The Relationship between Trading Volume, Returns and Volatility: Evidence from the Greek Futures Markets CHRISTOS FLOROS. Abstract

Transcription

1 The elaionship beween Trading Volume, eurns and Volailiy: Evidence from he Greek Fuures Markes CHISTOS FLOOS Deparmen of Economics, Universiy of Porsmouh, Locksway oad, Porsmouh, PO4 8JF, UK. Tel: +44 (0) , Fax: +44 (0) Absrac The relaionship beween reurns, volailiy and rading volume has ineresed financial economiss and analyss for a number of years. A widely documened resul is he posiive conemporaneous relaionship beween price reurns and rading volume. This paper invesigaes he conemporaneous and dynamic relaionships beween rading volume, reurns and volailiy for Greek index fuures (FTSE/ASE-20 and FTSE/ASE Mid 40). For FTSE/ASE-20, we find ha price volailiy does no significanly impac volume s volailiy, and also, we conclude ha a conemporaneous relaionship does no hold. Using GACH mehods, he resuls show a posiive and significan effec, indicaing ha volume conribues significanly in explaining he GACH effecs. Furhermore, he GMM sysem suggess ha marke paricipans use volume as an indicaion of prices. For FTSE/ASE Mid 40, he resuls are mixed. The price volailiy significanly impacs volume s volailiy, and also, a posiive conemporaneous relaionship holds. On he oher hand, boh GACH and GMM mehods confirm ha here is no evidence for posiive relaionship beween rading volume and reurns. Finally, his sudy also invesigaes he dynamic relaionship beween rading volume and acual reurns. For FTSE/ASE-20, he dynamic models show a bi-direcional Granger causaliy (feedback) beween volume and acual reurns. However, for FTSE/ASE Mid 40, he resuls indicae ha reurns do no Granger cause volume and vice versa. Keywords: Fuures, Trading Volume, eurns, Volailiy. * This is a preliminary version. Please do no quoe wihou permission. 1

2 1. INTODUCTION There are many reasons ha raders pay aenion o rading volume 1. Theoreically, low volume means ha he marke is illiquid. This also implies high price volailiy. On he oher hand, high volume usually implies ha he marke is high liquidiy, resuling in low price variabiliy. This also reduces he price effec of large rades. In general, wih an increase in volume, broker revenue will increase, and also, marke makers have greaer opporuniy for profi as a resul of higher urnover. However, raders who wish o paricipae in movemens in he marke may use index fuures more easily han shares. The exisence of index fuures allows index arbirage and risk hedging. Boh increase rading volume. The relaionship beween reurns and rading volume has ineresed financial economiss and analyss for a number of years. In general, previous empirical sudies have noed srong posiive correlaions beween rading volume and price volailiy/ absolue reurns (Karpoff, 1987). In oher words, i is concluded ha rading volume plays a significan role in he marke informaion. Therefore, he rading volume reflecs informaion abou changes and agreemen in invesors expecaions (Harris and aviv, 1993). Mos of he previous sudies have examined he leading heories (hypoheses) o explain he informaion arrival process in financial markes. The compeing hypoheses are he mixure of disribuions hypoheses (MDH) and he sequenial informaion arrival hypoheses. According o he mixure of disribuions hypohesis, informaion disseminaion is conemporaneous. In oher words, fuures prices (and volume) only change when informaion arrives, and hey evolve a a consan speed in even ime (Sucliffe, 1993). The MDH implies only a conemporaneous relaionship beween volume and (absolue) reurns. I is associaed wih Clark (1973), Epps and Epps (1976), Tauchen and Pis (1983) and Harris (1986). An imporan assumpion is ha he variance per ransacion is monoonically relaed o he volume of ha ransacion. In general, according o Grammaikos and Saunders (1986), under he MDH framework he correlaion beween price (reurns) and volume should be posiive because join dependence on a common direcing variable or even. The MDH iniially developed by Clark (1973). He argues ha he rae of informaion arrival implies a posiive conemporaneous correlaion beween volume and volailiy. Furhermore, Harris (1987) and Sucliffe (1993, p.188) repor he following implicaions of his model: 1. Provided he number of informaion arrivals is sufficienly large, he cenral limi heorem can be used o argue for normaliy in he disribuion of price changes and volume. 1 Volume is he number of ransacions in a fuures conrac during a specified period of ime (Sucliffe 1993). 2

3 2. For a given number of informaion arrivals, here is zero correlaion beween volailiy and volume. 3. For a given ime period, here is a posiive correlaion beween volailiy and volume. This is because boh are posiive funcions of he rae of arrival of informaion during he ime period. 4. There will be lepokurosis in he disribuion of price changes compued over equal ime periods. However, he empirical sudies by Najand and Yung (1991) and Bessembinder and Seguin (1992, 1993) repor evidence agains he MDH. In addiion, Bessembinder and Seguin (1993) sugges ha he volailiy-volume relaion in financial markes depends on he ype of rader. On he oher hand, he sequenial arrival of informaion hypohesis suggess he gradual disseminaion of informaion such ha a series of inermediae equilibria exis (Copeland; 1976, Tauchen and Pis; 1983). This model implies he coninuaion of higher volailiy afer he iniial informaion shock raher han spikes in volailiy (Wiley and Daigler, 1999). Also, according o Grammaikos and Saunders (1986, p. 326) sequenial informaion arrival models imply he possibiliy of observing lead relaions beween daily conrac price variabiliy and volume. The sequenial arrival informaion model argues ha each rader observes he informaion sequenially. Furhermore, McMillan and Speigh (2002, p.2) argue ha sequenial arrival hypohesis suppors a dynamic relaionship whereby pas volume provides informaion on curren absolue reurns, and pas absolue reurns conains informaion on curren volume. In oher words, he dynamic relaionship is very imporan as i gives useful informaion abou rading volume and forecass of reurns and volailiy. ecen empirical sudies have invesigaed he dynamic relaionship beween rading volume and reurns. Some heoreical papers sugges causaliy beween changes in volailiy and volume. This is due o he fac of he arrival of new (privae) informaion. In general, boh MDH and sequenial arrival of informaion hypoheses suppor a posiive and conemporaneous relaionship beween volume-absolue reurns and assume a symmeric effec for price increases and price decreases for fuures conracs (Karpoff, 1987). Noe ha, in he case of an efficien fuures marke, neiher a conemporaneous relaionship nor a dynamic relaionship hold. In his paper we invesigae he volailiy, reurns -volume relaionship from wo direcions: he conemporaneous and causal relaionships on he fuures markes of he Ahens Derivaives Exchange (ADEX). We look a he price-volume relaionship as i is relaed o he role of informaion in price formaion, wih volailiy and volume providing measures of he significance of he informaion refleced in he 3

