Global financial crisis and spillover effects among the U.S. and BRICS stock markets

Transcription

1 Acceped Manuscrip Global financial crisis and spillover effecs among he U.S. and BRICS sock markes Walid Mensi, Shawka Hammoudeh, Duc Khuong Nguyen, Sang Hoon Kang PII: S (15) DOI: doi: /j.iref Reference: REVECO 1189 To appear in: Inernaional Review of Economics and Finance Received dae: 16 April 2015 Revised dae: 26 November 2015 Acceped dae: 30 November 2015 Please cie his aricle as: Mensi, W., Hammoudeh, S., Nguyen, D.K. & Kang, S.H., Global financial crisis and spillover effecs among he U.S. and BRICS sock markes, Inernaional Review of Economics and Finance (2015), doi: /j.iref This is a PDF file of an unedied manuscrip ha has been acceped for publicaion. As a service o our cusomers we are providing his early version of he manuscrip. The manuscrip will undergo copyediing, ypeseing, and review of he resuling proof before i is published in is final form. Please noe ha during he producion process errors may be discovered which could affec he conen, and all legal disclaimers ha apply o he journal perain.

2 Global financial crisis and spillover effecs among he U.S. and Walid Mensi (Firs auhor) BRICS sock markes Deparmen of Finance and Invesmen, College of Economics and Adminisraive Sciences, Al Imam Mohammad Ibn Saud Islamic Universiy (IMSIU), P.O Box 5701, Riyadh, Saudi Arabia Deparmen of Finance and Accouning, Universiy of Tunis El Manar, B.P. 248, C.P. 2092, Tunis Cedex, Tunisia Shawka Hammoudeh (Co-auhor) Lebow College of Business, Drexel Universiy, Philadelphia, PA , Unied Saes IPAG Business School, Paris, France Duc Khuong Nguyen IPAG Lab, IPAG Business School, France Sang Hoon Kang (Corresponding auhor) Deparmen of Business Adminisraion, Pusan Naional Universiy, Busan , Republic of Korea Corresponding auhor: Tel ; fax:

3 Global financial crisis and spillover effecs among he U.S. and BRICS sock markes Absrac. This aricle examines he spillover effec beween he U.S. marke and five of he mos imporan emerging sock markes namely he BRICS (Brazil, Russia, India, China and Souh Africa), and draws implicaions for porfolio risk modeling and forecasing. I gives consideraion o periods before and afer he recen global financial crisis (GFC). To his end, he bivariae DCC- FIAPARCH model, he modified ICSS algorihm and he Value-a-Risk (VaR) are employed o capure volailiy spillovers, deec poenial srucural breaks and assess he porfolio marke risks. Using he U.S. and he BRICS daily spo marke indices for he period from Sepember 1997 o Ocober 2013, our empirical resuls show srong evidence of asymmery and long memory in he condiional volailiy and significan dynamic correlaions beween he U.S. and he BRICS sock markes. Moreover, we find several sudden changes in hese markes wih a common break dae cenered on Sepember 15, 2008 which corresponds o he Lehman Brohers collapse. The Brazil, India, China and Souh Africa markes are srongly affeced by he GFC, supporing he hypohesis of recoupling (wih increased linkages). In conras, he hypohesis of decoupling is suppored for he Russian sock markes only. Finally, he skewed Suden- FIAPARCH models ouperform and provide more accurae in-sample esimaes and ou-of-sample forecass of VaR han he normal and Suden- FIAPARCH models in almos all cases. These resuls provide helpful informaion o financial risk managers, regulaors and porfolio invesors o deermine he diversificaion benefis among hese markes. JEL classificaion: G14; G15. Keywords: Volailiy spillovers; global financial crisis; srucural breaks; VaR forecass; mulivariae DCC- FIAPARCH. Corresponding auhor. Tel.: ; fax: address: sanghoonkang@pusan.ac.kr (S.H. Kang) 2

4 1. Inroducion BRICS, as idenified by Goldman Sachs, is he acronym besowed on a group of he five fas growing markes in he universe of emerging marke economies. This group includes Brazil, Russia, India, China and Souh Africa. These economies are disinguished from oher emerging marke economies by heir demographic poenial and promising economic perspecive. Therefore, he BRICS have araced a grea deal of aenion from invesors, regulaors, financial agencies, porfolio managers, policymakers and financial media. Togeher, hese economies accoun for more han 40% of he world s populaion and rank among he world s larges and mos influenial counries in he 21s cenury. In paricular, China and India are among he counries ha experience he highes global economic growh over he las 15 years. I is also expeced ha he four BRIC counries (excluding Souh Africa) accoun for 41% of he world s sock marke capializaion and China alone become he larges equiy marke in he world by 2030 (Hammoudeh e al., 2013; Liu e al., 2013). Similar o oher emerging markes, he BRICS markes share several ineresing feaures in common. They have consisenly produced high average reurns wih relaively low correlaions wih hose of developed markes. However, heir reurns are relaively more predicable and volaile han hose of he developed markes. Barry e al. (1998) documen ha some of oday s emerging markes have become some of omorrow s developed markes, which is likely o apply o he BRICS markes. These feaures also show ha emerging markes have become an imporan asse class and ha heir holdings in inernaional and dedicaed porfolios are of growing significance since hey presen diversificaion benefis for invesors in he developed markes. These favorable characerisics of he BRICS markes can largely be explained by he gradual financial liberalizaion process ha has sared in he majoriy of emerging markes in early 1980s and by he wave of financial and economic reforms ha followed. This 3

