What pieces of limit order book information do are informative? An empirical analysis of a pure order-driven market *

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1 What peces of lmt order book nformaton do are nformatve? An emprcal analyss of a pure order-drven market * Roberto Pascual Dept. of Busness Unversdad de las Islas Baleares rpascual@ub.es Davd Veredas Dept. of Econometrcs & OR Tlburg Unversty D.Veredas@uvt.nl December 2003 (Frst verson) * We wsh to thank Klaus F. Zmmermann for useful suggestons and comments. We are grateful for the fnancal support of the Spansh DGICYT project BEC C Roberto Pascual also acknowledges the fnancal sponsorshp of the Fulbrght Grant and the Spansh Mnstry of Educaton, Culture and Sports. The frst verson of ths paper was fnshed whle Roberto Pascual was a Vstng Scholar at the New York Unversty Salomon Center. Correspondng author: Roberto Pascual, Departamento de Economa de la Empresa, Unversdad de las Islas Baleares, Ctra. Valldemossa Km. 7.5, Palma de Mallorca, Baleares, Span. Phone: , e-mal: rpascual@ub.es. 1

2 What peces of lmt order book nformaton do are nformatve? An emprcal analyss of a pure order-drven market ABSTRACT Ths paper studes the mportance of dfferent peces of lmt order book nformaton n characterzng order aggressveness and the tmng of trades, order submssons and cancellatons. Usng lmt order book nformaton on lqud and frequently traded Spansh stock, we evdence that most of the explanatory power of the book concentrates on the best quotes. However, the book beyond the best quotes also matters n explanng the aggressveness of traders. Lqudty provders beneft more from an ncreased degree of pre-trade transparency than lqudty consumers. Fnally, no pece of book nformaton matters n explanng the tmng of orders. Key words: Lmt order book, order aggressveness, duratons, order-drven markets. 2

3 1. Introducton Some recent trends n market desgn are towards the supply of lmt order book nformaton n real tme, the ntroducton of competng order drven venues n tradtonal dealer markets, and the creaton of new pure electronc lmt order book systems (Domowtz and Wang, 1994). Together wth the ncreasng avalablty of lmt order book data, these trends generate a renovated nterest n the mcrostructure of pure orderdrven markets. A characterstc feature of these tradng platforms s ther hgh degree of pre-trade transparency: the ablty of market partcpants to observe the content of the lmt order book. In ths paper, we analyze one of these transparent platforms, the Stock Exchange Interconnecton System (henceforth SIBE) of the Spansh Stock Exchange (SSE). In ths electronc market, real-tme nformaton about the fve best bds and offers on the book s wdely dssemnated through a computerzed nformaton system. We use sx months of lmt order book data of the SIBE to evaluate the nformaton content of the book and, partcularly, whether t nfluences the future behavor of traders. Ths paper s not, of course, the frst to address such ssue. Bas, Hllon and Spatt (1995), Grffths et al (2000), Coppejans and Domowtz (2002) and Ranaldo (2003), among others, provde evdence n the affrmatve. The value added of ths paper s that t evaluates what partcular peces of all the book nformaton do really matter n characterzng the upcomng order flow. We dstngush between two large sets of nformaton: the best bd and offer quotes and the second to ffth bd and offer quotes. Ths dstncton s not arbtrary snce even some of the most pre-trade opaque markets provde nformaton about the best quotes. Our man goals are, frst, to provde a measurement of the nformaton value of the lmt order book beyond that of the best bd 3

4 and offer quotes and, second, to nfer what traders do really beneft from the addtonal nformaton n the lmt order book data. Ths emprcal analyss s of great nterest not only to economsts, n terms of modelng pure order drven markets and characterzng the traders behavor, but also to polcy makers because our fndngs shed some lght on some basc questons of the pre-trade transparency lterature: how publcly revealng nformaton about the book affects tradng strateges and who benefts from pre-trade transparency. We characterze the order flow usng the order aggressveness and the tmng of trades, submssons and cancellatons. Our methodology merges the Grffths et al (2000) and Ranaldo (2003) approach of usng ordered probt models to study order aggressveness and the Coppejans and Domowtz (2002) approach of usng the famly of autoregressve condtonal duraton (ACD) models (Engle and Russell, 1998) to analyze the tme between consecutve events of some knd. We evdence that the whole lmt order book matters n explanng the aggressveness of traders, although the best quotes account for the most mportant part of the useful nformaton. The book beyond the best quotes s partcularly relevant n explanng the aggressveness of an upcomng lqudty provder but t does not affect to the strategc decson of an upcomng market-order trader. Fnally, nether the best quotes nor the book beyond the best quotes provdes noteworthy nformaton n determnng the tmng of orders. The paper proceeds as follows. In the next secton, we revew the pertnent lterature. In secton 3, we descrbe the data and the market. In secton 4, we analyze what peces of lmt order book nformaton matter n determnng order aggressveness. In secton 5, we 4

5 analyze what peces of book nformaton are mportant n explanng the tmng or trades, order submssons and cancellatons. Fnally, we conclude n secton Lterature revew Three topcs n market mcrostructure lterature are essental to set the lmts of ths paper: the ssue of whether the lmt order book contans nformaton about future prce movements and tradng decsons, the study of the determnants of order aggressveness, and the dscusson about the benefts and nconvenences of pre-trade transparent tradng systems. The nformatveness of the lmt order book has been the subject of recent theoretcal and emprcal research. Handa and Schwartz (1996), Parlour (1998) and Foucault (1999), among others, argue that the state of the lmt order book nfluences the forthcomng order flow. These models suggest that an unbalanced lmt order book reflects the market sentment. Smlarly, Huang and Stoll (1994) clam that the asymmetrc depth reflects nformaton asymmetres. Fnally, Sepp (1997) and Kanel and Lu (2001) theoretcally show that, contrary to the usual clam, nformed traders would prefer to submt lmt orders rather than market orders under certan condtons. Emprcally, Harrs and Panchapagesan (2003) and Madhavan and Panchapagesan (2000) conclude that the prvleged access of the NYSE specalst to the book turns out to be an nformatve advantage about short-run market movements. Corwn and Lpson (2000) evdence that the repostonng of lmt orders on the book durng tradng halts s nformatve about market movements when tradng resumes. Irvne, Benston and Kandel (2000) show that a lqudty measure computed usng lmt order book data s more nformatve about subsequent order flow than other tradtonal lqudty measures based on the best bd and 5

