Returns and Volatility Asymmetries in Global Stock Markets

Transcription

1 Reurns and Volaly Asymmeres n Global Sock Markes Thomas C. Chang, Marshall M. Ausn Professor of Fnance Drexel Unversy Cahy W.S. Chen, Professor of Sascs Feng Cha Unversy Mke K.P. So, Asssan Professor Hong Kong Unversy of Scence and Technology (Fle: C:\Research\ Asymmeres o JBF; Dae: Augus 4, 22) Correspondng Address Busness Address Dr. Thomas C. Chang Dr. Thomas C. Chang 7 Spl Ral C. Marshall M. Ausn Professor Hanespor, N.J. 836, USA Deparmen of Fnance, Drexel Unversy 34 Chesnu Sree Phladelpha, PA 94 USA Tel: Fax: emal:homas_c_chang@yahoo.com changc@drexel.edu

2 Reurns and Volaly Asymmeres n Global Sock Markes Absrac Ths paper examnes he hypohess ha boh sock reurns and volaly are asymmercal funcons of pas nformaon derved from domesc and US sock marke news. By employng a double-hreshold regresson GARCH model o nvesgae four major ndex reurn seres, we fnd sgnfcan evdence o susan he asymmercal hypohess of sock reurns. Specfcally, evdence srongly suppors he hypohess ha sock ndex reurns are posvely correlaed wh a compose of sock reurn news, whch s obaned by a weghed average of he lagged domesc and US sock ndex reurns. Moreover, we fnd ha negave news wll cause a larger declne n a naonal sock reurn han wll an equal magnude of good news. Ths also holds rue for he condonal varance. The varance appears o be more volale and perssen when bad news hs he marke han when good news does. Conssen wh exsng leraure, asymmeres n sock reurns are no ndependen of asymmeres n volaly snce a larger adjusmen n sock prces o bad news s lkely o cause domesc nvesors o change he deb-equy rao, leadng o hgher volaly n sock marke. Keywords: Asymmery, Threshold GARCH, Sock reurns, Volaly, Bayesan Esmaon JEL Classfcaon: C5; C32; C5 2

3 Reurns and Volaly Asymmeres n Global Sock Markes. Inroducon Recen emprcal sudes of naonal sock-ndex reurns have noed several emprcal regulares. Frs, daly sock reurns have been found o presen auocorrelaons. The exsence of an AR process has been arbued o nonsynchronous radng (Scholes and Wllams, 977; Lo and MacKnlay, 99), me-varyng shor-erm expeced reurns (Fama and French, 988; Senana and Wadhwan, 992), and coss of prce adjusmen (Amhud and Mendelson, 987; Damodaran, 993; Koumos, 998). Second, n mul-counry analyss, cross correlaons of sock reurns have been repored n sudes by Hamao e al (989), Koumos and Booh (995), Km and Rogers (995), and Chang (998). Ther fndngs ndcae ha naonal sock reurns are sgnfcanly correlaed and ha lnkages among nernaonal sock markes have grown more nerdependen over me. Thrd, evdence shows ha sock-ndex reurns and volaly spll over hrough auoregressve condonal heeroscedascy-ype (ARCH) models and dsplay meeor showers n nernaonal sock markes (Io e al, 992; Theodosou and Lee, 993; Ln e al, 994; Karoly, 995; Kofman and Marens, 997). Followng he approaches by Engle (982), Bollerslev (986), French e al (987), Schwer (989), Pagan and Schwer (99), Balle and DeGennaro (99), he cumulave evdence ndcaes ha sock volaly exhbs a cluserng phenomenon,.e. large changes end o be followed by large changes and small changes end o be followed by small changes. In her revew of hs marke phenomenon, Bollerslev e al (992) repor ha he GARCH(,) model appears o be suffcen o descrbe he volaly evoluon of sock-reurn seres. A drawback of sandard ARCH-ype models s ha he esmaed coeffcens are assumed o be fxed hroughou he sample perod and fal o ake no accoun he asymmercal effec beween posve and negave shocks o sock reurns. Ths leads o he fourh regulary - an asymmercal effec s found n sudyng sock-reurn seres. I has been shown ha a negave shock o sock reurns wll generae greaer volaly han wll a posve shock of equal magnude. By exendng he research mehods proposed by Nelson (99), Glosen e al (993), Engle and Ng (993) and Koumos (997, 998, and 999) fnd sgnfcan evdence o suppor he asymmercal hypohess 3

4 of sock-ndex reurns. More recenly, Bekaer and Wu (2) and Wu (2) hghlgh he leverage effec and volaly feedback effec n explanng asymmercal volaly n response o news and fnd supporve evdence n Nkke 225 socks. Noe ha n he specfcaon of he asymmercal paral-adjusmen prce model (Amhud and Mendelson, 987; Damodaran, 993; Koumous, 998), where prces ncorporae negave reurns faser han posve reurns, he news varable s mplcly embedded n he auoregressve process of he mean equaon. These models are useful and approprae f our neres s o focus on examnng wheher news of negave reurns s ncorporaed no curren prces faser han news reflecng posve reurns. On he oher hand, Bekaer and Wu s model (2) provdes a unfed framework o examne asymmercal volaly n response o news a he frm level and he marke level. However, hese models fal o ncorporae boh domesc and foregn sock news (ha s, US sock news) no an negraed model o analyze he asymmeres n reurn and volaly. In vewng he evdence ha reurns are nernaonally correlaed (Hamao e al, 989; Kng and Wadhwan, 99; Bae and Karoly, 994; Koumos and Booh, 995) and ha nnovaons n he US markes are ransmed rapdly o he res of he world (Eun and Shm, 989; Chang, 998; Mash and Mash, 2), s of neres o examne wheher sock reurns n he advanced capal markes also reac asymmercally o news from he US sock markes. The decson o choose he US marke as a reference, and hence as a cener of nformaon propagaon, s based on several facors. Frs, he US marke, wh s domnan radng poson n world capal markes, s also he mos nfluenal producer of nformaon. Wh he ad of s echnologcal advances and compuerzed radng sysems, hs has grealy faclaed he ransfer of nformaon flows from marke o marke. Second, emprcal evdence presened by Mash and Mash (2) confrms earler fndngs (Eun and Shm, 989) ha he US marke provdes prce leadershp n he world marke place. Thrd, nernaonal nvesors ofen overreac o news from he US markes and are less sensve o oher markes (Becker e al, 995). Therefore, sock news released from US markes s expeced o be ransmed o oher markes n an effcen way. 4

