The transitory and permanent components of return volatility in Asian stock markets

Transcription

1 Invesmen Managemen and Financial Innovaions, Volume 10, Issue 4, 013 Yung-Shi Liau (Taiwan), Chun-Fan You (Taiwan) The ransiory and permanen componens of reurn volailiy in Asian sock markes Absrac Moivaed by he asymmeric volailiy phenomenon ha invesors respond more srongly o bad news han o good news, his sudy uilizes sock index reurns from seven Asian markes o es wheher here is any change in asymmeric volailiy during Asian financial crisis. Specifically, he auhors examine he ransiory and permanen componens of reurn volailiy hrough he asymmeric componen generalized auoregressive condiional heeroskedasiciy (AC-GARCH) model and empirical resuls show ha boh volailiy componens have displayed an increasing sensiiviy o bad news afer he crisis, especially he ransiory par. In essence, i is consisen wih Schwer s (1990) marke crash sudy and has special implicaions for boh regulaory and pracical purposes, i.e., he governmen should no overly inervene marke urbulence because he volailiy revers o is normal level quickly afer he crush. Keywords: volailiy, financial crisis, AC-GARCH model. JEL Classificaion: G01, G10. Inroducion The asymmeric responses of volailiy o reurn shocks and he volailiy componens have been coninuously documened in he lieraure for various financial asses (Speigh and McMillan, 000; Balaban and Bayar, 005; Byrne and Davis, 005; Kian and Kuan, 006). The asymmeric volailiy demonsraes ha negaive reurn shocks resuling from bad news appear o cause more volailiy han posiive reurn shocks resuling from good news (see Chrisie, 198; Koumos, 1999; Blasco e al., 00; Leeves, 007). A firs, academics aribue his phenomenon o firms financial leverage, i.e., he declining securiy prices would produce a higher deb o equiy, resuling in an increase in he volailiy of equiy. Black (1976) pioneered he asymmeric volailiy sudy and aribued i o firms leverage effec. Laely, some scholars propose volailiy feedback being he reason for asymmeric volailiy. For insance, Bekaer and Wu (000) and Wu (001) argue ha if marke risk premium is an increasing funcion of expeced volailiy, an expeced increase in volailiy raises he required reurn on equiy, leading o an insan sock price decline. Meanime, boh sudies provide evidence ha volailiy feedback dominaes he leverage effec. The componen volailiy demonsraes ha he volailiy could be decomposed ino a ransiory or shor-run and a permanen or long-run componen 1. Engle and Lee (1993) applied he componen generalized auoregressive condiional heeroskedasiciy (C-GARCH) model o assess he mean reversion of volailiy in US and Japanese sock markes and found he ransiory componen had a srong force pulling he volailiy back o is permanen componen. Yung-Shi Liau, Chun-Fan You, Chou (1988) and Pagan and Schwer (1990) poin ha sock reurn volailiy is a non-saionary process. Therefore, he finding of a uniroo in he volailiy process shows ha here is a ransiory and a sochasic rend componen in sock reurn volailiy. Moreover, Summers (1986) demonsraed ha a slow mean-revering componen wih ransiory volailiy migh be he cause of excess volailiy. Recenly, Shively (007) finds ha ransiory shocks accoun for as much as 68% of he shocks in he negaive-reurn high-volailiy regime and less han 4% of he shocks in he posiive-reurn regime. When he wo regimes are examined based upon volailiy, he sandard deviaion of sock reurns is around 43% higher in he negaive-reurn regime han in he posiive-reurn regime. Given he marke urbulence will change invesors risk aiude oward financial asses, Yang and You (003) have examined he Asian sock reurn volailiy during Asian financial crisis period. This paper exends heir sudy abou he characerisics of decreasing absolue risk aversion o decompose he volailiy increases in he pos-crisis period 3. The decreasing absolue risk aversion indicaes ha invesors have become more risk averse afer he Asian financial crisis due o he grea wealh shrink, hus hey overweigh more severely he poenials of negaive shocks. In addiion, Schwer (1990) and Engle and Musafa (199) deec ha while sock reurn volailiy is high righ afer he Ocober 1987 crash, i revers o normal levels swifly a he end of Kim and Kim (1996) furher provide evidence ha he speculaive bubbles of 1987 is an example of unusually large ransiory shocks ha are shor-lived. This paper differs from earlier sudies in he following ways. While many sudies examine he effecs of financial urmoil on oal volailiy (see for example, Using a sandard dividend-discoun model o decide fundamenal value, LeRoy and Porer (1981) and Shiller (1981) demonsrae ha he sock prices are much more volaile han he underlying sream of dividend cash flows. This phenomenon is called excess volailiy. 3 Pra (1964) indicaes he absolue risk aversion is decreasing in wealh and he risk premium and invesors wealh are in he opposie direcion. Boh Campbell and Cochrane (1999) and Fang (001) suppor his decreasing absolue risk aversion. 181