6 offer quotes. Coppejans and Domowtz (2002) evdence that the nformaton gleaned from the book substantally affects the tmng of trades, order submssons and cancellatons. Conversely, Franke and Hess (2000) observe that the book s nformatve only durng perods of low nformaton ntensty. No one of these emprcal papers, however, has measured the nformaton content n the ndvdual peces of book nformaton. Bas et al (1995) proposed a categorzaton of order aggressveness. The most aggressve category (C1) corresponds to buy (sell) orders that demand more volume than s avalable at the best prevalng ask (bd) and are allowed to walk up (down) the book. Category C2 are buy (sell) orders that demand more volume than s avalable at the best ask (bd) but are not allowed to walk up (down) the book. Category C3 ncludes buy (sell) orders that demand less volume than s avalable at the best ask (bd). Category C4 orders have prces that le between the best bd and offer. Category C5 comprses buy (sell) orders that have prces equal to the best bd (ask). Category C6 ncludes buy (sell) orders that have prces above (below) the best bd (ask). Fnally, the less aggressve category (C7) s order cancellatons. Categores C1-C3 mply total or partal mmedate executon of the order. Categores C4-C6 mply non-mmedate executon. The theoretcal models of Parlour (1998), Foucault (1999), and Handa, Schwartz and Twar (2002) predct that the lmt order book condtons the aggressveness of traders. These models suggest that varables lke the mbalance between potental buyers and sellers and the volatlty of the asset determne the non-executon rsk of a lmt order and, hence, the mx between market (C1-C3) and lmt (C4-C6) orders. Consequently, the lower the nonexecuton rsk, the less aggressve the order flow. Emprcally, Ahn, Bae and Chan (2001) 6

7 and Daníelson and Payne (2001) observe that nvestors become less aggressve buyers (sellers) when lqudty drven volatlty rses from the ask (bd) sde of the book. Grffths et al (2000) and Ranaldo (2003) report that traders become more aggressve when the own (opposte) sde book s thcker (thnner), the spread narrower, and temporary volatlty ncreases. These two last papers, however, only use the pece of nformaton of the best bd and offer quotes on the book to explan order aggressveness. Madhavan (2000, pg. 234) defnes pre-trade transparency as the wde dssemnaton of current bd and ask quotatons, depths, and possbly also nformaton about lmt orders away from the best prces, as well as other pertnent trade related nformaton such as the exstence of large order mbalances. Electronc lmt order markets are usually characterzed as hghly pre-trade transparent snce they normally offer real-tme nformaton about the lmt order book. Bloomfeld and O Hara (1999) and Flood et al (1999) develop ndependent laboratory experments to evaluate the nfluence of quote nformaton dsclosure n mult-dealer settngs reportng mxed fndngs. Madhavan, Porter and Weaver (2000), for the Toronto Stock Exchange, and Boehmer, Saar and Yu (2003), for the NYSE, nvestgate the mpact of an exogenous ncrease n the level of publc nformaton about the lmt order book. These papers report mxed fndngs regardng the effect of greater transparency on dsplayed lqudty. In addton, Boehmer et al detect that greater transparence mproves nformatonal effcency. Harrs (1996) argues that pre-trade transparency ncreases the exposure-rsk of lmt order traders. Our emprcal study does not provde addtonal nsghts about the benefcal or pervasve effects of pre-trade transparency, but t sheds some lght on who benefts from an open 7

8 lmt order book n a pure order-drven market and provdes a measurement of how much valuable s the book nformaton beyond the best bd and offer quotes. In a recent unpublshed paper, Cao, Hansh and Wand (2003) also evaluate the nformatveness of the Australan Stock Exchange lmt order book beyond ts frst step. Although both papers nevtably overlap at some pont, the focus s dfferent and there are also remarkable methodologcal dfferences. Cao et al focus on the value of the book nformaton n determnng the true value of the stock. Usng depth-weghted estmators of the effcent prce from both the best quotes and the complete book, these authors estmate an error correcton model for 5-mnute snapshots of the book. They fnd that the best quotes lead the whole book and provde a better estmator of the true value. However, the averaged Hasbrouck s (1995) upper and lower nformaton shares attrbute a 70% of the prce dscovery to the best quotes and a 30% to the rest of the book. Nonetheless, the lower nformaton share bound for the book away from the best quotes s always very close to zero. These authors evdence that the lqudty nformaton derved from the secondary steps of the book has also some margnal explanatory power on future returns. Cao et al provde some nsght about the ssue ths paper focus on, the effect of the dfferent peces of book nformaton on order submsson, performng a probt analyss of order aggressveness. However, they do not provde a measurement of the value added of the book beyond the best quotes and do not study patent and mpatent traders behavor ndependently. In addton, we beleve that those traders that contnuously montor the market may be able to nfer about the state of the book beyond the best quotes by closely studyng the evoluton of the best quotes. Consequently, some of the nformaton derved from the secondary quotes may be redundant. We take ths 8

