THE NEW MARKET EFFECT ON RETURN AND VOLATILITY OF SPANISH STOCK SECTOR INDEXES

Transcription

1 THE NEW MARKET EFFECT ON RETURN AND VOLATILITY OF SPANISH STOCK SECTOR INDEXES Juan Ángel Lafuene Universidad Jaume I Unidad Predeparamenal de Finanzas y Conabilidad Campus del Riu Sec. 1080, Casellón Jesús Ruiz Insiuo Compluense de Análisis Económico (ICAE) Universidad Compluense Campus de Somosaguas, 83 Madrid ABSTRACT Recenly (April 000), he New Marke index began o be compued in he Spanish Sock Exchange as a relevan indicaor of he new echnological firms behavior in he Spanish economy. This paper provides empirical evidence abou he relaionships beween he reurn and volailiy of Spanish secor indexes and he New Marke index volailiy. Using GARCH mehodology, empirical resuls reveal a posiive significan impac on he financial, indusrial and uiliies secor volailiy, ha is, high volailiy in New Marke end o increase volailiy in he oher secors. On he oher hand, only saisical effec is deeced on reurn of indusrial secor, suggesing ha only his secor require a risk premium when shocks in he echnological secor increase he global marke risk. RESUMEN Desde abril del 000 el índice del llamado Nuevo Mercado empezó a conabilizarse en la Bolsa española como un indicador relevane del comporamieno de las empresas ecnológicas en la economía española. Ese rabajo proporciona evidencia empírica sobre las relaciones enre el rendimieno y la volailidad de los índices bursáiles secoriales españoles y la volailidad del índice bursáil del Nuevo Mercado. Uilizando la meodología GARCH, los resulados empíricos revelan un impaco significaivo imporane sobre la volailidad de los índices de los secores financiero e indusrial, es decir, la ala volailidad del Nuevo Mercado iende a incremenar la volailidad en los oros secores. Por oro lado, sólo se deeca un efeco significaivo sobre el rendimieno del secor indusrial, sugiriendo que sólo ese secor precisa de una prima de riesgo cuando los shocks en el secor ecnológico incremenan el riesgo de odo el mercado.

2 1 Inroducion In he mos recen years echnological firms have become a very imporan facor in he world economic developmen. They mos ofen provide efficien ways for evenual communicaions, leading o a general reducion of ransacion coss. Spanish economy has also seen he increasing size of his secor and, as a consequence, in April 7, 000 he echnical advisory commiee of Ibex 35 1 decided he launching of he New Marke index wih an iniial marke value of 10,000 basis poins. This marke index ries o capure he behavior of Spanish echnological companies. The valuaion of hose kind of firms becomes very complicaed because of sandard ne presen value can no be fully applied o heir specific capial srucure. The recen shorsighed suppor of invesors o any idea around Inerne produced speculaive bubbles, enailing high increasing valuaions in he shor run. However, his rend has dramaically changed, and he marke has performed a drasic downward adjusmen in he share marke prices. For example, along he period covering January o April 001 one hundred fory-six companies have been removed in he Nasdaq index because of is marke price decreased beyond he one dollar. This is an imporan change relaive o similar ime period in he previous year, where only fory-six firms are removed. In he Spanish Sock Exchange he companies concerning he New Marke, especially Terra, have been also evolved according o a decreasing paern in he marke value. As a consequence, he New Marke index, wih a sysemaic fall in is level, achieved in May 31, 001 a negaive accumulaed reurn from is launching, exceeding he wo hundred per cen. I is readily apparen ha here is a connecion beween he Nasdaq and he oher echnological markes in he world. However, anoher ineresing issue is o es for possibly ineracions beween he echnological secor and oher ones concerning a cerain economy. This is a relevan quesion for porfolio managers rying in every ime period o allocae efficienly he resources of invesors. In his paper we provide empirical evidence for he Spanish Sock Exchange abou he relaionship beween he volailiy in he echnological secor (New Marke), and reurn and volailiy in he oher main Sock Exchange secors, ha is: financial, uiliies and indusry. 1 The Ibex 35 is a weighed index by capializaion level, composed of he 35 securiies quoed on he Join Sock Exchange sysem of he four Spanish Sock Exchanges, which are he mos liquid during he period conrol (here are wo ordinary revisions each year, in January and July, respecively).

