Sensitivity, Persistence and Asymmetric Effects in International Stock Market Volatility during the Global Financial Crisis

Transcription

1 REVISTA DE MÉTODOS CUANTITATIVOS PARA LA ECONOMÍA Y LA EMPRESA (9). Págnas Juno de 5. ISSN: X. D.L: SE URL: hp:// Sensvy, Perssence and Asymmerc Effecs n Inernaonal Sock Marke Volaly durng he Global Fnancal Crss Gabrel, Víor UDI - Research Un for Inland Developmen Polyechnc Insue of Guarda (Porugal) E-mal: vgab@pg.p ABSTRACT Fnancal marke volaly s an mporan elemen when seng up porfolo managemen sraeges, opon prcng and marke regulaon. The Subprme crss affeced all markes around he world. Daly daa of welve sock ndexes for he perod of Ocober 999 o June are suded usng basc GARCH ype models. The daa were hen dvded no hree dfferen sub-perods o allow he behavor of sock marke n dfferen sub-perods o be nvesgaed. The followng sub-perods are denfed: Do-Com crss, Que and Subprme crss. Ths paper revealed ha he Subprme crss urned ou o have bgger mpac on sock marke volaly, namely a sensvy, perssence and asymmerc effecs. Keywords: global fnancal crss; nernaonal sock markes; GARCH models; condonal volaly. JEL classfcaon: G; G5. MSC: 9G8; 6M; 6P. Arículo recbdo el 6 de juno de 4 y acepado el de juno de 5. 4

2 Efecos de sensbldad, perssenca y asmería en la volaldad de los mercados bursáles nernaconales en el enorno de la crss fnancera global RESUMEN La volaldad de los mercados fnanceros es un mporane elemeno para la esraega de careras de nversón y para la regulacón de los mercados. La crss subprme afecó a los mercados bursáles mundales. Para realzar ese esudo, fueron omados daos daros relavos a doce mercados bursáles, desde el 4 de ocubre de 999 hasa el 3 de juno de. El período de la muesra consderado ha sdo subdvddo en res subperíodos dsnos: crss de las empresas ecnológcas, ranqulo y crss fnancera global. Para esudar la volaldad de los mercados bursáles, se ha recurrdo a modelos de po GARCH. Los resulados demuesran la nfluenca de la crss fnancera global en el comporameno de la volaldad del mercado bursál, sobre odo en cuano a la sensbldad, la perssenca y la asmería. Palabras clave: crss fnancera global; mercados bursáles; modelos GARCH; volaldad condconal. Clasfcacón JEL: G; G5. MSC: 9G8; 6M; 6P. 43

3 . INTRODUCTION Accordng o Claessens e al. (), Bekaer e al. () and Ln and Trechel (), he curren fnancal crss s he frs global crss and he mos severe snce he Grea Depresson. Alhough he crss had s orgn n he Uned Saes, parcularly n subprme cred, would be ransmed o oher economc secors as well as oher developed and emergng economes. The quanfcaon of rsk, as a fnancal varable, has represened a major challenge for researchers, regulaors and fnancal professonals. In modern fnance heory, Markowz (95) consders he volaly of asse s reurns as a measure of rsk. Accordng o Ln (996), he rsk s usually assocaed wh volaly. When he volaly of a fnancal asse rses, so does he rsk. However, volaly measures only he magnude, bu no he drecon. The fnancal markes volaly s an mporan ndcaor of he dynamc flucuaons n asse prces (Raja and Selvam, ). Undersandng sock markes volaly s also an mporan elemen o calculae he cos of capal and o suppor nvesmen decsons. Volaly s synonymous wh rsk. Bollerslev e al. (99) argue ha volaly s a key varable for a large majory of fnancal nsrumens, playng a cenral role n many areas of fnance. Bala and Premarane (3) consder ha subsanal changes n fnancal marke volaly can cause sgnfcan negave effecs on rsk averson, and make markes more unsable, ncreasng he uncerany for marke players, parcularly n her predcons and her ncome. Usually, fnancal seres reveal some engmac emprcal regulary. These regulares are called sylzed facs and correspond o observaons so conssen, confrmed n many conexs, markes and nsrumens, whch are evenually acceped as ruh (Con, and 5). Thus, he sylzed facs are based on a common denomnaor, whch resuls from he properes observed n mulple sudes, abou markes and nsrumens. Due o s general naure, he sylzed facs reveal a qualave dmenson, bu no accurae enough o dsngush beween dfferen paramerc models (Coolen, 4; Dng e al., 993). Several sudes have confrmed some of he mos common sylzed facs, ncludng volaly cluserng and asymmerc effec (Brock and de Lma, 996; Campbell e al., 996; Mandelbro and Hudson, 6). The frs s relaed o auocorrelaon. Accordng o Mandelbro (963) and Engle (98), f volaly s hgh a a gven momen, ends o connue hgh n he nex perod. If volaly s low n a gven momen, ends o connue low n he nex perods, because he new nformaon ha arrves o he marke s correlaed n me. For s par, he asymmerc effec resuls from he dverse reacon of volaly o he arrval of news n he marke, reflecng he effec of good and bad news on volaly, whch resuls n a negave correlaon beween lagged reurns and volaly. The asymmerc effec was frs observed by Black (976). 44

