Wenjin Kang and Wee Yong Yeo. Department of Finance and Accounting National University of Singapore. This version: June 2007.

Transcription

1 LIQUIDITY BEYOND THE BEST QUOTE: A STUDY OF THE NYSE LIMIT ORDER BOOK Wenjn Kang and Wee Yong Yeo Department of Fnance and Accountng Natonal Unversty of Sngapore Ths verson: June 2007 Abstract We conduct a comprehensve analyss for the New York Stock Exchange (NYSE) lmt order book at both the aggregate market-level and the ndvdual stock-level based on a sample coverng all the NYSE ordnary stocks. We provde detaled descrpton of the lmt order book and show that t supples consderable lqudty beyond the best quote posted on the market. We fnd that at the market-level, volatlty s a key factor determnng the lmt order book s lqudty provson. When market volatlty ncreases, the book becomes more dsperse and the lqudty provded by the lmt order book decreases. Past market movements, especally market declnes, exert sgnfcant mpact on the lmt order book as well. Our lmt order book measures possess sgnfcant explanatory and predctve power on other lqudty measures such as bd-ask spread or Amhud llqudty. The cross-sectonal analyss of the ndvdual stock s lmt order book suggests that market volatlty and returns only affect the systematc component of the lqudty t provdes. JEL Classfcaton: G19 Keyword: Lmt order, Lqudty, Market return, Volatlty * Kang and Yeo are from the Department of Fnance and Accountng, NUS Busness School, Natonal Unversty of Sngapore, Sngapore , Tel: and , Fax: , E-mal: bzkwj@nus.edu.sg and bzyeowy@nus.edu.sg. ** The usual comment apples. 1

2 LIQUIDITY BEYOND THE BEST QUOTE: A STUDY OF THE NYSE LIMIT ORDER BOOK Ths verson: June 2007 Abstract We conduct a comprehensve analyss for the New York Stock Exchange (NYSE) lmt order book at both the aggregate market-level and the ndvdual stock-level based on a sample coverng all the NYSE ordnary stocks. We provde detaled descrpton of the lmt order book and show that t supples consderable lqudty beyond the best quote posted on the market. We fnd that at the market-level, volatlty s a key factor determnng the lmt order book s lqudty provson. When market volatlty ncreases, the book becomes more dsperse and the lqudty provded by the lmt order book decreases. Past market movements, especally market declnes, exert sgnfcant mpact on the lmt order book as well. Our lmt order book measures possess sgnfcant explanatory and predctve power on other lqudty measures such as bd-ask spread or Amhud llqudty. The cross-sectonal analyss of the ndvdual stock s lmt order book suggests that market volatlty and returns only affect the systematc component of the lqudty t provdes. JEL Classfcaton: G19 Keyword: Lmt order, Lqudty, Market return, Volatlty 2

3 1. Introducton Lmt orders are ndspensable to fnancal markets. Many equty markets, ncludng stock exchanges and Electronc Communcaton Networks (ECNs), are pure lmt order markets. A trader submttng a lmt order sacrfces the mmedacy to trade for the possblty of tradng at a prce better than the prevalng market prce. The lmt order book s a vtal source of lqudty wth whch market orders can be executed aganst. In an order-drven market, the lmt order book s the sole provder of lqudty. 1 In a hybrd market such as the NYSE, the lmt order book stll plays an essental role n lqudty provson. Chung et al. (1999) show that the number of quotes n whch at least one sde orgnates from lmt orders accounts for 74.9% of all quotes on the NYSE, whle the number of quotes posted exclusvely by specalsts amounts to only 5.9%. Gven the mportance of lqudty n asset prcng and market effcency, 2 a better understandng of the lmt order book and ts lqudty provson should mprove the desgn and regulaton of fnancal exchanges and ultmately, the nvestor s welfare. Notwthstandng the mportance of the lmt order book as a source of lqudty, most of the exstng emprcal studes are conducted wth small-sze samples of securtes over short tme span. The TORQ data used n Chung et al. (1999) covers 144 randomly-selected NYSE stocks from November 1990 to January Bas, Hllon, 1 Examples of order-drven market nclude the Australan Stock Exchange, Pars Bourse, Shangha Stock Exchange, Sngapore Exchange, Tokyo Stock Exchange, and Toronto Stock Exchange. 2 The nfluence of lqudty on expected return of rsky asset s documented by Amhud and Mendelson (1986), Brennan and Subrahmanyam (1996), Pastor and Stambaugh (2003). Chorda et al. (2005) show that the ncrease of lqudty mproves the effcency of the stock market. 3

4 and Spatt (1995) provde an emprcal analyss of the lmt order book, ncludng ts lqudty provson, wth 19 tradng days of data for 40 stocks from the Pars Bourse. Benston, Irvne, and Kandel (2002) examne the cost to execute market orders aganst the lmt order book based on two months of lmt order data of 263 frms from the Toronto Stock Exchange. Domowtz, Hansch, and Wang (2005) analyze the lmt order book from the Australan Stock Exchange for 19 of the ASX-20 ndex stocks from March to December 2000 and show that lqudty (return) comovement s caused by cross- sectonal correlaton n order types (order flows). 3 The paucty of extensve order-level data lmts our understandng about the lmt order book. For example, what s the shape of the lmt order book and how much lqudty does t provde at the aggregate market-level? We are nterested n the determnants of the tme-seres varaton of the lqudty provded by the lmt order book. Partcularly, we are nterested n the way t nteracts wth market state varables such as return and volatlty. In addton, we would lke to examne how the lmt order book s lqudty provson at the ndvdual stock-level s related wth these market state varables and ts frm characterstcs. The answers to these research questons depend on the avalablty of lmt order data that covers an extensve sample of stocks over a long sample perod. Ths paper uses the lmt order book data recently released by the NYSE to study the 3 Other emprcal works on lmt orders nclude Sandas (2001), Hollfeld, Mller, and Sandas (2004), Cao, Hansch, and Wang (2005), Wa-Man Lu (2005), Hollfeld et al. (2005), et al. 4

