Trading Volume and Returns Relationship in Greek Stock Index Futures Market: GARCH vs. GMM

Transcription

1 Inernaional esearch Journal of Finance and Economics ISSN Issue (007) EuroJournals Publishing, Inc. 007 hp:// Trading Volume and eurns elaionship in Greek Sock Index Fuures Marke: GACH vs. GMM Chrisos Floros Deparmen of Economics, Universiy of Porsmouh Porsmouh Business School, Porsmouh, PO 3DE, UK Tel: +44 (0) Dimirios V. Vougas Deparmen of Economics, Universiy of Wales Swansea Singleon Park, Swansea, SA 8PP, UK Tel: +44 (0) Absrac This paper examines he relaionship beween rading volume and reurns in Greek sock index fuures marke. For boh available sock index fuures conracs of he Ahens Derivaives Exchange (ADEX), we sudy GACH effecs in our daa and es how well hese effecs are explained by rading volume (under boh GACH and GMM). For FTSE/ASE-0, rading volume conribues significanly in explaining GACH effecs. However, GMM sysem esimaion 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. For FTSE/ASE Mid 40, he empirical resuls give differen conclusions. Boh GACH and GMM mehods confirm ha here is no evidence of posiive relaionship beween rading volume and reurns. These findings are helpful o financial managers dealing wih Greek sock index fuures. Keywords: Fuures, Volume, MDH, ADEX, GACH, GMM. Jel Classificaion Codes: G3, G5. I. Inroducion There are many reasons ha raders pay aenion o rading volume. 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 highly liquid, resuling in low price variabiliy. This also reduces he price effec of large rades. In general, wih an increase in volume, broker revenue will Volume is he number of ransacions in a fuures conrac during a specified period of ime (Sucliffe 993). According o Telser (98) higher margins will raise he cos of rading in fuures. Margins use up par of he rader's precauionary balances, and his money is no longer available o deal wih unexpeced evens. This increase in he cos of rading leads o lower rading volume and open ineres. He argues ha his lower volume will resul in a less liquid marke, which will lead o a rise in price volailiy.

2 Inernaional esearch Journal of Finance and Economics - Issue (007) 99 increase, and marke makers have greaer opporuniy for profi as a resul of higher urnover. However, raders who wish o paricipae in movemens of 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, see Karpoff (987). 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, see Harris and aviv (993). Mos previous sudies have examined he leading heories (hypoheses) ha explain he informaion arrival process in financial markes. The compeing hypoheses are he mixure of disribuions hypohesis (MDH) and he sequenial informaion arrival hypoheses. According o he MDH, informaion disseminaion is conemporaneous. In oher words, fuures prices (and volume) change only when informaion arrives, and evolve a a consan speed in even ime, see Sucliffe (993). MDH suggess ha daily price changes and rading volume are driven by he same underlying laen "news" arrival, or informaion flow, variable (Luu and Marens, 003). News arrivals can be proxied by he volume of rade (Clark 973; Epps and Epps, 976). Under MDH, he daily reurns and he daily rading volume is he sum of a random number of individual price incremens and volumes. This random number depends on he rae of informaion arrival during he day. MDH implies only a conemporaneous relaionship beween volume and (absolue) reurns. I is associaed wih Clark (973), Epps and Epps (976), Tauchen and Pis (983) and Harris (986). 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 (986), under MDH framework he correlaion beween price (reurns) and volume should be posiive due o join dependence on a common direcing variable or even. MDH is iniially developed by Clark (973) who argues ha he rae of informaion arrival implies a posiive conemporaneous correlaion beween volume and volailiy. Clark (973) shows ha he values of he consequenial price change and rading volume are disribued independenly from each oher. Hence, each variable is independenly and idenically disribued over a series of informaion arrivals. Also, he number of arrivals of informaion per ime period varies. Tauchen and Pis (983) develop a model in which average daily volume and he variance of daily price change are posiive funcions of he daily flow of informaion. Furhermore, Harris (987) and Sucliffe (993, p.88) repor he following implicaions of MDH model: 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. For a given number of informaion arrivals, here is zero correlaion beween volailiy and volume. 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. There will be lepokurosis in he disribuion of price changes compued over equal ime periods. In addiion, according o he MDH, a serially correlaed mixing variable measuring he rae a which informaion arrives o he marke explains he GACH effecs in he reurns (Lamoureux and Lasrapes, 990). According o Lamoureux and Lasrapes (990), using daily rading volume as a proxy for he mixing variable, he inroducion of volume as an explanaory variable in he condiional variance equaion eliminaes he GACH effecs. Furhermore, Sharma e al. (996) exend he work of Lamoureux and Lasrapes (990) by esing for he GACH effecs in marke reurns. According o Sharma e al. (996, p. 338), he empirical sudy by Lamoureux and Lasrapes (990) can be furher enhanced on wo main forms: (i) he abiliy of he daily daa on rading volumes o fully capure he