4 Numerous sudes have nvesgaed daly volaly, parcularly volaly cluserng and asymmerc effec, usng auoregressve condonal heeroskedascy models (Schwer, 998; Chaudhur and Klaassen, ; Paev and Kanaryan, 3; Ramlall, ; Chong, ; Angabn and Wasuzzaman, ). In hs work condonal heeroskedascy models are appled, n order o analyze he mpac of global fnancal crss on condonal volaly, sensvy, perssence and asymmerc effec n he nernaonal sock markes. Ths sudy s srucured as follows: Secon presens nformaon abou he daa and he mehodology chosen, Secon 3 shows he emprcal resuls, whle Secon 4 summarzes he man conclusons.. DATA AND METHODOLOGY In order o analyze he evoluon of daly volaly sock markes, welve ndces were seleced, evolvng European, non-european, developed and emergng ndces, accordng o he Morgan Sanley Capal Inernaonal classfcaon, represenng abou 6% of world sock marke capalzaon, n, as can be seen n Table. The se of developed markes ncluded European and non-european markes. From he European connen, Germany (DAX 3), France (CAC 4), UK (FTSE ), Span (IBEX 35), Ireland (ISEQ Overall), Greece (ATG) and Porugal (PSI ) were seleced. The se of non- European developed markes ncluded he U.S. (Dow Jones), Japan (Nkke 5) and Hong Kong (Hang-Seng). Addonally, Brazl (Bovespa) and Inda (Sensex) were seleced as emergng sock markes. We beleve ha he use of a large se of sock marke ndexes (emergng and developed), n dfferen regons, wh dfferen capalzaon levels, ncludng some of he major sock markes of he world and he European markes under soveregn deb suppor program, helps o undersand he consequences of he global fnancal crss. Table : Marke capalzaon as a percenage of global capalzaon USA UK France Japan Span Brazl Germany Porugal Greece Hong-Kong Índa Ireland 3,5 5,5 3,4 7,3,,8,5,, 4,8,9,6 Source: World Bank The daa used n hs sudy were obaned from EconoSas and cover he perod from Ocober 4 h 999 o June 3 h, whch was subdvded no hree sub-perods. To analyze he Do-Com crss, he perod from /4/999 o 3/3/3 was consdered. The laes epsode of crss, whch 45

5 began n he U.S. wh he subprme cred, consdered he day of 8//7 as he begnnng of he crss. For many auhors, ncludng Hora e al. (8), Toussan (8) and Lquane e al. (), hs day marked he begnnng of subprme crss, as a resul of he rsng raes of Cred Defaul Swaps. In addon o he sub-perods of crss, a hrd sub-perod was sll consdered, desgnaed as que subperod, from 4//3 o 7/3/7, correspondng o a general ncrease of global sock ndces. The me seres n he level form were ransformed no seres of reurns hrough he applcaon of he expresson ( P ) ln P and, respecvely., where P and P represen he closng values of a parcular ndex n days To esmae he condonal volaly, GARCH (,) and EGARCH (,) models were consdered. GARCH models were proposed by Bollerslev (986) and hey are conssen wh he phenomenon of volaly cluserng. where: The GARCH (p, q) specfcaon s gven by: y = ϕ z + ε () ε = σ µ () q p jε j + j= = σ = + β σ (3) (,..., q); (4) j j = > ; j ( j =,..., q); β ( =,..., p); j + β < ~ N(,); ε τ N(, σ ); = { ε ε } q j= p = µ Cov( µ ; ε ) = ; τ,,... s he se of he avalable nformaon a me, z s a vecor of explanaory varables, q s he order of he ARCH process and p s he order of he GARCH process, ε corresponds o he vecor of esmaed resduals; j represens he shor-erm perssence shocks (ARCH effec) and β represens he long-erm perssence shocks. c >, j ( j =,..., q) β = p are he basc condons for he condonal varance o be posve ( σ ). and ( ),..., > The expresson q j= p + β < s he saonary condon of he GARCH models. Verfyng j = hs condon ensures ha condonal varance s no fne, whle he condonal volaly vares n me, beng posve and saonary. Accordng o Alexander (8), n a GARCH (,) model, he parameer measures he condonal volaly reacon o unexpeced marke shocks. When hs parameer s relavely hgh (above.), volaly s very sensve o marke evens. The volaly 46

6 perssence s consdered usually as he sum of and β parameers. An alernave measure o evaluae perssence s volaly half-lfe. Engle and Paon () defne half-lfe as he medan me spen by volaly o move halfway, back o s uncondonal mean. Ths parameer provdes a more approprae descrpon of perssence, represenng he longes perod n whch he marke shock wll de. In a GARCH model, he half-lfe marke shock s gven by (,5) ln( + β ) 47 ln. To accommodae he asymmerc effec, Nelson (99) proposed he EGARCH model, also called exponenal GARCH. In hs model, he condonal varance s descrbed by an asymmerc funcon of pas values of ε. where: k The EGARCH (p, q) model specfcaon s gven by: y = ϕ z + ε (5) ε = σ µ (6) q r p ε ε k log( σ ) = c + + γ k + β j log( σ j ) (7) σ σ = k= k γ measures he asymmerc effec; ~ N(,); { ε ε } j= µ Cov( ; ε ) = ; τ =,,... s he se of nformaon avalable a he me µ ε τ N(, σ );, z s a vecor of explanaory varables, q s he order of he ARCH process and p s he order of he GARCH process, ε s he vecor of esmaed resduals. Accordng o (McAleer, 5), f β <, he condonal varance s fne. As saed above, n he EGARCH (,) model, he asymmerc effec s capured by coeffcen γ. The negave sgn of hs coeffcen ndcaes he exsence of an asymmerc effec; ha s, ndcaes a negave relaonshp beween reurn and volaly. When he coeffcen s negave, he posve shocks produce less pronounced volaly han negave shocks of equal sze. Ths has been deeced n several emprcal sudes, concludng ha small nvesors are panckng abou he mpac of negave shocks and leave her marke posons n order o avod more pronounced losses. Consequenly, here s an ncrease n volaly. To verfy he correc specfcaon of he esmaed models, he Ljung-Box and ARCH-LM ess were performed. Under he null hypohess, H : = ( ε ) = = ρm = ( ε ) = assumes ha quadrac resdues are no correlaed. ( ) beween ε and ε. u σ ρ L, he Ljung-Box es ρ = concerns he correlaon coeffcen ε ε = concerns he sandardzed quadrac resdues. The Ljung-Box

