International Journal of Applied Econometrics and Quantitative Studies Vol.2-4 (2005)

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1 Inernaional Journal of Applied Economerics and Quaniaive Sudies Vol.2-4 (2005) MODELING MARKET VOLATILITY IN EMERGING MARKETS: THE CASE OF DAILY DATA IN AMMAN STOCK EXCHANGE ROUSAN, Raya * AL-KHOURI, Riab Absrac This paper aemps o invesigae he volailiy of he Jordanian emerging sock marke using daily observaions from Amman Sock Exchange Composie Index (ASE) for he period from January 1, 1992 hrough December 31, Preliminary analysis of he daa shows significan deparure from normaliy. Moreover, reurns and residuals show a significan level of serial correlaion which is relaed o he condiional heeroskedasiciy due o he ime varying volailiy. These resuls sugges ha ARCH and GARCH models can provide good approximaion for capuring he characerisics of ASE. The empirical analysis suppors he hypohesis of symmeric volailiy; hence, boh good and bad news of he same magniude have he same impac on he volailiy level. Moreover, he volailiy persiss in he marke for a long period of ime, which makes ASE marke inefficien; herefore, reurns can be easily prediced and forecased. JEL classificaion: C32, C5, G1 Keywords: Sock Exchange, Modeling Volailiy, Emerging Markes, Jordan 1. Inroducion The measure of asse s volailiy is a measure of is oal risk. Risk is one of he feaures usually analyzed by invesors in he process of deermining heir opimal efficien porfolio. Esimaing and forecasing financial marke volailiy is very imporan o invesors as well as o policy makers. I helps in invesmen decisions, securiy valuaion, risk managemen, and in selecing and choosing appropriae hedging insrumens (Anderson e al. 2000). In addiion, * Raya Rousan and Riab Al-Khouri, Professor of Finance, Deparmen of Banking and Finance, Yarmouk Universiy, Irbid-Jordan. riab_alkhouri@yahoo.com

2 Inernaional Journal of Applied Economerics and Quaniaive Sudies Vol.2-4 (2005) undersanding, measuring and pricing risk is imporan for allocaive efficiency, which has a grea impac on he economy as a whole. Many financial ime series such as he reurns on sock price indexes have cerain characerisics which are well cied in he lieraure. Previous research found ha asse reurns have lepokuric uncondiional disribuions (Mandelbro 1963, Fama 1963, Fama 1965), which is relaed o he ime varying volailiy (Corhay & Rad, 1994). They are characerized by volailiy clusering (Mandelbro 1963, Fama 1965). A any ime, any causal observaion of financial ime series reveals high and low volailiy episodes (Schwar 1989). This implies ha volailiy chocks oday will influence he expecaion of volailiy many periods in he fuure. Skewness can be relaed o he fac ha sock prices end o cluser; large (small) changes are followed by large (small) changes (Bollerslev, 1987), (Lo, 2000). Anoher feaure of sock reurns is mean reversion; hence, here is normal level of volailiy o which volailiy will evenually reurn. This implies ha curren informaion has no effec on long reurn forecas. Also one of he major findings in he lieraure is ha differen ypes of news have differen impacs on he volailiy level. This phenomenon is called he asymmeric or he leverage effec (Black 1976, Koumos e al., 1993, Anderson e al., 2000). I suggess ha sock price movemens are negaively correlaed wih volailiy. Empirical evidence repored by Black, Chrisie (1982), and Schwar 1989), however, suggess ha leverage alone is oo small o explain he empirical asymmeries observed in securiy process. Finally, i was found in he lieraure ha volailiy is highly persisen. Emerging markes have received grea aenion in recen years due o many facors. Firs, many emerging sock markes grew fas in erms of rading volume, number of lised companies and marke capializaion. Therefore, inernaional invesors have renewed ineres in hese markes o ge he benefi of heir aracive prospecs. Second, previous research found a low correlaion beween he developed and emerging markes, which made emerging markes ineresing for porfolio diversificaion. Alhough, Bekaer and Harvey (1995) suggesed ha many emerging markes are 100

