Limit Orders, Depth, and Volatility. City University of Hong Kong Kowloon, Hong Kong

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1 Limi Orders, Deph, and Volailiy Hee-Joon Ahn a, Kee-Hong Bae b, and Kalok Chan b a Deparmen of Economics and Finance Ciy Universiy of Hong Kong Kowloon, Hong Kong b Deparmen of Finance Hong Kong Universiy of Science and Technology Clear Waer Bay, Hong Kong Curren version: May 999 *Correspondence: Kee-Hong Bae, Deparmen of Finance, The Hong Kong Universiy of Science and Technology, Clear Waer Bay, NT, Hong Kong, Tel) , Fax: , khbae@us.hk. We are graeful o Warren Bailey, Ira Horowiz, Jun-Koo Kang, Michael Melvin, René Sulz (he edior), an anonymous referee, and seminar paricipans a he Hong Kong Universiy of Science and Technology for heir helpful commens. We hank Karen Lam of he Sock Exchange of Hong Kong for her descripion of he exchange rading sysem. We also hank Sandra Moore for ediorial assisance. Any remaining errors are our own.

2 Limi Orders, Deph, and Volailiy Absrac We invesigae he role of limi orders in he liquidiy provision in he Hong Kong sock marke, which is based on a compuerized limi-order rading sysem. Consisen wih Handa and Schwarz (996), resuls show ha marke deph rises subsequen o an increase in ransiory volailiy, and ransiory volailiy declines subsequen o an increase in marke deph. We also examine how ransiory volailiy affecs he mix beween limi orders and marke orders. When ransiory volailiy arises from he ask (bid) side, invesors will submi more limi () orders han marke () orders. This resul is consisen wih he exisence of limi-order raders who ener he marke and place orders when liquidiy is needed. JEL Classificaion Numbers: G0, G, G3 Keywords: limi orders, marke orders, deph, volailiy, and liquidiy raders.

3 Ineres in limi-order rading has grown rapidly in recen years as i plays a vial role in he liquidiy provision in he world s sock exchanges of differen marke archiecures. In an order-driven marke, such as he Paris Bourse or he Tokyo Sock Exchange, all liquidiy is provided by limi orders submied by naural ers and ers. In a specialis marke, such as he New York Sock Exchange (NYSE), a subsanial amoun of he liquidiy is supplied by public limi orders. For example, Harris and Hasbrouck (996) documen ha 54% of SuperDo orders are limi orders, and Ross, Shapiro, and Smih (996) repor ha limi orders accoun for 65% (75%) of all execued orders (execued shares). Even in a dealership marke, such as he NASDAQ or London s SEAQ Inernaional, some forms of limi-order rading have been inroduced in recen years. Alhough limi-order rading is of paramoun imporance, i was no unil recenly ha researchers began o invesigae in deph he role of limi-order rading in he marke microsrucure. On he heory side, Glosen (994), Kumar and Seppi (994), Chakravary and Holden (995), Handa and Schwarz (996), Parlour and Seppi (997), Foucaul (997), Handa, Schwarz and Tiwari (998), and Viswanahan and Wang (998) develop equilibrium models of he limi order book. On he empirical side, several sudies examine he role of limi order books in supplemening he liquidiy provided by he specialiss in he NYSE. 3 Alhough many sock exchanges around he world are based on pure limi order books, very few empirical papers invesigae he role of limi-order raders in an order-driven marke wihou any designaed marke maker. One noable excepion is Biais, Hillion, and Spa (995), who sudy he compuerized limi-order marke of he Pairs Bourse, invesigaing he dynamics of he order flow and order book. See Lehmann and Modes (994) and Hamao and Hasbrouck (995) for he Tokyo Sock Exchange, and Biais, Hillion, and Spa (995) for he Paris Bourse. NASDAQ marke makers are now required o display cusomer limi orders. The London marke uses an elecronic order book for smaller orders while large orders are sill roued hrough a dealership mechanism. 3 Harris and Hasbrouck (996) compare he performance of marke and limi orders submied hrough he NYSE SuperDo. Greene (996) develops a mehodology for inferring limi-order execuions from ransacions and quoe daa. Kavajecz (999) pariions quoed deph ino he specialis s conribuion and he limi order book s conribuion. Chung, Van Ness, and Van Ness (999) examine he inraday variaion in spreads esablished by limi-order raders.

4 The objecive of his paper is o exend he analysis of he role of limi-order rading in liquidiy provision in a pure order-driven marke. While Biais, Hillion, and Spa (995) examine he inerwined dynamics of he order flow and order book, we focus on he ineracion beween shor-erm volailiy and order flow composiion. The sudy is moivaed by Handa and Schwarz (996), Foucaul (997), and Handa, Schwarz, and Tiwari (998) who model he choice of invesors in placing limi orders and marke orders in a pure order-driven marke. There is no designaed marke maker who is obligaed o provide liquidiy o he marke. Insead, he suppliers of liquidiy are he naural ers and ers hemselves who choose o place limi orders. A he same ime, hese ers and ers could also rade via marke orders and consume liquidiy in he marke. The choice beween limi and marke orders depends on he invesor s beliefs abou he probabiliy of his or her limi order execuing agains an informed or a liquidiy rader. When here is emporary price movemen due o liquidiy shocks, his will arac public raders o submi limi orders raher han marke orders, as he ne gain from supplying liquidiy insead of consuming liquidiy is greaer han he risk of being picked off by informed raders. Therefore, Handa and Schwarz (996) and Foucaul (997) argue ha in an order driven marke, ransiory volailiy affecs he profiabiliy and choice of invesors in placing limi and marke orders. In his paper, we examine he empirical relaions beween he ransiory volailiy and he order flow in a pure order-driven marke. Firs, we invesigae he dynamic relaion beween he ransiory volailiy and he marke deph. According o Handa and Schwarz (996), when here is a pauciy of limi orders so ha here is an increase in shor-erm price flucuaion, invesors will find i more profiable o place limi orders. Such an influx of limi orders provides liquidiy o he marke, so ha shor-erm volailiy will decline. Second, we sudy how he ransiory volailiy affecs he mix of limi and marke orders. In paricular, since he ransiory volailiy could arise from eiher he bid or he ask side, we examine wheher hey have differen impacs on he ers and ers in heir order placemen sraegies. We perform an empirical analysis on he elecronic limi order books of he Hong Kong sock marke. Consisen wih Handa and Schwarz (996), resuls show ha a rise in ransiory volailiy is

