Market Liquidity and Depth on Floor-Traded and E-Mini Index Futures: An Analysis of the S&P 500 and Nasdaq 100

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1 Marke Liquidiy and Deph on Floor-Traded and E-Mini Index Fuures: An Analysis of he S&P 500 and Nasdaq 100 AUTHORS ARTICLE INFO JOURNAL FOUNDER Yu-shan Wang Huimin Chung Yung-Ching Yang Yu-shan Wang, Huimin Chung and Yung-Ching Yang (2007). Marke Liquidiy and Deph on Floor-Traded and E-Mini Index Fuures: An Analysis of he S&P 500 and Nasdaq 100. Invesmen Managemen and Financial Innovaions, 4(4) "Invesmen Managemen and Financial Innovaions" LLC Consuling Publishing Company Business Perspecives NUMBER OF REFERENCES 0 NUMBER OF FIGURES 0 NUMBER OF TABLES 0 The auhor(s) This publicaion is an open access aricle. businessperspecives.org

2 80 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, 2007 MARKET LIQUIDITY AND DEPTH ON FLOOR-TRADED AND E-MINI INDEX FUTURES: AN ANALYSIS OF THE S&P 500 AND NASDAQ 100 Yu-shan Wang *, Huimin Chung ** and Yung-Ching Yang *** Absrac This paper aims o examine he marke liquidiy of regular fuures and E-mini fuures of CME. The bid-ask spread and marke deph are explored o compare he marke liquidiy of floorraded fuures and elecronically raded fuures. The bid-ask model consiss of a srucural equaion of bid-ask spread, rading-volume, and price-volailiy. This paper finds ha E-mini conracs boas superior marke liquidiy as measured boh by bid-ask spread and marke deph. This finding indicaes ha he auomaed rading marke is more efficien in handling orders. Moreover, he mechanism of limied order books faciliaes beer ransparency of informaion regarding rading prices and volume and he coninuous bidding process helps o improve he reducion of liquidiy cos. Key words: marke liquidiy, deph, S&P 500, Nasdaq 100, E-mini fuures. JEL Classificaion: G14, C Inroducion The advancemen of informaion echnology and he ubiquiy of he Inerne have been dismanling he barriers of individual financial markes around he globe. The mos direc blow o he fuures markes is he fierce compeiion from oher markes. Therefore, he major fuures exchanges around he world spare no effors o innovae heir produc offerings as well as o improve heir rading sysems, in order o mainain heir compeiiveness. The adopion of auomaed rading sysems and he launch of mini-insrumens have been big innovaions from fuure exchanges over he pas years. The majoriy of fuure exchanges in Europe and Asia, including EUREX, Euronex, Korean Sock Exchange (KSE), and Tokyo Sock Exchange (TSE) have compleely adoped he auomaed rading sysem. Some exchanges, such as he Chicago Mercanile Exchange (CME), Chicago Board of Trade (CBOT), and Singapore Exchange (SGX), adop a side-by-side rading sysem in which open oucry and auomaed rading sysems co-exis. The pros and cons of he open oucry and auomaed rading sysems are a criical issue for any exchange ha is considering swiching o he auomaed rading sysem from he open oucry sysem or simply allowing he wo sysems o co-exis. According o he sudies by Ulibarri and Schazberg (2003), Aiken e al. (2004), Cheng, Fung and Tse (2005), Fung, Lien, Tse and Tse (2005) and Mizrach and Neely (2006) he spread beween bids and offers in auomaed rading sysems is smaller han ha of he open oucry sysems. In oher words, he auomaed rading sysem provides beer marke liquidiy compared o he open oucry sysem. However, Tse and Zaboina (2001) argued ha, in conras o he smaller spread beween bids and offers seen in he auomaed rading sysems, open oucry sysems have a smaller price error variance. Anoher argumen was made by Kappi and Siivonen (2000) ha he spread beween bids and offers in open oucry sysems is smaller, bu he auomaed rading sysems provide beer marke deph. To sum up, he pros and cons of he open oucry and auomaed rading sysems remain a conroversy and here is no uniform conclusion so far. The index fuures markes in he U.S. have reained boh elecronic and open-oucry rading sysems operaing simulaneously during regular rading hours. This marke mechanism provides a naural experimen o direcly compare he liquidiy and deph beween regular and elecronically raded index fuures. The curren se-up of CME serves as a unique opporuniy for his paper o explore he pros and cons of he open oucry and auomaed rading sysems. * Naional Kaoshiung Firs Universiy of Science and Technology, China. ** Graduae Insiue of Finance a Naional Chiao Tung Universiy, Taiwan. *** Graduae Insiue of Finance a Naional Chiao Tung Universiy, Taiwan.