3 Rousan, R., Al-Khouri, R. Modeling Marke Volailiy in Emerging Markes becoming more inegraed ino he global capial marke, here sill many differences beween emerging and developed sock markes. Third, emerging markes are found o provide higher reurn han hose of developed markes. The high reurn in emerging markes is associaed, however, wih high volailiy and high serial correlaion. Previous lieraure concenraed on few emerging markes as hose of Lain American and Asian markes as good candidaes for porfolio diversificaion. This moivaed researchers o sudy he reurn and volailiy behavior of hese markes. Even hough he Jordanian Marke is considered one of he mos imporan markes in he Middle Eas, lile aenion has been given o his marke by foreign invesors and by researchers. Therefore, his sudy is ineresed in capuring sock prices behavior by economerically modeling volailiy of Amman Sock Exchange Composie Index (ASE) for he period January 1, 1992 hrough December 31, We will show ha he volailiy of ASE is high and persiss for a long period of ime despie he 5% price limi imposed. We will examine if GARCH effecs do exis in he volailiy of ASE index reurns, and wheher sock reurns in he said marke display symmeric or asymmeric volailiy. We used he economeric models previously used in he lieraure, such as ARCH, and GARCH models, o find he mos appropriae one ha can capure ASE sock index reurns. Preliminary analysis of he daa shows significan deparure from he normaliy. Moreover, reurns and residuals show a significan level of serial correlaion which is relaed o he condiional heeroskedasiciy due o he ime varying volailiy. Since heeroskedasiciy makes he esimaion of asse pricing relaionships inefficien, herefore, appropriae economeric echniques should be implemened o conrol for heeroskedasiciy in our model. Our preliminary resuls sugges ha ARCH-ype models can provide a good approximaion for capuring he characerisics of ASE. The empirical analysis suppors he hypohesis of symmeric volailiy; hence, boh good and bad news of he same magniude have he same impac on he volailiy level. Moreover, he volailiy persiss in he 101

4 Inernaional Journal of Applied Economerics and Quaniaive Sudies Vol.2-4 (2005) marke for a long period of ime, which makes ASE marke inefficien; herefore, reurns can be easily prediced and forecased. The paper is organized as follows. Secion 2 will provide an overview of he main characerisics of Amman Sock Exchange. Daa and mehodology will be presened in secion 3. Secion 4 will provide an empirical analysis and shows he resuls of our analysis. In his secion, preliminary resuls will be provided firs which will pave he way o he volailiy analysis. Finally, he las secion will summarize and concludes he paper. 2. Characerisics of Amman Sock Exchange The emporary law No. 31 of he year 1976 gave he permeaion o esablish a marke known as Amman Financial Marke (AFM), and operaion were officially sared on he 1 s of January, AFM was esablished o regulae he issuance of securiies, a place ha could ensure safe, speedy and easy rading for suppliers and demanders and o proec small savors hrough a mechanism ha would define a fair price based on supply and demand. Moreover, wo major asks were given o AFM; firs o ake he role of Securiy and Exchange Commission (SEC), and he role of a radiional Sock Exchange. In March 1999 AFM was legally spli up o creae Jordan Securiy Commission (JSC) and Amman Sock Exchange, or he securiy marke. ASE is considered o be one of he mos imporan markes in he Meddle Eas, which currenly lifed all resricions on foreign invesmens. I consiss of wo markes; he primary and he secondary markes, and four major secors: Banking, Services, Insurance and Indusries. The secondary marke in ASE is subdivided ino six major markes; firs marke, second marke, hird marke, bonds marke, muual funds marke and ransacions off he rading floor. The ASE marke has winessed an increase in he number of lised companies hrough ou he years, which gives an indicaion of an economic growh in Jordan. Marke capializaion also increased since he esablishmen of he ASE marke. A he end of 2004, 192 companies were lised on he marke wih a oal marke capializaion of million JDs (Key Saisics of he ASE). 102