4 marke (Wiley and Daigler, 1999; p.1). Karpoff (1987, pp ) explains he imporance of he price-volume relaionship as follows: 1. The models predic various price-volume relaions ha depend on he rae of informaion flow o he marke. 2. I is imporan for even sudies ha use a combinaion of price and volume daa. 3. The price-volume relaion is criical o he debae over he empirical disribuion of speculaive prices. 4. Price-volume relaions have significan implicaions for research ino fuures markes. Price variabiliy affecs he volume of rade in fuures conracs. This has bearing of he issue of wheher speculaion is a sabilizing or desabilizing facor on fuures prices. The pricevolume relaion can also indicae he imporance of privae versus public informaion in deermining invesors demands. Our analysis of he relaionship beween reurns/volailiy and volume in ADEX may help us o undersand wheher rading volume provides any informaion abou fuure reurns in fuures markes. In oher words, he main issue is o idenify wheher informaion abou rading volume is useful in improving forecass of reurns in a conemporaneous and dynamic conex. Also, his sudy is imporan since raders and hedgers should idenify he facors ha influence he rading volume because as he volume increases hen he price changes also end o increase (which leads o a definie increase in margin requiremens). This sudy seeks o follow he works of Sharma e al. (1996), Gwilym e al. (1999), Ciner (2001) and McMillan and Speigh (2002). We invesigae he relaionship beween price changes and rading volume for index fuures conracs raded in he ADEX, and also, we give an answer o he research quesion wheher volume conains informaion useful for predicing fuure price movemens. In addiion, we sudy he GACH effecs in our daa and es how well he GACH effecs are explained by rading volume. In oher words, we invesigae he role of he rae of informaion arrival variable relaing o he Greek fuures prices. Noe ha no previous sudy has esed he relaionship beween price change (reurns) and rading volume in he Greek marke. The paper coninues as follows. In Secion 2 we review he lieraure relaing o he relaionship beween he fuures price (reurns) volailiy and volume. Secion 3 oulines he mehodology and Secion 4 presens he Greek Fuures Markes and daa used in his sudy. Empirical resuls are repored and discussed in Secion 5, and finally, concluding remarks are made in Secion 6. 4

5 2. LITEATUE EVIEW The relaionship beween reurns/ volailiy and rading volume in financial markes coninues o be of empirical ineres. Alhough he major of exising resuls suggess ha here is a posiive relaionship beween he variables, some oher empirical sudies (Najand and Yung; 1991 and Bessembinder and Seguin; 1992, 1993) repor evidence agains he MDH. Nex, we review he previous sudies abou conemporaneous and dynamic relaionships beween reurns/volailiy and rading volume. I. eurn-volume - Conemporaneous elaionship As we menioned above, he MDH suggess ha he correlaion beween price variabiliy and volume should be posiive. Previous empirical sudies have noed a srong posiive relaionship. Firsly, Clark (1973) and Epps and Epps (1976) argue ha he disribuion of fuures prices can be explained by he MDH. Epps and Epps (1976) presen a heoreical model in which rading volume and absolue reurns form a posiive funcion of he amoun of disagreemen beween raders. Then, Copeland (1976) also develops a simple sequenial informaion arrival model in which he informaion is received by one rader a a ime, and each rading on his informaion before i becomes known o anyone else. However, he majoriy of he empirical evidence is summarized in he paper by Karpoff (1987). In paricular, Karpoff (1987) cies several reasons why he price-volume relaionship is posiive (see also Board and Sucliffe, 1990). Oher research papers include Cornell (1981) and Tauchen and Pis (1983). Cornell (1981) shows a posiive correlaion beween he changes in average daily volume and changes in he sandard deviaion of daily log price relaives for 14 of he 18 commodiies. Also, Tauchen and Pis (1983) suppor he MDH and show ha he join disribuion of changes in price and volume are modelled as a mixure of bivariae normal disribuions. Nex we review he previous empirical sudies relaed o he conemporaneous relaionship beween reurns and rading volume. Ying (1966) suggess ha a small (large) volume is usually accompanied by a fall (rise) in price. Cornell (1981) finds posiive relaions beween volume and changes in he variabiliy of prices for 17 fuures conracs. In addiion, Harris (1983, 1984), Grammaikos and Saunders (1986) and Karpoff (1987) repor a posiive and conemporaneous correlaion beween volume and price variabiliy. This kind of correlaion appears o be consisen wih he MDH (Grammaikos and Saunders, 1986). Also, 5

6 Harris (1984) repors ha he rae of informaion flow is a direcing variable ha leads o a posiive conemporaneous change in response o he new informaion. Mos of recen papers exend he work of Lamoureux and Lasrapes (1990) by invesigaing he effec of rading volume o he marke reurns using he generalized auoregressive condiional heeroscedasiciy (GACH) model. They esimae a GACH model where rading volume is included as an explanaory variable in he condiional variance equaion. They find ha volume has a posiive effec on condiional volailiy. Alhough previous research suggess ha volume is a good proxy for informaion arrival, he opposie may be rue for he marke. Sharma e al.(1996) examine he GACH effecs in he NYSE. The paper exends he work of Lamoureux and Lasrapes (1990), and shows how he GACH effecs in marke reurns are explained by marke volume. For ha reason, he simple GACH (1,1) model wih and wihou daily volume is considered. Also, Sharma e al. (1996) ake ino consideraion he assumpion of condiional normaliy and condiional -disribuion. The resuls sugges ha volume may conribue significanly in explaining he GACH effecs. In oher words, he inroducion of volume does no eliminae he GACH effecs compleely. However, he coefficien of volume is found o be posiive and saisically significan. II. Volailiy-Volume As we menioned, Karpoff (1987) reviews previous sudies on he price-volume relaion and concludes ha here is a posiive correlaion beween volailiy and volume. Lamoureux and Lasrapes (1990) show ha he inroducion of volume in he condiional variance equaion eliminaes he GACH effecs. They find ha all he oher coefficiens in he condiional variance equaion (i.e. GACH model) are saisically insignifican when volume is included. In addiion, hey argue ha volume has a posiive effec on condiional volailiy. However, pas residuals do no conribue much informaion regarding he variance when volume is included. Also, Kawaller, Koch and Koch (1990) find ha he daily volume of rading in he S&P 500 fuures conrac has a significanly posiive effec on he volailiy. In anoher sudy, Board and Sucliffe (1990) also find a suppor o he hypohesis of a posiive relaionship beween volailiy and volume for he FTSE-100 index. Furher, Bessembinder and Seguin (1993) divide volume ino expeced and unexpeced componens o examine he relaion beween price volailiy and rading volume for fuures markes. In general, he resuls show a posiive relaion beween volume and volailiy. Also, Bessembinder and Seguin (1993) sugges ha he effec of unanicipaed volume shocks on volailiy is asymmeric. As hey conclude, heir findings are consisen wih he hypohesis ha volailiy is affeced by exising marke deph. 6