5 nature of the lmt order book and answers the questons rased above. To the best of our knowledge, ths s the frst paper that provdes a comprehensve study of the lmt order and ts lqudty provson based on a sample that ncludes all of the NYSE ordnary stocks. We construct varous measures desgned to capture the essence of the lmt order book, especally the lqudty t provdes, and report both the market-wde and the portfolo-level averages of these measures. The lmt order book database n ths paper s of ndependent nterest because, to our knowledge, ths s the frst tme that such volumnous data have been nvolved to examne the lmt order book at the aggregate market level. Specfcally, we constructed three lmt order book lqudty measures: depth, dsperson, and cost-to-trade. The lmt order depth measure represents the weghted average of the number of lmt order shares placed at each prce pont n the lmt order book. 4 The dsperson of the lmt order book measures how far apart from each other, or from the mdquote, the lmt orders are placed n the book. It captures the executon prce nnovaton whch the lmt order trader expects when he sacrfces the demand of mmedacy and nstead provdes lqudty to the market. 5 Our cost-to-trade measure follows the cost-of-round-trp measure proposed n the study of Benston, Irvne, and Kandel (2002). 6 It measures how much an nvestor have to pay to buy and 4 Goldsten and Kavajecz (2000) use cumulatve depths, the sum of all depths wthn a certan prce range away from the mdquote, to compare the lqudty provded by the lmt order book before and after the 1997 tck-sze change on the NYSE. 5 Foucault et al. (2005) and We (2005) suggest that the lmt order book dsperson s lnked wth the patence of lmt order traders and the pck-off rsk they face. 6 Benston et al (2002) use trade dollar amount to specfy the round-trp trade sze. Instead we use trade 5

6 sell the same number of shares smultaneously by market orders: a small cost represents a lqud market. If the round-trp trade sze s large, t needs to walk up and down further n the lmt order book, and hence our cost-to-trade measure consders the lqudty beyond the best quotes posted on the market. 7 Smlar tradng cost measures have been used by Kavajecz and Odders-Whte (2004) to study the relatonshp between lmt order book shape and techncal tradng rules. Our analyss about the lmt order book s lqudty provson focuses on the nteracton between the cost of executng (large) market orders aganst the lmt order book and market state varables. We pay specal attenton to the role of return volatlty n the lmt order book s functon of provdng lqudty. There s an extensve lterature addressng the nteracton between lqudty and volatlty. Earler papers, such as Stoll (1978), Ho and Stoll (1980), Grossman and Mller(1988), suggest that hgh volatlty wll ncrease the market maker s nventory rsk and therefore ncrease the transacton cost. Recently, Vayanos (2004) show that, f nvestors wthdraw ther nvestment when fund performance falls below an exogenous threshold, fund managers wll develop a tme-varyng preference for lqudty that ncreases wth the volatlty n the market. Deuskar (2006) show that when market perceves hgh volatlty, the lqudty wll dry up and ths n turn wll lead to an ncreasng realzed volatlty. Furthermore, Placng lmt buy (sell) order can be vewed as wrtng an Amercan-type share amount to avod the nfluence of day-to-day prce fluctuaton on trade sze specfcatons. 7 The bd-ask quote spread s a specal case of our cost-to-trade measure when the round-trp sze s less than the best bd and ask quote depth on the market. Chorda et al (2001) provde the tme-seres study for quote spread at the aggregate market level. 6

7 out-of-money put (call) opton. The opton-nature of lmt orders only amplfes the nfluence of volatlty on the cost of lqudty t provdes. Chacko et al. (2006) suggest n ther opton-based model that when the competton n the market makng sector s mperfect, volatlty s a key drver of the cost to trade aganst the lmt order book. In our emprcal test, we dfferentate the nfluence from nvestor s expectaton on future volatlty and the observed past volatlty on lmt order book by usng opton-market mpled volatlty and hstorcal return varance. Another lne of lterature that s related to our study nvolves recent theoretcal works wth regard to how the declne of asset prces reduces lqudty. Morrs and Shn (2003) and Bernado and Welch (2006) show that the declne n asset prces ntroduces sellng pressure that trggers further prce drops. As a result, traders rush to lqudate ahead of each other and the lqudty on the market s reduced by the stock-run phenomenon descrbed above. Kyle and Xong (2001) suggest that a large drop n market valuaton level ncreases the rsk averson of arbtrageurs and hampers ther lqudty provson to the market. Brunnermeer and Pedersen (2005) lnk the lqudty on the market wth the fundng constrant of the market makng sector. When market declnes, the market makers who pledge the securtes they hold as collateral has to face stff fundng constrant and can only provde less lqudty to the market. Motvated by the models mentoned above, we separate returns nto postve and negatve realms to examne whether there s any asymmetrc relatonshp between the lmt order book and the sgned returns. 7

8 We show that a consderable porton of lqudty les beyond the best quote posted on the NYSE. We fnd that the average lmt order book depth on each prce pont s close to the best bd/offer depth, and the lmt order book provdes reasonable lqudty for large-sze market order tradng. When movng away from the best quotes, both the sze of the lmt orders at each prce pont and the dstance between them (.e. the dsperson of the book) ncreases. Our lmt order book measures are persstent over the daly frequency at the aggregate market level and ndvdual stock level. Our emprcal results suggest that hgh market volatlty ncreases the dsperson of the lmt order book. Hgh volatlty ncreases the opton value of lmt orders and lmt order traders wll ask for hgher compensaton by puttng ther orders further away from the best quote. As a result, the lmt order book cost-to-trade and dsperson ncrease as volatlty ncreases. We also fnd that the depth of the lmt order book s also postvely correlated wth market volatlty, snce when volatlty ncreases tradng va market orders becomes more costly and more traders wll fnd t optmal to use lmt orders. We fnd that past market movements nfluence the dsperson of the lmt order book and the cost-to-trade. The mpact from market returns s asymmetrc: market declne leads to a stronger ncrease n the lmt order dsperson and cost-to-trade than market rse. Our lmt order book measures can explan and predct other frequently-used lqudty measures such as Amhud llqudty rato and bd-ask spread at the aggregate market level. 8

