Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios Koulakiois *, Aposolos Dasilas **, Phil Molyneux *** Absrac This paper examines wheher rading volume has any impac on GARCH and GJR- GARCH esimaes for he Greek banking secor and he Greek FTSE/ASE Mid 4 sock price index for he period of -5. The resuls from he GARCH and GJR-GARCH models wih and wihou volume indicae ha GARCH and GJR-GARCH effecs become smaller when rading volume is aken ino accoun. In paricular, hese effecs are seen mainly hrough he influence on he pas condiional volailiy coefficien in boh he models ha include rading volume. However, he coefficien of squared innovaions improves afer he inclusion of rading volume. This means ha here sill remains unexplained informaion in he marke ha i is no capured hrough he modelling approach used. The resuls sugges ha rading volume parly affecs he GARCH and GJR-GARCH esimaes implying a negaive relaionship beween sock price volailiy and rading volume. I is also found ha bad news can have a significan impac on sock price volailiy. Key words: Volailiy clusering, GARCH models, Greek Banking Secor, Ahens Sock Exchange. JEL Classificaion: G15. 1. Inroducion A number of sudies bring o ligh empirical evidence on volailiy clusering wih regard o he impac of he news on sock price volailiy. Seminal sudies finding evidence on volailiy clusering are provided by Engle (198), Pindyck (1986), French e al. (1987), Poerba and Summers (1986) and Bollerslev (1986). All of hese sudies suppor he view ha news ends o be clusered ogeher and his has an influence on sock price volailiy. More recenly, Friedman and Sanddorf-Kohle () analyzed volailiy dynamics in he Chinese sock markes comparing he EGARCH wih he asymmeric model proposed by Glosen, Jagannahan, and Runkle (1993), known as he GJR-GARCH model. Their empirical resuls find ha he dynamics of he Chinese marke are bes represened by he GJR-GARCH model, a finding ha confirms Engle and Ng s (1993) asserion ha asymmeric GARCH models similar o ha proposed by Glosen, Jagannahan, and Runkle (1993) are superior for esimaing sock marke dynamics. Anoher srand of he lieraure examines wheher rading volumes have any effec on GARCH esimaes of sock marke volailiy. For insance, Lamoureux and Lasrapes (199) found ha GARCH esimaes vanish when rading volumes are aken ino accoun. Sudies ha examine similar relaionships include hose of Omran and McKenzie (1995) for he UK and by Sharma, Mougoue and Kamah (1996) on he US marke (NYSE). The former found ha auocorrelaion of he squared innovaions sill exhibis a highly significan paern in he UK marke afer he inclusion of rading volume in heir GARCH esimaes. The laer also noed ha GARCH effecs did no compleely vanish in he US marke when hey conrol for rading volume. The aim of his paper is o exend he aforemenioned analysis by examining he impac of rading volume using boh GARCH and he asymmeric GARCH approach suggesed by Glosen, Jagannahan, and Runkle (1993). The empirical analysis is conduced on daa from he Greek sock marke, deails of which are oulined in he following secion. Ahanasios Koulakiois, Aposolos Dasilas, Phil Molyneux, 7 * Universiy of Aegean, Greece. ** Universiy of Macedonia, Greece. *** Universiy of Wales, UK.
