Investment Management and Financial Innovations, 3/2005

Transcription

1 46 Invesmen Managemen and Financial Innovaions, 3/5 The Relaionship beween Trading Volume, Volailiy and Sock Marke Reurns: A es of Mixed Disribuion Hypohesis for A Pre- and Pos Crisis on Kuala Lumpur Sock Exchange Huson Joher Ali Ahmed, Ali Hassan, Annuar M.D Nasir Absrac The issue of sock volailiy on sock reurn has gained a remendous aenion among academics and praciioner alike as his reflecs behaviour of marke microsrucure. Therefore, umos objecive is o examine he volailiy characerisics of Kuala Lumpur Sock Exchanges by considering mixing variable (volume) as innovaion. This sudy presens a comprehensive analysis of he disribuional and ime series properies of reurns o deermine using GARCH model ha allows for ime varying variance in a process and can adequaely represen reurn volailiy. The resuls of our sudy indicae ha he reurn volailiy is bes described by a GARCH (,) specificaion. Curren volailiy can be explained by pas volailiy ha ends o persis over ime. We add volume as an addiional explanaory variable in he GARCH model o examine if volume can capure GARCH effecs. Consisen wih resuls of Najand and Yung (99) and Foser (995) and Huang, and Yong, C.W. () conrary o hose of Lamoureux and Lasrapes (99), our resuls show ha he persisence in volailiy remains in reurn series even afer volume is included in he model as an explanaory variable. This finding holds for conemporaneous volume when i is included in he variance equaion. Key words: volailiy, mixure of disribuion, GARCH, Mixure of Disribuion. Inroducion One of he conenious issue in he marke microsrucure lieraure has been he volailiy and sock expeced reurns. Issue has received considerable aenion boh in developed and developing counries due o imporan implicaion for invesors porfolio posiioning and liquidiy of heir invesmen porfolio. However, he issue remains illusive wih regard o he quesion of he asymmeric impac of good news (marke advances) and bad news (marke rereas) or informaion arrival on volailiy in hese emerging markes. I is General phenomena ha, he negaive shocks raise volailiy more han posiive shocks in he marke. This phenomenon has been aribued o he "leverage effec" (see Black (976), Nelson (99) and Engle and Ng (993)). In mos cases volailiy is an inpu used for purposes of marke measuremen. More recenly, here has been an emphasis on iner-emporal dependence models o explain he observaion of volailiy clusering in sock pricing. Financial ime series such as sock prices ofen exhibi he phenomena of volailiy clusering as he arrival of diverse informaion from various sources such as economic evens and news and oher exogenous economic evens such as war, and oher undesirable evens ha have greaer impac on he ime series paern of sock price. Thus in mos cases, financial ime series behave such a way ha does no conform o he normaliy disribuion. Hence, he volailiy observed in he marke is a naural applicaion for he auoregressive condiional heeroskedasiciy (ARCH). To observe his phenomena, ARCH model inroduced by Engle (98) and Bollerslev s (986) generalized ARCH (GARCH) model is used. The GARCH specificaion allows he curren condiional variance o be a funcion of pas condiional variances. Seminal works of Mandelbro (963) and Fama (965) indicaed ha he raes of reurns (percenage changes in price) implici in he ime series of sock prices are ime dependen. The evidence shows ha he disribuion of daily sock prices is characerized by lepokurosis, skew- Huson Joher Ali Ahmed, Ali Hassan, Annuar M.D Nasir, 5