5 ransformaion process has principally exended he emerging markes invesors base by allowing foreign invesors o hold domesic marke asses. I has also made emerging markes more liquid, increased heir credibiliy, visibiliy and ransparency, improved heir marke size and deph, and srenghened invesor proecion paricularly he minoriy shareholders. In a more recen sudy, Buchanan e al. (2011) highligh he imporance of including he emerging marke asse class in developed markes porfolios as i enables invesors o achieve higher risk-adjused performance. On he oher hand, he onse of he GFC which is deemed as he wors crisis since he Grea Depression of he 1930s, has called for a careful invesigaion of he rade-off beween reurn-seeking behavior in inernaional markes and high risks from conagion owing o he increased financial openness and marke inegraion. While he higher inegraion of financial markes around he world has enabled free capial mobiliy, i has also led o increasing volailiy spillovers, paricularly beween emerging and developed markes. Indeed, emerging markes are very sensiive and vulnerable o exernal shocks coming from developed markes paricularly he Unied Saes, due o he weakness and immauriy of heir financial insiuions and regulaory sysems. The successive financial and currency crises over he las wo decades are he ideal siuaions o observe he sharp changes in marke inerdependence and volailiy ransmission. For insance, King and Wadhwani (1990) find ha Japan, he U.S. and he U.K. sock marke correlaions have significanly increased following he sock marke crash in Similar resuls are obained by Dimiriou e al. (2013) for he BRICS sock markes, and Toyoshima and Hamori (2013) for he Japan and Singapore sock markes. Given heir specificiies and he imporan role hey play in he global economy in erms of boh marke share and economic growh, he BRICS emerging markes need special research in several ways, predominanly in erms of volailiy spillovers wih he Unied Saes. This research aims o examine he dynamic spillovers beween he five fas growing 4

6 BRICS economies and he world s mos imporan developed marke of he Unied Saes, wih emphasis on he GFC of The U.S. marke is seleced based on is size and influence on he inernaional sock markes and i is also he U.S. economy from where he GFC originaed and spread o oher economies. We invesigae, in paricular, he spillover effecs of he GFC on he volailiy ransmission beween he Unied Saes and he BRICS. We hen provide he financial implicaions of he volailiy spillovers in regard o porfolio risk managemen hrough an analysis of in- and ou-of-sample Value a Risk (VaR) forecass for porfolios of he emerging and U.S. socks under consideraion. Empirically, we adop he mulivariae Dynamic Condiional Correlaion Fracionally Inegraed Asymmeric Power ARCH (DCC-FIAPARCH) model o invesigae he spillover effecs beween he daily spo indices of he U.S. sock markes and BRICS over he period spanning he period Sepember 29, 1997 o Ocober 14, This model accommodaes several mos imporan sylized facs of sock reurns such as he persisence, long memory and asymmery properies of he condiional variance processes (see, e.g., Con, 2001). Our emphasis is on he changes in hose properies as a resul of he onse of he GFC which has implicaions for marke conagion, porfolio allocaion and risk managemen. This empirical approach which ness he FIAPARCH model of Tse (1998) and he DCC specificaion of Engle (2002) hus allows one o synergize heir advanages. Specifically, he FIAPARCH models offer he flexibiliy o model he condiional second momen aking ino accoun he long memory propery, he predicabiliy srucure of reurn volailiy and he volailiy asymmeric characerisics (i.e., negaive shocks o sock prices have greaer effecs on he condiional volailiy han posiive shocks of he same magniude). For is par, he DCC modeling provides an efficien way o capure he condiional correlaions among he sample markes which change hrough ime wih respec o marke condiions. This exended model is also less resricive in erms of he number of variables 5

7 included, compared o oher mulivariae volailiy models such as he full BEKK-GARCH model and he VEC-GARCH model. Ahmad e al. (2013) sugges ha he esimaed parameers of DCCs allow one o analyze in deph he changes in correlaion during he sabiliy/crisis periods. Our sudy makes a number of conribuions o he exising lieraure. Firs, i examines he dynamic linkages of he BRICS sock markes wih he Unied Saes which is he larges developed sock marke. The BOVESPA index, he RTS index, he BSE SENSEX index, he Shanghai Composie index, and he FTSE/JSE index are used as he represenaive porfolios for he Brazilian, Russian, Indian, Chinese, and Souh African sock markes, respecively. The S&P500 index is also used as he represenaive for he sock marke of he Unied Saes since i provides an accurae proxy for a diversified equiy porfolio and has long been seen as he benchmark for measuring porfolio performance. Second, o he exen ha financial crises and heir associaed spillover effecs may direcly affec reurn and volailiy srucures, we invesigae how he GFC of impacs he spillovers among he BRICS and he dominan U.S. markes. I is worh noing ha we ake he GFC effecs ino accoun by firs deecing he poenial of srucural breaks wih he use of he adjused ieraive cumulaive sum of squares (ICSS) algorihm of Sanso e al. (2004) which modified he original Inclán and Tiao (1994) procedure in order o differeniae beween he impacs of he ranquil or sable period and he volaile/crisis period. Third, we esimae our DCC-FIAPARCH model which explicily accommodaes long-range memory shifs, leverage effecs and asymmery in he volailiy processes during boh periods. Finally, we analyze he implicaions of he esimaion resuls on porfolio decision making and risk forecasing. More specifically, we show how hese resuls help improve he porfolio s VaR forecasing for boh shor and long posiions. 6

8 On he whole, using he pairwise Granger causaliy ess as a preliminary analysis, we find ha he U.S. sock marke Granger-causes each of he BRICS sock markes (he resuls are no provided in his sudy bu are available upon reques). In addiion, here is evidence of significan cross volailiy effecs beween he U.S. and hose five emerging indices. We deec seven srucural breaks for he U.S. sock markes and a leas en such breaks for he BRICS sock markes, which may accoun for he imporance of regional and local evens, in addiion o global facors. The dae of Sepember 15, 2008 is generally found as a common break dae for he sample markes. This break dae corresponds o he occurrence of he bankrupcy of Lehman Brohers, which sparked off he severe period of he GFC. We also show a linkage beween he U.S. and each of BRICS sock markes excep Russia, supporing he phenomenon of heighened recoupling for mos of he BRICS afer he Lehman Brohers collapse. For he Russian case, we do no find spillovers from he U.S. marke o he Russian marke afer he Lehman Brohers collapse, indicaing a sign of decoupling beween hese wo markes. Finally, he skewed Suden- FIAPARCH model is he mos suiable specificaion for improving he VaR forecasing efficiency. The remainder of his sudy is organized as follows. Secion 2 presens a brief review of he lieraure. Secion 3 discusses he mehodology used in his sudy. Secion 4 describes he daa and conducs some preliminary analysis. Secion 5 repors he empirical resuls. Secion 6 provides concluding remarks. 2. Lieraure review One of he key challenges for marke paricipans (e.g., individual invesors, insiuional invesors, raders, porfolio managers, policy makers, ec.) is o undersand he volailiy of sock markes and he volailiy ransmission beween hem, especially beween emerging and developed sock markes afer a major crisis srikes. Indeed, hese marke 7

