volailiy in a dynamic VAR sysem, whereas variance decomposiion or forecas error decomposiion allows us o spli he forecas error variance ino slices aribuable o he various sysem shocks. For example, wha percenage of he 1-sep ahead error variance in predicing volailiy index i is due o shocks in he oher volailiy indices (see Mills and Markellos, 2008; Diebold and Yilmaz, 2009). Figure 3 depics he variance decomposiions for VIX, VXEFA, and VXEEM for 30 11

12 seps ahead. There are hree panels in Figure 3; he y-axis shows he percenage of error variances in forecasing a volailiy index i due o shocks in oher volailiy indices. While he x-axis of each panel shows he number of seps ahead error variance forecas. Panel A plos he variance decomposiion of he fear index (he ΔVIX). As can be seen, he fear index explains all of is own 1-sep ahead forecas error variance, and on average 99.76% of is 30-day ahead forecas error variance. However, he oher volailiy indices conribue o he forecas error variance of he VIX marginally, on average abou 0.12% each. The variance decomposiion of he developed marke volailiy (VXEFA) is ploed in Panel B of Figure 3. VXEFA can forecas 39.92% of is own 1-day ahead error variance and on average abou 42.14% for 30-day ahead forecas error variance. However, VIX seems o dominae here as i explains abou 60.08% of he error variance of VXEFA 1-sep ahead and on average abou 57.07% for 30-sep ahead. While he emerging marke volailiy index conribues marginally o he oal predicabiliy of VXEFA. Panel C of Figure 3 shows he variance decomposiion of he emerging marke volailiy index (VXEEM) for 30-sep ahead. As can be seen, VXEEM can forecas is own 1-sep ahead error variance abou 31.42%, and on average abou similar explanaion for 30-sep ahead. On he oher hand, VIX seems o dominae in 1-sep ahead error variance forecasing for he emerging marke volailiy (VXEEM) as well, as VIX can predic up o 64.50% of he error variance for VXEEM, and on average abou 63.77% for 30-sep ahead. However, he forecasing abiliy of he developed sock marke volailiy is found quie low for he VXEEM. The main conclusion drawn from he Variance decomposiion resuls is ha he fear index clearly drives he volailiies of boh developed and emerging sock markes. As a shock o he fear index spillovers o boh developed and emerging marke volailiies and can explain he variance of volailiy shocks o developed and emerging marke volailiies on average abou 57.07% and 63.77%, respecively. However, he spillovers from he oher volailiy 12

13 indices o he fear index are negligible. One imporan observaion from he spillover resuls can be seen ha VIX influences emerging marke more han he developed marke. These resuls furher verify our earlier resuls of VAR, and impulse response analysis. Cross-marke Linkages in Second Momens of Volailiies The Mulivariae GARCH-ADCC Model We furher invesigae wheher he US marke, developed markes and emerging markes are dynamically correlaed in second momens of volailiies. How srongly hey are correlaed, are heir correlaions ime-varying or saic? Are heir correlaions asymmeric? Answers o hese quesions are imporan for inernaional invesors. We employ he asymmeric dynamic condiional correlaion GARCH model (ADCC-GARCH) of Cappiello e al. (2006). I is a generalizaion of he DCC-GARCH model of Engle (2002) o accoun for he condiional asymmeries in correlaion. ADCC-GARCH model allows correlaions o vary over ime, while i involves wo-sep procedure o isolae he dynamic condiional correlaion process. In sep 1, a univariae asymmeric GARCH model is fied for each volailiy residuals series (residuals are received from VAR (2) specificaion) and use he ime varying esimaed sandard deviaion o obain sandardized residuals series for each volailiy index. In sep 2, he sandardized residuals (sandardized volailiy shocks) are used o esimae he ime-varying dynamic condiional correlaions. Le u denoes a n 1 vecor of volailiy residuals a ime, which is assumed o be condiional normally disribued wih mean zero and covariance marix V as u ~ N (0, H ) (2) 1 Where 1 is he informaion se available a ime 1, and he condiional covariance marix V is as V D C D (3) 13