5 Thus, nsead of smply exendng an AR-EGARCH (Koumos,999) or an EAR-TGARCH (Koumos, 997) model by emphaszng an auocorrelaon specfcaon based on domesc sock-reurn news, we specfy a mean equaon by lnkng curren reurns o a news ndex conanng pas nformaon from domesc markes as well as from he US markes. Moreover, we are neresed n examnng he possbly of an asymmercal effec n volaly n reacon o he news ndex. To capure hese feaures, we propose a double-hreshold auoregressve GARCH model (DTAR-GARCH), wh he laer esmaed by a Bayesan mehod. Thus, our sudy dffers from prevous researches n several respecs. Frs, nsead of focusng exclusvely on pas sock nformaon emboded n he auocorrelaon erm (Senana and Wadhwan, 992; Koumos, 997, 998), we employ compose news derved from boh domesc and foregn markes and analyze he asymmeres n reurns and varances. Ths specfcaon allows us o examne ndvdual news effecs or combnaons from boh sock sources. Thus, our fndngs wll provde a broader avenue for processng pas nformaon n a mul-asse framework and wll shed some lgh on he asymmercal effec on nernaonal sock reurns. Second, n an emprcal esmaon, a Bayesan mehod wll be ulzed o esmae a vecor of unknown parameers, Θ, n he DTAR-GARCH model, ncludng a hreshold value, r, and a me delay, d. I allows us o generae approxmaed samples from he poseror dsrbuon of Θ va a Markov Chan Mone Carlo mehod (MCMC). Thus, he usual resrcon of pre-seng r and d n esmang a hreshold model can be avoded. Ths paper s organzed no he followng secons. Secon 2 descrbes he daa used n hs sudy and presens some sascal properes of sock reurns n a sandard GARCH(,) specfcaon. Secon 3 provdes he raonale and procedures for usng a Bayesan esmaon of a DTAR-GARCH model. Secon 4 presens he esmaed resuls for boh mean and condonal varance equaons. Secon 5 carres ou he esmaon based on opmal weghng of sock reurn news. Secon 6 conans concludng remarks. 5

6 2. The Daa and Basc Sascs 2.. Daa sample The daa used n hs sudy are daly sock-prce ndexes for fve sock markes from January, 985, hrough November 4, 2. The daa conss of he Dax 3 (Germany), he FTSE (Uned Kngdom), he Nkke 225 Index (Japan), he Torono SE 3 (Canada), and he S&P 5 Index (Uned Saes). All he daa were aken from Daa Sream Inernaonal. Followng he convenonal approach, akng he logarhmc dfference of he daly sock ndex mes generaes daly sock-reurn seres. Tha s, R = * (log P log P ). I s mporan o noe ha our nvesgaon covers he major sock ndces n he global marke place, ncludng Japan, Germany, he Uned Kngdom, Canada, and he Uned Saes. Ths wde coverage of daa allows us o nvesgae marke behavor nvolvng spaal dfferenals, whch may be unque o counry facors. However, sock markes n dfferen counres operae n dfferen me zones wh dfferen openng and closng mes. To compare he realzed reurns for sock ndces n a gven calendar day n dfferen real-me perods s no an easy job. Ye, sock radng a New York Cy (he S&P 5 Index n he US marke) s he las one o close among he dfferen world exchanges under nvesgaon. So closng news n he US marke a day (-) wll have suffcen me o be ransmed o he Japanese and he varous European markes. I s possble o examne he ssue by consrucng synchronous daa (Marens and Poon, 2). However, marke behavor, such as n he Japanese marke, would have o be excluded. As a resul, emprcal evdence and s mplcaons would be resrced o he Wesern Hemsphere raher han a global seng Basc sascs To provde a general undersandng of he naure of each marke s reurns, we summarze he sascs of daly reurns n Table. The sascs n Panel A conan mean ( µ ), sandard devaon (σ ), and Ljung-Box Q() a values for he reurns and reurns squared. The mean values for Canada and he wo European sock reurns exhb very smlar performances. However, he Japanese marke appears o show a negave reurn as well as he hghes sandard devaon. The unfavorable oucome of Japanese sock reurns s arbuable o he fac ha he Japanese marke has run been a bear marke snce 989; he marke was furher 6

7 Table Esmaes of major sock ndex reurns for he GARCH(,) model Coeffcen UK Canada Germany Japan Panel A. Basc Sascs µ σ LB() a * * 28.95* 39.8* LB 2 () a * 37.25* 93.38* * Panel B. Esmaes of mean and uncondonal varance.383*.5.467*.367* (.24) (.5) (.65) (.35) γ *.66*.92 (.6) (.24) (.65) (.58) ψ.722*.489*.2673*.267* (.5) (.52) (.97) (.6).2*.5*.637*.26* (.36) (.) (.59) (.2).852*.23*.35*.* (.59) (.64) (.66) (.52).89*.8679*.85*.8883* (.838) (.73) (.) (.42) LB () b * 4.755* LB 2 () b Noes: µ and σ are he sample mean and sandard devaons. LB() and LB 2 () are Ljung-Box sascs esng for auocorrelaons n he level of reurns and he squared reurns up o he h lag. The me perod covered s from //985 o /4/2 for 44 observaons. The esmaed equaons n Panel B are as follows: j = ψ 2 R + γ R + R + u and h = + u + h An asersk ndcaes sascal sgnfcance a leas a he 5% level or beer. The numbers n parenheses are sandard errors. 7

8 aggravaed by he Asan crss and he recen US recesson, jeopardzng he performance of he sock marke. Tesng he ndependence of sock reurns up o he h order, he Ljung-Box sascs, LB() a, show hgh sgnfcance, rejecng he absence of auocorrelaons n he daly daa. The exsence of auocorrelaon may resul from marke frcons or slow adjusmens. The LB 2 () a sascs for examnng he null hypohess of dependency on he squared reurns are also very sgnfcan, suggesng ha he varance s presenng a cluserng phenomenon. Based on hs sascal nformaon and he evdence of exsng leraure, s convenen o sar wh a convenonal model o se a benchmark. Thus, he curren sock reurn s relaed o an auoregressve erm and a lagged cross-asse reurn n he mean equaon. The AR() here denoes domesc sock reurn news, and he lagged cross-asse reurn capures he recen foregn sock reurn news. By assumng ha he condonal varance can be represened by a GARCH (,) process, as popularzed by Bollerslev e al (992), we wre: j + R R = + γ R ψ + u () where h R 2 = + u + h, j and R are sock reurns from counres ( = Canada, Uned Kngdom, Germany, and Japan) and j (he Uned Saes), respecvely; h s he condonal varance;, γ, ψ,,, and are consan parameers; and s a random error erm. Esmaes of Equaons () and are presened n Panel B of Table, whch conans he parameers of (, γ, ψ,,, ) and he correspondng sandard errors. Conssen wh he fndngs n he leraure (Koumos, 998), he resuls show ha, wh he excepons of he Uned Kngdom, he auoregressve erm s posve. However, only he coeffcens of Canada and Germany are sascally sgnfcan. Wh respec o he coeffcens of he US reurn, he esmaed sgns are all posve, rangng from.7 o.4, wh he Canadan coeffcen he hghes. By checkng he performance of he regressors, he coeffcen of he US ndex reurn appears o play a more sgnfcan role han ha of he AR() erm. Evdenly, he hypohess of ndependence of sock-ndex reurns from he US marke s unformly rejeced. The sgnfcance of he lagged US sock reurns and AR componen frusraes he effcen-marke hypohess. Furher checkng he varance equaon, we fnd ha all he coeffcens n he GARCH(,) equaons are sascally u 8