5 Rousan, R., Al-Khouri, R. Modeling Marke Volailiy in Emerging Markes ASE, like any emerging marke, is characerized by low urnover raio, low liquidiy, low ransparency, and he nonexisence of marke makers. The urnover raio for he period under invesigaion was 15.77% and he average daily urnover was 0.064%. These raios are considered o be very low and he rading aciviy in ASE marke is considered o be very hin (Chandrasekhar, 2001). One of he major acions ha migh affec he rading aciviy and by hen he average daily urnover is he ownership srucure of he marke. The ASE marke ownership is a composie of individual invesors (Jordanian and foreign invesors), insiuional, and governmen. Table 1 presens he ownership percenage on average for he period from 1992 o As can be seen from he able below, ha individual invesors own he highes percenage of securiies. Bu sill he average daily urnover is very low and can no be aribued o he ownership srucure. I can be said ha ASE is a shallow marke and he idea of invesmen in he sock marke is no popular ye especially o individual invesors. Table 1. Ownership srucure Average ownership percenage Foreigners 1.9% Arabs 9.2% Jordanian 88.9% Toal 100% Individuals 53.6% Companies 28.9% Governmen Agencies 4.6% Governmen 6.4% Ohers 6.5% Toal 100% In addiion, ASE imposes daily price limis on he sock prices. These limis are saed in erms of plus or minus a specific 103

6 Inernaional Journal of Applied Economerics and Quaniaive Sudies Vol.2-4 (2005) percenage of he previous day s closing price. This acion is aken o proec small invesors from big invesors who can influence sock prices by selling and buying large quaniies in he rading session. These limis were changed hrough he years, i was 10% before he Gulf War, and was reduced o 2% during he Gulf War on Afer 1991 unil now he price limi are se a 5%. The wo main resricions of 5% daily price limis along wih he resricion on shor selling have major implicaion on sock prices, such as producing high correlaion beween sock prices, making fuure prices predicable and reducing he efficiency of he marke. The resuls from he previous lieraure abou price limi is, however, conroversial (Kim and Sweeney 2002), while some argue ha price limis reduce he marke volailiy and invesor s overreacion (Ma e al. (1989)), ohers found ha price limis neiher reduce marke volailiy nor he invesor s overreacion (Kim and Rhee 1997) 3. Daa and Mehodology 3.1.Daa and variables definiion. The daa used in his sudy is he daily closing prices of he weighed index of ASE, from which he daily raes of reurns are calculaed as he firs difference in he logarihmic closing prices for he period form January 1, 1992 hrough December 31, A he end of 2004 he number of companies ha were included in he weighed index is 70. The rae of reurn on he index is calculaed by: R = (logp logp 1) *100 (1) where: R : is he reurn index a ime. P, P -1 : are closing index price a he curren day and previous day respecively. Two measures of volailiy are used in he lieraure: hisorical also known as realized volailiy, and implied volailiy. While implied volailiy represens he marke expecaions of a sock fuure price, hisorical volailiy is he measure of a sock movemen based on hisorical prices. I measures how a specific sock or an index moves over a cerain period of ime (Acive rader, 2001). In his paper we will use hisorical volailiy, measured by he sandard deviaion of he sock reurns. 104

7 Rousan, R., Al-Khouri, R. Modeling Marke Volailiy in Emerging Markes HV = n = 1 ( R R n 1 ) 2 m (2), S R = log S 1 R = R m= 1 (3), n (4) n where HV: hisorical volailiy; R : sock reurn; R m : average sock reurn; S : sock s price a curren day: S -1 : sock s price a previous day. To annualize hisorical volailiy, we muliply i by he square roo of he average number of rading days Mehodology. In order o esimae and forecas he volailiy of sock index reurn in Amman Sock Exchange (ASE) marke, four differen ARCH-ype models will be used, wo models for esing he symmeric volailiy; he ARCH and GARCH models and wo models for esimaing he asymmeric volailiy which are he EGARCH and GJR-GARCH models. Engle (1982) inroduced he Auoregressive Condiional Heeroskedasiciy (ARCH) model ha can capure mos of he sock prices behavior. ARCH model was generalized by Bollerslev in 1986 ino he Generalized Auoregressive Condiional Heeroskedasiciy model (GARCH). This generalizaion allowed for a more flexible lag srucure by including auoregressive erms of he volailiy (Sharma e al., 1996). To capure he asymmeric effec in sock prices, we will apply he Exponenial Generalized Auoregressive Condiional Heeroskedasiciy (EGARCH) model inroduced by Nelson (1991); his model can capure he asymmeric effec because he condiional variance depends on he sign of he lagged residuals (Helan, 2002). Anoher asymmeric model was inroduced by Golsen, Jagannahan, and Runkle in (1993); he GJR-GARCH model, in which conrary o he GARCH model he squared residuals have differen values depending on wheher hey are posiive or negaive (Helan, 2002). Finally, we will apply he Threshold ARCH (TARCH) model inroduced by Zakoian (1990) which is he same as he GJR-GARCH model, bu insead of modeling he condiional variance, i accouns for modeling he sandard deviaion. ARCH model inroduced by Engle (1982) is as follows (Sharma e al., 1996): 105