2 Invesmen Managemen and Financial Innovaions, Volume 10, Issue 4, 013 Schwer, 1990; Engle and Musafa, 199), his paper emphasizes boh he asymmeric volailiy and volailiy componens of sock reurns during he Asian financial crisis. In essence, he asymmeric componen generalized auoregressive condiional heeroskedasiciy (AC-GARCH) model makes i possible o deec wheher here is any change in boh permanen and ransiory volailiy during his paricular window. The empirical resuls show ha a rising degree of ransiory and permanen asymmeric volailiy has been exhibied righ afer he Asian financial crisis, especially he shor-run par. The ransiory volailiy, however, dropped slowly aferwards, which means ha he regulaory auhoriy should no overly inervene during marke urbulence because volailiy revers back o is normal level afer a crash. The remainder of his paper is organized as follows. Secion 1 describes he daa and mehodology. Secion hen repors and compares he empirical resuls for he pre- and pos-crisis period as well as for he reversion period. Finally, concluding remarks and suggesions for fuure research are presened in he las secion. 1. Daa and research design This sudy uses closing prices for he sock indexes of Hong Kong (HK), Japan (JPN), Souh Korea (KOA), Malaysia (MAL), Singapore (SIG), Taiwan (TWN) and Thailand (THA). The daa has been rerieved from Daasream and sudy period exends from January 3, HK JPN KOA MAL SIG TWN THA o June 30, 004. Since Thai Bah s one-day devaluaion of 17% on July, 1997 ignied he Asian financial crisis, he whole period is accordingly pariioned ino hree nearly equal sub-periods: he pre-, pos-crisis and reversion period o alleviae he srucural break problem. I is worh menioning ha, in order o observe wheher he change of volailiy is a ransiory phenomenon, his sudy defines he hird sub-period, call reversion period. The pre-crisis period covers from January 3, 1994 o July 1, 1997 and he pos-crisis period sars from July, 1997 o December 31, 000, wih he reversion period begins from January, 001 and ends on June 30, 004. Daily index reurns descripive saisics of he hree sub-periods are lised on Table 1. The mean reurn ranges from in Thailand o in Taiwan for he pre-crisis sub-period. The mean reurns for each marke are negaive afer he crisis period excep for Singapore. In reversion sub-period, Thailand exiss he maximum mean reurn. Meanwhile, he volailiy is higher in he pos-crisis sub-period han pre-crisis and reversion sub-periods. The skewness saisics indicae ha all reurn series are eiher posiively or negaively skewed. The kurosis saisics sugges deparure from normaliy, ha is, all series are highly lepokuric. Thus, he Jarque-Bera saisics rejec he normaliy for each reurn series. The uni roo es resul of he Augmened Dicky-Fuller (ADF) shows ha all series are saionary. Table 1. The descripive saisics of seven daily sock reurn series Marke Period Mean Sandard deviaion Skewness Kurosis JB ADF Pre-crisis *** *** Pos-crisis *** *** Reversion *** *** Pre-crisis *** *** Pos-crisis *** *** Reversion *** *** Pre-crisis *** *** Pos-crisis *** *** Reversion *** *** Pre-crisis *** -6.5 *** Pos-crisis *** *** Reversion *** *** Pre-crisis *** *** Pos-crisis *** *** Reversion *** *** Pre-crisis *** *** Pos-crisis *** -9.4 *** Reversion *** *** Pre-crisis *** *** Pos-crisis *** *** Reversion *** *** Noes: *, ** and *** denoe significance a 10%, 5% and 1% level, respecively. Pre-crisis sub-period: HK, JPN, KOA, MAL, SIG, TWN and THA begin from January 3, 1994 unil July 1, Pos-crisis sub-period: HK, JPN, KOA, MAL, SIG, TWN and THA begin from July, 1997 unil December 31, 000. Reversion sub-period: HK, JPN, KOA, MAL, SIG, TWN and THA begin from January, 001 unil June 30, 004. JB represens Jarque-Bera saisics, esing for normaliy. ADF sands for he augmened Dickey-Fuller uni roo ess. The criical values of ADF a he 10%, 5%, and 1% level are -.57, -.86, and -3.43, respecively.