9 sgnfcan, ndcang ha he sock-reurn volales are characerzed by a heeroscedasc process. Noe ha he average varance measured by /( ) shows ha Japan has he hghes average varance, sgnfcanly hgher han n he oher markes suded. I s mporan o verfy he adequacy of a fed AR-GARCH model. Ths can be done by examnng he seres of sandardzed shocks, { u~ }, where u ~ = u / h. In parcular, we calculae he Ljung-Box sascs for he seres of ~ 2 u ~ and u, respecvely, o check he adequacy of he mean equaon as well as he valdy of he volaly equaon. The Ljung-Box sascs of he sandardzed shocks and he squared reurns, respecvely, up o he h lag are repored n he las wo rows of Table. Alhough hese sascs have been reduced sgnfcanly as compared wh hose shown n Panel A, nadequacy s found n GARCH models for he Canadan and German markes. Ths mples ha some sor of non-lnear specfcaon may be necessary n he varance equaon. In addon, even hough he sysem n Equaons () and provdes us a framework o descrbe he daly asse-reurn behavor n a GARCH(,) process, he esmaed coeffcens are fxed and fal o reflec he asymmercal naure of he marke news. In order o examne wheher pas sock news could produce asymmercal effecs on he mean and condonal varance equaons, we consruc a hreshold-garch model characerzng regme swchng, whch we shall presen nex. 3. The Double TAR-GARCH model 3.. The model represenaon The quanave model we adop here s he Double TAR-GARCH model (DTAR-GARCH), whch s a generalzaon of he hreshold ARCH models proposed by L and Lam (995), L and L (996), and Chen (998) or a self-excng hreshold auoregressve model (SETAR) by Tong (99) and Tsay (998). Ths model s movaed by several nonlnear characerscs commonly observed n pracce o capure he asymmery n declnng and rsng paerns of a process. I uses pecewse lnear models o oban a beer descrpon of condonal mean and condonal volaly equaons. To smplfy he process, he condonal mean n a wo-regme model s specfed as: R = + z d + u, (3) 9

10 where z -d reurns: s an nformaon varable a me wh d perod delay, carryng he news of sock j z -d = wr + ( w) R (4) d d where w s a posve wegh, lyng beween and. To apprecae he specfcaon of Equaon (4), z -d s assumed o be a weghed average of wo ses of nformaon, and, beng used by nvesors o assess he sock markes. If he observed sock-ndex reurn varable ( and j) reflecs purely random error of sock-ndex change, we do no expec auocorrelaon o be presen n sock reurns. However, f he sock-ndex reurns reflec a paral adjusmen of he pas prce level o s marke fundamenals (Amhud and Mendelson, 987; Damodaran, 993; Koumous, 998; Bekaer and Wu, 2) or form expecaons n an exrapolave fashon, he changes n sock ndex wll be auocorrelaed. 2 R d j R d The ncluson of j R d n z-d hghlghs he sgnfcance of sock-reurn news from global markes due o ndusral srucure (Roll, 992), conagon effecs (Kng and Wadhwan, 99), or oher forms of spllover. Wh he domnan share of he US marke, whch s also he las marke o close on he global clock for a gven calendar day, he foregn nformaon on he US sock-ndex reurn news. Thus, he sgn of n our conex manly reles n Equaon (3) ough o be posve and sgnfcanly dfferen from zero. The me lag for news o arrve n naonal markes s expeced o be relavely shor from an effcen marke pon of vew. Addonally, he parsmonous prncple suggess ha he lag lengh should be based on model fng of avalable daa whou usng any unnecessary parameers. The decson for he choce of he delay varable d n hs sudy wll be dependen on he emprcal regulary, whch s he mode of our emprcal smulaon. 3 By subsung Equaon (4) no Equaon (3), we oban: j R d R d = + wr + ( w) R j d + u, (5) where w s he wegh of counry h (domesc) sock reurn beng used o projec s own sock reurn; (- w) s he wegh of counry jh marke nformaon (he US sock reurn) beng used o projec he h marke reurn. Comparng Equaon (5) wh Equaon yelds he resrcons: γ = and ψ = ( w ). A specal feaure of he specfcaon of Equaon (5) s ha hs w

11 expresson conans compose news employed by he nvesor/economc agen o assess naonal sock reurns, raher han relyng on sngle news ems emergng from eher marke. The esmaed coeffcens depend on he parameer w. If one mposes w =, he specfcaon reduces o an auoregressve process and caches an exrapolave behavor or paral prce-adjusmen model (L and Lam, 995). If one mposes w =, he sock reurn s governed by he cross-counry sock-ndex reurn. In fac, he wegh can vary n me and space across dfferen counres. Thus, Equaon (5) parsmonously summarzes marke news pernen o explanng naonal sock reurns. To hghlgh he asymmercal feaure of he sock marke behavor, we rewre Equaon (5) n a wo-regme model based on he hreshold nformaon r as: R () () () j + wr d + ( w) R = ( 2) ( 2) ( 2) + wr d + ( w) R d j d + u, + u, f z f z -d -d r > r (6) The correspondng GARCH(,) specfcaons for he condonal varances are gven by: h u () () () 2 + u + h = ( 2) ( 2) 2 ( 2) + u + h = h ε, where { ε } s a sequence of ndependen and dencally dsrbued normal random varables wh ( ) ( ) ( ) mean zero and varance ; >,, and for =, 2 ; and (), (), (), (), (),,,,,, r, and d are unknown parameers. The posve neger d s commonly referred o as a delay (or hreshold lag), r s a hreshold value, and w s a wegh parameer lyng beween and. The hreshold varable z -d n hs model s an exogenous varable. f z f z -d -d r > r (7) I dffers from a sandard SETAR model (Tong, 99) or a smple hreshold model, as ha of R d n L and Lam (995), L and L (996), or n Koumos (998). Accordng o he model specfcaon, he dynamc srucure of he mean equaon s sll dependen on an auocorrelaon erm and he pas U.S sock reurn news as emboded n he compose-news varable; he varance equaon follows a GARCH(,) process. However, he model s dvded no wo dfferen regmes n response o bad news, z-d r, whch we defne as regme, and good news, z -d > r, whch we label regme 2, o capure he mean and volaly asymmeres.