9 When examnng the lqudty of the lmt order book at a cross-sectonal ndvdual stock-level, we decompose the lqudty provded by ndvdual stock s lmt order book nto ts systematc and dosyncratc components. We fnd that the dosyncratc component of ndvdual stock s lmt order book lqudty provson s not affected by market volatlty or market return movements. We also fnd that the negatve relatonshp between volatlty and lqudty documented above becomes stronger as the market value of the stock decreases. Furthermore, we fnd that the lqudty provded by the ndvdual stock s lmt order book decreases after a negatve market return and ncreases weakly after a postve market return, whle the stock s dosyncratc return has lttle nfluence on ts own lmt order book lqudty provson. The rest of the paper s organzed as follows. Secton 2 descrbes the data set. In Secton 3 we construct our lmt order book lqudty measures, and n Secton 4, we provde the summary statstcs of the lmt order book at the aggregate market level. Secton 5 dscusses what causes the tme-seres varaton of our lmt order book measures and Secton 6 examnes whether our lmt order book measures can explan or predct other lqudty measures. Secton 7 analyzes the lqudty n the lmt order book at a cross-sectonal level. Fnally, Secton 8 concludes our paper. 2. Data Our lmt order book data, the NYSE OpenBook database, s provded by the New 9

10 York Stock Exchange (NYSE). It contans detaled nformaton on the lmt order book for all the securtes traded on NYSE. There are two fles for each day of tradng. The frst fle, called the Open Fle, contans the total number of shares for each prce pont for each stock at the close of the operaton of the OpenBook system on a specfc day. The second fle, called the Day Fle, contans the ncremental changes to the number of shares for each prce pont for each stock from the close of the OpenBook on that partcular day to the close of the OpenBook on the next tradng day. Incremental changes nclude actvtes such as lmt order submsson, executon, and cancellaton. For every ncremental change, the amount of change n the number of shares and the correspondng prce pont s recorded, wth the tme stamp for the change. For order submsson, the number of shares n the order s recorded as a postve change at the correspondng prce pont. For order executon (ether partal or full) or cancellaton, the number of shares nvolved s recorded as a negatve change at the correspondng prce pont. The ncremental changes before 8 a.m. are recorded wthout tme stamps. The tme stamps start from 8 a.m. to the tme when the lmt order book closes for the partcular day. On average there are at least fve mllon records of ncremental changes of lmt order book per day, resultng n a total of more than one bllon observatons n our lmt order book data. For every stock, we construct ts lmt order book for up to the best 100 quotes on both the bd and offer sdes. The lmt order book thus can be recorded as a vector of ts best 100 lmt buy (sell) order szes and prce ponts for each stock at any gven 10

11 moment. Due to the massveness of the data, we only consder the lmt order book at fve mnutes ntervals from 8 a.m. (the start of the tme stamps) to 4 p.m. (when the lmt order book closes). The closng poston of the lmt order book that we constructed matches wth the Open Fle of the NYSE OpenBook of the next tradng day. The ntraday lmt order book snapshots we have constructed at every fve mnute ntervals allow us to compute varous depths, dsperson, and cost-to-trade daly measures for each stock n our sample. Our sample stocks are ordnary U.S. stocks lsted on the NYSE, and our sample covers the perod from January 2003 to December We exclude ADRs, unts, shares of benefcal nterest, companes ncorporated outsde U.S., Amercus Trust components, close-ended funds, preferred stocks, and REITs. We only nclude stocks wth an average prce between $3 and $100. We also requre that, on the average, our sample stock must have at least best ten quotes on both the bd and the offer sdes of ts lmt order book. 8 After all these flterng, our sample contans more than 1,000 stocks. The large sample sze and relatvely long sample perod enable us to conduct a comprehensve analyss on the relaton of our lmt order book measures wth other lqudty measures, market return and volatlty, and frm-level characterstcs. Besdes the lmt order data we descrbed above, we also collect transacton-level data from the NYSE Trades and Automated Quotatons (TAQ) 9 and daly stock prce and return 8 The ordnary U.S. stocks that on average have less than 5 quotes on ether the bd or the offer sdes of ther lmt order book accounts for no more than 3% (do you have an dea how much ths s for less than 10 quotes?) of the total sample. 9 For the transacton data, f the trades are out of sequence, recorded before the market open or after 11

12 data from the Center for Research n Securty Prces (CRSP). 3. Measurng the Lmt Order Book In ths secton we construct three measures to measure the shape of and the lqudty provded by the lmt order book,whch are the depth, the dsperson, and the cost-to-trade of the lmt order book. Depth measures the amount of lmt buy and sell orders that are placed on the lmt order book. Dsperson measures how close to the best quotes and to each other these orders are placed. The cost-to-trade proxes the cost to trade a hypothetcally large market order as t walks up and down the lmt order book. 3.1 The Depth of the Book We measure the depth of the book by takng nto account both the number of shares and where they are placed. Ths s done by computng the weghted average of the number of shares that are placed across dfferent postons. 10 The lmt order book depth of stock j, LDepth j, s gven by the followng: the market close, or wth specal settlement condtons, they are not used n the computaton of the daly spread and other lqudty varables. Quotes posted before the market open or after the market close are also dscarded. The anomalous transacton records are deleted accordng to the followng flterng rules: () Negatve bd-ask spread; () Quoted spread > $5; () Proportonal quoted spread > 20%; (v) Effectve spread / Quoted spread > In the lterature, the best bd-ask depth s often used to represent the depth of the market, snce the data for depth beyond the best quotes are usually unavalable. Where data of orders beyond the best quotes are avalable, the sum or the smple average of all the orders at the avalable quotes behnd the best quotes s used. However, both methods do not accurately represent the depth of the lmt order book. For example, one share queung at the best bd s unlkely to represent the depth at the buy sde f there are a thousand shares queung at one tck behnd the best bd. 12

