International Journal of Marketing & Financial Management (IJMFM)

Transcription

1 Inernaional Journal of Markeing & Financial Managemen (IJMFM) ISSN: (Online) ISSN: (Prin) Available online a : hp:// 2issue-6-july us: edior@arseam.com Insrucions for auhors and subscripion informaion: hp:// MULTIVARIATE GARCH MODEL OF TRANSMISSION OF VOLATILITY: A STUDY OF BRIC STOCK MARKETS Joshi Prashan Uka Tarsadia Universiy, Bardoli, India Absrac The sudy examines he volailiy spillover among BRIC markes using a four-variable symmeric GARCH-BEKK model during January 2009 o June We find evidence of bi-direcional shock spill over among Brazil and Russia, Brazil and China, Russia and India and bidirecional volailiy spill over among sock markes of Brazil and Russia, beween Brazil and India and among Brazil and China. The magniude of volailiy linkages is low indicaing weak inegraion of BRIC sock markes. The sudy finds ha own volailiy spillover is higher han cross marke spillover. The overall persisence of sock marke volailiy is highes for China (0.987) and lowes for Russia (0.889). The implicaion of weak inegraion is ha invesors will benefi from reducion of diversifiable risk. Keywords: Reurn and Volailiy spillovers, Uni Roo Tes, Mulivariae GARCH model, JEL Classificaion: C32, G15 1. Inroducion The exen of he global linkage of emerging markes improves access o he inernaional capial markes. Srong global linkage reduces he insulaion of he emerging sock markes from exernal shocks, hence limiing he scope for independen moneary policy (Li and Majerowska, 2007). From he perspecive of he global invesors, weak sock marke linkage in he form of less han perfec correlaion beween heir reurns offers poenial gains from inernaional porfolio diversificaion, while srong marke linkage or co-movemen in reurns eliminaes he poenial benefis of diversificaion. 1 P a g e

2 Alhough here is no dearh of lieraure on financial inegraion, here are only a few sudies relaed o emerging sock markes of Asia. Moreover, he limied lieraure on he emerging sock markes in Asia has sudied he co-movemens beween he sock markes using coinegraion and Vecor Auoregression framework (Eun and Shin, 1989,Chung and Ng, 1992, Bhaacharya and Samanha, 2001, Wong, Agrawal and Du, 2005, Voronkova, 2004, Ahmad, Ashraf and Ahmed, 2005, Cheeley and Seeley, 2005, Yang, Hsiao, Li and Wang, 2006, Hoque, 2007). The sudies do no ake ino accoun he ineracions in erms of volailiy among he markes. I is believed ha if markes are inegraed, an unanicipaed even in one marke will influence no only reurns bu also variance in he oher markes. The analysis of volailiy is paricularly imporan because i can proxy for he risk of asses. Joshi(2011) examined he reurn and volailiy spillover among Asian sock markes in India, Hong Kong, Japan, China, Jakara and Korea using a six-variable asymmeric GARCH-BEKK model during 2nd February 2007 o 20h February, The sudy found he evidence of bi-direcional reurn; shock and volailiy spill over among mos of he sock markes. The magniude of volailiy linkages was low indicaing weak inegraion of Asian sock markes. I found ha own marke volailiy spillover was higher han cross marke spillover. Li (2007) examined he linkages beween he wo emerging sock exchanges namely Shanghai and Shenzen of China and he esablished sock markes Heng Seng of Hong Kong and S & P of he US by a mulivariae GARCH-BEKK framework using he daily share price indices of he sock markes, January 4, 2000 o Augus 17, The resuls indicaed ha here was no evidence of spillover effec in erms of reurn and volailiy beween he sock exchanges in China and US marke. There was an evidence of unidirecional volailiy spillover from sock exchange in Hong Kong o hose in Shanghai and Shenzhen. The sudy found ha Chinese sock exchanges were inegraed wih he regional developed sock exchange in Hong Kong bu he exen of he linkages beween he sock exchange in Hong Kong and China was weak. The resuls furher showed ha here was a bidirecional shock spillover beween he wo Chinese sock exchanges. The sudy also found ha here was an asymmeric response of volailiy in all four sock exchanges under sudy. Harris and Pisedasalasai (2006) applied consan condiional correlaion MGARCH framework o invesigae reurn and volailiy spillover effecs beween he Financial Times Sock Exchange (FTSE)100, FTSE 200 and FTSE small cap equiy indices of UK sock marke using daily reurn during January 1, 1986 o December 2002 using GJR specificaions of MGARCH model o capure asymmeric effec. The sudy found ha reurn and volailiy ransmission mechanism beween large and small socks in he UK were asymmeric. There were significan posiive spillover effecs from porfolio of larger socks o he porfolio of smaller socks. Worhingon and Higgs (2004) examined he ransmission of equiy reurns and volailiy among hree developed Asian markes (Hong Kong, Japan and Singapore) and six emerging markes of Asia (Indonesia, Korea, Malaysia, he Philippines, Taiwan and Thailand) using weekly reurns from January 15, 1988 o Ocober 6, They employed BEKK (Baba, Engle, Kraf and Kroner) parameerizaion of mulivariae GARCH model o idenify he source and magniude of volailiy spillover. The sudy found he presence of posiive mean and volailiy spillovers. The mean reurn spillovers from he developed markes o he emerging markes were no homogenous across he emerging markes. Applicaion of MGARCH suggesed ha own sock marke volailiy spillovers were generally higher han cross-volailiy spillovers for all markes, especially for emerging sock markes. Scheicher(2001) sudied he regional and global inegraion of sock markes in erms of reurn and volailiy shocks in Hungary, Poland and Czech Republic and Financial Times/S&P s world acuaries index by using MGARCH(Mulivariae Generalized Auo regressive condiional heeroscedasiciy) wih a consan condiional correlaion. Using daily closing price values of he sock markes from January 1, 1995 o Ocober 7, 1997, resuls revealed ha he emerging sock exchanges were inegraed wih he 2 P a g e