12 Two addonal feaures are assocaed wh hs model. Frs, he value of r s no necessarly zero. Ths means ha he sum of sock reurns ha are negave does no necessarly mply bad news. The bad news n our conex s ha negave pas reurns, z -d, are suffcenly smaller han he hreshold value, r. Second, he d value s no necessary equal o as mpled by mos convenonal models (LeBaron, 992; Koumos, 998; Bekaer and Wu, 2). In he curren model, he values of r and d, along wh he oher parameers, are esmaed smulaneously by he Markov Chan Mone Carlo mehod (MCMC) as we dscuss below Esmaon procedures Classcal esmaon of parameers n he hreshold class of models s usually done by a leas-squares mehod wh r and d prefxed (Tong, 99). Esmaes of r and d are hen deermned by usng nformaon crera such as AIC and BIC (Tsay, 998; Shen and Chang, 999). The shorcomng of hs samplng approach s ha by fxng r and d n advance, before esmang oher parameers by leas squares, he uncerany of r and d canno be aken no accoun when performng sascal nference for oher parameers. Moreover, he choces of r and d are lkely o be dependen on he crera we choose for model comparson. To allevae he problems arsng from predeermnng r and d, we adop a Bayesan approach, whch allows us o esmae r and d as well as oher parameers smulaneously. 4 Specfcally, we can generae approxmaed samples from he poseror dsrbuon of unknown parameers, ncludng d and r, va MCMC mehods (Chb and Greenberg, 995; Chen, 998; So and Chen, 22). The esmaon procedures of Bayesan analyss are oulned as follows: Sep : Wre he lkelhood funcon p(r Θ) as: p(r Θ ) n Π (2 π h ) -/2 s () () () j 2 exp [ Rπ wr ( ) ] k π w R k π k = 2 2 k= h π k exp 2 n k= s+ h π k [ R π k j 2 wrπ ( w) R ] k π, (8) k () () () () () where Θ = (,,,,,,,,,, r, )'; d 2

13 R = ( Rπ Rπ..., R )';, 2 π n k π s he me ndex of he kh smalles observaon of z,, z n ;and s sasfes he resrcon zπ s r < z. d π s d + Sep 2: Choose he pror dsrbuon p (Θ) for Θ : () () () p( Θ) I( >, + < ) I( >, + < ) I( a < r < b) I( w ), I (. ) s he ndcaor funcon ha I(A) = f he even A s rue, a and b are 25 and 75 percenles of he hreshold varable, z -d, respecvely. Sep 3: Oban poseror dsrbuon p(θ R) by he Bayes rule: p(θ R) p(r Θ) p( Θ). () Sep 4: Sample eravely from p(θ R) o generae a poseror sample Θ M+,..., Θ N by usng Markov Chan Mone Carlo mehods, where M=, s he number of burn-n eraons for convergence and N = 2, s he oal number of eraons. The samplng s done n seven blocks: () () () () Sample (, ) from p(, R, Θ ); () () () (, ) (9) () () () Sample (,, () ) from p( () () (),, R, Θ () () () (,, ) ); () Sample (, ) from p(,, R Θ (, ) ); (v) Sample (,, ) from p(,, R, Θ (,, ) ); (v) Sample r from p( r R, Θ ) ; (v) Sample w from p( w R, Θ ) ; and (v) Sample d from p( d R, Θ ), r w d where Θ x represens he vecor Θ whou he parameer x. Sep 5: Oban pon esmaes of he unknown parameers by he sample mean of he poseror sample. The pon esmae of Θ, oher han d, s gven by: 3

14 Θ = N M N Θ k= M + k. () Sep 6: Esmae d by observng he value occurrng mos frequenly n he poseror sample. 4. Esmaed resuls from he Bayesan mehod The Bayesan esmaes of sysem Equaons (6) and (7) for he major sock markes are generaed n wo sages. Frs, we esmae he equaons wh a gven wegh prefxed and hen allow he wegh o vary n order o deec changng coeffcens n response o dfferen emphases on he componens of news n prcng behavor. Those resuls are repored n Tables 2 hrough 5. Second, we rea he wegh as an endogenous varable and search for he opmal level of he wegh pernen o he daa. In hs way, he nvesors/economc agens wll be nformed of he opmal nformaon combnaon. The resuls are presened n Table 6. The esmaed parameers repored n Tables 2 hrough 6 are he values of he poseror means, whle he numbers n parenheses are he correspondng poseror sandard devaons of he parameers. 5 As may be seen from Tables 2 hrough 5, he ( ) ( =, 2) n general are posve and her values suffcenly large as compared wh he correspondng sandard errors, ndcang ha he esmaed parameers are hghly sgnfcan a sandard sgnfcance levels. Ths suggess ha naonal sock reurns are no ndependen of news released from he laes domesc and US sock reurns. The esmaon s dvded no wo regmes based on he hreshold varable r for each marke. 6 The evdence suggess ha only when a loss, produced by weghng he average of domesc and he US sock-ndex reurns, exceeds he hreshold level s consdered bad news. Dependng on he wegh (w =.,.,.2,,.) assgned o consruc he nformaon ndex of sock reurns, our fndngs show ha he hreshold values under nvesgaon are n he ranges of [-.3636%, -.224%], [-.4%, -.78%], [-.436%, %], and [-.5889%, -.25%] for he Canadan, Brsh, German, and Japanese markes, respecvely. I should no be surprsng snce a loss, such as.3636% (when w =. n he Canadan marke, he frs column of Table 2), does no necessarly consue a sgnfcan hrea ha causes nvesors o reallocae her porfolos. 7 4

