Information-based trading, price impact of trades, and trade autocorrelation

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1 Informaon-based radng, prce mpac of rades, and rade auocorrelaon Kee H. Chung a,, Mngsheng L b, Thomas H. McInsh c a Sae Unversy of New York (SUNY) a Buffalo, Buffalo, NY 426, USA b Unversy of Lousana a Monroe, Monroe, LA 729, USA c Unversy of Memphs, Memphs, TN 382, USA Absrac In hs sudy we show ha boh he prce mpac of rades and seral correlaon n rade drecon are posvely and sgnfcanly relaed o he probably of nformaon-based radng (PIN). The posve relaon remans sgnfcan even afer conrollng for he effecs of sock arbues. Hgher radng acvy (.e., shorer nervals beween rades) nduces boh larger prce mpac and sronger posve seral correlaon n rade drecon. The effec of me nerval beween rades on quoe revson s sronger for socks wh hgher PIN values. These resuls provde drec emprcal suppor for he nformaon models of rade and quoe revson. 24 Elsever B.V. All rghs reserved. JEL classfcaon: G4 Key words: quoe revsons; asymmerc nformaon; prce mpac; rade auocorrelaon Correspondng auhor. Tel.: ; fax: E-mal addresses: [email protected] (K.H. Chung), [email protected] (M. L), [email protected] (T.H. McInsh).

2 . Inroducon In hs sudy we address he followng hree quesons usng rade and quoe daa: () Wha s he exen o whch quoe revsons are drven by nformaonal reasons? (2) Does nformed raders sraegc radng resul n seral correlaon n rade drecon? (3) How does nformed radng nfluence he effec of radng nensy on quoe revson? We address hese quesons by analyzng he relaon beween he probably of nformaon-based radng (PIN), he prce mpac assocaed wh rades, rade drecon seral correlaon, and me nerval beween rades. Marke mcrosrucure heory posulaes ha rades convey nformaon and exer a permanen mpac on share prce. Theory also predcs ha he prce mpac of a rade s posvely relaed o he exen of nformaon-based radng (see Hasbrouck, 99a; Easley, Kefer, and O Hara, 997b). Alhough pror sudes (see Hasbrouck, 988; Hasbrouck, 99b) show ha rades rgger quoe revsons, here s lmed evdence as o wheher he observed quoe revsons are ndeed drven by nformaon moves or some oher reasons. For example, he prce mpac of rades may resul manly from he specals s nvenory conrol (see Soll 978, 989). 2 Boh he nformaon and nvenory models predc ha markemakers rase quoes afer buyer-naed rades and lower quoes afer seller-naed rades. We dfferenae beween hese heores by examnng he relaon beween quoe revsons and PIN. If he relaon s prmarly drven by nvenory conrol hen he prce mpac of orders should be ndependen of PIN. Alernavely, f quoe revsons are drven, a leas n par, by nformaon moves, hen we should documen a posve relaon beween PIN and prce mpacs. Alhough Hasbrouck (99a) shows ha he prce mpac of a rade s greaer for smaller frms, frm sze s lkely o be a nosy proxy for nformaon-based radng. Our sudy offers a more drec and How new nformaon s mpounded no asse prces n markes wh asymmercally nformed agens s one of he nrgung quesons n modern fnancal economcs. Major conrbuors n hs area nclude Bageho (97), Copeland and Gala (983), Glosen and Mlgrom (98), Kyle (98), Easley and O Hara (987), Adma and Pflederer (988), and Sepp (992). 2 Markemakers conrol her nvenores prmarly by nfluencng he buyng and sellng decsons of her clens. When markemakers wan o decrease (ncrease) her nvenores, hey lower (rase) her bd and ask prces.

3 dscrmnang es of nformaon vs. nvenory models of quoe revsons usng a beer measure (.e., PIN) of nformaon-based radng. Alhough numerous sudes fnd posve seral correlaon n rade drecon, wha drves such correlaon s no clear. Hasbrouck (99a) holds ha posve seral correlaon n rade drecon could be arbued o prce connuy rules, specals nvenory conrol, rade reporng pracces, and oher nsuonal/marke mcrosrucure facors. Chan and Lakonshok (993, 99) sugges ha nsuonal nvesors may spread rades n a sngle secury across me o mnmze execuon coss, even n he absence of prvae nformaon. 3 Hence, n hese sudes, posve seral correlaon n rade drecon s sad o arse due o nsuonal or lqudy reasons. Alernavely, seral correlaon n rade drecon may be drven by he sraegc radng of nformed raders. Kyle (98) analyzes he radng sraegy of an nformed rader usng a dynamc model of prce formaon. Kyle assumes ha he nformed rader chooses rade sze sraegcally o maxmze hs expeced prof and shows ha he nformed rader rades n such a way ha hs prvae nformaon s ncorporaed no prces gradually. 4 To he exen ha he nformed rader explos hs prvae nformaon by breakng up rades, rade drecon s lkely o be serally correlaed when he nformed agen rades. Covrg and Ng (24) fnd ha nsuonal radng produces greaer cluserng of rades han ndvdual nvesor radng durng perods of hgh nformaon flow. In addon, Kelly and Segerwald (2) predc ha he sze of seral correlaon n rade drecon ncreases wh he probably of nformed-based radng. 3 Madhavan, Rchardson, Roomans (997) repor a smlar fndng. Ths radng behavor may no necessarly resul n posve seral correlaon n rade drecon f here are many concurren rades n he same sock by oher nvesors. 4 Back, Cao, and Wllard (2) show ha when wo raders have uncorrelaed sgnals, each rader wll rade less nensely han would a sngle rader wh he same aggregae nformaon. Back, Cao, and Wllard also show ha aggregae radng s less nense and he nformaon s revealed o he marke less quckly when here are wo nformed raders han when here s only one nformed rader. In conras, Holden and Subrahmanyam (992) show ha when a leas wo raders have he same nformaon, her nformaon s revealed almos mmedaely because each rader res o bea he ohers. In a smlar spr, Chowdhry and Nanda (99) hold ha when rades can be execued on mulple markes, nformed raders hde her nformaon by dspersng her rades across dfferen markes, whch causes a posve correlaon n he volume across exchanges. Conssen wh hs predcon, Ascoglu, McInsh, and Wood (22) fnd a sascally sgnfcan ncrease n he correlaon beween NYSE and NASDAQ/regonal radng volume precedng merger announcemens. 2

4 Alhough boh he lqudy- and nformaon-based heores predc posve seral correlaon n rade drecon, only he laer makes an addonal predcon ha he sze of seral correlaon ncreases wh PIN. Ths enables us o dfferenae he nformaon hypohess from he lqudy hypohess and allows us o es he former by examnng wheher seral correlaon n rade drecon s posvely relaed o PIN. For nsance, absence of a sgnfcan relaon beween seral correlaon n rade drecon and PIN would be nerpreed as evdence ha he seral correlaon s drven manly by lqudy reasons. On he oher hand, f he sze of seral correlaon n rade drecon ncreases wh PIN, he resul would gve credence o he nformaon hypohess. Dufour and Engle (2) exend Hasbrouck s (99a) vecor auoregressve model of rade and quoe revson by ncorporang he me nerval beween rades no he emprcal esmaon. Dufour and Engle fnd ha he prce mpac of rades, he speed of prce adjusmen o rade-relaed nformaon, and he posve auocorrelaon n sgned rades all ncrease as he me duraon beween ransacons decreases. They nerpre hese resuls as evdence ha mes of acve radng reflec an ncreased presence of nformed raders. Pror sudes (see Soll, 978) sugges ha dealer nvenory problem decreases wh radng acvy because s easer for dealers o reverse her nvenory posons when volume s hgher. Hence, he nvenory model predcs ha he prce mpac of rades decreases as he me duraon beween ransacons decreases. We exend Dufour and Engle s sudy by examnng wheher he effec of rade me nerval on prce mpac vares wh PIN across socks. We use he mehodology dealed n Easley, Kefer, and O Hara (997b) (EKO) o measure he probably of nformaon-based radng and he vecor auoregressve (VAR) models of Hasbrouck (988, 99a, 99b) and Dufour and Engle (2) o measure he prce mpac of a rade and seral correlaon n rades. 6 We hen provde emprcal evdence on he nformaonal role 6 Pror sudes employ PIN o analyze a varey of nformaonal ssues. Easley, Kefer, and O Hara (996) compare he nformaon conen of orders beween New York and Cncnna. Easley, Kefer, and O Hara (997a) examne wheher large and small rades have dfferen nformaon conen. Easley, Kefer, O Hara, and Paperman (996) nvesgae wheher dfferences n nformaon-based radng can explan observed dfferences n spreads for acve and nfrequenly 3