5 followed by an increase in marke deph, and a rise in marke deph is followed by a decrease in ransiory volailiy. We also find ha an increase in ransiory volailiy affecs he order flow composiion. However, i is imporan o disinguish beween volailiy arising from he bid side and he ask side, as hey have differen impacs on he and order flows. Evidence indicaes ha more limi orders han marke orders are placed if he ransiory volailiy arises from he bid side, and ha more limi orders han marke orders are placed if he ransiory volailiy arises from he ask side. These resuls are consisen wih he exisence of liquidiy providers who ener he marke and place limi orders on eiher he bid or he ask side, depending on which side will earn profis for he liquidiy provision. Criics of an order-driven rading sysem wihou marke makers ofen argue ha raders can be relucan o ener orders ino he sysem in a volaile marke environmen, since rading via limi orders is cosly when he adverse selecion problem is severe. Conrary o his view, he evidence presened in our sudy indicaes ha here exiss a sufficien number of poenial liquidiy suppliers who are ready o sep in by placing limi orders when liquidiy is mos needed. The evidence is consisen wih he view ha an order-driven rading mechanism wihou he presence of marke makers can be viable and selfsusaining. The paper proceeds as follows. Secion I develops hypoheses on he dynamic relaion beween ransiory volailiy and order flows. Secion II describes he rading mechanism of he Hong Kong sock marke and he daa used. Secion III describes he empirical mehodology and consrucion of variables. Secion IV presens empirical resuls, and Secion V concludes he paper. I. Limi-Order Trading in a Pure Order-Driven Marke In a pure order-driven marke, here is no designaed marke maker who has he obligaion o provide liquidiy o he marke. Invesors can choose o pos limi orders or marke orders. While limi orders are sored in a limi-order book awaiing fuure execuion, marke orders are execued wih cerainy a he posed prices in he marke. Traders face he following dilemma. Wih a limi order, if 3

6 a rade occurs, he invesor will execue i a a more favorable price han a marke order. On he oher hand, here is he danger of he order no being execued. Furhermore, because he limi order prices are fixed, he invesor faces an adverse selecion risk due o he arrival of informed raders. In Glosen s (994) framework, raders can be broadly classified ino wo groups according o heir aiude on immediacy: he paien raders who can pospone heir rading and he urgen raders who need o rade immediaely. The paien raders place limi orders and supply liquidiy o he marke, while he urgen raders place marke orders and consume liquidiy. According o Glosen (994), informed invesors are more likely o be urgen raher han paien raders. There are a leas wo reasons. Firs, he value of privae informaion depreciaes as ime lapses, so an informed rader favors an immediae execuion over waiing. Second, compeiion among he informed raders makes choosing a limi order an inferior sraegy. For example, suppose informed invesor A submis a limi order while anoher compeing informed invesor B undercus he price by submiing a marke order. If invesor B s marke order consumes all he limi orders a he bes ask price, he chance ha invesor A s limi order is execued will be reduced. Given he exisence of informed raders in he marke, Glosen (994) argues ha he paien rader will no choose o place a limi order unless he expeced gain from ransacing wih a liquidiy rader exceeds he expeced loss from ransacion wih an informed rader. Like many oher limi-order rading models, Glosen (994) does no allow raders o choose beween marke and limi orders. For his reason, hese models canno derive implicaions regarding he deerminans of order flow composiion. Foucaul (997) explicily incorporaes an invesor s decision o rade via limi order or marke order, and develops a model in which he mix beween marke and limi orders can be characerized in equilibrium. He finds ha he volailiy of he asse is a main deerminan of he mix beween marke and limi orders. When he asse volailiy increases, he probabiliy of being picked off by informed invesors and he poenial losses o hem are larger. Limi order raders have o pos higher ask prices and lower bid prices relaive o heir reservaion prices in 4

7 markes wih high volailiy. Bu in his case, marke orders become less aracive. Consequenly, more raders use limi orders insead of marke orders when he asse volailiy is high. Handa and Schwarz (996) also examine he raionale and profiabiliy of limi order rading in a rading environmen where invesors could submi eiher limi order or marke order. The choice depends on he probabiliy ha he limi order is execued agains an informed or a liquidiy rader. An imporan difference beween informed rading and liquidiy rading is ha he former riggers permanen price changes, bu he laer resuls in emporary price changes. While execuing limi orders agains he liquidiy-driven price changes is profiable, execuing he orders agains permanen price changes is undesirable. By endogenizing he decision o rade via marke or limi order, Handa and Schwarz (996) illusrae he ecological naure of he pure-order driven marke where he supply of, and demand for, liquidiy can be in naural balance. Suppose here is a pauciy of limi orders. An increase in liquidiy rading will cause a emporary order imbalance and lead o shor-erm flucuaion in ransacion prices. The liquidiy-driven price volailiy will arac public raders o submi limi orders raher han marke orders, as he gains from supplying liquidiy can more han offse he poenial loss from rading wih informed raders. This influx of limi orders will coninue unil shor-erm volailiy decreases and limi-order rading is no longer profiable. In urn, a decrease in volailiy resuls in fewer limi orders, which causes emporary order imbalance. These consideraions lead o he following wo hypoheses: Hypohesis : An increase (a decrease) in shor-erm price volailiy is followed by an increase (a decrease) in he placemen of limi orders relaive o marke orders, so ha he marke deph will increase (decrease) subsequenly. Hypohesis : An increase (a decrease) in marke deph is followed by a decrease (an increase) in shorerm price volailiy. 5