9 paricipans are mindful of porfolio losses and sysemaic risk paricularly during crises and conagious shocks and when hey inves simulaneously in sock markes of differen counries. The recen financial crisis has severely affeced he marke microsrucure as such invesmen, liquidiy, asse pricing and financial risk managemen of he fronier, emerging and developed economies. As inernaional capial markes have become more and more inegraed wih each oher, a number of sudies have addressed he issue of marke comovemen and inerdependence, paricularly wih careful consideraion of financial crisis periods. Using daily open-o-close, close-o-open, and inraday daa over he period from Augus 1, 1991 o December 31, 1992, Wei e al. (1995) es he volailiy ransmission beween developed and emerging sock markes, and also quesion he effecs of marke openness on reurn and volailiy spillovers. They provide evidence of significan spillover effecs from developed o emerging markes. On he oher hand, Wang e al. (2003) sudy he dynamic causal linkages beween he five larges emerging African sock markes and he U.S. marke over he 1997/1998 Asian financial crisis. These auhors show evidence ha boh he shor-run causal linkages and he long-run relaionships beween hese markes are subsanially weakened afer ha crisis. Aloui e al. (2011) use a GARCH-copula approach o analyze he condiional dependence srucure beween he four BRIC and he U.S. sock markes and find srong evidence of ime-varying dependence beween each of hose BRIC markes and he U.S. marke. However, he dependency is sronger for he more commodiy price-dependen BRIC markes (Brazil and Russia) han for he finished-produc expororiened markes (India and China). They also observe high levels of dependence persisence for all marke pairs during boh bullish and bearish markes In anoher sudy ha deals wih emerging markes, Bhar and Nikolova (2009) use he bivariae EGARCH model o examine he level of inegraion and he dynamic relaionship 8

10 beween he four BRIC counries (Brazil, Russia, India and China), oher regions and he world. They find ha India shows he highes level of regional and global inegraion among hose BRIC counries, followed by Brazil, Russia, and China. In addiion, heir resuls provide srong evidence of a negaive volailiy relaionship beween he Indian and he Asia-Pacific regional markes, and beween he Chinese and he world markes, which suggess poenial diversificaion opporuniies for porfolio invesors. Using he same model as in Bhar and Nikolova (2009), Abbas e al. (2013) invesigae he presence of volailiy ransmission among regional Asian equiy markes (Pakisan, China, India and Sri Lanka) and hree regional and developed sock markes (Unied Saes, Unied Kingdom and Singapore). These auhors find evidence of significan volailiy spillovers beween friendly counries of differen regions ha have economic links. Moreover, here is evidence of volailiy ransmission beween counries which are on unfriendly erms among regional equiy markes including Pakisan, China, India and Sri Lanka. By applying he rivariae VAR-GARCH models for 41 emerging markes in Asia, Europe, Lain America, and he Middle Eas and Norh Africa (MENA), Beirne e al. (2010) find volailiy spillovers from regional and global markes o he majoriy of emerging markes. 1 Moreover, he naure of he cross-marke linkages varies across counries and regions. However, he reurn spillovers dominae he ransmissions in emerging Asia and Lain America, while he spillovers in variance appear o play a key role in emerging Europe. Finally, he relaive imporance of he regional and global spillovers varies, wih he global spillovers dominaing in Asia while he regional spillovers prevail in Lain America and he Middle Eas. Bekiros (2014) examines he responsiveness of he BRIC markes o he inernaional reurn and volailiy shocks afer he recen U.S. financial crisis and he 1 The global marke reurns are calculaed as a weighed average of he reurns of he sock marke indices of he Unied Saes, Japan, and Europe (France, Germany, Ialy, and Unied Kingdom). The regional marke reurns are calculaed as a weighed average of he reurns of he sock marke indices of all sample emerging markes in he region, excep he local marke. 9

11 subsequen Eurozone sovereign deb crisis. The auhor shows ha almos all markes have become more inernaionally inegraed afer hose crises. In a recen sudy, Chiang e al. (2013) invesigae he spillover effecs of reurns and volailiy of he U.S. sock marke on he sock markes of Brazil, Russia, India, China and Vienam (BRICV) by using he auoregressive condiional jump inensiy (ARJI) model. They reveal ha Russia receives he greaes conagious effecs of reurns and volailiy from he U.S. marke before he 2007/2008 financial crisis, while Vienam is he receiver of he mos inense spillover effecs following his crisis. In addiion, India exhibis he lowes long-run oal risk, while he greaes risk is found for China and Brazil. Several sudies employ he DCC-GARCH model o show he conagion of he GFC for emerging sock markes, especially for he BRICS markes. Xu and Hamori (2012) examine he dynamic linkages beween he BRIC counries and he Unied Saes (as represened by Dow Jones Indusrial Average Index) in he mean and variance of he sock prices for he pre- and pos-2007/2008 crisis periods. 2 They show ha he inernaional ransmission of sock prices beween he BRICs and he Unied Saes weaken in boh he mean and variance during he GFC. Hwang e al. (2013) sudy he ime-varying condiional correlaions among he Unied Saes and emerging sock markes including he BRICS, Souh Korea, Thailand, Philippines, Taiwan, and Malaysia, and find differen paerns of spillovers among hese emerging economies due o he U.S. financial crisis. They also show ha increases in he credi defaul swaps (CDS) spread and he TED spread (i.e., he yield difference beween he hree-monh LIBOR and he US hree-monh Treasury bills) decrease he condiional correlaions. However, increases in he foreign insiuional invesmen, 2 Given he drasic plunge of he U.S. sock marke index on Sepember 28, 2008 ha reached 6.9%, hose auhors selec his dae as a break poin in order o divide he enire sample period ino he pre-crisis period and he during and pos-crisis period. 10