3 global marke, proxied by Financial Times/S&P s acuaries world index only in erms of reurn. MGARCH resuls showed ha he regional influences were he major cause of volailiy of he markes. Inernaional volailiy had no impac on he markes. Chou, Lin and Wu (1999) examined he price and volailiy linkages of Taiwan sock marke wih Unied Saes using close-o-open, open-o-close and close-o-close reurns of indices of Taiwan known as Taikex and Unied saes Sandard and Poor s 500 (S&P 500) composie index during January 1, 1991 o December 31, The resuls found ha he volailiy and reurn spil over from US o Taiwan. The resuls of MGARCH indicaed some imporan linkage from he US sock marke o he Taiwan sock marke. The spillover effecs occurred for boh he mean and he variance of Taiwan Sock reurns. I furher poined ou ha he volailiy in US sock markes affeced oal daily volailiies of he Taiwan sock marke. Alhough here is a voluminous lieraure on equiy marke inegraion inernaionally, lile research has been underaken o sudy he inerdependence srucure of he BRIC sock markes. BRIC sands for Brazil, Russia, India and China. These counries were originally grouped in o BRICs by Goldman Sachs s James O Neal. BRIC counries are formed because of heir crucial role in he oday s world economy. The Figure 1 highlighs he imporance of he BRICs in he world s fuure economy as hey may become he larges economies in he world by 2050 (Glodman Sachs1). The economic growh raes for hese counries are well above he mos of he indusrialized counries like USA, Japan, Figure 1: Ten Larges Economy of he World in 2050, measuerd in GDP( billions of 2006 USD) Source: hp://en.wikipedia.org/wiki/file:top_five_larges_economies_in_2050.jpg Unied Kingdom and Canada. During , he Chinese economy grew a an average of 10 percen per year while India grew a an average of 8 percen per year (Balakrishnan e el 2009). China also gradually became he world s larges exporer wih $1,897 rillion worh of expors (CIA s The Worlds Fac book 2011). Meanwhile, he BRICs are also increasing heir rade wih one anoher: especially he Chinese and Indian rade has increased by $60 billion in 2010 while seing a $100 billion bilaeral rade arge by The BRICs large share of foreign exchange reserves in he world economy provides hem a srong compeiive advanage. All four counries are among he en larges accumulaors of foreign exchange reserves in dollars, accouning for over 40 percen of he world s oal ( The rillion Dollar Baby, The Economis Magazine February 2012). 1 Goldman Sachs : hp:// 3 P a g e