5 of rades by examnng wheher he prce mpac of rades and seral correlaon n rades are greaer for socks wh hgher PIN values. Chung and L (23) show ha he adverse-selecon componen of he spread and PIN are posvely and sgnfcanly relaed o each oher. They nerpre he resul as evdence of he emprcal valdy of he spread componen models hey examned. Alhough boh he adverse selecon componen and our prce mpac measure are esmaes of he rade-nduced quoe revsons, he laer capures he nformaon-drven quoe revsons more accuraely. If here were o be any prvae-nformaon nferred from a rade, mus be nferred no from he oal rade bu from ha componen whch was unancpaed. Our prce mpac model nfers he nformaon conen of a rade from he unancpaed rade whereas he spread componen model nfers he nformaon conen of a rade from he oal rade. Our emprcal resuls are conssen wh all hree hypoheses. Boh he oal and permanen prce mpacs of rades are posvely and sgnfcanly relaed o he exen of nformed radng. The posve relaon beween he prce mpac of rades and nformed radng remans sgnfcan even afer we conrol for he effecs of socks arbues. Socks wh hgher PIN values exhb hgher seral correlaon n rade drecon, ndcang ha nformed raders spl her orders. Hgher radng acvy (.e., shorer nervals beween rades) nduces boh larger prce mpac and sronger posve seral correlaon n rade drecon. The effec of me nerval beween rades on quoe revson s sronger for socks wh hgher PIN values. These resuls provde drec emprcal suppor for he nformaon models of rade and prce formaon. The paper s organzed as follows. Secon 2 esablshes heorecal lnk beween he prce mpac of rades and PIN. Secon 3 descrbes our mehodology. Secon 4 explans daa sources and he sample selecon process. Secons and 6 presen our emprcal fndngs. Secon 7 concludes. raded socks. Easley, O Hara, and Paperman (998) nvesgae he nformaonal role of fnancal analyss. Easley, Hvdkjaer, and O Hara (22) analyze he effec of nformaon-based radng on asse reurns. 4

6 2. Prce mpac of rades, seral correlaon n rades, and PIN The VAR models advanced by Hasbrouck (988, 99a, 99b) measure he mpac of a rade on prce due o asymmerc nformaon. 7 The basc premse of he VAR model s ha he markemaker revses quoes based on sgned rades (.e., + for buy, - for sell). The markemaker makes an upward adjusmen n quoe mdpon (.e., hs percepon of he rue value of he underlyng asse) afer a buyer-naed rade and a downward adjusmen afer a seller-naed rade. In shor, he VAR model analyzes how prvae nformaon s mpounded no asse prces hrough rades. 8 The VAR model s slen, however, on whch socks are lkely o exhb greaer prce mpacs of rades. The EKO model helps us beer undersand (and predc) he cross-seconal dfference n he prce mpac of rades because shows how he markemaker revses quoes accordng o he probably of nformaon-based radng. In essence, he basc srucure of he EKO model s analogous o ha of he VAR model: he markemaker ses prces equal o he expeced value of he asse, condonal on he ype of rade (buy, sell, or no rade). The EKO model assumes ha he markemaker s a Bayesan who uses he arrval of rade and he rae of radng o updae belefs abou he occurrence of nformaon evens. To deermne quoes a me, he markemaker updaes prors, condonal on he arrval of an order of he relevan ype. Analogous o he VAR model, he EKO markemaker ses he bd prce a me as he expeced value of he asse condonal boh on he hsory pror o and on he fac ha someone wans o sell a un. Lkewse, he ask prce a me s he expeced value of he asse condonal boh on he hsory pror o and on he fac ha someone wans o buy a un. The EKO model 7 Hasbrouck (988) holds ha he nformaon conen of a rade can be measured by he permanen or ulmae prce mpac of he unexpeced componen of he rade. Hasbrouck (988) measures he unexpeced componen of he rade, whch he calls he rade nnovaon, usng only pas rade hsory. Hasbrouck (99a) ncorporaes broader nformaon ses (such as hsores of quoe revsons and nonlnear funcons of he rade varables) o measure he rade nnovaon and models he neracons of rade and quoe revsons as a vecor auoregressve sysem. Hasbrouck (99b) presens new measures of rade nformaveness based on a decomposon of he varance of changes n he effcen prce no rade-correlaed and rade-uncorrelaed componens. He nerpres he rade-correlaed componen as an absolue measure of rade nformaveness and fnds ha rades are more nformave for smaller frms.

7 predcs ha he sze of he markemaker s quoe revson s posvely relaed o he probably ha he rade a me s nformaon based. Because he prce mpac of a rade s measured by he sze of he markemaker s quoe revson, he EKO model esablshes a drec heorecal lnk beween he prce mpac of rades and he probably of nformaon-based radng (PIN). Kelly and Segerwald (2) consder a varan of Easley and O Hara (992) model and show ha he enry and ex of nformed raders n response o he random arrval of prvae nformaon mples ha rades are serally correlaed. Gven ha nformed raders are radng n he curren perod, hey are lkely o rade n he followng perod agan, whch generaes seral correlaon n rades. Kelly and Segerwald show numercally ha he magnude of seral correlaon n rades ncreases wh he probably ha a rade comes from an nformed rader ( µ ). Because PIN s a posve funcon of µ, we expec ha seral correlaon n rade drecon ncreases wh PIN. 3. Mehodology We use Hasbrouck s (99a) vecor auoregressve model o esmae he prce mpac of rades and seral correlaon n rade drecon. Transacons are characerzed by a sgned rade ndcaor varable ( Trade ), whch akes he value of + for buyer-naed rades and - for sellernaed rades. The mdpon of he bd and ask prces ( Quoe ), condonal on all publc nformaon a me, represens he expeced value of he secury. Afer he ransacon a Trade ), he markemaker poss new bd ( q ) and ask ( q ) quoes. The nformaon nferred from ( b a Trade s revealed hrough he revson n he quoe mdpon (r ), whch s defned as: r b a b a = (lnquoe ln Quoe ) = [ln{( q + q ) / 2} ln{( q + q ) / 2}]. 8 The VAR model assumes ha nformed raders never rade passvely. However, several recen sudes sugges ha such an assumpon may no be warraned (see Werner, 23; Cooney and Sas, 24). 6