9 possblty nto account by consderng summary measures of the nformaton on the secondary levels of the book that are unconnected wth the nformaton on the best quotes. 3. Market background and data The Spansh Stock Exchange Interconnecton System (SIBE) s an electronc platform that connects the four stock exchanges that consttute the Spansh Stock Exchange (SSE), located n Barcelona, Blbao, Madrd and Valenca. Snce 1995, ths electronc system has held the tradng actvty of the most frequently traded and lqud stocks on the bass of a unfed lmt order book. Every order submtted to the system n any of the four markets s electroncally routed to the centralzed lmt order book to proceed wth ts mmedate executon or storage. The matchng of orders s, therefore, computerzed. The SIBE s a pure order-drven market wth a daly contnuous tradng sesson from 9:00 a.m. to 5:30 p.m. and two call auctons; the frst one determnes the openng prce (8:30-9:00 a.m.) and the second one determnes the offcal closng prce (5:30-5:35 p.m.). Orders are placed n the electronc system through authorzed brokers or brokerdealers. Durng the auctons, orders can be entered, altered or cancelled but no trade occurs, and the book s partally vsble snce tentatve equlbrum prces and volumes are publczed and contnuously revsed. Both auctons fnsh wth a 30-seconds randomend perod fxng the offcal openng or closng prce. Durng the contnuous tradng sesson, orders are submtted, modfed or cancelled. A trade takes place whenever a counterpart order hts the quotes. The market s governed by a strct prce-tme prorty. An order may lose prorty f modfed. Stocks are quoted n euros. The mnmum prce varaton (tck) equals 0.01 for prces below 50 and 0.05 for prces above 50. The 9

10 mnmum trade sze s one share. Durng the Specal Operatons Market (SOM) after the closng of the ordnary sesson (5:40 to 8:00 p.m.), the brokers can execute pre-arranged trades or applcatons, although they are subject to restrctve prce and mnmum sze/value condtons. In addton, brokers can also manage large volume orders through the Block Market (BM), from 9:00 a.m. to 5.30 p.m. The BM handles both pre-arranged trades and compettve large orders but, agan, under very rgd condtons. There are three basc types of orders n the SIBE. Market orders are executed aganst the best prces on the opposte sde of the book. Market orders n the SSE are not handled n the same way as n the Pars Bourse (see Bas et al, 1995) snce any excess that cannot be executed at the best bd or ask quote s executed at less favorable prces by walkng down (up) the book untl the order s fulflled. If the order sze exceeds the avalable book depth (a very unusual event for the most lqud stocks), the market order s stored and executed as soon as a new lmt order or market order of opposte sgn s submtted to the system. These unexecuted market orders have prorty over the lmt orders on the book. Market orders n the SSE belong to the C1 or C3 categores of aggressveness. Market to lmt orders do not specfy a lmt prce but are lmted to the best opposte-sde prce on the book at the tme of entry. Any excess that cannot be executed at that prce s converted nto a lmt order at that prce. Therefore, these are C2 orders. Lmt orders are to be executed at the lmt prce or better. Any unexecuted part of the order s stored n front of the book at the lmt prce. Notce that lmt orders at a prce equal to the best opposte-sde quote and for a smaller (larger) quantty that that avalable at that quote cannot be dstngushed n practce from C3-market (C2-market to lmt) orders. Therefore, we pool these two categores as market (market to lmt) orders. 10

11 Smlarly, we put together lmt orders that walk up or down the book and become totally fulflled wth C1-market orders. Lmt orders that walk up or down the book but become partally executed are very unusual n the SSE. They represent less than 0.3% of all orders submtted. These orders are also consdered C1. In concluson, we would need seven categores to analyze order aggressveness n the SSE (C1 to C7). By default, orders expre at the end of the sesson. Nonetheless, the broker can enter a specfc expraton date for each order submtted, wth a maxmum of 90 calendar days. For all type of orders and only durng the contnuous market, brokers may specfy specal condtons, lke mmedate executon or elmnaton, mnmum executon and fll or kll. In practce, orders wth these condtons are not dstngushable from some of the eght categores defned above. The SIBE also allows partally undsclosed lmt orders, known as ceberg orders. The nvestor chooses the dsplayed volume unt of the order, wth a mnmum of 250 shares. A new dsplayed volume unt emerges as soon as the current one s executed. The hdden part of the order loses, however, ts tme precedence. 1 In ths paper, we take nto account the presence of hdden depth when determnng the aggressveness of an order. Thus, a market order wth sze larger than the dsclosed depth at the best-opposte quote on the book s classfed as C1 only f t exhausts all the avalable depth, dsclosed plus undsclosed, at that quote. The SIBE s a hghly transparent market. The system provdes real-tme nformaton about the 5 best levels of the book and mmedate dssemnaton of tradng data through the Computerzed Dssemnaton Informaton System (IDS). The status of the book s updated nstantaneously on broker s screens each tme there s a cancellaton, executon, 1 Pardo and Pascual (2003) study the usage and mpact of hdden orders n the SSE. 11

12 modfcaton or submsson of an order. Our database conssts on all the movements of the 5 best bd and offer quotes of the lmt order book and all trades executed from July to December 2000 (124 tradng days) durng the contnuous tradng sesson. We use the frst fve months of data to perform the estmatons and n-sample analyses and the last month to carry out out-of-sample analyses. The lmt order book data ncludes quotes, dsclosed depth and the number of orders supportng each quote. All the movements of the book are tme stamped at the nearest hundredth of a second. Therefore, we have the same lmt order book nformaton than brokers of the SSE have n real tme durng the sesson. The tradng data detals the prce, the sze and the counter partes of each trade. We consder data on the 36 stocks that were ncluded n the IBEX-35 ndex sometme through the year. 2 One stock s excluded because of a merger. Quote and trade data for each stock has been perfectly matched. Usng ths matched data, t s straghtforward to classfy all the movements of the lmt order book nto one of the eght categores of aggressveness formerly defned. Buyer and seller ntated trades are also easly dentfed. Table I provdes some descrptve statstcs on the 36 stocks n the sample, ncludng nformaton about the book and daly tradng measures. Even though these are the most frequently traded and lqud stocks of the SSE, there are huge dfferences between them n terms of mmedacy costs, depth and actvty. [Table I] Table II provdes summary statstcs about order aggressveness. We classfy each update of the lmt order book nto the 7 categores, C1 to C7, of aggressveness defned 2 The IBEX-35 ndex s computed as a cross-stock average trade prce weghted by market captalzaton. It s composed of the 35 most lqud and actve SIBE-lsted stocks durng the most recent sx-month control perod. The composton s ordnarly revsed twce a year, but extraordnary revsons are possble due to major events lke mergers or new stock ssues. 12

