The Informativeness of the Limit Order Book in a Periodic Call Market. C.J. Wang 1 Ti Yang Chang Department of Finance National Sun Yat-Sen University

Transcription

1 Paper submission for he paricipaion of EFM 2010 Symposium on ASIAN FINANCE Renmin Universiy of China, Beijing, China, April 22-24, 2010 The Informaiveness of he Limi Order Book in a Periodic Call Marke C.J. Wang 1 Ti Yang Chang Deparmen of Finance Naional Sun Ya-Sen Universiy Curren version: Sepember, The corresponding auhor: C.J. Wang, cjwang@faculy.nsysu.edu.w, 70 Lien-Hai Road Kaohsiung, Taiwan, ROC.

2 The Informaiveness of he Limi Order Book in a Periodic Call Marke Absrac Using he inraday daa on he Taiwan Sock Exchange (TWSE), we address he issue of he informaiveness of he limi order book in he periodic call marke. We find ha he pre-call informaion variables, i.e., he marke order and he radius of he limi order book, have significan impacs on he rade variables, i.e., he rading volume, he pos-call bid-ask spread, and he rader surplus. Furhermore, we are able o show ha he radius, as well as he marke order, conains wo differenial forces in impacing on hese rade variables. JEL classificaion: G10; G20 Keywords: Bid-ask spread; Trading volume; Trader surplus; Heerogeneous informaion 2

3 The Informaiveness of he Limi Order Book in a Periodic Call Marke 1. Inroducion The core of a limi order marke is ha i provides informaion abou aggregae liquidiy supply and rading ineress. This is paricularly rue in an elecronic limi order marke wihou marke makers (Glosen, 1994). Bageho (1971) argues he necessiy of he exisence of he bid-ask spread due o informaion asymmery in he marke and he survivorship of he marke maker. Copeland and Galai (1983) show ha he marke maker s bid-ask spread is o cover he cos of rading wih informed raders. Glosen and Milgrom (1985) elaborae he characerisics of he bid-ask spread by showing he convergen naure of he bid and ask quoes as he number of rade geing large. Easley and O Hara (1987) offer a model ha he bid spread and he ask spread of he marke maker may no be symmeric 2. Their remark essenially show he complicaed informaion naure in he bid-ask spread. Bu how are he above informaion heories relaed o he limi order book? As poined ou by Handa and Schwarz (1996), [l]imi order raders resemble dealers in ha hey provide liquidiy and immediacy o he marke. This view is confirmed and enriched by he laboraory experimen of Bloomfield, O Hara, and Saar (2005) ha in a limi order marke informed raders no only use more limi orders han do uninformed raders bu also make and ake liquidiy in order o achieve round-rip rading in he marke. Kaniel and Liu (2006) model ha in equilibrium informed raders prefer limi orders o marke orders and he probabiliy of limi order preference is so high ha makes he limi orders more informaive han marke orders. Handa and Schwarz (1996) offer a model ha he choice beween limi and marke orders is based upon invesors beliefs wheher hey will encouner informed or uninformed raders. In Parlour (1998), an invesor choice beween limi and marke orders is based upon he curren and he fuure saes of he limi order book. Foucaul (1999) ackles invesors order-ype choice by inroducing winner s curse problem for limi order raders of being picked-off. Foucaul, Kadan, and Kandel (2005) address how raders impaience has effecs on order placemen sraegy. Goeler, Parlour, and Rajan (2005) model ha low valuaion raders end o submi orders wih ask prices lower han he consensus value of he asse. Similarly, high valuaion raders end o submi orders wih bid prices higher han he consensus value. An implicaion of heir model is ha raders who submi marke orders could benefi from negaive ransacion coss (i.e., hey could buy below or sell above he consensus value). This implies ha marke 2 Possibly he firs heoreical srucural claim of heerogeneous beliefs in a single bid-ask spread. 3

4 order 3 submiers can enjoy a higher degree of rader surplus. Foucaul, Moinas, and Theissen (2007) claim ha he saus of limi orders iself conain volailiy informaion because imbedded opion feaures in limi orders. Goeler, Parlour, and Rajan (2009) claim ha he characerisics of risky asses affec he way of informaion gahering, hus affec he rading sraegy of invesors, and hence affec he informaiveness of he limi order book. As o empirical findings, Chung, Van Ness, and Van Ness (1999) find ha on NYSE he main porion of bid and ask quoes is from he ineress of limi order raders. Specialiss are more likely o quoe for low-volume socks. Madhavan and Panchapagesan (2000) claim ha i is a valuable privilege for marke makers, such as specialiss on NYSE, o access informaion regarding he evoluion of he limi order book, and i is especially relevan a he marke open. Griffihs, Smih, Turnbull, and Whie (2000) find ha aggressive orders usually incur a larger price impacs bu smaller opporuniy coss. Furhermore, hey find ha when he bid-ask spreads are narrow and deph on he same (opposie) side of he book is hick (hin), aggressive orders end o be recursive. Ranaldo (2004) shows ha he aggressiveness of orders depends on he dephs, he bid-ask spread and he change in volailiy in he limi order book. Bae, Jang, and park (2003) find ha limi order prevails marke orders when he bid-ask spread is wider, he rade size is larger, and he marke anicipaes high volailiy. By aking one sep furher in informaion asymmery, Miller (1977) shows ha wih he shor-sales consrains if invesors have differen valuaions on he risky asse, he slope of he demand curve would be negaive. The implicaion is ha he marke clearing price will be above he mean evaluaion of all poenial invesors because of he combined effec of he shor-sales consrains and he divergence of opinion 4. Based up he heory of Miller (1977), Chen, Hong, and Sein (2002) form a framework in diversiy of opinion wih shor-sales consrains by examining he breah of ownership in muual funds. They find ha here is a posiive relaion beween he change in he breah and he subsequen reurns. Hong, Scheinkman, and Xiong (2006) offer a bubble model ha given heerogeneous beliefs wih shor-sell consrains, overconfiden invesors are willing o pay more han heir evaluaion because hey believe ha here are oher invesors who are willing o pay even more in he fuure. Kim, Lee, and Morck (2004) documen ha differenial demand and supply schedules exis when invesors having heerogeneous beliefs and he elasiciies of hese schedules reac differenly in financial crises. Bagwell (1992) find ha heerogeneous beliefs exis in Duch aucion sock repurchases and he supply of hese shares in he repurchasing programs 3 This also implies ha he size of he marke order needs o be limied. Oherwise, i may walk he book. 4 In his sudy, we use boh divergence of opinion, heerogeneous beliefs or heerogeneous informaion, inerchangeably. 4