8 VAR model: The dynamc neracon beween quoe revson and rade s characerzed by he followng r = a r + a 2r 2 + L + btrade + btrade + b 2Trade 2 + L + ν,, () Trade = c r + c 2r dtrade + d 2Trade 2 L + L + ν. (2) 2, In quoe revson equaon (), a and b are he coeffcens measurng seral correlaon n quoe revsons and he prce mpac of rades, respecvely, and ν, s he dsurbance erm reflecng nnovaon n he publc nformaon. We measure he prce mpac of rades by b. In rade equaon (2), c and d are he coeffcens measurng he effec of lagged quoe revsons on rade drecon and rade auocorrelaon, respecvely, and v 2, s he dsurbance erm capurng he unancpaed componen of he rade (relave o an expecaon formed from lnear projecon on he rade and quoe revson hsory). If here s any prvae nformaon o be nferred from rade, mus resde n v 2, because agens can use equaon (2) o form an expecaon abou he fuure rade based on he rade and quoe revson hsory. 9 Because nformaonal shocks are permanenly mpounded no prces, he oal prce mpac can be decomposed no nformaonal (permanen) and non-nformaonal (ransory) componens. Hasbrouck (99a, equaon (6)) shows ha he expeced cumulave quoe revson condonal on v2, capures he permanen prce mpac. Hasbrouck (99b) suggess ha he quoe revsons and rades can be expressed as a lnear funcon of curren and pas nnovaons and he above VAR model can be ransformed no he followng vecor movng average (VMA) model: 9 Ths does no mean ha he nnovaon s a deermnsc funcon of he new nformaon because he presence of unnformed lqudy raders can nroduce a nose ha s uncorrelaed wh prvae nformaon. 7

9 r ν + a ν + a ν + L + b v + b v + L, (3) =,, 2, 2 2, 2, Trade c ν + c ν + L + v + d v + d v + L; (4) =, 2, 2 2, 2, 2 2, 2 where ν,, L, are he curren and pas nnovaons n quoe revsons and v, v, L, are, ν, 2, 2, he curren and pas nnovaons n rades. We measure he permanen mpac of a un rade shock on quoe revson by b. We use he model developed by Easley, Kefer, and O Hara (997b) o measure he probably of nformaon-based radng. In hs model, he markemaker does no know wheher an nformaon even has occurred, wheher s a good or bad news gven ha has occurred, wheher any parcular rader s nformed, and wheher an nformed rader wll acually rade. Wha he markemaker does know s he probables assocaed wh each of hese. The model measures he nformaon conen of rades by exracng he markemaker s belefs from rade daa. The markemaker s belefs are characerzed by four parameers ( α, δ, µ, ε ): () he probably ha an nformaon even has occurred (α ); (2) he probably of a low sgnal (δ ) gven an even has occurred; (3) he probably ha a rade comes from an nformed rader ( µ ) gven an even has occurred; and (4) he probably ha he unnformed raders wll acually rade (ε ). In he model, he markemaker s assumed o know he rade process and hus he values of hese four parameers. The markemaker s assumed o be a raonal agen who observes all rades and acs as a Bayesan n updang belefs. Over me, hese observaons allow he markemaker o learn abou nformaon evens and o revse belefs accordngly. I s hs revson ha causes quoes and hus prces o adjus. The auhors show ha he above four parameers can be esmaed by maxmzng he followng lkelhood funcon: 8

10 D µ log[ α( δ )( + ) x B µ + αδ( + ) x + ( α)( ) µ S+ B+ N ] + d = d = S D log[(( µ )( ε)) N x S+ B ]; where x = ( µ) ε, B and S are he number of buys and sells, respecvely, whn a radng day, 2 N s he number of perods whn a day ha have no rades, and D s he oal number of radng days. Any radng day s characerzed by {B, S, N}. Inuvely, he four parameers are deermned n such a way ha hey make he observed daly radng process {B, S, N} closely mach s expeced value E{B, S, N}. equaon: Fnally, we calculae he probably of nformaon-based radng (PIN) usng he followng αµ PIN = ; () αµ + ε ( αµ ) whereαµ s he probably ha a rade s nformaon based and αµ + ε( αµ ) s he probably ha a rade occurs. 4. Daa sources, sample selecon, and he varable measuremen procedure We oban daa for hs sudy from he NYSE s Trade and Quoe (TAQ) and he Cener for Research n Secury Prces (CRSP) daabases for he sx-monh perod from Aprl, 999 hrough Sepember 3, 999. Our nal sample consss of, randomly chosen NYSE-lsed socks from he CRSP daabase. Of hese, socks, we nclude 38 socks n he fnal sudy sample based on he followng crera: () socks wh an average share prce beween $ and $ and a leas en rades per day and (2) socks for whch he EKO maxmum lkelhood esmaon converges. Easley, Kefer, O Hara, and Paperman (996) oban he same formula for PIN usng he connuous me radng model. Alhough a model developed by Easley, Engle, O Hara, and Wu (2) (EEOW) provdes more nformaon and capures he dynamc feaure of rade arrval raes, he EKO model serves our purpose well snce he prmary focus of he 9

11 The daa are resrced o NYSE rades ha are coded as regular rades and NYSE quoes ha are bes bd and offer elgble. We exclude he frs rade of he day f s no preceded by a quoe. We om quoes for whch he bd prce s greaer han he ask prce and for whch he rao of he quoed spread o he quoe mdpon, he bd prce, and he ask prce, n urn, s greaer han.. Our sample comprses 9,24,343 quoes. Snce he TAQ daabase does no conan nformaon regardng wheher a rade s buyer or seller naed, we deermne rade drecon usng he Lee and Ready (99) algorhm. A rade wh a ransacon prce above (below) he prevalng quoe mdpon s classfed as a buyer- (seller-) naed rade. The prevalng quoe for a rade s he neares avalable quoe a leas fve seconds pror o he ransacon (see Lee and Ready, 99). A rade a he quoe mdpon s classfed as seller-naed f he mdpon moved down from he prevous rade (downck), and buyer-naed f he mdpon moved up (upck). If here were no prce movemens from he prevous prce, we apply he above algorhm successvely o as many as four addonal prevous quoes (fve lags). If we could no deermne he rade drecon afer fve lags, we excluded he rade from he sample. 2 In consrucng he me seres of rades, rades are denfed by sgned ndcaors (+ for buy and - for sell) (see Hasbrouck, 99a). Furher, me s ndexed begnnng wh he frs rade of he day (omng he bach open). Specfcally, he frs rade for a sock s ndexed as equals, and hereafer s ncremened each me a rade occurs. The assgnmen of ransacon order sequence begns anew each day. presen sudy s he cross-seconal relaon beween he probably of nformaon-based radng and he prce mpac of rades. Several recen sudes show ha he Lee-Ready algorhm has a serous lmaon. Lee and Radhakrshna (2) show ha, alhough he Lee-Ready algorhm s 93% accurae for rades ha can be classfed, up o 4% of repored rades canno be unequvocally classfed as eher buyer- or seller-naed due o complexes n he NYSE aucon process. Werner (23) shows ha marke buy (sell) orders frequenly execue a or below (above) he quoe mdpon and almos 3% of all marke orders are msclassfed by he Lee-Ready algorhm. She fnds ha he exen of msclassfcaon s even larger for oher order ypes. As a resul, he algorhm drascally oversaes he nformaon conen for order ypes ha are usually hough of as demandng lqudy. Cooney and Sas (24) repor a smlar fndng. 2 The mean and medan percenages of rades ha canno be accuraely denfed are 2.9% and 2.3%, respecvely, for he whole sample. The mnmum, low quarle, upper quarle, and maxmum percenages of rades ha canno be denfed are.8%,.%, 3.3%, and 7.9%.