3 Invesmen Managemen and Financial Innovaions, Volume 10, Issue 4, 013 The diagnosics of condiional variance suggess ha a GARCH-class model would be appropriae. Neverheless, ordinary GARCH models of Bollerslev (1986) do no disinguish he differenial impacs of good news from bad news on volailiy. To examine he asymmeric responses of volailiy o posiive and negaive shocks, he Threshold GARCH (T- GARCH) improved by Glosen e al. (1993) is applied 1. The T-GARCH process is hen defined by: R R 1, (1) h d h (), where R and R -1 are he marke reurn a ime and -1, respecively. denoes a new marke shock a ime and ~ N(0, h ). d -1 sands for he dummy variable wih a value of uniy if -1 < 0 and zero oherwise. Equaion (1) describes he firs order auoregressive process for sock reurn, wih R 1 capuring he auocorrelaion. Equaion () expresses he process of condiional variance and describes condiional variance process o respond asymmerically o rise and fall in sock price. Specifically, posiive reurn shocks have an impac of, while negaive reurn shocks have an impac of +. If > 0, i indicaes he process of ransiory leverage effecs in he condiional variance. The Componen-GARCH (C-GARCH) model firs developed by Engle and Lee (1993) is employed o decompose volailiy ino a shor- and long-run componen. Engle and Lee (1993) applied he C- GARCH model o assess he mean reversion of volailiy in he US and Japanese sock markes and found he ransiory componen had a srong force pulling he volailiy back o is permanen componen. To observe wheher here is any volailiy change afer he financial crisis resuling from he shor-erm or long-run behavior, we combine he C-GARCH wih he T-GARCH ogeher, which allows for asymmeric news impac. Therefore, he asymmeric C-GARCH (AC- GARCH) can be described as follows: h q ( 1 q1) ( 1 q1) d1 (3) ( h q ), Nelson (1991) also used exponenial GARCH (E-GARCH) model o disinguish he effecs of good and bad news. However, E-GARCH model canno decompose volailiy ino a shor- and long-run componen. Therefore, he T-GARCH model in his sudy is adoped. Ané (006) agreed he abiliy of he C-GARCH model o capure he sandard feaures of sock reurn volailiy and significanly improves he goodness-of-fi. Furhermore, Gallagher (1999) and Hughes and Winers (005) also exhibied he presence of emporary and permanen componens in sock prices. q q ( h ). (4) Equaion (3) expresses he process of condiional variance and allows mean reversion o a ime-varying level q. I also describes condiional variance o reac asymmerically o reurn shocks, i.e., > 0 shows ha negaive reurn shocks will increase volailiy more han posiive reurn shocks of he equivalen magniude. Moreover, Hadsell (006) indicaes ha he volailiy move halfway back o is mean following a given deviaion, which is defined as in he T-GARCH model. A value less han one suggess a mean-revering condiional volailiy and shocks are ransiory in naure. Equaion (4) describes he permanen componen of variance, q, which converges o wih he speed of. If 1 > > , q represens he componen of variance wih he longes persisence, i.e., he permanen volailiy will dominae he condiional variance. Noe ha he AC-GARCH model reduces o he T-GARCH if eiher = = 0, or = = 0.. Empirical resuls Table liss he esimaion resuls by applying he T-GARCH model o he hree sub-periods. In all markes, 0, and is saisically significan a he 5% level excep for Japan