3 Using GARCH mehodology in order o measure New Marke volailiy we are ineresed o es if price flucuaions in he echnological secor affec boh reurn and volailiy in he oher exchange secor. Afer esimaing New Marke volailiy an univariae TARCH (Threshold ARCH) model for each secor, allowing for possibly asymmeries in he volailiy, is fied. For each specificaion, he New Marke esimaed condiional sandard deviaion and variance appear as a poenial explaining facor in he average reurn and condiional risk, respecively. Resuls sugges ha here is a posiive significan ransmission of volailiy from he New Marke o he oher secors. The grea impac is on he financial secor. Therefore, a shock in he echnological secor disseminaes on he oher ones producing an increase in he risk. This empirical finding suggess ha boh indusry and uiliies secors can be used as alernaive allocaions o financial secor for invesors rying o minimize he impac of he marke risk underlying he echnological firms. On he oher hand, even hough he impac of New Marke volailiy on he reurns in he oher secors (uiliies, indusry, financial) has he expeced sign, his is only saisically relevan in he indusrial secor. The res of he paper is organized as follows: secion II explains he daa se and presens preliminary saisics. In secion III he esimaion of New Marke volailiy and mehodology o es hypohesis is described. Secion IV provides empirical resuls and, finally, secion V summarizes and makes concluding remarks. The Daa The daa se used in he paper is available in he home page of Sociedad de Bolsas, he Ibex index manager. For each of he following indexes a) Financial Ibex, b) Uiliies Ibex, c) Indusry Ibex and d) New Marke Index, he highes, he lowes, he open and he close daily prices are available. The sample period covers from April 7, The formula used in he calculaion of each index is: Index K is he number of companies included in he index, = Index K i= 1 S K i= 1 S i, 1 i, P P i, 1, where i, 1 ± J P, is he marke price a ime of he share i, i S, is he number of compuable shares a ime and J is he correcion for possibly capial increases. i 3

4 000 o May 31, 001. Overall, we have 87 rading days. However, daa observaions of he indusry, uiliies and financial Ibex are used in he curren secion wih descripive purpose from January, Figure 1 (see appendix 1) presens he ime evoluion of he close Ibex indexes as well as he New Marke close Index. I can be clearly observed ha index level in he four secors are non saionary in mean. Figure (appendix 1) shows he average monhly Garman-Klass (1980) volailiy for each secor index before and afer he inroducion he New Marke joinly wih he New Marke Volailiy. where For each day, he Garman-Klass saisic is he following: MAX MIN 1 MAX OPEN p ln p GKV = MIN CLOSE p p [ ln() 1] ln = 1,... 87, OPEN p, p, p and CLOSE p denoe he daily maximum, minimum, open and close price, respecively. This is a more appropriae saisic han he sandard deviaion when he analyzed series are non saionary. In his case, sandard deviaion migh be misundersanding because of is value capures he rend raher han he risk or price flucuaion. Figure ries o moivae he analysis by allowing for an iniial visual calibraion of he impac of he New Marke volailiy on he oher secor volailiies. This figure plo he average per cen volailiy for each moh from January 1998 o May 001, compued from daily Garman-Klass saisics. Figure sugges ha, beyond April 000, only he volailiy in he financial Ibex seems o replicae slighly he behavior of he volailiy in he echnological secor. Because of he non-saionariy in he index levels we use in he analysis he secor reurns. Table 1 (appendix ) presens summary saisics: a) mean, b) sandard deviaion, c) asymmery coefficien and d) he excess of kurosis. Taking ino accoun ha he Normal disribuion has no asymmery and an excess of Kurosis equal o 3, no dramaic discrepancies wih his disribuion arise. As expeced wih daily closing index, he mean of reurns is close o zero. 3 Volailiy Measure and Tes Procedure. In his secion we explain he mehodology used in order o measure he volailiy in he New Marke and also how o es if volailiy in he echnological secor affec boh reurn and volailiy of indusry, uiliies and financial secor. 4