12 exchange marke volailiy, and he implied volailiy (VIX) on he S&P 500 index are found o drive up he condiional correlaions. Using an even sudy regression, Dooley and Huchison (2009) find ha over he period from January 1, 2007 o February 19, 2009, a range of financial and real economic news emanaing from he U.S. has saisically and economically large significan impacs on he 5-year CDS spreads on sovereign bonds of foureen emerging markes and ha several news evens uniformly move markes. The auhors address he decoupling recoupling opic by examining he changes in he srucural linkages beween he U.S. and emerging markes. Their resuls suppor he hypohesis of decoupling (signs of isolaion) beween emerging markes from early 2007 o summer However, hose auhors find re-coupling (linkage) among hose markes early fall 2008, confirming he resuls of he exising lieraure ha he recen GFC has severe repercussions on emerging markes. Similarly, Ahmad e al. (2013) apply he mulivariae DCC-GARCH model o examine he financial conagion effecs of he GIPSI counries, he Unied Saes, UK, Japan markes on he BRIICKS sock markes over he period During he Eurozone deb crisis period, he auhors show ha Ireland, Ialy and Spain appear o be he mos conagious o he BRIICKS markes, compared wih he conagion coming from Greece. Moreover, heir resuls also indicae ha Brazil, Russia, India, China and Souh Africa are srongly hi by he conagion shocks from he GIPSI sock markes. More imporanly, Bianconi e al. (2013) explore he behavior of he socks and bonds in he BRIC counries, and find ha he DCC esimaes beween he sock reurns, bond reurns and a U.S. financial sress indicaor have increased afer he Lehman Brohers collapse. 4 3 The acronym GIPSI refers o Greece, Ireland, Porugal, Spain and Ialy, while BRIICKS represens Brazil, Russia, India, Indonesia, China, Souh Korea and Souh Africa. 4 To undersand how volailiy spreads beween he BRICS counries, hose auhors use he hea map measure. For furher informaion, see he IMF repors (2008; 2009). 11

13 More recenly, Zhang e al. (2013) use he DCC decomposing mehod and show ha he 2007/2008 financial crisis causes a permanen change in he long-erm correlaions beween he BRICS and developed (U.S. and Europe) sock markes. They find srong evidence ha he recen GFC has changed he condiional correlaion relaionships beween he emerging BRICS and developed sock markes. More precisely, he sock markes in Brazil and Russia have sronger correlaions wih developed counries han wih India and China. Taking in consideraion he asymmeric effecs, he sudy of Gjika and Horváh (2013) adops he Asymmeric DCC (ADCC)-GARCH model o examine he ime-varying comovemens of he sock markes in he Cenral Europe, and finds evidence of srong correlaions among hose markes and beween hem and markes in he euro area counries. Applying he mulivariae consan condiional correlaions FIAPARCH model (CCC- FIAPARCH) for eigh naional sock indices namely FTSE 100 (UK), S&P 500 (US), DAX 30 (Germany), CAC 40 (France), Nikkei 225 (Japan), Srais Times (Singapore), Hang Seng (Hong Kong) and TSE 300 (Canada) wihin he period , Conrad e al. (2011) sugges ha he condiional volailiy of hese eigh indices ha are considered is bes modeled as a FIAPARCH process. Addiionally, boh he opimal fracional differencing LM parameer and he power ransformaion coefficien are remarkably similar across he eigh counries. Dimiriou e al. (2013) exend he mehodology of Conrad e al. (2011) o invesigae he conagion effecs of he GFC on he BRICS and he U.S. sock markes. They employ he mulivariae DCC-FIAPARCH model bu fail o find evidence of suppor for a conagion effec for mos of he BRICS markes during he early sages of he crisis. The linkage however re-emerged afer he Lehman Brohers bankrupcy, indicaing a shif in invesors risk appeie. The auhors show large dependence beween he BRICS and he Unied Saes from early 2009 onwards. The dependence is larger in he bullish han he bearish markes. 12

14 In all, our research is oally differen from he aforemenioned sudies. Indeed, all he cied works do no es he dynamic correlaion before and afer he Lehman Brohers collapse. Addiionally, hey do no consider he VaR forecasing analysis, which we ake ino accoun in his sudy and apply i o he BRICS markes. These are he major conribuions of our work. Our sudy complemens he relaed lieraure since we deal wih he issue of volailiy spillover effecs beween he BRICS and he U.S. sock markes, while accommodaing he long memory, volailiy power, volailiy asymmery, and srucural breaks properies. The repercussions of he onse of he GFC on he ime-varying condiional correlaions among he U.S. and BRICS sock markes are also considered in his analysis. We also go beyond his analysis by showing he impacs of he empirical resuls on he forecasing of porfolio marke risks for boh shor- and long posiions. Empirically, he aforemenioned individual models of he GARCH-based model family have some drawbacks as hey do no consider all sylized facs (as shown in he descripive saisics). For example, he bivariae EGARCH model, he DCC-GARCH model, he ADCC- GARCH model and he AR condiional jump inensiy model do no accoun for he long memory process in asse series. Concerning he CCC-FIAPRCH model, i assumes in his model ha he condiional correlaion is sable over ime, which is no realisic. In fac, he correlaions are of grea relevance for many of he common asks of financial managemen. Forecasing, asse allocaions and porfolio risk assessmens require esimaes of correlaions beween reurn series. If correlaions and volailiies are changing, hen porfolios should be rebalanced according o he mos recen informaion. Thus, building an opimal porfolio requires having a model wih dynamic correlaions. In he lieraure, here is unanimiy on he dynamic behavior of he condiional correlaions since he pioneering work of Engle (2002). The DCC model is hus proposed because he condiional correlaions are no consan bu are 13