and Taiwan in he precrisis period. Alhough he coefficiens of is insignifican in Japan and Taiwan, is sign is consisen wih oher markes. The resul of poscrisis and reversion sub-periods also shows ha is posiive. Esimaion resuls of 0 indicae he posiive firs order serial correlaion. This resul suggess a nonsynchronous rading exiss in all markes. The condiional variance shows ha he GARCH erms are highly saisically significan in all markes for he hree sub-periods and similar o hose findings in prior applicaions o financial daa. The asymmeric volailiy is capured by > 0 and he asymmeric response of volailiy o reurn shocks holds in each marke, i.e., negaive reurn shocks end o influence fuure volailiy more han posiive reurn shocks do. Relaive o pre-crisis and reversion sub-periods, all he are higher during he pos-crisis period excep for Thailand, showing ha invesors are more sensiive o pas negaive reurn shocks during he pos-crisis period. The volailiy persisence measure of ranges from in Singapore o in Malaysia for he pre-crisis sub-period and from in Singapore o in Malaysia for he pos-crisis sub-period and in Taiwan o in Souh Korea for he reversion sub-period. This resul furher presens ha in he pos-crisis period exiss larger oal volailiy. Furhermore, all is less han one in each marke for he hree subperiods, exhibiing ha shocks are largely ransiory. 183

4 Invesmen Managemen and Financial Innovaions, Volume 10, Issue 4, 013 Diagnosic ess for model appropriaeness are performed on he sandardized and squared sandardized residuals via Ljung-Box ess. We also uilize he sign bias, negaive size bias, posiive size bias, and join ess o capure he robusness of he asymmeric volailiy effec, all of which are proposed by Engle and Ng (1993) and he relevan supporing saisics are lised in he boom panel of Table (see Appendix). In order o examine wheher he shor- and long-run volailiy have changed afer he Asian financial crisis, Table 3 illusraes he esimaes of he AC- GARCH model for he hree periods. In each marke is posiive for he hree periods, meaning ha he ransiory asymmeric volailiy exiss in he pre-, pos-crisis and reversion sub-periods. Similar o he resuls of T-GARCH model, all he are higher during he pos-crisis period excep for Thailand. Moreover, he values of is larger in he pos-crisis period excep for Japan. In hese six markes, he average values of is in he pre-crisis period and in he pos-crisis period and in he reversion period. This resul is similar o ha of Shively (007), i.e., he ransiory volailiy resuling from negaive shocks is larger in he high volailiy regime han in he low-volailiy regime. Moreover, since he ransiory volailiy in he reversion period reurns o he level in he pre-crisis period, he oucome demonsraes ha he higher volailiy afer he financial crisis is a shor-run phenomenon. Normally, a high value of means he permanen volailiy is more persisen by naure. I can readily be observed ha all he figures of are larger in he pos-crisis period han oher wo sub-periods. For insance, he average values of is for he pre-crisis sub-period, and he value is for he pos-crisis sub-period, while i is for he reversion sub-period. This suggess ha in he poscrisis period sock markes are lighly increasing volaile and increasing asymmeric, i.e., alhough a higher long-run volailiy afer he Asian financial is found, he financial urmoil does no obviously