Determining the Intensity of Buy and Sell Limit Order Submissions: A Look at the Market Preopening Period

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1 Determnng the Intensty of Buy and Sell Lmt Order Submssons: A Look at the Market Preopenng Perod Mke Bowe Stuart Hyde Ike Johnson Abstract Usng a unque dataset we examne the behavor of market partcpants n the absence of tradng. Specfcally we nvestgate the duraton between arrval of orders of the same type durng the market preopenng perod. We fnd that the number of buy order submssons per unt of tme s more sgnfcantly mpacted by nformaton nferred from the characterstcs of ncomng orders and changes that mpact the current lmt order book n comparson to the mpact on sell order submssons. In addton, we fnd that traders on the buy sde of the market tend to act on lqudty provded by the sell sde and the sell sde of the markets tends to ncrease ther submssons when volume s removed from the sell sde of the lmt order book. JEL Classfcaton: G12, G14, G15, C32. Keywords: market mcrostructure, lmt order, duraton, ntensty, lqudty Manchester Busness School, Unversty of Manchester, Booth Street West, Manchester, M15 6PB, UK. emal: mke.bowe@mbs.ac.uk, tel: ; fax: Manchester Busness School, Unversty of Manchester, Booth Street West, Manchester, M15 6PB, UK. emal: stuart.hyde@mbs.ac.uk, tel: ; fax: Correspondng author. Manchester Busness School, Unversty of Manchester, Booth Street West, Manchester, M15 6PB, UK. emal: ke.johnson@postgrad.mbs.ac.uk.

2 Determnng the Intensty of Buy and Sell Lmt Order Submssons: A Look at the Market Preopenng Perod Abstract Usng a unque dataset we examne the behavor of market partcpants n the absence of tradng. Specfcally we nvestgate the duraton between arrval of orders of the same type durng the market preopenng perod. We fnd that the number of buy order submssons per unt of tme s more sgnfcantly mpacted by nformaton nferred from the characterstcs of ncomng orders and changes that mpact the current lmt order book n comparson to the mpact on sell order submssons. In addton, we fnd that traders on the buy sde of the market tend to act on lqudty provded by the sell sde and the sell sde of the markets tends to ncrease ther submssons when volume s removed from the sell sde of the lmt order book. JEL Classfcaton: G12, G14, G15, C32. Keywords: market mcrostructure, lmt order, duraton, ntensty, lqudty

3 1. Introducton In a lmt order market, traders submt orders to ether buy or sell an asset for a specfc prce and assocated volume. In other words, the lmt order represents a pre-commtment that the trader s wllng to ether buy or sell a specfed amount of an asset at a predetermned prce. Ths order remans open untl t s ether executed or cancelled. However, n a lmt order market there s no desgnated market maker, and orders are only executed when the prce assocated wth a lmt buy order s matched wth the prce of a lmt sell order. 1 In addton, lmt orders that are unexecuted are queued and form what s known as the lmt order book. The lmt orders that comprse the book have a prce and tme prorty rule assocated wth them, n that the hghest prce for a buy order and the lowest prce for a sell order s gven prorty to be executed before any other lmt order. In the case of two lmt orders havng the same prce, then the frst to be submtted to the book s executed before the most recent lmt order. In essence, the lmt order book represents a source of nformaton about the characterstcs of the market n general, ndvduals valuaton for an asset and the level of lqudty demanded and suppled at dfferent prces. 2 Hence, the obvous queston here s what nformaton can be nferred from the lmt order book by traders so as to shape ther expectatons about the fundamental value of the asset? Further, can traders nfer nformaton from an open lmt order book n the absence of tradng consderng that t s possble for prevous commtments to be revsed or cancelled at any tme? On some exchanges, after an overnght or weekend halt n the tradng process, there s a preopenng perod that precedes the ntaton of tradng. Durng ths perod traders can submt lmt orders smlar to a call aucton process n whch elgble orders are executed only at the openng sesson of the tradng day. In essence, ths perod represents an nformaton aggregaton process about the fundamental value of the asset, snce there s no trade executon takng place and traders are ndcatng ther valuaton of the asset. Consequently, by observng each other s actons, traders can detect trends n the order process and form expectatons about both the probable openng prce of the asset or the general drecton of prces. However, orders submtted durng ths perod are non-bndng and can be subsequently cancelled or revsed, makng nference somewhat more challengng. 1 The executon of trades s also possble usng market orders. However, market orders can be consdered as lmt orders that request a trade mmedately at the best avalable prce. 2 See Parlour and Sepp (2007) for a comprehensve survey of lterature on lmt order markets. 1

4 The man focus of ths paper s to determne whether traders utlse nformaton nferred from the characterstcs of recent lmt order submssons and changes n the lmt order book to form strateges to submt ether buy or sell orders durng the preopenng perod. In other words, do traders observe the actons of other traders and make nferences that mpact the ntensty of ther order submsson durng the market preopenng perod? If so, then order submssons should tend to cluster durng the preopenng, snce all traders act off the same nformaton. We further explore whch specfc nformaton from the order book s most sgnfcant n determnng the drvng factor behnd the submsson of lmt orders by traders. Addtonally, we seek to determne f dfferent sdes of the market are more or less mpacted by what can be nferred durng the preopenng perod. We make two key contrbutons to the lterature. Frst, prevous work on market preopenng (such as Vves, 1995; Medrano and Vves, 2001; Madhavan and Panchapagesan, 2000; Barclay and Hendershot, 2003; and Bass, Hllon and Spatt, 1999) mostly focuses on determnng the presence of prce dscovery and how t s mpacted by dfferences n the characterstcs of exchanges. To our knowledge we are the frst to model and explan the ntensty of buy and sell order submssons durng the market preopenng perod. Further, we determne the factors that are most mportant n drvng the ntensty of order submssons durng a perod of no actve trade executon. In addton, the theoretcal lterature on the market preopenng proposes that nformaton asymmetry drves order actvtes durng ths perod. In our analyss, we formulate and test hypotheses that are reflectve of nformaton asymmetry to determne f there s suffcent evdence to support the theoretcal predctons. Second, our model focuses solely on explanng lmt order submssons and thus provdes further nsghts nto the reasons why traders submt orders durng the preopenng perod. Prevous studes (Engle and Lunde, 2003; Bauwens and Got, 2000; and Hall and Hautsch, 2007) analyse the ntensty of order submssons durng the regular tradng perod, necessarly ncorporatng factors such as market orders and trade executon ntenstes to explan lmt order submssons. Snce we analyse the preopenng perod, we focus entrely on the effects of lmt order submssons and changes to the lmt order book on the ntensty of further order submssons. To analyse the preopenng order submsson processes, we model the bd and ask duraton processes separately usng the Log-ACD model proposed by Bauwens and Got (2000). A key advantage of ths approach s that t allows the ncorporaton of addtonal factors nto the 2