15 ime-varying. As for he bivariae DCC-FIAPARCH model applied in our sudy, his model embraces he majoriy of sylized facs, hus is more comprehensive and realisic han he sandard GRACH models. I increases he flexibiliy of he condiional variance specificaions by allowing: (i) an asymmeric response of volailiy o posiive and negaive shocks (i.e., being able o race he leverage effec); (ii) he daa o deermine he power of reurns for which he predicable srucure in he volailiy paern is he sronges; (iii) he long memory o be accouned for in volailiy dependence, depending on he differencing parameer d; and (iv) he condiional correlaion o be ime-varying. These feaures in he volailiy processes of asse reurns have major implicaions for asse allocaions, opimal porfolio design, benefis of porfolio diversificaion, and Value a Risk (VaR) forecasing analysis. I is also worh noing ha he FIAPARCH model is very flexible since i ness wo major classes of ARCH-ype models: he APARCH and he FIGARCH models. For a robus analysis and a fresh new look a spillover effecs, he ime-varying condiional correlaions are assessed wihin a bivariae FIAPARCH model. This process is well suied o invesigae financial conagion since i focuses on he dynamics of he second order momen of financial ime-series and overcomes he heeroskedasiciy problem when measuring correlaions, as raised by Forbes and Rigobon (2002). 3. Economeric modeling framework This secion describes he empirical mehods implemened in his sudy. I begins wih he mulivariae DCC-FIAPARCH model, followed by he adjused version of he Inclán and Tiao (1994) s es for srucural breaks and ends wih he VaR forecasing analysis. 3.1 The mulivariae DCC-FIAPARCH model 14

16 We assume ha he reurn-generaing process can be described by an AR(1) model in which he dynamics of curren sock reurns are explained by heir lagged reurns. The AR (1) model is defined as follows Lr 1,, wih z h, (1) where, 0,, 1 and he innovaions disribued (i.i.d) process ~ N0,1 z are an independenly and idenically z. The condiional variance h is posiive wih probabiliy one and is a measurable funcion of he variance-covariance marix, 1. h The FIGARCH p, d, q model is expressed as follows 1 1 L 1 1 L L1 L d 2 1, (2) where,,, and d are he parameers o be esimaed, and 0 d 1. L denoes he lag operaor. The FIGARCH model provides a greaer flexibiliy for modeling he condiional variance and can disinguish beween he covariance saionary GARCH model for d 0 and he non-saionary IGARCH model when d 1, while for 0 d 1 he FIGARCH model is sufficienly flexible o allow an inermediae range of persisence. Tse (1998) exends he FIGARCH model ino FIAPARCH model by adding he funcion ( ) of he APARCH. This model is given by h / 2 d L 1 1 L L1 L, (3) where is he power erm of reurns for he predicable srucure in he volailiy persisence and 0 means ha negaive shocks give rise o higher volailiy han posiive shocks do. The FIAPARCH model is superior o he FIGARCH model in he sense ha i can deec he presence of boh asymmery and long memory in he condiional volailiy (Tse, 1998). 15

17 As we aemp o evaluae he volailiy spillovers across several BRICS and Unied Saes markes, a mulivariae FIAPARCH model needs o be se up. We decide o model he srucure of condiional correlaions by using he DCC approach of Engle (2002). The laer allows us o no only invesigae he ime-varying correlaions across he sample markes, bu also o insure he posiive definieness of he variance-covariance marix H under simple condiions imposed on specific parameers. The parameerizaion of a DCC-FIAPARCH model allows for direcly inferring he ime-varying correlaions beween he Unied Saes and BRICS sock markes and for dealing wih a relaively large number of variables in he sysem, wihou having a numerical convergence problem a he esimaion sage. In he general mulivariae case which we use, he variance-covariance marix of he residuals is defined as follows H D R D 1/ d 2 where D diag h h 1/ is he N 11 NN (4) N diagonal marix of condiional sandard deviaions of he residuals, which are obained from aking he square roo of he condiional variance modelled by an univariae AR(1)-FIAPARCH 1, d,1 model. Moreover, R is a marix of ime-varying condiional correlaions, which is given by diag Q ij, 1/ 2 1/ 2 Q diag Q R, (5) The N N symmeric posiive-definie marix Q depends on he squared sandardized residuals u i, i, / hii, and is own lagged value according o Eq. (6) as, he uncondiional variance-covariance marix ( Q ), _ ' 1 Q Q u u Q, wih 1, 2 0 and 12 1 (6) The N N variance-covariance marix of h is given by u i, i, / ii, 16

18 1 ui mu 1, j, m, 1 i j M, (7) m M 2 M 2 ui, m u j, m m1 M m1 where u, are he sandardized residuals calculaed from he residuals of he univariae AR(1)- i FIAPARCH 1, d,1 model. We can hen derive he correlaion coefficien in a bivariae case beween hose emerging and Unied Saes markes a ime from Eqs. (6)-(7) as follows ij, 1 k1 k2 ij k2ij, k 1 m M 2 M 2 ui, m u j, m m1 M 1 j, m j, m m1 u u, (8) The parameers of he DCC-FIAPARCH model are esimaed by using he quasimaximum likelihood (QML) mehod wih respec o he log-likelihood funcion in Eq. (9) and according o a wo-sep esimaion procedure. I 1, 2 T nlog2 2 2 T 1 log D D log C uc u uu 1 1 (9) In he firs sage, we fi he univariae FIAPARCH 1, d,1 model for each of he reurn series and obain he esimaes of h,. In he second sage, he esimaed parameers of he ii, firs sage are used o compue he dynamic condiional correlaions The adjused ICSS algorihm Several srucural break ess can be used o es for he sudden changes in financial marke volailiy. The Bai and Perron (2003), he CUSUM and he Inclán and Tiao (1994) ess are among he mos popular in his regard. For example, he Bai and Perron (2003) es discloses he exac number of breaks and heir corresponding daes of occurrence. This es 17

19 however has a size disorion problem when heeroscedasiciy is presen in he ime series daa (Arouri e al., 2012). The CUSUM es is unable o provide he full informaion on he exac number of break poins and heir corresponding daes. On he oher hand, he Inclán and Tiao (1994) s ICSS es assumes he Gaussian disribuion. Ineresingly, he ICSS algorihm allows one o deec boh he beginning and he ending of volailiy regimes for he series. We describe his es below. We suppose ha ~ N 0, h where For each inerval j, he variance is given by for j, h denoes he uncondiional variance in Eq. (1). j 1,2, NT, where T N is he oal number of variance changes or jumps in he T observaions. The se of hose poins of sudden variance shifs is given by 1 K1 K2 K N. The variance over he N T inervals is defined as follows: 2 0, 2 1, h 2 1 K K K 1 N T N T 1 K 2 T T, (10) In order o assess he number of changes or jumps in he variance and he ime poin for each variance shif, we apply he cumulaive sum of squares procedure. The cumulaive sum of he squared observaions from he sar of he series o he k h poin in ime is specified as follows: C k k, where k 1,2,, T, (11) 1 2 The D k saisic is given by D k Ck k, C where D 0 D T 0, (12) T T and C T is he sum of squared residuals from he whole sample period. 18