2 Invesmen Managemen and Financial Innovaions, 3/5 47 ness and volailiy clusering. Several recen sudies provide evidence ha he GARCH mehodology is capable of capuring hese characerisics. Examples of such sudies include Schwer and Sambaugh (987), Akgiray (989), Connolly (989), and Ballie and DeGennaro (99) and o individual socks by Lamoureux and Lasrapes (99) and Kim and Kon (994) applied he GARCH model and o boh individual socks and indexes. These sudies generally found ha he GARCH processes fi he daa beer han ARCH and normal process. GARCH imposes an auoregressive srucure on he condiional variance, allowing volailiy shocks o persis over ime. A number of sudies have been carried ou o examine he impac of volailiy on sock marke reurns using differen mehodologies such as (a) simple analysis of variances, (b) linear regression analysis, (c) GARCH Models, and (d) causaliy analysis. These sudies, however, have largely been concerned wih he developed capial markes such as hose of he US., UK., Japan, and Hong Kong. In recen years, some effors have been made o examine hese issues for some emerging markes such as Malaysia, Porugal and Taiwan. In he developed capial markes such as hose of he US., UK., Japan, and Hong Kong, mos of he sudies find lile or no evidence of increased sock marke volailiy. While a sudy on he Malaysian marke done by Ibrahim e al. (999) using daily daa for Kuala Lumpur Composie Index (KLCI) and KLCI fuures conracs found no evidence of any increase in volailiy of he underlying marke following inroducion of fuures conracs in December 995 Anwar, Ariff and Shamsher (99), used Absolue Price Change and Trading Volume Mehod by running OLS regression o deermine volailiy in sock markes. However, in his sudy we diver our search by applying Lamourex and Lasrapes (99) model which accommodaes mixure of disribuion in volailiy clusering. Their model shows ha auoregressive condiional heeroscedasiciy (ARCH) phenomena end o vanish if he volume is considered in explaining he reurns volailiy. In paricular, rading volumes are found o be a good proxy for informaion arrivals in he US marke (Lamourex and Lasrapes, 99). However mos of previous sudies in developing markes fail o include volumes ino analysis (e.g., Ibrahim, 999 Huang & Liu, 995). Therefore, his paper aims a examining he volailiy of reurns using Lamourex and Lasrapes model o he Malaysian Sock Exchange Marke. More imporanly his paper seeks o address hree conenious issues. Firs, how far he reurns volailiy persiss in Malaysian Sock Marke Exchange. Such ess are insrumenal in supporing or refusing he MD hypohesis and have he poenial o provide inuiively clear inerpreaions o many ARCH relaed empirical finding? Second, does rading volume explain he informaion arrival o he marke? Third, Malaysia experienced an economy crisis in 997. Therefore, his paper also seeks o examine he naure of volailiy reurns of he Malaysian sock exchange marke (KLSE) prior and period covering he crisis period as differen resuls are expeced, since hese periods exhibi differen economic characerisics. The paper is organized as follows: secion reviews he lieraure o demonsrae wheher or no volailiy clusering exiss in he marke. While secion 3 of his paper highlighs he mehodology used o examine he sock price volailiy secion 4 presens and discusses he findings. The las secion concludes his paper. Lieraure Review Many sudies have documened he empirical evidence of a posiive conemporaneous correlaion beween rading volume and price volailiy. Schwer (989) using monhly aggregaes of daily daa on Sandard and Poor (S&P) composie index in NYSE evidenced a posiive relaionship beween esimaed volailiy and curren and lagged volume growh raes using linear disribued lag and VAR models. Similar issue was also addressed by Lamoureux and Lasrapes (99) using individual socks from he S&P index. They documened a posiive condiional volailiyvolume relaionship in models wih Gaussian errors and Generalized Auoregressive Condiional Heeroskedasiciy (GARCH)-ype volailiy specificaions. However, he finding was cauiously inerpreed as i may be biased due o he simulaneiy beween sock reurns and volume. Similar resuls were also found in Bessembinder and Seguin (993) for a variey of fuures markes. Finally, Gallan e al. (99), using nonparameric mehods, confirmed he posiive correlaion beween condiional volailiy and volume, when examining daily S&P daa from 98 o 987.