8 II. Descripion of he Marke and he Daase A. The Open Limi-Order Sysem of he Sock Exchange of Hong Kong The Sock Exchange of Hong Kong (SEHK) is a good example of a pure order-driven marke. In he absence of designaed marke makers, securiy prices are deermined by he and orders submied by public invesors. Trading is conduced hrough erminals in he rading hall of he Exchange and hrough erminals a he members office. Orders are placed hrough brokers and are consolidaed ino he elecronic limi-order book and execued hrough an auomaed rading sysem, known as he Auomaic Order Maching and Execuion Sysem (AMS). 4 While an invesor could place a marke order or a limi order o he broker, he rading sysem only acceps limi orders. Thus, he broker submis he cusomer s marke order in he form of a limi order ha maches he bes price on he oher side of he book. Invesors are allowed o cancel or decrease orders a any ime prior o maching, bu hey canno enlarge he order already submied. Trading is conduced on weekdays excluding public holidays and is carried ou on he exchange floor in wo sessions each day, from 0:00 o :30 and from 4:30 o 5:55. Orders in auomach socks are execued on a sric price and ime prioriy basis. Orders are mached following he sequence in which hey are enered ino he AMS, based on he bes price. An order enered ino he sysem a an earlier ime mus be execued in full before he execuion of an order enered a a laer ime a he same price. An order wih a price equal o he bes opposie order is mached wih opposie orders a he bes price queue residing in he sysem, one by one, according o ime prioriy. The queue posiion in he sysem is mainained unil whichever occurs firs: he order is compleely filled, he order is cancelled, or he rading day ends, a which poin all orders are purged from he AMS. 4 Mos of he orders are execued hrough he AMS, alhough a few orders are manually mached hrough brokers. During he one-year period beween July 996 and June 997, auomached rades accouned for 96.4% of all ransacions of he 33 Hang Seng Index componen socks in our sample. 6

9 The order-and-rade informaion is disseminaed o he public on a real-ime basis using an elecronic screen. All brokers are direcly conneced o he AMS sysem. Invesors can obain informaion in real ime hrough he Teleex sysem, a suppor sysem of he Exchange. The AMS displays he bes five bid-and-ask prices, along wih he broker ideniy (broker code) of hose who submi orders a he respecive bid/ask prices being shown, and he number of shares demanded or offered a each of he five bid-and-ask queues. The rading mechanism of he SEHK is similar o he elecronic limi-order marke modeled by Glosen (994). Firs, he marke is fully cenralized and compuerized. The informaion regarding he limi-order book (up o he bes five queues) is immediaely available o all marke paricipans hrough he elecronic screen. This ransparency is no available in some oher limi-order markes in he world. 5 For example, in he Tokyo Sock Exchange, only he members lead offices can observe he orders, and hey are no allowed o disseminae his informaion. In he NYSE, only he bid-ask quoaion is elecronically disseminaed o raders. In he Paris Bourse, orders can be hidden (Biais, Hillion, and Spa (995)). There are no such hidden limi orders in he SEHK. Second, execuion of a rade agains he limi order book occurs in a discriminaory fashion. Tha is, if he size of he marke order is large enough o consume several limi orders a differen prices, each limi order is execued a is own limi price. B. Daa We obain our daa from he Trade Record and he Bid and Ask Record, boh provided by he SEHK. The Trade Record includes all ransacion price-and-volume records wih a ime samp recorded o he neares second. The Bid and Ask Record conains informaion on limi-order prices and order 5 However, here is no consensus on he relaion beween ransparency and liquidiy. See O Hara (995) for discussion. 7

10 quaniy. I racks he number of orders in he same queue and records up o five queues a every 30- second inerval. We focus on he 33 componen socks in he Hang Seng Index (HSI) beween July 996 and June 997. The 33 HSI componen socks are he mos acively raded and provide a reasonable represenaion of he marke, since hey accoun for abou 70% of he oal marke capializaion. Limiing our analysis o he mos acively raded socks in he marke guaranees ha here are enough observaions necessary for our inraday ime-series analysis. Table describes some of he characerisics of our sample firms. The average (median) number of rades per sock per day in our sample is 387 (346), suggesing a high level of rading aciviy in our sample socks. 6 The average (median) dollar spread is $HK0. ($HK0.07). For mos of he socks in our sample, he average dollar spread is abou one ick size. The average (median) percenage spread is 0.47% (0.39%) during he sample period, which is comparable o ha of mos liquid socks in he U.S. For example, Angel (997) repors ha he median bid-ask percenage spread is 0.3% for he Dow Jones Indusrial Average index socks. Figure shows he average levels of quoed deph and volailiy a each 5-minue inerval of he rading day. The saisics are expressed as percenage deviaions from heir respecive full-day averages. The figure shows a U-shaped paern in volailiy as repored in previous sudies. The quoed deph follows a reverse U-shaped paern. This deph paern is consisen wih hose of he NYSE documened by Lee, Mucklow, and Ready (993) and hose of he Paris Bourse by Biais, Hillion, and Spa (995). Overall, Figure underscores he imporance of conrolling he ime-of-he-day effec in invesigaing he relaion beween volailiy and deph. 6 The average (median) number of rades per sock per day for he CAC 40 index socks repored in Biais e al. (995) is 49 (4). 8

11 III. Empirical Mehodology A. Time Inervals In our empirical analysis, we will es he heoreical predicion of Handa and Schwarz (996) regarding he ineracion beween shor-erm price volailiy and order flow. However, he heory does no guide us in choosing he lengh of he ime inerval in he measuremen of volailiy. On he one hand, since we are ineresed in shor-erm price flucuaion caused by order imbalance, he ime inerval should no be oo long, oherwise he volailiy we measure is likely o be permanen raher han emporary. On he oher hand, he ime inerval should no be oo shor, or else here are no enough ransacions ha rigger price flucuaion. Wih hese consideraions, he empirical analysis is conduced based on 5-minue inervals. Each day, rading hours will be pariioned ino fifeen 5-minue inervals, and one 0-minue inerval. This is because he SEHK is open from 0:00 o :30 and from 4:30 o 5:55, so ha he las measuremen inerval is 0 minues long. We do no include an overnigh inerval in our analysis, since all orders in he limi-order book are purged a he end of each daily session. In oher words, all limi orders in he SEHK are day orders and here are no good ill canceled orders. B. Shor-Term Price Volailiy We compue shor-erm price volailiy ( ) in he ime inerval as = N i R i,, where R i, is he reurn of he i h ransacion during ime inerval, and N is he oal number of ransacions wihin he inerval. This price volailiy measure differs from he convenional variance measure N ( (R i, R) N i= ) in a couple of ways. Firs, in compuing, we do no subrac he mean reurn from R i. Implicily, we assume ha he mean reurn is zero, which is quie reasonable considering ha he average reurn wihin he inraday inerval is close o zero. Second, we do no divide he sum of squared reurns by he oal number of observaions. This is because we would like o measure he 9