7 m ˆ ρ sasc s gven by ( ) ( ˆ ε ) Q = n n + parameers. ~ χ n = ( m k ), where k represens he number of esmaed The ARCH-LM es s consdered under he null hypohess H : = = L =, where q s q he order of he process. The es sasc s gven by NR, followng an asympoc dsrbuon of χ, wh q degrees of freedom, where R s he deermnaon coeffcen and N he number of observaons. To conclude f sock markes volaly has ncreased, wo ypes of ess are appled. The frs nvolves he equaly of means, usng he -es and he analyss of varance wh one facor; he second es, he equaly of varances by applyng he F sasc and he Barle es. These ess are presened brefly below. Tess for equaly of means The -es s calculaed based on gven by: = ( x x ) ( µ µ ) S n S + n The es s compared wh Suden- dsrbuon, where he number of degrees of freedom s S S + n n v = ( ) ( ) (9) S S + n n n n The es for equaly of means, by analyss of varance wh one facor, allows o evaluae he sascal sgnfcance of he dfference beween means, for a specfc probably level, nvolvng he calculaon of he F sasc, whch s based on he varably whn and among sub-perods. where: The es sasc s gven by: F = MSE MSD SSE MSE = : s he average sum of squares beween sub-perods; k (8) 48

8 SSD MSD = : s he average sum of squares whn sub-perods. N k whereas SSE s he sum of squares beween sub-perods, SSD s he sum of squares whn subperods, k s he number of sub-perods and N s he oal number of observaons. In boh ess, he null hypoheses and alernave hypoheses are: H H : µ = µ H : µ = µ GFC Do Com and GFC Que : µ µ H : µ µ a GFC Do Com and a GFC Que Tes for equal varances The F es for equaly of varances s gven by S F = ~ FT hgher ; T lower, S hgher lower where S hgher( lower ) s he esmaed varance of he sub-perod wh hgher (lower) value. The Barle's es s used o es equaly/homogeney of varances among groups versus he alernave of varances beng unequal, for a leas wo groups. The es sasc s gven by: where: q =,36 () c q = k ( N k) S ( n ) log log S () p k c = + ( ) ( ) ( ) n N k k () 3 = S p = k = ( n ) N k S (3) where n s he sample sze of he p-h group, sample sze and S p s he pooled varance. In boh ess, he null hypoheses and he alernave hypoheses are: H H : µ = µ S s he sample varance of he p-h group, N s he GFC Do Com and GFC Que : µ µ 49 H : µ = µ H : µ µ a GFC Do Com and a GFC Que

9 3. EMPIRICAL RESULTS Fgure shows he daly reurns seres n he full perod. The vsual analyss ndcaes he endency for volaly cluserng n ceran perods. The second sub-perod was relavely que. However, he remanng sub-perods showed grea urbulence and volaly, suggesng volaly cluserng, as we wll see laer on. The year of 8 revealed he hghes volaly concenraon as he resul of he emergence of he global fnancal crss. Fgure. Evoluon of daly reurns ATG_CLOSE_R BOV_CLOSE_R CAC_CLOSE_R DAX_CLOSE_R DJ_CLOSE_R FTSE_CLOSE_R HANG_SENG_CLOSE_R IBEX_CLOSE_R ISEQ_CLOSE_R NIKKEI_CLOSE_R PSI_CLOSE_R SENSEX_CLOSE_R 5

10 Table presens he descrpve sascs of condonal volaly for he hree sub-perods and for he welve markes, generaed by he GARCH (,) models. The values shown n Table allow he concluson ha he esmaed condonal volaly reveals sgns of devaon from normaly assumpon, akng no accoun he skewness and kuross coeffcens. In order o confrm he appropraeness of he adjusmen o he normal dsrbuon, n each of he sub-perods and for he welve seres, he Jarque-Bera es was consdered. The sascs of hs es s gven n Table. Based on he resuls, we conclude ha all he seres are sascally sgnfcan a a sgnfcance level of %, clearly rejecng he hypohess of normaly. In Do-Com sub-perod, he BOV ndex showed he hghes average condonal volaly, hree mes hgher han ISEQ and PSI ndces, as he leas volale markes. For s par, he DAX ndex showed he greaes degree of varably, measured by he sandard devaon. In he que sub-perod, Sensex and BOV ndces showed hgher average of condonal volaly. The remanng markes showed lower levels of volaly. In eher case, he recorded values were below hose seen durng Do-Com sub-perod. Regardng condonal volaly varably, he Sensex ndex showed he greaes varably. Conversely, DJ and PSI were he leas varable. Durng global fnancal crss sub-perod, he dfferences n volaly levels of varous ndces were no as pronounced as n he prevous sub-perods. HANG-SENG ndex recorded he hghes average condonal volaly, followed by ATG and ISEQ ndces. For s par, DJ and PSI ndces were he leas volale. Some esmaes are somehow unexpeced. Ths s wha happens wh he Poruguese marke, whch has regsered he lowes volaly beween all he markes, alhough s a small developed marke, and especally for beng under foregn fnancal asssance snce. Fgure shows he graphcal evoluon of he condonal volaly of each of he welve daly ndces n he full perod, esmaed accordng o GARCH (,) and EGARCH (,) specfcaons. Durng Do-Com and global fnancal crss sub-perods, he welve ndces recorded hgher levels of volaly (see Fgure ). Ths s relaed o a se of evens ha led o a hgh volaly n he fnancal markes. In he frs sub-perod, some relevan marke evens (as he bursng of he Inerne bubble, he errors aacks n Sepember and he accounng scandals a Enron and WorldCom, among ohers) dsruped markes. In he las sub-perod, here was a sequence of evens dsurbng he envronmen of fnancal markes, as he subprme cred crss and he soveregn deb crss. In he que sub-perod, he markes showed more moderae volaly levels, excep for he Sensex ndex. 5