3 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, The pros and cons of hese wo sysems can be examined in various perspecives, ha is why here are differen conclusions. Marke liquidiy is a widely acceped measuremen, while he BAS serves as a major indicaor. Our paper follows his convenion and examines he BAS and marke deph as key indicaors. The focus of his paper is on he four index fuure conracs which are mos raded on CME, including regular S&P 500 index fuures (hereafer referred o as SP) and regular Nasdaq 100 index fuures (hereafer referred o as ND) raded on he open oucry sysem as well as E-mini S&P 500 index fuures (hereafer referred o as ES) and E-mini Nasdaq 100 index fuures (hereafer referred o as NQ) raded on he auomaed rading sysem. The purpose of his paper is o compare he marke liquidiy of he open oucry and auomaed rading sysems. Our research is differen from previous sudies. Pas lieraure usually resored o he bidask spreads o compare marke liquidiy of he open oucry and auomaed rading sysems (Kappi and Siivonen, 2000; and Ulibarri and Schazberg, 2003). Noneheless, McInish and Wood (1992) believed ha if here are considerable discrepancies beween he rading volume and price volailiy, hen a misundersanding may occur if he average bid-ask spreads of he wo markes are used as an indicaor of he relaive marke liquidiy. Therefore, hey suggesed ha effecs from a relaive variable should be aken ino accoun when i comes o examining he difference in marke liquidiy of hese wo markes. Alhough some of he lieraure poined ou he effecs from relevan variables when i comes o comparing he liquidiy of hese wo markes, such as Frino e al. (1998), he possibiliy of a srucural relaionship beween variables ges ignored and, hus, here is a bias in he esimaes of model coefficiens. In order o compare he differences in bid-ask spread of E-mini conracs on he auomaed rading sysem and regular conracs, we decide o consruc a hreeequaion srucural model ha consiss of rading volume, bid-ask spread, and price volailiy. This approach enables his sudy o ake ino accoun he possible srucural relaionship beween variables while, a he same ime, o conrol oher facors ha affec bid-ask spreads when i comes o he analysis of he differing bid-ask spreads in differen markes. I is also possible o discuss he relaionship among he rading volume, bid-ask spread, and price volailiy as hree variables. The major conribuion of his paper lies in he findings ha he E-mini conracs raded on he auomaed rading sysem boas superior marke liquidiy o ha of he regular conracs on he open oucry sysem, independen of wheher he marke liquidiy is measured in bid-ask spread or marke deph. This finding also indicaes ha he auomaed rading sysem feaures superior efficiency in he execuions of orders. Moreover, he ransparency of informaion regarding rading volume and ransacion prices and coninuous aucions offered by he auomaed rading sysem helps o reduce he liquidiy cos. Secondly, he majoriy of pas lieraure of marke microsrucure heory focused is discussions on he relaionship of only wo ou of he hree variables, i.e. rading volume, bid-ask spread and price volailiy. These discussions include (1) he relaionship beween rading volume and bid-ask spread, (2) he relaionship beween rading volume and price volailiy, and (3) he relaionship beween bid-ask spread and price volailiy. Some scholars aemped o compare he liquidiy of differen ransacion ypes of conracs by using bid-ask spreads, bu such an approach may lead o an exreme bias conclusion, because differences may reside in he facors ha affec bid-ask spreads of he regular and E-mini conracs, such as rading-volume and price volailiy. Therefore, his sudy aims o explore he simulaneously-deermined relaionship among radingvolume, bid-ask spread, and price volailiy based on he Hausman es and hen, by consrucing hree-equaion srucural equaion, furher prove ha he auomaed rading sysem boass superior marke liquidiy by demonsraing ha E-mini conracs exhibi narrower bid-ask spreads wih oher affecing facors under conrol. The organizaion of he paper is as follows. Secion 2 provides a brief lieraure review. Secion 3 summarizes he economeric mehodology. Secion 4 describes daa sources and empirical resuls. The conclusion is in secion 5.

4 82 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, Lieraure Review TV, BAS, and PV are he hree variables ha consanly are sudied and examined by he marke macrosrucure heory. McInish and Wood (1992) argued ha he TV and PV are he major deerminans of he BAS. Noneheless, we need o ake heed of he causal relaionships in our discussion of marke liquidiy. Is i rue ha TV and PV impac marke liquidiy and, if so, in wha manner? Or, is i ha he difference in marke liquidiy affecs TV and PV? Wha are he implicaions? The pas lieraure focused mos of heir discussions on he relaionship beween wo of he hree variables, such as he relaionship beween TV and BAS, he relaionship beween TV and PV, and he relaionship beween BAS and PV. Therefore, we can safely assume ha here may exis a correlaion among TV, BAS, and PV. Much of he pas lieraure also indicaed ha here may exis endogenous relaionships among any wo of he hree variables. Therefore, our sudy decided o simulaneously explore he relaionship among all he hree variables, i.e. TV, BAS, and PV. Possible srucural relaionships among hese variables will be aken ino consideraion in order o avoid esimaion errors in our modelling parameers. Our discussion on he relaionship among hese hree variables sars wih he definiion of he cos componens of BAS. We believe ha order processing cos, adverse informaion, and invenory carrying cos are he hree componens for he BAS. In heory, here is an inverse relaionship beween hese hree coss and TV. Wang and Yau (2000) and Aes and Wang (2004) conduced heir analysis of he relaionship among TV, BAS, and PV as hree variables. The hree-equaion srucural model hey consruced showed ha here exiss a posiive correlaion beween TV and PV and an inverse correlaion beween TV and BAS, wih he oher variable conrolled. A he same ime, here exiss a posiive correlaion beween PV and BAS, whereas here exiss an inverse correlaion beween lagged 1 period value of PV and TV. To sum up he above discussions, here may exis an endogenous variable relaionship among TV, BAS, and PV. I maers a grea deal o he esimaes of he hree-equaion srucural model wheher hese hree variables are endogenous. Therefore, we need o deermine wheher here is an endogenous or exogenous relaionship beween heese variables. Wang and Yau (2000) used he Hausman es o confirm ha here exiss a srucural deerminan relaionship among TV, BAS, and PV. 3. Mehodologies 3.1. Bid-Ask Spread Esimaor BAS and marke deph are he mos frequenly-used measuremens of marke liquidiy. In his paper, BAS is defined as he esimaes of BAS according o he TW bid-ask spread esimaor of Thompson and Waller (1988, hereafer TW) and Commodiy Fuures Trading Commiee (hereafer CFTC) BAS esimaor. The TW bid-ask spread esimaor is ariculaed as he follows: T 1, (1) where P is non-zero price change series. TW p T 1 The rading price changes may be caused by noise rading. On he oher hand, rading price changes may be caused by he inflow of new informaion. The CFTC 1 BAS esimaor is a mehod pu forward by he Commodiy Fuures Trading Commiee (CFTC) of he US o measure BAS. I is a commonly used mehod in he business. This mehod is similar o TW esimaor, bu CFTC esimaor akes ino accoun he possible effecs on ransacion prices from he changes of real prices. Therefore, in heory, he esimaors derived will be smaller han TW esimaors. 1 Since CFTC and Thompson and Waller bid-ask spread esimaors are highly correlaed, we use CFTC mehod o re-do he analysis and he resuls are very similar.