12 cumulaive price flucuaion wihin he inerval, raher han he average price flucuaion for each ransacion. Neverheless, our shor-erm price volailiy measure will be posiively relaed o he oal number of ransacions. We will herefore have o conrol for he impac of he oal number of ransacions in our empirical analysis. In addiion, we perform robusness es based on an alernaive measure of price volailiy, which we will discuss in Secion IV.D. We furher decompose he ransiory volailiy ino upside and downside measures. The upside volailiy ( ) is compued based on posiive reurn observaions R i, >0 R i,, while he downside volailiy ( ) is based on negaive reurn observaions R Ri, <0 i,. When here is a pauciy of limi orders on he ask (bid) side, he emporary order imbalance resuls in upside (downside) volailiy, and his will encourage public raders o place more limi () orders. C. Marke Deph and Order Flow Throughou he empirical analysis, we measure he deph, order flow and rading aciviy based on he number, insead of he size, of orders and ransacions. This is moivaed by Jones, Kaul and Lipson (994) who show ha he number of ransacions, no he share volume, is a major deerminan of price volailiy. We compile he marke deph (DEPTH ) based on he oal number of limi orders posed a he bid and ask prices a he end of ime inerval. Since he elecronic order books in he SEHK record he ousanding limi orders a he bes five quoes, we can compile he marke deph a any of hese five quoes. In addiion, we compue he deph a he bid and ask quoes respecively ( bid ask DEPTH and DEPTH ). We also calculae he change of marke deph for he inerval ( DEPTH ). There is an ineresing inerpreaion for he variable DEPTH. Suppose we define NPLO as he number of newly 0

13 placed limi orders during ime inerval 7, and NLOE as he number of limi orders ha are execued during he inerval. Then by definiion, DEPTH = DEPTH NPLO NLOE. () Since marke orders mus be execued agains limi orders, and if we define NTRADE as he number of rades (which is also he number of marke orders) during ime inerval, hen NLOE = NTRADE. We can rewrie equaion () as: DEPTH = NPLO NTRADE. () The variable DEPTH provides us informaion on he order flow composiion, ha is, he difference beween he number of newly placed limi orders and marke orders during ime inerval. We will focus on his variable when we examine he relaion beween ransiory volailiy and order flow composiion. We also consruc variables for he mix beween he newly placed limi orders and marke orders for he and sides, respecively. By definiion, he number of marke orders ( NTRADE ) during ime inerval is equal o he number of limi orders execued during he same inerval ( NLOE ). We can obain he number of newly placed limi orders during ime inerval ( ask NPLO ) by adding NTRADE o he change of deph a he ask ( DEPTH ). If we define DIFF as he difference beween he number of newly placed limi orders ( NPLO ( NTRADE ) during ime inerval, i could be compued as: ) and marke orders 7 Since some limi orders are cancelled wihou being execued, NPLO is more accuraely defined as he ne number of newly placed limi orders (i.e., number of newly placed limi orders minus he number of cancelled limi orders).

14 ask DIFF = DEPTH NTRADE - NTRADE. (3) Similarly, by definiion, he number of marke orders during ime inerval ( NTRADE he number of limi orders execued during he same inerval ( NLOE ). We can obain he ) is equal o number of newly placed limi orders during ime inerval ( NPLO ) by adding NTRADE o he bid change of deph a he bid ( DEPTH ). If we define DIFF as he difference beween he number of newly placed limi orders ( NPLO ) and marke orders ( NTRADE ) during ime inerval, i could be compued as: bid DIFF = DEPTH NTRADE - NTRADE. (4) In he empirical analysis, we will relae DIFF and DIFF o he volailiy arising from he ask and bid sides ( and ). The hypohesis is ha if ransiory volailiy arises from he ask (bid) side a ime -, his will encourage public raders o place limi () orders raher han marke () orders a ime, so ha DIFF ( DIFF ) will increase. IV. Empirical Resuls A. Impacs of Transiory Volailiy on Marke Deph To examine he effec of ransiory volailiy on subsequen marke deph, we firs esimae he following regression for each sock:

15 DEPTH 4 = α β θ NTRADE γ ktime k, ρ DEPTH ε (5) where DEPTH is he marke deph (number of ousanding limi orders) a he end of ime inerval, - is he ransiory volailiy during ime inerval -, NTRADE is he number of rades during ime inerval, TIME k, is an inraday dummy variable ha akes he value of one if inerval belongs o he ime inerval k, and zero oherwise. The inclusion of TIME k, and DEPTH - on he righ-hand side is o conrol for inraday variaion and auocorrelaion in he marke deph. Alhough here are sixeen inraday ime inervals every day, we only have fifeen inraday observaions because we use DEPTH - as an explanaory variable. Since we do no assign a dummy variable for one of he ime inervals o avoid mulicollineariy, we have only foureen inraday dummy variables. We esimae Equaion (5) for each sock using Generalized Mehod of Momens (GMM) and obain -saisics ha are robus o heeroskedasiciy and auocorrelaion (Newey and Wes (987)). We use differen measures of marke deph as he dependen variable, including he oal number of limi orders in he bes five queues, in he bes queue, and in he second hrough fifh queues. We repor he regression resuls in Table, which conains he cross-secional means of he esimaes and -saisics, and he number of socks (ou of 33 socks) ha have significanly posiive and negaive esimaes a he 0 percen level, respecively. For breviy, we do no repor he esimaes of γ k. However, i should be noed ha hese coefficiens are significanly differen from zero, indicaing he imporance of conrolling he ime-of-day effec in he marke deph. Theoreically, here are mixed effecs of he number of rades on marke deph. On he one hand, since he ransacions consume he liquidiy available in he marke, here is a mechanical relaion such ha an increase in rading volume drives down he marke deph. Lee, Mucklow, and Ready (993) presen empirical evidence ha he deph and volume are negaively correlaed. On he oher hand, higher rading aciviy may capure marke ineres and induce public invesors o supply more liquidiy o he marke. Admai and Pfleiderer (988) show ha in equilibrium, discreionary liquidiy 3