12 . Emprcal resuls Ths secon examnes how he prce mpac of rades and seral correlaon n rade drecon are relaed o he exen of nformed radng... Informaon conen parameers and frm characerscs To esmae he probably of nformaon-based radng and relaed parameers, we calculae he number of buys and sells whn each radng day for each sock. We also desgnae perods wh no rade. The number of no-rade perods whn a radng day depends on he lengh of he un me nerval. As n Easley, Kefer, and O Hara (997b, p. 8), we deermne he un me nerval n such a way ha each nerval s long enough o accommodae one rade by dvdng he oal daly radng hours (39 mnues) by he average daly number of rades (M). For example, f a sock has 78 rades per day, we consder fve mnues (39/78) as he un me nerval. 3 If no rade occurs whn an nerval, ha perod s couned as a no-rade nerval. To assess he sensvy of our resuls wh respec o dfferen mehods of deermnng norade nervals, we also replcae our analyses usng he algorhm employed by Easley, Kefer, and O Hara (997b). Specfcally, we calculae he number of no-rade nervals usng a sngle me nerval of en mnues across all socks and esmae PIN. We repea he same procedure usng, 2, and 3 mnues nervals, respecvely. We esmae he nformaon conen parameers and PIN for each sock and oban her mean values for our sample of 38 socks accordng o hese dfferen mehods. The frs four columns of Table show he resuls when we oban he number of no-rade nervals usng a sngle me nerval of,, 2, and 3 mnues, respecvely, and he las column shows he resuls when each nerval s deermned by dvdng he oal daly radng hours by he average daly number of rades. Alhough PIN ncreases slghly from 3 We cluser our sample of socks no en porfolos accordng o he average daly number of rades and calculae he mean value of M across socks whn each porfolo. We hen use hs mean M value o deermne he number of no-rade perods for each sock. The man reasons we ook hs approach were () o smplfy our SAS code and (2) o reduce compuaonal burden.

13 .43 o.439 as he nerval ncreases from o 3 mnues, we fnd ha PIN s que robus o dfferen mehods of deermnng no-rade nervals. To furher assess he robusness of our resuls, we also replcae all he relevan ables n he remander of he paper usng PIN values based on en mnues nervals. We fnd ha he resuls are qualavely dencal o hose presened here. Hence, for brevy, we repor only he resuls based on 39/M nervals. To examne how PIN s relaed o frm characerscs, we dvde our sudy sample no quarles accordng o PIN. Porfolo comprses socks wh he lowes PIN and porfolo 4 comprses socks wh he hghes PIN. For each porfolo, we calculae he means of several sock arbues ha are lkely o reflec he frm s nformaon envronmen,.e., he bd-ask spread, deph, rade sze, share prce, radng frequency, and marke capalzaon. Table 2 shows ha porfolo has an average PIN of.68 and porfolo 4 has an average PIN of.847 and he dfference s sgnfcan a he % level. The average dollar (percenage) spread s $.46 (.66%) for porfolo and $.942 (.9%) for porfolo 4 and he dfference s sascally sgnfcan a he % level. The average quoed deph ($9,87) for porfolo s sgnfcanly larger han he correspondng fgure ($67,78) for porfolo 4. These resuls are conssen wh our pror ha markemakers pos wder spreads and smaller dephs for socks wh hgher probables of nformaon-based radng. As n Easley, Kefer, O Hara, and Paperman (996), we fnd a negave relaon beween radng frequency and PIN. Table 2 also shows ha smaller companes have hgher degrees of nformaon-based radng. Ths s n lne wh he resuls repored n Jones, Kaul, and Lpson (994), Kavajecz (999), and Lakonshok and Lee (2). We fnd ha low-prced socks exhb hgher probables of nformaon-based radng. We fnd a negave relaon beween dollar rade sze and PIN, bu hs relaon dsappears when rade sze s measured n number of shares. Hence, he observed negave relaon beween rade sze (n dollars) and PIN appears o reflec he negave relaon beween share prce and PIN. 2

14 .2. Prce mpac of rades and seral correlaon n rade drecon We frs esmae he VAR model for each sock and hen calculae he mean values of he esmaed coeffcens across socks. We calculae boh - and z-sascs o deermne wheher he mean values of he esmaed coeffcens are sgnfcanly dfferen from zero. We oban z- sascs by dvdng he sum of ndvdual regresson -sascs by he square roo of number of coeffcens. 4 We use only he frs fve lags because he coeffcens for longer lags are small. Our prmary neres s n he b coeffcens (whch measure he prce mpac of rades) n quoe revson equaon () and he rade equaon (2). d coeffcens (whch measure seral correlaon n sgned rades) n Panel A of Table 3 shows ha he mean value of he b esmaes s posve and sgnfcan (-sasc =.6 and z-sasc = 728.2), ndcang ha he markemaker rases (lowers) he quoe mdpon mmedaely subsequen o a purchase (sell) order. 6 The mean values of esmaed coeffcens for lagged rades ( b ~ b ) are subsanally smaller han he mean value of b esmaes, ndcang ha conemporary rades are he prmary cause for prce movemen. Panel B shows ha he mean values of d ( = o ) for lagged rades are all posve and sgnfcan, ndcang ha rades are serally correlaed. 4 See Warner, Was, and Wruck (988), Meulbroek (992), and Chung, Van Ness, and Van Ness (999) for a descrpon of hs mehod. Oher sudes (Hasbrouck, 99a; DuFour and Engle, 2) also use fve lags. 6 The relably of he - and z-sascs repored n Table 3 depends on esmaon error beng ndependen across equaons (.e., socks). To examne hs ssue, we rank our sudy sample of 38 socks accordng o he number of quoe revsons and esmae he followng regresson model usng he resduals from quoe revson equaon () for each of 37 pars of adjacen socks: ν,+, = λ, + λ, ν,, + ξ, ( =,., 37), where ν,+, and ν,, are he resduals from quoe revson equaon () for wo adjacen socks, λ, and λ, are regresson coeffcens, and ξ, s an error erm. We mach he resduals of wo socks accordng o he proxmy of quoe revson me. The -sascs for λ, provde evdence on cross-equaon dependence. Smlarly, we esmae he above regresson model usng resduals from rade equaon (2) for each of 37 pars of adjacen socks ha are formed accordng o he number of rades. We fnd ha he average correlaon beween ν,+, and ν,,, he sample mean and medan -sascs of he regresson slope coeffcen λ,, and he frequency of absolue -sascs exceedng ypcal sgnfcance levels, % and 2.%. Alhough here are a few observaons n he als, he mean and medan slope coeffcens are very close o zero. In addon, he average correlaon beween ν,+, and ν,, s close o zero for boh he quoe revson and rade equaons, ndcang ha adjusng for cross-equaon dependence would no change our resuls n any sgnfcan manner. 3

15 c,...,c Conssen wh he resul n Hasbrouck (99a), we fnd ha he mean values of he esmaes n he rade equaon are sgnfcan and negave, mplyng Granger-Sms causaly runnng from quoe revsons o rades. Ths resul may reflec he fac ha he markemaker wh an nvenory surplus lowers hs quoes o elc more buyer-naed rades. The resul s also conssen wh he prce expermenaon hypohess advanced by Leach and Madhavan (993) n whch he markemaker ses quoes o exrac nformaon from he raders..3. Cross-seconal es of prce mpac and rade seral correlaon We now examne how he prce mpac of rades s relaed o PIN across socks. Smlarly, we analyze wheher seral correlaon n rade drecon s a funcon of PIN. Panel A of Table 4 shows he mean values of he esmaed coeffcens for each of he four PIN porfolos. Panel B shows he resuls of Tukey s Sudenzed Range es for mulple comparsons among he four porfolos. The resul shows ha he average prce mpac of rades for porfolo 4 (.34) s sgnfcanly greaer han he correspondng fgure (.9) for porfolo. Panel B shows ha he prce mpac s sgnfcanly dfferen beween mos of he neghborng porfolos. For nsance, he average prce mpac of rades for porfolo 4 s larger han ha of oher porfolos and he dfferences are all sgnfcan a he % level. The mulple comparson resuls n Panel B show ha he average prce mpac s sgnfcanly dfferen among porfolos as a whole wh a F-sasc of 23.7 (p-value =.). These resuls provde drec evdence n suppor of he nformaon hypohess. Table 4 shows ha he mean seral correlaon ( d ) n rades for porfolo s.47 whereas he correspondng fgure s.27 for porfolo 4. We fnd ha he mean seral correlaon n rades for porfolo 4 s sgnfcanly greaer han he correspondng fgures for he oher hree porfolos. The resuls of Tukey s Sudenzed Range es show ha he mean seral correlaon n rades dffers across he four porfolos wh a F-sasc of (p-value =.). These resuls 4