3 48 Invesmen Managemen and Financial Innovaions, 3/5 Volume and volailiy daa are also examined in a bivariae GARCH (Generalized Auoregressive Condiional Heeroskedasiciy) framework, as discussed by Engle e al. (984) and Bollerslev e al. (988), in order o deermine he inerrelaed characerisics of hese wo series. A bivariae GARCH model provides insighs ino he ineracions ha are no apparen in an ordinary leas squares model. Specifically, his approach provides esimaes of he imporance of volume and volailiy condiional upon he pas volailiy informaion of each of hese variables. Empirical aspecs of he volume-volailiy relaionship in he lieraure for various insrumens have been examined by Bessembinder and Seguin (993), Chang and Schacher (99), Gallan e al. (99), Harris and Raviv (993), Jain and Joh (988), Karpoff (987), Lang e al. (99), and Schwer (989). These sudies consisenly showed ha a significan relaionship exiss beween volume and volailiy, wih volailiy measured as he absolue price change or he squared price change While laes phenomena in he examinaion of voliiy of reurn have been he Mixure of Disribuions hypohesis, Clark (973), Epps and Epps (976), Tauchen and Pis (983), and Harris (986). Developed he hypohesis based on he assumpion ha he variance per ransacion is monoonically relaed o he volume of ha ransacion. Furher, i is assumed ha a mixing variable is he cause of he join volailiy-volume relaionship. Ofen he number (and implicily he imporance) of informaion arrivals are designaed as he mixing variable Each of he sudies under he mixure of disribuion models conains unique feaures. Clark's model employs volume as a proxy for he speed of informaion flow. He associaed volume and volailiy on a conemporaneous basis, wih no causal relaionship beween hem. Clark's model implies ha all groups who rade on informaion will have a similar relaionship beween volume and volailiy. Epps and Epps' model is based on he disagreemen beween raders: he greaer he disagreemen is, he larger he level of rading volume will be. They suggesed a causal relaionship from volume o volailiy. Also, heir model implies ha groups wih greaer disagreemen will have a more pronounced relaionship beween volailiy and volume. The Mixure of Disribuion model has received he mos aenion in he lieraure for he volailiy-volume sudies. Harris (987) and Tauchen and Pis (983) showed ha he join disribuion of changes in price (variabiliy) and volume are modeled as a mixure of bivariae normal disribuions and hey demonsraed ha he variance or absolue price change is a funcion of volume. The Sequenial Arrival of Informaion model was developed and exended by Copeland (976, 977), Jennings and Barry (983), Jennings, Sarks, and Fellingham (98), and Morse (98). This model assumed ha informaion is disseminaed sequenially from one group o anoher. This movemen of informaion creaes numerous price changes and volume. I also implies he coninuaion of higher volailiy afer he iniial informaion shock raher han spikes in volailiy. Admai and Pfleiderer (988) and Kyle (985) provided rading behavior models by associaing he iming of informed rades wih he size of uninformed volume. Consequenly, Admai and Pfleiderer show ha rading is bunched in ime, which jusifies he inraday U-shape volume and volailiy curves prevalen in he lieraure. Brock and Kleidon (99) associae he U-shape curves o marke closure, he power of dealers, and porfolio rebalancing. Harris and Raviv (993) and Shalen (993) developed he dispersion of beliefs/expecaions as he key facor deermining he addiional volailiy and addiional expeced volume associaed wih noisy informaion (as well as developing oher rading behavior relaionships in he fuures marke). Daa and Mehodology The secion sars wih he descripion of he general feaures of he KLSE CI reurns and volume series. The invesigaion period sars on January, 99 and ends on December 6,, giving a oal of 7 reurn observaions. The analysis periods are divided ino hree sub-periods: () pre-crises January, 99 o June 3, 997 (856 daily observaions); () during he crises July, 997 o December 3, 998 (374 daily observaions); and (3) pos-crises January 4, 999 o December 6, (49 daily observaions). This gives a oal of years (99 o ) wih 7 daily observaions.