14 where D is he diagonal marix of ime-varying sandard deviaions obained from he fied univariae asymmeric GJR-GARCH models a sep 1, whereas C is he ime-varying condiional correlaion marix given by 1/ 2 1/ 2 C diag( Q ) Q diag( Q ), (4) Where diag( Q ) is he diagonal marix ha is formed from he diagonal elemens of Q which is a posiive definie marix which follows he follows he asymmeric dynamic condiional correlaion srucure Q u u Q g (5) where min[ u,0], he produc of i, j, is nonzero if and only if boh shocks are negaive (for deail see e.g. Cappiello e al., 2006); Alexander, 2008; Engle, 2009). Table 4 repors he resuls for he ADCC-GARCH model of boh sep1 and sep 2. In sep 1, an asymmeric univariae GARCH model is fied for each of volailiy index residuals series (residuals received from VAR (2) specificaion). Resuls are repored in Panel A, as be seen he coefficien,, he GARCH coefficien is highly significan for all hree volailiy i indices. I implies ha shock o each volailiy index is highly persisen, paricularly he emerging markes volailiy followed by he US volailiy and he leas persisen is he developed markes volailiy. However, he shock o variance, i, he ARCH coefficien is also found o be significan for each volailiy index bu he ARCH effec is high in magniude for he VIX and followed by VXEFA and he leas is found in he VXEEM. Finally, if we look ino, i, he asymmeric effec of negaive and posiive shocks of volailiy on he volailiy of each marke, he VIX and VXEEM presen asymmeric volailiy; however, he asymmery in volailiy is found insignifican for he VXEFA. The sighs of he asymmeric effecs are negaive and consisen wih he inuiion ha negaive shocks o volailiy indices decreases fuure volailiies which should be opposie in he case of reurn shocks. 14

15 In panel B of Table 4 repors he resuls for sep 2, he ADCC resuls. The firs row shows he average dynamic condiional correlaions beween he volailiy indices over he sample period from March 16, 2011 o Ocober 30, I is found ha on average hese volailiy indices are highly correlaed, correlaion of 0.76 beween he US and emerging marke volailiies, followed by he US and developed marke 0.73, and he leas beween developed markes and emerging markes abou The persisence in correlaion beween he pair is capured by 2. As can be seen, he correlaion beween VIX and VXEFA is highly persisen followed beween he VIX and VXEEM. The asymmery in correlaion beween he pair is capured by g, as can be observed all pairs show asymmery in correlaions. Implies ha simulaneous decline in volailiies beween he pair and simulaneous spikes in volailiies have asymmeric impac on correlaions. Figure 4 shows he pairwise dynamic condiional correlaions (DCCs) received from ADCC-GARCH model from March 16, 2011 o Ocober 30, Panel A depics he DCCs beween he VIX and VXEFA. As can be seen he DCCs vary considerably during he sample period; herefore, we can easily rejec he assumpion of consan correlaions. The variaion in correlaions is in he range from 0.15 (lowes) o 0.95 (highes). The highes correlaion beween he wo indices is seen during he second of half of 2011, can be aribued o he European deb crises. Whereas he lowes level of correlaion is found in early par of 2013 which is a more ranquil period. Panel B of Figure 4 shows he evoluion of DCCs beween he VIX and VXEEM. Here also we can observe variaion in DCCs hough in a smaller range from 0.44 (lowes) o 0.93 (highes). The highes correlaion beween VIX and VXEEM is found during he European deb crises (hird quarer of 2011). Finally, he DCCs beween VXEFA and VXEEM is depiced in Panel C of Figure 4. The variaions in DCCs are considerable as i varies beween 0.14 (lowes) and 0.95 (highes). 15

16 The highes correlaion beween he wo indices is found during he recen Chines sock marke crises (second quarer of 2015). In summary, he ADCC-GARCH resuls provides some imporan findings: Firs, we asser ha here is noiceable evidence ha he fear index has higher ime-varying linkages in second momens of volailiies wih he developed and emerging markes over he sample period. In paricular, he fear index and emerging markes are highly correlaed and he dynamic correlaion is more of persisen in naure. However, he DCCs beween he developed markes and emerging markes vary over ime and no ha persisen. Second, he dynamic correlaions among he markes increases during he crises periods, for example, as we can observe high degree of correlaions during he hird quarer of 2011, when he euro zone sovereign deb crisis erups, and during he Chines sock marke crises (hird quarer of 2015); however, in he ranquil periods he DCCs among he markes decrease, ha can be noiced in Conclusions In his paper, we invesigae he cross-marke volailiy dependencies and spillover effecs in boh firs and second momens of volailiies for he US, developed, and emerging sock markes. We use CBOE volailiy indices as proxies for heir respecive markes for insance, he VIX index (for he US sock marke), he VXEFA (for developed markes), and he VXEEM (for emerging marke). We find significan cross-marke dependencies in firs as well as well as in second momens of volailiies. The fear index leads he emerging and developed marke volailiies hus has informaion conen for volailiies of boh markes. An unexpeced shock o he fear index spillovers conemporaneously o he developed and emerging markes and explain 57.07% and 63.77% heir volailiy shocks, respecively; while he effec of he volailiy shock says for abou 7 days. Moreover, we find inerdependencies in second 16