13 LDepth j 1 = 2 n w Q = 1 n = 1 w Buy + n w Q = 1 n = 1 w Sell (1) h Q refers to the number of shares placed at the th best bd or offer prce, where the best bd or offer prce s denoted by =1, wth h { Buy, Sell} representng the bd or offer sde of the lmt order book. We wll call Q ( Q Buy Sell ) the th bd (offer) sze henceforth. We wegh h Q accordng to ts proxmty to the best quotes. Snce orders placed closer to the best quotes contrbute more to the depth of the market than those placed further away, they are assgned a larger weght. Partcularly, we assgn a lnearly declnng weghted average (LDW), where w =n+1-. Hence, for example, f we are only concerned wth the frst fve best quotes, the LDW weght from the best to the ffth best quotes, normalzed by the denomnator, wll be 5/15, 4/15, 3/15, 2/15, and 1/15 respectvely. 11. After calculatng the weghted depth measures on the bd and offer sdes of the book, we report the average of these two as the lmt order book depth. 3.2 The Dsperson of the Book The lqudty provded by the lmt order book s not only dependent on the amount of lmt buy and sell orders, but also on how close to the best quotes and to each other they are placed. We construct the dsperson measures to show how clustered or dspersed these shares are n the book. The dsperson of the book can be thought of as 11 We also use varous exponentally declnng weghts. The results are smlar to those of the lnearly declnng weghts. 13

14 the nverse of the densty of the lmt order book. It measures how dsperse or spread out the orders are n the book. The hgher the dsperson, the less dense the book s, and the less clustered the orders are to each other. There are two dsperson measures. The frst dsperson measure, LDsperson j for stock j, s computed as follow. LDsperso n j 1 = 2 n = 1 w Buy n = 1 w Dst Buy Buy + n = 1 w Sell n = 1 w Dst Sell Sell (2) h Dst s the prce nterval between the th best bd or offer and ts next better quote. buy sell Hence, Dst = Bd Bd ) and Dst Offer Offer ) ( 1 = ( 1. We weght the dstance measure by the sze of the orders. The weghts, w, are the bd and offer sze,.e. Q as defned above (where h {Buy, Sell } represents the bd or offer sde of h the lmt order book), and normalzed by dvdng each weght by the sum of all the weghts. If =1, we calculate the nterval between the poston of the best lmt buy (sell) order and the md-quote nstead. The second dsperson measure s LDstance, where h Dst s the prce nterval between the th best quotes and the md-quote. 12 For both the weghted average measures of dsperson, the larger the Dst h, the more dsperse the orders are at that sde of the lmt order book. The LDsperson shows the 12 The dfference between LDsperson and LDstance can be llustrated wth the followng example. The md-quote s at $10.00 and Bd 1 through Bd 5 s at $9.99, $9.00, $8.99, $8.98, and $8.97 respectvely. For the LDsperson measure, only Bd 2 wll be penalzed heavly as t s 99 cents away from ts next better quote, whle the dstances between Bd 3 through Bd 5 and ther respectve next better quotes are only one cent. However, for the LDstance measure, snce every Dst measures the dstance of the respectve bd prces from the md-quote, Bd 1 through Bd 5 wll be heavly penalzed. Hence, n ths example, the book s deemed to be more dspersed for the LDstance measure than the LDsperson measure. 14

15 compettveness between the lmt order traders. Under ferce competton, where the lmt order traders undercut one another to gan prce prorty, the LDsperson measure of dsperson wll be small. On the other hand, the LDstance measures the economc rent that the lmt order traders wsh to capture as a compensaton for bearng executon rsk. The hgher the LDstance, the larger the potental economc rent they can collect. Naturally, hgh competton among lmt order traders leads to smaller economc rent for them. Thus, we expect postve correlaton between the LDsperson and the LDstance measures of the lmt order dsperson. 3.3 The Cost-to-trade One gauge of the lqudty provded by the lmt order book s to examne how well the book handles large trades. Wthout the nterference of the specalst and wthout new lmt order submsson, a market buy (sell) order wll frst be executed aganst the lmt sell (buy) orders at the best offer (bd) quote. If the sze of the market order s larger than the best offer (bd) sze, the remander of the unexecuted market order wll be executed aganst the lmt orders queung at the next best offer (bd) quote. Such s the process n whch a large market buy (sell) order wll walk up (down) the lmt order book. The further, the market order walks up or down the book, the further away from the ntrnsc value (assumng that ths value les wthn the spread) wll the executon prce be, and the more t wll cost the market order trader. The lower the lqudty of the lmt order book, the hgher ths cost wll be. Ths, n essence, s the prncple behnd the cost-to-trade measure. Our cost-to-trade measures follow closely 15

16 the Cost of Round Trp (CRT) measure as proposed by Benston, Irvne, and Kandel (2002). For each stock, we look at the cost to buy and sell 1% and 2% of ts average tradng volume smultaneously. Let T be the total number of shares to be bought or sold. Followng the conventon above, we denote the th best bd (offer) prce by Buy P ( P Sell ) and the th best bd (offer sze) by Q ( Q Buy Sell ). We defne two ndcator varables, I and I Sell Buy k k, whch refer to number of shares bought or sold respectvely at each prce pont: I Buy k Buy Q = ( T 0 k 1 = 1 Q Buy ) f f T > T > otherwse k 1 = 1 k = 1 Q Q Buy Buy and T < k = 1 Q Buy and I Sell k Sell Q = ( T 0 k 1 = 1 Q Sell ) f f T > T > otherwse k 1 = 1 k = 1 Q Q Sell Sell and T < k = 1 Q Sell Assumng the true prce of the stock s the mdquote, we compute the cost-to-trade as follows: Cost to Trade = K K Buy Buy I k ( Mdquote Pk ) + k = 1 k = 1 I Sell k T Mdquote ( P Sell k Mdquote) (3) 16