11 Table. Descrpve sascs from condonal volaly esmaes n each sub-perod. Do-Com Que G.F.C ATG BOV CAC DAX DJ FTSE HANG IBEX ISEQ NIKKEI PSI SENSEX Mean,3,4,33,39,9,,6,9,6,3,5,3 Medan,3,36,4,6,5,5,,4,3,,, Maxmum,8,59,33,78,75,,89,4,57,8,88,8 Mnmum,7,8,8,7,4,4,7,5,3,6,,7 Sd. Dev.,6,6,6,33,,8,5,8,,,,6 Skewness,843,976,789,63,9477,433,865,67,8536,4875,5563,4363 Kuross 8,6393,8999 5, ,4 7,3387 8, , ,36 6,94 5,768,466,8377 Jarque-Bera (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) Mean,3,8,,4,6,7,,9,9,5,5, Medan,,5,8,,5,5,9,7,7,,4,5 Maxmum,68,79,94,9,9,47,8,54,5,45,4,98 Mnmum,4,4,4,4,3,,4,4,3,5,,7 Sd. Dev.,8,,9,3,3,5,4,6,6,8,3,4 Skewness,953,6766 4,8389 4,77,96 3,778,5398,9467 3,543,378, ,5438 Kuross 4,9383 6,35 34,3499 6,888 6,565, ,354 6,5838 5,43 4,54 8, ,4548 Jarque-Bera (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) Mean,45,44,33,9,4,6,46,36,45,35,4,38 Medan,35,3,9,6,3,4,5,,8,,3,3 Maxmum,76,397,83,45,43,63,473,33,4,4,7,383 Mnmum,5,3,7,5,3,4,6,6,5,7,4,7 Sd. Dev.,37,53,4,36,37,36,58,45,5,5,34,4 Skewness, ,795 3,373 3, ,4533 3, ,638 3,494 3,4559 4,3598 3,987 3,33 Kuross 3,7556 8,79 5,34 5,5876 5,799 9, ,4766 6,53 7, ,898,5388 8,43735 Jarque-Bera (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) (,) 5

12 Fgure. Evoluon of condonal volaly consderng GARCH and EGARCH models ATG_GARCH ATG_EGARCH BOV_GARCH BOV_EGARCH CAC_GARCH CAC_EGARCH DAX_GARCH DAX_EGARCH DJ_GARCH DJ_EGARCH FTSE_GARCH FTSE_EGARCH HANG_GARCH HANG_EGARCH IBEX_GARCH IBEX_EGARCH 53

13 ISEQ_GARCH ISEQ_EGARCH NIKKEI_GARCH NIKKEI_EGARCH PSI_GARCH PSI_EGARCH SENSEX_GARCH SENSEX_EGARCH Table 3 presens he GARCH (,) esmaon resuls. All he coeffcens of he esmaed models showed he expeced sgnals, excep for β parameer for BOV ndex durng he Do-Com subperod, whch has a negave coeffcen (-.538). The remanng coeffcens are non-negave, ensurng ha he condonal varance s posve. Consderng he varance equaon coeffcens ( and β ),, only he Bovespa coeffcens, and β, n Do-Com sub-perod, are no sascally sgnfcan, a a sgnfcance level of %. Boh he DAX coeffcen ( ) n Do-com sub-perod and he HANG-SENG ndex n Do-Com and Global Fnancal Crss sub-perods, were sgnfcan a a sgnfcance level of %. The remanng coeffcens proved o be sgnfcan a a sgnfcance level of 5%, alhough mos were for he mos demandng level (%). Ths reveals he exsence of ARCH and GARCH effecs. Moreover, he sum of GARCH coeffcens s less han one for all he ndces and for all he sub-perods, whereby he volaly process s saonary. 54

14 Table 3. Esmaon resuls for he GARCH (,) model ATG BOV CAC Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC 3,9E-5 3,E-6 9,3E-6 6,5E-4,6E-5 3,64E-6 5,77E-6,69E-6 6,54E-6 (,) (,) (,4) (,) (,) (,3) (,8) (,) (,4),9,7,5,38,44,77,7,5,6 (,) (,) (,) (,8) (,) (,) (,) (,) (,),64,9,879 -,538,99,93,9,95,866 β (,) (,) (,) (,6) (,) (,) (,) (,) (,) + β,87,97,984 -,5,953,99,985,966,98 DAX DJ FTSE Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC 5,5E-6,75E-6 4,E-6,3E-5,8E-6,36E-6 5,4E-6,7E-6 3,3E-6 (,5) (,) (,) (,) (,7) (,) (,6) (,) (,),93,63,,5,3,3,,75, (,) (,) (,) (,) (,4) (,) (,) (,) (,),897,99,885,837,99,887,856,88,885 β (,) (,) (,) (,) (,) (,) (,) (,) (,) + β,99,97,986,94,96,99,979,955,987 HANG-SENG IBEX ISEQ Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC 5,74E-6 8,8E-7,8E-6 7,57E-6 5,8E-6,3E-5,58E-5 3,39E-6 5,89E-6 (,8) (,5) (,7) (,45) (,) (,) (,) (,) (,9),68,7,,74,86,34,,78, (,) (,) (,) (,) (,) (,) (,) (,) (,),93,963,893,9,839,84,78,88,87 β (,) (,) (,) (,) (,) (,) (,) (,) (,) + β,98,99,995,975,95,975,895,958,99 NIKKEI PSI SENSEX Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC,6E-5,E-6,4E-5,98E-5,7E-6 8,E-6,9E-5,4E-5,47E-6 (,) (,) (,) (,) (,) (,) (,) (,) (,7),76,6,54,7,47,69,47,5, (,) (,) (,) (,) (,) (,) (,) (,) (,),87,9,87,697,9,8,789,79,897 β (,) (,) (,) (,) (,) (,) (,) (,) (,) + β,948,984,97,867,969,97,936,94,999 Noe: Ths able presens he GARCH (.) model esmaons, appled o daly reurns of he welve ndces suded n he hree sub-perods. All esmaes are based on Maxmum Lkelhood esmaon. In order o es auocorrelaon, he Box-Ljung es (see Table 4) was appled. The resuls ndcae ha, for a sgnfcance level of 5%, here s a srong evdence of accepng he null hypohess, 55