3 00 Inernaional esearch Journal of Finance and Economics - Issue (007) informaion flow effecs on he marke reurns would parly res on he degree of marke efficiency, and (ii) volailiy can be generaed by firm-specific facors and marke-wide facors (boh of which affec volume). This should make volume a good or poor proxy for informaion (news arrival) which conribues o condiional heeroscedasiciy. However, empirical sudies by Najand and Yung (99) and Bessembinder and Seguin (99, 993) repor evidence agains MDH. In addiion, Bessembinder and Seguin (993) 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 gradual disseminaion of informaion such ha a series of inermediae equilibria exis, see Copeland (976) and Tauchen and Pis (983). Copeland (976) develops a model of he effecs of he arrival of a single piece of informaion on price and rading volume. Clark (973) shows ha volume is a posiive funcion of he logarihm of he number of raders, and a posiive funcion of he logarihm of he srengh of he informaion. He argues ha if he informaion is simulaneously received by all raders, here will be a negaive correlaion beween volume and he absolue value of price changes. In oher words, i is he sequenial arrival of informaion ha leads o he posiive relaionship beween volume and value of price changes (volailiy). Furher, he model implies he coninuaion of higher volailiy afer he iniial informaion shock raher han spikes in volailiy, see Wiley and Daigler (999). Also, according o Grammaikos and Saunders (986, p. 36) 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 (00) argue ha he 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 arrival of new (privae) informaion. In general, boh MDH and sequenial arrival of informaion hypoheses suppor a posiive and conemporaneous relaionship beween volume and absolue reurns and assume a symmeric effec for price increases and price decreases for fuures conracs, see Karpoff (987). Noice ha in he case of an efficien (fuures) marke, neiher a conemporaneous relaionship nor a dynamic relaionship hold. The price (reurns)-volume relaions have significan implicaions ino fuures markes. Price changes affec he rading volume in fuures conracs. In paricular, he ime o delivery of a conrac affecs no only he rading volume bu possibly also he changes of price (Karpoff, 987). Previous sudies show a srong posiive relaionship beween volume of fuures rading and volailiy (reurns) of fuures prices. They es he MDH using GACH models (Hogan e al., 997; Jacobs and Onochie, 998; Monalvo, 999) or a Generalized Mehod of Momens (GMM) sysem of equaions (Gwilym e al., 999; Wang and Yau, 000). In his paper, we invesigae he volailiy (reurns)-volume relaionship from one direcion: he conemporaneous relaionship 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 marke, see Wiley and Daigler (999, p.). Karpoff (987, pp. 09-0) explains he imporance of he price-volume relaionship as follows: The models predic various price-volume relaions ha depend on he rae of informaion flow o he marke. I is imporan for even sudies ha use a combinaion of price and volume daa. The price-volume relaion is criical o he debae over he empirical disribuion of speculaive prices.