5 condtonal expectaton equaton of the ACD model wthout the necessty of mposng postvty constrants on the coeffcents. In addton, the error structure s assumed to follow a Webull dstrbuton, whch allows for some degree of flexblty n the hazard functon. To determne the mpact of actvty n the lmt order book and ncomng orders, we ncorporate explanatory varables nto the condtonal expected duraton equaton that reflect the mpact lmt order arrval, the current spread, md-quote volatlty and revsons or cancellaton of orders prevously submtted to the lmt order book. In order to present a clearer nterpretaton for the arguments beng proposed, we formulate the arguments around order submsson ntenstes as opposed to duratons. The ntensty s the recprocal of expected duraton and represents the nstantaneous rate at whch orders arrve to the lmt order book. The emprcal results reveal that the ntensty of buy order submssons react more to nformaton regardng the nformaton content of an ncomng order and any changes to the state of the current order book when compared to the reacton of the sell order ntensty. In fact, we fnd that the greater the prce of an ncomng bd order relatve to the best bd prce, then the greater the ncrease n the ntensty of bd order submssons. However, there s no substantal evdence that the ntensty of ask order submssons s affected. Whenever the prce of an ncomng ask order s small relatve to the best ask prce, ths concdes wth a perod of low sell order submsson ntensty. Ths reducton n sell order ntensty s attrbutable to sell sde traders tryng not to propel addtonal negatve sgnal nto the market. However, there s no evdence that the prce assocated wth an ncomng ask order mpacts the ntensty of bd order submssons. Addtonally, we fnd that the ntensty of bd (ask) order submssons ncreases (decreases) whenever the prce assocated wth an ncomng bd order s greater than or equal to the best ask prce, thus resultng n the spread beng locked or crossed. Smlarly, when the prce of an ncomng ask order s equal to or less than the best bd prce, ths ncreases the ntensty ask order submssons and reduces the submssons of bd order submssons. Essentally, ths fndng s consstent wth that of Cao, Ghysels and Hatheway (2000), who conclude that a locked or crossed nsde spread s ndcatve of nformaton based tradng. Changes made to the lmt order book, such as cancellatons and revson of prevously submtted lmt orders have a mxed mpact on the ntensty of order submssons. For nstance, we fnd that the cancellaton of a bd or ask order has a negatve mpact on the ntensty of both the bd and ask order submssons. In addton, the volume assocated wth a cancelled ask order ncreases the ntensty of ask submssons as traders take the opportunty 3

6 to submt sell orders when volume s removed from the order book. On the bd sde, we fnd that the volume assocated wth a cancelled bd or ask order reduces the ntensty of bd order submssons. In effect, ths ndcates that traders cancel bd orders n an envronment of low bd submssons and as a result traders on the sell sde tend to reduce the number of sell orders n the book snce the demand for lqudty s low. Revsons of prevous order do not seem to have a consstent mpact on the ntensty of bd order submssons and do not sgnfcantly affect the ntensty of sell order submssons. The remander of the paper s organzed as follows: n secton 2 we outlne the economc ntuton and derve testable hypotheses based on the exstng lterature. Secton 3 descrbes the econometrc methodology whle secton 4 provdes detals of the data and the explanatory varables. Secton 5 reports and dscusses the emprcal results and secton 6 concludes these fndngs. 2. Economc Intuton and Testable Hypotheses 2.1 Is there evdence of clusterng n the bd and ask quote duraton processes durng the preopenng perod? The market preopenng perod serves as an nformaton aggregaton process after a halt n the tradng due to an overnght or weekend closng of the exchange. Durng ths perod, traders who receve prvate nformaton about the fundamental value of the asset devse strateges to explot ther nformatonal advantage snce there s no executon of trades. However, by placng lmt orders, nformed traders nadvertently reveal a porton of ther prvate nformaton. In an open lmt order book market, prvate nformaton s revealed as every trader observes the actons of other traders n an effort to determne the drecton of prces and form expectatons about the fundamental value of the asset. Informaton revelaton s further amplfed durng preopenng snce there s no executon and traders have the opton to cancel or revse prevous quotes wthout any cost or oblgatons. As such, unnformed traders observe the order flow and any adjustments to prevous orders and form expectatons about the potental openng prce for the asset. For nstance, n Vves (1995), compettve nformed traders and nose traders submt lmt orders to buy or sell an asset durng the preopenng perod wthout knowng whether ther trades wll be executed at the openng of tradng. However, towards the end of the preopenng perod, nformed traders reveal a sgnfcant 4