15 I s of neres o noe ha when w =., meanng ha he nvesor uses US ndex-reurn performance as an ndcaor, he hreshold values are very sable, lyng n he neghborhood of.36%. However, when w =. or w s close o uny, he nvesor merely ulzes nformaon from he domesc sock-ndex reurn o assess subsequen sock reurns, he esmaed coeffcens appear o have more varaon across dfferen counres. The esmaed ( ) (= and 2) shows nsgnfcan or even generaes conflc sgns. Ths suggess ha he mpac of US sock news has a more conssen and unform effec on he me-seres srucures of he major sock-ndex reurns. Ths s n agreemen wh marke observaon, n he sense ha he US marke closes las n a gven radng day, and hus carres more nformaon conen wh respec o marke developmens. Nex, he d values (he hrd row from he boom) derved from he poseror modes ndcae ha he mos approprae me delay ha nvesors employ o assess he marke condons s one day. Ths holds rue generally for he markes of Canada, he Uned Kngdom, and Japan. In he case of he German marke and wo nsances n he Canadan marke (w = and ), he hghes frequency of d occurs a lag 2 among he lags {,2,3,4} n our smulaon. 8 However, as he wegh ncreases n he German marke (w.7 ), he d values swch o, suggesng ha he value of d s no ndependen of w n he modelng process. Ths s conssen wh common nuon or asymmercal nformaon, where local-marke nformaon appears o be more accessble o domesc nvesors. As a resul, marke reacons appear o respond more rapdly. 4.. Esmaon resuls for he mean equaon As shown n Tables 2 hrough 5, he Bayesan analyss of each sock-ndex reurn n reacng o sock news exhbs dfferen behavor. The esmaed mean coeffcens and her correspondng sandard errors obaned from regme (bad news) are n general much larger n magnude han hose appearng n regme 2 (good news), dsplayng asymmercal effecs n he dfferen regmes. Specfcally, he esmaes for markes n he Uned Kngdom, Germany, Japan, and Canada (for w up o.7) exhb a very smlar behavor. The sgn of he parameer s posve and sascally sgnfcan. The esmaed values of are n general larger han hose of, ndcang ha he response of sock reurns o pas nformaon s more sensve n regme (bad news) han n regme 2 (good news). Ths s conssen wh exrapolave, rsk averse behavor ha suggess when nvesors receve news, good or bad, hey end o carry he marke momenum o 5 () ()

16 presen an exrapolave behavor, gvng rse o a posve AR() process. However, he rsk averson wll lead nvesors o reac more sensvely and hence produce a more profound effec on shor sales upon recevng a bad news han wll on her buyng acves n response o good news. I s hs asymmercal behavor ha generaes asymmercal prces movemens. Snce nvesors are assumed o use wo ses of nformaon as npu o projec marke prce movemens, he asymmercal effec s lkely o vary as he weghng parameer changes. We found he asymmercal effec becomes less sgnfcan when sock-reurn news s measured by placng a heaver wegh on he domesc marke. In an exreme case, whch we mpose a w =, he evdence for Canada, he Uned Kngdom, Germany, and Japan appears o be conssen wh he paral prce-adjusmen model (Amhud and Mendelson, 987; Damodaran, 993; Koumous, 998) n ha he esmaed mean coeffcens lnkng curren reurns o pas reurns are larger n a good news regme han n a bad news envronmen. In comparson wh he earler analyss shown n Table 2, wh he excepon of some Canadan cases, he esmaed mean equaon s domnaed by 9 US marke news, as seen by varyng he w values from zero o abou.7. The ndvdual coeffcens for US and domesc sock reurns can be obaned by he producs of () ( ) w and ( w), respecvely. For nsance, f we are neresed n knowng he UK sock reurn equaon n he regme, he coeffcens are.39375(= ) and.4375(=.4375.) for a lagged US sock reurn and a lagged U.K sock reurn, respecvely. Thus, he esmaes produced by varyng he weghs provde a broader specrum of paramerc sensbly, reflecng varous reacons of fnancal behavor Esmaon resuls for varance equaon The sascal performance from Tables 2 hrough 5 also ndcaes ha condonal varance equaons are well represened by a GARCH(,) process as evdenced by he hgh level of sgnfcance of he esmaed coeffcens, supporng he phenomenon of volaly cluserng. In addon o hs sandard oucome, wo sgnfcan fndngs are worh nong. Frs, an asymmercal effec s also presen n he varance equaons. Ths can be seen from he consan componen of () () he varance versus. The esmaed values for are unformly hgher han hose of. In addon, he values of he average varance n regme, ( () / () () ), are much larger han hose n regme 2, ( / ), exhbng an asymmercal reacon of sock 6

17 Table 2 Bayesan esmaes for double TR-GARCH model: Canadan sock reurns and volaly Wegh () -.88* -.3* -.6*.526*.535*.694* (.53) (.53) (.93) (.222) (.228) (.349) ().479*.4693*.5322*.8975*.978*.8783* (.8) (.84) (.3) (.2) (.246) (.497).57*.475*.465*.335*.268*.23* (.82) (.8) (.96) (.96) (.9) (.2).4529*.545*.54*.5838*.639*.6756* (.) (.) (.7) (.89) (.98) (.234) ().248*.226*.28*.253*.36*.35* (.4) (.39) (.45) (.53) (.54) (.6) ().462*.453*.7*.972*.57*.52* (.9) (.95) (.62) (.65) (.6) (.78) ().8476*.8485*.922*.8974*.8799*.887* (.2) (.25) (.6) (.74) (.66) (.84) ( 2 ).49*.46*.44*.55*.69*.77* (.7) (.6) (.7) (.7) (.8) (.2).797*.783*.53*.97*.7*.282* (.8) (.4) (.4) (.45) (.43) (.57).882*.887*.85*.85*.84*.893* (.44) (.34) (.79) (.9) (.95) (.92) r * -.39* -.293* -.276* * -.252* (.2) (.53) (.264) (.325) (.32) (.445) d 2 2 () () ()

18 Table 2 (Connued) Coeffcen () (.23) (.35) (.385) (.364) (.48) ().863*.7589*.456*.28*.39* (.36) (.472) (.556) (.543) (.589) **.256*.3* (.2) (.28) (.6) (.2) (.2).6732*.624*.593*.3699*.2328* (.247) (.38) (.262) (.275) (.222) ( ).444*.479*.842*.99*.98* (.67) (.7) (.37) (.36) (.77) ().62*.27*.47*.452*.2229* (.2) (.53) (.2) (.93) (.35) ().8365*.8697*.8793*.8499*.773* (.25) (.56) (.9) (.99) (.36) ( 2 ).9*.2*.72*.25*.833* (.23) (.27) (.27) (.7) (.7).28*.234*.33*.229*.52* (.59) (.74) (.59) (.23) (.75).83*.865*.7866*.7549*.6394* (.2) (.23) (.68) (.29) (.36) r * -.224* * * * (.26) (.484) (.46) (.45) (.7) d () () () Noes: The horzonal headng n Table 2 s he wegh mposed on domesc news, w =.,.,,. n j z = wr + ( w) R The esmaed parameers are he poseror means, he numbers n parenheses are he poseror sandard errors; r-values are he hreshold values, whle he d values (he hrd row from he boom) are he poseror mode esmae of he delay parameer. The * ndcaes sascal sgnfcance a he 5% level or beer. 8