4 Inernaional esearch Journal of Finance and Economics - Issue (007) 0 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 price-volume relaion can also indicae he imporance of privae versus public informaion in deermining invesors demands. Furhermore, according o Sucliffe (993, p.94), if price volailiy increases as delivery approaches, and price volailiy increase as volume increases, i is implied ha volume increases as delivery approaches. This paper follows Sharma e al. (996), Gwilym e al. (999), Ciner (00) and McMillan and Speigh (00). We invesigae he empirical relaionship beween price changes and rading volume for index fuures conracs raded in he ADEX (Greece). In addiion, we sudy GACH effecs in our daa and es how well hese effecs are explained by rading volume. We provide a es o invesigae if GACH effecs arise from ime variaion in informaion arrival. We examine he role of volume as a proxy for informaion arrival in explaining he condiional variance of he marke reurn. In addiion, we invesigae he role of he rae of informaion arrival variable relaing o Greek fuures prices (reurns). Furhermore, we analyse he conemporaneous relaionship beween reurns and volume using a sysem of simulaneous equaions (GMM). Noice ha no previous paper has esed he relaionship beween price change (reurns) and rading volume in he Greek fuures markes. The paper coninues as follows. Secion II presens he lieraure review, while in Secion III we ouline he mehodology. Secion IV presens he daa used in his sudy. Empirical resuls are repored and discussed in V. Finally, concluding remarks are made in Secion VI. II. Lieraure eview We examine empirically he conemporaneous relaionship beween reurns-volailiy and rading volume. The Mixure of Disribuions Hypohesis (MDH) suggess ha he correlaion beween price variabiliy and volume should be posiive. Previous empirical sudies have noed a srong posiive relaionship. Firs, Clark (973) and Epps and Epps (976) argue ha he disribuion of fuures prices can be explained by he MDH. Epps and Epps (976) presen a heoreical model in which rading volume and absolue reurns form a posiive funcion of he amoun of disagreemen beween raders. Copeland (976) 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 empirical evidence is summarized in he paper by Karpoff (987). In paricular, his paper cies several reasons why he price-volume relaionship is posiive (see also Board and Sucliffe, 990). Oher research includes Cornell (98) and Tauchen and Pis (983). Cornell (98) shows a posiive correlaion beween changes in average daily volume and changes in he sandard deviaion of daily log price relaives for 4 of he 8 examined commodiies. Also, Tauchen and Pis (983) 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 (966) suggess ha a small (large) volume is usually accompanied by a fall (rise) in price. Cornell (98) finds posiive relaions beween volume and changes in he variabiliy of prices for 7 fuures conracs. In addiion, Harris (983, 984), Grammaikos and Saunders (986) and Karpoff (987) 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, 986). Also, Harris (984) 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 (990) by invesigaing he effec of rading volume o he marke reurns using he generalised auoregressive condiional heeroscedasiciy (GACH) model. They esimae a GACH model where rading volume is included

5 0 Inernaional esearch Journal of Finance and Economics - Issue (007) 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. (996) examine he GACH effecs in he NYSE. The paper exends he work of Lamoureux and Lasrapes (990) and shows how he GACH effecs in marke reurns are explained by marke volume. For his reason, a simple GACH (,) model wih and wihou daily volume is considered. Also, Sharma e al. (996) ake ino consideraion he assumpion of condiional normaliy and condiional -disribuion. The daa covers he period 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. As menioned, Karpoff (987) reviews previous sudies on he price-volume relaion and concludes ha here is a posiive correlaion beween volailiy and volume. Lamoureux and Lasrapes (990) show ha he inroducion of volume in he condiional variance equaion eliminaes GACH effecs. They find ha all 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 (990) find ha 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 (990) also find suppor o he hypohesis of a posiive relaionship beween volailiy and volume for he FTSE-00 index. Furher, Bessembinder and Seguin (993) divide volume ino expeced and unexpeced componens o examine he relaion beween price volailiy and rading volume for fuures markes. They use daily prices and rading volumes for eigh fuures markes over he inerval May 98 o March 990. In general, he resuls from A and AMA models show a posiive relaion beween volume and volailiy. Also, Bessembinder and Seguin (993) 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. Using VA, Granger-causaliy es and GACH models, Hiemsra and Jones (994), Gallan e al. (993) and Tauchen e al. (996) repor a posiive correlaion beween volailiy and rading volume. Brailsford (994) examines empirically he relaionship beween rading volume and volailiy in he Ausralian Sock marke. The sample covers he period 4 April 989 o 3 December 993. This 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 (996) 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 (,) model are found o be insignifican when he volume is aken ino consideraion. agunahan and Pecker (997) focus on he relaionship beween volume and price variabiliy for he Ausralian fuures marke. They consider reurn series of he conracs for he period January 99 o December 994. Using he models developed by Schwer (990) and Bessembinder and Seguin (993), hey provide srong evidence ha unexpeced volume has a greaer impac on volailiy han expeced volume. Hogan e al. (997) use a bivariae GACH model o es he relaionship beween program rading volume and marke volailiy. They use daily daa, from 3 January 988 o 3 December 99, of he S&P 500 cash and he CME S&P 500 near-erm fuures conracs. Their resuls show ha here is a srong posiive relaionship beween rading volume and volailiy. Also, Daigler and Wiley (999) examine he volailiy-volume relaion in fuures markes. They use he Chicago Board of Trade s Liquidiy Daa Bank o examine he Cusomer Trade Indicaor (CTI) daa ha separaes oal fuures volume ino four ypes of raders. Accordingly, he general public