7 porton of ther prvate nformaton through lmt order submssons contnuously mprovng the nformaton set of other traders. As a result, the relatvely rapd eroson of the prvate nformaton set dramatcally reduces the ncentve for nformed traders to post further quotes towards the end of the preopenng perod. Vves (1995) predcts that the ntensty of both the bd and ask order processes ncreases durng the early stages of the preopenng and through contnuous revelaton of nformaton about the fundamental value of the asset by nformed traders, the ntensty of both order processes dmnshes towards the end of the preopenng. However, ths predcton rests on the assumpton that unnformed traders learn about the fundamental value of the asset by observng the order flow from the ncepton of the preopenng perod towards the openng of trade. As a result, ths assumpton s not supported by the emprcal fndngs of the preopenng perod by Bass, Hllon and Spatt (1999), who fnd that there s no evdence of learnng durng the early stages of the preopenng only durng the last half an hour of the preopenng perod. Consequently, two possble scenaros can be contemplated. On the one hand, the nformed traders may decde not to submt orders durng the early stages of the preopenng and only submt ther nformaton based orders close to the end of the preopenng perod. Utlsng such a strategy elmnates both the revelaton of nformaton and learnng by other market partcpants durng the early stages of the preopenng perod. However, towards the end of the preopenng perod when nformed traders begn to submt ther nformaton based quotes the learnng process resumes and the ntensty of the quote processes ncreases. On the other hand, the nformed traders mght act strategcally and nduce addtonal nose n the early stages of the preopenng perod. Actng strategcally, nformed traders ntentonally nduce dstortons nto the learnng process of the unnformed traders dmnshng ther ablty to form expectatons about the fundamental value of the asset from the order flow. Medrano and Vves (2001) show that when manpulatve behavor s ncorporated nto the nformaton aggregaton process the strategc nformed trader posts contrary orders durng the early stages of the preopenng ntendng to offset the nformaton revealed when other compettve nformed traders submt orders. However, towards the end of the preopenng perod, the strategc nformed trader reverses the contrary orders and places orders consstent wth ther nformaton set. As a consequence, contrary to the predctons of Vves (1995), Medrano and Vves (2001) post that manpulatve behavor by an nformed trader causes the ntensty of order submsson to ncrease towards the end of the preopenng perod. 5

8 The predctons presented above are conflctng wth regards to whch stage of the preopenng that s charactersed by an ncrease n the order submsson ntensty. However, they make one smlar concluson that there s tendency for clusterng of order submsson durng the preopenng perod due to nformed tradng. Further, f the prvate nformaton set of the trader mples a hgher fundamental value than the prce mpled by the market, then the ntensty of order submssons wll be more focused on the bd sde of the market and vce versa. However, f prvate nformaton arrves randomly to the market then both sdes should dsplay smlar degrees of clusterng. Therefore, n such a stuaton the ntensty of orders on both sde of the market wll be examned separately. The testable mplcatons are as follows: (a) The preopenng perod exhbts clusterng n the bd and ask order submsson processes. (b) The ntensty of the bd and ask submsson processes wll dsplay smlar levels of clusterng. 2.2 The mpact of lmt order prces on the ntensty of the bd/ask order processes Submttng lmt orders reveals the wllngness of a trader to purchase or sell a number of unts at a specfc prce. Both the prce and the volume that consttutes the lmt order contan sgnfcant prvate nformaton about the trader s valuaton of the asset. However, n the preopenng perod, snce there s a sgnfcant delay between the submsson of orders and the executon of tradng, the trader s valuaton becomes publc nformaton before any potental benefts can be realsed. Thus wth each lmt order submsson market partcpants revse ther expectatons about the probable fundamental value of the asset and devse strateges to proft from ther updated nformaton set. For nstance, n the case where the lmt order s placed by an nformed trader, the unnformed trader wthout knowng the type of trade (nformed or lqudty motvated) that s submtted, assesses the aggressveness of the order based on ts characterstcs. As a result, f the unnformed trader nfers that the quote s nformaton based then ther order strategy wll reflect the updated nformaton set. Hence, we predct that the ntensty of the order processes wll be affected by the nformaton that can be nferred from the posted lmt orders. Though the prces assocated wth lmt orders contan sgnfcant nformaton about traders valuaton of the asset, ths nformaton cannot be revealed n solaton. In effect, the nformaton that s nferred from the prce of an ncomng lmt order s n relaton to the prce 6

9 of the best bd/ask order n the lmt order book. To determne the relatonshp between the prce assocated wth an ncomng lmt order and the bd/ask order ntensty, we follow applcable arguments from Hall and Hautsch (2007). In ther analyss, the ntensty of the buy and sell arrval process n the lmt order book of the Australan Stock Market s estmated usng an Autoregressve Condtonal Intensty (ACI) model. They argue that when a trader submts a lmt buy order wth a prce that s hgher than the current best bd, ths reveals that the trader s more aggressve to get ther order executed and places a hgher valuaton on the asset. Hall and Hautsch (2007) further argues that a trader who sets the bd lmt prce above the prevalng best bd prce ndcates that they are only faced wth a low adverse selecton rsk and dsplays an upper tal expectaton that s hgher than the best bd prce. Effectvely, ths wll consttute a postve sgnal to the market and as a result the net buyng pressure s expected to ncrease. 3 Smlarly, when the prce of an ncomng ask lmt order s set above the best ask, ths conveys a postve sgnal n that the trader s upper tal expectaton s hgher than the prevalng best ask prce. Accordngly, the net buyng pressure s expected to ncrease. In addton, the converse of these relatonshps also holds true, n that, the prce of an ncomng lmt bd (ask) order that s set below the current best bd (ask) represents a negatve sgnallng effect and as a result, the net buy pressure s expected to decrease. However, wthn the context of the preopenng perod we further argue that due to the absence of trade executon, the magntude of the dfference between the prce of the ncomng bd (ask) and the best bd (ask) prce has a more relevant mpact on the ntensty of the order processes. For nstance, f there s manpulaton by an nformed trader durng the preopenng perod such as n Medrano and Vves (2001), then the manpulatve trader wll mplement negatve sgnallng strateges to offset any postve sgnal revealed by other nformed traders. In essence, f the nformaton s consstent wth a hgher fundamental asset value, the strategc trader would mpose a negatve sgnal by placng ask lmt orders. Thus, for the effect to be strong or credble the prce of the lmt ask orders must be close to or lower than the prce of the best ask. The converse of ths argument also holds true. However, as Medrano and Vves (2001) show, towards the end of the preopenng perod the strategc trader s compelled to place orders that are n lne wth the prvate nformaton n order for the strategy to yeld a postve payoff. Therefore, towards the end of the preopenng perod the strategc trader wll 3 Hall and Hautsch (2007) defne the net buy pressure as the rato of the estmated buy and sell ntenstes. 7