5 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, Marke Deph In order o measure he differences in marke deph of regular conracs raded on he open oucry marke and E-mini conracs raded on he auomaed rading marke, his paper uses he Two-Sage Leas Squares (2SLS) regression analysis proposed by Kappi and Siivonen (2000) o measure he marke deph based on an inerval of 15 minues. During he firs sage, we divide he TV (number of conracs) ino ETV and UTV as in he following equaions: TV a P j k k, i V i j (2) i 1 j 1 k 1 where TV is he acual aggregaion of rading-volume a ime inerval ; changes wihin ime inerval ; erm. is he price-volailiy wihin ime inerval ; p are he price is an error p refers o price changes, i.e. he difference beween he firs and las rading prices wihin each ime inerval, while refers o price-volailiy, i.e. he difference beween he larges and smalles rading prices wihin each ime inerval. Relevan facors ha may affec TV are aken ino accoun in he measuring of ETV wihin he firs sage. These facors include lagged TV and lagged absolue price change. The fied value of he esimaions based on Equaion 2 is ETV and is residual is UTV. A he second sage, he ETV and UTV compued a he firs sage are used o measure he impacs of rading aciviies on rading prices (including he absolue price changes and PV). The measuremen is expressed as he following equaion. r, (3) P E TV E TV U TV U TV U TV U TV POS POS k 1 s k k 1 k k k. (4) The impacs of ETV and UTV on rading prices may exhibi an asymmeric relaionship. The price-change absolue-value equaion and PV equaion boh ake ino accoun he expeced rading-volume (ETV) and unexpeced rading-volume (UTV ). Boh posiive and negaive values of UTV may also exhibi an asymmeric relaionship wih impacs on rading prices. Therefore, our model incorporaes a posiive-valued UTV variable (UTVPOS ) o reflec such heerogeneiy. When he UTV exceeds zero, UTVPOS = UTV ; when he UTV falls below zero, UTVPOS = 0. The coefficien of UTV indicaes he marginal impacs of negaive-valued UTV on rading prices. The summaion of he coefficiens of UTV and UTVPOS indicaes he marginal impacs of posiive-valued UTV on rading prices. The second-sage price-change absolue-value and PV equaions also ake ino accoun he effecs of PV in he lagged period Trading-Volume, Bid-Ask Spread, and Price-Volailiy In order o examine he difference in marke liquidiy of regular conracs raded on he open oucry marke and E-mini conracs raded on he auomaed rading marke, his paper resors o he hree-equaion srucural model consruced by Wang and Yau (2000) and Aes and Wang (2004) in exploring he relaionship among TV, BAS, and PV. However, cerain modificaions are made o he model in order o conrol facors ha affec BAS. This approach makes i possible no only o compare he differences in marke liquidiy of regular conracs raded on he open oucry marke and E-mini conracs raded on he auomaed rading marke, bu also o scruinize he differences in TV and PV of he regular and E-mini conracs. Moreover, his paper aims o invesigae he relaionship among TV, BAS, and PV as hree variables. Among our invesigaions, he model of S&P 500 index fuures is referred o as he SP-ES model and he model of Nasdaq 100 index fuures is referred o as he ND-NQ model. The empirical model of his paper is esablished as he following equaions.,(5) TV a 0 a1bas a 2 PV a 3 INT a 4OI 1 a 5TV 1 a Dummy BAS b 0 b1tv b2pv b3sp b4 BAS 1 b5dummy 6, (6)

6 84 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, 2007 PV c 0 c1tv c BAS 2 c3tv 1 c4pv 1 5 c Dummy, (7) where TV indicaes he aggregaed daily rading-volume; TV -1 is TV lagged 1 day; BAS indicaes he esimaed average daily BAS based on TW BAS esimaors; PV indicaes daily PV, measured by he difference beween he highes and lowes ransacion prices wihin a rading day; INT indicaes he hree-monh ineres rae of T-bills; OL -1 indicaes he open ineress of he firs lag; SP indicaes he selemen price of he rading day for fuure conracs; Dummy indicaes a dummy variable o conrol he difference beween he regular and E-mini conracs. When Dummy = 1, i refers o regular conracs; when Dummy = 0, i refers o E-mini conracs. Equaion 5 is he key deerminan of TV. In heory, here is an inverse relaionship beween ransacion cos and TV. When he ransacion cos is high, profi opporuniies ge squeezed and marke paricipans will seek alernaive insrumens hereby offering lower ransacion coss. This move will subsequenly reduce he rading-volume of he insrumens ha demand high ransacion coss. Among he ransacion coss, BAS is he major variable cos componen. Therefore, i is expeced o exhibi an inverse relaionship beween TV and BAS. The changes of reservaion prices are he main moivaion for speculaors o conduc ransacions. Speculaors adjus reservaion prices in accordance wih PV; in oher words, hey use PV as he proxy for changes in reservaion prices. In he MDH model, TV and PV are boh funcions of he informaion inflow rae, according o Harris (1987), and Tauchen & Pis (1983). Therefore, here is expeced o be a posiive correlaion beween TV and PV. The changes in he expeced posiions held by hedgers are anoher key facor for TV and such changes are deermined based on he informaion available o hedgers. The proxies for he informaion se wihin his model are he hree-monh ineres raes of T-bills and unseled volume in he firs lag. The hree-monh ineres raes of T-bills are used o reflec he cos of invenory carrying for spo posiions, as a higher ineres rae increases he cos of invenory carrying and hus reduces he willingness of hedgers o operae in he fuures marke. Therefore, an inverse relaionship is expeced o be beween TV and he hree-monh ineres raes of T-bills. Unseled volume in he firs lag reflecs he number of conracs ousanding in he firs lag. A high level of unseled volume implies ha more rading will happen in he fuure. Therefore, here is expeced o be a posiive correlaion beween TV and unseled volume in he firs lag. In Equaion 5, dummy variables are used o conrol oher facors ha affec TV in order o deermine wheher he differences are significan beween he TV of regular conracs raded on he open oucry marke and E-mini conracs raded on he auomaed rading marke. If he dummy variables are significanly posiive, hen i means he TV of regular conracs is obviously larger han ha of E-mini conracs. If he dummy variables are negaive, hen i means he TV of E-mini conracs is larger han ha of regular conracs. Equaion 6 is he main deerminan of BAS. The increase of TV means ha liquidiy providers have more opporuniies o adjus heir invenory posiions in order o reduce he price risks hey face. Therefore, here is expeced o be an inverse relaionship beween expeced BAS and TV. The changes of ransacion prices imply wo ypes of risks o liquidiy providers. The firs ype of risk is non-sysemaic risk due o under-diversificaion of asse allocaion by he liquidiy providers. The second ype of risk derives from he implied exisence of informaion raders as signalled by he flucuaions of prices. This siuaion generaes he cos of informaion asymmery. This model uses PV as a proxy o measure his ype of price risk and, herefore, he relaionship beween BAS and PV is expeced o be posiive. The selemen price of he conrac dae can be used o conrol he impacs of he index level on BAS. Bryan and Haigh (2002) indicaed ha he BAS ends o be mainained a a cerain percenage in relaion o price levels, so ha he cos required per ransacion uni is consisen. Therefore, he relaionship beween anicipaed BAS and selemen prices is expeced o be posiive. In Equaion 6, a dummy variable is used o measure he significance of differences in BAS beween he regular conracs raded on he open oucry marke and E-mini conracs raded on he auomaed rading marke when oher facors ha affec BAS are under conrol. This approach avoids he misinerpreaion of comparing he marke liquidiy of regular conracs and E-mini conracs by direcly using BAS. This approach is illusraed by he TV equaion in Equaion 5.