7 Under differen echniques, Hiemsra and Jones (1994), Gallan e al. (1993) and Tauchen e al. (1996) repor also a posiive correlaion beween volailiy and rading volume. Brailsford (1994) examines empirically he relaionship beween rading volume and volailiy in he Ausralian Sock marke. The sudy suppors he hypohesis ha he asymmeric relaionship beween volume and price changes. Also, he resuls show a reducion in GACH coefficiens and in he persisence of variance when rading volume is used. Furher, Brailsford (1996) use daa from Ausralian sock marke in order o examine he relaionship beween rading volume and sock reurn volailiy and rading volume and condiional volailiy. The resuls from he GACH (1,1) model are found o be insignifican when he volume is aken ino consideraion. agunahan and Pecker (1997) focus on he relaionship beween volume and price variabiliy for he Ausralian fuures marke. Following he models developed by Schwer (1990) and Bessembinder and Seguin (1993), hey provide srong evidence ha unexpeced volume has a greaer impac on volailiy han expeced volume. Hogan e al. (1997) use a bivariae GACH model o es he relaionship beween program rading volume and marke volailiy. esuls show ha here is a srong posiive relaionship beween rading volume and volailiy. Also, Daigler and Wiley (1999) examine he volailiy-volume relaion in fuures markes. Accordingly, he general public drives he posiive volailiy-volume relaion 2. In addiion, hey find ha he unexpeced volume series is more imporan han he expeced volume series in explaining volailiy. Jacobs and Onochie (1998) examine he relaionship beween reurn variabiliy and rading volume in fuures markes. A bivariae GACH-in-mean model is used. The resuls indicae a posiive relaionship beween rading volume and price volailiy. In addiion, Monalvo (1999) examines he Spanish Governmen Bond Fuures Marke using he approach proposed by Lamoureux and Lasrapes (1990). Monalvo (1999) suggess ha he daily volume and frequency have a posiive effec on volailiy. Consisenly, Gwilym e al. (1999) analyse he conemporaneous relaionship beween volailiy and volume for sock index (FTSE-100), shorerm ineres rae (Shor Serling) and governmen bond (Long Gil) fuures conracs raded a he LIFFE. The resuls srongly suppor a significan posiive and conemporaneous correlaion beween volailiy and volume. 2 Also, Bessembinder and Seguin (1993, p. 38) sugges ha he volume-volailiy relaion depends on he class of raders involved. 7

8 Wang and Yau (2000) examine he relaionship beween rading volume and price volailiy for fuures markes. The resuls show a posiive relaionship beween rading volume and price volailiy, and a negaive relaionship beween price volailiy and lagged rading volume. ecenly, Waanabe (2001) examines he relaion beween price volailiy and rading volume for he Nikkei 225 sock index fuures. Following he mehod developed by Bessembinder and Seguin (1993), his paper shows a saisically significan and posiive relaion beween volailiy and unexpeced volume. Also, for he period when he regulaion increased gradually, Waanabe (2001) suggess ha here is no relaion beween price volailiy and volume. Finally, Pilar and afael (2002) analyse he effec of fuures on Spanish sock marke volailiy and rading volume. For his purpose, he GJ model wih a dummy variable is used. The resuls show a decrease in he volailiy and increase in rading volume. - Dynamic elaionship The second par of our empirical analysis examines he dynamic relaionship beween rading volume and reurns. ecenly, some empirical sudies have explicily invesigaed he dynamic relaionship beween rading volume and reurns. Firsly, Epps and Epps (1976) sugges a posiive causal relaionship beween rading volume and volailiy (absolue sock reurns). Then, Tauchen and Pis (1983) examine he relaionship on he speculaive markes and conclude ha informaion arrival causes raders o revise heir asse valuaions. Hiemsra and Jones (1994) use linear and non-linear Granger causaliy mehods, and Gallan e al. (1993) and Tauchen e al. (1996) use impulse response analysis. Furher, Herber (1995) examines he behaviour of rading volume and naural gas fuures price volailiy. The resuls confirm ha he volume of rade explains beer he variance of he volailiy. In addiion, i is confirmed ha volume does Granger cause price changes. There have been only a few empirical sudies of he relaionship beween rading volume and volailiy for index fuures. Merrick (1987) uses daily daa of he S&P 500 and NYSE Composie indices for he period from 1982 o 1986 and finds evidence of srong causaliy for index fuures. Kocagil and Shachmurove (1998) invesigae he volume-reurn relaionship for real and financial fuures conracs. The sudy uses also a VA framework o check for causaliy and feedback relaionships among he variables. Almos all values are found o be posiive and saisically significan. Also, he causaliy ess confirm ha here is a causaliy from absolue rae of reurn o volume. However, Kocagil and Shachmurove (1998) repor he absence of causaliy from pas values of volume o reurns in fuures markes (i.e. presence of efficiency in fuures markes). 8