15 concludng ha he sandardzed resdues are no correlaed. In all he cases, he Ljung-Box es resuls reveal ha he p-values are above he sgnfcance level of 5%. Table 4. Ljung-Box and LM ess resuls o GARCH (,) resduals LB: Q ( ) LM es: F ( ) LB: Q ( ) LM es: F ( ) LB: Q ( ) LM es: F ( ) LB: Q ( ) LM es: F ( ) ATG BOV CAC Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC 3,39 5,559,658 86,35 5,655,76,75 7,53 8,58 (,86) (,8) (,97) (,987) (,738) (,9) (,45) (,68) (,584),64,89,645 8,8 4,59,69,95,86,9 (,884) (,55) (,88) (,99) (,84) (,894) (,5) (,683) (,586) DAX DJ FTSE Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC 8,67,775,93,35 4,8 6,34 9,83 5,698 7,846 (,547) (,4) (,88) (,93) (,86) (,696) (,97) (,76) (,598),86,7,64,63,7,786,497,33,879 (,695) (,45) (,884) (,89) (,87) (,73) (,968) (,54) (,64) HANG-SENG IBEX ISEQ Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC,969 7,79,839 5,389 3,58,83 8,6 4,735 6,53 (,947) (,4) (,349) (,87) (,87) (,35) (,577) (,79) (,683),53,383,8,,633,53,988,696,8 (,954) (,) (,364) (,37) (,89) (,89) (,474) (,833),69) NIKKEI PSI SENSEX Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC, 7,577 6,394 5,693,493,77 9,4 3,967 68,843 (,339) (,65) (,69) (,735) (,958) (,3) (,55) (,83) (,997),85,87,94,746,5,89,86,735,336 (,36) (,77) (,57) (,78) (,967) (,355) (,59) (,79) (,997) Noe: Ths able presens he resuls of Ljung-Box and ARCH LM ess, for he resduals from GARCH (,) esmaon, for he hree sub-perods, and consderng he lag. Values beween parenheses show probably values for each es. To verfy he varance perssence, he ARCH-LM es was appled. The resuls are shown n Table 4. The analyss of he coeffcens and s respecve probably values ndcaes ha hey are no sascally dfferen from zero. Tesng coeffcens n he group, he probably (F-sasc) s sgnfcan, so he null hypohess s acceped. There s reason o beleve ha esmaed models have he ably o model condonal heeroskedascy. 56

16 Sensvy and Perssence Durng he global fnancal crss, he esmaed coeffcens of he GARCH (,) model were above., wh he excepon of he Bovespa ndex. So he volaly n hs sub-perod was hghly sensve o marke evens. The ncrease n sensvy was parcularly sgnfcan n HANG-SENG (69%), PSI (58%) and DJ (34%) ndces. The resuls durng he global fnancal crss conrass wh he Do- Com sub-perod, n whch only fve ndces were above.. In he que sub-perod, only he SENSEX ndex descrbed such superory. Ths allows he concluson ha, durng he global fnancal crss subperod, sock markes were more sensve han n he precedng sub-perods. In he GARCH model, volaly perssence s measured summng and β parameers. When hs sum s close o he un, here s a srong ndcaon of perssence or long memory. Table 3 shows he values of volaly perssence for each ndex n each sub-perod, calculaed on he bass of GARCH esmaes. These resuls show ha n he que sub-perod, when compared o he precedng ones, perssence ncreased n egh of he welve ndces; whle n he global fnancal crss subperod, n comparson o he precedng ones, he ncrease dd no happen wh he excepon of he case of NIKKEI ndex. The esmaed coeffcens of he GARCH (,) model also allow o conclude abou saonary covarance. In all he cases, he sum of and β coeffcens s less han one. Accordng o Alexander (8), hs sum deermnes he rae of convergence of condonal volaly for he long-erm average level. When he sum of hese coeffcens s relavely hgh (above.99), he volaly erm srucure s relavely fla. Durng he global fnancal crss sub-perod, hs superory was found n he BOV, DJ, HANG, ISEQ and SENSEX ndces. For he precedng sub-perods, only he HANG-SENG ndex, n he second sub-perod, verfed hs superory. Fgure 3 shows he resuls of he half-lfe measure. As we have concluded above, only he NIKKEI ndex was no more perssen n he global fnancal crss sub-perod. 57

17 Fgure 3. Half-lfe esmaes n he hree sub-perods ATG BOV CAC DAX DJ FTSE HANG IBEX ISEQ NIKKEI PSI SENEX Do-Com Que GFC The resuls also ndcae ha, durng he hree sub-perods, he volaly of daly reurns proved o be que perssen, especally n he las sub-perod. Half-lfe was parcularly hgh n HANG-SENG (3) and SENSEX (744) ndces. In hs sub-perod, NIKKEI and PSI ndces had recorded he lowes half-lfe, wh a value of 4. In boh cases, an unancpaed shock n he daly reurns produces, on average, effecs on volaly for 4 days. Tess for equaly of means and varances A vsual analyss of Fgure leads o a frs concluson: Do-Com and Global Fnancal Crss subperods were characerzed by a hgher concenraon of volaly and showed peaks of volaly. The que sub-perod reveals ha volaly levels were much lower han ha n he oher wo sub-perods. The Sensex ndex was he excepon, whch showed peaks of volaly n he que sub-perod. For a more dealed concluson, we examned he ess for equaly of means and for equal varances beween he global fnancal crss sub-perod and he wo preceded sub-perods (see Table 5). 58