7 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, Equaion 7 is he key deerminan of PV. The larger he TV is, he beer he chance ha he price may move o higher or lower levels. The MDH model also predics ha he relaionship beween anicipaed PV and TV is posiive. TV lagged one period is also a facor ha affecs PV. Admai and Pfleiderer (1988) believed ha raders choose he ime when he recen TV is larger o conduc ransacions. Therefore, he relaionship beween he anicipaed PV lagged one period and TV lagged one period is expeced o be posiive. The sudies on he dummy variable are similar o hose on he TV equaion and BAS equaion and we decide no o repea hem again here. Bessembinder and Seguin (1993) believed ha here is coninuiy in boh TV and PV so heir auocorrelaion in he firs lag should be aken ino accoun. Therefore, he hree equaions in he model all incorporae lagged variables in order o reflec such coninuiy. In consrucing he hree-equaion srucural model, his sudy violaes he assumpion brough forward by he classical linear regression model, since he model consruced here may have a bi-direcional causal relaionship beween he dependen variable and explanaory variables. In oher words, he variables on he righ of he equaion may no be exogenous variables. Wang and Yau (2000) indicaed ha if here exiss a srucural relaionship beween dependen variable and explanaory variables in he hree-equaion srucural model, hen he esimaion based on he OLS mehod will be serious under-esimaion. Therefore, i is a mus o verify wheher he relaionship among he TV, BAS, and PV has an endogenous-variable relaionship before he model runs any esimaion. This paper uses wo-sage specificaion ess of Hausman (1978) o verify wheher here exiss a srucural relaionship among TV, BAS, and PV. In order o solve he srucural relaionship beween variables wihin he model and o avoid he inconsisency of esimaions based on he OLS mehod, his paper uses he 2SLS o conduc esimaions of he model afer he verificaion of a srucural relaionship of dependen variables and explanaory variables in he equaion. This approach eliminaes he issue of auocorrelaion beween explanaory variables and he error erm wihin he model and derives consisen esimaions of he model. In addiion o he above-menioned verificaion of a srucural relaionship among he variables prior o he esimaions run by he model, some seps are aken in order o reduce he quaniaive issues associaed wih ime series. Firs of all, all he variables wihin he model are convered ino log. The advanages are wofold. Firs, his sabilizes he variance of he error erm so ha he disribuion of he error erm will reach a normal disribuion. Second, he relaionship beween dependen variables and explanaory variables wihin he model can be inerpreed by using flexible conceps. As a uni roo of ime series daa causes a spurious regression, we mus conduc he Dickey and Fuller (1981) s Augmened Dickey-Fuller (hereafer ADF) es on all he variables wihin he model in order o verify wheher here exis uni roo phenomena. This will serve as a basis for deermining wheher he variables need difference in order o eliminae he possibiliy of spurious regression. In he SP-ES model and ND-NQ model, he ADF es resuls show ha here exis a uni roo in he INT and SP series. Afer firs differencing (d=1), INT are boh saion- and SP ary serials. Therefore, during he esimaion of he SP-ES model and ND-NQ models, in addiion o obaining he firs differencing of INT and SP, all he remaining variables in he model use level erm. In he model esimaions, we should consider he possibiliy of a sequenial correlaion of error erm and heerogeneous variances wihin he model. We use he procedure of Newey and Wes (1987) in order o derive consisen esimaion values and sandard errors for he parameers. 4. Empirical Resuls 4.1. Daa This sudy samples regular index fuure conracs (SP and ND) raded on he open oucry marke and E-mini index fuure conracs (ES and NQ) raded on he auomaed rading marke daing from May 2003 o February 2004, in order o measure and compare heir marke liquidiy.

8 86 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, 2007 In order o form a consisen comparison basis, his paper samples RTH imeslo rading daa o conduc measuremens. RTH refers o he imeslo when he auomaed rading marke and open oucry marke run in parallel. The daa sample includes Globex Time and Sales Daa File on he CME, and volume by Tick Daa File. Daasream is also used. Globex Time and Sales Daa File and Volume by Tick Daa File record daa of E-mini conracs and regular conracs, respecively. The inraday enries include monhly daa for each ransacion price, TV, rading ime, and rading conrac. This par of he daa can be used o esimae BAS and marke deph as well as o measure he relaionship among TV, BAS, and PV. On he oher hand, as he conracs raded on he same day expire in differen monhs, such a complex siuaion makes i difficul o conduc an analysis. In order o bypass he effecs of conracs ha expire in differen monhs, his sudy samples only nearby conracs ha enjoy brisk rading. As invesors usually rollover heir fuure conracs, we sample he conracs of he following monh in he case when he conracs expired nine days before. In he srucural equaions, he daa source for he number of unseled fuure conracs and he ineres raes of hree-monh T- bills is he Daasream daabase Bid-Ask Spread Table 1 The descripive saisics of S&P 500 index fuure and Nasdaq-100 index fuures, from May 2003 o February 2004 Regular conrac E-mini conrac SP ND ES NQ Average daily rading frequence 2, ,455 31,480 Average daily rading-volume (conrac size) 50,118 12, , ,602 Average daily rading-volume (million dollar) Average conrac size of one rading Average open ineres 621,633 81, , ,894 Average conrac index level 1, , , , Average bid-ask spread esimaed value (index poin)* Average bid-ask spread esimaed value (dollar)* $ $ $ $ Average bid-ask spread over rading dollars of one conrac (%) Sandard deviaion of bid-ask spread esimaed value % % % % Average inerval ime of rading (second) Sandard deviaion of price change Ticks % % % 1 Ticks % % % % % 2 Ticks % % % % More han 2 Ticks % % % % Noes: 1. All he saisic daa of he regular rading hour (RTH) of nearby conracs were measured and all he nearby conracs of nine days before expiraion were rolling ino he following nearby conracs. 2. Bid-ask spread esimaors are measured based on CFTC bid-ask spread esimaors. Table 1 summarizes he basic saisics of he four conracs sudied in his paper. According o hese saisics, E-mini conracs raded on he auomaed rading marke are highly liquid. ES conracs repor a daily TV of 570,000 conracs (of he nearby conracs), wih 0.47 seconds required o complee each ransacion. NQ conracs repor a daily TV of 260,000 conracs, wih 0.77