4 Moreover, he moneary policy acions of BRICs can influence he res of he world as hey hold a large porion of reasury bonds of many of he foreign counries including he US, UK and Canada. All hese above facors make he BRICs highly imporan in he world economy. So having a beer idea abou he moneary policy behavior of he BRICs would help oher economies o be efficien in heir paricipaion in he world economic aciviies (Tamazian & Chousa, 2009). Wih he growing imporance of BRIC counries in he world economy, i will be ineresing o examine how hose marke inerac wih each oher especially in erms of volailiy. The knowledge abou volailiy ineracions will help invesors o ake invesmen and porfolio diversificaion decision. Weak sock marke linkages benefis invesors from inernaional porfolio diversificaion, while srong marke linkage in reurns and volailiy eliminaes he poenial benefis of diversificaion. In he ligh of he review of he exising lieraure on he linkages beween he various sock markes, he presen sudy ries o analyze volailiy spill over among BRIC sock markes using MGARCH-BEKK framework. The res of he paper is organized as follows. Daa and Preliminary Analysis are presened in Secion 2. Secion 3 provides research design used in he sudy. Empirical resuls are discussed in Secion 4. Secion 5 summarizes. 2. Daa and Preliminary Analysis We colleced daa on BOVASPA, RTSI, Sensex and SSE of Brazil, Russia, India and China s closing price indices respecively from January 1, 2009 o June, I consiss of 1359 observaions. The period is he mos recen one. These sock markes have become increasingly inegraed. The rades beween counries have increased. They are playing an imporan role in he world economy. These migh have influenced he behavior and he paern of volailiy and herefore i will be insrucive o sudy volailiy in his period. Figure 1 presens ime plo of he price series of BRIC sock markes. The firs impression is ha all he indices have somewha a similar movemen. I can be noiced ha all he indices declined afer mid Overall, all he sock price indices are rending upwards during he recen ime. Figure 2 represens he reurns of he share price indices, he firs difference of he naural logarihm of he share price indices, during he period under sudy. All four indices are characerized by volailiy clusering where large (small) volailiy followed by large (small) volailiy. As he cluser ends o occur simulaneously, beween he indices, volailiy mus be modeled sysemaically. Figure 2: Sock indices during year 2001 o year ,000 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 I II III IV I II III IV I II III IV I II III IV I II III IV I II BOVASPA RTS SENSEX SSE Figure 3: Reurns of he share price indices 4 P a g e

5 I II III IV I II III IV I II III IV I II III IV I II III IV I II RBOVASPA RRTS RSENSEX RSSE Table 1 repors he summary saisics for he reurn series. Table 1: Descripive Saisics of Daily Reurns Saisic Bovaspa RTSI Sensex SSE Mean Sandard deviaion Skewness Kurosis Jarque-Bera Saisics (0.000) (0.000) (0.000) (0.000) Q 2 (12) (0.000) (0.000) 62.96(0.000) (0.000) ARCH LM saisics ( a Lag =1) 12.43(0.000) 28.58(0.000) 1.09(0.29) 3.15(0.076) ARCH LM saisics ( a Lag =5) 75.41(0.000) 67.82(0.000) 11.59( 0.041) 55.35(0.000) Bovaspa, RTSI, Sensex and SSE represen daily reurns of Brazil, Russia, India and Chinese sock indices. The performance of he indices as measured by he average reurn is beer in Sensex sock marke followed by Russia, Brazil and China sock markes. The average reurn of sock markes of China and Japan are negaive. The Russian sock marke exhibis higher volailiy han oher sock markes under sudy. The Jarque-Bera saisics rejec he null hypohesis ha he reurns are normally disribued for all cases. All Sock indices excep India have negaive skewness, indicaing ha large negaive sock reurns are more common han large posiive reurns. In conras, Furhermore all he reurns series are lepokuric, having significanly faer ails and higher peaks which can be seen from he kurosis saisics ha are greaer han 3. Generalized Auoregressive Condiional Heeroscedasiciy (GARCH) models are capable of dealing wih daa displaying he above feaures. When modelling wih GARCH, he nonzero skewness saisics indicae an ARCH order higher han one in he condiional variance equaion. Subsequenly, a Mulivariae GARCH (1, 1) model should be preferred o an ARCH (p) model o examine volailiy spillover effecs for he sake of parsimony (Li, 2007). 3. Mehodology On he basis of he feaures discussed in he previous secion, GARCH model is appropriae for he sudy. The aim of he paper is o examine he inerdependence across he four sock markes. The following model is used o examine he join process relaing o he share price indices under sudy. 5 P a g e