13 earler. The most frequent category s small market orders (C3) wth an average of 38.74% followed by lmt orders wthn the best offer and bd quotes (C4). The less frequent category s the most aggressve one, that of large market orders or alke (C1). On average, 38.42% of the orders submtted provde lqudty and 61.58% ether consume or wthdraw lqudty. [Table II] Table III provdes addtonal descrptve statstcs about duratons of trades, lmt orders and cancellatons. We dsaggregate the data nto offer and bd flow. These seres are hghly autocorrelated and overdspersed. A dfferental characterstc of our dataset s the absence of zero duratons because of the hgh precson at whch book updates are tme stamped. Another common feature of these seres s a strong ntra-daly seasonalty. [Table III] We consder two large sets of book nformaton. The frst pece of book nformaton conssts on the best quotes (BQ). Even tradtonally opaque markets, lke the NYSE, have provded ths nformaton to the market. We summarze ths pece of book nformaton nto the followng varables, all them defned wth respect to the ncomng order: SPR s the bd-ask spread, DS 1 (DO 1 ) s the pendng number of shares or depth on the same (opposte) sde of the market, and NS 1 (NO 1 ) s the number of orders on the same (opposte) sde of the market. Snce the correlaton between DS 1 and NS 1 and between DO 1 and NO 1 s very hgh, we wll consder two alternatve BQ sets: BQ 1 =(SPR, DS 1, DO 1 ) and BQ 2 =(SPR, NS 1, NO 1 ). The second pece of book nformaton conssts of the addtonal four levels of quotes (AQ) publcly avalable n the SSE. We summarze ths second set of quotes usng: DS 25 (NS 25 ) s the accumulated depth (number of orders) on 13

14 the same sde of the market, DO 25 (NO 25 ) s the accumulated depth (number of orders) on the opposte sde of the market, LS 12 (LS 25 ) s the dstance tcks- between the best and the second best (the second best and ffth best) quotes on the same sde of the market, LO 12 (LO 25 ) s the dstance between the best and the second best (the second best and ffth best) quotes on the opposte sde of the market. These latter length measures are less frequent n mcrostructure research and some justfcaton s n order. On the one hand, these length measures capture the expected prce mpact of large market orders. Thus, LS 12 and LO 12 measure de ncremental cost of consumng more than the depth avalable at the best quotes. Ths cost may nfluence the aggressveness of traders and the tmng of orders. On the other hand, the length of the books may sgnal the consensus among traders about the true value of the stock; t may be nformatve about future prce changes or t may ndcate the presence of nformed traders; t may also be nterpreted as a measure of the wllngness of traders to provde lqudty on a gven sde of the lmt order book. We wll also consder two alternatve AQ sets: AQ 1 =(DS 25, DO 25, LS 12, LO 12, LS 25, LO 25 ) and AQ 2 =(NS 25, NO 25, LS 12, LO 12, LS 25, LO 25 ). Fnally, the varables n the AQ set are defned as the resduals of a lnear regresson of each of ts components on the varables n the pertnent BQ set, so that the AQ sets have no redundant nformaton wth respect to the BQ sets. 4. Aggressveness Suppose that the degree of aggressveness (mpatence) of a gven trader s a (lnear) functon of a varety of factors k X, k = 1,, K. The lmt order book nformaton, we 14

15 presume, s ncluded among these aggressveness-nducng factors. Hence, the aggressveness ndex * A can be represented as, A * K k 1 k X k Z, [1] where k s the coeffcent assocated wth the k th factor. The error term ndcates that the relatonshp n [1] s not an exact one. The aggressveness ndex * A s dffcult, f not mpossble, to observe. Therefore, equaton [1] s a latent regresson. However, we can nfer about the degree of aggressveness of trader by observng the specfc order submtted by that trader. Therefore, the seven categores of order aggressveness (C1 to C7) prevously descrbed represent a partton of the state space that allows mappng the latent degree of aggressveness nto observable dscrete values. Let A be a ordnal response varable such that, * 1 f A 1 * A m f k1 A k, m 2,,6 [2] * 7 f A 6 wth m beng unknown thresholds, to be estmated along wth the k parameters n [1]. * For example, f A 6 the trader s extremely aggressve and submts C1-market orders * ( A 7), f 1 A 2 the trader s hghly patent and submts C6-lmt orders ( A 2), and so on. Assumng that the probablty dstrbuton of the error terms s normal, equatons [1]-[2] defne an ordered probt model. The probablty of A takng value m s, Pr( A m) Pr( m1 Z m Z ) ( m Z ) ( m1 Z ), [3] 15

16 wth, and (.) beng the normal cumulatve dstrbuton functon. 0 7 Fnally, the margnal effect of the k X factor on the probablty A takng value m s, P( A X m) k ( 1 - Z ) k ( m1 - Z ) ( ( 6 - Z ) k m - Z ) k f m 1 f m 2,,6 [4] f m 7 where (.) s the normal densty functon. 3, 4 In order to measure the nformaton content of the lmt order book beyond that of the best bd and ask quotes, we estmate three alternatve models. The Baselne Model (BM) only ncludes the frst lag of the dependent varable n the explanatory varable set; the Best Quotes Model (BQM) adds the BQ set of explanatory varables to the BM model; the Complete Book Model (CBM) adds the AQ set of explanatory varables to the BQM. Therefore, the BM assumes that the nformaton gleaned from the book s not relevant n explanng order aggressveness; the BQM presumes that only the best quotes of the lmt order book provde valuable nformaton and, fnally, the CBM s based on the noton that the book provde relevant nformaton away from the best quotes. We evaluate the relatve performance of each model both n-sample and out-of-sample. For the n-sample analyss, we use all orders submtted from July to November For the out-of-sample analyss, we use the n-sample estmated coeffcents on the December 2000 data. 3 Note that, gven a change n a exogenous varable, t s only possble to nfer the drecton of change n the probabltes from the sgn of the coeffcent assocated wth t for the extreme cases m=1 and m=7. 4 Alternatvely, we can assume that the error terms are logstcally dstrbuted. In such a case, equatons [1] and [2] defne an ordered logt model. There s no theoretcal reason to prefer a pror a normal or a logstc dstrbuton. The dfference between both dstrbutons s n the tals, much heaver n the case of the logstc dstrbuton. Generally, ether model wll gve dentcal substantve conclusons. In case of large number of observatons and a heavy concentraton of observatons n the tals of the dstrbuton, however, the estmates may dffer substantally (e.g., Lao, 1994). Snce both Grffths et al (2000) and Ranaldo (2003) consder the case of normalty, we also base our analyss on the ordered probt model. We have not found, however, remarkable dfferences usng the ordered logt model. 16