19 Table 3 Bayesan esmaes for double TR-GARCH model: UK sock reurns and volaly Coeffcen ().623*.542*.98* ** (.4483) (.49) (.476) (.56) (.52) (.528) ().498*.4375*.458*.392*.374*.354* (.399) (.49) (.448) (.59) (.542) (.555).34* *.346*.35**.258 (.65) (.78) (.65) (.62) (.6) (.6).2486*.272*.2674*.2698*.272*.269* (.238) (.266) (.265) (.28) (.284) (.297) ().846*.836*.24*.9*.78*.257* (.44) (.43) (.68) (.7) (.78) (.72) ().89*.6*.9*.98*.799*.76* (.78) (.72) (.75) (.6) (.48) (.37) ().8775*.8753*.88*.895*.948*.962* (.29) (.24) (.235) (.23) (.28) (.78).9*.76*.97*.24*.22*.257* (.73) (.66) (.67) (.65) (.64) (.69).6*.597*.623*.587*.679*.696* (.4) (.4) (.2) (.3) (.24) (.29).8784*.8767*.87*.879*.862*.854* (.9) (.75) (.8) (.86) (.86) (.93) r * -.277* -.333* -.346* * * (.272) (.498) (.298) (.29) (.86) (.77) d () () () Noes: (see Table 2). 9

20 Table 3 (Connued) Coeffcen () (.56) (.565) (.556) (.563) (.288) ().364*.2583*.9*.988**.369 (.579) (.585) (.565) (.549) (.33) (.6) (.7) (.68) (.69) (.443).2283*.968*.59*.78*.647 (.284) (.37) (.282) (.275) (.44) ().267*.99*.58*.965*.595* (.94) (.67) (.79) (.6) (.59) ().73*.724*.75*.78*.4* (.3) (.3) (.3) (.27) (.48) ().96*.957*.984*.95*.887* (.75) (.7) (.66) (.62) (.6).263*.258*.26*.262*.43* ( 2 ) (.7) (.7) (.72) (.7) (.).663*.63*.635*.625*.76* (.29) (.3) (.34) (.28) (.5).855*.8649*.8656*.8649*.8533* (.98) (.9) (.25) (.82) (.249) r * * -.4* *.78* (.3) (.389) (.479) (.47) (.2295) d () () () Noes: (see Table 2). 2

21 Table 4 Bayesan esmaes for double TAR_GARCH model: German sock reurns and volaly Coeffcen () -.398* -.422* * -.334* -.36* * (.36) (.335) (.338) (.344) (.36) (.366) ().4686*.5469*.5973*.5762*.4878*.447* (.343) (.37) (.425) (.622) (.539) (.54).959*.824*.684*.594*.376*.296* (.69) (.72) (.65) (.2) (.75) (.74).265*.2865*.372*.376*.295*.2444* (.27) (.23) (.255) (.278) (.294) (.278) ().232*.234*.2488*.2425*.2898*.2934* (.37) (.325) (.343) (.368) (.352) (.358) ().885*.856*.935*.644*.472*.48* (.23) (.223) (.234) (.26) (.24) (.98).7862*.797*.7876*.86*.832*.8433* () (.29) (.295) (.29) (.279) (.272) (.24) ( 2 ).35*.426*.453*.54*.52*.496* (.2) (.8) (.8) (.38) (.32) (.44).986*.6*.995*.4*.44*.98* (.) (.3) (.5) (.26) (.27) (.24).839*.8255*.827*.876*.827*.826* (.83) (.75) (.77) (.29) (.96) (.28) r * -.352* -.349* -.29* -.347* -.325* (.) (.24) (.7) (.54) (.78) (.9) d () () () Noes (see Table 2). 2

22 Table 4 (Connued) Coeffcen () -.676* * (.36) (.782) (.75) (.544) (.82) ().35*.47** (.426) (.758) (.634) (.522) (.562).287*.435*.454* (.76) (.99) (.2) (.238) (.282).8*.89*.235*.559**.583* (.287) (.337) (.32) (.38) (.294) ( ).237*.325*.282*.695*.65* (.274) (.394) (.36) (.246) (.37) ().34*.85*.76*.453*.89* (.84) (.68) (.57) (.7) (.232) ().8524*.8727*.8782*.844*.843* (.236) (.28) (.97) (.2) (.233) ( 2 ).324*.558*.48*.355*.927* (.26) (.3) (.9) (.32) (.2).925*.764* *.448* (.25) (.33) (.3) (.6) (.8).8232*.88* *.853* (.93) (.78) (.59) (.6) (.69) r * * -.436* * * (.32) (.92) (.25) (.57) (.224) d 2 () () () Noes (see Table 2)

23 Table 5 Bayesan esmaes for double TAR_GARCH model: Japanese sock reurns and volaly Coeffcen ().27*.264*.28*.2484*.2398*.263* (.4) (.395) (.388) (.462) (.52) (.556) ().488*.5329*.5835*.6499*.6474*.699* (.262) (.285) (.39) (.37) (.476) (.574).68*.64*.423*.56*.493*.352** (.99) (.97) (.24) (.86) (.97) (.9).257*.264*.2826*.253*.2357*.245* (.277) (.298) (.355) (.33) (.34) (.347) ( ).954*.38*.975*.266*.453*.846* (.7) (.68) (.97) (.72) (.8) (.2) ().322*.343*.389*.528*.467*.33* (.66) (.69) (.53) (.58) (.54) (.55) ().86*.86*.8572*.842*.8497*.8628* (.79) (.8) (.58) (.67) (.59) (.6) ( 2 ) **.57**.59** (.3) (.27) (.26) (.33) (.33) (.32).94*.89*.746*.536*.499*.472* (.99) (.) (.2) (.85) (.87) (.83).893*.893*.8955*.965*.8966*.889* (.4) (.2) (.4) (.92) (.94) (.96) r -.385* * -.25* * -.377* -.329* (.235) (.48) (.897) (.3837) (.24) (.25) d () () () Noes (see Table 2) 23

24 Table 5 (connued) Coeffcen ().25*.48** (.742) (.764) (.793) (.86) (.79) ().4753*.2287* (.679) (.686) (.654) (.596) (.537).322*.39*.329**.294**.378* (.75) (.76) (.74) (.73) (.77).777*.53*.87*.522*.9 (.36) (.36) (.286) (.258) (.238) ( ).282*.372*.3256*.34*.239* (.35) (.3) (.332) (.33) (.33) ().235*.328*.323*.299*.653* (.8) (.88) (.93) (.87) (.24) ().8689*.8582*.8586*.858*.827* (.96) (.28) (.2) (.22) (.234) ( 2 ).6*.69*.29*.99*.82* (.34) (.35) (.38) (.35) (.36).452*.462*.458*.423*.49* (.83) (.86) (.84) (.84) (.87).875*.8638*.8566*.8672*.8783* (.99) (.99) (.99) (.93) (.9) r * -.447* -.487* -.545* * (.5) (.64) (.62) (.32) (.395) d () () () Noes (see Table 2) 24