change is volailiy rend. The only excepion is Japan, wih is coefficien of much smaller in he pos-crisis sub-period. Furhermore, he values of are larger han in hree sub-periods. This resul shows ha even hough he permanen componen of volailiy has slighly changed afer he Asian financial crisis, he permanen volailiy sill dominaes he condiional variance. According o AC-GARCH model, () measures he varying ransiory (permanen) volailiy. The empirical resuls exhibi ha he values of () are larger in he pos-crisis sub-period excep for Japan. Furhermore, he incremen of ranges from in Hong Kong o in Thailand, while he incremen of is from in Singapore o 0.07 in Souh Korea for hese six markes, i.e., he incremen of is higher han he incremen of for he pos-crisis sub-period. Clearly, a higher volailiy following he Asian financial crisis is due primarily o shor-run bu no o long-run volailiy increase. Pang (000) indicaed ha a sharp decline of sock reurns in Thailand before he Asian financial crisis could be he reason why he ransiory asymmery in volailiy is no ha significan in he pos-crisis subperiod. For insance, he SET index of he Thai sock marke fell from is op of 1753 on January 4, 1994 o 57 on June 30, 1997, causing invesors o lose abou 70 percen of heir porfolio value before he financial crisis. The slower speed of mean reversion in Japan before he crisis may be he resuls of domesic asse bubbles emergence. However, he crisis did no seem o be oo much affeced (see Gong e al., 004). Shively (007) and ohers indicaed ha asymmeric ransiory volailiy was higher in he negaivereurn high-volailiy regime han in he posiivereurn regime. The reason why invesors reac much more srongly o pas negaive reurn shocks is heir wealh has shrunk markedly. Supporing prior findings, we furher decompose volailiy ino ransiory and permanen componens and he empirical findings exhibi ha sock marke volailiy increases afer invesors have suffered losses, wih his effec being displayed in relaion o boh ransiory and permanen componens of volailiy. In essence, boh a higher degree of ransiory and permanen volailiy afer he Asian financial crisis has been deeced. Moreover, he effec of shor-run volailiy increase is larger han ha of long-run volailiy afer he Asian financial crisis, exhibiing ha he higher volailiy following he Asian financial crisis is primarily aribuable o shor-run volailiy increase. Conclusions and implicaions Differen from previous research, his sudy ess boh he shor- and long-run volailiy in Asian sock markes using he AC-GARCH model. The empirical resuls no only suppor he asymmeric volailiy hypohesis bu also deec an increasing sensiiviy o bad news in boh ransiory and permanen volailiy, especially he ransiory par, which is consisen wih which is consisen wih Schwer s (1990) marke crash sudy. This means ha he governmen should no overly inervene marke urbulence because he volailiy revers o is normal level quickly afer he crush. And invesors have o emphasize socks fundamenal sides in lieu of shor-run volailiy. 184