5 A common feaure in financial reurns is ha volailiy is changing over ime. To incorporae his paern, Engle (198) iniially proposed he ARCH models and were generalized by Bollerslev (1986). Table (appendix ) shows he Lagrange-Muliplier ess for auoregressive condiional heeroskedasiciy in he marke reurn of all indexes. The empirical value of he es leads o rejec he null hypohesis of no ARCH a he 5% significance level, suggesing ha he four secor reurns have ime changing volailiy. On he oher hand, i is ofen observed ha downward movemens in he marke are followed by higher volailiies han upward movemens of he same magniude (see for example Engle and Ng (1993)). To accoun for his paern, Glosen, Jaganahan, and Runkle (1993) proposed asymmeric impac of he squared innovaions in he variance equaion hrough a dummy muliplicaive variable. Anoher alernaive is he EGARCH (exponenial GARCH) model iniially proposed by Nelson (1991) which capures volailiy clusering rough he size and he sign of lagged residuals. In order o provide preliminary evidence for he above highlighed paern Figures 3 o 6 show XY plos of reurn and Garman-Klass volailiy along he period ha covering from April 7, 000 o May 31, 001. I can be observed ha negaive and posiive reurns exhibis no similar paern in erms of volailiy suggesing ha volailiy responses are no symmeric in all secors. This is corroboraed by he saisics repored in Table 3. Even hough he absolue value of he average reurn is very close in he righ and lef hand side of he XY plo for al secors, average volailiy is higher under negaive reurns. Therefore, he previous discussion sugges ha o represen he dynamics of inraday reurns in each sock exchange secor a model should be used capuring a) ime changing volailiy and b) he presence of asymmeries in he response of volailiy under similar rends wih opposie sense. Our main objecive is o analyze he impac of New Marke volailiy in boh reurns and volailiy in he oher secors. To do his, firs we posi he following specificaion for New Marke index reurns: R NM = + βrnm, 1, α + ε, (1) ( 0 ) ε / Ω 1 ~ N, σ, () NM p q γ i σ NM, j + φ jε j + j= 1 j= 1 σ, = γ 0 + δε d, (3) 1 1 5

6 where d 1 1 = 0 if if ε ε 1 1 < 0, 0 ha is, an AR(1) in he mean equaion, wih a TARCH model for he condiional variance. The parameers φ j associaed wih he sandardized lagged innovaions measure he leverage effec in differen ime periods. Under asymmeries here would appear a leas one significan parameer a convenional levels. Under he previous assumpion of Gaussian condiional disribuion of disurbances, he log-likelihood funcion can be wrien as follows: T T 1 ε ( ) l µ = ln π lnσ, = 1 σ where T denoes he sample size and µ he parameer vecor o be esimaed. The log likelihood funcion is highly nonlinear in µ and a numerical maximizaion echnique is required. Table 4 presens he maximum likelihood esimaion of equaions (1) o (3) for p=1 and q= 3. As expeced, he esimaed parameer δ is significan a he 5% level, capuring he presence of asymmeries in he impac of new shocks in he marke. On he oher hand, as i is ofen observed in financial ime series, he parameer γ 1 is near o one, revealing high persisency in he condiional variance. This way, a shock in he variance equaion ends o produce very persisen effecs. Table 5 provides diagnosis saisics for he esimaed model, showing ha he considered specificaion successfully capures he behavior paern of New Marke reurns. No evidence of addiional ARCH srucure is deeced, and ineresingly, he null hypohesis of Normaliy in he empirical disribuion of sandardized residual is no rejeced a he 5% level. Also, Ljung-Box saisic exploring addiional srucure in he no sandardized residuals leads o accep he null hypohesis of no correlaion. Figure 7 shows he ime evoluion of he esimaed condiional variance in he New Marke. Once we have esimaed he New Marke volailiy, he following sep is o es if his measure of risk have explaining power abou he ime evoluion of reurns and volailiy in he oher sock exchange secors. We make joinly boh objecives wih GARCH mehodology since evidence of ime changing volailiy in he financial, indusrial and uiliies secors is previously provided. 3 The number of lags is chosen according o he maximum value of he likelihood funcion. The numerical algorihm used is he BHHH (Bernd, Hall, Hall, and Hausman). 6