5 are upward-sloping. Glosen (1994) models an elecronic limi order book when here is an exogenous large supply of limi orders. He argues ha due o he exisence of informed rade, he slope of he supply schedule is posiive, which reflecs he discriminaory naure of he book. Kandel, Sarig, and Wohl (1999) find ha he demand curves of 27 Israeli IPOs are elasic and downward-sloping. Kalay, Sade, and Wohl (2004) find an increasing paern in he esimaed mean quaniy-adjused elasiciy of he excess demand during he rading day. Tha is, he lower he elasiciy he larger he informaion asymmery and vice versa. Their finding is consisen o he predicions ha he informaion revealed during he rading day miigaes he severiy of he adverse selecion problem (Glosen and Milgrom, 1985). Kim, Lee, and Morck (2004) examine he differenial changes in esimaed demand and supply elasiciies among differen classes of invesor around he financial crises in Asia. They find ha he demand and supply curves of domesic insiuions and foreign invesors are more elasic han ha of domesic individuals. Naes and Skjelorp (2006) find ha here are differenial relaionships beween he slope and he number of rades in he book. Tha is, for he whole book here is a negaive relaionship beween he mean slope and he number of rades, bu a posiive relaionship if only focusing a he inner quoes. This phenomenon reflecs differenial informaion in differen segmens of he order book. The above heoreical and empirical works are more focusing on he informaiveness of he order book in a coninuous marke. Tha leads us o he purpose of his paper by addressing he following quesions: In a periodic call marke, does he limi order book conain informaion or even heerogeneous informaion? In paricular, will he order sraegy (marke vs. limi orders) makes any difference in informaion revelaion? Furhermore, will he number of he order price level in he book affec rade characerisics, such as he pos-call spread, rading volume, or rader surplus? The significance is ha in he call marke o make a rade mach i needs he full schedules of demand and supply, bu i is barely he case in he coninuous marke. In our analysis, firs, we offer an alernaive inerpreaion on he pos-call bid-ask spread in he periodic call marke. Conrary o he convenional concep of he pre-rade spread in a coninuous marke, he pos-call spread is o reflec he degree of informaion asymmery resolved a he ime of deermining he marke clearing price. In oher words, he gap beween he wo pos-call pricing schedules (demand and supply) is a realizaion of informaion symmery and i should be considered as he degree of informaion symmery achieved afer he call. Furhermore, as an alernaive o he slope of he order book (e.g., Kalay e al., 2004; Naes and Skjelorp, 2006), we offer a pair of new informaion variables o measure he degree of 5

6 heerogeneous beliefs. We call hem he radii of he order book. The basic inuiion is ha he order (price and deph) a each order price level basically reflecs differenial informaion in he book (Glosen, 1994). However, he farher he order price is away from he bes order price he less likely i will be considered in he game. Hence, we choose he number of he order price level beween he bes order price level and he mos popular order price level ha has he hickes deph in he book o be a proxy o reflec he degree of heerogeneous informaion in he book before a call. We find ha here is a negaive relaionship beween he radii of he order book and he pos-call spread. These negaive relaions are consisen o he analys underreacion hypohesis (Das, Levine, Sivaramakrishnan, 1998) and complemen o he resuls of Park (2008) and Zhang (2006). These findings imply ha he higher degree of heerogeneous beliefs in he pre-call environmen, he less achievemen of informaion symmery in he pos-call environmen. However, in examining he liquidiy characerisics of rading volume, we find ha he marke orders are posiively and he radii of he order book are negaively correlaed wih he rading volume. By decomposing he radius of he order book ino he lower radius (number of he mached order price level) and he upper radius (number of unmached order price level), we find ha he lower radii of he order book have a posiive correlaion 5 wih he rading volume, bu he upper radii, along wih he marke orders, have a negaive correlaion wih he rading volume. Since he radius of he order flow represens he number of he order price level beween he bes order price level and he mos popular order price level ha has he hickes deph in he limi order book, he marke order no only is a subse of he radius of he order flow, bu, more precisely, i is a subse of he lower radius of he order flow. If he radius of he order book has conained all of informaion, wha is he significance o inroduce he variable of he marke order? Wih respec o marke liquidiy (e.g., rading volume) he marke order normally has wo disinc characerisics: (1) low execuion risk: pro rading volume, and (2) smaller size of deph: con rading volume (Table 1). The variable of he radius of he order book is only able o pick up he firs characerisic of he marke order. By simulaneously inroducing he variable of he marke order in he regression, we hus are able o exrac he second characerisic of he marke order. Kalay e al. (2004) and Naes and Skjelorp (2006) focus on he informaiveness of he slope in he book. However, i is more inuiive ha he slopes of he demand and supply schedules direcly affec he surplus of he raders whose orders have been mached. Hence, i is relevan for us o ask: Wha is he relaion beween he rader 5 The coefficien of he radius of he order book on he sell side is saisically insignifican (see Table 3). 6