34 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7. Daa and Mehodology This paper compares he performance of GARCH and GJR-GARCH models fied o he daily Greek banks sock price reurns and he Greek FTSE/ASE Mid 4 sock price index. We focus our aenion on he Greek banking secor comprising welve banks socks rading in he Ahens Sock Exchange due o daa availabiliy and he liquidiy of such socks. However, bank socks accoun for eleven of he weny socks of he Greek FTSE/ASE, an index ha includes he firs weny socks in marke value. Due o he over-represenaion of bank socks in he Greek FTSE/ASE we need o choose a more represenaive and independen index excluding he over-emphasis of banks in order o compare he impac of volume on he volailiy of sock price reurns. For his we ake he Greek FTSE/ASE Mid 4 index ha comprises he fory socks in marke value afer he FTSE/ASE. The FTSE/ASE Mid 4 is an index for medium-sized firms, consising of 39 socks from various indusry secors and only one from he banking secor. This allows us o compare he impac of volume on he volailiy of sock price reurns in he banking secor and also on an index ha is no unduly influenced by banks socks. Daily daa on sock price reurns (R) and rading volume (TV) for boh he banking secor and for he FTSE/ASE Mid 4 index were obained from he Informaion Disseminaion Deparmen of he Ahens Sock Exchange and Globalsof over he period of -5. The daa for sock price reurns have been ransformed ino naural logarihm applying he formula: Ln (P / P - 1), while he daa for rading volume is acual. The GARCH model of Bollerslev (1986) provides a flexible and parsimonious approximaion o condiional variance dynamics. The GARCH (1, 1) model for he condiional variance of he innovaions, var( 1,,...) is given by he following equaions:, u i.i.d. wih ( u ), and ( ) 1 u R n u, (1) R, () i i i1 1 1 1, (3) and 1 1 1 1TV. (4) The parameer resricions, 1, and 1 1 ensure ha he sochasic process { } is well-defined (i.e., ) and covariance saionary wih ( ), Var( )=, Cov (, s )= s. In many sudies he GARCH (1, 1) process has been successfully applied o capure volailiy clusering in financial daa. In he simple GARCH (1, 1) approach bad and good news, i.e., negaive and posiive shocks, have he same impac on he condiional variance. This feaure of GARCH models does no correspond o he resuls of a number of researchers, who have found evidence of asymmery in sock price behaviour. Paricularly, negaive surprises seem o increase volailiy more han posiive surprises. To allow asymmeric volailiy effecs, Glosen, Jagannahan and Runkle (1993) add an addiional erm in he condiional variance Equaion (3): R n R i i, (5) i1 1( 1 1 ) 1 3 1, (6) and 1( 1 1) 1 3 1 1TV. (7) Here, 1 1 if and 1 If. 1 1
Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 35 This is an asymmeric GARCH model which we denoe as GJR-GARCH (1, 1) afer Glosen, Jagannahan, and Runkle (1993). The process is well-defined if he condiions,, 1 ) and are saisfied. 1 ( 1 3 3. Empirical Resuls Tables 1 and provide preliminary saisics for he sock price reurns and rading volume variables of he Greek banking secor and he Greek FTSE/ASE Mid 4 sock price index. Table 1 shows ha he mean for he sock price reurns of he banking secor and sock price index is negaive and equal o -.79% and -.15% respecively, while he mean for daily rading volume is equal o 17,.86 Euros and,19,684.7, Euros respecively. Bank sock price reurns and rading volume are, herefore, boh lower han ha of he FTSE/ASE Mid 4 sock index. There is also kurosis in he reurn series under invesigaion suggesing fa ails and his suppors he use of GARCH modelling approaches o invesigae marke dynamics. Descripive Saisics of he Greek banking secor and he Greek FTSE/ASE Mid 4 sock price index: -5 Table 1 Banking Secor Reurns Banking Secor Volume (in Euros) FTSE/ASE Mid 4 Reurns FTSE/ASE Mid 4 Volume (in Euros) Mean -.79 17,.86 -.15,19,684.7 S. Dev..18 157,978.44.,57,436.41 Skewness.1 9.68 -. 