6 Inernaional esearch Journal of Finance and Economics - Issue (007) 03 drives he posiive volailiy-volume relaion 3. In addiion, hey find ha he unexpeced volume series is more imporan han he expeced volume series in explaining volailiy. Jacobs and Onochie (998) examine he relaionship beween reurn variabiliy and rading volume in fuures markes. The daa se consiss of daily observaions for six fuures conracs raded on he LIFFE. A bivariae GACH-in-mean model is used. Their resuls indicae a posiive relaionship beween rading volume and price volailiy. In addiion, Monalvo (999) examines he Spanish Governmen Bond Fuures Marke using he approach proposed by Lamoureux and Lasrapes (990). Monalvo (999) suggess ha he daily volume and frequency have a posiive effec on volailiy. Consisenly, Gwilym e al. (999) analyse he conemporaneous relaionship beween volailiy and volume for sock index (FTSE-00), shorerm ineres rae (Shor Serling) and governmen bond (Long Gil) fuures conracs raded a he LIFFE. Tha daa covers he period 4 January 99 o 30 June 995. Evidence from esimaion of a GMM sysem for volailiy and volume suppors a significan posiive and conemporaneous correlaion beween volailiy and volume. Wang and Yau (000) examine he relaionship beween rading volume and price volailiy for fuures markes using OLS and GMM. The sample is based on wo financial fuures conracs (S&P 500 and DM) and wo meal fuures conracs (silver and gold), and covers he period January 990 o 9 April 994. Their resuls show a posiive relaionship beween rading volume and price volailiy and a negaive relaionship beween price volailiy and lagged rading volume. Waanabe (00) examines he relaion beween price volailiy and rading volume for he Nikkei 5 sock index fuures. The daa covers he period 4 Augus 990 o 30 December 997. Following he mehod developed by Bessembinder and Seguin (993), his paper shows a saisically significan and posiive relaionship beween volailiy and unexpeced volume. Also, for he period when he regulaion increased gradually, Waanabe (00) suggess ha here is no relaionship beween price volailiy and volume. Furhermore, Pilar and afael (00) analyse he effec of fuures on Spanish sock marke volailiy and rading volume. For his purpose, a GJ model wih a dummy variable is used. Their resuls show a decrease in he volailiy and increase in rading volume. However, Illueca and Lafuene (003) find no significan link beween spo volailiy and rading volume in he Spanish sock index fuures marke. Finally, Luu and Marens (003) es he MDH using realized volailiy. They find ha he mixed evidence on MDH in he exising lieraure can in par be aribued o he use of poor realized volailiy measures. III. Mehodology Following Bhar and Malliaris (998) and Malliaris and Urruia (998), he rading volume is a funcion of equilibrium fuures price and ime. Tha is V = V (, F) () where V denoes rading volume, F denoes fuures price and denoes ime. Assuming he price F follows an Io process wih drif μ and volailiy σ, hen: df = μ d + σdz () where Z denoes a sandardised Wiener process. Alhough () is a general model, he model described by equaion () is favourable, as Io s processes describe beer coninuous random walks wih a drif which lead o marke efficiency. Anoher applicaion of Io s lemma resuls in dv = V + Vpμ + Vppσ d + VpσdZ (3) 3 Also, Bessembinder and Seguin (993, p. 38) sugges ha he volume-volailiy relaion depends on he class of raders involved.