25 volaly o negave news versus posve news. Ths fndng of asymmercal volaly s conssen wh a number of resuls n he leraure (Campbell and Henschel, 992; Koumos, 998, Bekaer and Wu, 2, Marens and Poon, 2). The underlyng economcs s ha whenever bad news hs he marke, creaes fear and heghens sock volaly along wh large volume of sellng. Ths hgher level of volaly n he markes has o be compensaed by hgher expeced reurns, leadng o a declne n sock prces. Due o he very naure of volaly perssence, as mpled by he GARCH (,) process, he condonal volaly s expeced o be revsed upward furher due o marke momenum. Moreover, he leverage effec rgged by prce declnes could renforce he volaly acceleraon as n he sory descrbed by Bekaer and Wu (2). As a resul, we ancpae ha a negave shock n sock markes could generae a subsanal ncrease n condonal volaly. Noe ha when good news eners he marke, generaes an enhusasc spr ha smulaes marke volaly resulng from an ncrease of orders. However, hs ncrease n volaly wll be moderaed by prce declnes caused by demands for a hgher expeced reurn. A he same me, he leverage effec s also lkely o exhb downward pressure on he condonal volaly. Thus, he posve news does no necessarly creae a sgnfcan ncrease n condonal volaly. Pung hese wo sores ogeher, s clear ha he effec on condonal volaly s more profound when bad news hs he marke han when good news does () () Second, he sum of he esmaed coeffcens, ( + ), s close o uny, and ( + ) s no, mplyng ha he volaly n regme reveals hgh perssence or long memory. Ths suggess ha bad news ends o creae a longer negave effec han does good news. Ths emprcal fndng s que conssen wh nvesor behavor where experencng a loss n he sock marke wll creae a more perssen fear han would momenary gan and excemen derved from a posve sock reurn. 5. Esmaon resuls based on opmal weghng of sock news As shown n he prevous secon, he esmaed parameers and condonal varances vary wh he weghs used n consrucng he sock-reurn news varable. Ths sensvy analyss s useful snce changng coeffcens reflec markes responses oward dfferen emphass on he componens 25

26 of news n he prcng behavor. However, s mporan o search ou he opmal weghng ha s mos conssen wh he daa. In hs connecon, we also rea w as a parameer n our smulaon process. An opmal value of w s obaned from he MCMC samplng. The esmaed resuls are repored n Table 6. The evdence connues o show ha he esmaed values of and / ( ) are conssenly hgher n regme han n regme 2. Ths asymmercal evdence, ogeher wh he oucomes of, () () + beng close o uny, ndcaes ha sock reurns are more sensve n response o bad news and ha such unpleasan shocks ends o have long memory. The opmal weghs derved from he MCMC samplng are.2495,.25,.8, and.75 for Canada, he Uned Kngdom, Germany, and Japan, respecvely. Ineresngly, all of hese weghng values are relavely small and sascally sgnfcan. The wegh parameers range from.75 o These sascs sugges ha marke parcpans end o place a relavely smaller wegh on domesc sock-reurn news and greaer wegh on he US news n order o projec her sock reurns. Ths may be arbuable o he domnan economc and echnologcal power of he Uned Saes, as refleced n fnancal news, or smply o he fac ha he US marke s he las one o close secury radng n a gven busness day, or o boh facors. To see he precse mean equaons, we ncorporae he weghng nformaon no he esmaed coeffcens as shown n Table 7. The resuls n Table 7 provde more conssen and sable esmaed coeffcens, as compared wh he resuls n Table 2 hrough 5 obaned from he sandard model n Equaons () and. In parcular, esmaed coeffcens for boh lagged domesc sock reurns and he US sock reurns n regme are unformly greaer han hose n regme 2. A smlar resul s found n he average varance shown n Table 6. Tha s, [ / ( )] > [ / ( )]. The evdence, herefore, shows conssenly ha he coeffcens n boh he mean equaon and n he condonal varance dsplay an asymmercal effec. The esmaed resuls furher sugges ha he US sock reurns are a domnan facor n explanng naonal sock reurns, hus rejecng he effcen marke hypohess n our daa samples. An mporan mplcaon of denfyng he weghs n our sudy s ha he nformaon derved from Table 7 can be a sgnfcan npu for helpng fnancal managers o dfferenae he nformaonal mpac on () sock reurns and hence o manage her porfolos n response o dfferen ypes of shocks. () () 26

27 Table 6 Bayesan esmaes of naonal sock reurns for double TAR_GARCH model based on opmal weghed average of sock news Coeffcens Canada UK Germany Japan ().959*.675* -.459*.24* (.25) (.456) (.339) (.43) ().766*.4294*.5524*.499* (.29) (.45) (.338) (.265).49*.338*.833*.64* (.9) (.66) (.73) (.92).5322*.256*.287*.2545* (.85) (.239) (.238) (.269) ( ).65*.85*.225*.975* (.36) (.46) (.342) (.59) ().89*.*.82*.39* (.54) (.82) (.25) (.67) ().969*.8765*.7923*.866* (.59) (.222) (.293) (.76) ( 2 ).2**.88*.36*.37 (.) (.66) (.24) (.3).79*.64*.978*.946* (.93) (.5) (.6) (.97).8967*.878*.8322*.89* (.23) (.75) (.95) (.) r * * * -.385* (.32) (.276) (.44) (.82) 95%CI [-.3977,-.324] [-.3979,-.33] [-.3949,-.338] [-.43,-.3465] w.2495*.25*.8*.75* (.33) (.69) (.7) (.53) 95%CI [.2235,.2749] [.6,.664] [.929,.45] [.6,.58] d 2 () () () Noes: The esmaed parameers are he poseror means, he numbers n parenheses are he poseror sandard errors; r values are he hreshold values; d values are he poseror modes; w values are he opmal wegh. The * ndcaes sascal sgnfcance a 5% level or beer. 95% CI denoes he 95% credble nerval. 27

28 Table 7 Esmaes of naonal sock reurns based on opmal wegh of sock news n wo-regme model R CA R = R +.576R, CA US CA US f.2495r +.755R CA US CA US R, f.2495r +.755R.3765 >.3765 (Bad news) (Good news) R UK R = R UK UK +.426R R US US,, f.25r f.25r UK UK R R US US.3477 >.3477 (Bad news) (Good news) R GE GE US R +.496R, 2 2 = GE US R +.255R, 2 2 f.8r f.8r GE 2 GE R R US 2 US >.3552 (Bad news) (Good news) R JA R = R JA R JA +.25R us US,, f.75r f.75r JA JA R R US US.385 ) >.385 (Bad news) (Good news) Noe: Due o he negave sgn of r, he nequaly sgns can be confusng. To be specfc, f he prevous day s weghed average loses more han r %, s a bad news. However, f he prevous day s weghed average loses less han r % or has a gan, s good news. 28