17 4. The Emprcal Attrbutes of the NYSE Lmt Order Book 4.1 Sample statstcs Table 1 reports the market-level descrptve statstcs of the lmt order book. For the lmt order depth and dsperson, we compute the measures based on the best 5 and 10 quotes on both sdes of the book. For the cost-to-trade measure, we compute the cost to buy and sell 1% and 2% of the average daly tradng volume smultaneously. 13 For each of the lqudty measure, we obtan ts daly measure by averagng the fve-mnute nterval ntraday records for each stock every day. The market-level fgures reported n Table 1 Panel A represent the cross-sectonal equally-weghted average for the daly measures we obtaned above. To compare our lmt order book lqudty measures wth other lqudty measures, we also compute the cross-sectonal average daly share tradng volume and the daly share turnover rate, whch s the rato of the daly share volume to the total share outstandng. The quoted (effectve) spread and the TAQ depth are generated by averagng all quoted (effectve) spreads and best bd/offer depths reported n TAQ of all the transacton wthn any gven tradng day. The Amhud llqudty rato s the 13 Although we use only up to the 15 best quotes (only the best 5 and 10 quotes are reported) on both sdes of the lmt order book n our computaton of the depth and dsperson measures mentoned above, for the computaton of the cost to trade, the smultaneous buyng and sellng of hypothetcally large orders may walk up and down the lmt order book beyond the best 15 quotes. However, they never reach the best 50 quotes that are contaned n our lmt order daly vector record. We do not report the results for the smultaneously buyng and sellng of 3% of the average daly tradng volume as they are smlar to those of the 1% and 2%. 17

18 llqudty rato proposed n Amhud (2002), gven by the absolute value of the daly return dvded by the daly dollar tradng volume. The expected market volatlty (VIX) s a market volatlty measure computed by the Chcago Board Opton Exchange (CBOE) as a measure of market expectatons of near-term volatlty conveyed by S&P 500 stock ndex opton prces. Fnally, the hstorcal market volatlty s the computed by applyng the method of French, Schwert and Stambaugh (1987) to the tralng 20-day market daly returns. The average depth s 1491 shares and 1661 shares for the best 5 and best 10 lmt order quotes, respectvely. The ncreasng lmt order average depths suggest that the sze of lmt orders ncreases as we move away from the best quote. For the best 5 and 10 quotes, the mean of LDsperson are 6.14 and cents, respectvely. The results show that the lmt order book s more dsperse when far way from the best quotes. The mean of LDstance are and cents respectvely. As for the cost-to-trade on the lmt order book, t wll cost a trader, on average, 1.94% more than the ntrnsc value to smultaneously buy and sell 1% of the average tradng volume of a stock. 14 The proportonal transacton cost ncreases to 3.54% f he wshes to trade 2% of the average tradng volume. Gven that the daly tradng volume for an average stock s about 1 mllon shares, the data suggests a one-way tradng of 10,000 shares wll cost less than 1% of the transacton value. It ndcates 14 The ntrnsc value s assumed to be the transacton share volume multpled by the mdquote. 18

19 that the lmt order book on the NYSE provde reasonable lqudty to large market order tradng. The medan value of our market-level lmt order measures are close to the mean value, ndcatng that skewness s unlkely to be a concern. The coeffcents of varance are hghest for the cost-to-trade and lowest for the lmt order depth. We also show the average tradng volume for a stock s slghtly more than 1 mllon shares, equal to 0.66% of the total number of shares outstandng as the daly turnover rate. The average quoted (effectve) spread s 3.18 (2.49) cents, and the average of the best bd and offer sze (TAQ depth) s 1,696 shares, smlar to the weghted-average depth of the best 10 quotes posted by the lmt order book Table 2 shows the correlaton among our lmt order measures, other lqudty measures, and market volatlty. 15 The correlaton coeffcents between our dsperson or cost-to-trade measures of the lmt order book and other lqudty measures such as spread and Amhud rato are postve and sgnfcant. We fnd that hgh market volatlty s correlated wth a dsperse lmt order book and hgh cost-to-trade, a noteworthy pont we wll explore further n the subsequent sectons. One surprsng fndng s that our lmt order depth measure s postvely correlated wth the other lqudty measures, ncludng our dsperson and cost-to-trade measures. An ex ante expectaton could be that a larger lmt order depth should lead to hgher 15 For the sake of brevty we only present the results based on the best 10 quotes for depth and dsperson and the 1% average tradng volume as the trade sze for the cost-to-trade measure. Usng alternatve specfcatons such as the best 5 quotes for depth and dsperson and 2% average tradng volume for cost to trade measure wll yeld smlar results. 19

20 lqudty and less transacton cost. However, as Foucault (1999) pont out, hgher executon rsk wll lead to larger spread posted by the lmt order traders, whch n turn makes tradng va market orders more costly. Thus more traders wll fnd t optmal to carry ther trades usng lmt orders. Ths suggests a postve correlaton between the lmt order book depth and dsperson as we observe here. In any case, ths result suggests that depth alone s not a good measure of lqudty. 5. The Tme-Seres Analyss of Lmt Order Book Measures In ths secton we address the queston what causes the tme-seres varaton of the shape of the lmt order book and the lqudty t provdes. It s concevable that market returns, especally downsde market returns, wll have an mpact on the lmt order book measures we constructed above, gven that Chorda et al. (2001) and Hameed et al. (2006) document that stock market declnes lead to sgnfcant drop of market lqudty, whch s measured by spread, over both the daly and monthly frequency. Another canddate s volatlty. Submttng a lmt buy (sell) order s equvalent to wrtng an out-of-the-money put (call) opton. The economc rent the lmt order trader collects, that s, the dfference between ther lmt order prce and the mdquote, reflect the value of ther opton wrtng servce. Hgh volatlty ncreases the opton value embedded n the lmt order and thus should ncrease the cost for market-order traders to trade aganst the lmt order book. 20