4 Invesmen Managemen and Financial Innovaions, 3/5 49 The closing prices of (CI) were obained from he Kuala Lumpur Daily Diary Sock Guide. In order o explore he reurns volailiy and he rading volume, he reurns were calculaed based on he following formula: r m = * ln( CI / CI ), =,,,7, () where r m is he daily marke reurns, CI is he daily closing index a he ime Trading volume in day is expressed as equaion (): A. Model developmen V log( Vol / Vol ). () Since he seminal work (ARCH) of Engle (98), various hypoheses have been esed o explain he phenomenon in asse reurns. One plausible explanaion is ha daily reurns seem o be generaed by a mixure of disribuion (MD). In paricular, he rae of daily informaion arrivals can be viewed as a generaing process by he sochasic mixing variable. As poined ou by Diebold (986), a proper ARCH model can capure he ime series properies of such mixing variables. The Lamoureux and Lasrapes (99) model is presened below o illusrae ha he daily reurns can be presened as a subordinaed sochasic process: in which r u (3) (,,...) ~ N(, h ), (4) h p q h i j, (5) where r = Daily reurn; u = Consan; h = Condiional variance (volailiy) of a day ; = Consan; = Coefficien ha relaes o he pas values of he squared residuals o curren volailiy; = Coefficien ha relaes curren volailiy o he volailiy of he previous periods. Posiive parameers of and, ha he shocks adminisered o reurns volailiy persis over ime. The magniude of persisence is dependen on he size of hese parameers. Equaion (5) represens he persisence in erms of condiional variance ha can be esimaed by a GARCH (p, q) model. B. Operaional Model Using price daa alone excludes an imporan variable quaniy or rading volume, which may well lead o inadequae descripions of he marke. As Beaver (968) pu i, An imporan disincion beween he price and volume ess is ha he former reflecs change in he expecaions of he marke as a whole, while he laer reflecs changes in he expecaions of individual invesors. Viewed in his perspecive, i is imporan o examine join disribuion of boh price

5 5 Invesmen Managemen and Financial Innovaions, 3/5 and volume variables in order o provide more accurae saisical inferences. Well known in he lieraure, empirical invesigaions on speculaive prices have revealed kuroic properies as compared o he normal disribuion. The lepokuric disribuion of rae of reurns is a sampling consequence, when daa are pooled from a mixure of disribuions (MD) wih varying condiional variances. This is o say ha saisical ess employing boh price and volume variables end o suppor he MD hypohesis. In view of his assumpion, price daa can be viewed as a condiional sochasic process wih a changing variance parameer ha can be proxied by he volume (Karpoff, 987). Therefore, simulaneous consideraion of boh price and volume variables could shed new ligh on he undersanding of he financial marke. GARCH (,) Model The firs sep in esimaion procedure of Lamoureux and Lasrapes model is o esimae equaions () and (3) as illusraed above. Including volume variable ( V ) in equaions () and (3) gives he following generalized variance specificaion: r r, (6) ( V,,,...) ~ N(, h ), (7) h h 3V e, (8) where r = Daily reurns of CI; r = Condiional reurn on pas informaion; h = Condiional variance (volailiy) of a day ; V = Trading volume a day ; e = Whie noise; = Consan; = Coefficien ha relaes he pas values of he squared residuals o curren volailiy; = Coefficien ha relaes curren volailiy o he volailiy of he previous periods. As poined ou by Lamoureux and Lasrapes (99), a GARCH (,) specificaion is a parsimonious represenaion of condiional variance, while i fis comforably wih many economic ime series (e.g., Bollerslev,987). GARCH-in-Mean In 987, Engle e al. developed he GARCH-in-Mean o formulae he condiional mean as funcion of he condiional variance as well as an auoregressive funcion of he pas values of he underlying variable. r r h, (9) h h 3V ( V,,,...) ~ N(, h ), () e. () GARCH in he mean model is he naural exension due o he suggesion of he financial heory ha an increase in variance (risk proxy) will resul in a higher expeced reurns. Clark e al.