7 04 Inernaional esearch Journal of Finance and Economics - Issue (007) where V, V p and V pp denoe parial derivaives. Models () and (3) describe rading volume heoreically and show wheher i follows a random walk. If fuures prices follow a random walk, rading volume also follows a random walk. Furher, aking expecaions of (3), we obain he following expression: E ( dv ) = V + Vpμ + Vppσ (4) This expression shows ha he change in volume depends on V, he drif rae μ and he volailiy of fuures prices σ We can also es he above hypohesis wih he following model E( dv ) = a + βμ + γσ (5) This implies a posiive relaionship beween price variabiliy and rading volume. Finally, using sochasic calculus, he volailiy of rading volume is given by: 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: Var( dv ) = a + δσ (7) For empirical esing equaions (6) and (7), we ge he following expression: ΔV = a + δ ΔF (8) Equaion (8) ess he hypohesis ha price volailiy has a significan impac on volume volailiy, see Bhar and Malliaris (998) 4 and Malliaris and Urruia (998). Conemporaneous elaionship We analyse he conemporaneous relaionship beween volailiy and volume in line wih Sharma e al. (996), Gwilym e al. (999) and McMillan and Speigh (00). According o Grammaikos and Saunders (986), here are several measures of volailiy. For example, uledge (979) uses he absolue log change from one rading day o he nex while Tauchen and Pis (983) use he square of he firs difference of he fuures price of adjacen periods. In addiion, Karpoff (987) uses he absolue value of he firs difference o measure volailiy 5. In his sudy, we invesigae he reurn (volailiy)-volume relaionship using he definiion = ln( F ) ln( F ) where F is he daily closing fuures price. We also measure he volume parameer as follows: V LNVOL = ln V (9) Firs, an 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 (990) assume ha he presence of ACH in reurns is due o MDH. However, heir resuls show ha rading volume removes significance of ACH and GACH coefficiens in he GACH(,) 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 (99, 993) and Foser (995) sugges ha rading volume is no sufficien o remove he lagged volailiy effecs in curren variance. Furhermore, Brailsford (996), using he GACH(,) model, concludes ha here is a srong suppor for he above model only when absolue reurns are considered. 4 5 They sugges ha volume is relaed o price volailiy and volume volailiy is relaed o price volailiy. Also, Sucliffe (993, p. 76) presens some of he definiions of price volailiy

8 Inernaional esearch Journal of Finance and Economics - Issue (007) 05 Following he work of Sharma e al. (996), we sudy GACH effecs in our daa and examine he effec of volume on reurn volailiy using he GACH(,) model. We es how well GACH effecs are explained by rading volume and examine he effec of rading volume on condiional volailiy, see also Lamoureux and Lasrapes (990). The condiional variance equaion of he GACH(,) model is given by: σ = ω + aε + βσ + γlnvol (0) where LNVOL is he daily reurn of rading volume. The model given by Equaion (0) includes lagged condiional variance erms and errors. Daily rading volume is used as a proxy variable for he mixing variable (i.e. he number of daily price changes). The model given above is a GACH(,) model ha is found o be parsimonious and easier o idenify and esimae (Enders, 995). We use he GACH(,) model because i provides posiive and significan parameers for boh indices. Only GACH(,) is repored here because i is an adequae represenaion. Also, i is a welldocumened resul in he lieraure ha mos financial ime series follow a GACH(,) process, see Sharma e al. (996). We also selec he parsimonious GACH(,) model since many papers argue ha i accouns for emporal dependence in variance and excess kurosis, see Ciner (00). Here, we assume ha he errors are condiionally normally disribued. 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 A()-GACH (,) model is esimaed: = μ + a + alnvol + ε (-) σ = ω + aε + βσ (-) Equaion (-) presens he mean equaion and Equaion (-) he variance equaion. Finally, we analyse he conemporaneous relaionships using he mehodology proposed by Gwilym e al. (999) and Ciner (00). We model he series using he equaions: = ω + alnvol + γ + ε (-) = φ + λ + μlnvol + ξ (-) LNVOL Gwilym e al. (999) and Ciner (00) esimae a sysem of simulaneous equaions via Generalized Mehod of Momens (GMM). Also, ichardson and Smih (994) es MDH using a GMM esimaor. ecenly, Holmes and Tomse (004) use he GMM approach o demonsrae ha he link beween fuures volume volailiy can be aribued o he flow of informaion 6. Since he sysem uses volume and absolue value of reurns as endogenous variables, i would no possible o use OLS 7. The GMM is inroduced by Hansen (98). Accordingly, he idea is o choose he parameer esimaes so ha he heoreical relaion is saisfied as closely as possible. In general, he GMM approach allows esimaion of he conemporaneous relaionship whils avoiding any simulaneiy bias and yielding heeroscedasiciy and auocorrelaion consisen esimaes in he process, see Gwilym e al. (999). GMM esimaion requires a lis of insrumens. In his case, following Gwilym e al. (999) and Ciner (00), we use lagged volailiy and volume o idenify he GMM esimaor. In paricular, insrumenal variables conrol for simulaneiy bias and he GMM sysem conrols for possible heeroskedasiciy in error erms. We also selec he Weighing Marix: Time Series (HAC) opion o alleviae heeroscedasiciy and auocorrelaion. In addiion, GMM has he advanage of reporing he J-saisic o es he validiy of overidenifying resricions (usually, when here are more insrumens han parameers). Under he null hypohesis ha he overidenifying resricions are saisfied, he J-saisic imes he number of regression observaions is asympoically 6 7 They show ha price movemens are dominaed by informed raher han noise rading. Since is correlaed wih error erm, hen is no equal o zero, as required by OLS. Similarly for and.