6 Y Y, 1 / I N(0, H ) 1 Equaion 1 Where Y is a 4 1 vecor of daily reurns a ime and is a 4 4 marix for parameers associaed wih he lagged reurns. The diagonal elemens in marix,, measure he effec of own ii pas reurns while he off-diagonal elemens, ij, capures he relaion in erms of reurns across he markes, also known as reurn spillover. The 4 1 vecor of random error,, is he innovaion for each marke a ime and has a 4 4 condiional variance-covariance marix, H. The marke informaion available a ime -1 is represened by he informaion se I-1. The 4 1 vecor of α represens consans. Bollerslev e al. (1988) propose ha H is a linear funcion of he lagged squared errors and cross producs of errors and lagged values of he elemens of H as follows: The variance-covariance marix H is presened below: q p p vech( H ) vech( C) Avech( ) G vech( H ) D vech( H ) i 1 i i i i i i1 i1 i1 Equaion 2 Where vech is he operaor ha sacks he lower riangular porion of a symmeric marix ino a vecor. The problems wih his formulaion are ha he number of parameers o be esimaed is large and resricions on he parameers are needed o ensure ha he condiional variance marix is posiive definie. Engle and Kroner (1995) propose he following new parameerizaion for H, i.e. he BEKK model, o overcome he above wo problems. H CC A AGH G Equaion 3 The BEKK model provides cross-marke effecs in he variance equaion parsimoniously and also guaranees posiive semi-definieness by working wih quadraic forms. C is 4 4 lower riangular marix of consans while A and G are 4 4 marices. The diagonal parameers of marices A and G measures he effecs of own pas shocks and pas volailiy of marke i on is condiional variance. The off-diagonal parameers in marices A and G, aij and gij, measure he crossmarke effecs of shock and volailiy, also known as volailiy spillover. H is a variance-covariance marix. We will use Mulivariae GARCH in he syle of BEKK proposed by Engle and Kroner (1995) o analyze volailiy spill over among he sock markes. The BEKK sysems can be esimaed using maximum likelihood mehod. The log likelihood funcion of he join disribuion is he sum of all he log likelihood funcions of he condiional disribuions, i.e. he sum of he logs of mulivariae-normal disribuion. Leing L be he log likelihood of observaion, n be he number of sock exchanges and L be he join log likelihood which gives, L T L i1 L 1 n / 2ln(2 ) ln 2 H 1 H 2 1 Equaion 4 4. Empirical Resuls 6 P a g e