9 Furher, Gwilym e al. (1999) argue ha here is srong evidence of bi-direcional causaliy beween volailiy and volume for five-minue FTSE-100, Shor Serling and Long Gil LIFFE fuures. ecenly, McMillan and Speigh (2002) examine he dynamic relaionship beween he reurns and volume for equiy and bond fuures. The dynamic relaionship is examined using a VA mehodology. Also, Granger-causaliy ess are employed, indicaing a bi-direcional causaliy beween volume and reurns series for mos fuures. In addiion, a posiive relaionship beween volume and absolue reurns is repored. Similarly, Grammaikos and Saunders (1986) conclude ha here is a significan bi-direcional causaliy in five differen foreign currency fuures raded on he IMM. Also, Malliaris and Urruia (1998) use ess of long-run relaionships and coinegraion beween price and volume for six agriculural fuures conracs. The resuls show ha here is a bi-direcional causaliy beween price changes and changes in volume. Alhough now several sudies have repored ha pas volume and reurns can be used for forecasing purposes (e.g. Gallan e al., 1992) and show a srong causaliy, oher sugges ha fuures markes are weak-form efficien. In oher words, he sudies for a wide range of oher fuures show ha here is no causaliy from lagged volume o reurns (McCarhy and Najand, 1993). For insance, uledge (1977, 1978) finds weak evidence ha fuures price variabiliy causes rading volume. Also, Bhar and Malliaris (1998) show evidence of lack of causaliy beween price and rading volume in five foreign currency fuures. Only in he case of Briish Pound hey find ha he volume causes price. Finally, Walls (1999) finds ha he hypohesis ha rading volume (price volailiy) does no cause price volailiy (rading volume) canno be rejeced for any of he elecriciy fuures conracs. 3. METHODOLOGY Following he previous work of Bhar and Malliaris (1998) and Malliaris and Urruia (1998), he rading volume is a funcion of equilibrium fuures price and ime. Tha is, V = V (, F) (1) where V denoes rading volume, F denoes fuures price and denoes ime. Assuming ha he price F follows an Io process wih drif µ and volailiy σ, hen: df = µ d + σdz (2) where Z denoes a sandardised Wiener process. Alhough (1) is a general model, he model described by equaion (2) is favourable as he Io s processes describe beer coninuous random walks wih a drif which leads o he marke efficiency. Anoher applicaion of Io s lemma is given by: 1 2 dv = V + Vpµ + Vppσ d + VpσdZ (3) 2 9

10 where V, Vp and V pp denoe parial derivaives. Models (1) and (3) describe fuures prices and show wheher hey follow a random walk or no. If fuures prices follow a random walk, hen rading volume also follows a random walk. Furher by aking expecaions of (3) we ge he following expression: 1 E ( dv ) + σ 2 2 = V + Vpµ V pp (4) This expression shows ha he change in volume depends on V, he drif rae µ and he volailiy of fuures prices 2 σ. We can also es he above hypohesis wih he following model: 2 E ( dv ) = a + βµ + γσ (5) This model implies he posiive relaionship beween price variabiliy and rading volume. Finally, using sochasic calculus, he volailiy of rading volume is given by: 2 2 Var ( dv ) = V p σ (6) where he volailiy of rading volume is a funcion of he fuures price volailiy. This hypohesis can be esed by he following expression: 2 Var ( dv ) = a + δσ (7) To empirically es equaions (6) and (7), we run he following regression: V = a + δ (8) F Equaion (8) ess he hypohesis wheher he price volailiy significanly impacs volume s volailiy (Bhar and Malliaris 3 ; 1998, Malliaris and Urruia; 1998). - Conemporaneous elaionship To analyse he conemporaneous relaionship beween volailiy and volume we follow he recen works of Sharma e al. (1996), Gwilym e al. (1999) and McMillan and Speigh (2002). According o Grammaikos and Saunders (1986), here are several measures of volailiy 4. For example, uledge (1979) uses he absolue log change from one rading day o he nex, and hen Tauchen and Pis (1983) use he square of he firs difference of he fuures price of adjacen periods. In addiion, Karpoff (1987) uses he absolue value of he firs difference o measure volailiy. In his 3 Bhar and Malliaris (1998) sugges ha volume is relaed o price volailiy and volume volailiy is relaed o price volailiy. 4 Also, Sucliffe (1993, p. 176) presens some of he definiions of price volailiy. 10

11 sudy, o invesigae he reurn (volailiy)-volume relaionship we esimae reurn as follows: ETUN = ln( P ) ln( P 1) where P is he daily closing fuures price. We also measure he volume parameer as follows: VOLUME = ln V V LNVOL = ln V VOL = V 1 Firs, a simple OLS model ha can be used o regress he daily rading volume on sock index fuures reurns is given by: = a + bv + u (9) where V is he daily rading volume a ime, is he daily reurn a ime, and u is a random error erm. However, anoher approach ha has been used o explain he reurn-volume relaionship is based on (G)ACH models. Previous works sugges ha ACH effecs capure he properies of he informaion mixing variable. Firs, Lamoureux and Lasrapes (1990) assume ha he presence of ACH in reurns is due o he MDH. However, heir resuls show ha rading volume removes he significance of ACH and GACH coefficiens in he GACH (1,1) model, implying ha volume is a good alernaive for he GACH process. As a resul, he persisence in volailiy is reduced. On he oher hand, Bessembinder and Seguin (1992, 1993) and Foser (1995) sugges ha rading volume is no sufficien o remove he lagged volailiy effecs in curren variance. Furhermore, Brailsford (1996), using he GACH (1,1) model, concludes ha here is a srong suppor for he above model only when absolue reurns are considered. Following he work of Sharma e al. (1996), we sudy he GACH effecs in our daa and examine he effec of volume on reurn volailiy using he GACH (1,1) model. In oher words, we es how well he GACH effecs are explained by rading volume, and also, we examine he effec of rading volume on condiional volailiy (see also Lamoureux and Lasrapes, 1990). The condiional variance equaion of he GACH (1,1) model is given by: where h ω a 1 bh + γv (10) 2 = + ε + 1 V is he daily rading volume. The model given by Equaion 10 includes lagged condiional variance erms and errors. The daily rading volume is used as a proxy variable for he mixing variable (i.e. he number of daily price changes). The GACH model is inroduced by Bollerslev (1986) o accoun for volailiy persisence. The model given above is a simple GACH (1,1) model ha is 11