17 Table IV summarzes the estmaton of the CBM for the 36 stocks n our sample. We consder two alternatve specfcatons: model M1 ncludes BQ 1 and AQ 1 as exogenous varables and model M2 ncludes BQ 2 and AQ 2 nstead. We also dstngush between buyer-ntated-orders and seller-ntated-orders. The estmates of k and m (not reported) are obtaned by maxmum lkelhood (ML). Grffths et al (2000) for the Toronto Stock Exchange and Ranaldo (2003) for the Swss Stock Exchange estmate smlar ordered probt models. Ranaldo, however, only consders the best offer and bd quotes and Grffths et al do not dstngush the effect of dfferent peces of book nformaton. [Table IV] The estmated coeffcents for the varables n the BQ sets are consstent wth the hypotheses H1 to H3 dscussed and tested by Ranaldo (2003). A wder spread reduces the aggressveness of traders (H1), consstent wth Foucault (1999). As argued by Parlour (1989) and Handa et al. (2002), the thcker the book on the buy (sell) sde, the more aggressve the ncomng buyer (seller) (H2) and the thcker the book on the sell (buy) sde, the less aggressve the ncomng buyer (seller) (H3). These relatonshps are stronger n model M2 (number of orders) than n model M1 (quoted depth). We also fnd a strong frst order postve autocorrelaton n order aggressveness, an expected result gven the dagonal effect reported by Bas et al. (1995). The results for the number of orders (NS 25, NO 25 ) and depth (DS 25, DO 25 ) apart from the best quotes generally support H2 and H3, partcularly n model M2, but they are far less convncng. Regardng the length measures, we obtan a weak but clearly negatve effect of LS 12 and a strong postve effect of LO 12 on order aggressveness. A small value of LS 12 may sgnal a tght 17

18 or crowded book on the same sde of the market as the ncomng trader. In ths stuaton, ganng precedence by prce mght be dffcult and httng the best quotes would brng a longer-than-average tme to executon. Consequently, patent traders could become more aggressve and submt market orders. On the other hand, a hgher dsperson of the ask (bd) quotes may be assocated wth a lower probablty of executon of a lmt order to buy (sell), nducng the ncomng trader to be more aggressve. The results for the other explanatory varables are weak or nconclusve. Table V shows the relatve n-sample and out-of-sample performance of each of the three models estmated. We provde four alternatve goodness-of-ft measures that correspond to the n-sample (adjusted) pseudo-r 2 s of McFadden (1973, p.121), Maddala (1983, p.39) wth the Cragg and Uhler (1970) correcton, Aldrch and Nelson (1984) wth the Veall and Zmmermann (1992) correcton, and McKelvey and Zavona (1975). 5 Namely, Table V contans the medan psuedo-r 2 s for the BM model, the ncrease n the BQM pseudo-r 2 s wth respect to the BM and the ncrease of the CBM pseudo-r 2 s wth respect to the BQM. We observe that the n-sample ft mproves on the BM a medan % (289.45%) for sellers and % (446.54%) for buyers wth the M1 (M2) specfcaton when the varables from the best quotes of the book are added to the model. In addton, the ft mproves on the BQM a medan 47.33% (18.22%) for sellers and 78.86% (27.11%) for buyers when the whole lmt order book s taken nto account. Ths 5 No one of these measures s unversally accepted or employed. The values between zero and one have no natural nterpretaton, though t has been suggested that the pseudo-r 2 value ncreases as the ft of the model mproves. In a comparatve analyss performed by Veall and Zmmermann (1996), these authors conclude that, for the partcular case of the ordered probt model, the pseudo-r 2 due to McKelvey-Zavona outperforms the other measures and has a strong numercal relatonshp to the OLS-R 2 n the latent varable. The Veall-Zmmermann and the Cragg-Uhler s measures also perform reasonably well. We nclude the McFadden s pseudo-r 2 because t s the most common n statstcal packages. For a revew of all these goodness-of-ft measures see Veall and Zmmermann (1996). For a defnton see Appendx A. As n standard regresson analyss, we use adjusted versons of these measures to take nto account the change n degrees of freedom. 18

19 ncreasng pattern ndcates that the state of the book determnes, at least partally, the aggressveness of traders. Most of the explanatory power concentrates on the best quotes. However, traders examne not only the nformaton avalable at the best quotes but also the less aggressve quotes. A smlar concluson can be derved from the out-of-sample McKelvey-Zavona (adjusted) pseudo-r 2. The predctve capacty of the BQM outperforms that of the BM model by a medan % (156.46%) for sellers and 424.8% (157.69%) for buyers. When the complete book s consdered, there s an addtonal mprovement of 53.79% (37.36%) for sellers and (70.8%) for buyers. As an alternatve to the prevous pont measures of goodness-of-ft, we have also performed an addtonal experment to assess the predctve ablty of the three models. Usng the nsample estmated coeffcents, we have computed the one-step-ahead probablty for each of the 7 categores of aggressveness and for each out-of-sample observaton. We have compared the predcted probabltes for the actual event wth a constant probablty gven by the n-sample relatve frequency. 6 Table V reports that the CBM usually outperforms the BQM and the BM on the bass that t allocates a hgher-than-ts-relatve-frequency probablty to the actual event more often than the other two models do. For example, the CBM s the best model aganst the relatve frequency rule for 80.56% of the stocks for the sellers-m2 specfcaton; only for 13.89% of the stocks the BQM outperforms the other two models. Table V also provdes a drect comparson between models. For example, the CBM does better than the BQM for 94.44% of the stocks n the buyers-m1 6 Snce all the categores of aggressveness are not equally frequent, the predcted probablty for the most frequent category (small market orders) s always the largest, ndependently of the specfcaton of the ordered probt model. However, the expected probabltes for each category and each observaton do are model-specfc. 19