16 are conssen wh he predcon of he nformaon hypohess and sugges ha prvae nformaon manfess self no only hrough he prce mpac of rades bu also hrough he radng paerns. The prce mpac of rades consss of permanen and ransory componens. The crossseconal dfference n he prce mpac of rades shown n Table 4 may also be due o some nonnformaonal reasons such as he nvenory effec. In hs secon, we employ Hasbrouck s (99b) mehod o measure he permanen prce mpac of rades and examne wheher he permanen mpac of rades s relaed o PIN. We measure he permanen prce mpac by b n quoe revson equaon (3) of he VMA model. We runcae he lagged rade nnovaon v 2, a he ffh lag because he coeffcens a longer lags are small. Panel A of Table shows ha he mean permanen prce mpac (b ) ncreases monooncally from.46 for porfolo o.2674 for porfolo 4. The resuls (see Panel B) of Tukey s Sudenzed Range es show ha he dfferences among porfolos are sgnfcan a he % level, wh a F-sasc of.62 (p-value =.). These resuls are conssen wh our expecaon ha he permanen prce mpac of rades s hgher for socks wh he hgher PIN. The mean seral correlaon ( d ) n unexpeced rades for porfolo s.88 whereas he correspondng fgure s.72 for porfolo 4. We fnd ha he mean seral correlaon n unexpeced rades for porfolo 4 s sgnfcanly greaer han he correspondng fgures for porfolos and 2. The resuls of Tukey s Sudenzed Range es show ha he mean seral correlaon n unexpeced rades dffers across he four porfolos wh a F-sasc of 2. (p-value =.). These resuls are qualavely smlar o he resuls from he VAR model repored n Table 4, ndcang ha seral correlaon n rades ncreases wh PIN. As n Table 4, we also fnd ha he mean values of he c esmaes n he rade equaon are sgnfcan and negave,,...,c and decrease n absolue values wh PIN.

17 .4. Robusness es Alhough our resuls show ha boh he oal and permanen prce mpacs of rades are posvely relaed o PIN, s possble ha he observed relaon s drven by her respecve correlaon wh oher varables. For example, he posve relaon beween he oal prce mpac of rades and PIN may be drven by her respecve assocaons wh frm sze, quoed deph, rade sze, urnover rae, or radng frequency. In addon, Dufour and Engle (2) show ha he prce mpac of rades s posvely and sgnfcanly relaed o he bd-ask spread. To examne he relaon beween he prce mpac of rades and PIN afer he conrollng for he effecs of sock arbues, we esmae he followng regresson models: ( b ) = α + α PIN + α Freq + α LnSze + α LnCap + α Spread + α Rsk + α Turnover + α LnDeph + ε, ( 7 + β Turnover + β LnDeph + ζ ; b ) = β + β PIN + β Freq + β LnSze + β LnCap + β Spread + β Rsk (6) (7) whereb measures he oal prce mpac of rades, b measures he permanen prce mpac of rades, PIN s he probably of nformaon-based radng, Freq s he average daly number of rades, LnSze s he (log) dollar rade sze, LnCap s he (log) marke value of equy, Spread s he average quoed bd-ask spread, Rsk s he sandard devaon of daly reurns, Turnover s he urnover rao, and LnDeph s he (log) number of shares quoed a bd and ask prces. 7 Because he permanen prce mpac of rades s relaed o he oal prce mpac of rades, error erms n 7 Inspecon of he correlaon marx of explanaory varables ndcaes ha selec varables are hghly correlaed wh each oher. For example, he correlaon coeffcen beween LnCap and LnSze s.9 and beween LnCap and Freq s.66. Thus, we follow he dagnosc procedure of Belsley e al. (98) o assess he exen of mulcollneary problem among he varables. We frs search for he presence of lnear dependences and solae whch explanaory varables are correlaed. We hen assess any adverse effecs of lnear dependency on he precson of esmaed regresson coeffcens. The resuls ndcae a moderae lnear dependency among LnCap, LnSze, and Turnover. However, we do no fnd any sgnfcan lnear dependency beween PIN and oher explanaory varables. 6

18 regresson models (6) and (7) are lkely o be conemporaneously correlaed. To accoun for hs and he heeroskedascy n he errors, we esmaed he above models usng he Seemngly Unrelaed Regresson (SUR) mehod. We repor he regresson resul n Table 6. The resuls show ha boh he oal and permanen prce mpacs of rades are posvely and sgnfcanly relaed o he probably of nformaon-based radng. We fnd ha PIN has a sronger effec on he permanen prce mpac ( = 6.) han on he oal prce mpac ( = 2.26), suggesng ha he observed oal prce mpac may conan non-nformaonal componens (such as he nvenory effec). PIN, ogeher wh oher explanaory varables, explans % of ner-sock varaon n he oal prce mpac and 44% n he permanen prce mpac. The lower R 2 value of he permanen prce mpac model s due, n par, o he fac ha he effec of rade sze (LnSze) on he oal prce mpac s much sronger han s effec on he permanen prce mpac. Overall, hese resuls ndcae ha he posve correlaon beween PIN and he prce mpac of rades shown n Table s no spurous and ha he average prce mpac of rades s ndeed greaer for socks wh greaer lkelhood of nformaon-based radng. To deermne wheher he posve relaon beween seral correlaon n rade drecon and PIN shown n Table 4 and Table can be explaned by her respecve correlaon wh oher varables, we esmae he followng regresson models usng he SUR mehod: ( 7 d ) = γ + γ PIN + γ Freq + γ LnSze + γ LnCap + γ Turnover + γ LnDeph + ν ; γ Spread + γ Rsk 6 (8) ( 7 d ) = τ + τ PIN + τ Turnover 8 + τ Freq 2 + τ LnDeph + υ; + τ LnSze 3 + τ LnCap 4 + τ Spread + τ Rsk 6 (9) 7

19 where d measures seral correlaon n rade drecon, d measures seral correlaon n unexpeced rades, and all oher varables are he same as prevously defned. Alhough we do no have a pror expecaons as o how hey may nfluence seral correlaon n rade drecon, we nclude varous sock arbues n he regresson model o conrol for any unknown effecs of sock arbues on he dependen varable. Table 7 shows ha he esmaed coeffcens for PIN are posve and sgnfcan a he % level, ndcang ha socks wh hgher PIN values exhb greaer seral correlaon n rade drecon. Ths resul s conssen wh he nformaon hypohess ha he sraegc radng of nformed rades resuls n serally correlaed rades. 6. Effec of me nerval on prce mpac Hasbrouck (99a) assumes ha he me beween rades s exogenous and plays no role n prce nnovaon. Damond and Verrecha (987) nvesgae how shor-sellng consrans affec prce adjusmen o prvae nformaon. Damond and Verrecha hold ha perods whou rades are more lkely o ndcae he presence of bad news because of consrans on shor sellng. In Easley and O Hara (992), he markemaker faces wo unceranes: wheher an nformaon even occurred and, f dd, wheher he counerpary s an nformed rader. The me nerval beween rades sgnals he exsence of nformaon evens, whle radng self provdes sgnals regardng he drecon of nformaon,.e., good or bad news. Easley and O Hara predc ha spreads ncrease as me nervals beween rades decrease because acve radng ndcaes a hgh probably of nformaon even. Dufour and Engle (2) provde emprcal evdence regardng he prce mpac of me nerval beween rades. They show ha hgher radng acvy nduces a larger prce mpac and sronger posve seral correlaon n rades. 8