8 Inernaional Journal of Applied Economerics and Quaniaive Sudies Vol.2-4 (2005) R = β + ε ε ~ N(0, h ) X p Ω 1 2 h = α 0+ α iε 1 i= 1 (6) where: Y : is a random variable, he sock reurns. X β: is he condiional mean of he random variable, represening a linear combinaion of lagged endogenous and exogenous variables in he informaion se Ω available a ime -1, he residual is normally disribued wih zero mean and condiional variance h. p: is he order of he ARCH process, he number of lags. α 0, I α 1 and β: coefficiens o be esimaed using maximum likelihood esimaion. p > 0, α 0 > 0 and α i >0 mus be assured o ge a condiional variance h > 0. The condiional variance h in financial lieraure is called volailiy (Lo, 2000). The ARCH model was exended by Bollerslev in 1986, because i was found ha he ARCH model needed long lag lengh o be able o capure and explain he financial daa (he excess kurosis in daa), in which GARCH model allows for a more flexible lag srucure. Tha GARCH model is presened as follows: p q = + 2 ω α + iε i i= 1 j= 1 h β h Where j j p 0, q 0 α 0 0, α i 0 β j 0 These condiions are needed as in ARCH model so he condiional variance h > 0. The main difference beween GARCH and ARCH is ha GARCH model allows he condiional variance o be dependen on is pas values. The coefficien of α i represens he impac of curren news on he condiional variance process (volailiy), β j shows he impac of old news on he volailiy, or he persisence of volailiy o a shock. The level of persisence of volailiy as was shown by Engle and Bollerslev (1986) depends on he sum of α+β. If he sum equals or higher han uniy, hen he persisence of volailiy o a shock will las in he fuure and i is said o be an inegraive GARCH (IGARCH) process. However; if he sum is less han a uniy hen he persisence of volailiy is no expeced o las in he long 106 (5) (7)

9 Rousan, R., Al-Khouri, R. Modeling Marke Volailiy in Emerging Markes fuure, volailiy response o shocks diminishes by ime. The exisence of GARCH effecs in sock reurns requires ha α and β o be more han zero and significan (Sharma e al., 1996). ARCH and GARCH models could no capure he asymmeric effec in he financial daa, which is differen ype of news have differen impac on fuure sock marke volailiy. To solve his problem, Nelson (1991) inroduced a model ha can capure he sock marke behaviour including he asymmeric effec. This model is he exponenial GARCH (EGARCH) model wih he following equaion: ε 1 2 ε 1 logh = ω + α + β log( h 1) + δ h π 1 h 1 (8) Where ω, α, β and δ are coefficiens o be esimaed, and δ is he measure for he asymmeric effec, where he sign of yeserday s shock eners he model in conras o simple GARCH. The advanage of using he logarihmic consrucion on he EGARCH model is ha he condiional variance will be posiive, so here will be no need o impose a resricion of non-negaive coefficiens. If δ is less han zero or greaer han zero and significan, hen he daa is said o have a leverage effec. However, if he asymmeric coefficien (δ) is equal o zero hen boh posiive and negaive shocks of he same magniude will have he same effec on marke volailiy. The persisence of shocks o he volailiy is given by β (Lilien e al., 1995). Anoher asymmeric model is he GJR-GARCH model, which was inroduced by Golsen, Jagannahan and Runkle in 1993: 2 2 h = ω + αε 1+ βh 1+ δd 1ε 1 (9) d -1 : is a dummy variable ha is added o capure he asymmeric effec in daa. This dummy variable akes he value of one if ε -1 less han zero, and zero oherwise (Lilien e al., 1994, 1995). α shows he impac of good news, while α+δ he impac of bad news. The leverage effec exiss if δ is significanly greaer han zero. β measures he persisen in he condiional variance, he sum of α + β+ δ/2 provide he persisence of shocks on volailiy. If he sum is less han one hen he shock is no expeced o las for a long ime, close o one means ha he shock will affec volailiy and he volailiy 107