12 found o be parsimonious and easier o idenify and esimae he parameers (Enders, 1995). We also selec he simple GACH (1,1) model since many papers argue ha he GACH (1,1) model accouns for emporal dependence in variance and excess kurosis (Ciner, 2001). In addiion, we examine he conemporaneous relaionship beween daily rading volume and fuures reurns using several differen echniques. In paricular, o es wheher he posiive conemporaneous relaionship beween rading volume and sock index fuures reurns exiss, he following GACH (1,1) model is esimaed: h a0 a a V + ε (11.1) = = ε 1 1 ω a bh (11.2) Equaion (11.1) presens he mean equaion and Equaion (11.2) he variance equaion. Finally, we analyse he conemporaneous relaionships using he mehodology proposed by Gwilym e al. (1999) and Ciner (2001). We model he series using he equaions: = ω + av + γ 1 + ε (12.1) V = φ + λ + µ V 1 + ξ (12.2) Gwilym e al. (1999) and Ciner (2001) esimae a sysem of simulaneous equaions via Generalized Mehod of Momens (GMM). Also, ichardson and Smih (1994) es he MDH using a GMM esimaor. Since he sysem uses volume and absolue value of reurns as endogenous variables, i would no possible o use OLS 5. The GMM is inroduced by Hansen (1982). According o he Eviews 3.1 Help he idea is o choose he parameer esimaes so ha he heoreical relaion is saisfied as closely as possible. In general, GMM approach allows esimaion of he conemporaneous relaionship whils avoiding any simulaneiy bias and yielding heeroscedasiciy and auocorrelaion consisen esimaes in he process (Gwilym e al., p. 595). For ha reason, o esimae an equaion by GMM we need o lis he names of he insrumens. In our case, following Gwilym e al. (1999) and Ciner (2001), we use he lagged volailiy and volume o idenify he GMM esimaor. In paricular, he insrumenal variables conrol for he simulaneiy bias and he GMM sysem conrols for possible heeroskedasiciy in error erms. We also selec he Weighing Marix: Time Series (HAC) opion in order o yield heeroscedasiciy and auocorrelaion. In addiion, he GMM has he advanage of reporing he J-saisic o es he validiy of overidenifying resricions (usually when here are more insrumens han parameers). 5 Since is correlaed wih error erm Similarly for V and ξ. ε, hen Cov, ε ) is no equal o zero, as required by OLS. ( 12

13 According o Ciner (2001), he significance of a and λ shows a conemporaneous relaion beween rading volume and absolue reurns. Also, he significance of he parameer µ indicaes ha lagged volume conains informaion abou absolue reurns. As a resul, marke raders use rading volume as an indicaion of marke (prices) on previous rading volume (see also Foser, 1995 for deails). - Dynamic elaionship To examine furher he relaionship beween fuures volailiy and volume, causaliy ess are employed (for a emporal ordering beween he wo variables). The dynamic relaionship beween volailiy and volume is examined using Granger Causaliy ess hrough he Vecor Auoregressive (VA 6 ) mehodology. Granger causaliy is based on he heory ha if an even x occurs before an even y, hen we say ha x causes y. Suppose ha x and y are rading volume and reurns, respecively. Then, he following models are used o es for causaliy beween he wo variables: x m n = ω + a x + b y + ε (13) i i i i= 1 i= 1 i y m n = +ci x i + di y i i= 1 i= 1 φ + ξ (14) If he b i ( c i ) coefficiens are saisically significan hen we conclude ha reurns (volume) cause volume (reurns). However, if he F-es (via Wald es) does no rejec he hypohesis ha he b i =0 ( c i = 0 ), hen he reurns (volume) do no cause rading volume (reurns). If boh b i and c i are differen from zero, hen here is a feedback relaion beween hose wo variables. Hence, a bidirecional causaliy exiss and causaliy runs in boh direcions. Under he null hypohesis (Ho), x does no Granger-cause y, and alernaively, y does no Granger-cause x. According o Pindyck and ubinfeld (1998), x causes y if (i) x helps o predics y, and (ii) y does no help o predic x. For he esimaion of Granger causaliy ess, we use lags considering he Akaike informaion crierion (AIC). 6 The benefi of VA models is ha hey accoun for linear ineremporal dynamics beween variables wihou imposing any a priory resricions. 13

14 4. GEEK FUTUES MAKET AND DATA - The Ahens Derivaives Exchange (ADEX) The ADEX is a new Exchange (since Augus 27, 1999). The mos popular producs of ADEX include index fuures and opions on he FTSE/ASE-20 and FTSE/ASE Mid 40, and he bond fuure conrac. During 2000, he increased volailiy of fuures in FTSE/ASE-20 (30% average) indicaes ha he marke condiions allow for inraday rading. Also, according o he deviaions from he heoreical price of he FTSE/ASE-20 index fuure conrac, i may be possible for quasi-arbirage in he marke (as he deviaions have reached 5% of he heoreical price). On he oher hand, i is very clear ha FTSE/ASE Mid 40 index fuures are mos successful as he larger par of he daily volume in Ahens Sock Exchange is done in middle and low capializaion socks. - DATA Daily closing prices and volume for FTSE/ASE-20 index are used over he period Sep Augus The FTSE/ASE-20 index was inroduced in Sep. 1997, while he FTSE/ASE-20 index fuures conrac began rading in Augus 1999 a ADEX. For FTSE/ASE Mid 40 index, he daily closing prices and rading volume are used over he period Dec Augus Also, he FTSE/ASE Mid 40 index was inroduced in Dec. 1999, while he FTSE/ASE Mid 40 index fuures was inroduced in January All daa informaion s were obained from he official web page of he Ahens Derivaives Exchange ( Graphical plos of reurn-volume coefficiens are presened in Appendix 1 and Appendix 2 for FTSE/ASE-20 and FTSE/ASE Mid 40, respecively. 5. EMPIICAL ESULTS We begin he empirical analysis by firs invesigaing he summary saisics of reurns and volume and he uni roo ess. Firs, Table 1 provides he sample summary saisics for FTSE/ASE-20 and Table 2 for FTSE/ASE Mid 40 sock index fuures. 14