9 06 Inernaional esearch Journal of Finance and Economics - Issue (007) chi-squared wih degrees of freedom equal o he number of overidenifying resricions (we also repor he p-value of he es saisic). Noice ha we always esimae GMM using Heeroscedasiciy Consisen Sandard Errors. According o Ciner (00), he significance of and shows a conemporaneous relaion beween rading volume and absolue reurns. Also, he significance of he parameer 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 (995) for deails. IV. Daa Descripion Daily closing prices and volume for FTSE/ASE-0 index are used over he period Sepember 999- Augus 00. For FTSE/ASE Mid 40 index, daily closing prices and rading volume are used over he period January 000- Augus 00. Here, rading volume 8 is he number of rades in a fuures conrac during a specified period of ime (i.e. number of daily conracs in one day). Focusing on he above periods, (i) we es he hypoheses using daa from he early sage of he ADEX (sared is official operaion on 7 Augus 999), and (ii) we invesigae wheher he hypoheses exis afer he dramaic rise of Ahens Sock Exchange (ASE) sock prices 9. Graphical plos of reurn-volume coefficiens are presened in Appendix and Appendix for FTSE/ASE-0 and FTSE/ASE Mid 40, respecively. The FTSE/ASE-0 comprises 0 Greek companies, quoed on he Ahens Sock Exchange (ASE), wih he larges marke capialisaion (blue chips), while he FTSE/ASE Mid 40 comprises 40 mid-capialisaion Greek companies. Fuures conracs are quoed on he Ahens Derivaives Exchange (ADEX). The price of a fuures conrac is measured in index poins muliplied by he conrac muliplier, which is 5 Euros for he FTSE/ASE-0 conrac and 0 Euros for he FTSE/ASE Mid 40 conrac. There are four delivery monhs: March, June, Sepember and December. Trading akes place in he 3 neares delivery monhs, alhough volume in he far conrac is very small. Boh fuures conracs are cash-seled and marked o marke on he las rading day, which is he hird Friday in he delivery (expiraion) monh a 4:30 Ahens ime. For more informaion abou he Greek sock index fuures, see Floros and Vougas (006, 004). V. Empirical esuls Firs, we provide summary saisics of absolue reurns and (log-)volume, and presen uni roo ess. Table provides informaion for FTSE/ASE-0 and Table for FTSE/ASE Mid 40 sock index fuures. Table : Saisics for FTSE/ASE-0 (Abs. eurn Tr. Volume) FTSE/ASE-0 ABS. ETUN T. VOLUME MEAN MEDIAN MAXIMUM MINIMUM STD. DEV SKEWNESS KUTOSIS JAQUE-BEA POB Some oher measures of volume used in empirical sudies are: he value of conracs raded, he level of open ineres, and he level of open ineres muliplied by he price. The Ahens Sock Exchange (ASE), an imporan European emerging equiy marke, experienced a dramaic rise of sock prices beween he years , followed hen by an equally dramaic fall.