10 Inernaional Journal of Applied Economerics and Quaniaive Sudies Vol.2-4 (2005) can be prediced for some ime. However, if he sum of he coefficiens is one hen shock is o affec volailiy for he indefinie fuure. Like he GARCH model when coefficiens are equal o one he model will be (IGARCH) (Helan, 1993). 4. Empirical Resuls 4.1. Preliminary Resuls: Table 2 shows descripive saisics for he daa, sock price index and for he reurn on he index. I is obvious from his ha neiher he sock price index nor reurn index are normally disribued. They are boh significanly skewed o he righ and have an excess kurosis, and he series are lepokuric. The Jarque-Bera saisic es for normaliy confirms he resuls based on skewness and kurosis; he hypohesis of normaliy is rejeced a he level of 1% for boh price and reurn index. Ljung-Box es is used o es for he auocorrelaion beween daa by aking he firs-order up o he weny second-order. Table 2. Saisics for Price Index and he Reurn Index Price Index Reurn Index N Mean µ Sa. Dev. σ Skewness Kurosis Jarque-Bera *** *** Q(1) Q 2 (1) *** *** *** Q(2) Q 2 (2) *** *** *** Q(6) Q 2 (6) 18404*** *** *** Q(10) Q 2 (10) 30011*** *** *** Q(12) Q 2 (12) 35632*** *** *** Q(22) Q 2 (22) 61886*** *** *** Noes: Q (1-22) is Ljung-Box es for serial correlaion in he price index and reurn, Q 2 (1-22) is he Ljung-Box es in he squared reurn index. Jarque-Bera is he es for normaliy. *** denoe significance a he 1% level. Criical range of skewness for price index and reurn index are ± , ± respecively, as for he criical range of kurosis for price and reurn index; ± ,± respecively. 108

11 Rousan, R., Al-Khouri, R. Modeling Marke Volailiy in Emerging Markes The hypohesis of no serial correlaion is significanly rejeced a he level of 1% implying high level of auocorrelaion. The price index showed higher auocorrelaion han he reurn, his is due o he fac ha he reurns are calculaed by using he firs differences of he logarihmic price index, and differencing daa reduces he serial correlaion. Moreover; he auocorrelaion for he squared reurns are much higher han hose of raw reurn daa which is consisence wih he lieraure for he characerisics of financial series daa suggesing he presence of condiional heeroskedasiciy (Lo, 2000) and he persisence of volailiy. The high level of auocorrelaion can be caused by he imposiion of daily price limis on sock prices on ASE (Chiang & Doong, 2001). Figure 1 shows price index. 500 Figure 1. Price Index /01/92 11/01/95 9/01/99 7/02/03 PRICE For he price index and by applying boh uni roo ess, he hypohesis of non-saionariy is rejeced implying ha he price series is no highly saionary. However, when applying he same ess o he reurn index (by aking he firs differences of he price index), he hypohesis of non-saionariy is srongly rejeced by having a large negaive -saisics for he ADF and PP es, hese findings are supporive o he maringale process for sock prices. Unil his poin of analysis and afer esing daa for normaliy and uni roo, he daa is shown o be no normally disribued, and he exisence of condiional heeroskedasiciy. The nex sep is o make 109