20 The D k saisic will oscillae around zero if no changes or jumps in he variance occur bu, if here is a leas one sudden change in he variance of he series, he D k saisic deviaes from zero. These criical values define he upper and lower limis for he drifs. If he maximum of he absolue value of he saisic D k is greaer han he criical value, hen he null hypohesis of no sudden change in variance is rejeced. In his case, by leing value a which hen max k Dk is reached, and if k T / 2Dk * k be he max exceeds he criical value, * k is aken as an esimae of he change or jump poin. The erm / 2 sandardize he disribuion. k T is used o The criical value of is he 95h percenile of he asympoic disribuion of T / 2 Dk max. Therefore, he upper and lower boundaries can be esablished a in he D k plo. A change or jump poin in variance is idenified if boundaries. However, if he series harbors muliple change poins, he Dk exceeds hese Dk funcion alone will no be sufficienly powerful o deec he change poins a differen inervals. To overcome his shorcoming, Inclán and Tiao (1994) amended an algorihm ha uses he funcion o search sysemaically for change poins a differen poins in he series. This algorihm works by evaluaing he D k funcion over differen ime periods, and hose periods are deermined by he breakpoins, which are hemselves idenified by he D k plo. In his sudy, he original IT (1994) es is no appropriae and may reveal spurious regressions because he financial ime-series under consideraion exhibi sylized facs (e.g., asymmery, lepokuriciy and condiional heeroscedasiciy). Given hese drawbacks, we use he adjused IT (AIT) es developed by Sanso e al. (2004), which is more flexible han he original IT es because i considers he fourh momen properies of he disribuions and he 19

21 condiional heeroscedasiciy. 5 The saisical hypohesis es is expressed as follows: he null hypohesis of a consan uncondiional variance of sock reurns is esed agains he alernaive of presence of srucural breaks in he uncondiional variance. The AIT empirical saisic, using a non-parameric adjusmen based on Barle and Kernel, is given by AIT sup T, (13) where i 0.5 k G k G 1 k i 1 k m ˆ C C, ˆ 1 ˆ 2 im ˆ 1 1 i 1 T, 0.5 k k T r ˆ r ˆ ˆ T and 2 ˆ T 1 CT. The parameer m refers o a lag 1 runcaion parameer and is seleced using he procedure in Newey and Wes (1994), and he oher variables are defined earlier. The asympoic disribuion of he AIT saisic under general condiions is given by sup l W * l, and he finie-sample criical values can be generaed by simulaions. 6 The 95 h percenile criical value for he asympoic disribuion of AIT saisic is Value a Risk (VaR) forecasing VaRs have become he popular ool for measuring porfolio marke risk. Several i sudies use his approach including Jorian (2007), Wu and Shieh (2007), Chrisoffersen (2009), Hammoudeh e al. (2011), and Hammoudeh e al. (2013). We esimae and compare he performance of he DCC-FIAPARCH model esimaed under he hree innovaion disribuion assumpions for he normal, Suden-, and skewed Suden - disribuions. A 5 The IT es is widely used by researchers o deec sudden changes in he volailiy of financial ime-series (see among ohers Aggrawal e al., 1999; Kang e al., 2011; Kumar and Maheswaran, 2013; Malik, 2003; Todea and Perescu, 2012; Liu e al., 2014). Fewer sudies have used he adjused IT es including Arouri e al. (2012) and Charles and Darné (2014), Ewing and Malik (2010) and Vivian and Wohar (2012), among ohers. 6 W*(l)=W(l) lw(1)is a Brownian bridge and W(l) is a Brownian moion. 20

22 one-day-ahead VaR is calculaed based on he resuls of he esimaed condiional volailiy models and he given disribuions. The VaRs for long and shor rading posiions can be specified for each of he hree disribuion assumpions. Under he normal disribuion hypohesis, hey are given by VaR VaR Where, long z (14) ˆ shor z ˆ, 1 (15) and ˆ denoe he condiional mean and variance forecased a ime 1, respecively, and z is he lef quanile a he % level for he normal disribuion, while z1 is he righ quanile a he % level for his disribuion. While under he Suden- disribuion hypohesis, he VaR is VaR VaR where, long s ˆ (16), shor 1 s ˆ (17) s is he lef quanile a % for he Suden- disribuion, while s is he righ quanile a % for his disribuion. Finally, under he skewed Suden- disribuion hypohesis, he VaR is 1 VaR VaR, long sks, k ˆ (18), shor 1 where sks,k sks, k ˆ (19) is he lef quanile a % for he Skewed Suden- disribuion, while sks 1,k is he righ quanile a % for his disribuion. 7 7 The value of he parameer measures he degree of fa ails in he VaR densiy. If 2, he densiy has fa ails. The value of k deermines he degree of asymmery in he VaR densiy. If k 1, he VaR for he long 21

23 We calculae he VaR a he pre-specified significance level of % and hen evaluae he performance by calculaing he failure rae for boh he lef and righ ails of he disribuion in he sample reurn series. The failure rae, denoed f, is defined as he raio of he number of imes in which posiive (negaive) reurns go beyond (below) he forecased VaR o he sample size. Following Gio and Lauren (2003), esing he accuracy of he model is equivalen o esing he hypohesis H H 0 1 : f. If he VaR model is correcly specified, : f hen when he failure rae is close o he pre-deermined VaR level %, i indicaes ha VaR is compued efficienly. The Kupiec (1995) LR es saisic is expressed as follows: LR 2ln Nx x 1 2ln 1 f ˆ Nx x f, (20) x where fˆ and x is he number of observaions exceeding he forecased VaR and N is N he sample size. 4. Daa and summary saisics 4.1. Daa Our analysis is based on he daily closing spo price index daa for he pool of he five BRICS markes namely Brazil, Russia, India, China, and Souh Africa, as well as for one major developed marke which is he S&P 500 represening he U.S. sock marke. Among he emerging markes, he growh of he BRICS sock markes is fashionable. The S&P 500 index is widely regarded as he bes single gauge of he U.S. large cap equiies. The index includes 500 leading companies and capures approximaely abou 80% of he coverage of he available marke capializaion. Thus, i is he mos represenaive index in rading posiions will be larger for he same condiional variance han he VaR for he shor rading posiions. When k 1, he opposie holds rue. 22