15 << Table 1- abou here >> << Table 2- abou here >> I is observed ha boh FTSE/ASE-20 and FTSE/ASE Mid 40 reurns and absolue reurns have posiive skewness, posiive kurosis and high value of J-B saisic es. This means ha he disribuion is skewed o he righ, and also, ha he pdf is lepokuric. Also, he J-B saisic es suggess ha he null hypohesis of normaliy is rejeced. In addiion, he resuls for he rading volume indicae negaive skewness, low posiive kurosis and low value of J-B saisic es. Hence, he summary saisics for rading volumes show ha he disribuion is skewed o he lef, and also ha he null hypohesis of normaliy is acceped. UNIT OOT TESTS The causaliy ess (and VA models) assume ha he variables (i.e. reurns and rading volume) in he sysem are saionary. Therefore, we es for he saionariy of reurns and rading volume series. Noe ha if he resuls indicae ha he daa are nonsaionary hen we may produce misleading resuls. To es log(reurns) and log(volume) for a uni roo we employ he augmened Dickey-Fuller (ADF) es. The ADF es is given by: x 1 n = a0 + ax +δ x (15) Table 3 shows ha he null hypohesis ha he fuures reurn series and rading volume series are nonsaionary is rejeced for boh FTSE/ASE-20 and FTSE/ASE Mid 40 sock index fuures. Hence, we conclude ha he rading volume and reurn series are boh saionary. i= 1 i i << Table 3- abou here >> I. CONTEMPOANEOUS ELATIONSHIP FTSE/ASE-20 The firs hypohesis invesigaed in his paper is ha suggesed in Equaion 8, i.e. he volailiy of rading volume as a funcion of price volailiy. Table 4 presens he resuls of his hypohesis for 15

16 FTSE/ASE-20 index. I shows ha price volailiy does no significanly impac volume s volailiy. This finding differs wih wha Malliaris and Urruia (1998) sugges for agriculural fuures. << Table 4- abou here >> Table 5 repors he coefficiens of regressing fuures reurns on rading volume using he simple OLS (Equaion 9). All he coefficiens are posiive bu no significan. Therefore, we sugges ha here is no posiive conemporaneous relaionship beween rading volume and fuures reurns (in all hree cases). << Table 5- abou here >> Furher, o invesigae wheher rading volume explains he GACH effecs for fuures marke reurns, GACH (1,1) model wih a volume parameer in he variance equaion is esimaed. Table 6 repors he resuls for FTSE/ASE-20 sock index fuures. As can been seen, in Panels A and B he parameer γ is posiive and saisically significan (i.e. here is a posiive effec), indicaing also ha i is reflecive of he conribuion of volume in explaining he GACH effecs in fuures markes reurns. In oher words, he volume conribues significanly in explaining he GACH effecs (Sharma e al., 1996). << Table 6- abou here >> Then, we es wheher he conemporaneous relaionship beween rading volume and fuures reurns exiss using he GACH (1,1) model wih a volume parameer in he mean equaion. As repored in Table 7, he coefficiens of rading volume are all posiive using he GACH (1,1) model given by Equaions (11.1) and (11.2). However, only in one case (Panel B), he coefficien is posiive and significan (i.e. here exiss a posiive conemporaneous relaionship beween rading volume and reurns). <<Table 7- abou here>> Furhermore, he resuls from he GMM sysem for FTSE/ASE-20 sock index fuures are presened in Table 8. In all cases, he coefficiens a and λ are no significan, and herefore, we conclude ha here is no posiive conemporaneous relaionship beween volailiy and volume. In addiion, he resuls sae ha here is a saisically significan relaionship beween lagged volume and absolue reurns. The parameer µ indicaes ha lagged volume conains informaion abou absolue reurns. 16

17 Noe also ha, in all of he cases, he J-es is very small indicaing ha here exiss a good fi of he model o he daa. << Table 8- abou here>> FTSE/ASE MID 40 Table 9 presens he resuls of he firs esable hypohesis suggesed in Equaion 8. The coefficien of price volailiy is significan, and herefore, we conclude ha price volailiy significanly impacs volume s volailiy. This is consisen wih he sudy of Malliaris and Urruia (1998) for six agriculural fuures conracs. <<Table 9- abou here>> Then, Table 10 shows he resuls obained from he OLS model (Equaion 9). As can been seen, in Panels A and C he volume coefficien is posiive and significan. So, we conclude ha here exiss a posiive conemporaneous relaionship beween rading volume and fuures reurns in FTSE/ASE Mid 40 sock index fuures. <<Table 10- abou here>> Furher, Table 11 repors he resuls obained from he Equaion 10 following he work of Sharma e al. (1996). I is obvious ha he volume parameers are no saisically significan, and so, rading volume does no conribue significanly in explaining he GACH effecs. <<Table 11- abou here>> 17

18 Table 12 repors he resuls obained from he GACH (1,1) model wih a volume parameer in he mean equaion. The coefficiens of rading volume are all posiive bu no significan. Hence, here is no evidence for posiive conemporaneous relaionship beween rading volume and fuures reurns in FTSE/ASE Mid 40 index. <<Table 12- abou here>> Table 13 repors he resuls from he GMM sysem. The resuls for he FTSE/ASE Mid 40 index show ha here is no posiive and significan conemporaneous relaionship beween volailiy and volume. A furher poin of noe is ha he effec of lagged volume is found o be posiive (Panels A and C) in he volume equaions, suggesing ha he knowledge of increased curren volume is a predicor of reduced fuure volume. Also, he fac ha he lagged reurn is posiive in he reurn equaions indicaes ha knowledge of increased curren reurn is a predicor of reduced fuure reurn. In addiion, he J-es saisics are very small in all of he cases, supporing a good fi o he daa. <<Table 13- abou here>> II. DYNAMIC ELATIONSHIP As we menioned above, in his paper we also es wheher rading volume leads fuures reurns, or vice versa. This is he heory behind he Granger-causaliy es, which is based on he fac ha he fuure canno cause he presen or he pas. In his sudy our resuls are mixed. For FTSE/ASE-20, here is srong evidence of bi-direcional causaliy (i.e. rejec he null hypohesis of no Granger-causaliy), and herefore, here is a feedback relaion beween rading volume and acual reurns. Hence, we conclude ha FTSE/ASE-20 index may suppor he sequenial arrival of informaion hypohesis over he MDH, and rading volume helps o predic reurn and vice versa. These findings are in agreemen wih hose of Clark (1973), Bessembinder and Serguin (1993) and ohers. However, for FTSE/ASE Mid 40, he resuls show evidence of acceping he null hypohesis of no Granger-causaliy indicaing ha here is no emporal ordering in he volume-reurns relaionship. Hence, FTSE/ASE Mid 40 index does no suppor a dynamic relaionship beween reurns and rading volume. Therefore, we conclude ha here is no evidence of greaer suppor o he sequenial informaion arrival. In oher words, consisen wih weak-form efficiency, we find ha here is no 18