9 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, seconds required o complee each ransacion. Such a shor urnover highlighs he efficiency advanage of an auomaed rading sysem. In addiion, he informaion ransparency of limied order books faciliaes he provision and consumpion of liquidiy. Regular conracs raded on he open oucry marke repor a higher number in each ransacion han ha of E-mini conracs. SP conracs repor an average conrac number of 20 per ransacion, while he number for ND conracs is 13. The average amoun of unseled volume of regular conracs is far higher han is daily TV, an indicaor ha marke paricipans of regular conracs are mosly insiuional invesors funded wih large capial. Regular conracs are used as a hedging ool by hese invesors. This may be due o he fac ha an open oucry marke offers flexibiliy o large orders or paricular rading sraegies. On he oher hand, E-mini conracs raded on he auomaed rading marke repor a lower number of conracs per ransacion, as hey are designed o caer o he needs of reail invesors. Moreover, he mechanism of limied order books, perhaps o some degree, helps o reduce losses due o adverse informaion ransacion for limied order providers. Therefore, a rading sraegy of placing small orders is employed, according o Tse and Zaboina (2001). The fac ha he daily unseled volume of E-mini conracs is smaller han he daily TV indicaes ha mos of he rading aciviies are wrien off on he same day and are from arbirage. To sum up he above discussions, here are a large number of differences beween regular conracs raded on he open oucry marke and E-mini conracs raded on he auomaed rading marke. Therefore, such differences may be clearly refleced in he form of liquidiy cos. According o CFTC BAS esimaor, he average BAS of E-mini conracs raded on he auomaed rading marke is smaller han ha of regular conracs raded on he open oucry marke. The average BAS for ES conracs is 0.25 index poins, ha for SP conracs is 0.49 index poins, ha for NQ conracs 0.51 index poins, and ha for ND conracs is 1.17 index poins. The sudy conduced by Kurov and Zaboina (2003), who sampled from January 2001 hrough June 2001, indicaed ha he BAS of Nasdaq 100 index fuures was larger han ha of E-mini conracs. However, he BAS for S&P 500 index fuures is smaller han ha of E-mini conracs. Apparenly, as far as S&P 500 index fuure conracs are concerned, heir BAS rose dramaically during he sample period of his paper. Figure 1 and Figure 2 show ha here was no drasic flucuaion in he BAS of ES conracs and NQ conracs raded on he auomaed rading marke, as hese BAS were largely mainained a he minimum price change uni. This finding is in line wih he general percepion ha boh ES conracs and NQ conracs are one ick size markes. Fig. 1. Average daily bid-ask spread esimaors of SP conracs and ES conracs

10 88 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, 2007 Fig. 2. Average daily TW bid-ask spread esimaors of ND conracs and NQ conracs I also shows ha he minimum price change uni may resric he BAS o levels ha are no compeiive. As he price change unis mosly mainain he same level or change one ick size, ES conracs and NQ conracs are he markes where ransacion prices are more coninuous. This fac has much o do wih he superior informaion ransparency of TV and prices provided by limied orders books and coninuous bids. Compared wih E-mini conracs raded on he auomaed rading marke, SP and ND conracs raded on he open oucry marke repor larger BAS flucuaions. Approximaely 50% of he price changes from SP conracs exceed 2 ick sizes. The majoriy of price changes of ND conracs fell below 2 ick sizes; however, i is worh noing ha 20% of he price changes are 2 ick sizes. As for he percenage of ransacion cos refleced in he form of BAS in relaion o he conrac value, he cos for regular conracs raded on he open oucry marke is significanly higher han ha of E-mini conracs raded on he auomaed rading marke. Among hem, ND conracs repor he highes liquidiy cos, wih a ransacion cos in he form of a BAS of US$ per conrac, i.e % of he conrac value. Therefore, as far as marke liquidiy measured by BAS is concerned, E-mini conracs raded on he auomaed rading marke have he upper hand agains he regular conracs raded on he open oucry marke. This fac indicaes he grea efficiency of he auomaed rading sysem in handling orders and helps o explain he shif of TV from regular conracs o heir E-mini counerpars Marke Deph In order o assure he validiy of he saisics of he marke-deph model, all he variables wihin he model are esed wih he Augmened Dickey-Fuller es (ADF) o verify wheher hey are saionary, in order o avoid misinerpreaions of he model due o a spurious regression. The es resuls showed ha all he variables wihin he model are saionary, and so we carried ou esimaions direcly by using level values. PV equaions consider he effecs of auo-correlaion in he lag, and so his paper used Akaike s (1973) Akaike Informaion Crieria (hereafer AIC) o deermine he opimal lag. As a resul of his operaion, which found ha a choice of he fifh lag is he mos appropriae, his paper uses he effecs of he fifh lag.

11 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, Marke deph model SP conracs and ES conracs Table 2 Panel 2A: Absolue value of price change equaion Type Inercep ETV UTV UTVPOS R 2 PARMS ** ** * SP STDERR P-VALUE < < ES PARMS ** ** ** ** STDERR P-VALUE < < < < Panel 2B: Price-volailiy equaion Type Inercep ETV UTV UTVPOS R 2 PARMS ** ** ** ** SP STDERR P-VALUE < < < ES PARMS ** ** ** ** STDERR P-VALUE < < < < Noe: 1. To faciliae he measuremen, he absolue value of price change P and price-volailiy are boh muliplied by 100. The coefficiens of expeced rading-volume (ETV), unexpeced rading-volume (UTV) and posiive-valued unexpeced rading-volume (UTVPOS) can be viewed as esimaors of marke deph. 2. * Significance a he 5% level. ** Significance a he 1% level. Marke deph model-nd conracs and NQ conracs Table 3 Panel 3A Absolue value of price change equaion Type Inercep ETV UTV UTVPOS R 2 PARMS *** *** *** *** ND NQ STDERR P-VALUE < < PARMS *** *** *** *** STDERR P-VALUE < < < < Table 3 (coninued)