7 where d The following specificaion for he secor s is used: R s, = s,0 + β s,1rs, 1 + β s,σˆ NM, 1 + us, u 1 β, (4) ( 0 σ ) Ω, (5) s, / 1 ~ N, s, p q s, = γ s,0 + γ s, i σ s, j + φs, jus, j + δ sus, 1d 1 + ϑsσˆ NM, 1 j= 1 j= 1 σ, (6) 1 = 0 if if ε ε 1 1 < 0, 0 and s = f, in, u, denoes he financial, indusrial and uiliies secor, respecively. The previous specificaion have he wo following characerisics: a) in he mean equaion he lagged condiional sandard deviaion of he New Marke is included as an explicaive variable 4 and b) he lagged condiional variance of he New Marke appears as a poenial explaining facor in he variance equaion. These wo characerisics allow for esing he impac of condiional risk in he New Marke on boh reurn and volailiy in each sock exchange secor from one rading session o he nex one. If New Marke volailiy is a relevan facor o explain reurn and (or) volailiy in a secor he parameer β s, and (or) ϑ would be significan a convenional levels. Under significan ransmission of volailiy from he New Marke, he sign of ϑ s deermine he naure of he ineracion. If New Marke flucuaions end o produce a higher desabilizaion of marke prices in oher secor he esimaed parameer should be posiive. Relaive o parameer β s, his can be inerpreed as price of he risk in erms of reurns, ha is, a risk premium. I is expeced ha a higher risk in he echnological secor, which definiely increases he global risk of a diversified porfolio, will produce a ransiory higher claim in he marke abou he performance in each secor. Therefore, he sign of he esimaed parameer δ s concerning equaion (4) should be posiive for each sock exchange secor. 4 Empirical Resuls In his secion we provide explanaion abou empirical resuls underlying in he esimaion of Equaions (4) and (6) under he assumpions poined ou in secion 3. 4 We include he sandard deviaion raher he variance in order o preserve he measure unis. 7

8 Tables 6 o 8 provide he maximum likelihood esimaion for each secor wih he following lag srucure: a) financial secor: p=1 and q=0, b) indusrial secor: p= and q=1, and c) uiliies secor: p=1 and q=1. All specificaions are seleced according o he maximum level achieved in he likelihood funcion. Several ineresing aspecs arise from hese ables. Relaives o he esimaed premium risk in each secor respec o he New Marke volailiy, all esimaed parameers ( β ˆ s, ) have he expeced sign. Moreover, he null hypohesis H β 0 agains he alernaive one H β 0 is rejeced a he 5% significance 0 : s, = 1 : s, > level. The addiional risk in he marke produced hrough shocks in he echnological secor induce o averse risk agens requiring an addiional reurn for suppor a high level of uncerainy in he marke value of heir porfolios. Even hough ˆ β s, > 0, s = f, in, u, no rejecion of he null hypohesis a he 5% significance level is observed, excep for he indusrial secor. This can be inerpreed as only agens invesing in equiies in his secor effecively require, in aggregae erms, a risk premium as a consequence of he increase in he global marke risk. The naure of his effec is ransiory. To clarify his, under he assumpion β < 1 s f, in u, s, 1 =, recursively subsiuing ino equaion (4), he secor reurn can be expressed as follows: R s, = β s,0 j + β s, β s,1σ NM, 1 j + 1 β s,1 j= 0 j= 0 β j s,1u s, j. (7) For all he secors, esimaed parameer β s, 1 saisfies he above resricion concerning he absolue value. Therefore, equaion (7) applies. I can be observed ha σˆ R s, NM, j = β s, β j 1 s,1. Therefore, if he esimaed parameer β s, 1 is no significan, an increase in he New Marke volailiy will only produce insananeous effecs in he s secor reurn. Relaive o he impac of New Marke volailiy on he oher secor volailiies our empirical resuls show a significan effec in all hree analyzed secors. All ˆs, =, parameers ϑ > 0, s f, in u are significan a he 5% level, suggesing ha here is a posiive ransmission of volailiy. Therefore, a higher risk in he New Marke ends o anicipae an increase of volailiy in he oher secors. Even hough he risk in all hree secors is no independen of he one concerning he New Marke, he impac on indusrial and uiliies secor is negligible relaive o he effec on he financial one. Even hough he financial secor is more volaile, he raio beween he esimaed 8