20 model n the sense that the CBM usually allocates a hgher probablty to the true event than the BQM. Both book models usually mprove on the BM. [Table V] The prevously estmated ordered probt model does not allow to study the relevance of the dfferent peces of book nformaton n the tradng decsons of passve and actve traders ndependently. Alternatvely, the submsson of an order can be though as a sequental process wth two steps. In the frst step, the trader chooses between submttng a cancellaton, a lmt order or a market order. In the second stage, the patent trader places the lmt order ether away from the best quotes, at the best quotes or wthn the best quotes, and the mpatent trader fxes the sze of the order: less volume than avalable at the best opposte quote, a market to lmt order or more volume than avalable at the best opposte quote. These stages n the decson process conform a sequental ordered probt analyss (e.g., Lao, 1994), whch conssts n estmatng an ordered probt model n each stage of the sequence. Table VI summarzes the estmaton of the second stage of the sequental ordered probt CBM for the entre sample. We do not report the results for the frst stage snce they are smlar to those n Table IV. In ths frst step, model M2 s more consstent wth the hypotheses n Ranaldo (2003) than model M1 for whch H3 s generally rejected. Table IV shoes that patent traders submt more aggressve lmt orders as the spread ncreases. Ths s consstent wth Bas et al. (1995) concluson that n pure order drven markets the traders provde lqudty when t s valuable for the marketplace. Large mpatent traders are also more frequent when the spread s large, probably because the hgh mmedacy costs dscourages the small nvestor. The aggressveness of the patent traders ncreases wth DS 1 or NS 1 and decreases wth the 20

21 length of ther sde of the market (LS 12 and LS 25 ). All these varables may proxy for the proporton of traders wth a smlar valuaton. In order to gan precedence when the book s thck the patent trader has to submt orders wthn the best quotes. When the book s long, the patent trader wll demand a larger compensaton so as to provde lqudty. The mpatent trader s also more aggressve the more crowded the book on her sde of the market (n terms of DS 1, LS 12 and LS 25 ) and the more dsperse the book n the opposte sde of the market (n terms of DO 1, NO 1, LO 12 and LO 25 ). An ncrease n LO 12, for example, means a larger cost of submttng C1-market orders, whch reduces the aggressveness of the mpatent trader. 7 [Table VI] Table VII reports the relatve n-sample and out-of-sample performance of the sequental ordered probt models CBM, BQM and BM. Snce the results for the frst step of the model are very close to those of the ordered probt model n Table V, we only report the results for the second step. The n-sample analyss shows that passve traders strategc decsons clearly depend on the book nformaton. There s a medan mprovement of % (134.48%) for sellers and % (177.09%) for buyers wth the M1 (M2) specfcaton when the best quotes of the book are consdered. More mportant, the CBM mproves on the BQM by a medan of % (263.19%) for sellers and % (210.51%), whch means that the order submssons by lqudty provders are (at least partally) based on an examnaton of the state of the whole lmt order book. From ths pont of vew, lqudty traders undoubtedly beneft from an 7 The strong negatve effect of the number of orders on the same sde of the book on the decson of the mpatent trader reported n Table VI Panel B suggests that what matters s nether the depth nor the number of orders but the number of large orders on the same sde of the book. The larger the average sze of the orders supportng the best quotes the larger the aggressveness of the ncomng mpatent traders. 21

22 ncreased degree of pre-trade transparency. The out-of-sample (adjusted) pseudo-r 2 leads to the same concluson showng a smlar ncreasng pattern from BM to BQM and from BQM to BCM. In addton, the CBM obtans the best scores aganst the relatve frequency rule, and ts estmated probabltes always outperform those of the BQM: for all the stocks n the sample, the CBM allocates hgher probabltes to the actual event than the BQM and the BM. The results for the actve traders (lqudty consumers) are remarkably dfferent. The strategc decson of actve traders at ths second step s to choose the sze of ther market order. Table VII evdences that ths decson strongly depends on the state of the best quotes of the book. There s a medan n-sample ft mprovement of 15112% ( %) for sellers and % (991.06%) for buyers wth the M1 (M2) specfcaton when the best quotes are added to the BM. However, the CBM mproves on the BQM only by a medan 12.97% (23.75%) for sellers and 3.71% (34.03%) for buyers. Ths means that the most aggressve traders n the market barely base ther strategc decsons on the state of the lmt order book beyond the best quotes. The out-of-sample predctve performances support ths concluson: the pseudo-r 2 for sellers-m1 (buyers-m1), for example, ncreases a neglgble 0.36% (0.71%) from the BQM to the CBM. Moreover, the book-based models rarely do better than the relatve frequency rule and the BQM probabltes outperform those of the CBM as many tmes as the CBM outperforms the BQM. Table II showed that 80.8% of the orders that are executed nstantaneously n the SSE are small market orders (C3) and 11.1% are marketto-lmt orders (C2). Ths suggests that the Spansh actve traders tend to adjust the sze of ther orders to the avalable depth on the best quote of the opposte sde of the market. 22