12 90 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, 2007 Type Inercep ETV UTV UTVPOS R 2 Panel 3B: Price-volailiy equaion PARMS *** ** *** *** ND NQ STDERR P-VALUE < < < PARMS *** *** *** STDERR P-VALUE < < < Noes: 1. To faciliae he measuremen, he absolue value of price change P and pricevolailiy are boh muliplied by 100. The coefficiens of expeced rading-volume (ETV), unexpeced rading-volume (UTV) and posiive-valued unexpeced rading-volume (UTVPOS) can be viewed as esimaors of marke deph. 2. *** Significance a he 1% level. Table 2 and Table 3 summarize he esimaions of he marke-deph models of he four conracs. In boh absolue values of he price change equaion and price-volailiy equaion, he coefficiens of anicipaed TV indicae ha all he conracs repor significanly posiive values of below 1%. This indicaes ha he changes in anicipaed TV do affec price changes. Among hem, he anicipaed TV of E-mini conracs raded on he auomaed rading marke have a smaller impac on he ransacion prices compared wih regular conracs raded on he open oucry marke. A he same ime, coefficiens of non-anicipaed TV also indicae ha all he conracs repor significan posiive values of below 1%, bu heir values are all bigger han hose of he anicipaed TV. This indicaes ha here exis obviously asymmeric effecs o he prices from effecs creaed by he anicipaed and non-anicipaed TV. Among hem, E-mini conracs raded on he auomaed rading marke repor a smaller impac from non-anicipaed TV o ransacion prices han ha of regular conracs raded on he open oucry marke. This fac indicaes ha he auomaed rading marke boass superior marke deph. However, he more significan asymmeric effecs repored by E-mini conracs imply ha he auomaed rading marke sees a more rapid reducion in marke deph when here are unexpeced shocks o he marke. The posiive and negaive values of non-anicipaed TV have differen asymmeric impacs on prices when i comes o differen conracs. As far as ND conracs are concerned, he posiive valued non-anicipaed TV has a larger impac (han ha of he negaive valued non-anicipaed TV) on he absolue values of price changes, bu a smaller effec on price changes. This fac indicaes ha when he TV is lower han he anicipaed TV, ND conracs are quicker in recovering from price shocks. As far as NQ conracs are concerned, here is no significan difference in he effec on price changes from eiher posiive valued non-anicipaed TV or negaive valued non-anicipaed TV. As for SP conracs and ES conracs, heir asymmeric relaionship is compleely he opposie from he one observed for ND conracs. The posiive valued non-anicipaed TV of SP and ES conracs have smaller impacs on he absolue values of price changes han he negaive valued non-anicipaed TV do, bu impose impacs o price changes are larger han he negaive valued non-anicipaed radingvolume. This finding indicaes ha boh SP and ES conracs are slower in recovering from price shocks when he TV is lower han he anicipaed levels. According o he above analysis, boh ES and NQ conracs raded on he auomaed rading marke repor a sronger marke deph han SP and ND conracs raded on he open oucry marke. This finding indicaes ha he mechanism of limied order books on he auomaed rading marke and he disclosure of informaion of bids and offers work o enhance he marke deph. However, he auomaed rading marke sees a more rapid decline in marke deph when here are abrup shocks o he marke. A he same ime, here exiss a significan heerogeneiy in he impacs on prices from anicipaed and non-anicipaed TV, and such heerogeneiy varies in differen conracs.

13 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, Trading-Volume, Bid-Ask Spread, and Price-Volailiy Table 4 Hausman's Specificaion Tes rading-volume equaion Conracs (1) F Tes (Augmened Regression Approach) (2) 2 (3) 2 SP-ES ( 2, 419 ) *** *** ND-NQ *** ( 2, 419 ) *** Noes: 1. As far as he siuaion 1 is concerned, null hypohesis H0: In he rading-volume equaion, boh bid-ask spread and price-volailiy are exogenous variables. Alernaive hypohesis Ha: Nei her bid-ask spread nor price-volailiy are an exogenous variable. As far as he siuaion 2 is con cerned, null hypohesis H0: In he rading-volume equaion, providing ha price-volailiy is an endogenous variable, bid-ask spread is an exogenous variable. Alernaive hypohesis Ha: Bid-ask spread is an endogenous variable. As far as he siuaion 3 is concerned, null hypohesis H0: In he rading-volume equaion, providing ha bid-ask spread is an endogenous variable, price-volailiy is an exogenous variable. Alernaive hypohesis Ha: Price-volailiy is an endogenous variable. 2. F saisics are 3.0 and 4.61, respecively when he degree of freedom is (2, ) and significan levels =0.05 and = Chi square saisics are 3.48 and 6.63, respecively when he degree of free dom is 1 and significan levels =0.05 and = *** Significance a he 1% level. 5. The numbers in parenheses denoe he degree of freedom of he numeraors and denominaor. Hausman's Specificaion Tes bid-ask spread equaion Table 5 Conracs (1) F Tes (Augmened Regression Approach) (2) 2 (3) 2 SP-ES ( 2, 419 ) X a X ND-NQ ** ( 2, 419 ) *** *** Noes: 1. As far as he siuaion 1 is concerned, null hypohesis H0: In he bid-ask spread equaion, boh rading-volume and price-volailiy are exogenous variables. Alernaive hypohesis Ha: Neiher rading-volume nor price-volailiy are an exogenous variable. As far as he siuaion 2 is concerned, null hypohesis H0: In he bid-ask spread equaion, providing ha rading-volume is an endogenous variable, price-volailiy is an exogenous variable. Alernaive hypohesis Ha: Pricevolailiy is an endogenous variable. As far as he siuaion 3 is concerned, null hypohesis H0: In he bid-ask spread equaion, providing ha price-volailiy is an endogenous variable, radingvolume is an exogenous variable. Alernaive hypohesis Ha: Trading-volume is an endogenous variable. 2. F saisics are 3.0 and 4.61, respecively when he degree of freedom is (2, ) and significan levels =0.05 and = Chi square saisics are 3.48 and 6.63, respecively when he degree of freedom is 1 and significan levels =0.05 and = ** Significance a he 5% level. *** Significance a he 1% level. 5. The numbers in parenheses denoe he degree of freedom of he numeraors and denominaor. 6. a If he null hypohesis is no rejeced, wo-sep es is no required.