10 submt bd orders and n order to ncrease the probablty that ther orders are executed at the openng, the prce of the lmt order must be close to or greater than the best bd prce. The more aggressve the strategc trader s the hgher the prce of the submtted bd lmt order. Alternatve, n terms of the Vves (1995) framework whch does not ncorporate manpulatve behavor by an nformed trader, the mpact of the prce of an ncomng lmt order and the ntensty of the order processes wll be the same as expressed above, though the arguments are dfferent. Essentally, Vves shows that the order flow conveys sgnfcant nformaton about the traders valuaton of the asset from whch other traders can nfer and learn about the fundamental value of the asset throughout the preopenng perod. Therefore, an nformed trader wll ncrease the probablty that ther order s executed by submttng lmt orders wth prces that are close to or greater (less) than the best bd (ask) prce. We propose that unnformed traders that notce ths trend wll adjust ther order strateges n a smlar fashon and as such the ntensty of the bd or ask orders wll ncrease. Consequently, ths process wll contnue recursvely untl prces converge to ther fundamental value, at whch the ntensty of orders by nformed agents reduces dramatcally due to the eroson of ther prvate nformaton. The mplcaton s that the more aggressve a trader s n gettng ther bd order executed at the openng, then the hgher dfference between the prce of the best bd and the prce of an ncomng bd order. Accordngly, f a trader s aggressvely seekng to get ther ask order executed at the openng, then the dfference between the prce of ther ncomng lmt order and the best ask wll be hgher. The same arguments are applcable f a strategc trader ntentonally nduces a negatve sgnal to offset the nformaton that s revealed by other nformed traders. Thus n both cases, due to the presence of nformed tradng and learnng by unnformed traders, the ntensty of the order processes wll be postvely mpacted the greater the dfference between the prce of the lmt order and the prce of the best bd/ask. From these arguments we propose three testable hypotheses. (c) The ntensty of bd order submssons ncreases wth the dfference between the best bd prce and the prce of an ncomng bd order. (d) The ntensty of ask order submssons decreases wth the dfference between the best bd prce and the prce of an ncomng bd order. 8

11 (e) The ntensty of ask order submssons ncrease wth the dfference between the prce of an ncomng ask order and the best ask prce. (f) The ntensty of bd order process decreases wth the dfference between the prce of an ncomng ask order and the best ask prce. 2.3 The mpact of locked or crossed nsde spreads on the ntensty of the bd/ask process Durng the regular tradng perod, a trade s executed whenever the prce assocated wth an ncomng bd (ask) order s equal to or greater (less) than the prevalng best ask (bd) prce n the lmt order book. Essentally, ths makes t mpossble for the prce of the best bd to be equal to or greater than the prce of the best ask n the lmt order book. However, durng the preopenng perod there s no executon of traders takng place. As a consequence, the prce of an ncomng bd (ask) can be set at or above (below) the best ask (bd) whch results n a locked or crossed nsde spread. A locked nsde spread refers to the stuaton were the prces of the best bd and ask are equal. Accordngly, a crossed nsde spread refers to the stuaton where the best bd s greater than the best ask n the lmt order book. Cao, Ghysels and Hatheway (2000) examnes the mpact of locked and crossed nsde spread on the prce dscovery process of the Nasdaq market preopenng perod and fnds that when the market s locked or crossed, sgnfcant nformaton s beng revealed about the fundamental value of the asset. Therefore, we argue that a trader who locks or crosses the nsde spread by submttng a bd lmt order that s equal to or greater than the best ask, sends a postve sgnal by revealng that ther valuaton for the asset s ether equal to or greater than the prevalng best ask prce. Addtonally, by employng such an aggressve strategy to ncrease the probablty that ther order s executed at the openng of trades also ncreases the probablty that the trader possesses prvate nformaton about the fundamental value of the asset. Consequently, ths should postvely mpact the ntensty of the bd order submssons and negatvely mpact the ask order process, snce the nformaton s on the bd sde of the market. However, based on the same arguments, f the market s locked or crossed by an ncomng ask order, then ths sends a negatve sgnal regardng the fundamental value of the asset. Thus, the ntensty of the bd submssons s expected to be negatve mpacted and the ntensty of the ask order submssons postvely mpacted. The testable hypotheses n ths stuaton are as follows: 9