5 Despie achieving he major objecives of his invesigaion, numerous issues remain unsolved and warran fuure research. For insance, fuure sudy could examine wheher he ransiory and permanen References Invesmen Managemen and Financial Innovaions, Volume 10, Issue 4, 013 componen of volailiy also exiss in condiional beas. I is hoped ha he findings of his sudy can simulae furher research and shed more lighs on he sock behaviors in emerging markes. 1. Ané, T. (006). Shor and long erm componens of volailiy in Hong Kong sock reurns, Applied Financial Economics, 16, pp Balaban, E. and A. Bayar (005). Sock reurn and volailiy: Empirical evidence from foureen counries, Applied Economics Leers, 1, pp Bekaer, R. and G. Wu (000). Asymmeric volailiy and risk in equiy markes, Review of Financial Sudies, 13, pp Black, F. (1976). Sudies of sock price volailiy changes, proceedings of he 1976 Business Meeings of he Business and Economical Saisics Secion, American Saisical Associaion, pp Blasco, N., P. Corredor and R. Sanamaria (00). Is bad news cause of asymmeric volailiy response? A noe, Applied Economics, 34, pp Bollerslev, T. (1986). Generalized auoregressive condiional heeroskedasiciy, Journal of Economerics, 31, pp Byrne, J.P. and E.P. Davis (005). The impac of shor- and long-run exchange rae uncerainy on invesmen: A panel sudy of indusrial counries, Oxford Bullein of Economics and Saisics, 67, pp Campbell, J.Y. and J.H. Cochrane (1999). By force of habi: A consumpion-based explanaion of aggregae sock marke behavior, Journal of Poliical Economics, 107, pp Chou, R.Y. (1988). Volailiy persisence and sock valuaions: Some empirical evidence using GARCH, Journal of Applied Economerics, 3, pp Chrisie, A.A. (198). The sochasic behavior of common sock variances-value, leverage and ineres rae effecs, Journal of Financial Economics, 10, pp Engle, R.F. and C. Musafa (199). Implied ARCH models from opions prices, Journal of Economerics, 5, pp Engle, R.F. and V.K. Ng (1993). Measuring and esing he impac of news on volailiy, Journal of Finance, 48, pp Engle, R. and G. Lee (1993). A permanen and ransiory componen model of sock reurn volailiy, Working Paper No. 9-44R, Universiy of California San Diego. 14. Fang, W. (001). Sock reurn process and expeced depreciaion over he Asian financial crisis, Applied Economics, 33, pp Gallagher, L. (1999). A muli-counry analysis of emporary and permanen componens of sock prices, Applied Financial Economics, 9, pp Glosen, L., R. Jagannahan, and D. Runkle (1993). On he relaion beween he expeced value and he volailiy of he normal excess reurn on socks, Journal of Finance, 48, pp Gong, S.C., T.P. Lee and Y.M. Chen (004). Crisis ransmission: Some evidence from he Asian financial crisis, Inernaional Review of Financial Analysis, 13, pp Hadsell, L. (006). A TGARCH examinaion of he reurn volailiy-volume relaionship in elecriciy fuures, Applied Financial Economics, 16, pp Hughes, M.P. and D.B. Winers (005). Wha is he source of differen levels of ime-series reurn volailiy? The inraday U-shaped paern or ime-series persisence, Journal of Economics and Finance, 9, pp Kian, T.K. and N.K. Kuan (006). Exchange rae volailiy and volailiy asymmeries: An applicaion o finding a naural dollar currency, Applied Economics, 38, pp Koumos, G. (1999). Asymmeric index sock reurns: Evidence from he G-7, Applied Economics Leers, 6, pp Leeves, G. (007). Asymmeric volailiy of sock reurns during he Asian crisis: Evidence from Indonesia, Inernaional Review of Economics and Finance, 16, pp LeRoy, S. and Poror, R. (1981). The presen-value relaion: Tess based on implied variance bounds, Economerica, 49, pp Nelson, D.B. (1991). Condiional heeroskedasiciy in asse reurns: A new