7 surplus and he radius of he order book, which is a proxy of he degree of heerogeneous informaion? We find ha he lower (upper) radii represening mached (unmached) orders on boh sides of he marke have a posiive (negaive) conribuion on he rading volume. Furhermore, he marke order has a posiive conribuion on he rader surplus of he same side, bu a negaive conribuion on he rader surplus of he opposie side. This phenomenon is consisen o he exension of he crowding ou effec in Parlour (1998) ha due o he ime prioriy of he exising orders, deph a he bes price on he same side of he book decreases he likelihood of incoming limi orders, while deph a he bes price on he opposie side increases his probabiliy. If so, for example, a hick deph of limi orders on sell side will increase he likelihood of marke order submission on he same side, which in urn will decrease he probabiliy of marke order submission on he buy side. In shor, an increase in marke order on he sell side may cause a decrease in marke order on he buy side. Hence, he crowding ou effec in Parlour (1998) may explain our finding ha here is a negaive relaion beween he rader surplus of his side and he marke order submied from he opposie side. The paper is organized in he following way. In secion 2, we describe our sample daa, including he raionale of he pos-call bid-ask spread and he inuiion of he radius of he order book and is formaion. Secion 3 presens he regression analyses of he pos-call spread and he rading volume wih respec o he slope and he radius of he order book. Also, we analyze he relaion beween he rader surplus and he radius of he order book. Secion 4 concludes he paper. 2. Daa and Mehodology 2.1 Daa The sample inraday daa ha we choose are he consiuen socks in he TWSE Taiwan 50 Index 6 on he Taiwan Sock Exchange (TWSE) from January o May, Our sample includes he ime-samped rade relaed variables, such as marke clearing price and volume, he ime-samped order relaed variables, such as he order prices and he order shares. This informaion is enough for us o reconsruc he demand and supply schedules wih is inersecion a he marke clearing price and volume for each rade during he day. TWSE is an order-driven periodic call marke. On a ypical rading day, i opens a 9:00 a.m. and closes a 1:30 p.m. A 8:30 a.m., invesors may sar heir order submissions. The second las rade of he day is a 1:25 p.m. Afer 1:25 p.m. and before 1:30 p.m., i only allows order accumulaion. 6 The TWSE Taiwan 50 Index, launched on Ocober 29, 2002, was he firs radable index in Taiwan marke. To be included in he Index, hese firms mus be ranked in he firs fify by marke capializaion. 7

8 On TWSE, invesors can only submi limi orders and here is no opion of submiing convenional marke orders. However, here are daily price limis, i.e., on a rading day, he price range of any sock is wihin 7% of he previous closing price. Hence, by local convenion, he marke order on TWSE is an order wih is limi price reaching is daily price limi, considering he ick size requiremen. In Table 1, we presen descripive saisics on marke capializaion, marke clearing price, rade size, pos-call spreads, limi and marke order sizes, and he sizes of he radius in he order book. The mean marke capializaion is abou NT$184 billion wih he mean price level of NT$39.54 and he mean rade size of lo 7. The mean (median) limi order sizes are 303 (215) los and 406 (318) los for he buy and sell sides, respecively. The mean (median) order sizes of he marke order, however, are much smaller, i.e., 24 (15) los and 33 (14) los for he buy and sell sides, respecively. The mean lower radii of he order book on he buy and sell sides are 1.53 and 1.57, respecively, which are much smaller han hose of upper radii, 5.87 and 7.08, respecively. 2.2 The raionale behind he pos-call bid-ask spread In heoreical work, such as, Glosen and Milgrom (1985), Easley and O Hara (1987), one of he imporan elemens in he bid-ask spread is he adverse-selecion cos componen. Glosen (1987) classifies his kind of adverse-selecion cos componen as an ex ane approach. In conras, he ex pos approach is ha in he end he marke maker will need o offse he loss o he informed raders by profiing from he liquidiy raders. In he seing of he coninuous marke rading mechanism, he adverse-selecion cos componen in he quoed bid-ask spread is more geared o he descripion of he ex ane view, and he adverse-selecion cos componen in he realized bid-ask spread (e.g., Blume and Goldsein, 1992; Copeland and Galai, 1983; Lee, 1993; Peersen and Fiakowski, 1994; ) is more geared o ha of he ex pos view. In he environmen of he periodic call rading mechanism, such as he Taiwan Sock Exchange, immediaely before a successful call, normally here is no bid-ask spread because he pricing schedules from boh he demand and supply sides run across. Oherwise, for sure here will be no successful call. However, immediaely afer he call, normally here is a gap beween hese wo pricing schedules in he limi order book. This gap may have a shape like he bid-ask spread in he coninuous marke bu can carry a differen meaning. Tha is, immediaely before a successful call, he secions in he demand and supply schedules evenually cleared can be viewed as o reflec he degree of informaion asymmery resolved a he marke clearing price. 7 On TWSE, a round lo is 1,000 shares. 8