12 (g) The ntensty of bd order submssons s postvely mpacted when the nsde spread s locked or crossed by an ncomng bd order. (h) The ntensty of ask order submssons s negatvely mpacted when the nsde spread s locked or crossed by an ncomng bd order. () The ntensty of ask order submssons s postvely mpacted when the nsde spread s locked or crossed by an ncomng ask order. (j) The ntensty of bd order submssons s negatvely mpacted when the nsde spread s locked or crossed by an ncomng ask order. 2.4 The mpact of ncomng lmt order volume on the ntensty of the bd/ask process The volume that s assocated wth a submtted lmt order s sad to be related wth nformed tradng as relatvely hgher volume s an ndcaton of a trader s aggressveness to proft from prvate nformaton [O Hara (1997)]. Specfcally, order flow durng the preopenng perod s vtal n the nformaton aggregaton process as market partcpants can nfer valuable nformaton about the fundamental value of the asset. In both Vves (1995) and Medrano and Vves (2001), order flow durng the preopenng represents an mportant varable n the determnaton of the prces set durng the perod. In other words, the prce at each pont durng the preopenng s condtonal upon the order flow that emanates from the traders. They show that an ncrease n order flow sgnfes the arrval of prvate nformaton and prces are mpacted accordngly. In essence, order flow s a major conveyor of nformaton regardng the fundamental value of the asset, from whch unnformed traders can make nferences. There are a few ponts here to note, frst, n Vves (1995) order flow durng the preopenng perod frst ncreases and then dmnshes towards the end of the preopenng as more and more nformaton about the fundamental value of the asset s revealed by the nformed traders. In the lmt, prces equal ther fundamental value and nformed traders have no ncentve to place addtonal orders snce ther nformaton advantage has been eroded. Second, Medrano and Vves (2001) contend that due to the manpulatve behavor of the strategc nformed trader, order flow durng the preopenng perod wll be U shaped due to the submsson of manpulatve orders durng the early stages of the preopenng and then the resubmsson of serous orders towards the end of the preopenng perod. They further 10

13 predct that the ntensty of order submsson ncreases towards the end of the preopenng perod. However, both Vves (1995) and Medrano and Vves (2001) predct that the ncreased order flow wll be postvely related to the ntensty of the order processes durng the preopenng perod. Essentally, the mpact here s twofold. Frst, f volume s a purveyor of prvate nformaton durng the market preopenng perod, then the volume assocated wth an ncomng bd (ask) lmt order wll be postvely related to the ntensty of the bd (ask) order process and nversely related to the ntensty of the ask (bd) quote process. In essence, a hgh order volume on the bd sde ndcatve of prvate nformaton that s reflectve of a hgher fundamental value compare wth the present prces, whch leads to a tendency for the ntensty of the bd quote process to ncrease. However, snce there s no tradng durng the preopenng perod, other traders n the market observe ths trend, and learn from the order flow. Hence, under the assumpton of learnng, hgh order flow on the bd sde of the market should reduce the ntensty of orders on the ask sde of the market and vce versa. Therefore, the testable hypotheses are as follows: (k) The ntensty of bd order submssons ncreases wth the volume of an ncomng bd order. (l) The ntensty of ask order submssons decreases wth the volume of an ncomng bd order. (m) The ntensty of bd order submssons decreases wth the volume of an ncomng ask order. (n) The ntensty of ask order submssons ncreases wth the volume of an ncomng ask order. 2.5 The mpact of order revsons and cancellatons on the bd/ask ntensty Lmt orders that are submtted durng the preopenng perod are non-bndng and traders have the opton to cancel or revse ther order wthout cost or oblgaton anytme before the order s flled at the openng. An order revson corresponds to any modfcaton that a trader makes to a prevous order that does not alter the type of order (bd or ask). For nstance, f a trader changes the prce or volume of a prevously submtted order, then ths consttutes a 11

14 revson. However, f a trader contemplates modfyng the type of order from say a buy to a sell, then the order wll have to be cancelled and the desred type of order submtted. The exact reason for a cancellaton wll be unknown snce there are a varety of reasons that can be contemplated when an order s cancelled. For nstance, f a strategc trader possesses prvate nformaton about the fundamental value of the asset n the framework of Medrano and Vves (2001), the strategc trader submts lmt orders durng the early stages of the preopenng that are contrary to what s mpled by ther prvate nformaton. If the strategc nformed trader s to proft from the prvate nformaton, the contrary orders need to be cancelled and an order reflectve of the prvate nformaton s submtted. In essence, the cancellaton of a prevous order wll be assocated wth an nformed event and as such should have a sgnfcant mpact on the ntensty of the bd/ask process. Alternatvely, f the nformaton aggregaton process commences towards the end of the preopenng perod as n Bass, Hllon and Spatt (1995), then ths provdes addtonal reasons for cancelatons and revsons. Essentally, ther analyss found that towards the end of the preopenng perod quotes become nformatve and reflects learnng among traders. Therefore, unnformed at ths tme wll be able to form more nformed estmaton about the fundamental value of the asset and as such wll modfy ther prevous orders to reflect ther updated nformaton set. Thus, f the prce of ther ntal order was under or over estmated then they wll revse ther orders close to ther latest estmaton of the fundamental value. Addtonally, f based on the nformaton that s beng revealed by the nformed traders, unnformed traders realses that they are on the wrong sde of the market, whch therefore means that the prevous order wll have to be cancelled and a new order submtted. Nonetheless, under these assumptons, cancelaton and/or revson of a prevously submtted order s nformaton drven and wll sgnfcantly mpact the ntensty of the order processes. The man mplcatons are, frst, the cancellaton of a prevous bd order s expected to negatvely mpact the bd order ntensty and postvely mpact the ask order ntensty. Accordngly, the cancellaton a prevous ask order s expected to negatvely mpact the ask order ntensty and postvely mpact the bd order process. The argument here s that n lght of learnng, a cancelled order mples that the trade drecton of the trader s order strategy has changed sgn. In essence, the trader may nfer that the nformaton flow s concentrated on the opposte sde of the market and therefore no longer have an nterest n ther current order. Further, we expect that the mpact should be more sgnfcant the hgher the volume 12