10 Inernaional esearch Journal of Finance and Economics - Issue (007) 07 Table : Saisics for FTSE/ASE MID 40 (Abs. eurn Tr. Volume) FTSE/ASE MID 40 ABS. ETUN T. VOLUME MEAN MEDIAN MAXIMUM MINIMUM STD. DEV SKEWNESS KUTOSIS JAQUE-BEA (J-B) POB Boh FTSE/ASE-0 and FTSE/ASE Mid 40 absolue reurns have posiive skewness, posiive kurosis and high J-B saisic. This implies ha he disribuion is skewed o he righ and ha he pdf is lepokuric. The J-B saisic es indicaes ha he null hypohesis of normaliy is rejeced. In addiion, he resuls for he rading volume series indicae negaive skewness, low posiive kurosis and lower value of J-B saisics (sill rejecing normaliy). Hence, summary saisics for rading volumes show ha he disribuion is skewed o he lef and ha he null hypohesis of normaliy is also no rejeced, bu no as srongly. Uni oo Tess Empirical ess assume he variables (i.e. reurns and rading volume) in he sysem are saionary. We es for he saionariy of log-fuures and rading volume series. eurns and rading volume are expeced o be saionary (in line wih he lieraure). To es fuures and log(volume) for a uni roo we employ he augmened Dickey-Fuller (ADF) es. Table 3 shows ha he null hypohesis ha he fuures rading volume series are non-saionary is rejeced for boh FTSE/ASE-0 and FTSE/ASE Mid 40 sock index fuures. We conclude ha he rading volume is saionary (for boh indices), while fuures series are boh non-saionary. However, he logarihmic reurns of fuures series are saionary. Table 3: Uni oo Tess (Price Tr. Volume) FTSE/ASE-0 INDEX ADF (PICE) ADF (VOLUME) Criical Values: Criical Values (Lags: 3) %: %: %: %: %: %: ADF ST DIFF. ADF FTSE/ASE MID 40 INDEX ADF (PICE) ADF (VOLUME) Criical Values: Criical Values (Lags: ) %: %: %: %: %: %: ADF ST DIFF. ADF I. Conemporaneous elaionship (FTSE/ASE-0) Furher, we invesigae wheher rading volume has any explanaory power for fuures marke reurns by fiing a GACH (,) model wih volume included in he condiional variance equaion. Table 4 repors he resuls for FTSE/ASE-0. The 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., 996).

11 08 Inernaional esearch Journal of Finance and Economics - Issue (007) Table 4: GACH (,) Model σ = ω + aε + βσ + γlnvol Dependen Variable: Mean Equaion Coefficien -Saisic Consan * Variance Equaion ω 5.37E * a * β * LNVOL * * Significan a he 5% or 0% level. In addiion, we examine he conemporaneous relaionship beween rading volume and fuures reurns, using a GACH (,) model wih volume included in he mean equaion only. From Table 5, rading volume coefficiens are posiive. The coefficien is posiive and significan (i.e. here exiss a posiive conemporaneous relaionship beween rading volume and reurns). Furhermore, resuls from he GMM sysem for FTSE/ASE-0 sock index fuures are presened in Table 6. The coefficiens a and λ are no significan and 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. Noe also ha, he J-es is very small indicaing ha here exiss a good fi of he model o he daa. Table 5: GACH (,) Model = μ + a + alnvol + ε σ Dependen Variable: = ω + aε + βσ Mean Equaion Coefficien -Saisic μ * * LNVOL * Variance Equaion ω 5.4E * a * * Significan a he 5% or 0% level. β *

12 Inernaional esearch Journal of Finance and Economics - Issue (007) 09 Table 6: GMM Models ω + alnvol + γ + ε = LNVOL = φ + λ + μlnvol + ξ Dependen Variable: Insrumen lis: Variable Coefficien -Saisic ω * LNVOL * LNVOL J-saisic.68E-3 (p-val. ) Dependen Variable: LNVOL LNVOL Insrumen lis: Variable Coefficien -Saisic φ LNVOL * J-saisic.68E-30 (p-val. ) * Significan a he 5% or 0% level. II. Conemporaneous elaionship (FTSE/ASE MID 40) Table 7 repors resuls obained from esimaing Equaion 0, following Sharma e al. (996). Volume parameer is no saisically significan, when included in he condiional variance equaion, hus rading volume does no conribue significanly in explaining he condiional variance when a GACH (,) model is esimaed. Table 7: GACH (,) Model: σ = ω + aε + βσ + γlnvol Dependen Variable: Mean Equaion Coefficien -Saisic Consan Variance Equaion ω a β * LNVOL * Significan a he 5% or 0% level. Furhermore, Table 8 repors resuls obained from a GACH (,) model wih volume indicaed in he mean equaion only. The coefficien of rading volume is posiive bu no significan. Hence, here is no evidence of posiive conemporaneous relaionship beween rading volume and fuures reurns for FTSE/ASE Mid 40.