14 92 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, 2007 Table 6 Hausman's Specificaion Tes price-volailiy equaion Conracs (1) F Tes (Augmened Regression Approach) (2) 2 (3) 2 SP-ES ** ( 2, 419 ) *** ND-NQ ( 2, 419 ) X a X Noes: 1. As far as he siuaion 1 is concerned, null hypohesis H0: In he price-volailiy equaion, boh rading-volume and bid-ask spread are exogenous variables. Alernaive hypohesis Ha: Neiher rading-volume nor bid-ask spread are an exogenous variable. As far as he siuaion 2 is concerned, null hypohesis H0: In he price-volailiy equaion, providing ha rading-volume is an endogenous variable, bid-ask spread is an exogenous variable. Alernaive hypohesis Ha: Bid-ask spread is an endogenous variable. As far as he siuaion 3 is concerned, null hypohesis H0: In he price-volailiy equaion, providing ha bid-ask spread is an endogenous variable, rading-volume is an exogenous variable. Alernaive hypohesis Ha: Trading-volume is an endogenous variable. 2. F saisics are 3.0 and 4.61, respecively when he degree of freedom is (2, ) and significan levels =0.05 and = Chi square saisics are 3.48 and 6.63, respecively when he degree of freedom is 1 and significan levels =0.05 and = ** Significance a he 5% level. *** Significance a he 1% level. 5. The numbers in parenheses denoe he degree of freedom of he numeraors and denominaor. 6. a If he null hypohesis is no rejeced, wo-sep es is no required. Before we conduc he 2SLS esimaions on he hree-equaion srucural model, we mus clarify he srucural relaionship beween dependen variables and explanaory variables. Table 4, Table 5, and Table 6 summarize wheher here exiss a srucural relaionship among he TV equaion, BAS, and PV equaion, based on he wo-sep Hausman hypohesis es mehod. According o hese resuls, for boh SP-ES and ND-NQ models, here exis srucural relaionships in all he equaions. Taking for example he TV equaion in he SP-ES model, he es resul as shown in Table 4 indicaes ha he BAS should be viewed as an endogenous variable, and he PV should be viewed as an exogenous variable in he TV equaion. Therefore, i is necessary o use he 2SLS mehod o conduc he esimaions of he TV equaion in order o eliminae he correlaed effecs of BAS and residual iems. (Please refer o Table 4, Table 5, and Table 6 for he srucural relaionships of oher dependen variables and explanaory variables.) Trading-Volume Equaion (TV Equaion) Empirical resuls of rading-volume, bid-ask-spread and price-volailiy equaions of SP-ES conracs from May 2003 o February 2004 Table 7 Variable TV BAS PV Consan *** (4.04) *** (-3.23) (-0.01) TV ** (2.07) *** (3.33) BAS *** (5.53) (1.95) PV *** (6.78) *** (3.27) --- SP (0.75) --- INT (1.40)

15 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, Table 7 (coninued) Variable TV BAS PV OI (-0.45) PV *** (7.60) *** (-2.83) BAS *** (6.17) --- PV (1.38) Dummy *** (-8.51) *** (2.64) (1.79) Adj R Noes: 1. Each equaion is esimaed by he wo Sage Leas Square (2SLS). 2. Numbers in parenheses are saisics. denoes he firs difference operaor. 3. When Dummy = 1, i refers o SP (regular conrac); when Dummy = 0, i refers o ES (E-mini conrac). 4. ** Significance a he 5% level. *** Significance a he 1% level. Empirical resuls of rading-volume, bid-ask-spread and price-volailiy equaions of ND-NQ conracs from May 2003 o February 2004 Table 8 Variable TV BAS PV Consan *** (3.01) ** (-2.52) (0.88) TV (1.77) *** (3.20) BAS *** (3.05) ** (2.24) PV 0.44 *** (5.73) ** (2.33) --- SP (1.05) --- INT 1.28 (0.78) OI (-0.66) PV *** (5.61) (-1.23) BAS *** (7.98) --- PV ** (-2.34) Dummy *** (-6.20) *** (2.837) ** (2.21) Adj R Noes: 1. Each equaion is esimaed by he wo Sage Leas Square (2SLS). 2. Numbers in paren heses are saisics. denoes he firs difference operaor. 3. When Dummy = 1, i refers o ND (regular conrac); when Dummy = 0, i refers o NQ (E-mini conrac). 4. ** Significance a he 5% level. *** Significance a he 1% level. In he TV equaion, here is a posiive relaionship beween BAS (column #2, variable #3) and TV which is saisically significan a he 1% level for boh he SP-ES and ND-NQ conracs (0.206 and 0.145). This finding indicaes ha as liquidiy cos increases, TV also rises when oher affecing facors are under conrol. This seems o conradic he expecaions in he heory. However, as here exiss a srucural relaionship beween BAS and TV, his means ha hey are deermined a he same ime and he causal relaionship is bi-direcional. In boh he SP-ES and ND-NQ conracs, PV (column #2, variable #4) is saisically significan a he 1% level and exhibis a posiive relaionship wih TV. The elasiciy of TV wih