6 If Invesmen Managemen and Financial Innovaions, 3/5 5 V represens as reasonable proxy for informaion arrival and is serially correlaed, es- are signifi- imaion based on previous equaions, would yield 3 >, and values of and canly smaller han ha when V is no included (Lamoureux and Lasrapes, 99). In oher words, he mixing variable ( V ) is saisically significan in explaining he volailiy of sock reurns. According o he MD hypohesis, he inclusion of he mixing variable is expeced o rid he ARCH effec in sock reurns. In erms of empirical esimaes, i is manifesed in he size of +, a measure of persisence of shocks adminisered o he volailiy. Tha is, + is expeced o fall far below uniy, and boh end o be saisically insignifican wih he presence of V. The size of he sum of he coefficiens and denoes he degree of persisence in he condiional variance given a shock o he marke. In paricular, he persisence in volailiy as measured by he sum of and in GARCH (,) models should be less han in order o have a saionary variance. As he sum ends o he higher is he insabiliy- volailiy- in he variance and shocks end o persis insead of dying ou (see Engle and Bollerslev, 986). This implies ha curren volailiy of daily reurns can be explained by pas volailiy ha ends o persis over ime. Findings and discussions A. Characerisics of reurns To assess he disribuion properies of he daily reurns series, we use descripive saisics which are repored in Tables and. These saisics include he following disribuional parameers: mean, sandard deviaion, skewness, kurosis, maximum, minimum, median, value when a normal disribuion is fied o daa, Ljung-Box, and Durbin-Wason saisics (.9643). The ime series of reurn and volumes used for empirical analysis are shown in Fig.. Corresponding hisograms for he reurns and volume series are also shown in Fig R V Fig.. Time Series of Reurns and Volume

7 5 Invesmen Managemen and Financial Innovaions, 3/ Fig.. Hisogram of Reurns and Volume Series The sample mean of reurns is very small and he corresponding variance of reurns is much higher. The sample mean of he series is indisinguishable from zero a he 5% significan level. Daily reurns series display high measures of skewness and kurosis, indicaing subsanial deparures from normaliy. Likewise, he Jarque-Bera es resuls indicae ha he daily reurns do no have normal disribuion a he % significan level. Furher evidence on he naure of deparure from normaliy may be gahered from he sample skewness and excess kurosis (larger han 3) measures. The excess kurosis esimae for reurns is large, clearly a sign of peaked (lepokuric) end relaive o he normal disribuion (Fig. ). The skewness esimae is posiive, indicaing he disribuion has a righ ail (Fig. ). These wide ranges of saisics provide a conclusive rejecion of he hypohesis ha reurns series is sric whie-noise process. Descripive Saisics for Volume and Reurn Table Volume Reurn Mean Median Maximum Minimum Sd. Dev Skewness Kurosis Jarque-Bera Probabiliy.. A common finding in ime series regression is ha he residuals are correlaed wih heir own lagged values. This serial auocorrelaion violaes he sandard assumpion of regression heory ha disurbance is no correlaed wih oher disurbance. Before fiing any probabiliy disribuion model o daa, he underlying assumpions of he model need o be verified empirically. Almos all of he popular models of sock reurns require ha reurns be independen random variables, and many also require ha hey be idenically disribued. In order o es he hypohesis of independence, a es of whie noise process given by Ljung-Box-Pierce (Q-Saisic ) is preferred

8 Invesmen Managemen and Financial Innovaions, 3/5 53 in his sudy. The resuls of he ess are repored in Table, he Q-Saisics are significan a all lags, indicaing he presence of serial correlaion in he residuals. The values for hese Box- Pierce saisics are indisinguishable from zero indicaing ha hese saisics are significan even a low level. Thus, he hypohesis ha he reurn series is whie noise process is rejeced. Indeed, he presence of significan firs-order correlaion in reurns implies he rejecion of whie noise oo. Similarly, rading volumes exhibi a good deal of auocorrelaion phenomenon as shown in Table, which is consisen wih he finding of he Lamoureux and Lasrapes (99) model or Eq. 6. Auocorrelaion for lags Table Reurn Volume AR MA Q-Sa Prob. AR MA Q-Sa Prob Q () = Box Pierce Saisics wih lag period of. These resuls are evidence ha he reurns end no o be independen bu exhibi volailiy clusering. This is where periods of large absolue changes end o cluser ogeher followed by periods of relaively small absolue changes. This implies ha large reurns end o be followed by large reurns (of eiher sign); while small reurns end o be followed by small reurns. This suggess ha usual measures of reurns volailiy are emporally dependen (heeroskedasic). In oher words, he daa are characerized by ineremporal dependence in boh mean and variance. The auocorrelaion coefficiens of daily reurns of KLSE CI have one imporan implicaion. Tha is, using a condiional reurns ( r ), insead of a consan represened in Eq. 6 is preferred for he ime series wih significan auocorrelaion. In summary, he daa display all he previously documened characerisics of he uncondiional disribuion of reurns ha are used o jusify he various GARCH specificaions ha follow. B. All Sample Analysis (99-) Table 3 presens he resuls of fiing GARCH (,) - model I - process o he reurn series of KLSE. The parameers are esimaed joinly by using numerical echniques o maximize he loglikelihood funcions. The ieraion is carried ou unil convergence o he opimum is obained. The parameer esimaes of model I in Table 3 are saisically significan. The persisence in volailiy as measured by sum of and in model I is close o uniy. The fac ha he sum of and is fairly close o one indicaes he persisence of pas volailiy in explaining curren volailiy (see Engle and Bollerslev (986)). Moreover, hese resuls provide srong evidence ha he daily reurn series can be characerized by a GARCH (,) specificaion.