23 Consequently, an ncrease n the pre-trade transparency would have only a margnal mpact on the order submsson strategy of lqudty consumers. 5. The tmng of cancellatons, lmt orders and market orders In ths secton, we analyze what peces of book nformaton are mportant n explanng the tme between two consecutve trades, lmt order submssons and cancellatons on the same sde of the market. These three types of orders concde wth the three levels of aggressveness n the frst step of the sequental ordered probt model estmated n the prevous secton. Therefore, we also analyze order aggressveness n ths secton but from a dfferent statstcal pont of vew. The analyss of duratons s performed usng Engle and Russell s (1998) autoregressve condtonal duraton (ACD) models. The ACD ( p, q) model for the duraton d s defned as, d w p j1 j d j q j1 j j where (for ) are d nnovatons wth 1,, n E, such that Ed I 1. An alternatve, and convenent, specfcaton s d 1, where and hence 1 E and Ed I 1. The condtonal duraton ( ) s specfed as a lnear functon of the prevous p duratons and q condtonal duratons. As n the GARCH lterature, numerous studes have shown that the ACD (1,1 ) captures correctly the dynamcs of a very general class of models (e.g., Bauwens et al., 2003). Therefore, we 23

24 restrct our attenton to the ACD (1,1 ) case, w d 1 1, where 0, 0 and 0. Bauwens and Got (2000) argue that when addtonal explanatory varables mpled by mcrostructure theory are added lnearly n the condtonal expectaton and negatve slope coeffcents are expected for some of those varables, then the condtonal duraton may become negatve. Ths s not admssble snce duratons have to be non-negatve. Imposng non-negatvty restrctons on the slope coeffcents, however, s tantamount to delete the correspondng varables, whch s self-destructve. Ths led Bauwens and Got to ntroduce a logarthmc verson of the ACD model. The Log-ACD model s wrtten as, d exp( ), [5] such that s the logarthm of the condtonal duraton exp( ). Compared to the ACD (1,1) model, the autoregressve equaton of the Log ACD(1,1 ) model bears on the logarthm of the condtonal duraton rather than on the condtonal duraton tself, ln. [6] d 1 1 Snce no sgn restrctons are needed on the parameters to ensure the postvty of the condtonal duraton, we can lnearly ntroduce any set of exogenous varables n [6], regardless of the expected sgn of ts accompaned parameter, ' ln d x, [7] 1 1 where x s a row vector of dmenson s ncludng the exogenous varables. 24

25 A parametrc model s obtaned when the dstrbuton of s specfed up to a fnte number of parameters. We use a three-parameter dstrbuton, the generalzed gamma. 8 Let follow a generalzed gamma dstrbuton,.e. GG( 1,, ), wth densty functon, ( ) 1 f GG ( ) exp, where and are the shape parameters. The scale parameter s fxed to one and t s replaced by exp( ) when computng the dstrbuton of the duratons. In other words, gven the Log-ACD model, f GG( 1,, ) then d GG( 1/ exp( ),, ) and hence, where,,,, 1 d f GG ( d I 1; ) d exp, exp ( ) exp( ) s the parameter set. The parameters of the Log-ACD model can be estmated by maxmzng the lkelhood functon, n f ( d I ; ) L log GG 1. 1 All duratons we analyse have a strong seasonal ntra-daly nverted U-shaped pattern. 9 We model tme-of-day adjusted duratons, 8 Engle and Russell (1998) proposed the standard exponental dstrbuton and, as an extenson, the Webull dstrbuton. However, as documented by Bauwens and Veredas (2003) and Grammg and Maurer (2000), the Webull dstrbuton may not be flexble enough for duraton processes wth a hgh ntensty, or hazard, rate. Ths s our case, where orders, trades and cancellatons arrve at a hgh rate and extreme events (very short and very long duratons) are often observed. Ths s why we choose an even more general dstrbuton; the generalzed gamma dstrbuton nests the exponental and Webull ACD models as specal cases. 9 The duratons can be thought of as consstng of two parts: a stochastc component to be explaned by the Log-ACD model, and a determnstc part, namely the seasonal ntra-daly pattern. Ths effect arses from the systematc varaton of the market actvty durng each tradng day. 25

26 where D s the orgnal duraton, d t D, ' d s the adjusted duraton, t ' s the tme-of-day effect at tme t ', and t ' s a bounded random varable that measures the number of accumulated seconds snce the openng. It s obtaned from the arrval tmes usng, t ' t t t t c t t 0 0 t c t 0 f t t c otherwse, where x s the nteger part of x, and t o and t c stand respectvely for the market openng and closng (n hundredths of a second). Ths gves a sequence of arrval tmes that are, everyday, monotoncally ncreasng from t o to t c. They are hence bounded and the whole process looks lke a toothed sequence. The estmated seasonal pattern t ' s computed by a nonparametrc regresson of the observed duraton on the tme of the day, a methodology ntroduced by Veredas et al (2001). The result s the Nadaraya-Watson estmator, n ' 1 t 0 t K d nh h ' 0 t o, n ' 1 t t 0 K nh 0 h 26

27 wth the functon K beng a kernel estmator and h the bandwdth. The kernel chosen 1 5 s the quartc and the bandwdth s 2.78sn, where s s the sample standard devaton and n s the number of observatons. 10 For each stock n the sample, we compute sx dfferent tme-of-day adjusted duratons: trades, lmt orders, and cancellatons, dstngushng between buyer and seller-ntated orders. As n the ordered probt analyss, we estmate three alternatve models for each duraton: the Log ACD(1,1 ) s our baselne model (BM) n ths case; the BQM- Log ACD(1,1) adds the BQ set of explanatory varables to the BM model; the CBM- Log ACD(1,1) adds the AQ set of explanatory varables to the BQM. Fnally, for the BQM and CBM models we consder two alternatve specfcatons: model M1 ncludes BQ 1 and AQ 1 as exogenous varables and model M2 ncludes BQ 2 and AQ 2 nstead. We evaluate the relatve performance of each model both n sample (July to November 2000) and out-of-sample (December 2000). The estmaton results are not reported because of space lmtatons. 11 However, only the bd-ask spread (SPR) shows a strongly sgnfcant effect on all sx duratons and for all the model specfcatons. As the SPR ncreases, the tme between consecutve trades (ether buyer or seller-ntated) ncreases and the tme between consecutve cancellatons and lmt order submssons decreases n both sdes of the lmt order book. Ths result s consstent wth the former evdence from the ordered probt models: a wde bd-ask 10 We also observe ntra-daly determnstc patterns n some of the exogenous varables, n partcular n the varables that correspond to the best quotes of the book. All these explanatory varables have been tme-ofday adjusted usng the same nonparametrc regresson as for the duratons. 11 The estmaton results are avalable upon request from the authors. 27