9 To pu i differenly, he gap beween he wo pos-call pricing schedules (demand and supply) is a realizaion of informaion symmery from he pre-call o he pos-call demand and supply pricing schedules. I is because he buy orders wih limi prices higher han he call price and he sell orders wih limi prices lower han hen call price will for sure be compleely cleared. Any remaining mached volume is deermined and cleared a he call price. Hence, his pos-call gap 8 beween he wo pricing schedules canno be viewed as he bid-ask spread in he coninuous marke, bu on he conrary i should be considered as he degree of informaion symmery achieved afer he call. We offer a more elaboraed illusraion of his idea in Appendix A. 2.3 The inuiion and measure of he radius of he limi order book Given he inerpreaion of he pos-call bid-ask spread, he follow-up quesion hen becomes: Given he exisence of informaion asymmery, wha is he level of heerogeneous informaion 9 in he pre-call demand and supply pricing schedules? Naes and Skjelorp (2006) claim ha he slopes of he bid and ask pricing schedules reflec he degree of heerogeneous informaion 10. They argue ha he pricing schedules from boh sides of he marke conain differenial informaion. Hence, here is a negaive relaion beween he level of he disagreemen among analyss and he Q average absolue slopes (i.e., a smaller ) of he limi order book. Noneheless, P he measuremen of slope (or elasiciy) can be problemaic as indicaed in Kalay e al. (2004). Thus, his encourages us o explore anoher pair of proxy o measure heerogeneous informaion in he limi order book. If he above claim in Naes and Skjelorp (2006) is correc, hen i also implies ha he pricing schedule on each side of he marke should be more spread ou he greaer he disagreemen among analyss. If his is rue, here should be a posiive relaionship beween heerogeneous informaion and he number of order price level in he limi order book. This poin of view is also consisen o Figure 1 in Miller (1977): A seeper differenial valuaion schedule is caused by sronger heerogeneous informaion (i.e., divergence of opinion). Furhermore, Biais, Hillion, and Spa (1995) empirically find ha on Paris Bourse he dephs are lower a he inside bid-ask quoes han hose of away from he bes quoes. 8 Any unsuccessful call ofen will have a gap beween he demand and supply schedules. Our inerpreaion only goes o he gap afer a successful call. 9 As poined ou by Hong e al. (2006), here are several ways of having divergence in opinion (i.e., heerogeneous informaion) in he marke, e.g., based upon he same piece of privae informaion, bu one group of invesor is more confiden han ohers or differen groups of invesor have differen se of privae informaion. 10 Their daa used are from a coninuous rading environmen. 9

10 In a heoreical framework, Seppi (1997) suggess ha in he book he supply of limi orders beyond he inside bid-ask quoes are a source of liquidiy for large orders from he opposie side. These above views imply ha in he limi order book (1) he bes quoes may no be he only source of privae informaion, (2) quoes beyond he bes quoes do carry differenial informaion. Noneheless, shor-sales on Taiwan Sock Exchange (TWSE) are permied. Does his meaning ha he divergence of opinion will no work on TWSE? No, Miller (1977) only says ha he co-exisence of shor-sales consrains and heerogeneous informaion will cause an over-valuaion in marke clearing prices. He is no saying ha heerogeneous informaion could no exis wihou shor-sales consrains. For example, Hong and Sein (2003) model marke crash ha is caused by he divergence of opinion wihou he consideraion of he shor-sales consrains bu wih a class of raional arbirageurs. Having esablished he line of reasoning ha he number of order price level can be considered as a proxy for heerogeneous informaion in he book, we need o ake a closer look a hese order price levels. In he book on TWSE, orders wih higher buy prices or lower sell prices have beer chances o be cleared and orders far away from he bes prices are less likely o be cleared and possibly remain in he book hrough ou he whole rading day. From ime-series poin of view, hese sale orders are simply a facade of he change in heerogeneous informaion in he book. Hence, he raw form of he order price level needs o be culivaed before suiable for our purpose. To ge a feeling on he characerisic of hese order price levels in he book, we plo he mean buy and sell order flows (dephs) of he firs eigh order price levels in he book. On each side of he book, we firs compue he mean order sizes of he marke open, close, inraday 30-min (mean), and he whole rading day for each of he firs eigh order price levels 11 for each firm over he five monh sample period (from January o May, 2005). Then, we compue he cross secional means over all hese consiuen socks in he TWSE Taiwan 50 Index. Excep marke open and close, in Figure 1 we observe ha he dephs vary significanly among differen order price levels and presen an inverse U-shaped paern when hey are away from he bes order prices 12. Tha is, he average deph a each order price level reaches is hickes poin somewhere in he middle of he pricing schedule and hen declines. In he book here is a mos popular order price level 13 ha has he hickes deph on each 11 In our sample arrangemen, we only consider he firs eigh price levels in our analysis, bu we have examined he schedules of en or welve order price levels. They yield similar resuls. 12 In he quoe-driven coninuous marke, he lowes ask and he highes bid usually are called he inside quoes. In he order-driven periodic call marke, we call he lowes ask and he highes bid in he limi order book as he bes order prices mainly because hese prices may run across each oher. 13 If here are more han one order price levels ha have he hickes deph, hen we shall choose he farhes order price level in he limi order book as our mos popular order price level. 10