9 parameer ϑ ˆs, and he average esimaed condiional volailiy is exremely higher in he financial secor 5. The naure of he impac is no similar in all secors. As a difference of he impac on he indusrial and uiliies secor, he effec on financial secor volailiy impac is only ransiory. To beer undersanding, recursively subsiuing ino equaion (6) and assuming ha γ 1 he condiional volailiy in he secor s can be expressed as follows: s, 1 < γ j σ s, = z γ,1σ, (8) s,0 j + γ s,1 1 j + ϑs 1 γ s,1 j= 0 j= 0 s NM, 1 j where z q 1 = φ s, jus, j + δ s j= 1 u s, 1 d 1. Taking ino accoun ha he esimaed parameer saisfies his consrain equaion (8) applies for all hree analyzed secors. From equaion (8) yields σ σ s, j 1 = ϑ sγ s,1 NM, j, and as a consequence, if esimaed parameer γ s, 1 is no significan he increase of he New Marke volailiy will produce only insananeous effecs on he s secor volailiy. The specificaion of he variance equaion in he financial secor does no require he parameer γ, 1. On he oher hand, for boh indusrial and uiliies secor he esimaed parameer γ in, 1 and γ u, 1 are significan, respecively. Boh characerisics sugges ha indusrial and uiliies secor accommodaes shocks iniially carried ou in he echnological firms wih a lower speed ha he financial one. Figures 8 o 10 show he ime evoluion of he esimaed condiional variance in he financial, indusrial and uiliies secors. Figures 7 and 8 reveal ha condiional volailiy in he financial and echnological secor evolves wih a similar ime changing paern. This characerisic does no appear when comparing figure 7 wih figures 9 and 10. This is due o he differen naure in he impac. Whereas he impac of New Marke volailiy on indusrial and uiliies secor is highly persisen he effec on he financial secor is only ransiory and insananeous. Figures 7 and 8 sugges ha financial and echnological secors share a common ARCH feaure. Under such hypohesis, here is a linear combinaion of boh marke index reurns wih consan risk along ime. This is an ineresing issue for furher research ha can be esed following mehodology in Engle and Kozicki (1993) for any wo secors. f 5 These raios are: a) financial secor: 1,89.; b) indusrial secor: 19. and c) uiliies secor:

10 Finally, Tables 9 o 11 provides hree diagnosis kinds of saisics for he esimaed models. The Lagrange muliplier es on he sandardized residuals shows no remaining ARCH srucure. This is confirmed by he Ljung-Box saisic. Relaive o mean specificaion he Ljung-Box saisic also reveals no addiional srucure of correlaion in he no sandardized residuals. Also, he Bera-Jarque (1981) reveals ha he assumpion of Normal condiional disribuion is adequae in order o represen he sochasic behavior of he reurn for he hree analyzed secors. 5 Summary and concluding remarks In his paper we provide empirical analysis abou he relaionships beween New Marke volailiy and he sochasic behavior of Spanish Sock Exchange Secors. In paricular, wo issues are explored: a) he impac of New Marke volailiy in he marke reurns in oher secor (financial, indusrial and uiliies), and b) he link beween he New Marke volailiy and he risk in each of he previous secors. Daily closing daa covering he period from April 7, 000 (he launching dae for he New Marke index in he Spanish economy) o May 31, 001 are used. We firs esimaed he volailiy in he New Marke by fiing a hreshold auoregressive condiional heeroskedasiciy (TARCH) model, which allows for capuring asymmeries in he impac of innovaions in he condiional variance. We es he wo above hypohesis by esimaing again a TARCH model for each marke reurns of he financial, indusrial and uiliies secor, where he lagged condiional sandard deviaion appears as a poenial explaining facor in he mean equaion. Similar characerisic applies o he variance equaion relaive o he condiional variance of he New Marke. Our empirical resuls show a posiive ransmission of volailiy from he New Marke o he oher ones, ha is, a higher volailiy in he echnological secor ends o anicipae a increase in he volailiy in he financial, indusrial and uiliies secor. This empirical paern is a relevan issue for porfolio managers. The increase in he New Marke risk produces a higher volailiy in he oher secors, being he financial one in where a mos relevan impac appears. Even hough here is no secor wih orhogonal volailiy behavior relaive o New Marke volailiy, he naure of he effec is no similar. In boh indusrial and uiliies secors he New Marke volailiy impac is 10