20 We exend Dufour and Engle s sudy by examnng wheher he effec of rade me nerval on prce mpac vares wh PIN across socks. We employ he followng exended verson of Hasbrouck s VAR model, whch s smlar o he one used n Dufour and Engle (2): Trade = a r + ( b + γ ln( T )) Trade +, () = c r + ( d +θ ln( T ) ) Trade + ξ ; () r µ wheret s he me lengh beween wo consecuve rades a me and plus one second, n s he number of lags, and all oher varables are he same as prevously defned. Our man concern here s wheher cross-seconal varaons n γ can be explaned by PIN. We conjecure ha wo consecuve buys (or sells) whn a shor me nerval exer larger mpacs on prce for socks wh hgher PIN values because markemakers are lkely o vew hese orders as nformaon movaed. Thus, we expec ha γ n quoe revson equaon () s no only negave, bu also larger n absolue value for socks wh hgher PIN values. Panel A of Table 8 shows ha he mean value of γ esmae s -.46 wh a -sasc of -4.2 and a z-sasc of for he whole sample. The esmaed coeffcens for lagged neracon erms are mosly negave, alhough her magnudes are much smaller. These resuls sugges hgher radng acves (.e., shorer nervals beween rades) nduce larger prce movemens n general. Conssen wh he fndng of Dufour and Engle (2), we also fnd (see Panel B) ha he esmaes of θ n rade equaon () are all negave, ndcang ha hgher radng acvy nduces sronger posve seral correlaon n rade drecon. To deermne wheher he effec of me nerval beween rades on he prce mpac of rades dffers across socks wh dfferen levels of nformaon-based radng, we calculae he average coeffcensγ for each PIN porfolo and conduc Tukey s Sudenzed Range es for 9

21 mulple comparsons. The resuls (see Table 9, Panel A) show ha he magnude of he summed coeffcens (γ ) n he quoe equaon ncreases from -.2 for porfolo o -.23 for porfolo 4. These resuls show ha radng nensy has a posve effec on prce mpac n general and ha he effec s sronger for socks wh hgher PIN values. The resuls (see Table 9, Panel B) of Tukey s Sudenzed Range es show ha dfferences n he esmaes of neghborng porfolos are sgnfcan a he % level, excep porfolo and porfolo 2. γ beween mos 7. Concluson Pror emprcal research provdes evdence ha rades affec asse prces: buyer-naed rades have a posve mpac on share prce and seller-naed rades have a negave mpac. Surprsngly however, no drec evdence exss on he relaon beween he exen of nformaonbased radng and he prce mpac of rades or seral correlaon n rade drecon. Alhough pror research shows ha he prce mpac ncreases wh spreads and decreases wh frm sze, boh spreads and frm sze are lkely o be a nosy proxy for he exen of nformaon-based radng. In he presen sudy, we shed furher lgh on he effec of nformaon-based radng on he prce mpac of rades and rade auocorrelaon usng a drec measure of nformaon-based radng. Our emprcal resuls show ha boh he oal and permanen prce mpacs of rades are posvely and sgnfcanly relaed o he probably of nformaon-based radng. The resuls also ndcae ha socks wh a hgher probably of nformaon-based radng exhb hgher seral correlaon n rade drecon. These resuls provde drec emprcal suppor for he nformaon models of rade and prce formaon advanced n he leraure durng he las decade. 2

22 Acknowledgemens The auhors hank wo anonymous referees, he edor, Quenn Chu, Davd Kemme, Bruce Lehmann, Yuman Tse, Rober Wood, and sesson parcpans a he 22 FMA Conference for valuable commens and helpful dscussons. The auhors are solely responsble for he conen of he paper. 2

23 References Adma, A.R., Pflederer, P., 988. A heory of nra-day paerns: volume and prce volaly. Revew of Fnancal Sudes, 3-4. Ascoglu, N., McInsh, T., Wood, R., 22. Merger announcemens and radng. Journal of Fnancal Research 2, Back, K., Cao, H., Wllard, G., 2. Imperfec compeon among nformed raders. Journal of Fnance, Bageho, W., 97. The only game n own. Fnancal Analyss Journal 27, 2-4. Belsley, D., Kuh, E., Welsch, R., 98. Regresson Dagnoscs. John Wley and Sons, Inc., New York, NY. Chan, L., Lakonshok, J., 993. Insuonal rades and nra-day sock prce behavor. Journal of Fnancal Economcs 33, Chan, L., Lakonshok, J., 99. The behavor of sock prces around nsuonal rades. Journal of Fnance, Chowdhry, B., Nanda, V., 99. Mul-marke radng and marke lqudy. Revew of Fnancal Sudes 4, Chung, K.H., L, M., 23. Adverse-selecon coss and he probably of nformaon-based radng. Fnancal Revew 38, Chung, K.H., Van Ness, B., Van Ness, R., 999. Lm orders and he bd-ask spread. Journal of Fnancal Economcs 3, Cooney, J., Sas, R., 24. Informed radng and order ype. Journal of Bankng and Fnance, forhcomng. Covrg, V., Ng, L., 24. Volume auocorrelaon, nformaon, and nvesor radng. Journal of Bankng and Fnance, forhcomng. Copeland, T., Gala, D., 983. Informaon effecs on he bd/ask spread. Journal of Fnance 38,

24 Damond, D.W., Verreccha, R.E., 987. Consrans on shor-sellng and asse prce adjusmen o prvae nformaon. Journal of Fnancal Economcs 8, Dufour, A., Engle, R.F., 2. Tme and he prce mpac of a rade. Journal of Fnance, Easley, D., Engle, R., O Hara, M., Wu, L., 2. Tme-varyng arrval raes of nformed and unnformed rades. Workng paper, Fordham Unversy. Easley, D., Hvdkjaer, S., O Hara, M., 22. Is nformaon rsk a deermnan of asse reurns? Journal of Fnance 7, Easley, D., Kefer, N., O Hara, M., 996. Cream-skmmng or prof-sharng? he curous role of purchased order flow. Journal of Fnance, Easley, D., Kefer, N., O Hara, M., 997a. The nformaon conen of he radng process. Journal of Emprcal Fnance 4, Easley, D., Kefer, N., O Hara, M., 997b. One day n he lfe of a very common sock. Revew of Fnancal Sudes, Easley, D., Kefer, N., O Hara, M., Paperman, J., 996. Lqudy, nformaon, and nfrequenly raded socks. Journal of Fnance, Easley, D., O Hara, M., 987. Prce, rade sze, and nformaon n secures markes. Journal of Fnancal Economcs 9, Easley, D., O Hara, M., 992. Tme and he process of secury prce adjusmen. Journal of Fnance 47, Easley, D., O Hara, M., Paperman, J., 998. Fnancal analyss and nformaon-based rade. Journal of Fnancal Markes, 7-2. Glosen, L., Mlgrom, P.R., 98. Bd, ask and ransacon prces n a specals marke wh heerogeneously nformed raders. Journal of Fnancal Economcs 4,