11 side of he marke a each call in he book. Invesors who eager o complee rades would consider o submiing orders wih more aggressive feaures, such as marke orders or orders wih compeiive prices. Invesors who wish o minimize rading cos or maximize rading profi would consider o submiing orders wih less aggressive feaures, such as limi orders wih prices farher away from he bes prices. Thus, he former invesors may incur a higher rading cos and he laer may suffer a higher execuion risk (i.e., he possibiliy of no rades). If weighing order submission by hese wo facors, invesors can submi orders ha are neiher a he bes price nor a he farhes order price level in he book, bu somewhere in beween as observed in our Figure 1, which is also consisen o Figure 1 in Naes and Skjelorp (2006). Hence, for our purpose, we measure he number of he order price level beween his mos popular price level and he bes order price level as he (buy or sell) proxy for he degree of heerogeneous informaion before a call in he pricing schedule. We call hem he radii of he order book. Before, we have chosen he pos-call bid-ask spread as he resoluion of informaion asymmery (or he achievemen of informaion symmery) afer a call. Then now one may raise he quesion: Wha is he relaionship beween he pre-rade radius of he order price level and he pos-call spread? Specifically, if a wider pre-rade radius of he order price level implies ha a higher degree of heerogeneous informaion causes his archipelago-like pricing schedule, hen when he pre-rade heerogeneous informaion is high, will he call rading mechanism on TWSE produce a narrower pos-rade bid-ask spread (i.e., achieving a smaller degree of informaion symmery) or a wider pos-rade bid-ask spread (i.e., achieving a larger degree of informaion symmery)? Sickel (1991), Gleason and Lee (2003), among ohers, demonsrae ha he immediae sock price reacion o analyss forecas revisions is incomplee, in ha prices, on average, coninue o drif in he same direcion for a leas hree o nine monhs afer he revision. Zhang (2005) and Jiang e al. (2005) documen ha informaion uncerainy is posiively relaed o he pos-analys-revision drif. Zhang (2006) and Park (2008) furher show ha analyss underreac o new informaion and hey underreac even more when here is higher informaion uncerainy. In shor, analys forecas raionaliy predics zero ex ane forecas errors following good or bad news and provides no role for informaion uncerainy. However, analys opimism ends o predic negaive forecas errors. On average, more negaive forecas errors he higher informaion uncerainy regardless of he naure of news (Das e al., 1998). The idea of heerogeneous informaion or he divergence of opinion in he lieraure, such as in Miller (1977), Bagwell (1992), Kandel e al. (1999), Chen e al. (2002), Hong and Sein (2003), Kim e al. (2004), and Hong e al. (2006), is acually informaion asymmery among informed invesors. This kind of complexiy in 11

12 informaion asymmery may cause even more negaive forecas errors in he sense of Das e al. (1998). Hence, for his modified analys underreacion hypohesis we predic ha here is a negaive correlaion beween he pre-rade radius of he order price level ha represens he degree of he pre-call heerogeneous informaion and he pos-call bid-ask spread ha represens he pos-call achievemen in informaion symmery due o he call. 3. Empirical Resuls The purpose of our empirical sudy has wo folds: one is o examine he informaion conen in he limi order book, and he oher is o perform he comparison of he resuls beween our model specificaion and he ones in he lieraure. In paricular, Kalay e al. (2004) and Naes and Skjelorp (2006) sugges ha he slopes in he limi order book reflec he degree of informaion asymmery. If so, informaion variables suggesed in he heory, such as, he bid-ask spread and rading volume should be affeced by he slope. However, he measure of he slope is problemaic as indicaed in Kalay e al. (2004, pp. 463). Thus, we choose he radii of he order book as he alernaive informaion proxies in he limi order book. 3.1 The slopes and he radius of he limi order book Naes and Skejelorp (2006) claim ha he slopes of he bid and ask pricing schedules reflec he degree of heerogeneous informaion 14. They argue ha he greaer he disagreemen among analyss, he flaer he average slope of he order book. However, here are wo pricing schedules in he limi order book, one is on he demand side and he oher one on he supply side. While he demand and supply pricing schedules reflec liquidiy needs and heerogeneous informaion of heir own side of he marke, normally, he slope of he demand pricing schedule carries a negaive sign and, however, ha of he supply pricing schedule carries a posiive sign. If he fundamenal elemens ha deermine he pricing schedule on each side of he marke are differen, hen a simple average of hese wo pricing schedules slopes may likely o obscure he informaion conen in each of hese wo pricing schedules. Our raionale is sraigh forward ha if here are wo informaion proxies in he limi order book, why jus use he ne measure, even i is a combinaion 15 of he wo proxies? A 14 Their daa are mainly in a coninuous rading environmen seing. 15 Naes and Skejelorp (2006) combine he slopes of demand and supply schedules by averaging he wo slopes. Kalay e al. (2004) combine hese wo slopes by examining he slope of he excess demand (demand minus supply). However, in his fashion, he slope of he excess demand sill presens he mixed feaures of he original slopes. 12

13 direc usage of hese wo informaion proxies, such as, he radii of he order book of he demand and supply pricing schedules, may yield no only wo separae resuls bu possibly differenial and comparable resuls. We hus conduc a series of regression es o examine hese wo ses of informaion proxies in he limi order book. There are wo aspecs in his examinaion: (1) he relaion beween he pos-call bid-ask spread (a proxy for he resoluion of informaion asymmery) and our informaion variables (i.e., he slopes and he radii of he book), (2) he relaion beween he rading volume and our informaion variables. The candidaes of he dependen variable are (a) he one-sided rading volume a each call, and (b) he pos-call bid-ask percenage spread. Dependen MkOdr _ buy Informaion _ buy 5 1 MkOdr _ sell 2 Informaion _ sell 6 Open Close 3. 4 We choose six independen microsrucure variables for each regression model. MkOdr _ buy ( MkOdr _ sell ) is an indicaor variable ha is equal o one, if he orders a he firs level 16 of order price on he demand (supply) pricing schedule are he marke order, i.e., heir order prices reach he daily price limi 7% ( 7% ), wih he consideraion of he relevan ick size. Oherwise, i is equal o zero. The indicaor variable Open 1 (and Close 1), if he call is a he marke open (close). Oherwise, Open 0 (and Close 0 ). The independen variable of Informaion _ buy (Informaion _ sell ) is he informaion variable o proxy he heerogeneous informaion on he demand (supply) pricing schedule. In Kalay e al. (2004) and Naes and Skjelorp (2006), hey claim ha he slope of he demand or supply pricing schedule reflecs heerogeneous beliefs in he marke. Hence, in regression models II and IV, we use he absolue slopes of he demand (supply) pricing schedule as he independen variable of Informaion _ buy ( Informaio n _ sell ). We, however, believe ha he variables of he radii of he order book ha measure he numbers of order price level beween hese mos popular price levels and he bes order price levels in he demand and supply pricing schedule acually conain beer informaion. Thus, in regression models I and III we use he radius of he order book of he demand (supply) pricing schedule as he independen variable of Informaion _ buy ( Informaio n _ sell ). The sample daa in our regression analyses are in he form of panel daa, i.e., we sack up individual firms inraday daa one on he op of anoher. Hence, i may conain biased effecs of 16 If i is he marke order (defined by he pracice in he Taiwan sock marke), hen i has o be a he firs level of he order book, buy or sell side, bu no vice versa. 13