11 highly persisen, as a difference of he financial secor in where only a ransiory impac is deeced. Concerning he relaionship beween he New Marke volailiy and reurns in he oher secors, even hough he sign of he esimaed parameer is he expeced one, empirical resuls only show a significan link in he indusrial secor. This implies ha only he indusrial secor requires a risk premium when marke risk increases from echnological shocks. Taking ino accoun ha he New Marke produces significan impac in all secors volailiy, an ineresing furher research is o es for common ARCH feaures beween each wo secors, following mehodology proposed in Engle and Kozicki (1993). If here were such paern here would be possible o idenify a combined porfolio wih wo secors having consan risk raher han changing volailiy. References Bera, A.K. and C. M. Jarque (1981): An Efficien Large Sample Tes for Normaliy of Observaions and Regression Residuals, Working Paper in Economerics, 40, Ausralian Naional Universiy, Canberra. Bollerslev, T. (1986) Generalized Auoregressive Condiional Heeroskedasiciy, Journal of Economerics, 31: Engle, R. F. (198) Auoregressive Condiional Heeroskedasiciy wih Esimaes of he Variance of U.K. Inflaion, Economerica, 50: Engle R. F. and S: Kozicki (1993) Tesing for Common Feaures, Journal of Business & Economic Saisics, 11 (4): Engle, R. F. and V. K. Ng (1993) Measuring and Tesing he Impac of News on Volailiy, Journal of Finance, 48: Garman, M. and M. Klass (1980): On he Esimaion of Securiy Price Volailiies from Hisorical Daa, Journal of Business, 53: Glosen, L.R., 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: Nelson, D. B. (1991) Condiional Heeroskedasiciy in Asse Reurns: A New Approach, Economerica, 59:

12 Appendix 1. Figures Daily Closing Index Sample: January, 1998 o May 31, New Marke launching: April 7, Figure 1 Indusry Uiliies Financial New Marke Average monhly Garman-Klass Volailiy Sample: January, 1998 o May 31, New Marke launching: April 7, 000 January-98 May-98 Sepember-98 January-99 May-99 Sepember-99 January-00 May-00 Sepember-00 January-01 May-01 Figure Indusry Uiliies Financial New Marke 14

13 0.15 XY Plo Reurn-Volailiy Financial Secor Volailiy Reurn Figure XY Plo Reurn-Volailiy Indusrial Secor 0.03 Volailiy Reurn Figure 4 15

14 XY plo Reurn-Volailiy Uiliies Secor Volailiy Reurn Figure XY Plo reurn-volailiy Technological Secor Volailiy Reurn Figure 6 16

15 New Marke Condiional Variance June 30, 00 Sepember 9, 00 December 9, 00 March 31, 01 Figure Condiional Variance of Financial Secor June 30, 00 Sepember 9, 00 March 31, 01 December 9, 00 Figure 8 17

16 Condiional Variance of Indusrial Secor June 30, 00 Sepember 9, 00 December 9, 00 March 31, 01 Figure Condiional Variance of Uiliies Secor June 30, 00 Sepember 9, 00 March 31, 01 December 9, 00 Figure 10 18

17 Appendix. Saisical Tables Table 1. Main saisics of Daily Index Reurns Ibex Index Indusry Uiliies Financial New Marke Mean Sandard Deviaion Asymmery Excess of Kurosis Table. LM es for ARCH(p) srucure in secor reurns p Indusry Uiliies Financial New Marke (*) (0.000) 1.91 (0.000) (0.000) 9.6 (0.00) (0.000) (0.000) (0.000) 5.74 (0.003) (0.000) 7.98 (0.000) (0.000) 4.09 (0.007) (0.000) 6.70 (0.000) 8.63 (0.000).9 (0.036) Noes: The sample period used is from January, 1998 o May 31, 001. (*) The sample period is from April 7, 001 o May 31, 001. In all cases he es is performed using he residuals from a leas squares regression of he marke index on a consan. The es saisic for he join significance of he p-lagged squared residuals is he number of observaions imes he R-squared from he regression. The asympoic disribuion of he F-saisic is a χ p. In parenhesis are he p-values. Table 3. Average reurn and volailiy under posiive or negaive reurns. Posiive Reurns Negaive Reurns Secor Average reurn Average Volailiy Average reurn Average Volailiy Financial Indusrial Uiliies New Marke