approach, Economerica, 59, pp Pagan, A.R. and G.W. Schwer (1990). Alernaive models for condiional sock volailiy, Journal of Economerics, 45, pp Pang, E. (000). The financial crisis of and he end of he Asian developmenal sae, Conemporary Souheas Asia,, pp Pra, J. (1964). Risk aversion in he small and in he large, Economerica, 3, pp Schwer, G.W. (1990). Sock volailiy and he crash of 87, Review of Financial Sudies, 3, pp Shiller, R. (1981). Do sock prices move oo much o be jusified by subsequen dividends?, American Economic Review, 71, pp

6 Invesmen Managemen and Financial Innovaions, Volume 10, Issue 4, Shively, P.A. (007). Asymmeric emporary and permanen sock-price innovaions, Journal of Empirical Finance, 14, pp Speigh, A.E.H. and D.G. McMillan (000). Inra-day volailiy componens in FTSE-100 sock index fuures, Journal of Fuures Markes, 0, pp Summers, L. (1986). Does he sock marke raionally reflec fundamenal values? Journal of Finance, 43, pp Wu, G. (001). The deerminans of asymmeric volailiy, Review of Financial Sudies, 14, pp Yang, J.J.W. and S.J. You (003). Asymmeric volailiy: Pre and pos financial crisis, Journal of Managemen, 0, pp

7 Appendix Table. Maximum likelihood esimaes of T-GARCH model for he pre-, pos-crisis and reversion sub-periods R 1, R h d h Pre-crisis sub-period Pos-crisis sub-period Reversion sub-period HK JPN KOA MAL SIG TWN THA HK JPN KOA MAL SIG TWN THA HK JPN KOA MAL SIG TWN THA *** *** ** (0.039) (0.06) (0.037) (0.03) (0.08) (0.046) (0.039) (0.065) (0.041) (0.075) (0.061) (0.048) (0.055) (0.064) (0.040) (0.041) (0.05) (0.05) (0.040) (0.05) (0.043) ** *** *** 0.07 *** *** ** ** ** *** *** ** * *** (0.038) (0.033) (0.037) (0.035) (0.037) (0.038) (0.031) (0.036) (0.036) (0.03) (0.035) (0.034) (0.034) (0.033) (0.037) (0.036) (0.035) (0.036) (0.039) (0.038) (0.035) *** 0.0 ** 0.08 *** 0.0 *** 0.10 *** 0.16 *** *** *** *** *** *** *** ** *** ** * *** 0.15 *** 0.06 *** 0.35 ** (0.009) (0.010) (0.09) (0.004) (0.07) (0.030) (0.047) (0.034) (0.05) (0.071) (0.01) (0.101) (0.036) (0.194) (0.008) (0.039) (0.039) (0.060) (0.040) (0.019) (0.098) ** ** *** *** ** * *** *** ** * (0.014) (0.013) (0.015) (0.008) (0.036) (0.013) (0.00) (0.010) (0.013) (0.05) (0.011) (0.041) (0.008) (0.036) (0.008) (0.018) (0.018) (0.054) (0.01) (0.011) (0.035) *** *** ** *** *** *** 0.04 *** *** *** ** 0.10 *** 0.3 *** *** *** ** ** *** 0.08 *** ** (0.019) (0.07) (0.035) (0.019) (0.040) (0.019) (0.063) (0.05) (0.06) (0.036) (0.01) (0.078) (0.06) (0.058) (0.013) (0.034) (0.03) (0.091) (0.03) (0.01) (0.049) *** 0.94 *** 0.87 *** 0.93 *** *** *** 0.84 *** *** *** *** *** *** *** *** 0.94 *** *** 0.94 *** *** 0.80 *** *** *** (0.013) (0.03) (0.033) (0.011) (0.05) (0.00) (0.038) (0.016) (0.06) (0.016) (0.008) (0.053) (0.018) (0.05) (0.010) (0.037) (0.04) (0.105) (0.040) (0.016) (0.069) Log L Diagnosics for T-GARCH model LB(1) * *** LB (1) * *** Sign bias *** *.346 ** Negaive size ** ** 1.07 Posiive size * Join es ***.511 ** ** 1.30 Noes: *, ** and *** denoe significance a 10%, 5% and 1% level, respecively. Numbers in parenheses are sandard errors. LB(1) and LB (1) are he Ljung-Box es saisics esing for auocorrelaion in he sandardized residuals and sandardized squared residuals of T-GARCH model up o he welfh lags. The regressions for he asymmeric volailiy ess are as follow: (1) Sign bias es: Z a bs e ; () Negaive size bias es: Z a bs 1 e ; (3) Posiive size bias es: Z a b ( 1 S ) 1 e ; (4) Join es: Z a b 1 S b S 1 b 3 ( 1 S ) 1 e, where squared sandardized residuals and S is a dummy ha akes he value of uniy if < 0 and zero oherwise. Asymmeric volailiy ess are -ess for coefficien b in (1), (), and (3). The join es is an F-es for regression (4). z is. Invesmen Managemen and Financial Innovaions, Volume 10, Issue 4,