21 Table 3 examnes whether our lmt order measures can be predcted by market returns and volatlty after controllng for ther own lagged values. Thus, the daly market-level lmt order cost-to-trade, dsperson, and depth are regressed on the lag opton-market mpled volatlty (VIX), the hstorcal market volatlty, the past market upsde and downsde movements, as well as the frst-order lagged values of the correspondng lmt order measures. Panel A reports the estmate from the regresson of the lmt order book cost-to-trade measure on the ndependent varables descrbed above. The results for the cost to trade based on 1% and 2% of the average daly volume are smlar. They show hghly postve frst- order auto-correlaton of the cost-to-trade measure. We fnd that the cost-to-trade on the lmt order book s postvely correlated wth market volatlty, measured by ether the opton-mpled volatlty or hstorcal volatlty. When both volatlty measures are ncluded n the regresson, the opton-mpled market volatlty domnates the hstorcal market volatlty. It suggests that t s the forecasted or expected volatlty that matters for lmt order traders, snce ther orders wll be executed at an uncertan tme n the future, as suggested by Deuskar (2006) and Chacko et al. (2006). If the expected market volatlty ncreases from two standard devatons below the mean to two standard devatons above t, the market-order trader who wants to trade 1% (2%) of the average daly tradng volume aganst the lmt order book needs to pay an addtonal transacton cost of approxmately 0.5% (0.6%) of hs transacton s ntrnsc value. 21

22 The lmt order book s cost-to-trade ncreases sgnfcantly mmedately after a large negatve market movement. However, ths relatonshp between cost-to-trade and the declne n market returns s not sgnfcant beyond the frst lag. Although, the reverse occurs after market advance, ths relatonshp s not statstcally sgnfcant for postve returns. Our results are consstent wth prevous studes such as Chorda et al. (2001) and Hameed et al. (2006), whch show that transacton cost, measured by the bd-ask spread, ncreases sgnfcantly after market declne and decreases only weakly after postve return. Panel B reports the tme-seres regresson result for the lmt order dsperson measure. 16 The persstency of the lmt order dsperson s reflected by the sgnfcantly postve auto-correlaton coeffcents. The dsperson measures for both the best 5 and best 10 quotes show that, the lmt order book becomes more dspersed as market volatlty ncreases. It suggests that when volatlty ncreases, the opton value embedded n the lmt order ncreases and, as a result, lmt order traders ask for hgher compensaton by placng ther orders further away from the best quote and from each other. The domnance of the expected market volatlty over hstorcal realzed volatlty s once agan evdenced here. Smlar to the results n Panel A, and consstence wth the lterature, lqudty n the lmt order book represented by our dsperson measure decreases sgnfcantly after market downturn and ncreases 16 We only report the results for the LDstance measure. The results for the LDsperson measure are smlar. 22

23 weakly after market advance. In terms of the lmt order book depth, Panel C shows a postve relatonshp between market volatlty and the depth n the lmt order book. As stated above, hgh volatlty leads to lmt order traders demandng hgher economc rent for provdng lqudty. Thus, tradng va market orders becomes more costly, and more traders wll fnd t optmal to use lmt orders. Ths s also consstent wth the postve correlaton between the lmt order book depth and dsperson (cost-to-trade) we observe above. We fnd that past market movements seem to have lttle relaton wth the depth of the lmt order book. Depth n the lmt order book seems to decrease generally n respond to market movements n ether drecton. However, the coeffcents are not statstcally sgnfcant. Smlar to the cost-to-trade and the dsperson measures, our depth measures are exhbt hgh frst-order auto-correlaton. 6. Can Lmt Order Book Predct Market Lqudty? In a pure lmt order market, the lmt order book s the sole source for all lqudty; n a hybrd market such as the NYSE, both the specalst and the lmt order book provde the lqudty. Nevertheless, how the lmt order book, a crucal source of lqudty, can nfluence the market-wde lqudty on the stock market remans as an unexplored topc. In ths secton, we provde emprcal evdence on whether the lmt order book lqudty measures we construct above can explan or predct the nter-temporal varaton of the lqudty at the market level. 23

24 In Table 4, we regress two commonly-used lqudty measures, the Amhud llqudty rato (Panel A) and the quote spread (Panel B), on the contemporaneous and lagged values of our lmt order book lqudty measures at the market-level. In the contemporaneous regresson, the cost-to-trade and the dsperson measures carry sgnfcant postve mpact on the Amhud rato and spread. It s natural that a dspersed lmt order book and a hgh cost-to-trade for large-sze market orders reduce the lqudty n the market. However, we also fnd that larger lmt order book depth s negatvely correlated wth the lqudty n the market. Ths observaton s consstent wth our prevous arguments that more lmt orders placed on the book do not necessarly mprove the lqudty, snce nvestors prefer to trade by lmt orders when the cost of market-order tradng s hgh, that s, precsely the moment of low lqudty. To test the ablty of our lmt order lqudty measures to predct market-level lqudty, we frst regress the market-level lqudty (Amhud or spread measure) on ts own lagged values as the benchmark. Next we add the same lmt order measures, one at a tme, nto the regresson. We fnd that hgh cost-to-trade and large lmt order book dsperson predct low lqudty n the market for the next tradng day. Large lmt order depth agan predcts low lqudty nstead of hgh lqudty on the market, though the coeffcent for the regresson of quoted spread s not statstcally sgnfcant. 24

25 In summary, n ths secton we fnd that our lmt order book lqudty measures possess sgnfcant explanaton and predcton power to the market-level lqudty tme-seres varaton. Hgh cost-to-trade and large lmt order book dsperson lead to low contemporaneous and future lqudty at the market-wde level. Once agan, the data suggests that depth alone s not a good representaton of lqudty. Larger depth does not necessarly mean that the market s more lqud. 7. The Cross-Sectonal Analyss of the Lqudty n the Lmt Order Book Thus far we have looked at the lqudty provded by the lmt order book at a market level and our analyses have been based on equally-weghted market averages of our lmt order book lqudty measures. In ths secton, we wll examne the lqudty n the lmt order book at a cross-sectonal level. Snce, the results n the prevous sectons show that depth s not a good measure of lqudty and that our cost-to-trade and dsperson measures are very smlar n nature, we wll focus our analyss on the cost-to-trade measure of lqudty n the lmt order book. Furthermore, snce expected volatlty domnates hstorcal volatlty, we wll only enter the former nto the regressons. We wll examne how the lqudty n the book, as well as ts systematc and dosyncratc components, respond to volatlty and return movements. To decompose the lqudty provded by the lmt order book for each stock nto ts systematc and dosyncratc components, we compute for each day the daly cost-to-trade for each stock, whch s the average of the ntraday observatons, and regress t on the 25