15 assocated wth the cancelled lmt order and f the order that s beng cancelled s the best bd or ask n the order book. Second, the mpact of a revsed order wll be dependent on the drecton of the change n relaton to the best bd/ask order. If the lmt bd prce s revsed upwards closer to the best bd then ths represents a postve sgnal that the trader has placed an mproved valuaton on the asset, whch may be a result of learnng, and as such should have a postve relaton wth the ntensty of the bd order process. The converse of ths argument should also hold true n the case of the ask order process. We therefore post that on the one hand, a revson of a bd order prce n the drecton of the best bd wll ncrease the ntensty of the bd order submssons and reduce the ntensty of the ask order submssons. On the other hand, f there s a revson n a prevous ask order prce n the drecton of the best ask then ths bears a negatve sgnal and as such should ncrease the ask order ntensty and reduce the bd order ntensty. In addton, the magntude of these relatonshps should also be ncreasng n the volume of the order beng revsed and f the revsed order s the best bd or ask. Thus the testable hypotheses are as follows: (o) The cancellaton of a bd order negatvely mpacts the ntensty of bd order submssons and postvely mpacts the ntensty of ask order submssons. Ths mpact ncreases wth the volume of the cancelled bd order and when the cancelled bd order s the best bd. (p) The cancellaton of an ask order negatvely mpacts the ntensty of ask order submssons and postvely mpacts the ntensty of bd order submssons. Ths mpact ncreases wth the volume of the cancelled ask order and when the cancelled bd order s the best bd. (q) The revson of a bd order prce closer to the best bd prce ncreases the ntensty of bd order submssons and reduces the ntensty of ask order submssons. Ths mpact ncreases wth the volume of the revsed bd order and when the revsed order s the best bd. (r) The revson of an ask order prce closer to the best ask prce ncreases the ntensty ask order submssons and reduce the ntensty of bd order submsson. Ths mpact ncreases wth the volume of the revsed ask order and when the revsed order s the best ask. 13

16 2.6 The mpact of the bd-ask spread and md-quote volatlty on the bd/ask process In a lmt order market the nsde spread s computed by fndng the dfference between the prces of the best bd and best ask order n the order book. Ths measure s closely assocated wth the level of lqudty n the lmt order book. Essentally, a wde spread s ndcatve of low market lqudty and a narrow spread ndcates a relatvely hgh level of lqudty n the market. In the context of the preopenng perod n whch there s no actve executon of trades, the best bd represents the hghest valuaton that a trader has placed on the asset under consderaton. Smlarly, the best ask s the lowest prce that a trader s wllng to sell the same asset. Therefore, we can argue that f the hghest value to buy s close to the lowest value that a trader s wllng to sell, then ths should sgnfy a greater level of lqudty n the market. 4 As a consequence, we expect the ntensty of both the bd and the ask order processes to also be postvely mpacted by a narrow spread. In essence, wth greater level of lqudty supplers n the market, t should hold true that the ntensty of the order process also ncreases. Another source for nference used by traders durng the preopenng s the past behavor of order prces durng the perod. Under the assumpton of learnng, traders observe the evoluton of prces as a bass to form ther own expectaton of the fundamental value of the asset. In fact, the preopenng perod s preceded by a halt n the tradng process whch may have resulted n varaton n traders expectatons about the fundamental value of the asset when trade resumes. As a consequence, the dfferences n expectatons that manfest tself durng the order submsson process should provde sgnfcant nformaton about the drecton of the asset s fundamental value when observed by unnformed traders. Further, as market partcpants learn from these dfferences n valuaton that are realsed over tme and the drecton of the fundamental value can be nferred, they wll begn submttng orders. Consequently, we expect the ntensty of both the bd and the ask order submssons to ncrease. To measure the mpact of varaton n expectaton about the fundamental value on the ntensty of the bd and ask order processes, we use the md quote volatlty as a proxy. In essence, f there s a hgh level of varaton n valuaton (or uncertanty) about the fundamental value of the asset after the overnght or weekend halt n the tradng process, then 4 A smlar argument s artculated by Hall and Hautsch (2007). They argue that the nsde spread drectly affects the ntensty of the trade process on both sdes of the market. However, they do not present a case for the response to the quote processes. 14

17 ths should be reflected n the volatlty of the md-quote. We therefore expect that n lght of learnng, a hgh md-quote volatlty should have a negatve mpact on both the bd and ask order submsson ntensty. Therefore, the testable hypotheses n ths case are as follows: (s) The ntensty of both the bd and ask order submssons should decrease when there s an ncrease n the nsde spread. (t) The ntensty of both the bd and ask order submssons should be postvely mpacted when there s a decrease n the volatlty of the md-quote. 3. Econometrc Methodology 3.1 The ACD Model To model the bd and the ask order duraton processes we utlse the Log ACD model of Bauwens and Got (2001), whch s an extenson of the ACD model frst ntroduced by Engle and Russell (1998). To present a clear case for the use of the Log ACD model we frst dscuss the theoretcal underpnnngs of the basc ACD framework. In the model proposed by Engle and Russell (1998), the seres { t, t t } 1 represents the clock tme that quotes are 1,..., posted and the duraton of each quote relatve to the occurrence of the prevous quote s defned as x = t t 1. Engle and Russell (1998) further defne ψ as the condtonal expectaton of the th duraton, such that ψ = ψ x,..., x ; θ ) E( x x,..., ), where θ ( 1 1 = 1 x1 s a vector of parameters. In addton, they propose that the th duraton s the product of the condtonal duraton at perod and an ndependently and dentcally dstrbuted (d ) varable ε, such that x = ψ ε, where ε ~ d wth densty functon f (, φ) where φ s a ε parameter vector. By constructon, the error structure for the ACD model s defned as ε =, where E( ε ) = 1. x ψ In order to derve the framework for modellng the condtonal duraton ψ, Engle and Russell (1998) assume that the duratons are condtonally exponentally dstrbuted and as such the hazard functon s constant and equal to one. Specfcally, the hazard functon λ ( ) s the rato of the probablty densty functon P ( ) to the survval functon S ( ), such that 0 t 0 t 0 t 15