19 causaliy from FTSE/ASE Mid 40 reurns o volume and volume o reurns. This implies ha rading volume does no show any predicive power for fuure reurns in he presence of curren and pas reurns, since we deal wih heavily raded conracs. In consisen wih Campbell e al. (1993) and McMillan and Speigh (2002), his is also due o he fac ha FTSE/ASE Mid 40 index is he mos successful and he mos frequency raded fuures index. Also, his finding is expeced since he larger par of he daily volume in Ahens Sock Exchange is done in middle and low capializaion socks. The empirical resuls are presened in Table 14 and Table 15 for FTSE/ASE-20 and FTSE/ASE Mid 40 respecively. <<Table 14- abou here>> <<Table 15- abou here>> 6. SUMMAY The relaionship beween reurns, volailiy and rading volume has ineresed financial economiss and analyss for a number of years. A widely documened resul is he posiive conemporaneous relaionship beween price reurns and rading volume. The wo mos imporan heoreical models, which have been used o explain his relaionship, include he mixure of disribuions hypoheses (MDH) and sequenial informaion arrival hypoheses. Currenly empirical resuls show ha he MDH by Clark (1973), Epps and Epps (1976) and Harris (1987), and he sequenial informaion model by Copeland (1976) are used o explain his posiive correlaion. Also, Karpoff (1987) reviews previous sudies on price-volume relaion and confirms he posiive correlaion beween volailiy (reurns) and volume on various financial markes. Firs, we invesigae he conemporaneous relaionship beween volume and reurns. For FTSE/ASE- 20, we find ha price volailiy does no significanly impac volume s volailiy, and also, we conclude ha a conemporaneous relaionship does no hold. Using GACH mehods, he resuls show a posiive and significan effec, indicaing ha volume conribues significanly in explaining he GACH effecs (in consisen wih Sharma e al., 1996), and lile suppor o he MDH or sequenial informaion arrival models. Furhermore, he GMM sysem suggess ha here is a significan relaionship beween lagged volume and absolue reurns, while a posiive conemporaneous relaionship does no hold. Taken ogeher, hese findings indicae ha marke paricipans use volume as an indicaion of prices (Foser, 1995), and ha volume and reurns do no respond o he same 19

20 exogenous variable in he GMM sysem, he daily flow of informaion o he marke. The laer is in conras wih Ciner (2001). For FTSE/ASE Mid 40, he resuls are mixed. The price volailiy significanly impacs volume s volailiy, and also, a posiive conemporaneous relaionship holds. These resuls are in conras wih previous resuls for FTSE/ASE-20. However, boh GACH and GMM mehods confirm ha here is no evidence for posiive relaionship beween rading volume and reurns. This sudy also invesigaes he dynamic relaionship beween rading volume and acual reurns for Greek index fuures. For FTSE/ASE-20, using linear Granger causaliy ess, we conclude ha pas volume provides informaion on curren reurns, and pas reurns conains informaion on curren volume. Therefore, he bi-direcional causaliy suggess ha speculaors pay aenion o price changes and changes in rading volume. In oher words, he finding of srong bi-direcional fuures reurnsvolume causal relaionships implies ha knowledge of curren rading volume improves he abiliy o forecas fuures reurns. These resuls are in line wih hose of Grammaikos and Saunders (1986), Bessembinder and Seguin (1993), Malliaris and Urruia (1998), Gwilym e al. (1999) and McMillan and Speigh (2002), who repor a bi-direcional relaionship beween volume and price variabiliy. Furhermore, he fac ha here is causaliy from volume o reurns indicaes ha a financial rader akes volume o make prices move (Ciner; 2001, p. 3). Hence, for he FTSE/ASE-20 index fuures marke we show evidence for he sequenial arrival of informaion hypohesis. However, for FTSE/ASE Mid 40, we find ha here is no causaliy from volume o reurns and reurns o volume, consisen wih weak-form efficiency. This finding is consisen wih McCarhy and Najand (1993), Kocagil and Shachmurove (1998), Bhar and Malliaris (1998), Walls (1999) and Gwilym e al. (1999) for daily fuures daa. They sugges ha major US and UK (LIFFE) fuures markes are weak-form efficien. The lack of causaliy (and efficiency) beween reurns and volume is possibly explained by he fac ha he FTSE/ASE Mid 40 index is he mos frequency raded sock index in Ahens Sock Exchange. Overall, saisical analysis shows ha rading volume and reurns do no clear suppor a posiive conemporaneous relaionship on Greek fuures marke. On he oher hand, for FTSE/ASE-20, he dynamic models show a bi-direcional Granger causaliy (feedback) beween volume and acual reurns. However, for FTSE/ASE Mid 40, he resuls indicae ha reurns do no Granger cause volume and vice versa. The resuls of his sudy should be useful o financial researchers-analyss, praciioners and derivaive (fuures) marke paricipans whose success depends on he abiliy o forecas price movemens in he ASE and ADEX. 20

21 APPENDIX 1 FTSE/ASE Fig. 1 ABS. ETUN Fig. 2 ETUN Fig. 3 LNVOL Fig. 4 VOL Fig. 5 VOLUME * Graphical plos of abs. reurn, reurn, lnvol, vol and volume for FTSE/ASE

22 APPENDIX 2 FTSE/ASE MID Fig. 1 ABS. ETUN Fig. 2 ETUN Fig. 3 LNVOL Fig. 4 VOL Fig. 5 VOLUME * Graphical plos of abs. reurn, reurn, lnvol, vol and volume for FTSE/ASE Mid