16 raders have incenives o rade ogeher, so ha an increase in rading volume aracs more liquidiy rading. Chung, Van Ness, and Van Ness (999) argue ha since invesors place more limi orders when he probabiliy of order execuion is high, which in urn is an increasing funcion of he inensiy of rading aciviy, he number of limi orders increases wih rading volume. Therefore, he coefficien θ could be eiher posiive or negaive. Empirical resuls in Table show ha he firs effec dominaes he second effec, as DEPTH is significanly and negaively relaed o NTRADE. The average esimae of θ is (average -value is -9.6) when he dependen variable is he oal deph in all five queues, and is (average -value is -9.) when he dependen variable is he deph in he bes queue. The focus of our ineres in regression (5) is he coefficien β, which measures he impac of ransiory volailiy on subsequen marke deph. We find ha a rise in ransiory volailiy generally leads o an increase in marke deph. When DEPTH is defined as he deph in he bes queue, he average esimae of β is 0.00 (average -value = 4.4). When DEPTH is defined as he deph in he second hrough fifh queues, he average esimae of β is (average -value = 3.76). These resuls suppor he noion ha an increase in ransiory volailiy is followed by an increase in marke deph. 8 B. Impacs of Transiory Volailiy on Order Flow Composiion The above resuls are consisen wih he conjecure ha an increase in liquidiy-driven price volailiy encourages more invesors o supply liquidiy. Bu according o our hypohesis, an increase in ransiory volailiy no only causes he marke deph o increase, bu i also affecs he order flow composiion, as invesors will be encouraged o submi limi orders raher han marke orders. To shed ligh on his issue, we esimae he following regression model for each of he 33 socks in our sample: 8 Since Chung, Van Ness, and Van Ness (999) find ha lagged spread affecs he placemen of limi orders, we have also modified equaion (5) by including he spread a ime - as an explanaory variable. Resuls, which are qualiaively similar, are no repored here. 4

17 DEPTH =α β 3 γ ktime k,ρ DEPTH ε, (6) where DEPTH is he change of deph from ime - o. The reason ha we have one fewer inraday dummy variable in equaion (6) han in equaion (5) is ha we lose one more observaion per day as we use he change of marke deph insead of he level. Unlike equaion (5), we do no include NTRADE as an explanaory variable. This is because implici in he calculaion of DEPTH, NTRADE is subraced from he deph a ime - and is already aken ino consideraion. Following our discussion in Secion III, DEPTH is a measure of order flow composiion, as i equals he difference beween he number of newly placed limi orders and marke orders submied during ime inerval. According o our hypohesis, an increase in ransiory volailiy induces invesors o submi more limi orders insead of marke orders. Therefore, we predic ha DEPTH is posiively relaed o -. Table 3 repors he esimaes for regression (6). I is noed ha he variable DEPTH is negaively auocorrelaed. For example, when we compue DEPTH based on all five queues, he average esimae of he firs-order auocorrelaion coefficien (ρ ) is (average -value = -4.53). This resul reflecs he self-adjusing mechanism of he order flow. Suppose, in period -, more marke orders are submied han limi orders so ha here is a scarciy of liquidiy. Then, in period, here will be a naural force for liquidiy o ge replenished as here will be more influx of limi orders han marke orders. The evidence is consisen wih Biais, Hillion, and Spa (995), who find ha in he elecronic limi-order book of he Paris Bourse he order flow is affeced by he sae of he book. In general, here are more rades when he order book is hick, and here are more limi orders submied when he book is hin. The impac of ransiory volailiy on he deph change is no very srong. When we use deph change in all five queues as he dependen variable, he average esimae of coefficien β is (average -value =.55). However, when we use deph changes in he bes queue as he dependen variable, he coefficien β is significanly posiive for only 7 socks. Therefore, he evidence is no 5

18 oally consisen wih he hypohesis ha an increase in liquidiy-driven price volailiy will arac public raders o submi limi orders raher han marke orders. There is, however, one problem wih regression (6). If he increase in ransiory volailiy arises from eiher he ask side or he bid side, is impac on he order flow composiion will be on eiher he or orders. In ha case, we migh no be able o find a srong relaion beween he ransiory volailiy and he order flow composiion for and orders ogeher. To address he above problem, we examine explicily how order flow composiion is relaed o he liquidiy-driven price volailiy arising from he bid and ask sides. We esimae he following regression models: DIFF 3 = α β β γ,ktime k,ρ DIFF ε (7) DIFF 3 = α β β γ,ktime k, ρ DIFF ε (8) where DIFF orders during ime inerval, is he difference beween he number of newly placed limi orders and marke DIFF is he difference beween he number of newly placed limi orders and marke orders during ime inerval, and and are he upside (ask side) volailiy and downside (bid side) volailiy during ime inerval -. As we do no observe marke orders and marke orders direcly, we classify our rades ino er- or er-iniiaed by ick es whereby we infer he direcion of a rade by comparing is price o he preceding rade s price. 9 The es resuls are displayed in Panel A (for regression (7)) and Panel B (for regression (8)) of Table 4. There is pervasive evidence ha DIFF and DIFF are posiively auocorrelaed, regardless 9 We also classified he rade by comparing he rade prices wih he prevailing bid/ask quoes and obained similar resuls o he ick es. See Lee and Ready (99) for deails of rade classificaion. 6