25 Hasbrouck, J., 988. The quoes, nvenores and nformaon. Journal of Fnancal Economcs 22, Hasbrouck, J., 99a. Measurng he nformaon conen of sock rades. Journal of Fnance 46, Hasbrouck, J., 99b. The summary nformaveness of sock rades: an economerc analyss. Revew of Fnancal Sudes 4, 7-9. Holden, C, Subrahmanyam, A., 992. Long-lved prvae nformaon and mperfec compeon. Journal of Fnance 47, Jones, C.M., Kaul, G., Lpson, M.L., 994. Transacons, volume, and volaly. Revew of Fnancal Sudes 7, Kavajecz, K.A., 999. A specals s quoed deph and he lm order book. Journal of Fnance 4, Kelly, D.L., Segerwald, D.G., 2. Prvae nformaon and hgh-frequency sochasc volaly. Workng paper, Unversy of Calforna a Sana Barbara. Kyle, A.S., 98. Connuous aucons and nsder radng. Economerca 3, Lakonshok, J., Lee, I., 2. Are nsder rades nformave? Revew of Fnancal Sudes 4, 79-. Leach, C., Madhavan, A., 993. Prce expermenaon and secury marke srucure. Revew of Fnancal Sudes 6, Lee, C., Radhakrshna, B., 2. Inferrrng nvesor behavor: Evdence from TORQ daa. Journal of Fnancal Markes 3, 83-. Lee, C., Ready, M.J., 99. Inferrng radng drecon from nraday daa. Journal of Fnance 46, Madhavan, A., Rchardson, M., Roomans, M., 997. Why do secury prces change? A ransaconlevel analyss of NYSE socks. Revew of Fnancal Sudes,

26 Meulbroek, L., 992. An emprcal analyss of llegal nsder radng. Journal of Fnance 47, Sepp, D.J., 992. Block radng and nformaon revelaon around quarerly earnngs announcemen. Revew of Fnancal Sudes, Soll, H., 978. The supply of dealer servces n secures markes. Journal of Fnance 33, 33-. Soll, H., 989. Inferrng he componens of he bd-ask spread: Theory and emprcal ess. Journal of Fnance 44, -34. Warner, J., Was, R., Wruck, K., 988. Sock prces and op managemen changes. Journal of Fnancal Economcs 2, Werner, I., 23. NYSE order flow, spreads, and nformaon. Journal of Fnancal Markes 6,

27 Table Summary of nformaon conen parameers No-rade nervals mn mn 2 mn 3 mn 39/M Parameer PIN α (.49) (.392) (.397) (.442) (.32) (.288) (.28) (.33) (.297) (.774) δ µ (.267) (.228) (.249) (.24) (.924) ε (.886) (.68) (.734) (.844) (.666) (.27) (.86) (.89) (.8) (.4) We esmae he nformaon conen parameers (,, ) for each sock usng he algorhm n Easley, α δ µ, ε Kefer, and O Hara (997b) and calculae her mean values for our sudy sample of 38 NYSE socks. The parameers are defned as: α = he probably ha an nformaon even has occurred; δ = he probably of an unfavorable sgnal; µ = he probably ha an nformed rader rades gven an nformaon even has occurred; and ε = he probably ha an unnformed rader rades. PIN = αµ /( αµ + ε ( αµ )) s he probably ha a rade s nformaon based gven a rade occurs. We esmae hese parameers usng he followng maxmum lkelhood funcon (Easley e al., 997b, p. 89): D µ log[ α ( δ )( + ) x B µ + αδ ( + ) x + ( α)( ) µ S + B+ N ] + d = d = S D log[(( µ )( ε)) where B and S are he number of buys and sells, respecvely, whn a radng day, N s he number of perods whn a day ha have no rades, D s he oal number of radng days durng he es perod, and x = ( µ)ε 2. We dvde he radng day no,, 2, 3, and 39/M mnues nervals, n urn, o deermne he number of no-rade nervals, where M s he average daly number of rades. Numbers n parenheses are sandard devaons. N x S + B ],

28 Table 2 Frm characerscs and he probably of nformaon-based radng (PIN) Whole sample (38 socks) Porfolo (3 socks) Porfolo 2 (34 socks) Porfolo 3 (3 socks) Porfolo 4 (34 socks) PIN Spread ($) %Spread (%) Deph ($) Trade sze ($) Prce ($) Frequency Cap (n $,) ,423 32, , ,87 34, ,298, ,778 33, ,, ,27 3, , ,78 29, ,79 Porfolo ,77 -, ,74 -sa p-value We group our sample of socks no four porfolos accordng o PIN. Porfolo ncludes socks wh he lowes PIN and Porfolo 4 ncludes socks wh he hghes PIN. For each porfolo, we repor he mean value of he followng varables: PIN = he probably of nformaon-based radng; Spread = he dollar spread; %Spread = he percenage spread (.e., he rao of he dollar spread o he quoe mdpon); Deph = he quoed deph n dollars; Trade sze = ransacon sze n dollars; Prce = ransacon prce; Frequency = daly number of rades; and Cap = marke value of equy. We calculae -sascs o deermne wheher observed dfferences (beween porfolo and porfolo 4) are sascally sgnfcan.

29 Table 3 Coeffcen esmaes of he vecor auoregressve (VAR) model Panel A: Quoe equaon ( r ) Mean -sa p-value z-sa p-value Mean -sa p-value z-sa p-value a b a b a b a b a b b Adj R =.2666 Panel B: Trade equaon ( Trade ) Mean -sa p-value z-sa p-value Mean -sa p-value z-sa p-value c d c d c d c d c d Adj R =.472 Ths able shows he resuls of he followng vecor auoregressve (VAR) model: r a r + a r + L + b Trade + b Trade + b Trade + L + ν, = Trade = c r + c 2r 2 + L + dtrade + d 2Trade 2 + L + ν 2, ; where r = (lnquoe lnquoe ), Trade s a rade ndcaor varable (+ for buyer-naed rades and for seller-naed rades), and ndexes ransacon sequences. We esmae he above model for each sock and repor he mean values of he esmaed coeffcens for our sudy sample of 38 NYSE socks. We calculae boh - and z-sascs o deermne wheher he mean values of he esmaed coeffcens are sgnfcanly dfferen from zero. We oban z-sascs by dvdng he sum of ndvdual regresson -sascs by he square roo of number of coeffcens. We repor he cross-seconal mean value of Adj-R 2 from he ndvdual sock VAR resuls.,

30 Table 4 Summary and comparson of he VAR model coeffcens Panel A: Sum of he coeffcens for each porfolo a Porfolo Mean (3 socks) -sa p-value Adj-R Porfolo 2 Mean (34 socks) -sa p-value.... Adj-R Porfolo 3 Mean (3 socks) -sa p-value Adj-R The able shows he resuls of he followng vecor auoregressve (VAR) model: r a r + a r + L + b Trade + b Trade + b Trade + L + ν, = Trade = c r + c 2r 2 + L + dtrade + d 2Trade 2 + L + ν ; 2, where r = (lnquoe lnquoe ), Trade s a rade ndcaor varable (+ for buyer-naed rades and for seller-naed rades), and ndexes ransacon sequences. We esmae he above model for each of our sudy sample of 38 NYSE socks and repor he mean values of he esmaed coeffcens for each of he four porfolos ha are formed accordng o PIN (see Panel A). Porfolo ncludes socks wh he lowes PIN and Porfolo 4 ncludes socks wh he hghes PIN. Panel B repors he resuls of Tukey s Sudenzed Range es for mulple comparsons among he four porfolos. We repor he crossseconal mean value of Adj-R 2 from he ndvdual sock VAR resuls. n Panel B ndcae % sgnfcance level. Porfolo 4 Mean (34 socks) -sa p-value.4... Adj-R Panel B: Tukey s Sudenzed Range es for mulple comparsons among porfolos Porfolo Porfolo Porfolo Porfolo Porfolo Porfolo F-value p-value.... b c, d