18 λ t ) = P ( t) S ( ). 5 They further propose that the condtonal ntensty of the ACD model 0( 0 0 t can be expressed as ( t ( t), t,..., t λ ( t t ψ )( ψ ) 1 1 ( t) ) = 0 ( t ) ( t ) + 1 ( t ) + 1 λ, where (t) s a countng functon, t (t ) and ψ (t ) are the tme and condtonal duraton when the countng functon s evaluated respectvely. 6 Therefore, f the survval functon λ ( ) s assumed to be equal to one by mposng the assumpton of exponentally dstrbuted duratons, then the 1 condtonal ntensty becomesλ ( t x,..., x ψ. As a result, Engle and Russell (1998) ( t) 1) = ( t) + 1 propose the followng parameterzaton for the condtonal duraton process whch s referred to as the Exponental ACD (EACD) model: EACD(m,q): m α j x j β = jψ = + + q ω j= 1 j 1 ψ (1) where ω, α, β 0 snce ψ 0 and for statonarty α +β < 1 However, Engle and Dufour (2000) argue that the standard ACD specfcaton n equaton (1) has several dsadvantages. For nstance, the mposton of a lnear parameterzaton structure for the condtonal duraton ψ combned wth the non-negatve attrbute of duratons n general, necesstates postvty constrants when estmatng the model coeffcents ( ω, α, β ). Wthout ths constrant t would be possble for the model to predct negatve duratons. Ths problem s further amplfed f addtonal explanatory varables whch are negatvely related to the duraton process are ncluded n the ACD structure. An attempt to crcumvent ths problem s proposed by Bauwens and Got (2000) n ther Log- ACD model. Estmatng the log of the condtonal duraton (logψ ) nstead of the condtonal duraton ( ψ ), elmnates the need to place postvty restrctons on the coeffcents. In addton, by estmatng the log of the condtonal duraton the autocorrelaton wll exhbt a more approprate hyperbolc decay and as such wll be able to capture a greater degree of persstence n the duraton seres. Bauwens and Got (2000) propose the followng structure for the parameterzaton of the Log-ACD model, whch they referred to as the Log 2 ACD model. 7 j 0 5 If F ( ) s the cumulatve probablty dstrbuton correspondng to the probablty densty P ( ), then the 0 T 0 t survval functon S0( t) = 1 F0 ( t). 6 See Engle and Russell (1998) for a complete outlne and explanaton of these arguments and ther proofs. 7 Bauwens and Got (2000) also propose an alternatve parameterzaton Log 1 -ACD whch s not consdered here. 16

19 + j= 1 j= Log 2 ACD(m,q): ( ) = + m q expω α jε j β j lnψ j where β < Error Dstrbuton ψ (2) 1 Another mportant pont n the estmaton process s that ε ~ d wth probablty densty functon f (, φ), where φ s a coeffcent vector whch determnes the shape of the ε dstrbuton. However, due to the non-negatve nature of duraton data seres n general, f (, φ) should have a non-negatve support whch restrcts the dstrbutons that can be ε consdered. In the basc model, Engle and Russell (1998) propose the use of the exponental dstrbuton for the densty functon. Essentally, assumng exponentally dstrbuted error terms mposes a flat hazard curve on the condtonal duraton structure whch s tested and rejected n the emprcal analyss of Engle and Russell (1998). They argue that greater flexblty s needed n the hazard functon and estmate the standard ACD model assumng a Webull dstrbuton resultng n the Webull ACD (WACD) model. To ncorporate a more flexble hazard functon n the ACD structure, dfferent dstrbutons have been proposed. For nstance, Dufour and Engle (2000) mplement the Generalsed Gamma dstrbuton, Grammg and Maurer (2000) proposes the use of the Burr dstrbuted error structure and Hautsch (2002) employs the Generalsed F dstrbuton for the ACD specfcatons. The Exponental and Webull dstrbutons are specal cases of the Burr, Generalsed Gamma and Generalsed F dstrbutons. However, due to the complexty of these dstrbutons, not all moments may exst wthout placng restrctons on the dstrbuton parameters durng the estmaton process, complcatng the estmaton process of the models under consderaton. Consequently, due to the number of parameters to be estmated n ths analyss, we wll assume a Webull dstrbuted error structure (equaton (3)) so as to mnmse the number of estmated parameters and the complexty of the estmaton process. Addtonally, by ncorporatng addtonal explanatory varables nto the condtonal expectaton equaton, we expect that a greater amount of the persstence wll be captured by the model, whch makes utlsng a more flexble dstrbuton unnecessary. 17

20 f γ ( 1 1γ) xγ( 1+ 1γ) γ γ x Γ + 1,..., x ; θ ) exp (3) x ψ ψ ( x x 1 where γ s a non-negatve parameters related to the slope of the dstrbuton and Γ ( ) s the gamma functon. 3.3 Estmaton and Inference Snce x represents the pooled process of the bd and ask order duratons, let a t and t b be the clock tme assocated wth the submsson tme of an ask order and a bd order respectvely. Therefore, the duraton of a specfc order to the next order of the same type s k k k x t t 1 =, where k = a, b. Thus, the condtonal expectaton of the duraton of type k s defned as ψ, k such that k ε = and E( ε ) = 1. For smplcty, we ncorporate only one lag of the k k k x ψ error and condtonal expectaton n the model, whch s refer to as the LogACD(1,1). Addtonally, gven we wsh to explan the fundamental drvers of the order submsson processes, addtonal factors enter nto the condtonal expectaton equaton. Let k Z 1 be a vector of explanatory varables that are know at tme t 1 wth correspondng parameter k vector η : k k k k k k k ( ω + α ε + β ψ Z η ) k ψ exp 1 ln 1+ 1 = (4) The augmented LogACD(1,1) model s estmated usng maxmum lkelhood mplementng the BHHH algorthm. The log-lkelhood functon s: L= k k k x Γ + (1 1/ γ ) ln( γ ) ln( x + Γ + ) γ ln[ x (1 1/ γ )] γψ (5) ψ 4. Data and Explanatory Varables The data used n ths analyss s extracted from the Maltese Stock Exchange hstorcal data base over the perod January 2000 to June The Maltese Stock Exchange s an electronc contnuous lmt order market wth actve executon of trades begnnng at 10:00 am and ends at 12:30 pm. Pror to the ntaton of tradng, the preopenng perod begns at 8:30 am and 18