23 EFEENCES Anderson,. W. (1985), Some Deerminans of he Volailiy of Fuures Prices, Journal of Fuures Markes, 5, Anoniou, A., Ergul, N., Holmes, P. and Priesley,. (1997), Technical analysis, rading volume and marke efficiency: evidence from an emerging marke, Applied Financial Economics, 7, Bessembinder, H. and Seguin, P. J. (1992), Fuures rading aciviy and sock price volailiy, Journal of Finance, 47, Bessembinder, H. and Seguin, P. J. (1993), Price Volailiy, Trading Volume, and Marke Deph: Evidence from Fuures Markes, Journal of Financial and Quaniaive Analysis, 28, Bhar,. and Malliaris, A. G. (1998), Volume and volailiy in foreign currency fuures markes, eview of Quaniaive Finance and Accouning, 10, Board, J. L. G. and Sucliffe, C. M. S. (1990), Informaion, volailiy, volume and mauriy: an invesigaion of sock index fuures, eview of Fuures Markes, 9. Bollerslev, T. (1986), Generalised Auoregressive Condiional Heeroskedasiciy, Journal of Economerics, 30, Brailsford, T. J. (1994), The Empirical elaionship Beween Trading Volume, eurns and Volailiy, esearch Paper 94-01, Deparmen of Accouning and Finance, Universiy of Melbourne. Brailsford, T. J. (1996), The Empirical elaionship Beween Trading Volume, eurns and Volailiy, Accouning and Finance, 36, Campbell, J., Grossman, S. and Wang, J. (1993), Trading volume and serial correlaion in sock reurns, Quarerly Journal of Economics, 108, Chen, Y-J, Duan, J-C, and Hung, M-W (1999), Volailiy and Mauriy Effecs in he Nikkei Index Fuures, Journal of Fuures Markes, 19, Ciner, C. (2001), Informaion conen of volume: an invesigaion of Tokyo commodiy fuures markes, Pacific-Basin Finance Journal, Aricle in press. Clark, P. (1973), A subordinaed sochasic process model wih finie variance for speculaive prices, Economerica, 41, Copeland, T. (1976), A model of asse rading under he assumpion of sequenial informaion arrival, Journal of Finance, 31, Cornell, B. (1981), The elaionship beween Volume and Price Variabiliy in Fuures Markes, Journal of Fuures Markes, 1,

24 Daigler,. T. and Wiley, M. K. (1999), The Impac of Trader Type on he Fuures Volailiy-Volume elaion, Journal of Finance, 6, Enders, W. (1995), Applied Economeric Time Series, John Wiley & Sons, New York. Epps, T. and Epps, M. (1976), The sochasic dependence of securiy price changes and ransacion volumes: implicaions for he Mixure-of-Disribuions hypohesis, Economerica, 44, Faff,. W. and McKenzie, M. D. (2002), The Impac of Sock Index Fuures Trading on Daily eurns Seasonaliy: A Mulicounry Sudy, Journal of Business, 75, Foser, A. J. (1995), Volume-volailiy relaionships for crude oil fuures markes, Journal of Fuures Markes, 15, Gallan, A.., ossi, P. E. and Tauchen, G. (1992), Sock prices and volume, eview of Financial Sudies, 5, Gallan, A.., ossi, P. E. and Tauchen, G. (1993), Nonlinear dynamic srucures, Economerica, 61, Galloway, T. and Kolb,. W. (1996), Fuures prices and he mauriy effec, Journal of Fuures Markes, 16, Grammaikos, T. and Saunders, A. (1986), Fuures Price Variabiliy: A Tes of Mauriy and Volume Effecs, Journal of Business, 59, Gwilym, O., McMillan, D. and Speigh, A. (1999), The inraday relaionship beween volume and volailiy in LIFFE fuures markes, Applied Financial Economics, 9, Han, L. M., Kling, J. L. and Sell, C. W. (1999), Foreign Exchange Fuures Volailiy: Day-of-he- Week, Inraday and Mauriy Paerns in he Presence of Macroeconomic Announcemens, Journal of Fuures Markes, 19, Hansen, L. P. (1982), Large sample properies of generalized mehod of momens esimaors, Economerica, 50, Harris, L. (1983/1984), The join disribuion of speculaive prices and of daily rading volume, Working paper no , Los Angeles: Universiy of Souhern California, Deparmen of Finance and Business Economics. Harris, L. (1984), Transacions daa ess of he mixure of disribuions hypohesis, Working paper no , Los Angeles: Universiy of Souhern California, Deparmen of Finance and Business Economics. Harris, L. (1986), Cross-securiy ess of he Mixure of Disribuions hypohesis, Journal of financial and Quaniaive Analysis, 21, Harris, L. (1987), Transacion daa ess of he Mixure of Disribuions Hypohesis, Journal of Financial and Quaniaive Analysis, 22,

25 Harris, M. and aviv, A. (1993), Differences of opinion make a horse race, eview of Financial Sudies, 6, Herber, J. H. (1995), Trading Volume, Mauriy and Naural Gas Fuures Price Volailiy, Energy Economics, 17, Hiemsra, C. and Jones, J. D. (1994), Tesing for linear and non-linear Granger causaliy in he sock price-volume relaionship, Journal of Finance, 49, Hogan, K. C. J., Kronner, K. F. and Sulan, J. (1997), Program Trading, Nonprogram Trading, and Marke Volailiy, Journal of Fuures Markes, 17, Jacobs, M. J. and Onochie, J. (1998), A Bivariae Generalized Auoregressive Condiional Heeroscedasiciy-in-Mean Sudy of he elaionship beween eurn Variabiliy and Trading Volume in Inernaional Fuures Markes, Journal of Fuures Markes, 18, Johnson, J. (1998), Does he Samuelson Effec Hold for SPI Fuures?, Deparmen of Accouning and Finance, Universiy of Wesern Ausralia, Working Paper. Karpoff, J. M. (1986), A heory of rading volume, Journal of Finance, 41, Karpoff, J. M. (1987), The elaion Beween Price Changes and Trading Volume: A Survey, Journal of Financial and Quaniaive Analysis, 22, Kawaller, I. G., Koch, P. D. and Koch, T. W. (1990), Inraday relaionships beween volailiy in S&P500 fuures prices and volailiy in he S&P index, Journal of Banking and Finance, 14, Kocagil, A. E. and Shachmurove, Y. (1998), eurn-volume Dynamics in Fuures Markes, Journal of Fuures Markes, 18, Lamoureux, C. G. and Lasrapes, W. D. (1990), Heeroskedasiciy in sock reurns daa: volume versus GACH effecs, Journal of Finance, 45, Malliaris, A. G. and Urruia, J. L. (1998), Volume and Price elaionships: Hypoheses and Tesing for Agriculural Fuures, Journal of Fuures Markes, 18, McCarhy, J. and Najand, M. (1993), Sae space modelling of price and volume dependence: evidence from currency fuures, Journal of Fuures Markes, 13, McMillan, D. and Speigh, A. (2002), eurn-volume dynamics in UK fuures, Applied Financial Economics, preview aricle, 1-7. Merrick, J. J. (1987), Volume deerminaion in sock and sock index fuures markes: an analysis of arbirage and volailiy effecs, Journal of Fuures Markes, 7, Milonas, N. T. (1986), Price Variabiliy and he Mauriy Effec in Fuures Markes, Journal of Fuures Markes, 6,