26 equally-weghted market-level average cost-to-trade measure. Panel A n Table 5 reports the cross-sectonal average of the coeffcents of the ndependent varable (the beta) and the R 2 of the regressons for all the stocks n the sample. The cross-sectonal mean of the beta s a lttle more than one and s sgnfcant at the 1% level of sgnfcance. The dstrbuton of the beta s skewed to the rght. On average, the R 2 for the regressons are around 35%. Almost all the stocks has postve beta and 981% of the coeffcent estmates are statstcally sgnfcant. The systematc and dosyncratc components of the lqudty for each stock are defned as the ftted and resdual value of the regresson above respectvely. In Panel B, we perform the stock-by-stock regresson of the cost-to-trade measure, as well as ts systematc and dosyncratc component for each stock, on the lag expected market volatlty, the lag stock return, the lag market return, the lag dosyncratc return, as well as ts own lag. The market return s measured by the return on the S&P500 ndex and the dosyncratc return s defned as the resdual from the one-factor market-return model. We report the cross-sectonal mean of the coeffcent estmates. An ncrease n the expected market volatlty ncreases the cost-to-trade provded by ndvdual stock s lmt order book. A closer examnaton shows that only the systematc component of the lqudty measure s sgnfcantly related to the expected market volatlty. As n the market-level analyss, lqudty of the stocks decreases mmedately after a negatve return and ncreases weakly mmedately after a postve return. However, the decrease n lqudty after a negatve return s due to the market 26

27 component and not the dosyncratc component of the return. The relatonshp between past returns and lqudty s much stronger for the systematc component of the lqudty than the dosyncratc component. In Panel C, we enter the stock-level expected volatlty nto the regressons. The expected total stock return volatlty s the opton mpled volatlty of the ndvdual stock. Ths expected total volatlty s regressed aganst the expected market volatlty VIX to obtan the expected dosyncratc stock return volatlty s the resdual of the regresson. The results show that lqudty of the stocks decreases as expected total stock volatlty ncreases. Both expected market volatlty and expected dosyncratc volatlty affect the lqudty of the stocks. The expected market volatlty affects only the systematc component of lqudty. The dosyncratc component affects both the systematc and dosyncratc components of lqudty, althought to a lesser extent. Next we dvde the full sample of stocks nto three sze-based portfolos accordng to ther market value at the end of year We perform the above regresson analyss on these sze-based portfolos to see how the lqudty of stocks n these portfolos respond to the lag expected market volatlty, the lag stock return, and ts own lags. The results are shown n Table 6. In Panel A, we report the portfolo-level average cost-to-trade, lmt order depth, dsperson and dstance for the sze-based portfolos. The results show substantal nter-portfolo varatons n the cost-to-trade and 27

28 dsperson measures. It cost 1.43% more than the ntrnsc value to trade 1% of the average daly tradng volume for the large-sze portfolo. Ths cost ncreases to 1.85% and 2.54% for the medum- and small-sze portfolo respectvely. Lmt orders n the lmt order book for the large-sze portfolo are only 2.54 (7.01) cents away from each other (from the best quotes). Ths dstance ncreases to (29.75) for the small-sze portfolo. Stocks n the large-sze portfolo have a deeper lmt order book. However, there s not much dfference n the depth for stocks of the other two portfolos. Overall, the data suggests that the lmt order book of large stocks provdes more lqudty than the book of smaller ones. Panel B shows the results when we regress the cost-to-trade of each stock on ts frst lag, the lag expected market volatlty, and the lag postve and negatve stock returns. The large-sze (small-sze) portfolo exhbts the hghest (lowest) auto-correlaton. Increasng past market volatlty reduces sgnfcantly the lqudty n the lmt order book for all the portfolos. The effect s stronger (weaker) for the small-sze (large-sze) portfolo. The larger the fall n stock prces, the larger the reducton of the lqudty n the book for all the portfolos. The effect of the ncrease n prces on the lqudty n the book s not sgnfcant for the large-sze portfolo. In Panel C, the stock s lag return varables are replaced wth the lag market and lag dosyncratc return varables. The coeffcents for the market return varables are smlar to those of the stock return varables n Panel B except that the effect of a 28

29 postve return on the lmt order book lqudty becomes statstcally nsgnfcant. Past negatve dosyncratc return does not have an effect on the lqudty n the lmt order book, whle past postve return ncreases the lqudty for the medum and small-sze portfolos. In general, the cross-sectonal analyss shows that hgher volatlty n the market leads to a decrease n the lqudty of the lmt order book for ndvdual stocks and ths effect s stronger for small stocks than large stocks. The lmt order book lqudty decreases mmedately after a market downturn for all stocks and ncreases weakly after a market upturn for stocks wth medum and small market value. Moreover, we fnd that the dosyncratc component of lqudty s not affected by market volatlty or market downturns. In addton, we also fnd dosyncratc return movements do not affect lmt order book lqudty as much as market returns. 8. Concluson The large lterature of lqudty has greatly advanced our understandng of the tradng and prcng of securtes n fnancal markets. However, our knowledge of the lmt order book, whch s a vtal source of lqudty, remans lmted due to the lack of data. In ths paper we used by far the most comprehensve lmt order data, n terms of the sample stock coverage and sample perod, to conduct thorough analyss for the lmt order book on the NYSE at both the aggregate market-level and the ndvdual 29