14 auocorrelaion and heeroskedasiciy in he error erms. We apply Newey and Wes (1987) consisen variance/covariance marix o correc hese biases for he -saisics. In examining he pos-call bid-ask percenage spread, in models I and II boh marke open and marke close variables have posiive conribuion o he size of he spread. These resuls are consisen o he well-known findings in he lieraure, such as Lee, Mucklow, and Ready (1993) as well as heoreical work, such as Admai and Pfleiderer (1988) and Brock and Kleidon (1992) ha a wider spread corresponds o an environmen of higher informaion asymmery or liquidiy needs, such as marke open and close. The coefficiens of marke orders from boh sides of he marke have negaive signs. This resul implies ha in boh models I and II he exisence of marke orders, eiher buy or sell, conribue less in he achievemen of informaion symmery han ha of limi orders. The popular view in he lieraure indicaes ha informed raders end o use marke orders 17 because hey are less paien or heir privae informaion has a higher decay rae. However, Bloomfield, O Hara, and Saar (2005) show ha informed and uninformed boh will use marke and limi orders, bu only have a preference in iming when choosing he order ypes. Perhaps of his mixed order sraegy, i makes marke orders a less revealing vehicle han limi orders in achieving informaion symmery. Alernaively, insead of marke orders, if informed raders do predominaely use limi orders, hen marke orders carry less informaion (Kaniel and Liu, 2006). Thus, he evidence of a negaive relaion beween he marke order and he pos-call spread is consisen o he analys underreacion hypohesis and he claim in Kaniel and Liu (2006) ha he higher he degree of informaion asymmery in a pre-rade environmen, he less he degree of informaion symmery achieved in he pos-rade environmen by using marke orders. Furhermore, if he hypohesis of he analys forecas raionaliy ha predics zero ex ane forecas errors is correc, hen we should observe no relaion beween he informaion variables (i.e., he slopes or he radius of he book) and he pos-call bid-ask percenage spread. Alernaively, if he analys underreacion hypohesis is correc, we should observe a negaive relaion beween he informaion variables and he pos-call bid-ask percenage spread. In model II, he informaion variables are he slopes of he demand and supply schedules, as sudied in Kalay e al. (2004) and Naes and Skjelorp (2006). The coefficien of he absolue slope on he demand side has a negaive sign and he absolue slope on he supply side has a posiive sign. This 17 Glosen (1994) and Seppi (1997) explicily incorporae informed raders ino heir models, bu assume ha hey always ener marke orders insead of limi orders. However, Chakravary and Holden (1995) and Kaniel and Liu (2002) include boh marke and limi orders in informed raders order preference. 14

15 empirical evidence from he absolue slopes offer mixed resuls on he modified analys underreacion hypohesis. In model I, he informaion variables are he radii of he order book. Boh of he coefficiens of he radius carry a negaive sign ha suppors he modified analys underreacion hypohesis and complemens o he resuls of Park (2008) and Zhang (2006). This finding from he radius of he book implies ha he higher heerogeneous informaion in he pre-call environmen, he less achievemen in informaion symmery in he pos-call environmen. When examining he dependen variable rading volume, we find ha he relaionship beween marke orders and rading volume is posiive in boh models III and IV (Table 2). I implies ha marke orders have a posiive conribuion o rading volume. I is inuiively appealing ha due o heir price advanageous marke orders enjoy a higher degree of maching opporuniy han ha of limi orders. Bu is his he only characerisic of he marke order refleced in he book? Again, before addressing his quesion, we wish o examine he relaion beween he informaion variables and rading volume firs. In model IV, he proxies for he informaion variables are he absolue slopes of he demand and supply ha have a posiive correlaion wih he rading volume. However, in model III, he proxies for he informaion variables are he radii of he order book ha have a negaive correlaion wih he rading volume. Osensibly, hese wo resuls are conradicing o each oher. The absolue slopes used in our regression models are he average absolue slopes beween each pair of order price in he demand and supply schedules. The way we measure our radii of he order price level is o coun he number of he order price level beween he price level of he hickes deph and he bes order price level in he buy and sell pricing schedules. These radii of he order price level hus could conain boh mached and unmached orders. The reason ha he coefficiens of he radii of he order book are negaive is perhaps because he radii are predominanly occupied by unmached orders. In oher word, he informaion variables (he radii of he order book) ha we choose may conain wo disinc characerisics relaive o he convenional informaion variables (i.e., he absolue slopes of he demand and supply schedules). To examine his double-feaured characerisics in he radii of he order book, we furher divide hese radii ino wo porions 18. Tha is, he porion ha is cleared a he call price and he res lef in he book. We call he former he lower porion of he radius (i.e., he lower radius, see deails in Appendix B) and he laer he upper porion of he radius (i.e., he upper radius) o reflec graphical presenaion of he demand and supply schedules wih price in he horizonal axis and he 18 This radius decomposiion pains a pah for us o answer he previous quesion: Is his he only characerisic in he marke order refleced in he relaion wih he rading volume? 15