24 he U.S. and has dehroned he Dow Jones Indusrial Average. The S&P 500 also represens he mos liquid sock index for he larges 500 U.S. firms and is value reflecs he marke capializaion of companies included in he index. The S&P 500 deecs however broad movemens in sock markes during economic expansion/recession periods. I is paricularly ineresing o invesigae he cross-marke linkages beween he U.S. and BRICS sock markes. Krishnamurhy (2010) documens ha he adjusmen in he S&P 500 occurs wih a delay, compared o he burs of he crisis on he deb and morgages markes. 5,000 4,000 3,000 2,000 1, USA BRAZIL RUSSIA INDIA CHINA S. AFRICA Fig. 1. Time-pahs of he daily indices for he U.S. and BRICS sock markes The sudy spans he period from Sepember 29, 1997 o Ocober 14, The daa for BRICS and US marke indices are obained from he MSCI daabase. These indices are quoed in U.S. dollars in order o have conformiy and o avoid he effecs of local inflaion and naional currency flucuaions on he indexes, as indicaed by Bekaer and Harvey (1995) and Dimiriou e al. (2013). 23

25 Figure 1 illusraes he dynamics of he daily U.S. and BRICS indices over he sample period. The red doed line indicaes he break dae Sepember 15, 2008 which corresponds o he Lehman Brohers collapse. This figure displays a significan decline in he S&P 500 index as well as in each BRICS sock index since he bankrupcy of he Lehman Brohers. This dae is seleced as break poin of he GFC Summary saisics We calculae he coninuously compounded daily reurns by aking he difference in he logarihms of wo consecuive prices of a series. The descripive saisics and he resuls of he saisical ess of he daily reurns for he BRICS and he U.S. markes are presened in Table 1. Table 1 Saisical properies: daily reurns of U.S. and BRICS sock indices. U.S. Brazil Russia India China S. Africa Mean Max Min Sd. dev Skewness Kurosis Jarque-Bera Q(20) Q 2 (20) ADF PP KPSS ARCH-LM (10) Noes: Q(20) refers o he Ljung-Box es for auocorrelaion, respecively. ADF, PP and KPSS are he empirical saisics of he Augmened Dickey-Fuller (1979), and he Phillips-Perron (1988) uni roo ess, and he Kwiakowski e al. (1992) saionariy es, respecively. ARCH-LM(10) es of Engle (1982) is o check he presence of ARCH effecs. + denoes he rejecion of he null hypoheses of normaliy, no auocorrelaion, uni roo, non-saionariy, and condiional homoscedasiciy a he 1% significance level. The resuls reveal ha he highes average reurn is for he Indian index, while volailiy (as measured by he sandard deviaion) is he highes for he Russian index, hereby indicaing ha invesmen in he Russian sock marke may prove o be more risky han in he 8 More deails are provided in Subsecion

26 oher BRICS markes. Russia is he larges borrower on he global deb marke and is revenues from is hydrocarbon expors accoun for 45% of is governmen budge. Conversely, he U.S. marke is found o have he lowes volailiy. The skewness and kurosis resuls, along wih he Jarque-Bera es for normaliy, indicae ha he daily reurns for boh he BRICS and he U.S. markes are asymmeric, faailed and high-peaked han he Gaussian disribuion. These resuls are consisen wih he GARCH effecs. Moreover, based on he ARCH effecs of Engle (1982), we srongly rejec he null hypohesis of no ARCH effecs. As shown in Table 1, he resuls of he Ljung-Box es saisics of he residuals, Q(20), and he squared residuals, Q 2 (20), rejec he null hypohesis of no serial correlaion. The reurn series for all considered markes are also found o be saionary based on wo uni roo ess (i.e., he ADF and PP) and a saionariy es (KPSS). Table 2 Uncondiional correlaions of sample reurns among he U.S. and BRICS sock reurns U.S. Brazil Russia India China S. Africa U.S Brazil Russia India China S. Africa To jusify he use of FIAPARCH model, we carry ou he Pearson correlaions, he pairwise Granger causaliy ess beween he U.S. and BRICS marke reurns and he convenional long memory (LM) ess for hese reurns. Furhermore, he Pearson correlaion resuls which are provided in Table 2 show evidence of low correlaions beween he BRICS and he U.S. markes. The lowes correlaion coefficiens are clearly observed for China and he Unied Saes. For a while, China did no allow foreigners o inves in is A-shares. To examine he presence of he LM propery for he differen BRICS and he Unied Saes sock markes, we run a baery of LM ess on hose markes. Indeed, we consider four 25

27 kinds of procedures of he LM es, namely he Hurs-Mandelbro R/S es, Lo s modified R/S es, he Gaussian semi-parameric (GSP) es of Robinson and Henry (1999), and he GPH es of Geweke and Porer-Hudak (1983). 9 Table 3 summarizes he resuls of he LM ess for all reurn and squared reurn series (as a proxy variable of volailiy) for he U.S. and BRICS markes, respecively. For he reurn series, he resuls rejec evidence of he LM propery. The evidence for he squared reurns is oally differen from hose of he reurns. In fac, he LM propery is found o be highly significan (a he 1% level of significance) for all squared reurn series, whaever he applied LM ess under consideraion are. Overall, he squared reurns may be governed by a fracionally inegraed model. The FIAPARCH specificaion is hus suiable for capuring hese sylized facs (asymmery, long memory, heeroscedasiciy). 9 In he case of he Hurs-Mandelbro R/S and Lo s modified R/S ess, he Hurs exponen (H) is calculaed using he R/S saisic. If H 0. 5, hen his exponen indicaes a random walk process which means shor memory. If 0 H 0. 5, i suggess ha he series is ani-persisen process (i.e., a long-range negaive dependence) bu if 0.5 H 1, he series is a persisen process. To es for he saisical significance of he H esimaes, we use he -es saisic, where he null hypohesis is H : H 0. 5 and he alernaive hypohesis is 0 H : H 0.5. On he oher hand, boh he GSP and GPH mehods es he null hypohesis H : d 0 versus 1 0 H 1 : d 0 using he -es saisic. If d 0, he series is a random walk or has a shor-memory process; if 0.5 d 0, i is an ani-persisen process; if 0 d 0. 5, i has a long memory; and if 0.5 d 1, i is non-saionary. In order o ensure he robusness of he GSP and GPH ess, his paper uses several choices of he low-frequency ordinaes. These choices regarding he number of low-frequency ordinaes, n, vary wih he sample size T and are esablished in erms of n T wih = {0.45, 0.50, 0.55,and 0.6}. 26