9 54 Invesmen Managemen and Financial Innovaions, 3/5 GARCH (,) Table Model I* Model II** * Equaion variance does no include he volume. ** Equaion variance includes he volume. All he saisics are significan a he 5% level. Lamoureux and Lasrapes (99) argued ha using volume, as a mixing variable in he condiional variance equaion would disappear he GARCH effecs. They hypohesize ha he persisence of volailiy as measured by + would become small and saisically insignifican if he rae of informaion flow, as measured by conemporaneous volume, explains he presence of GARCH in he reurn series. Najand and Yung (99) examined T-bond fuures wih a GARCH model and used conemporaneous volume in he GARCH equaion while Huang and Yang () examined reurns of he Taiwan Sock Index (TSI). Unlike Lamoureux and Lasrapes, hey found ha GARCH effecs remain when curren volume is included in he equaion for he condiional variance. This sudy also found ha volume does no remove he GARCH effec. Table 3 repors heses resuls which are similar o hose of Najand and Yung (99), Foser (995), Huang and Yang () and differ from hose of Lamoureux and Lasrapes (99) in ha he GARCH effec remains srongly significan. Wih respec o he impac of conemporaneous volume on volailiy, saisically significan coefficiens are obained for reurn series. These coefficiens are posiive and heir sum is fairly close o uniy, and do no undergo noiceable change when compared o he model wihou he proxy variable and heir impac on GARCH coefficiens is negligible. In Table 4, he GARCH-in-Mean analysis of Model I wihou volume and Model II including he volume are repored. Similar o resuls of GARCH (,) he ARCH effec is consisenly significan across reurns series. There is a posiive and saisically significan relaionship beween volume and reurns volailiy. Moreover, he sums of and are close o uniy (.84787), and do no undergo noiceable change when compared o he model wihou he proxy variable ( ). There is acually no improvemen over he resuls obained using volume. The resuls of using GARCH and GARCH-in-Mean are consisen wih hose of Foser (995) and indicae ha he presence of simulaneiy problem is less serious han ha suggesed by Lamoureux and Lasrapes (99). The failure of conemporaneous volume o capure GARCH effecs in condiional volailiy equaion is consisen wih he proposiion by Blume, Easley and O Hara (994) ha he volume provides informaion on he precision and dispersion of informaion signals, raher han serving as proxy for he informaion signal iself. GARCH-in-Mean Table Model I* *** Model II** *** * Equaion variance does no include he volume. ** Equaion variance includes he volume. *** significan a 5% level