12 Inernaional Journal of Applied Economerics and Quaniaive Sudies Vol.2-4 (2005) sure ha daa displays heeroskedasiciy hrough esing he unpredicable par of sock reurns, he error (residual) erm. This is done by running an Auoregressive regression for he reurn series by aking he sixh-lag order and es he sandardized residual for excess skewness and kurosis. Resuls showed ha he sandardized residual is no normally disribued, alhough he skewness coefficien is small, sill significanly skewed o he righ. However, he kurosis coefficien is significanly larger han hree so he residuals display excess kurosis hus, he residual is lepokuric. The Jarque-Bera saisics rejecs he hypohesis of normaliy a he level of 1%. The serial correlaion, using he Ljung-Box, shows ha he sandardized residuals are no correlaed up o he weny secondorder, bu he squared residuals is highly correlaed; he hypohesis of no serial correlaion for he squared residuals is rejeced a he level of 1%. This resul indicaes he exisence of ime-varying volailiy (volailiy clusering) in sock prices (Chiang & Doong, 2001). Table 3. Uni Roo Tes Price Index Reurn Index ADF PP Noes: ADF sands for he Augmened Dickey-Fuller es for he presence of uni roo. PP sands for Phillips-Perron uni roo es. The criical values for ADF and PP saisics are aken form Mackinnon (1991). Criical values: a 1%, a 5% and a 10%. Lag lengh: 4 for ADF and 8 for PP. A his sage i is clear ha ASE daa are no normally disribued and he exisence of condiional heeroskedasiciy (volailiy clusering) can no be rejeced. These characerisics herefore, sugges ha he ARCH-ype models provide a good approximaion ha capures he ime-series characerisics of he daily reurns in he Jordanian sock marke during he period under consideraion (Corhay & Rad, 1994) Volailiy Resuls: Table 4 presens he resuls for he four differen ARCH-ype models for he period from January 1, 1992 hrough December 31, The mean equaion in all models 110

13 Rousan, R., Al-Khouri, R. Modeling Marke Volailiy in Emerging Markes includes AR (1) o remove any serial correlaion in he reurns which may be caused by non-synchronous rading in he socks (Schwer, 1989). The firs lag order in he mean equaion was seleced based on he saisical significance of auocorrelaions (Chiang & Doong, 2001). Since reurn series showed significan auocorrelaions from he firs lag, we will include one lag in he mean equaion. Moreover, he number of lags order of he mean equaion mus be seleced based on he lowes Schwarz (SIC) and Akaike (AIC) informaion crieria (Corhay & Rad, 1994), which was also achieved by he firs lag order. The SIC and AIC crieria are also he main deerminan of he opimal lag srucure in he ARCH-ype models. Table 4. Esimaes of ARCH-Type Models ARCH (1) GARCH (1,1) EGARCH (1,1) GJR-GARCH (1,1) µ γ (1.7267)* (0.9971) (2.1712)** (1.6875)* (8.1087)*** ( )*** ( )*** ( )*** ω ( )*** (5.5384)*** ( )*** (5.5293)*** α (7.9988)*** (9.1114)*** ( )*** (7.3272)*** β ( )*** ( )*** ( )*** δ (1.2196) ( ) Log likelihood SIC AIC Noes: SIC and AIC are he Schwarz and Akaike informaion crieria respecively. The numbers in he parenheses are Bollerslev and Wooldridge robus -values. *, **, *** significan a 10%, 5% and 1% respecively. Resuls showed ha p=1 for he ARCH model, and p=1 and q=1 specificaions for he condiional variances of he GARCH, EGARCH and GJR-GARCH is opimal in erm of SIC and AIC crieria. 111

14 Inernaional Journal of Applied Economerics and Quaniaive Sudies Vol.2-4 (2005) Mean Equaion: R = µ + γar( 1) + ε Variance Specificaions: 2 GARCH (1, 1): h = ω + αε 1+ βh 1 EGARCH(1,1): ε 1 log h = ω + α 2 + β log ( h ) GJR-GARCH (1, 1): h ω h αε π β δ 2 2 = + 1+ h 1+ d 1 1 ε ε δ h Saring wih he mean equaion, he AR (1) coefficien for all specificaions are highly significan implying ha even afer aking ino accoun he impac of non-synchronous rading, reurn series sill exhibi serial correlaion. From he ARCH (1, 1) model, he coefficien ha represens he impac of curren news on volailiy α is highly significan. This resul implies ha he level of volailiy is direcly affeced by he impac of news ha eners he marke. ARCH model does no capure or measure he impac of old news on volailiy (he persisence of volailiy). In GARCH (1, 1) model, boh he ARCH and GARCH coefficiens (α and β respecively) are posiive and highly significan, hus he firs null hypohesis is rejeced agains he alernaive which means ha he reurn series in ASE marke is volaile and symmeric (ASE daa displays GARCH effecs). However, he persisence of he volailiy o a shock is esed by he sum of he ARCH and GARCH coefficiens. Resuls showed ha he sum is equal o which is less han a uniy; however, i is very close o one which indicaes a long persisence of volailiy in ASE marke (Corhay & Rad, 1994). In order o es for he asymmeric effec; wo models are used; EGARCH (1, 1) and GJR-GARCH (1, 1). From he EGARCH (1, 1) model, boh curren news and old news have grea impac on he volailiy level. Moreover, he persisence of volailiy given by β is and highly significan a he level of 1% indicaing a long memory in variance. The asymmeric effec coefficien (δ) is no significanly differen from zero, which means ha differen ypes of news have he same impac on he volailiy level. The asymmeric coefficien (δ) for GJR-GARCH (1, 1) model is also no significanly