21 ends at 10:00 am when the clearng algorthm that determnes the equlbrum prces s executed. 8 The sample studed n ths analyss comprses the three most actve stocks durng the market preopenng perod. These are HSBC Bank Malta plc (HSB), Bank of Valletta plc (BOV) and the Malta Internatonal Arport plc (MIA). Table 1 provdes summary statstcs. The total number of events occurrng n the samples s 24,189 for BOV, for MIA and 19,770 for HSB. The events comprse the submsson, revson and cancelaton of lmt orders, whch accounts for approxmately 57%, 12% and 31% of the total n the case of BOV. For MIA, approxmately 50%, 13% and 35% of the total events represents lmt order submssons, cancellaton and revson of orders respectvely. The proportons for HSB are 61% for lmt order submssons, 9% for cancelled orders and 30% of the events represents order revsons. Other events that occur n the data are omtted snce they consttute a very small percentage of the total events and lack any economc nterpretaton. From the summary statstcs n Table 1, t s evdent that there s a hgh degree of persstence n both the bd and ask duraton seres for all three stocks snce the Ljung-Box statstc s hghly sgnfcant even at 30 lags. The HSB bd duraton seres seems to be the most persstent and the ask duratons of HSB appear to be the least persstent based on the Ljung- Box statstc. In fact, the bd duraton seres tend to be sgnfcantly more persstent than the ask duraton seres for all stocks, whch s ndcatve of a buyer s market or the effect of short sale constrants. To test the hypotheses dscussed n secton 2, we construct explanatory varables by recreatng the lmt order book at each pont n tme for the entre sample. Table 2 provdes an outlne of the varables, ther defntons and correspondng coeffcents. We argue n secton 2.2 that the dfference between the prce assocated wth an ncomng bd order and the best bd postvely (negatvely) mpacts the ntensty of the bd (ask) processes. 9 Smlarly, we argue that the dfference between the prce of the best ask order and the prce assocated wth an ncomng ask wll mpact the ntensty of bd and ask order submssons negatvely and postvely respectvely. To capture these mpacts, the varables lbb and lba are ncorporated, to measure the dfference between the log prce of best bd and the log 8 As of 23 October 2006, the preopenng perod changed to 9:30 am to 10:45 am wth the contnuous open from 10:45am to 12:30pm. Ths has been accounted for n our estmaton. 9 For hypothess a and b, whch speaks to the presence of clusterng durng the market preopenng perod, are k tested by examnng the coeffcent ( β ) assocated wth the lagged condtonal expected duraton. 19

22 prce of the ncomng bd order and the dfference between the log prce of an ncomng ask order and the log prce of the best ask n perod respectvely. 10 In secton 2.3, the dscussons hghlght the mpact of a locked or crossed nsde spread on the ntensty of the bd (ask) order process. To test ths hypothess, we construct two varables. Frst, to determne the mpact of an ncomng bd order that lock or crosses nsde spread, we defne the dummy varable bgba, whch takes the value of one when the prce of an ncomng bd s greater than or equal to the best ask prce. Second, to measure the mpact of an ncomng ask order that locks or crosses the nsde spread, we defne the varable albb, whch assgned a value of one when the prce of an ncomng ask order s less than or equal to the best bd prce. Hypothess k n secton 2.4 proposes that the ntensty of the bd order submssons ncreases wth the volume assocated wth an ncomng bd order. However, hypothess l proposes the opposte mpact on the ask submsson, as the volume assocated wth an ncomng bd order negatvely mpacts the ntensty ask order submssons. In addton, hypothess m and l proposes that the volume assocated wth an ncomng ask order postvely mpacts the ntensty of the ask order submssons and negatve mpacts the ntensty of the bd order submssons. To test these hypotheses, the log volume of the ncomng bd order ( lbv ) and the log volume of the ncomng ask order ( lav ) are ncorporated nto the model. To measure the mpact of cancelatons of orders and ther assocated volume on the order submsson processes as proposed n hypotheses o and p n secton 2.5, we defne several varables. Frst, the dummy varables dcb and dca are constructed, whch assgn a value of one f a bd or an ask order s cancelled respectvely. Further, to examne the mpact of the best bd/ask beng cancelled, we defne dcbb and dcba as dummy varables that ndcate when the cancelled order s the best bd or the best ask respectvely. In addton, the mpact of volume assocated wth the cancelled order s measure usng the varables lcbv and whch are the log volumes assocated wth the cancelled bd and ask order respectvely. lcav, In hypotheses q and r, we propose that revson of a bd (ask) order closer to the best bd (ask) postvely mpacts the ntensty of the bd (ask) order submsson and negatvely mpacts the 10 The order of the varables are reversed n ths case snce we want to examne the effect of the prce assocated wth an order gettng close to the best bd/ask. In other words the value of these varables should be closer to zero the closer the order s to the best bd/ask n the lmt order book. 20