18 Table 5. Mean and varance equaly ess and her p-values GFC/Do-Com GFC/Que Mean Equaly Varance Equaly Mean Equaly Varance Equaly -es ANOVA F-es Barle -es ANOVA F-es Barle ATG 3,67 3,48 75,55 67,84 7,73 768,997 9, ,98 (,) (,) (,) (,) (,) (,) (,) (,) BOV,794 3,8,65 39,594 9,8 96,39 6,388 78,78 (,73) (,73) (,) (,) (,) (,) (,) (,) CAC,83,33,43 69,574 7,53 36,358 8,74 743,5 (,855) (,855) (,) (,) (,) (,) (,) (,) DAX -6,57 43,84,83 6,36,745 6,43 7, ,367 (,) (,) (,) (,) (,) (,) (,) (,) DJ 4,43 7,68 9,4 897,986 6,36 66,554 47, ,46 (,) (,) (,) (,) (,) (,) (,) (,) FTSE 4,4 6, 3,986 39,6 7,8 37,3 47,9 668,864 (,) (,) (,) (,) (,) (,) (,) (,) 9,39 87,9 5,696 89,555 9,7 388,975 78,9 46,99 HANG-SENG (,) (,) (,) (,) (,) (,) (,) (,) IBEX 4, 7,73 6,33 67, 9,6 384,56 6,734 97,58 (,) (,) (,) (,) (,) (,) (,) (,) ISEQ 5,87 5,98 6,86 74,44,554 58,674 85,44 383,633 (,) (,) (,) (,) (,) (,) (,) (,) NIKKEI 6,7 45,3 8,37 46,947 3,4 75,355 46,3 645,536 (,) (,) (,) (,) (,) (,) (,) (,) PSI 7,35 5,99 8, ,533 7,93 3,535 47, , (,) (,) (,) (,) (,) (,) (,) (,) SENSEX 4,8 3,58,43 68,393,76 4,84,84 7,776 (,) (,) (,) (,) (,) (,) (,) (,) Noe: Values beween parenheses show probably values. The resuls shown n Table 5 allow several conclusons. Comparng global fnancal crss and Do-Com sub-perods, we conclude ha he average condonal volaly ndcaes sascal dfferences, a a sgnfcance level of %, wh he excepon of he BOV, CAC and DAX ndces. The BOV ndex showed a sascal dfference a a sgnfcance level of %. The CAC ndex revealed no sascal dfference, whereas he DAX ndex showed a decreasng average of condonal volaly, a a sgnfcance level of %. Addonally, he es of equaly of varances, appled o he condonal volales comparng he frs and he hrd sub-perods, suppors he concluson ha all he repored ndces ncrease, a a sgnfcance level of 5%. The comparson of he las sub-perods allows he concluson ha all he daly average volales recorded srong ncreases, wh sascal sgnfcance a a sgnfcance level of %. In some cases, ncreases were greaer han 3%. Ths happened wh he ISEQ (49%), PSI (36%), Hang- Seng (338%) and DJ (33%) ndex. The Brazlan marke ncreased by 58%. Moreover, ncreases on average volaly were complemened by ncreases n varably and evdenced by esng he equaly of varances, whch n all he cases were sgnfcan a a sgnfcance level of %. The resuls ndcae 59

19 he occurrence of a generalzed ncrease n condonal volaly. Ths ncrease was no resrced o he U.S. marke (whch led o he subprme crss) or he euro area markes (n he epcener of he soveregn deb crss), revealng a global scale. Asymmerc effec To analyze he asymmerc effec, EGARCH (.) models were esmaed, from he reurns of he welve ndces. The esmaed resuls are shown n Table 6. Table 6. Esmaon resuls for he EGARCH (,) model. γ β γ β γ β γ β ATG BOV CAC Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC -,5 -,455 -,378 -,63 -, -, -,3 -,33 -,375 (,) (,) (,) (,4) (,) (,) (,) (,) (,),34,54,65,4,7,46,37,68,39 (,) (,) (,) (,36) (,474) (,) (,) (,) (,) -, -,44 -,79 -,74 -,38 -,9 -,55 -,9 -,94 (,) (,) (,) (,) (,) (,) (,) (,) (,),894,963,969,875,758,987,977,97,969 (,) (,) (,) (,) (,) (,) (,) (,) (,) DAX DJ FTSE Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC -,37 -,338 -,37 -,39 -,579 -,349 -,36 -,365 -,9 (,) (,) (,) (,) (,) (,) (,) (,) (,),87,3,4,56,75,4,39,7,4 (,) (,) (,) (,35) (,) (,) (,) (,4) (,) -,49 -, -,55 -, -,7 -,47 -,94 -,5 -,49 (,) (,) (,) (,) (,) (,) (,) (,) (,),97,97,975,978,947,973,978,968,977 (,) (,) (,) (,) (,) (,) (,) (,) (,) HANG-SENG IBEX ISEQ Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC -,9 -,9 -,59 -,335 -,39 -,333 -,734 -,968 -,349 (,) (,6) (,) (,) (,) (,) (,) (,) (,),47,7,78,9,38,47,,34, (,) (,) (,) (,3) (,) (,) (,) (,) (,) -,6 -,8 -,66 -,85 -,6 -,6 -,4 -,35 -,7 (,) (,4) (,) (,) (,) (,) (,) (,) (,),979,985,985,97,9,974,98,98,978 (,) (,) (,) (,) (,) (,) (,) (,) (,) NIKKEI PSI SENSEX Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC -,56 -,5 -,46 -,93 -,489 -,558 -,98 -,9 -,38, (,) (,) (,) (,) (,) (,) (,) (,),46,7,96,68,8,5,84,74, (,) (,) (,) (,) (,) (,) (,) (,) (,) -,55 -,78 -,6 -,8 -,5 -,34 -,5 -,7 -,74 (,9) (,) (,) (,),735 (,) (,) (,) (,),947,959,968,88,96,957,98,88,983 (,) (,) (,) (,) (,) (,) (,) (,) (,) Noes: Ths able presens he EGARCH (,) model esmaons, appled o he daly reurns of he welve ndces suded n he hree sub-perods. All he esmaes are based on Maxmum Lkelhood. 6