16 cumulaed order size in he verical axis such as he one shown in Figure 1 of Mendelson (1982). Since we choose he radius of he order book as he informaion variable, hus, he upper and lower radii of he order price level mus also conain informaion. If heerogeneous privae informaion conains wo pars, one ha can be revealed 19 (i.e., becomes public informaion) and he oher canno be revealed in he rade, hen he revealed 20 porion of heerogeneous privae informaion mos likely is due o he mached orders and he unrevealed porion of heerogeneous privae informaion mosly likely is sill wihheld in he unmached orders. Hence, our lower radius of he order price level is a proxy for he par of heerogeneous privae informaion ha has been revealed and our upper radius of he order price level is a proxy for he par of heerogeneous privae informaion has no been revealed in he rade. In regression model VI: Trading volume, we find ha he lower radii of he order price level have a posiive correlaion wih he rading volume and he upper radii have a negaive correlaion wih he rading volume. I implies ha he upper radius of he order price level ha conains he porion of unrevealed heerogeneous privae informaion in he book checks he size of he rading volume. This also implies ha given heerogeneous informaion raders wih more precise informaion may submi more aggressive orders ha are mos likely o be cleared. Ineresingly, Naes and Skjelorp (2006, pp. 424) also find ha he parameer esimae swiches sign and becomes more posiive he closer hey ge o he inner quoes. Tha is, he slope a he inner quoes is posiively relaed o he number of rades, while he average slope for he full book is negaively relaed o he number of rades. In oher words, he order book slope seems o conain differen informaion abou rading aciviy depending on wha subse of he order book we use o calculae he slope. Furhermore, we observe ha he coefficiens of marke orders are negaive, conrasing o he posiive coefficiens of he lower radii of he order price level ha reflec he number of mached order price level in he pricing schedules. This finding ouches our long delayed quesion: Bu is his he only characerisic of he marke order refleced in he book? I is ha he lower radii of he order price level may have conained par of he informaion in he marke order variables. This informaion duplicaion is due o ha he mached orders could be included in boh he radii of he order book and he marke order variables. However, here is anoher piece of informaion ha is rapped in he marke order variables bu is no refleced in he radii of he order book. Tha is, he sizes of he marke orders on boh sides are 19 There are numerous heoreical models discuss he privae informaion revelaion, such as Admai and Pfleiderer (1988), Easley and O Hara (1987), Kyle (1985) and Glosen and Milgrom (1985). 20 Here, he revealed porion of privae informaion means ha he par of privae informaion is refleced in he rading volume and he marke clearing price in a periodic call marke. 16

17 on average smaller han ha of limi orders (see Table 1). This is he reason ha he coefficiens of marke orders are negaive in our regression model VI: Trading volume. Similarly, in model V: Pos-call spread, afer conrolling for marke open and close 21, we find negaive coefficiens for he marke order variables as well as for he upper radii. The coefficien of he lower radius on sell side is posiive, bu saisically insignifican. Overall, hese findings enhance our belief ha he radii of he order book are preferred informaion variables over he convenional measures, e.g., he absolue slopes of he demand and supply schedules. In order o furher addressing he previous quesion regarding he characerisics of he marke order in relaion o he rading volume, we regress he lower radii of he order price level on marke orders of he boh sides, conrolling for marke open and close. The basic noion is ha for any successful call here is a posiive rading volume. Marke orders, if exis, mus be aking par in his rading volume and so does he conen in he lower radii (because hey represen he number of order price level). Hence, here mus be a common feaure beween marke orders and he radii of he order book. Tha is, LowerRadiusBuy, i, 1 MkOrderBuy, i, 2 MkOrderSell, i, 3 Open LowerRadiusSell, i, 1 MkOrderBuy, i, 2 MkOrderSell, i, 3 Open i, i, Close 4 Close 4 i, i, i,,. LowerRadiu s Buy, LowerRadiu s Sell, ( ) is he number of mached order price level on Open MkOrder Buy, MkOrder Sell, he buy (sell) side, ( ) is he buy (sell) indicaor variable ha is equal o one if here is a marke order and is equal o zero, oherwise. ( Close ) is he indicaor variable ha is equal o one, if he rade is a marke open (close), and zero, oherwise. and are regression error erms, respecively. In Table 4, afer conrolling for he marke open and close in boh regression models, as we prediced here is a posiive correlaion beween LowerRadiu, s Buy ( LowerRadiu s Sell, ) and MkOrder Buy, ( MkOrder Sell, ). Furhermore, here is also a 21 We would expec a posiive coefficien on he marke close variable, bu insead, we have a negaive sign, only insignifican. 17

18 posiive correlaion beween LowerRadiu s Buy, ( LowerRadiu s Sell, ) and MkOrder Sell, ( MkOrder Buy, ). This finding implies ha he marke order of he sell (buy) side can also have he posiive conribuion on he number of buy (sell) side mached order price level. This is likely because he marke order from one side no only faciliaes is own side of rade compleion bu also helps he oher side maching possibiliy (Parlour, 1998; Bloomfield, O Hara, Saar, 2005). However, by observing heir adjused 2 R, we are also aware of ha LowerRadius Buy, ( LowerRadius Sell, ) and MkOrder ( MkOrder ) are no wo idenical variables. Beween hem, Buy, Sell, hey do share some common informaion, bu a leas one of hem conains some differenial informaion as we suggesed in he previous secion (e.g., Model VI, Table 3). We conjecure ha he marke order conains wo salien feaures: he firs feaure is is aggressive price and he second feaure is is relaive smaller size (han ha of limi orders). The former feaure gives he marke order a posiive relaion wih he rading volume, bu he laer feaure conribues a negaive relaion wih he rading volume. The marke order shares is aggressive price feaure wih he lower radius ha represens he number of mached order price level. This is he main reason ha in Table 2 he coefficiens of he marke orders are posiive bu in Table 3 hey are negaive (due o he second feaure of relaively smaller size) because he appearance of he lower radii of he order price level has refleced is firs feaure. 3.2 Trader Surplus and Informaion Asymmery As discussed in Kalay e al. (2004) and Naes and Skjelorp (2006), he slopes in he limi order book summarize he level of heerogeneous informaion. However, i is more inuiive ha he slopes of he demand and supply schedules should direcly affec he surplus of he raders who submi orders; in paricular, hose raders whose orders are mached in he rades. Thus, i becomes relevan for us o know: Wha is he relaion beween he rader surplus and he level of heerogeneous informaion? By placing he price on he horizonal axis and he quaniy on he verical axis as suggesed in Mendelson (1982), in Figure 2 we observe ha he flaer he demand (supply) curve, which implies a higher he degree of heerogeneous informaion and he larger he size of he rader surplus on he demand (supply) side. Recall our argumen ha as in Naes and Skjelorp (2006) if he greaer he disagreemen among 18