19 of wheher we measure he deph based on he bes quoe or he bes five quoes. This is ineresing considering ha he sum of DIFF and DIFF equals DEPTH, which we show o be negaively auocorrelaed in Table 3. This indicaes ha here is ineracion beween marke orders and limi orders ha will resore he marke liquidiy. The reason why DIFF and DIFF are posiively auocorrelaed is ha marke orders are bached over consecuive ime inervals marke () orders a ime - will be followed by marke () orders a ime. On he oher hand, he arrival of marke () orders a ime - is likely o arac more limi () orders a ime. If he placemen of limi orders is more han he marke orders submied a ime, hen DEPTH will be negaively auocorrelaed. Table 4 shows ha DIFF is posiively and significanly relaed o he downside volailiy ( ). When we compue marke deph based on he bes bid, he coefficien β is on average and is significanly posiive for 7 socks. Resuls are even sronger when we compue marke deph based on he second hrough fifh bid prices, as he coefficien β is significanly posiive for 30 socks. This indicaes ha when here is a pauciy of limi orders so ha liquidiy-driven price volailiy arises from he bid side a ime -, his will induce poenial ers o submi limi orders raher han marke orders a ime. There is also a srong and posiive relaion beween DIFF he upside volailiy ( ). The esimae of β is significanly posiive for 0 (3) socks when we compue marke deph based on he bes ask price (second hrough fifh ask prices). Therefore, when here is a pauciy of limi orders so ha liquidiy-driven price volailiy arises from he ask side a ime -, poenial ers will submi limi orders raher han marke orders a ime. and I is ineresing o noe ha DIFF is negaively relaed o he upside volailiy ( ), and ha DIFF is negaively relaed o he downside volailiy ( ). This indicaes ha when he price moves up (down), invesors submi marke () orders insead of limi () orders. An explanaion is ha he placemen of limi orders depends on he probabiliy of order execuion. Some 7

20 raders who place limi orders migh need o execue he ransacion wihin a specified period of ime (Handa and Schwarz (996)). When he price moves up (down), i becomes less likely ha he limi () orders posed a he original bid (ask) prices will be execued. Therefore, insead of waiing any longer, he impaien er (er) will cancel he limi () orders and submi marke () orders. Overall, our resuls indicae ha an increase in ransiory volailiy affecs he order flow composiion. Furhermore, i is imporan o disinguish beween he volailiy arising from he bid side and he ask side, as hey have differen impacs on he and order flows. While more limi orders are placed han marke orders if he ransiory volailiy arises from he bid side, more limi orders are placed han marke orders if he ransiory volailiy arises from he ask side. These resuls are consisen wih he exisence of liquidiy providers who ener he marke and place limi orders on eiher he bid or ask side, depending on which side will earn profis for he liquidiy provision. C. Impacs of Marke Deph on Shor-Term Volailiy To examine he effec of marke deph on subsequen shor-erm volailiy, we esimae he following regression model for each sock: 4 = α βdepth θ NTRADE γ ktime k,ρ ε. (9) The inclusion of TIME k, and - on he righ hand side is o conrol for inraday paerns and auocorrelaion in he shor-erm volailiy. As we discuss in Secion III, he variable is likely o be dependen on he number of ransacions during he inerval. We herefore include NTRADE as an explanaory variable o conrol for is impac on. Resuls are presened in Table 5. Consisen wih our hypohesis, he ransiory volailiy a ime 8

21 is negaively relaed o he deph a ime -. For example, when DEPTH is compued based on he bes five quoes, he average esimae of β is (average -value = -.), and he esimae is significanly negaive for socks. We also noe ha he associaion beween - and DEPTH is mosly driven by he deph in he firs queue. When DEPTH is compued based on he second hrough fifh queues, he average esimae of β is (average -value =-.4). These resuls sugges ha while he whole limi order book (a leas up o five queues) provides us wih more informaion abou marke deph, wha really maers is he amoun of deph a he bes quoe. Our resuls show ha ransiory volailiy arises mainly from he pauciy of limi orders a he bes queue. There is no evidence ha a reducion in he marke deph beyond he firs queue will exacerbae he price volailiy. We also separae he deph ino he bid and ask sides, and relae hem o he downside and upside volailiy. We esimae he following regression models: 4 bid ask = α β DEPTH β DEPTH θnbuy γ,ktime k,ρ ε (0) 4 bid ask = α β DEPTH β DEPTH θnsell γ,ktimek, ρ ε () where bid ask DEPTH is he bid deph a ime, DEPTH is he ask deph a ime -, NBUY is he number of marke orders a ime, and NSELL is he number of marke orders a ime. Table 6 shows ha he upside or downside volailiy is significanly relaed o he marke deph in he firs queue. The upside volailiy is significanly negaively relaed o he ask deph bu no o he bid deph, while he downside volailiy is significanly negaively relaed o he bid deph bu no o he ask deph. These resuls sugges ha by disinguishing beween deph on he bid side and on he ask side, we have beer informaion in predicing he direcion and magniude of ransiory volailiy. 9

22 D. Sensiiviy Tess Since our empirical resuls could depend on measures of volailiy, deph, and he choice of ime inerval, we evaluae heir robusness by conducing a variey of sensiiviy ess. D. Alernaive measure of volailiy A drawback of our volailiy measure ( = N i R i, ) is ha i may proxy he number of orders execued raher han price movemen. The fac ha here are many rades means ha a lo of limi orders are being execued, so ha invesors will replenish limi orders. Therefore, we may observe ha more limi orders are submied subsequen o an increase in our volailiy measure regardless of wheher here is an increase in price movemen. We herefore consider an alernaive measure of volailiy ha is less dependen on he number of ransacions. The alernaive measure is he absolue reurn for he 5-minue inerval, or R = (P /P )-, where R is he reurn of he sock from inerval - o, and P - and P are he las ransacion prices a inerval - and. The absolue reurn is no direcly relaed o he number of ransacions, bu is drawback is ha i migh no be able o deec ransiory price volailiy. 0 We replicae our ess using he absolue reurn as volailiy measure, and resuls are insensiive o he alernaive measure of volailiy. This suggess ha our empirical resuls are no purely driven by he number of ransacions, bu are relaed o he magniude of price flucuaion wihin he inerval. D. Alernaive measures of deph and order flow In previous empirical ess, all deph and order flow measures are based on he number of rades. We also calculae he deph and order flow based on he share volume, and repea he empirical 0 Suppose here are only wo rades wihin he inerval - he firs one is on an up-ick and he second one is on a down-ick. The reurn (or absolue reurn) during he inerval is equal o zero. Based on he absolue reurn measure, one would infer ha he ransiory volailiy is zero and here would be no effec on he liquidiy provision. Bu since he ransacions bounce beween he bid and ask prices, i is likely ha hey are liquidiydriven and should induce an increase in he placemen of limi orders. 0