20 Esmaes show ha all he γ coeffcens had a negave sgn. Addonally, n he hree subperods, hese coeffcens were sascally dfferen from zero, a a sgnfcance level of %. The excepons were he HANG-SENG ndex n he que sub-perod, whch was sascally sgnfcan a a sgnfcance level of 5%, and he PSI ndex n he que sub-perod, where asymmery coeffcen was no proved o be sascally dfferen from zero. The hgh sgnfcance of he asymmery coeffcen clearly shows he exsence of asymmerc shocks n he volaly process. In hs sense, one can conclude ha n he hree sub-perods, bad news was more mpacful han good news. A comparson of he asymmery coeffcens n he hree sub-perods, allows he concluson ha a rsng rend of hese values has been verfed. From he frs o he second sub-perod, egh ndces repored an ncrease n he asymmery coeffcen (n absolue value). From he second o he hrd subperod, here was an ncrease n nne asymmery coeffcens. When comparng he frs and he hrd sub-perods, he same happens n nne markes. The resuls showed ha markes are, n general, more sensve o bad news han o good news, especally durng he global fnancal crss. To fnd he correc EGARCH (,) model specfcaons, we examned he resduals n order o see wheher hey exhb a whe nose process. For hs purpose, we urn o he Ljung-Box and ARCH- LM ess (see Table 7). Table 7. Ljung-Box and LM ess resuls for EGARCH (,) resduals Q LB: ( ) LM es: F ( ) Q LB: ( ) LM es: F ( ) Q LB: ( ) LM es: F ( ) Q LB: ( ) LM es: F ( ) ATG BOV CAC Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC 9,99 7,74 6,7 7,89 34,5 5,57 9,83 7,643 7,47 (,463) (,6) (,7) (,996) (,3) (,743) (,47) (,6) (,3),9,34,854,333,568,763,96,766,43 (,588) (,54) (,647) (,998) (,53) (,76) (,5) (,757) (,) DAX DJ FTSE Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC 38,65,3 8, 6,85 5,783,664,745,98 9,66 (,8) (,395) (,5) (,75) (,73) (,36) (,888) (,38) (,479),863,988,98,858,836,57,679,984,993 (,) (,474) (,7) (,643) (,67) (,39) (,85) (,479) (,468) HANG-SENG IBEX ISEQ Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC 7,77 34, 3,67 5,93 5,87 3,66 8,589,9 7,8 (,635) (,6) (,6) (,69) (,78) (,76) (,549) (,44) (,65),94,654,487,3,735,9,997,947,87 (,536) (,35) (,77) (,) (,793) (,76) (,463) (,56) (,67) NIKKEI PSI SENSEX Do-Com Que GFC Do-Com Que GFC Do-Com Que GFC 3,864,3 5,676 6,3 3,6 8,9 6,77,86 8,5 (,48) (,34) (,737) (,7) (,866) (,58) (,76) (,44) (,988),,6,837,777,63,938,935,4,396 (,9) (,45) (,669) (,744) (,89) (,538) (,54) (,43) (,99) Noes: Table 7 presens he Ljung-Box and ARCH LM ess for he resduals from he GARCH (,) esmaon for he hree sub-perods, and consderng he lag. Values beween parenheses show probably values for each es. 6

21 The Ljung-Box es does no accep he null hypohess for BOV (que sub-perod), DAX (Do- Com sub-perod) and HANG-SENG (que sub-perod) ndces a he sgnfcance level of 5%. For he remanng ndces, here s a srong evdence of accepance of he null hypohess, concludng ha he sandardzed resdues are no correlaed because he resuls of he es showed ha he p-value s very above he sgnfcance level of 5%. The LM es resuls (see Table 7) confrmed he prevous conclusons. The group es (F-Sasc) showed ha he probably s no sgnfcan n he cases menoned above, rejecng he null hypohess. 4. SUMMARY, CONCLUSIONS AND LIMITATIONS In hs work, we have suded he curren fnancal crss. Accordng o several auhors, hs crss s he mos severe afer he Grea Depresson and he frs global fnancal crss he world has known. To analyze he crss, varous sock markes were consdered, whch all ogeher represen abou 6% of he world sock marke capalzaon, n order o undersand he mpac of global fnancal crss on he level of volaly, sensvy, perssence and asymmerc effec. For hs purpose, we suded he perod from Ocober 4 h 999 o June 3 h, whch was dvded no hree sub-perods: One correspondng o he Do-Com crss; oher relave o a phase of rse and accumulaon for global ndces; and fnally, one correspondng o he global fnancal crss. To esmae he marke volaly, generalzed and exponenal auoregressve condonal heeroskedascy models were consdered. The fndngs confrm ha, n mos cases, he condonal volaly n he global fnancal crss sub-perod experenced a sgnfcan ncrease compared wh he prevous wo sub-perods, bu parcularly n relaon o he que sub-perod. Noe ha he PSI ndex showed, n all sub-perods analyzed, lower levels of condonal volaly, whch s somehow surprsng f we ake no accoun he small sze of hs marke. Addonally, he model esmaon confrms, n general, a hgher perssence n volaly durng he fnancal crss sub-perod; s he same wh sensvy. Smlarly, all he markes consdered n he analyss revealed an asymmerc effec; n oher words, her volales were more nfluenced by bad news han by good news, especally durng he global fnancal crss. Several lmaons of our analyss should be noed. Frs, he sample perod covers only he frs years of he global fnancal crss, bu fnancal markes are sufferng wh hs crss because has no fnshed ye. Second, hs sudy consdered only welve sock markes, ncludng some major capalzaons and markes drecly relaed o soveregn deb crss. For more robus conclusons, fuure work may cover he full perod of he global fnancal crss and consder a large se of developed and emergng markes. 6