13 0 Inernaional esearch Journal of Finance and Economics - Issue (007) Table 8: GACH (,) Model = μ + a + alnvol + ε σ = ω + aε + βσ Dependen Variable: Mean Equaion Coefficien -Saisic μ * LNVOL Variance Equaion ω 5.9E * a * * Significan a he 5% or 0% level. β * Table 9 repors resuls from GMM sysem esimaion. The resuls show ha here is no posiive and significan conemporaneous relaionship beween volailiy and volume for FTSE/ASE Mid 40. A furher poin is ha he effec of lagged volume is negaive in he volume equaion, suggesing ha he knowledge of increased curren volume is a predicor of reduced fuure volume. Also, he fac ha he lagged reurn is posiive (and significan) in he reurn equaion indicaes ha knowledge of increased curren reurn is a predicor of reduced fuure reurn. In addiion, he J-es saisic is very small, supporing a good fi o he daa. Table 9: GMM Models ω + alnvol + γ + ε = LNVOL = φ + λ + μlnvol + ξ Dependen Variable: Insrumen lis: Variable Coefficien -Saisic ω * LNVOL * LNVOL J-saisic 5.85E-3 (p-val. ) Dependen Variable: LNVOL LNVOL Insrumen lis: Variable Coefficien -Saisic φ LNVOL * J-saisic 7.0E-3 (p-val. ) * Significan a he 5% level. VI. Summary and Conclusions The relaionship beween reurns 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, are he mixure of disribuions hypoheses (MDH) and sequenial informaion arrival hypoheses. MDH is examined by Clark (973), Epps and Epps (976) and Harris (987), while sequenial informaion is used by Copeland (976). Karpoff (987) reviews

14 Inernaional esearch Journal of Finance and Economics - Issue (007) previous sudies on price-volume relaion and confirms he posiive correlaion beween volailiy (reurns) and volume on various financial markes. In his paper, we invesigae he conemporaneous relaionship beween volume and reurns in Greek sock index fuures marke. Using GACH models, he resuls for FTSE/ASE-0 show posiive and significan effec, indicaing ha volume conribues significanly in explaining he condiional variance (in line wih Sharma e al., 996), and lile suppor o MDH or sequenial informaion arrival models. Furhermore, GMM sysem esimaion 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, see Foser (995). Also, volume and reurns do no respond o he same exogenous variable in he GMM sysem, ha is he daily flow of informaion o he marke. The laer is in conras wih Ciner (00). For FTSE/ASE Mid 40, he resuls are mixed (he findings are in conras wih previous resuls for FTSE/ASE-0). Boh GACH and GMM mehods confirm ha here is no evidence of posiive relaionship beween rading volume and reurns. Also, GMM resuls show ha he knowledge of increased curren volume could be a predicor of reduced fuure volume for FTSE/ASE Mid 40 index. These findings are helpful o financial managers dealing wih Greek sock index fuures.

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17 4 Inernaional esearch Journal of Finance and Economics - Issue (007) [47] Sucliffe, C. M. S. (993), Sock Index Fuures: Theories and Inernaional Evidence, Chapman & Hall. [48] Tauchen, G. E. and Pis, M. (983), The price variabiliy volume relaionship on speculaive markes, Economerica, 5, [49] Tauchen, G. E., Zhang, H. and Liu, M. (996), Volume volailiy and leverage: a dynamic relaionship, Journal of Economerics, 74, [50] Telser, L. G. (98), Margins and fuures conracs, Journal of Fuures Markes,, [5] Wang, G. H. K. and Yau, J. (000), Trading Volume, Bid-Ask Spread, and Price Volailiy in Fuures Markes, Journal of Fuures Markes, 0, [5] Waanabe, T. (00), Price volailiy, rading volume, and marke deph: evidence from he Japanese sock index fuures marke, Applied Financial Economics,, [53] Wiley, M. K. and Daigler,. T. (998), Volume elaionships among Types of Traders in he Financial Fuures Markes, Journal of Fuures Markes, 8, 9-3. [54] Wiley, M. K. and Daigler,. T. (999), A Bivariae GACH Approach o he Fuures Volume-Volailiy Issue, Aricle Presened a he Easern Finance Associaion Meeings, Florida. [55] Ying, C. C. (966), Sock Marke Prices and Volumes of Sales, Economerica, 34, Appendix Appendix : Graphical plos of FTSE/ASE-0* 0.0 Figure : ETUN 3 Figure : LNVOL

18 Inernaional esearch Journal of Finance and Economics - Issue (007) 5 0 Figure 3: VOLUME * Graphical plos of reurn, lnvol, and volume (in levels) for FTSE/ASE-0. Appendix : Graphical plos of FTSE/ASE MID 40* Figure : ETUN 3 Figure : LNVOL Figure 3: VOLUME. * Graphical plos of reurn, lnvol and volume (in levels) for FTSE/ASE Mid 40