19 analyss, he more genle he average absolue slopes 22 of he order book, hen his also implies ha on each side of he marke, he greaer he disagreemen among analyss, he more spread ou he pricing schedules, which leads o a larger size of he radii of he order book. Furhermore, by decomposing he radius of he order book ino LowerRadius and UpperRadius of he buy and sell sides, respecively, given is rade mach saus, we expec ha only LowerRadius on each side of he marke has he posiive conribuion o is corresponding rader surplus. However, UpperRadius ha represens he unmached orders should have a negaive conribuion o he rader surplus. On he surface, i seems ha UpperRadius and LowerRadius are he wo componens in he radius of he order book. The larger he size of one componen will lead o a smaller size of he oher componen. However, as we explained before ha he lower (upper) radius represens he revealed (unrevealed) porion of privae heerogeneous informaion. Goeler e al. (2005) suggess ha a rader willing o incur a high ransacion cos has a large benefi (i.e., welfare gain) from rade. We hus predic a posiive (negaive) relaion beween he rader surplus and he lower (upper) radius of he order price level. We regress he rader surplus of he demand and supply sides, respecively, on UpperRadius and LowerRadius of boh sides of he marke, conrolling for he order ypes, and marke open and close. Tha is, Surplus MkOdr _ buy MkOdr _ sell UpperRadius _ buy LowerRadius _ buy Open UpperRadius _ sell LowerRadius _ sell 3 Close 4. The candidaes for he dependen variable are he rade surpluses on he demand and supply sides. MkOrder Buy, ( MkOrder Sell, ) is he buy-(sell-) side indicaor variable ha is equal o one if here is a marke order and is equal o zero, if here is no marke orders, Open ( Close ) is he indicaor variable ha is equal o one if he rade a marke open (close), and is he regression error erm. UpperRadius _ buy ( UpperRadiu s _ sell ) is o proxy heerogeneous informaion of he unmached orders and LowerRadius _ buy ( LowerRadiu s _ sell ) is o proxy heerogeneous informaion of he mached orders on he buy-side (sell-side) pricing schedule. From Table 5, we observe ha he coefficiens of marke open and close 22 To compue slope, we need a leas wo pairs of price and deph observaions in he mached secion or he enire pricing schedule. From ime o ime, however, here is only one pair off order price/deph in he mached secion or even in he enire pricing schedule. This feaure makes slope applicaion limied han ha of our radius of he order price level. 19

20 indicaor variables are posiive. This finding is consisen o he predicion in he lieraure ha around marke open and close he level of heerogeneous informaion and rading volume are higher (e.g., Admai and Pfleiderer, 1988; Brock and Kleidon, 1992). Thus, we should expec a higher rader surplus around marke open and close. Furhermore, we find ha: Negaive coefficiens of upper radii: buy and sell, Posiive coefficiens of lower radii: buy and sell, Posiive coefficiens of marke order: he same side as he rader surplus. As discussed above, he upper radii of he order price level represen unrevealed heerogeneous privae informaion ha should check he size of rading volume, and hus he rader surplus. Goeler e al. (2005) suggess ha a rader willing o incur a high ransacion cos has a large benefi (i.e., welfare gain) from rade. This can explain ha he lower radii of he buy and sell sides boh conribue he revelaion of heerogeneous privae informaion by pricing aggressively and hus should have a posiive correlaion wih he rader surplus. However, here is a wis. The coefficien of he lower radii on he same side as ha of he rader surplus is smaller han ha of he opposie side. For insance, in he rader surplus of he demand side regression model, he coefficien of he lower radius on he buy side is , which is smaller han he coefficien of he lower radius on he sell side, The reason is ha he par of informaion in he lower radius on he buy side is also refleced in he buy marke order variable (2.0227) ha is on he same side as he rader surplus dependen variable. The submission of he buy marke order increases he rader surplus of he buy side because heir orders are aggressively priced. This is he reason on he surface ha when regressing he rader surplus of he demand side, he size of he coefficien of he radius on he buy side is smaller han ha of he radius on he sell side. Bu why he size of he coefficien (2.0227) of he marke order on he buy side is greaer han ha of he radius on he buy side (0.3076)? All orders included in he lower radius are he mached orders because of aggressive pricing. Among hem, he marke orders 23 have he mos aggressive prices and hus hey should conribue he mos in he rader surplus on he same side. A similar siuaion can be found in he rader surplus of supply side regression. 23 Alernaively, marke orders are aggressive orders ha add weighs on is own side of pricing schedule in deermining he marke clearing price. Tha is, if he size of he marke order on he demand (supply) side is relaively larger, hen he marke clearing price deermined ends o be higher (lower). Thus, he buy (sell) marke order will increase he rader surplus on he demand (supply) side because of he aggressive price of he marke order bu i also will decreases he rader surplus because of a higher (lower) marke clearing price. The ne effec of he marke order, hus, becomes an empirical issue. 20