22 ACKNOWLEGDMENTS Ths paper was suppored by projec PEs-OE/EGE/UI456/4, fnanced by Foundaon for Scence and Technology (FCT) from he Poruguese Mnsry of Educaon and Scence. REFERENCES Angabn, A. and Wasuzzaman, S. (). GARCH Models and he Fnancal Crss A Sudy of he Malaysan Sock Marke. The Inernaonal Journal of Appled Economcs and Fnance, 5 (3), Bala, L. and Premarane, G. (3). Sock marke volaly: Examnng Norh Amerca, Europe and Asa. Naonal Unversy of Sngapore, Economcs Workng Paper. hp://papers.ssrn.com/sol3/papers.cfm?absrac_d= Rereved n. Bekaer, G.; Ehrmann, M.; Frazscher, M. and Mehl, A. (). Global Crses and Equy Marke Conagon. Naonal Bureau of Economc Research. Workng Paper 7. hp:// Rereved n. Black, F. (976). Sudes n sock prce volaly changes. Proceedngs of he 976 Busness Meeng of he Busness and Economcs Sascs Secon, Amercan Sascal Assocaon, pp Bollerslev, T. (986). Generalzed Auoregressve Condonal Heeroskedascy. Journal of Economercs, 3, Bollerslev, T.; Chou, R. and Kroner, K. (99). ARCH Modelng n Fnance: A Revew of he Theory and Emprcal Evdence. Journal of Economercs, 5, Brock, W.A. and de Lma, P.J.F. (996). Nonlnear Tme Seres, Complexy Theory and Fnance. In: Maddala, G.S. and Rao, C.R. (eds.). Handbook of Sascs. Vol. 4: Sascal Mehods n Fnance. Elsever: New York, pp Campbell, J.Y.; Lo, A.W. and MacKnlay, A.C. (996). The Economercs of Fnancal Markes. Prnceon Unversy Press: New Jersey. Chaudhur, K. and Klaassen, F. () Have Eas Asan Sock Markes Calmed Down? Evdence from a Regme-Swchng Model. Deparmen of Economcs Workng Paper, Unversy of Amserdam. 63

23 Chong, C. (). Effec of Subprme Crss on U.S. Sock Marke Reurn and Volaly. Global Economy and Fnance Journal, 4 (),. Claessens. S.; Dell Arcca, G.; Igan, D. and Laeven, L. (). Lessons and Polcy Implcaons from he Global Fnancal Crss. IMF Workng Paper No. /44. Con, R. (). Emprcal properes of asse reurn: Sylzed facs and sascal ssues. Quarerly Fnance,, Con, R. (5). Long range dependence n fnancal markes. In: Lévy-Véhel, J. and Luon, E. (eds.). Fracals n Engneerng. Sprnger-Verlag: London, pp Coolen, A.C.C. (4). The Mahemacal Theory of Mnory Games: Sascal Mechancs of Ineracng Agens. Oxford Unversy Press: Oxford. Dng, Z.; Granger, C.W.J. and Engle, R.F. (993). A long memory propery of sock marke reurns and a new model. Journal of Emprcal Fnance, (), Engle, R.F. (98). Auoregressve condonal heeroscedascy wh esmaes of he varance of Uned Kngdom nflaon. Economerca, 5, Engle, R.F. and Paon, A.J. (). Wha good s a volaly model? Quanave Fnance,, Hora, P.; Mendes, C. and I. Vera. (8). Conagon Effecs of he U.S. Subprme Crss on Developed Counres. CEFAGE-UE Workng Paper 8/8, Unversy of Évora. Ln, C. (996). Sochasc Mean and Sochasc Volaly. Blackwell Publshers: Cambrdge. Ln, J.Y. and Trechel, V. (). The Unexpeced Global Fnancal Crss: Researchng s Roo Cause. Polcy Research Workng Paper WPS5937, World Bank. WPS5937. Lquane, N.; Naou, K. and Brahm, S. (). A dynamc condonal correlaon analyss of fnancal conagon: The case of he subprme cred crss. Inernaonal Journal of Economcs and Fnance, (3), Mandelbro, B. (963). The varaon of ceran speculave prces. The Journal of Busness, 36 (4), Mandelbro, B. and Hudson, R. (6). O (Mau) Comporameno dos Mercados: Uma Vsão Fracal do Rsco, da Ruína e do Rendmeno. Gradva: Lsbon. Markowz, H. (95). Porfolo selecon. The Journal of Fnance, 7,

24 McAleer, M. (5). Auomaed Inference and Learnng n Modellng Fnancal Volaly. Economerc Theory, (), 3 6. Nelson, D.B. (99). Condonal Heeroskedascy n Asse Reurns: A New Approach. Economerca, 59 (), Paev, P.G. and Kanaryan, N.K. (3), Sock Marke Volaly Changes n Cenral Europe Caused by Asan and Russan Fnancal Crses, Tsenov Academy of Economcs Deparmen of Fnance and Cred Workng Paper, No. 3-. Raja, M. and Selvam, M. (). Measurng he me varyng volaly of fuures and opons. The Inernaonal Journal of Appled Economcs and Fnance, 5 (), 8 9. Ramlall, I. (). Has he US Subprme Crss Accenuaed Volaly Cluserng and Leverage Effecs n Major Inernaonal Sock Markes? Inernaonal Research Journal of Fnance and Economcs, 39, Schwer, G.W. (998). Sock Marke Volaly: Ten Years afer he Crash. Brookngs-Wharon Papers on Fnancal Servces, 998, Toussan, E. (8). The US Subprme Crss Goes Global. In Counerpunch, Weekend Edon, January /3. 65