16 94 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, 2007 respec o BASs can be found in Table 7 and Table 8 for SP-ES (0.438) and ND-NQ (0.44), respecively. In heory, he rise in PV promps speculaors o adjus reservaion prices and hedgers o shif risks, and boh effecs increase TV. Therefore, he finding of his paper is in line wih expecaions of he heory. In order o undersand wheher here is a significan difference in TV beween regular conracs on he open oucry marke and E-mini conracs on he auomaed rading marke, we consider dummy variables in our model (column #2, variable #11). The empirical resuls show ha he TV of E-mini conracs on he auomaed rading marke is significanly larger han ha of regular conracs raded on he open oucry marke ( and ). This finding is in line wih he saisical daa ha E-mini conracs have higher TV Bid-Ask Spread Equaion (BAS Equaion) In he BAS equaion, he rading-volume (column #3, variable #2) of he SP-ES model is a he significan level of 5% and is in a posiive relaionship wih he BAS (0.136) when he oher facors are under conrol. The ND-NQ model has also a posiive relaionship, bu is insignifican (0.063). This posiive relaion is possibly due o he fac ha raders of regular conracs inerpre he rise in TV as he exisence of informaion providers and so hey expand BAS o reduce possible losses. To marke liquidiy providers, he increase of PV implies wo ypes of risks, i.e. adverse informaion risks and non-sysemaic risks of under-diversificaions. As such, hey end o expand BAS o compensae he possible risks. In conclusion, in boh he SP-ES model and ND-NQ model, heir PV (column #3, variable #4) has a significanly posiive relaionship wih BAS (0.203 and 0.104). Such a finding is in line wih expecaion of he heory. According o he above measuremens and analysis, he average BAS of regular conracs raded on he open oucry marke is larger han ha of E-mini conracs raded on he auomaed rading marke when he facors affecing BAS are no under conrol. However, as here may exis differences in TV, PV, and BAS beween regular and E-mini conracs, using heir average BAS o examine heir marke liquidiy may cause misinerpreaions in comparisons. Therefore, wih facors affecing he variances of he TV of regular and E-mini conracs under conrol, he coefficiens of he dummy variables (column #3, variable #11) indicae ha he liquidiy cos of regular conracs on he open oucry marke is significanly higher han ha of E-mini conracs on he auomaed rading marke (0.488 and 0.371). This finding is in line wih he measuremens of BAS as menioned above Price-Volailiy Equaion (PV Equaion) Wang and Yau (2000) and Aes and Wang (2004) divided he sources of PV ino wo componens, one from he inflow of new informaion, wih TV as he proxy, and he oher from he inra-day liquidiy, wih BAS as he proxy. The more new informaion here is, he worse he liquidiy will be and, herefore, he more volaile he PV becomes. In he price-volailiy equaion, in boh he SP-ES model and ND-NQ model, TV (column #4, variable #2) has a significanly posiive relaionship wih PV (0.348 and 0.282). The larger he TV is, he more obvious he price changes become. This finding is in line wih our expecaions. A he same ime, he BAS (column #4, variable #3) in boh he SP-ES model and ND-NQ model exhibi a posiive relaionship wih PV (0.103 and 0.072). This finding is in line wih expecaions of he heory, which holds ha he qualiy of inra-day liquidiy does affec he flucuaions of ransacion prices. Admai and Pfleiderer (1988) believed ha here exiss a posiive relaionship beween PV lagged one and TV lagged one. As far as he SP-ES model is concerned, during he sample period, he finding urns ou o be he opposie of he conclusion reached by Admai and Pfleiderer (1988). However, he finding of he SP-ES model is consisen wih he argumens brough forward by Foser (1995) and Wang and Yau (2000). Moreover, he dummy variables of he PV equaion (column #4, variable 11) indicae ha he ND conracs raded on he open oucry marke demonsrae a larger PV (0.614) han he NQ conracs raded on he auomaed rading marke. However, here is no significan differ-

17 Invesmen Managemen and Financial Innovaions, Volume 4, Issue 4, ence in PV (0.422) beween he SP conracs raded on he open oucry marke and heir counerpar E- mini conracs raded on he auomaed rading marke. 5. Conclusion The mos commonly-used measuremens of marke liquidiy are marke deph and BAS. This sudy finds ha in boh he auomaed rading marke and open oucry marke, rading aciviies significanly impac ransacion prices. This finding implies ha here is room for improvemen in deermining marke deph. Among hem, he E-mini conracs raded on he auomaed rading marke exhibi beer marke deph han he regular conracs raded on he open oucry marke. This finding indicaes ha he mechanism of limied order books and disclosure of bids and offers on he auomaed rading marke provide useful informaion regarding marke deph and help o inensify marke deph. In boh regular conracs raded on he open oucry marke and E- mini conracs raded on he auomaed rading marke, anicipaed TV and non-anicipaed TV exhibi significan asymmery in erms of shocks o ransacion prices. However, non-anicipaed TV exhibis sronger shocks o ransacion prices han anicipaed TV does. Moreover, here exiss a heerogeneiy beween he shocks o ransacion prices, and he shocks from he negaive and posiive non-anicipaed TV. Noneheless, such heerogeneiy varies when differen conracs are sudied. According o he TW and CFTC BAS esimaor, he average BAS of E-mini conracs raded on he auomaed rading marke is smaller han ha of regular conracs raded on he open oucry marke. This finding illusraes he advanage of he execuion efficiency of order handling under he GLOBEX rading sysem of CME. Is mechanism of limied order books provides beer ransparency of informaion on prices and TV and he characerisics of coninuous bidding help o reduce he liquidiy cos. Alhough he anonymous naure of E-mini conracs on he auomaed rading marke may produce adverse selecion ransacions, such informaion asymmery is no apparen in he index fuures marke. A he same ime, invesors also have access o a considerable amoun of real-ime informaion regarding he marke condiions. Therefore, he effecs of informaion asymmery are smaller in he auomaed rading marke. However, here exis differences in TV and PV, which are wo facors ha affec he BAS of he regular conracs and E-mini conracs. Therefore, using BAS o compare he liquidiy of hese wo conracs may cause misundersandings. The resul of he srucural equaion ess also shows ha he effecs of E-mini conracs on he auomaed rading marke exhibi a smaller BAS han ha of regular conracs on he open oucry marke, when he facors ha affec BAS are under conrol. This finding furher proves ha he auomaed rading marke boass superior marke liquidiy. References 1. Admai, A.R., and P. Pfleiderer (1988), A Theory of Inraday Paerns: Volume and Price Variabiliy. The Review of Financial Sudies, 1, Aiken, M.J., A. Frino, A.M. Hill, and E. Jarnecic, (2004), The impac of elecronic rading on bid-ask spreads: Evidence from fuures markes in Hong Kong, London, and Sydney. Journal of Fuures Markes, 24, Akaike, H. (1973), A New Look a he Saisical Model Idenificaion. IEEE Transacion on Auomaic Conrol, Aes, A. and G.H.K. Wang (2004), When Size Maers: The Case of Equiy Index Fuures. European Financial Managemen Associaion Annual Meeing, Basel, Swizerland. 5. Bessembinder, H., and P.J. Seguin (1993), Price Volailiy, Trading Volume, and Marke Deph: Evidence from Fuures Markes. Journal of Financial and Quaniaive Analysis, 28, Bryan, H.L., and M.S. Haigh (2004), Bid-Ask Spreads in Commodiy Fuures Markes. Applied Financial Economics, 14 (13),