15 Rousan, R., Al-Khouri, R. Modeling Marke Volailiy in Emerging Markes differen from zero. Based on hese empirical resuls, he volailiy of ASE marke is no asymmeric i.e. good and bad news has he same impac on fuure volailiy. The persisence level of volailiy is given by he sum of α+β+δ/2 in he GJR-GARCH (1, 1) model, and i is equal o , less han uniy bu very close o one. This resul is no differen from he resuls found from he GARCH (1, 1) and EGARCH (1, 1) models. This means ha shocks in ASE marke affec he volailiy for a quie ime in he fuure and will no be forgoen in a shor ime, his is consisence wih he resuls of Corhay and Rad (1994) Which Model Fis Daa Bes? In order o examine which one of he four models used fi daa bes, one mus look a he Schwarz (SIC) and Akaike (AIC) informaion crieria and he log likelihood value. The bes model mus have he lowes SIC and AIC and he highes log likelihood value. The Schwarz informaion crieria ranks ARCH (1) firs wih he lowes value, followed by GARCH (1, 1), and he highes values are given EGARCH (1, 1) and GJR-GARCH (1, 1) wih he same values. As for he Akaike informaion crieria, ARCH (1) also shows he lowes value followed by GARCH (1, 1) and GJR-GARCH (1, 1) wih he same value and EGARCH (1, 1) is he highes value. Alhough SIC and AIC rank ARCH (1) firs, he log likelihood value ranks i in he las place wih he lowes value. The firs place based on he log likelihood is o be given o EGARCH (1, 1) followed by he GJR-GARCH (1, 1) and GARCH (1, 1) models. Unil his poin i is no obvious which model can capure bes he characerisics of ASE reurns. So he deermining poin will be by looking a he diagnosic ess for he sandardized residuals for each model and compare i wih he sandardized residuals for he auoregressive for he raw daa. The bes model will be he model ha can reduce he kurosis of he daa and shows he highes level of normaliy. Resuls showed ha he ARCH (1) model has he highes Jarque-Bera es which indicae ha he residual from ARCH (1) is no normally disribued. Moreover, his model has he highes level of kurosis. This resul is similar o wha was found in he lieraure ha ARCH model can no capure high excess kurosis (Bera & Higgins, 1993). As for he auocorrelaion, i was found ha 113

16 Inernaional Journal of Applied Economerics and Quaniaive Sudies Vol.2-4 (2005) all researchers were ineresed in he Ljung-Box Q-saisic for he welfh order for he daily frequency (Sharma e al., 1996), (Chiang & Doong, 2001); so i will be appropriae o use Q (12) as he benchmark for comparing beween models in erms of auocorrelaion. Ljung-Box saisic for ARCH (1) for he raw residuals and squared are significan a 1% level which implies ha his model could no capure he ime-varying volailiy in ASE daa; so his model will be excluded from he comparison process. For he oher models, he Jarque-Bera saisic es for normaliy ranks GJR- GARCH (1, 1) firs wih he lowes value, followed by EGARCH (1, 1) and hen GARCH (1, 1). And by comparing hem wih he values from able 4, he Jarque-Bera is lower for all models bu sill significan and he hypohesis of normaliy is rejeced a he level of 1%. Furhermore; GJR-GARCH (1, 1) reduced he kurosis level he mos bu sill significanly higher han 3.As for he serial correlaion GARCH (1, 1) and GJR-GARCH (1, 1) could capure he imevarying volailiy of he daa, since he squared values of he Ljung- Box for he welfh order are no significan. On he oher hand, EGARCH (1, 1) which gave he highes value of he log likelihood could no capure his feaure. From he discussion above, ARCH (1) show he lowes values for SIC and AIC bu he lowes value of he log likelihood and is excluded from he comparison as menioned above. The highes log likelihood value is given by he EGARCH (1, 1) model followed by GJR-GARCH (1, 1) and he GARCH (1, 1). Alhough of hese facs, he EGARCH (1, 1) is hough o capure he volailiy clusering in ASE daa, which will lead o he second highes log likelihood, he GJR-GARCH (1, 1). The GJR-GARCH model show he lowes Jarque-Bera saisic value and is he model ha could reduce he kurosis values he mos, and moreover could capure he ime-varying volailiy of he marke under sudy. Since i was found ha he GJR-GARCH model was he bes o capure ASE reurn characerisics, he esimaed condiional volailiy using his model is shown in figure 2. The shaded areas in his figure represen he periods wih highes level of volailiy hrough ou he inerval under invesigaion. The firs shaded area is around he Oslo reay beween Palesine and Israel which were signed in he whie house on 13/9/