10 C. Sub-Period Analysis Invesmen Managemen and Financial Innovaions, 3/5 55 The effec of he financial crisis on he level of he presence of volailiy was invesigaed by classifying he daa ino hree sub-caegories. The period from January 99 o July 997 was designaed as pre-crisis period, while July 997 o December 997 was classified as during-crisis period and January 998 o December was caegorized as pos-crisis period. Pre-crisis period Jan, 99-Jun, 997 Descripive saisics for he hree sub-periods are shown in Table 5. The mean for he period before he crisis is much beer han even he mean of he overall sample (Table ). I is worh recalling here ha he significan economic growh and invesmen boom experienced by Malaysia and he Eas Asian Region from he early 99s hroughou he period from 995 o996 helped much in he sabilizaion of he economic performance and business condiions. Under such circumsances i became easier for firms o predic he fuure earnings. The persisence in volailiy as measured by he sum of and in model I are close o uniy (.89385). Tha indicaes he presisence of pas volailiy in explaining curren volailiy. By including he conemporaneous value of volume ino he he condiional variance equaion model II yield a posiive and saisically significan relaionship beween volume and reurns volailiy. Moreover, he sums of and are close o uniy (.89676), compared o he model wihou he proxy variable. I is noiceable ha, when using he volume as a proxy of informaion conen of he marke reurns has failed o capure GARCH effecs in his period. The reason could be ha he volume urns ou o be imporan o demonsrae he economic growh and invesmen boom experienced by Malaysia. This period was characerized by large volailiy in sock prices which rose by 45% beween 99 and he end of 996. During crisis period Jul, 997-Dec, 997 In such fragile economy and flucuaing business condiions i would no be surprising o observe large impac on reurns. The high negaive mean of reurn ( 6.7%) suggess ha he reurns made a he end of he year 996 and he beginning of 997 were based on he predownurn of businesses. However, he assumpions upon which hese saisical signals were made did no hold any more as he economy slowed-down and businesses declined. The resuls are presened in Table 6. Sill he coeffiecens, and 3 are significan a he 5% level. The sum of and is fairly close o uniy (.9868). I indicaes ha he GARCH effec is consisen across reurn series. Including volume o model I do no vanish GARCH effecs; hey remains srongly significan. I is ineresing o see ha, his period has higher volailiy in prices han he oher periods. The possible reason is ha he Malaysian economy, paricularly Kuala Lumpur Sock Marke Exchange experienced a sharp financial collapse. Pos-crisis period Jan, 998-Dec, The mean for his period is 3%, which has improvemen compared o is level during he crisis period. This improvemen can be explained due o he economic recovery winessed by he Eas Asian Region, paricularly Malaysia. This remarkable recovery was a consequence of an increase in expor of elecoronic and elecrical producs and he fiscal expansion policy (increase in puplic consumpion expendiure). This in urn, improved he business cycle and as a resul firms made somewha beer reurns han he reurns derived during he economic downurn. In Table 6, he resuls of GARCH analysis of Model I and Model II are repored. Similar resuls have been obianed, GARCH effecs are consisenly significan. There is a posiive and saisically significan relaionship beween volume and reurns volailiy. I is observable ha, his period has less volailiy in prices han he previous periods. The reason could be due he improvemen of he Malaysian economy which experienced more sabiliy in he period.

11 56 Invesmen Managemen and Financial Innovaions, 3/5 Descripive saisics of reurn and volume for pre, during and pos crisis Table 5 Descripive Saisics of reurn and volume before crisis period (Jan 99-Jun 997) Mean SD Max. Mini. N Reurn Volume Descripive Saisics of reurn and volume during crisis period (Jul 997-Dec 998) Mean SD Max. Mini. N Reurn Volume Descripive Saisics of reurn and volume afer crisis period (Jan 998-Dec ) Mean SD Max. Mini. N Reurn Volume GARCH Model Table 6 Esimaions for he period before crisis (Jan 99-Jun 997) 3 + Model I Model II Esimaions for he period during crisis (Jul 997-Dec 998) 3 + Model I Model II Esimaions for he period afer crisis (Jan 998-Dec ) 3 + Model I Model II All he saisics are significan a he 5% level Conclusion This sudy presens a comprehensive analysis of he disribuional and ime series properies of reurns o deermine wheher a GARCH model ha allows for ime varying variance in a process can adequaely represen reurn volailiy. This sudy se ou o examine he volailiy of reurns in he Malaysian Sock Marke using 7 daily reurns from 99 o. The resuls of our sudy indicae ha he reurn volailiy is bes described by a GARCH (,) specificaion. Curren volailiy can be explained by pas volailiy ha ends o persis over ime. We add volume as an addiional explanaory variable in he GARCH model o examine if volume can capure GARCH effecs. Consisen wih resuls of Najand and Yung (99) and Foser (995) and Huang, B.N. & Yong, C.W. () and conrary o hose of Lamoureux and Lasrapes (99), our resuls show ha he persisence in volailiy remains in reurn series even afer volume is included

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