7 In his secion, we perform uni roo es o check for nonsaionariy of he sock markes series. We repor he esimaed resuls abou marke linkages. We will look for any saisically significan crossmarke effecs as evidence of linkages and measures he exen of he linkages by he esimaed imevarying covariances using MGARCH asymmeric model. We organize he secion as follows. In secion 4.1, we discuss Augmened Dickey Fuller Tes (ADF) resuls. In secion 4.2, we repor he evidence of marke linkages in he esimaed six-variable asymmeric GARCH-BEKK model. 4.1 Uni roo es resuls Saionariy condiions of he sock marke indices are esed by Augmened Dickey-Fuller Tes (ADF). A uni roo es is a saisical es for he proposiion ha in an auoregressive saisical model of a ime series, he auoregressive parameer is one. I is a es for deecing he presence of saionariy in he series. The early and pioneering work on esing for a uni roo in ime series was done by Dickey and Fuller (Dickey and Fuller 1979, Fuller 1976). If he variables in he regression model are no saionary, hen i can be shown ha he sandard assumpions for asympoic analysis will no be valid. In oher words, he usual -raios will no follow a -disribuion; hence hey are inappropriae o underake hypohesis ess abou he regression parameers. Saionariy ime series is one whose mean, variance and covariance are unchanged by ime shif. Nonsaionary ime series have ime varying mean or variance or boh. If a ime series is nonsaionary, we can sudy is behaviour only for a ime period under consideraion. I is no possible o generalize i o oher ime periods. I is, herefore, no useful for forecasing purpose. The presence of uni roo in a ime series is esed wih he help of Augmened Dickey-Fuller Tes. I ess for a uni roo in he univariae represenaion of ime series. For a reurn series R, he ADF es consiss of a regression of he firs difference of he series agains he series lagged k imes as follows: Equaion 5 r r r 1; r p ln( R ) r r r 1 i i The null hypohesis is H0: 0 i1 accepance of null hypohesis implies nonsaionariy. and H1: 1. The We can ransform he non saionary ime series o saionary ime series eiher by differencing or by derending. The ransformaion depends upon wheher he series are difference saionary or rend saionary. We repor he resuls of uni roo es in Table 2. Table 2: Uni Roo Tesing of Daily Reurns Augmened Dickey-Fuller Tes 7 P a g e

8 .ADF saisics repored in he Table 2 show ha he null hypohesis of a uni roo in case of all four indices is rejeced. The absolue compued values for all he indices are higher han he MacKinnon criical value a 1% level. Thus, he resuls show ha he reurn series are saionary. As he resuls sugges ha he underlying reurn series are saionary, our nex sep is o examine he sock markes linkages. 4.2 The Evidence of sock marke linkages The ime-varying variance-covariance Equaion 3 are esimaed simulaneously by he maximum likelihood mehod. Noe ha he sock exchanges Brazil, Russia, India and China are indexed 1, 2, 3 and 4 respecively. We examine he esimaed resuls of he ime varying variance-covariance Equaion 3 in he sysem. The resuls of four-variable GARCH model are repored in Table 3. Table 3 : Esimaed coefficiens for four variable symmeric MGARCH Bovaspa(i=1) rsi(i=2) Sensex(I=3) SSE(i=4) ai (0.00) 0.055(0.02) 0.253(0.00) (0.02) ai (0.00) (0.00) (0.00) (0.00) ai (0.22) (0.00) 0.049(0.05) 0.047(0.04) ai (0.00) (0.69) (0.01) 0.059(0.00) gi (0.00) (0.00) (0.00) (0.01) gi (0.00) 0.889(0.00) (0.00) (0.41) gi (0.00) 0.029(0.11) 0.974(0.00) (0.02) gi (0.00) (0.50) (0.00) 0.987(0.00) Mulivariae Q saisics(10) (sandardized Residuals): (0.23) Mulivariae ARCH : (0.15) Noes a. Figures in he parenhesis indicae probabiliy values. b. Coefficiens a and g capures ARCH and GARCH Now we examine he esimaed resuls. I can be noed ha he Ljung Box Q saisics for he 10 he order and Mulvariae Q saisics for 10h orders in sandardized and squared sandardized residuals show ha here is no series dependence in he residuals indicaing he appropriaeness of he fied variance-covariance equaions by he six variable asymmeric BEKK model. The marices A and G repored in Table 3 help us o examine he relaionship in erms of volailiy. The diagonal elemens in marix A capure he ARCH effec, while he diagonal elemens in marix G measure he GARCH effec. As shown in Table 3, he esimaed diagonal parameers a22 hrough a44 are saisically significan implying presence of ARCH effec in he sock markes of Brazil, Russia, India and China while parameers g11 hrough g44 are all saisically significan, indicaing a srong GARCH (1,1) process driving he condiional variances of all he indices. The magniude of own volailiy presened by GARCH parameer is highes in sock marke of China followed by India, Brazil and Russia suggesing own volailiy largely affec heir condiional variance. The off-diagonal elemens of marix A and G capure he cross-marke effecs such as shock spillover and volailiy spillover among he six sock exchanges. Firsly, we find evidence of bidirecional shock ransmissions beween Bovaspa and RTSI, Bovaspa and SSE, beween BSE and RTSI as he pairs of off-diagonal parameers a12 and a21, a14 and a41, a23 and a32 are saisically significan. The wo way shock spillover indicaes srong connecion beween he sock markes. The bidirecional shock spillover indicaes he news abou shocks in one sock exchange affec he volailiy of oher sock exchange and vice-versa. In erms of cross-shock spillover effecs in he markes, pas innovaions in Brazil have he greaes effec (0.314) on fuure volailiy in India. The significan a42 and a31 (heir couner pars are insignifican) indicae unidirecional shock spillover from China o Russia, From India o Brazil. 8 P a g e