5.74 Kurosis 4.38 19.5.9 53.6 Table shows ha here is srong serial correlaion in he banking secor reurn series and he FTSE/ASE Mid 4 sock price index when we consider daily 8, 16 and 4 lags, respecively This suggess ha he mehodology should adop a model ha is bes suied o capure his feaure. As menioned above, we use he GARCH and he GJR-GARCH models o analyse he impac of rading volume on he sock price volailiy of he banking secor and he FTSE/ASE Mid 4 sock price index. Serial Correlaion of he Greek banking secor reurns and he Greek FTSE/ASE Mid 4 sock price index: -5 Table lags. Banking Secor Reurns FTSE/ASE Mid 4 Reurns LB(8) 31.58* 46.97* LB(16) 45.56* 65.63* LB(4) 63.5* 14.9* Noe: * shows significance a he 5% level. LB is he Ljung Box saisic wih daily 8, 16 and 4 The impac of rading volume on GARCH and GJR-GARCH esimaes is esed for he Greek banking secor and he Greek FTSE/ASE Mid 4 sock price index, following Lamoureux and Lasrapes (199). Using GARCH esimaes, Table 3 shows ha he impac of rading volume on volailiy in he Greek banking secor is no significan a he 5% level. In paricular, we find ha he relaionship beween rading volume and volailiy of sock price reurns in he Greek banking secor is negaive and equal o -1.11. This means ha a 1% change in rading volume will decrease he coefficien of volailiy by 1.11%. In addiion, a comparison of he GARCH coefficiens wihou and wih volume reveals ha he pas condiional volailiy coefficien ( 1 ) has re-
36 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 duced from.69 o.3 afer he inclusion of rading volume in he GARCH model. This finding is in accordance wih Lamoureux and Lasrapes (199) who found ha GARCH esimaes deeriorae when rading volume is added ino such models. In conras o his finding, he coefficien of squared innovaion ( ) has been increased from.1 o.58 afer he inclusion of rading volume in he GARCH model. Overall, he resuls in Table 3 reveal ha he inclusion of rading volume in he GARCH model parly reduces he GARCH effecs for he banking secor sock price reurns. Similar resuls are also observed for he FTSE/ASE Mid 4 sock price index. GARCH esimaes of he Greek banking secor and he Greek FTSE/ASE Mid 4 sock price index: -5 Table 3 Banking Secor Reurns FTSE/ASE Mid 4 Reurns Variables Wihou Volume Wih Volume Wihou Volume Wih Volume Reurn Coefficiens -.7 (.56) 1.18* -.7* 3.55** GARCH Coefficiens 3.4* (6.18) 1.69* (.3).1* (.3) -.69 (.56).18* -.69* (.54).54**.6* (1.33).3* (.11).58* (.9) TV -1.11 (1.38) -.13* (.6).* -.93* 5.4* (.9).87* (.16).1* (.16) -.14* (.6).* -.93* 3.14* (.57).5* (.3).49* (.11) 7.96 (9.35) Log-Likelihood 3588.95 3513.57 3544.79 3441.1 Noe: *shows significance a he 5% level. ** shows significance a he 1% level. The Akaike crierion is used o idenify he number of lags in he reurn equaion. Table 4 presens he resuls from he GJR-GARCH (1, 1) model wih and wihou rading volume for he Greek banking secor and he Greek FTSE/ASE Mid 4 sock price index. For he banking secor sock price reurns, he GJR-GARCH coefficiens wihou and wih volume reveal ha he pas condiional volailiy coefficien ( 1 ) has reduced from.71 o.4 afer he inclusion of rading volume in he GJR-GARCH model. Similar resuls are obained for he FTSE/ASE Mid 4 sock price index, ha is, he coefficien ( 1 ) has reduced from.89 o.4 afer he inclusion of rading volume. In conras, he coefficien of squared innovaion ( ) increases from.16 o.47, for he banking secor sock price reurns and from.56 o.47 for he FTSE/ASE Mid 4 sock price index, afer he inclusion of rading volume. Similar increases are obained for boh he banking secor sock price reurns and he FTSE/ASE Mid 4 sock price index when we include he addiional coefficien ( 3 ) ha capures asymmeric volailiy effecs. In paricular, he relaionship of he impac of bad news on banking secor reurns and FTSE/ASE Mid 4 sock price index is found o be negaive (-.57 and -1.66, respecively) wihou he inclusion of volume in he GJR- GARCH (1, 1) model and posiive wih he inclusion of volume (.71 and.71, respecively). This means ha he GJR-GARCH esimaes do no deeriorae when he coefficiens of he bad news for
Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 37 he Greek banking secor and he Greek FTSE/ASE Mid 4 sock price index are concerned. In addiion, he impac of bad news is found o increase wih he inclusion of rading volume. GJR-GARCH esimaes of he Greek banking secor and he Greek FTSE/ASE Mid 4 sock price index: -5 Table 4 Banking Secor Reurns FTSE/ASE Mid 4 Reurns Variables Wihou Volume Wih Volume Wihou Volume Wih Volume Reurn Coefficiens -.7 (.56) 1.18* -.7* 3.55** CJR-GARCH Coefficiens.85* (5.36) 1.71* (.8).16* (.) 3 -.57* (.4) -.69 (.56).18* -.69* (.54).54** 3.91* (3.9).4* (.74).47* (.13).71* (.1) TV -1.98 (1.45) -.13* (.6).* -.93*.45* (.17).89* (.14).56* (.15) -1.66* (.61) -.13* (.6).* -.93* 4.46* (6.94).4* (.11).47* (.19).71* (.14) -1.71 (9.54) Log-Likelihood 3584.89 3439.55 3549.88 3363.41 Noe: *shows significance a he 5% level. ** shows significance a he 1% level. means no available. The AKAIKE crierion is used o idenify he number of lags in he reurn equaion. 4. Concluding remarks This paper examines wheher rading volume has any impac on GARCH and GJR- GARCH esimaes for he Greek banking secor and he Greek FTSE/ASE Mid 4 sock price index. Overall, he resuls from he GARCH and GJR-GARCH models wih and wihou volume indicae ha GARCH and GJR-GARCH effecs become smaller when rading volume is aken ino accoun. In paricular, hese effecs are seen mainly hrough he influence on he pas condiional volailiy coefficien in boh he models ha include rading volume. However, he coefficien of squared innovaions improves afer he inclusion of rading volume. This means ha here sill remains unexplained informaion in he marke ha i is no capured hrough he modelling approach used. Our resuls, herefore, parly concur wih he findings of Lamoureux and Lasrapes (199) who find ha rading volume reduces GARCH effecs alhough i seems ha hese effecs are smaller when asymmeric GARCH models such as GJR-GARCH are used o model such relaionships. An ineresing possible area for fuure research would be o use asymmeric models wih long memory (see Hwang, 1; and Ruiz and Perez, 3) o furher examine he impac of rading volume on sock price volailiy.
38 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 References 1. Bollerslev, T., 1986, Generalised auoregressive condiional heeroscedasiciy, Journal of Economerics 31, 37-37.. Engle, R.F., 198, Auoregressive condiional heeroskedasiciy wih esimaes of he variance of UK inflaion, Economerica 5, 987-18. 3. Engle, R.F., and V.K. Ng, 1993, Measuring and esing he impac of news on volailiy, Journal of Finance 48, 1749-1776. 4. French, K.C., G.W. Schwer, and R.F. Sambaugh, 1987, Expeced sock reurns and volailiy, Journal of Financial Economics, 199, 3-9. 5. Friedmann, R., and W.G. Sanddorf-Kohle,, Volailiy clusering and nonrading days in Chinese sock markes, Journal of Economics and Business 54, 193-17. 6. Glosen, L.R., R. Jaganahan, and D.E. Runkle, 1993, On he relaion beween he expeced value and he volailiy of he nominal excess reurns on socks, Journal of Finance 48, 1779-181. 7. Hwang, Y., 1, Asymmeric long memory GARCH in exchange reurns, Economics Leers 73, 1-5. 8. Lamoureux, G.C., and W.D. Lasrapes, 199, Heeroscedasiciy in sock reurns daa: Volume versus GARCH effecs, Journal of Finance 45, 1-9. 9. Omran, M.F., and E. Mckenzie, 1995, Heeroscedasiciy in sock marke prices revisied: Unexpeced volume versus GARCH effecs, Universiy of Sirling, Discussion Paper No. 95/8, 1-4. 1. Pindyck, R.S., 1986, Risk, inflaion and he sock marke, American Economic Review 74, 335-351. 11. Poerba J.M., and L.H. Summers, 1986, The persisence of volailiy and sock marke reurns, American Economic Review 76, 114-1151. 1. Ruiz E. And A. Perez, 3, Asymmeric long memory GARCH: a reply o Hwang s model, Economics Leers 78, 415-4. 13. Sharma, J.L., M. Mougoue, and R. Kamah, 1996, Heeroscedasiciy in sock marke indicaor reurn daa: Volume versus GARCH effecs, Applied Financial Economics, 337-34.