17 momens of volailiies among sudied markes. The correlaions of he hree markes are imevarying no saic. The degree of ime-varying corrosions of he fear index wih he oher wo marke is high comparaively. And he fear index drives he ime-varying correlaions wih he emerging markes wih highly persisen manner. The dynamic correlaions increase in crises period decreases in he ranquil periods. These significan cross-marke volailiy linkages in boh momens of volailiies. Paricularly, a dominan role of he US volailiy and is unexpeced shock spillover o he emerging sock markes would reduce he benefis of diversificaion for he inernaional invesors in he emerging markes. However, sraegies can be devised o hedge he risks arising from he equiy posiions in he emerging markes by aking long posiions in he call opions on he emerging marke volailiy index (he VXEEM) or buying fuures on he VXEEM. Such sraegy would offse he losses on he equiy posiions in he emerging markes. Noes 1. Paricularly insiuional invesors who acively seek o inves in high yield emerging marke equiies and diversify heir porfolios across borders o receive he benefis of diversificaion (i.e. reducing risks). 2. The VIX index is widely dubbed as he invesors fear index (see Whaley 2000, 2009) References Äijö, J Implied Volailiy Term Srucure Linkages beween VDAX, VSMI and VSTOXX Volailiy Indices. Global Finance Journal 18, no.3: Alexander, C Marke Risk Analysis: Pracical Financial Economerics. Wiley; Volume II ediion. 17

18 Bekaer, G., and C. Harvey Emerging Equiy Markes in a Globalizing World. Columbia Business School Working Paper, New York. Bekaer, G.; C. Harvey.; C. Lundblad.; and S. Siegel Wha Segmens Equiy Markes? Review of Financial Sudies 24, no.12: Blair, B.; S. Poon.; S. Taylor Forecasing S&P 100 Volailiy: The Incremenal Informaion Conen of Implied Volailiies and High-frequency Index Reurns. Journal of Economerics 105, no.1:5-26. Bollerslev, T.; G. Tauchen.; and H. Zhou Expeced Sock Reurns and Variance Risk Premia. Review of Financial Sudies 22, no.11: Cappiello, L.; R. Engle.; and K. Sheppard Asymmeric Dynamics in he Correlaions of Global Equiy and Bond Reurns. Journal of Financial Economerics 4, no.4: Diebold, F., and K.Yilmaz Measuring Financial Asse Reurn and Volailiy Spillovers, wih Applicaion o Global Equiy Markes. The Economic Journal 119, no. 534: Engle, R Dynamic Condiional Correlaion a Simple Class of Mulivariae GARCH Models. Journal of Business and Economic Saisics 20, no.3: Engle, R Anicipaing Correlaions. Princeon Universiy Press. Granger, J Invesigaing Causal Relaions by Economeric Models and Cross-specral Mehods. Economerica 37, no.3: Kenourgios, D On Financial Conagion and Implied Marke Volailiy. Inernaional Review of Financial Analysis 34, Mills, T., and R. Markellos The Economeric Modelling of Financial Time Series. Cambridge Universiy Press; 3rd ediion. Nikkinen, J., and P. Sahlsröm Inernaional Transmission of Uncerainy Implici in Sock Index Opion Prices. Global Finance Journal 15,no.1: Nikkinen, J.; P. Sahlsröm.; and S. Vähämaa Implied Volailiy Linkages among Major European Currencies. Journal of Inernaional Financial Markes, Insiuions, and Money 16, no.2: Peng, W., and W, Ng Analysing Financial Conagion and Asymmeric Marke Dependence wih Volailiy Indices via Copulas. Annals of Finance 8, no.1: Persaran, M., and Y. Shin Generalized Impulse Response Analysis in Linear Mulivariae Models. Economics Leers 58, no.1: Rizova, S Trade Momenum. Journal of Inernaional Financial Markes, Insiuions, and Money 24, Skiadopoulos, G The Greek Implied Volailiy Index: Consrucion and Properies. Applied Financial Economics 14, no.16 : Whaley, R The Invesor Fear Gauge. Journal of Porfolio Managemen 26, no.3:12-17., Undersanding he VIX. Journal of Porfolio Managemen 35, no.3:

19 70 Volailiy Indices (Levels) VIX VXEFA VXEEM Figure 1. Figure 1 shows a ime series plo of he VIX, VXEFA, and VXEEM over he sample period March 16, 2011 o Ocober 30,

20 Table 1 Descripive saisics for volailiy indices Volailiy Levels Volailiy Log Changes VIX VXEFA VXEEM VIX VXEFA VXEEM Mean Median Maximum Minimum Sd. Dev Skewness Kurosis Jarque-Bera Prob *** 0.973*** 0.967*** ** *** *** 0.953*** 0.940*** * *** ADF -3.80*** -3.56*** -3.00** *** *** *** No. Obs Table repors he descripive saisics for he hree implied volailiy indices. Descripive saisics for volailiy levels are repored in firs hree columns of he able. While log volailiy changes are repored in las hree columns. ADF is he -saisics for he Augmened Dicky-Fuller (an inercep is included in he es equaion). ***, ** and * denoe rejecion of he null hypohesis a he 1%,5% and 10% significance levels, respecively. 20

21 Table 2 Vecor Auoregression (2) esimaes VIX VXEFA VXEEM Inercep [-0.252] [-0.379] [-0.105] VIX ** *** *** [-2.101] [3.425] [3.468] VIX *** *** [0.582] [2.758] [2.811] VXEFA *** [-0.063] [-7.319] [-0.274] VXEFA *** * [-0.932] [-5.652] [-1.319] VXEEM *** *** [1.110] [2.875] [-3.301] VXEEM ** * [-0.188] [1.954] [-1.438] R % 5.47% 1.57% ***,**and * denoe rejecion of he null hypohesis a he 1%,5% and 10% significance levels respecively. 21

22 Table 3 Granger causaliy ess for implied volailiy indices Null Hypohesis 2 Lags F-Saisics P-Value VXEFA does no Granger Cause VIX VIX does no Granger Cause VXEFA *** VXEEM does no Granger Cause VIX VIX does no Granger Cause VXEEM *** VXEEM does no Granger Cause VXEFA *** VXEFA does no Granger Cause VXEEM ***, ** and * Denoe rejecion of he null hypohesis a he 1%,5%, and 10% significance levels respecively. 22

23 Panel A VIX VXEFA VXEEM Panel B VIX VXEFA VXEEM Panel C VIX VXEFA VXEEM Figure 2. This figure shows he accumulaed generalized impulse response funcions for he hree volailiy indices. Panels A, B and C depic responses of he VIX, VXEFA, and VXEEM o a uni shock in each volailiy index, respecively. Red line represen he impulse response funcion of each volailiy index o a uni shock in he VIX, blue line wih a uni shock in he VXEFA, and green line wih a uni shock in he VXEEM, respecively. 23

24 Panel A: Variance Decomposiion of VIX VIX VXEFA VXEEM Panel B: Variance Decomposiion of VXEFA VIX VXEFA VXEEM Panel C: Variance Decomposiion of VXEEM VIX VXEFA VXEEM Figure 3. This figure shows variance decomposiion of log changes in volailiy indices. Panel A, B and C repors variance decomposiions of log changes in VIX, VXEFA, and VXEEM, respecively. For each volailiy index, red line represen conribuions from he VIX, blue line from he VXEFA, and green line from he VXEEM, respecively. 24

25 Table 4. DCC Model resuls for boh sep 1 and 2 Panel A: DCC Models resuls wih univariae GARCH fied in sep 1. VIX VXEFA VXEEM i *** *** *** [3.981] [2.910] [3.380] *** *** *** i [4.868] [2.947] [3.976] *** *** *** i [26.536] [6.455] [46.889] *** *** i [-5.703] [-1.387] [-4.677] Panel B: ADCC model Resuls Sep 2 VIX- VXEFA VIX- VXEEM VXEFA- VXEEM Cor ij *** *** *** [4.380] [3.247] [3.999] *** *** *** [25.025] [8.803] [11.173] g ** ** *** [-2.050] [-2.256] [-2.643] ***, ** and * Denoe rejecion of he null hypohesis a he 1%, 5%, and significance levels respecively. 25

26 Panel A: ADCC beween VIX and VXEFA Panel B: ADCC beween VIX and VXEEM Panel C: ADCC beween VXEFA and VXEEEM Figure 4. This figure shows he dynamic condiional correlaions among he hree volailiy indices. Panel A shows dynamic condiional correlaions beween VIX and VXEFA, panel B beween VIX and VXEEM, and Panel C beween VXEFA and VXEEM indices from March 16, 2011 o Ocober 3,