9 Secondly, here are bidirecional volailiy linkages beween Brazil and Russia, Brazil and India, beween Brazil and China as respecive coefficiens in g are saisically significan. I indicaes ha he condiional variance of one index depends on pas volailiy of he oher index, implying srong connecion beween hem. Own-volailiy spillovers in all markes are large and significan. The overall persisence of sock marke volailiy is highes for china (0.987) and lowes for Russia (0.889). In erms of cross volailiy persisence in he sock markes, he pas volailiy shocks in Brazil have effec (0.379) on he fuure volailiy in Russia. In he meanwhile, he saisically significan g32 and insignifican g23 indicae unidirecional volailiy spillover from India o Russia. There is no bidirecional volailiy linkages beween Russia and China. 5. Summary The sudy invesigaes volailiy spillover effec beween he sock markes in Brazil, Russia, India and China. Summary saisics of reurns series of all he sock exchanges sugges ha hey are lepokuric, having significanly faer ails and higher peaks. Generalized Auoregressive Condiional Heeroscedasiciy (GARCH) models are capable of dealing wih he propery of he daa. By applying a mulivariae asymmeric GARCH approach o he daily sock indices, he sudy found evidence of linkages in erms of volailiy. We find evidence of bidirecional shock ransmissions beween Brazil and Russia, Brazil and China and beween Russia and India. In erms of cross-shock spillover effecs in he markes, pas innovaions in Bovaspa of Brazil have he greaes effec (0.314) on fuure volailiy in India. Our resuls reveal unidirecional shock spillover from China o Russia, From India o Brazil. There are bidirecional volailiy linkages beween Brazil and Russia, Brazil and India, beween Brazil and China. There is also unidirecional volailiy spillover from India o Russia. The overall persisence of sock marke volailiy is highes for China (0.987) and lowes for Russia (0.889). References: Ahmad, Ashraf and Ahmed (2005), Is he Indian sock marke inegraed wih he US and Japanese sock markes?: An empirical analysis Souh Asia economic journal, Bhaacharya and Samana (2001), A ale of wo indices: he sory of he NASDAQ and The Sensex, Journal of Quaniaive Economics, 1(1), pp Bollerslev, Engle and Wooldridge (1988), A capial asse pricing model wih ime-varying covariances, Journal of poliical economy, 96, Brooks Chris(2008), Inroducory Economerics for Finance, Cambridge Universiy Press, UK. Chelley and Seeley (2005), Modeling equiy marke inegraion using smooh ransiion analysis: a sudy of easern European sock markes, Journal of Inernaional Money and Finance, 24, Chou, Lin and Wu(1999), Modeling he Taiwan sock marke and inernaional linkages, Pacific Economic Review, 4, Chung Yin-Wong and Ng Lillian (1992), Ineracions Beween he U.S. and Japan Sock Marke Indices, Journal of Inernaional Financial Markes, Insiuions and Money, 2(2), pp Dickey D. and Fuller W., (1979) Disribuion of he esimaes for Auoregressive ime series wih a uni roo, Journal of American Saisical Associaion, 74, Dickey, D. & Fuller W., (1981) Likelihood Raio Saisics for Auoregressive Time Series wih a Uni Roo, Economerica, 49, P a g e

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