30 stock-level. We construct multple measures to study the dfferent dmensons of the lmt order book and the lqudty t provdes. Detaled statstcs are provded to descrbe the lmt order book at both the market-level and the stock-level. We fnd that a consderable porton of lqudty les beyond the best quote posted on the market and the lmt order book provdes reasonable lqudty for large-sze market-order tradng. We examne the tme-seres varaton of the market-level lmt order book lqudty measures on a daly bass. Volatlty, especally the expected volatlty, matters for the shape (s there a better word?) of the lmt order book and the lqudty t provdes. The lmt order book cost-to-trade and dsperson ncrease when volatlty ncreases. The opton-mpled expected volatlty domnants the hstorcal realzed volatlty n our analyss, hghlghtng the opton-nature of lmt orders. Past market movement also nfluences the dsperson of the lmt order book and ts cost-to-trade. Market declne has a stronger mpact than market advance. The lmt order book s cost-to-trade and dsperson are postvely correlated wth other lqudty measures such as Amhud llqudty rato and bd-ask spread n both the contemporaneous and the predcton regressons. We also fnd postve correlaton between lmt order depth and other llqudty measures. It suggests that more nvestors prefer to trade by lmt orders when the cost to trade market orders s hgh, 30

31 whch mples low lqudty on the market. Hence, larger depth n the lmt order book alone does not necessarly mean more lqudty. At the cross-sectonal level, we show that lqudty provded by the ndvdual stock s lmt order book decreases as market volatlty ncreases. Ths relaton s stronger the smaller captalzaton the stock has. The ndvdual stock s lmt order book lqudty decreases n respond to a negatve return and ncreases weakly after a postve return. Further analyss suggests that market returns and volatlty only affect the systematc component of the lqudty provded by the ndvdual stock s lmt order book. The dosyncratc component of the lqudty provded by the ndvdual stock s lmt order book s not related wth these market state varables mentoned above and s only weakly related wth the dosyncratc return of the stock tself. Future research could seek to better understand the varaton of the lqudty provded by lmt order book on an ntraday bass. Wth the data set used n ths paper, ths wll be feasble. We have shown emprcally that market volatlty encourages traders to use lmt orders and ncreases the compensaton they demand. Theoretcal understandng about how volatlty affects lmt order traders tradng strategy appears to be a frutful area. 31

32 Reference Amhud, Y., Illqudty and Stock Returns: Cross-Secton and Tme-Seres Effects. Journal of Fnancal Markets 5, Amhud, Y., Mendelson, H., Asset prcng and the Bd-Ask Spread. Journal of Fnancal Economcs 17(2), Benston, G., Irvne, P., Kandel, E., 2002.,Workng Paper, Emory Unversty and Hebrew Unversty. Bas, B., Hllon, P., Spatt, C., An Emprcal Analyss of the Lmt Order Book and the Order Flow n the Pars Bourse. Journal of Fnance, 50.5, Brennan, M., Subrahmanyam, A., 1996, Market mcrostructure and asset prcng: On the compensaton for llqudty n stock returns, Journal of Fnancal Economcs Brunnermeer, Markus and Lasse Pedersen, 2005, Market Lqudty and Fundng Lqudty, Workng Paper, Prnceton Unversty. Cao, C., Hansch, O., Wang, X., 2005, The nformatonal content of an open lmt order book, Workng paper Chacko, George, Jakub Jurek, and Erk Stafford, 2006, Prcng Lqudty: The Quantty Structure of Immedacy Prces, Workng paper, Harvard Unversty Chorda, T., Roll, R., Subrahmanyam, A., 2001, Market lqudty and tradng actvty, Journal of Fnance LVI, Chorda, T., Roll, R., Subrahmanyam, A., 2005, Evdence on the Speed of Convergence to Market Effcency, forthcomng, Journal of Fnancal Economcs. Chorda, T., Roll, R., Subrahmanyam, A., 2006, Lqudty and Market Effcency, Workng paper. Chung, K., Van Ness, B., Van Ness, R., Lmt orders and then bd-ask spread Journal of Fnancal Economcs, 53, Copeland, T., Gala, D., 1983, Informaton effects and the bd-ask spread, Journal of Fnance 38,

33 Deuskar, Prach, 2006, Extrapolatve Expectatons: Implcatons for Volatlty and Lqudty, Workng Paper, New York Unversty Domowtz, I., Hansch, O., Wang, X., 2005, Lqudty commonalty and return comovement, forthcomng, Journal of Fnancal Markets. Foucault, T., 1999, Order flow composton and tradng costs n a dynamc lmt order market, Journal of Fnancal Markets 2, Foucault, T., Kadam, O., Kandel, E., 2005, Lmt order book as a market for lqudty, Revew of Fnancal Studes, 18, French, K., Schwert, G., Stambaugh, R., 1987, Expected stock returns and volatlty, Journal of Fnancal Economcs, 19, Goldsten, M., Kavajecz, K., 2000, Eghths, Sxteenths and Market Depth: Changes n Tck Sze and Lqudty Provson on the NYSE, Journal of Fnancal Economcs 56, Hameed, A., Kang, W., Vswanathan., 2006, Stock market declne and lqudty, Workng paper Hollfeld, B., Mller. R., Sandas., P., 2004, Emprcal analyss of lmt order markets, Revew of Economc Studes, 71, Hollfeld, B., Mller. R., Sandas., P., Slve, J., 2004, Estmatng the gans from trade n lmt order markets, Workng paper Kavajecz, K., Odders-Whte, E., 2004, "Techncal Analyss and Lqudty Provson," Revew of Fnancal Studes 17, Kyle, Pete, and We Xong, 2001, Contagon as a wealth Effect, Journal of Fnance, 4, Pastor, L., Stambaugh, R., 2003, Lqudty rsk and expected stock returns, Journal of Poltcal Economcs 111, Sandas, P., 2001, Adverse secton and compettve market makng: Emprcal evdence from a lmt order market, Revew of Fnancal Studes 14, Vayanos, Dmtr, 2004, Flght To Qualty, Flght to Lqudty and the Prcng of Rsk, NBER workng paper. 33