28 Table 3 Long memory ess for reurns and squared reurns of he U.S. and BRICS markes Reurns Squared Reurns U.S. Brazil Russia India China S. Africa U.S. Brazil Russia India China S. Africa Panel A: Hurs-Mandelbro R/S es Tes saisic *** *** *** *** *** *** Panel B: Lo s modified R/S es Tes saisic ( q 1) *** *** *** *** *** *** Tes saisic ( q 5) *** *** *** *** *** *** Panel C: GSP es d m T / *** *** *** *** *** *** *** (0.0156) (0.0156) (0.0156) (0.0156) (0.0156) (0.0156) (0.0156) (0.0156) (0.0156) (0.0156) (0.0156) (0.0156) d m T / *** *** *** *** *** *** *** *** (0.0313) (0.0313) (0.0313) (0.0313) (0.0313) (0.0313) (0.0313) (0.0313) (0.0313) (0.0313) (0.0313) (0.0313) d m T / *** *** *** *** *** *** (0.0443) (0.0443) (0.0443) (0.0443) (0.0443) (0.0443) (0.0443) (0.0443) (0.0443) (0.0443) (0.0443) (0.0443) d m T / *** *** *** *** *** *** (0.0629) (0.0629) (0.0629) (0.0629) (0.0629) (0.0629) (0.0625) (0.0629) (0.0629) (0.0629) (0.0629) (0.0629) Panel D: GPH es 0.45 d m T *** *** *** *** *** (0.1142) (0.1142) (0.1142) (0.1142) (0.1142) (0.1142) (0.1142) (0.1142) (0.1142) (0.1172) (0.1142) (0.1142) 0.5 d m T *** *** *** *** *** *** (0.0893) (0.0893) (0.0893) (0.0893) (0.0893) (0.0893) (0.0893) (0.0893) (0.0893) (0.0909) (0.0899) (0.0901) 0.55 d m T *** *** *** *** *** *** (0.0710) (0.0710) (0.0710) (0.0710) (0.0710) (0.0710) (0.0721) (0.0710) (0.0710) (0.0726) (0.0711) (0.0711) 0.6 d m T *** *** *** *** *** *** (0.0564) (0.0564) (0.0564) (0.0564) (0.0564) (0.0564) (0.0582) (0.0565) (0.0564) (0.0569) (0.0564) (0.0570) Noes: The criical values of he Hurs-Mandelbro R/S es and Lo s modified R/S analysis are a he 1% significance level, respecively. The numbers in parenheses are he sandard deviaion of he esimaes. q in Lo s modified R/S es is he number of lag of auocorrelaion. m denoes he bandwidh for he GSP and he GPH ess. The aserisk *** indicaes he significance level a 1%. 27

29 Table 4 Esimaion of he bivariae AR(1)-FIAPARCH(1,d,1)-DCC model (U.S.-BRICS) U.S.-Brazil U.S.-Russia U.S.-India U.S.-China U.S.-Souh Africa U.S. Brazil U.S. Russia U.S. India U.S. China U.S. S. Africa Panel A: Esimaes of he AR(1)-FIAPARCH model Cons.(M) (0.0001) (0.0003) (0.0001) (0.0003) (0.0001) ** (0.0003) (0.0001) (0.0003) (0.0002) (0.0003) AR(1) ** (0.0149) *** (0.0178) ** (0.0149) *** (0.0170) *** (0.0149) *** (0.0194) ** (0.0149) *** (0.0161) ** (0.0149) *** (0.0163) Cons. (V) (0.0001) (0.0003) (0.0002) (0.0002) (0.0002) (0.0002) (0.0002) (0.0002) (0.0002) (0.0006) d-figarch *** (0.0628) *** (0.0482) *** (0.0628) *** (0.0632) *** (0.0628) *** (0.1010) *** (0.0628) *** (0.0651) *** (0.0628) *** (0.0557) Arch (0.0991) (0.0873) (0.0992) (0.0778) (0.0992) *** (0.0449) (0.0992) *** (0.0560) (0.0992) *** (0.0691) Garch *** (0.1469) *** (0.0980) *** (0.1469) *** (0.1051) *** (0.1469) *** (0.0831) *** (0.1469) *** (0.0860) *** (0.1469) *** (0.0874) APARCH *** *** *** *** *** *** *** *** *** *** (Gamma) (0.0028) (0.1745) APARCH *** *** (Dela) (0.1027) (0.1328) Panel B: Esimaes of he DCC model Average *** CORij (0.0616) k *** (0.0054) k *** (0.0070) Panel C: Diagnosic Tess Q(20) [0.0163] [0.1260] (0.0027) *** (0.1027) *** (0.0250) *** (0.0018) *** (0.0019) (0.0623) *** (0.0910) (0.0027) *** (0.1027) *** (0.0501) *** (0.0013) *** (0.0017) (0.1436) *** (0.1288) (0.0027) *** (0.1028) *** (0.0159) (0.0018) *** (0.0024) (0.0616) *** (0.1200) (0.0027) *** (0.1027) *** (0.1235) *** (0.0018) *** (0.0020) (0.1486) *** (0.1511) [0.0030] [0.5325] [0.0312] [0.0134] [0.0085] [0.0182] [0.0025] [0.4591] Q 2 (20) [0.4355] [0.8306] [0.8116] [0.8966] [0.3170] [0.9751] [0.3550] [0.8172] [0.6247] [0.7172] Noes: Q(20) and Q 2 (20) are he Ljung-Box es saisics applied o he sandard residuals and he squared sandardized residuals, respecively. The aserisks ** and *** indicae significance a he 5% and 1% levels, respecively. The p-values are in brackes and he sandard errors are in parenheses. 28