31 Table Summary and comparson of he VMA model coeffcens Panel A: Mean value of he sum of he coeffcens a Porfolo Mean (3 socks) T-sa P-value.... Adj-R Porfolo 2 Mean (34 socks) T-sa P-value.... Adj-R Porfolo 3 Mean (3 socks) T-sa P-value.... Adj-R Porfolo 4 Mean (34 socks) T-sa P-value.8... Adj-R Panel B: Tukey s Sudenzed Range es for mulple comparsons among porfolos Porfolo Porfolo Porfolo Porfolo Porfolo Porfolo F-value P-value <. <. <. <. Ths able shows he resuls of he followng vecor movng average (VMA) model: r ν + a ν + a ν + L + b v + b v + L, =,, 2, 2 2, 2, Trade = cν, + c 2ν, 2 + L + v 2, + dv 2, + d 2v 2, 2 + L ; where r = (lnquoe lnquoe ) s he change of he logarhm md-pon of he quoed bdask prces caused by he rade a me. Trade s a rade ndcaor varable (+ for buyer naed order, and for seller naed order). v,, v,, L, are he curren and pas quoe nnovaons n quoes, and v 2,, v 2,, L, are he curren and pas rade nnovaons n rades. We measure he permanen prce mpac of rades by b. We esmae he above model for each sock n our sudy sample and repor he mean values for each of he four porfolos ha are formed accordng o PIN (see Panel A). Porfolo ncludes socks wh he lowes PIN and Porfolo 4 ncludes socks wh he hghes PIN. Panel B repors he resuls of Tukey s Sudenzed Range es for mulple comparsons among he four porfolos. Sgnfcance a he % level. b c d

32 Table 6 Cross-seconal regresson of he prce mpac of rades Panel A: Dependen varable = Inercep PIN Freq LnSze Lncap Spread Rsk Turnover Lndeph Adj-R (8.3) (2.26) (-2.39) (-6.99) (-4.8) (2.7) (-.84) (2.3) (2.) Panel B: Dependen varable = (7.3) (6.) (-.77) (-2.3) (-4.34) (.2) Ths able shows he resuls of he followng regresson models: b b -.8 (-.62).2 (.7) -.2 (-.4) ( b ) = α + α PIN + α Freq + α LnSze + α LnCap + α Spread + α Rsk + α Turnover + α LnDeph + ε, = ( b ) = β + β PIN + β Freq + β LnSze + β LnCap + β Spread + β Rsk + β Turnover + β LnDeph + ζ ; = where b measures he oal prce mpac of rades, b measures he permanen prce mpac of rades, PIN s he probably of nformaon-based radng, Freq s he average daly number of rades, LnSze s he (log) dollar rade sze, LnCap s he (log) marke value of equy, Spread s he average quoed bd-ask spread, Rsk s he sandard devaon of daly reurns, Turnover s he urnover rao, and LnDeph s he (log) number of shares quoed a bd and ask prces. We esmaed he above models usng he Seemngly Unrelaed Regresson (SUR) mehod. The numbers n he parenheses are - sascs. and sgnfcan a he % and % level, respecvely..4387

33 Table 7 Cross-seconal regresson of rade auocorrelaon Panel A: Dependen varable = Inercep PIN Freq LnSze Lncap Spread Rsk Turnover Lndeph Adj-R (.7) (2.29) (.7) (.32) (-3.4) (.87) (-.8) (.24) (-.6) d.287 (.8) (2.6).24 (6.46) Panel B: Dependen varable = (.) (-2.3) (-.37) d.2 (.79). (2.7) -.92 (-3.4).433 Ths able shows he resuls of he followng regresson models: ( d ) = γ + γ PIN + γ Freq + γ LnSze + γ LnCap + γ Spread + γ Rsk + γ Turnover + γ LnDeph + ν, ( d = ) = τ + τ PIN + τ Freq + τ LnSze + τ LnCap + τ Spread + τ Rsk + τ Turnover + τ LnDeph + υ ; d measures seral correlaon n rade drecon, = d measures seral correlaon n unexpeced rades, PIN s he probably of nformaon- where based radng; Freq s he daly number of rades; LnSze s he (log) dollar rade sze; LnCap s he (log) marke value of he equy; Spread s he quoed bd-ask spread; Rsk s he sandard devaon of daly reurn; Turnover s he monhly rade volume urnover rao; and LnDeph s he (log) number of shares quoed a bd and ask prces. We esmaed he above models usng he Seemngly Unrelaed Regresson (SUR) mehod. The numbers n he parenheses are -sascs. and sgnfcan a he % and % level, respecvely.

34 Table 8 Esmaes of he VAR model wh boh rade ndcaor and me lengh beween rades Panel A: Quoe equaon ( r ) Mean -sa p-value z-sa p-value Mean -sa p-value z-sa p-value Mean -sa p-value z-sa p-value a b γ a b γ a b γ a b γ a b γ b γ 2.26E Adj-R 2 =.2897 Panel B: Trade equaon ( Trade ) c d θ c d θ c d θ c d θ c d θ Adj-R 2 =. Ths able shows he resuls of he followng VAR model: = a r + ( b + γ ln( T )) Trade +, Trade = c r + ( d +θ ln( T ) ) Trade + ξ r µ where r = (lnquoe lnquoe ), Trade s a rade ndcaor varable (+ for buyer-naed rades and for seller-naed rades), T s he me beween wo consecuve ransacons plus one second, and ndexes ransacon sequences. We esmae he above model for each sock and repor he mean values of he esmaed coeffcens for our sudy sample of 38 NYSE socks. We calculae boh - and z-sascs o deermne wheher he mean values of he esmaed coeffcens are sgnfcanly dfferen from zero. We oban z-sascs by dvdng he sum of ndvdual regresson -sascs by he square roo of number of coeffcens. We repor he cross-seconal mean value of Adj-R 2 from he ndvdual sock VAR resuls. ;

35 Table 9 Summary and comparson of he VAR model coeffcens wh me nerval beween rades Panel A: Sum of he coeffcens for each porfolo a Quoe equaon ( r ) Trade equaon ( Trade ) b Porfolo Mean (3) -sa p-value Adj-R Porfolo 2 Mean (34) -sa p-value Adj-R Porfolo 3 Mean (3) -sa p-value Adj-R Porfolo 4 Mean (34) -sa p-value Adj-R Panel B: Tukey s Sudenzed Range es for mulple comparsons among porfolos Porfolo Porfolo Porfolo Porfolo Porfolo Porfolo F-value p-value Ths able shows he resuls of he followng vecor auoregressve (VAR) model: γ = a r + ( b + γ ln( T )) Trade +, = c r + ( d +θ ln( T ) ) Trade + r µ Trade where r = (lnquoe lnquoe ), Trade s a rade ndcaor varable (+ for buyer-naed rades and for seller-naed rades), T s he me beween wo consecuve ransacons plus one second, and ndexes ransacon sequences. We esmae he above model for each of our sudy sample of 38 NYSE socks and repor he mean values of he esmaed coeffcens for each of he four porfolos ha are formed accordng o PIN (see Panel A). Porfolo ncludes socks wh he lowes PIN and Porfolo 4 ncludes socks wh he hghes PIN. Panel B repors he resuls of Tukey s Sudenzed Range es for mulple comparsons among he four porfolos. We repor he cross-seconal mean value of Adj-R 2 from he ndvdual sock VAR resuls. Sgnfcan a he % level. c ξ ; d θ