18 Table 4. Maximum likelihood esimaion of he TARCH model for New Marke index reurns Mean Equaion Variance Equaion α β γ 0 γ 1 φ 1 φ δ (0.0013) ( ) (0.0000) ( ) (0.0493) ( ) ( ) Noe: In parenhesis are he asympoic sandard errors. Table 5. Diagnosis of TARCH specificaion for New Marke Index reurns LM es (a) Ljung-Box es (b) BJ es (e) 1 lag lags 3 lags SR (c) NSR (d) (0.81) (0.9) (0.81) (0.56) (0.51) (0.64) Noes: (a) Lagrange muliplier es o es ARCH srucure on sandardized residuals. (b) (e) Ljung-Box es uses 10 lags. (c) Sandardized residuals. (d) No sandardized residuals. Bera-Jarque es on sandardized residuals. In parenhesis are he p-values. Table 6. Maximum likelihood esimaion of TARCH specificaion for Financial secor index reurns Mean Equaion Variance Equaion β f,0 β f, 1 β f, γ f, 0 φ f, 1 δ f ϑ f ( ) ( ) ( ) ( ) ( ) ( ) (0.0613) Noe: In parenhesis are he asympoic sandard errors. Table 7. Maximum likelihood esimaion of TARCH specificaion for Indusrial secor index reurns Mean Equaion Variance Equaion β in,0 β in, 1 β in, γ in, 0 γ in, 1 φ in, 1 φ in, δ in ϑ in (0.0010) ( ) ( ) ( ) ( ) ( ) (0.0375) ( ) ( ) Noe: In parenhesis are he asympoic sandard errors. 0

19 Table 8. Maximum likelihood esimaion of TARCH specificaion for Uiliies secor index reurns Mean Equaion Variance Equaion β u,0 β u, 1 β u, γ u, 0 γ u, 1 φ u, 1 δ u ϑ u ( ) ( ) ( ) (0.0000) (0.0569) (0.065) (0.0696) ( ) Noe: In parenhesis are he asympoic sandard errors. Table 9. Diagnosis of TARCH specificaion for Financial index reurns LM es (a) Ljung-Box es (b) BJ es (e) 1 lag lags 3 lags SR (c) NSR (d) (0.96) (0.50) (0.67) (0.19) (0.09) (0.0) Noes: (a) Lagrange muliplier es o es ARCH srucure on sandardized residuals. (b) (e) Ljung-Box es uses 10 lags. (c) Sandardized residuals. (d) No sandardized residuals. Bera-Jarque es on sandardized residuals. In parenhesis are he p-values. Table 10. Diagnosis of TARCH specificaion for Indusrial index reurns LM es (a) Ljung-Box es (b) BJ es (e) 1 lag lags 3 lags SR (c) NSR (d) (0.55) (0.84) (0.91) (0.35) (0.39) (0.11) Noes: (a) Lagrange muliplier es o es ARCH srucure on sandardized residuals. (b) (e) Ljung-Box es uses 10 lags. (c) Sandardized residuals. (d) No sandardized residuals. Bera-Jarque es on sandardized residuals. In parenhesis are he p-values. Table 11. Diagnosis of TARCH specificaion for Uiliies index reurns LM es (a) Ljung-Box es (b) BJ es (e) 1 lag lags 3 lags SR (c) NSR (d) (0.48) (0.7) (0.79) (0.43) (0.77) (0.6) Noes: (a) Lagrange muliplier es o es ARCH srucure on sandardized residuals. (b) (e) Ljung-Box es uses 10 lags. (c) Sandardized residuals. (d) No sandardized residuals. Bera-Jarque es on sandardized residuals. In parenhesis are he p-values. 1