29 6. Summary and concludng remarks In hs paper, we have nvesgaed he dynamc behavor of daly sock-ndex reurns of fve major sock markes. In conformance wh well-esablshed emprcal regulares, he sock-ndex reurns presen some degree of perssence and have subsanal nernaonal spllover; he volaly evoluon process appears o be descrbed well by a GARCH(,) specfcaon. To examne he asymmercal behavor arbued o he oucomes of sock reurns, we employ a compose sock-reurn news varable by a weghng average of he mos recen domesc and US sock-reurn news. 2 The evdence from he es equaons based on a Double TAR-GARCH specfcaon shows ha sock reurns are posvely correlaed wh sock-reurn news. Ths fndng n urn suggess ha sock reurns are posvely auocorrelaed and cross-correlaed wh he US sock-reurn news. Furher analyzng he relave sgnfcance of sock news revealed from he daa, Bayesan esmaon resuls sugges ha he opmal wegh s raher low, meanng ha a lower wegh s placed on domesc sock news versus US sock news n formng he news ndex or hreshold varable. Our esng resul hus favors he hypohess ha US marke-reurn news plays a domnan role n predcng domesc sock reurns, alhough an AR() erm has some explanaory power. Moreover, he opmal me lag for news ha hs he marke s one day, excep ha Germany marke dsplays wo days. Ths sudy shows conssenly ha asymmercal effecs are presen n boh he mean equaon and he condonal varance equaon. The emprcal resuls ndcae ha he esmaed coeffcens n boh mean and varance equaons are n general more sensve and larger n he regme where bad news occurs n comparson wh a regme of good news. In parcular, he prce change s more sensve when bad news hs he marke han when good news arrves. By comparng he average varances ( ) ( ) ( /( + ) ), =, 2, across dfferen weghs, he evdence shows ha placng more wegh on US sock news wll generae lower average varance. More neresngly, he sum of he esmaed coeffcens for he varance equaon n regme, uny han he sum of coeffcens n regme 2, + + () (), s much closer o, mplyng ha he volaly exhbs hgh perssence or long memory upon bad news h he markes. Ths suggess ha he bad news ends o creae a much longer negave effec han does good news. 29

30 Endnoes. In examnng nne developed sock marke ndexes, Koumos (998) presens a model o nvesgae asymmercal effecs and fnds ha asymmeres n he condonal mean are lnked o asymmeres n he condonal varance snce he faser adjusmen of prces o negave reurns gves rse o hgher volaly durng down markes. 2. If he sock ndexes follow a random-walk process, he sock reurns reflec random news. In hs R j R j j R j j P j R way, = P P = ε and = P P = ε ( and are sock ndexes for counry and j, expressed n naural logarhm), where and are domesc and foregn sock reurn news, respecvely. However, f sock reurns, and hence changes of sock prces, reflec a paral adjusmen oward he marke fundamenal prce,, ha s, P P = (- γ )( P and f P s assumed o follow a marngale process, hen he reurn seres wll follow an auoregressve process (see Koumos, 999). f P j P f P ) 3. LeBaron (992) and Koumos (998) specfy only one lag for he auoregressve parameer. Balle and DeGennaro (99) fnd a longer lag n he auocorrelaon parameer. The opmal lag lengh n our model wll be searched ou hrough our samplng process. In mos cases, we fnd one lag s suffcen o capure he nformaon. 4. In sandard samplng heory, he esmaor and sascal nference are obaned and he rue value of he parameer locaed n ceran confdence nervals. The shorcomng of hs mehod s ha he confdence can be defned only for a ceran resrced ses of nervals. Ths resrcon would no occur n he Bayesan mehod snce we can defne a densy funcon over he parameer space and hereby consder he probably ha a parameer les n. In he Bayesan approach, he poseror dsrbuon provdes probably dsrbuon over he parameer space obaned from he sample as well as from he a pror nformaon (Amemya, 994). The dscusson of Bayesan analyss and s comparson wh samplng heory can be found n Greene (2, pp ). 5. We also esmae he values of he poseror medan. The resuls are smlar o he values of poseror mean. To save space, we do no repor he values of medan, whch wll be avalable upon reques. 6. I s possble o presen mulple regmes wh dfferen hreshold values. In parcular, when he number of changes (regmes) s known, he MCMC mehod can be appled n a sraghforward manner. However, n pracce, s no easy o decde he number of regmes havng a parcular economc meanng. Moreover, he compuaon can be very cumbersome. 3

31 In our sudy, dvdng he daa no wo regmes allow us o examne he asymmercal phenomenon, whch s he man concern n hs sudy. 7. Noe ha n he hreshold model, does no auomacally use r = as a benchmark o defne he gan or loss of sock nvesmens. Raher, he hreshold s searched o dvde he process no wo dfferen srucures, condonal on he me-seres propery. Our noon dffers from ha suggesed by Bekaer and Wu (2), who argue ha negave unancpaed reurns resul n an upward revson of he condonal volaly, where posve unancpaed reurns resul n a smaller upward or even a downward revson of he condonal volaly (see her equaon ). Ther concern s o esablsh a lnk beween volaly and news n order o explan he asymmery. Our focus here goes beyond he volaly ssue; also addresses he lnk beween sock reurns and lagged news varables. Moreover, he sources of he news are aken from boh domesc and foregn markes. Our model s also a varance wh Marens and Poon s model (2) n ha her focal pon s on he correlaon of reurns hrough comparng synchronous versus synchronzed daa. Ther model, however, places no concern on he asymmery of he mean equaon and sock-reurn dynamcs. 8. In mplemenng he Markov Chan Mone Carlo mehod, we employ d =, 2, 3 and 4. The resul shows ha d = for mos counres and d = 2 for Germany has he hghes frequency. () j j 9. Noe ha he oppose sgn of and n Japan and Germany when w = s conssen wh he fndng by L and Lam (995) n her sudy of Hong Kong Hang Seng sock ndex.. In esmang he coeffcens n Tables 2 hrough 5, a specfc wegh s assgned n each case. However, he wegh n Table 6 s reaed as an endogenous varable, whch s one of parameers o be esmaed n he samplng process as oulned n Secon 3.2, Sep 4-(v).. Ths means ha n he above esmaes (Tables 2 hrough 5), he resulng sascs are subopmal when weghs oher han he opmal level are used. 2. An explc reamen of he leverage effec and he role of radng volume have no been ncorporaed no hs paper. The research by Gallan e al (992), Cheung and Ng (992), Bekaer and Wu (2), and Wu (2) has addressed hese specfc elemens n explanng he dynamcs of asymmercal volaly. 3

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