23 analysis. Resuls based on he share volume are qualiaively similar, alhough we find ha he impac of deph measured in share volume on he price volailiy is weaker han he deph measured in number of rades (Table 5 and 6). This may be consisen wih Jones, Kaul and Lipson (994) who show ha he number of ransacions affecs he price volailiy more han he share volume. D.3 Alernaive measure of ime inerval All our empirical resuls are based on he 5-minue inerval (excep he las inerval) o measure he reurn volailiy and order flows. We replicae he empirical analysis, using 30-minue inerval. The resuls are qualiaively similar. However, he significance levels weaken as we increase he ime inerval. E. Discussion Overall, our findings are consisen wih Handa and Schwarz (996) who hypohesize ha here exis equilibrium levels of limi-order rading and ransiory volailiy. When here is a lack of limi orders, emporary order imbalance riggers ransiory volailiy, which will arac public invesors o place limi orders insead of marke orders. The influx of limi orders will coninue unil ransiory price volailiy decreases, which in urn resuls in a pauciy of limi orders ha causes emporary order imbalance again. Criics of he pure order-driven rading sysem wihou marke makers ofen argue ha limi order raders can be relucan o submi orders ino he sysem in a volaile marke environmen, since rading via limi orders is cosly in an environmen in which he adverse selecion problem is severe. Alhough limi-order raders resemble marke makers in providing liquidiy and immediacy o he marke, hey have he freedom o choose wheher o pos a bid or an ask quoe. This is differen from marke makers who have obligaions o provide an orderly and smooh marke by coninuously posing boh bid and ask quoes. Conrary o he above view, he evidence shown in our sudy indicaes ha limi-order raders

24 play a pivoal role in providing liquidiy o he marke. When here is an increase in liquidiy-driven price volailiy, invesors will be encouraged o place limi orders as he gains from supplying liquidiy can more han offse he poenial loss from rading wih informed raders. Our evidence is consisen wih he view ha an order-driven rading mechanism wihou he presence of marke makers can be viable and self-susaining. V. Conclusions This paper examines he role of limi orders in liquidiy provision in he Hong Kong sock marke, which uses a compuerized limi-order rading sysem. Consisen wih Handa and Schwarz (996), our resuls show ha a rise in ransiory volailiy will be followed by an increase in marke deph, and a rise in marke deph will be followed by a decrease in ransiory volailiy. We also find ha a change in ransiory volailiy affecs he order flow composiion. When here is a pauciy of limi () orders so ha here is an increase in upside (downside) volailiy, poenial ers (ers) will submi limi () orders insead of marke () orders. These resuls are consisen wih he exisence of liquidiy providers who ener and place limi orders o earn profis for heir liquidiy provision. Our resuls are closely relaed o some recen empirical sudies. Biais, Hillion, and Spa (995) find ha in he Paris Bourse, a hin order book aracs orders and a hick book resuls in rades. Chung, Van Ness, and Van Ness (999) find ha in he NYSE, more invesors ener limi orders when he spread is wide, and more invesors hi he quoes when he spread is igh. A disinc conribuion of our paper is ha while previous work examines he ineracion beween order flow and he sae of he order book, we focus on he dynamic relaion beween ransiory volailiy and order flow. Furhermore, we illusrae ha i is imporan o disinguish beween volailiy arising from he bid side or he ask side, as i provides informaion on which side needs liquidiy. Neverheless, our paper shares wih previous sudies he conclusion ha invesors provide liquidiy when i is valuable o he markeplace and consume liquidiy when i is pleniful. Alhough hese invesors do his for heir own benefi, his self-

25 moivaed rading behavior seems o resul in an ecological balance beween he suppliers and demanders of immediacy. 3

26 References Angel, J., 997, Tick size, share prices, and sock splis, Journal of Finance 5, Admai, A., and P. Pfleiderer, 988, A heory of inraday paerns: Volume and price variabiliy, Review of Financial Sudies, Biais, B., P. Hillion, and C. Spa, 995, An empirical analysis of he limi order book and he order flow in he Paris Bourse, Journal of Finance 50, Chung, K., B. Van Ness, and R. Van Ness, 999, Limi orders and he bid-ask spread, Journal of Financial Economics, forhcoming. Chakravary, S., and C. Holden, 996, An inegraed model of marke and limi orders, Journal of Financial Inermediaion 4, 3-4. Foucaul, T., 997, Order flow composiion and rading coss in a dynamic limi order marke, Working Paper, Carnegie-Mellon Universiy, Pisburgh, PA. Glosen, L., 994, Is he elecronic open limi order book ineviable? Journal of Finance 49, 7-6. Greene, J., 996, The impac of limi order execuions on rading coss in New York Sock Exchange socks, Working paper, Georgia Sae Unviersiy. Hamao, Y., and J. Hasbrouck, 995, Securiies rading in he absence of dealers: Trades and quoes in he Tokyo Sock Exchange, Review of Financial Sudies 8, Handa, P., and R. Schwarz, 996, Limi order rading, Journal of Finance 5, Handa, P., R. Schwarz, and A. Tiwari, 998, Deerminans of he bid-ask spread in an order driven marke, Working paper, Universiy of Iowa. Harris, L., and J. Hasbrouck, 996, Marke vs. limi Orders: The SuperDOT evidence on order submission sraegy, Journal of Financial and Quaniaive Analysis 3, 3-3. Jones, C., G. Kaul, and M. Lipson, 994, Transacions, volume, and volailiy, Review of Financial Sudies 7, Kavajecz, K., 999, A specialis's quoed deph and he limi order book, Journal of Finance 54, Kumar, P., and D. Seppi, 994, Limi and marke orders wih opimizing raders, Working paper, Carnegie Mellon Universiy. Lee, C., and M. Ready, 99, Inferring rade direcion from inradaily daa, Journal of Finance 46, Lee, C., B. Mucklow, and M. Ready, 993, Spreads, dephs, and he impac of earnings informaion: An inraday analysis, Review of Financial Sudies 6,