17 Rousan, R., Al-Khouri, R. Modeling Marke Volailiy in Emerging Markes 1.6 Figure 2. Condiional Volailiy /02/92 11/02/95 9/02/99 7/03/03 Condiional Sandard Deviaion As shown on figure 3 his period had high level of volailiy in he Jordanian marke. The second shaded area represens he period surrounding he signing of he peace reay beween Jordan and Israel on 25/7/1994 which also shows high level of volailiy, bu he volailiy level is lower han he level he marke showed surrounding he Oslo reay. The hird shaded area shows he period surrounding he deah of his Majesy King Hussein which surprisingly shows very low level of volailiy. The period from 11/9/2001 hrough 22/11/2001 is he period of he afermah of he elevenh of Sepember which was a shock o he enire world. And more recenly he Jordanian marke was affeced by he deah of he Palesinian Presiden Yasser Arafa on 11/11/2004 which is marked as he las shaded area in figure 3. As i is clear he Jordanian marke shows higher level of volailiy around he inernaional evens which means ha he Jordanian marke shows sabiliy when i comes o he naional even. Furhermore, each shaded area is more han wo monhs which means ha he volailiy level persiss for a quie ime in he fuure and shocks are no forgoen quickly, which is consisen wih he findings of he sudy. 115

18 Inernaional Journal of Applied Economerics and Quaniaive Sudies Vol.2-4 (2005) 5. Summary and Conclusions This paper aemps o invesigae and model he volailiy of he Jordanian emerging sock marke using daily observaions from Amman Sock Exchange Composie Index (ASE) for he period from January 1, 1992 hrough December 31, For achieving his purpose, he ARCH, GARCH, EGARCH and he GJR-GARCH models are employed. The firs wo models are for capuring he symmery effec whereas he second group is for capuring he asymmeric effec. ASE daa showed a significan deparure from normaliy and he exisence of condiional heeroskedasiciy (volailiy clusering). Therefore, he ARCH-ype models were used because i was found in lieraure ha hey are able o capure many of he financial daa characerisics, such as hick ails of he observaions, volailiy clusering and he asymmeric effec i.e. differen ype of informaion has differen impacs on volailiy level (Corhay & Rad, 1994). This sudy was buil on wo main hypoheses, he firs was o examine if ASE reurn display symmeric volailiy and he second was o invesigae if good and bad news have differen impac on he fuure volailiy a ASE marke (asymmeric effec). Empirical analysis came supporive o he symmeric volailiy hypohesis, which means ha ASE reurns are volaile and ha posiive and negaive shocks (good and bad news) of he same magniude have he same impac and effec on he fuure volailiy level. Also, i was found ha he volailiy response o a shock end o persis in he marke and no forgoen quickly. Alhough ASE reurn daa do no display asymmeric effec; he bes model ha could capure he characerisics of he said marke was he GJR-GARCH model which is an asymmeric model. The GJR-GARCH model was he bes according o he log likelihood value and o he diagnosic es of he model s residuals. The GJR- GARCH model reduced he kurosis level he mos and had he lower Jarque-Bera saisic value. Furhermore, his model capured he ime-varying volailiy in he daa; he squared residual was no correlaed 116

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