28 spread decreases order aggressveness as the ncrease n mmedacy costs dscourages market order traders. Table VIII summarzes the relatve n-sample and out-of-sample performance of the log-acd models BM, BQM and CBM. We provde four alternatve n-sample and outof-sample goodness-of-ft measures for each model. The adjusted pseudo-r 2 (1) s a functon of the mean square error (MSE), and the adjusted pseudo-r 2 (2) s a functon of the sample correlaton coeffcent between the actual (d ) and the ftted values of the duratons ( ˆ ). We also provde the Akake (AIC) and the Schwarz Bayesan (SBC) nformaton crtera computed from the resduals ˆ d. See the Appendx for a defnton of all these measures. Table VIII contans the medan psuedo-r 2 s, AIC and BIC for the BM model, the percent ncrease n the BQM measures wth respect to the BM and the percent ncrease of the CBM measures wth respect to the BQM. [Table VIII] The n-sample analyss shows that the tmng of orders barely depend on the book nformaton. The goodness-of-ft pseudo-r 2 measures mprove, n medan, a 1.3% for cancellatons, 0.87% for lmt order submssons and a 1.4% for trades when the best quotes of the book are consdered. More mportant, the CBM mproves on the BQM by a medan of 1.2% for cancellatons, 1.11% for lmt order submssons and 0.73% for trades. We report a smlar (or even more neglgble) decreasng pattern n the AIC and BIC nformaton crtera gong from BM to BQM and from BQM to BCM. No remarkable dfferences are observed between seller and buyer-ntated orders. The results for the out-sample analyss strongly reject that ether pece of book nformaton s relevant n explanng the tmng of cancellatons, lmt orders, or market orders. Many 28

29 adjusted pseudo-r 2 measures decrease and the AIC and BIC nformaton crtera ncrease as we add extra exogenous varables n the log-acd model. In summary, Table VIII evdences that no pece of book nformaton matters n explanng the tmng of orders. 12 Ths evdence may seem contradctory wth Coppejans and Domowtz s (2002) fndngs. These authors use ACD models to conclude that the nformaton gleaned from the electronc lmt order book substantally affects trader behavor. Usng unadjusted pseudo-r 2 measures, they compare the goodness of ft of a Generalzed ACD or GACD model (Lunde, 1999), whch ncludes book and order flow nformaton, wth a smple ACD(1,1) model. 13 The ACD and the GACD are not nested models. As a consequence, t s mpossble to dscern f, for example, the reported 293% (n-sample) and 149% (out-ofsample) ncrease n the pseudo-r 2 for seller-ntated trade duratons (see Table 4 n Coppejans and Domowtz, 2002) s due to the book nformaton, to the order flow nformaton or smply to the fact that the GACD s a more rch and complex model than the ACD(1,1) used as a reference. Our fndngs n Table VIII suggest that Coppejans and Domowtz s results would not vary f the book nformaton were dropped from ther GACD model. The results n Table VIII also refne to some extent the results of the ordered probt analyss n the prevous secton. The order aggressveness analyss concluded that the lmt order book nformaton was relevant n explanng the aggressveness of an ncomng order. Namely, the best quotes on the lmt order book were mportant n 12 We have performed some robustness tests. In partcular, we have consdered the exponental dstrbuton for nstead of the generalzed gamma and we have also used cubc splnes (e.g., Engle and Russell, 1998) nstead of the Veredas et al (2001) methodology to estmate the seasonal component of the duratons. The results n Table VIII are nvarant to these alternatve specfcatons. 13 For any two consecutve events of the same knd at tme t-1 and t, the GACD model ncludes book nformaton measured at t-1, namely the bd-ask spread and accumulated depth measures, and nformaton about the order flow n that nterval. 29

30 explanng the strategc decsons of any ncomng trader and at any stage of the decson process; the book nformaton beyond the best quotes, however, was only relevant n explanng the strategc decsons of an ncomng lmt order trader. In contrast, the analyss of cancellaton, lmt order, and trade duratons n ths secton ndcates that nether pece of book nformaton, apart from the bd-ask spread, matters n explanng the partcular submsson tme of an ncomng order of a smlar level of aggressveness than the most recent order submtted. Notce that n the order aggressveness analyss we study the capacty of the book to provde nformaton about an event that s gong to occur almost nstantaneously: the next order to be submtted. In the order duraton analyss, however, we evaluate the capacty of the book to explan an event that may take a longer tme to be accomplshed: the next order to be submtted wth a gven level of aggressveness. Therefore, a possble nterpretaton of our mxed fndngs s that the book nformaton has explanatory power only n the very short run. In addton, Franke and Hess (2000) show that the nformaton value provded by the nsght nto the lmt order book n an electronc tradng system declnes when the ntensty of prvate and publc nformaton arrval ncreases. The basc dea behnd ths result s that n tmes of low nformaton ntensty there are only a few updates n the state of the lmt order book and, consequently, the nsght nto the book may provde valuable nformaton. In tmes of hgh nformaton ntensty, however, the order flow ncreases and the book updates contnuously. Consequently, the snapshots of the book have lttle value. Ths feature of the book nformaton may be more relevant n our duraton analyss than n our aggressveness analyss. When the order flow between two consecutve events of the same type at tme t-1 and t s severe, the nformaton on the most recent orders 30