8 Table 3. Maximum likelihood esimaes of AC-GARCH model for he pre-, pos-crisis and reversion sub-periods R R 1, h q ( q ) ( q ) d ( h q ), q q 1 ( 1h1). Pre-crisis sub-period Pos-crisis sub-period Reversion sub-period HK JPN KOA MAL SIG TWN THA HK JPN KOA MAL SIG TWN THA HK JPN KOA MAL SIG TWN THA ** *** *** ** *** *** (0.03) (0.04) (0.036) (0.09) (0.05) (0.041) (0.040) (0.059) (0.038) (0.008) (0.049) (0.047) (0.046) (0.065) (0.038) (0.047) (0.06) (0.03) (0.034) (0.05) (0.044) *** *** *** *** * *** ** *** 0.14 *** ** * ** *** (0.08) (0.09) (0.006) (0.033) (0.033) (0.036) (0.035) (0.034) (0.07) (0.034) (0.031) (0.035) (0.03) (0.035) (0.030) (0.034) (0.016) (0.034) (0.034) (0.09) (0.034) * * * ** 0.05 ** *** * * (0.040) (0.041) (0.078) (0.043) (0.083) (0.031) (0.070) (0.014) (0.035) (0.018) (0.040) (0.0) (0.030) (0.053) (0.07) (0.177) (0.018) (0.107) (0.094) (0.0) (0.088) 0.09 ** *** *** * *** *** *** *** * * ** * (0.041) (0.016) (0.047) (0.071) (0.08) (0.04) (0.088) (0.00) (0.047) (0.0) (0.05) (0.035) (0.09) (0.060) (0.040) (0.047) (0.0) (0.093) (0.050) (0.016) (0.048) *** 0.91 *** *** *** 0.65 *** *** * *** *** *** *** 0.76 *** 0.91 *** *** *** *** *** *** *** *** * (0.054) (0.04) (0.135) (0.3) (0.137) (0.133) (0.8) (0.016) (0.8) (0.01) (0.066) (0.06) (0.039) (0.088) (0.163) (0.59) (0.061) (0.160) (0.1) (0.011) (0.36) 0.03 *** *** *** *** 0.01 *** 0.08 *** *** *** 0.08 *** *** ** *** 0.07 *** *** *** *** *** *** 0.48 *** (0.005) (0.003) (0.009) (0.005) (0.006) (0.004) (0.014) (0.005) (0.008) (0.013) (0.006) (0.004) (0.00) (0.040) (0.011) (0.015) (0.048) (0.05) (0.011) (0.016) (0.018) *** *** *** *** 0.98 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** (0.011) (0.011) (0.031) (0.008) (0.01) (0.016) (0.01) (0.005) (0.019) (0.003) (0.004) (0.007) (0.040) (0.013) (0.031) (0.045) (0.011) (0.01) (0.044) (0.010) (0.055) * *** * *** 0.03 ** * ** (0.05) (0.038) (0.07) (0.018) (0.07) (0.014) (0.01) (0.005) (0.03) (0.011) (0.005) (0.007) (0.033) (0.039) (0.073) (0.183) (0.007) (0.04) (0.085) (0.03) (0.084) Log L Diagnosics for AC-GARCH model LB(1) * *** LB (1) * ** Sign bias *.10 ** ** 1.88 * *.387 ** Negaive size ** * Posiive size ** * Join es ** ** ** ** 0.44 Noes: *, ** and *** denoe significance a 10%, 5% and 1% level, respecively. Numbers in parenheses are sandard errors. LB(1) and LB (1) are he Ljung-Box es saisics esing for auocorrelaion in he sandardized residuals and sandardized squared residuals of AC-GARCH model up o he welfh lags. The regressions for he asymmeric volailiy ess are as follow: (1) Sign bias es: Z a bs e ; () Negaive size bias es: Z a bs 1 e ; (3) Posiive size bias es: Z a b S ) ( 1 1 e ; (4) Join es: Z a b 1 S b S 1 b 3 ( 1 S ) 1 e, where z is squared sandardized residuals and S is a dummy ha akes he value of uniy if < 0 and zero oherwise. Asymmeric volailiy ess are -ess for coefficien b in (1), (), and (3). The join es is an F-es for regression (4).. Invesmen Managemen and Financial Innovaions, Volume 10, Issue 4,