27 Lehmann, B., and D..Modes, 994, Trading and liquidiy on he Tokyo Sock Exchange: A bird's eye view, Journal of Finance 48, Newey, W., and K. Wes, 987, A simple posiive semi-definie heeroskedasiciy and auocorrelaion consisen covariance marix, Economerica 55, Parlour, C., and D. Seppi, 996, Liquidiy based compeiion for he order flow, Working Paper, Carnegie-Mellon Universiy. O Hara, M., 995, Marke Microsrucure Theory, Blackwell Publishers, Cambridge, Mass. Ross, K., J. Shapiro, and K. Smih, 996, Price improvemen of SuperDo marke orders on he NYSE, Working Paper #96-0, New York Sock Exchange, New York, NY. Seppi, D., 997, Liquidiy provision wih limi orders and a sraegic specialis, Review of Financial Sudies 0, Viswanahan, S. and J. Wang, 998, Marke Archiecure: Limi-order books versus dealership markes, Working Paper, Duke Universiy, Raleigh, NC. 5

28 Table. Summary Saisics This able repors he cross-secional disribuions of he average price, spread in HK dollars, spread in he percenage of he sock price, daily number of rades, daily share volume, and daily dollar volume for he 33 componen socks of he Hang Seng Index. For a given sock, we compue he averages for he one-year period beween July 996 and June 997. Price (HK$) Spread (HK$) Spread (%) No. of rades Share volume (,000) Dollar volume (HK$,000) Mean ,367 8,03 Sd. dev ,43 9,76 Minimum ,70 s quarile ,37 7,03 Median ,40 6,5 3 rd quarile ,79 8,336 Maximum ,97 65,599 6

29 Table. Regression of Deph on Lagged Transiory Volailiy This able presens he GMM esimaes from he regressions esimaed for each of he 33 Hang Seng Index componen socks based on 5-minue inervals. The regression model is: DEPTH 4 = α β θ NTRADE γ k TIME k, ρ DEPTH where DEPTH is he deph measured as he oal number of limi orders ousanding a he bid and ask quoes a he end of ime inerval ; denoes he ransiory volailiy measured as sum of reurns squared during ime inerval -; NTRADE is he number of ransacions made during ime inerval ; TIME k represens a dummy variable ha akes he value of one if ime belongs o he 5-minue inraday inerval k, and zero oherwise; and ε is a random error erm. Regression coefficiens are cross-secional averages from he 33 socks. Average -saisics are in parenheses. Numbers in brackes are hose of coefficiens ha are significanly posiive a he 0.0 level and hose of coefficiens ha are significanly negaive a he 0.0 level, respecively. ε Definiion of deph β θ ρ () Bes 5 asks bes 5 bids (5.47) (-9.6) (69.6) [3,0] [0,33] [33,0] () Bes ask bes bid (4.4) (-9.) (3.06) [33,0] [0,33] [33,0] () () (3.76) (-.09) (60.3) [30,0] [,] [33,0] 7

30 Table 3. Regression of Deph Change on Lagged Transiory Volailiy This able presens he GMM esimaes from he regressions esimaed for each of he 33 Hang Seng Index componen socks based on 5-minue inervals. The regression model is: DEPTH = α β 3 γ k TIME k ρ DEPTH where DEPTH is he change of deph (oal number of ousanding limi orders a he bid and ask quoes) from ime inerval - o ; denoes he volailiy measured as sum of reurns squared during ime inerval -; TIME k represens a dummy variable ha akes he value of one if ime belongs o he 5-minue inraday inerval k, and zero oherwise; and ε is a random error erm. Regression coefficiens are cross-secional averages from he 33 socks. Average -saisics are in parenheses. Numbers in brackes are hose of coefficiens ha are significanly posiive a he 0.0 level and hose of coefficiens ha are significanly negaive a he 0.0 level, respecively. ε Definiion of deph β ρ () Bes 5 asks bes 5 bids (.55) (-4.53) [5,0] [0,30] () Bes ask bes bid (0.57) (-.83) [7,0] [0,33] () () (.40) (-5.7) [7,] [0.30] 8

31 Table 4. Regression of he Difference beween Limi Buy (Sell) Order and Marke Buy (Sell) Order on Lagged Upside and Downside Volailiy This able presens he GMM esimaes from he regressions esimaed for each of he 33 Hang Seng Index componen socks based on 5-minue inervals. The regression models are: where DIFF DIFF DIFF ( DIFF 3 = α β β γ,ktime k,ρ DIFF 3 = α β β γ,ktime k,ρ DIFF ) measures he difference beween he number of newly placed limi () orders and marke () orders during ime inerval ; ( ) denoes he upside (downside) volailiy during ime inerval -, being measured as he sum of reurns squared based on posiive (negaive) reurn observaions wihin he inerval -; TIME represens a dummy variable ha akes he value of one if ime belongs o he 5-minue inraday inerval k, and zero oherwise; and ε are usual random error erms. Regression coefficiens are cross-secional averages from he 33 socks. Average -saisics are in parenheses. Numbers in brackes are hose of coefficiens ha are significanly posiive a he 0.0 level and hose of coefficiens ha are significanly negaive a he 0.0 level, respecively. Panel A: Dependen variable is he difference beween limi order and marke order. Definiion of deph β β ρ () Bes 5 bids (-.79) (3.3) (6.86) [0,8] [3,0] [33,0] () Bes bid (-.68) (.8) (6.03) [0,6] [7,0] [33,0] () () (-4.0) (4.8) (5.66) [0,3] [30,0] [33,0] Panel B: Dependen variable is he difference beween limi order and marke order. Definiion of deph β β ρ () Bes 5 asks (3.78) (-.78) (4.58) [30,0] [0,6] [3,0] () Bes ask (.4) (-.56) (5.73) [0,0] [0,0] [3,0] () () (4.65) (-3.95) (3.38) [3,0] [0,9] [8,0] k ε ε ε 9