Time varying decomposition of posted bid-ask spreads

Transcription

1 Time varying decomposiion of posed bid-ask spreads Fredrik Berchold Deparmen of Finance, chool of Business, ockholm Universiy, ockholm, weden. Absrac In his sudy, Huang and oll s (1997) hree way decomposiion model for posed bid-ask spreads is esimaed using a daa se which consiss of observaions from 10 socks raded a ockholmsbörsen (B), randomly seleced from he OMX sock index. The Huang and oll (1997) model encompasses saisical and rade indicaor models by for example Ross (1984), oll (1989), George e al (1991), Glosen and Harris (1988), decomposing posed bid-ask spreads ino order processing, invenory and adverse selecion componens. This sudy suppors he Huang and oll s (1997) hree way decomposiion of posed bid-ask, when adjused o accommodae for he way ransacions are recorded a B. Fixed probabiliies of reversed rade s ranges from 1.38 o 1.5 percen, i.e. rade coninuaions are highly probable. The signs of esimaed adverse selecion cos coefficiens are posiive for all socks, ranging from 0.31 o percen. No bunching procedure is used, which yielded higher adverse selecion coefficiens in Huang and oll s (1997) sudy. Also, he adjused Huang and oll s model is exended o accoun for repeaing ime of day paerns in he probabiliy of a reversed rade. Noably, his exension does no affec he adverse selecion or invenory coefficiens. The paern is consisen wih he idea ha expeced mid quoe changes is diurnal. Also, he resuls are consisen wih informed rading righ afer he opening call. Keywords: Bid-ask, spread, quoe, decomposiion, ime varying, diurnal, invenory, asymmeric informaion JEL classificaion: G10; G13; G14 1

2 1. Inroducion New life has been brough o marke microsrucure models of he bid-ask spread by he availabiliy of large daa ses, ofen conaining hundreds of housands of ransacions. everal quesions have been answered, while some remain. How does he bid-ask spread evolve from ransacion o ransacion? How do differen ypes of invesors affec he oucome? Empirically, ransacions are irregularly spaced in ime. ome occur seconds apar while oher are separaed by minues or more. Also, agreed prices are discree and change in muliples of he smalles allowed price uni. Mos noably, repeaing ime of day, or diurnal, volailiy and rading volume paerns have been documened. Resen empirical research srongly suggess ha high frequency daa exhibi srong dependencies no found in daily, weekly or monhly daa. In addiion, daa ses differ. For example, he Trade and Quoe (TAQ) disribued by he NYE, have ransacion prices recorded wih posed bid-ask quoes. Ineresingly, he definiion of posed bid-ask quoes vary. A he NYE, posed quoes are valid for a fixed quaniy of shares (or deph ), and among elecronic exchanges, Taiwan sock exchange poss non binding reference bid-ask quoes. Also he iming convenion may differ, i.e. how ransacions are recorded in daabases. The marke micro srucure lieraure focuses on how ransaced prices and posed bid-ask quoes adjus. Ideally, informaion is made available o all invesors simulaneously and prices immediaely adjus o equilibrium. This is a fair approximaion in some siuaions, bu a he high frequency level informaion is likely o be unevenly disribued. For example, he processing speed migh differ among invesors. Also, he aiude o informaion and he availabiliy of informaion may be differen among invesors. In he mos exreme case, so called liquidiy invesors are assumed o inves simply when hey have excess funds and disinves when hey need money for oher purposes. Therefore hey inves wihou privae informaion 1, which is in conras o informed invesors who rade on privae informaion. 1 Privae informaion can be legal or illegal. For example, if one analys finds a paern in public informaion which all oher analyss fail o find, he privae informaion is legal. Ineresingly, ehical aspecs of informed rading have reached very differen conclusions. According o Kay (1988) insider rading is no really harmful, bu King and Roell (1988) argue ha asymmeric informaion increases he bid-ask bid-ask spread. Boh hese views are discussed in en (1993).

3 To accommodae for hese differences, asymmeric informaion bid-ask spread models have been proposed by Copeland and Galai (1983), Glosen and Milgrom (1985), Easley and O Hara (1987) and Foser and Viswanahan (1994). Ofen hree invesor caegories are proposed, where marke makers, or oher limi order invesors, have an informaion disadvanage relaive o informed invesors while liquidiy invesors rade randomly. To marke makers, informed and liquidiy invesors are indisinguishable. Informed invesors profi from rading wih marke makers and liquidiy invesors and marke makers pos bidask quoes wide enough o compensae for rading wih informed invesors. In addiion o order processing and asymmeric informaion models, invenory models have been proposed by for example oll (1978), Amihud and Mendelson (1980, 198), Ho and oll (1981) where marke makers are compensaed for holding unwaned invenories. Also, saisical models have been proposed. Following Roll (1984), covariance models have been proposed by for example George, Kaul and Nimalendran (1991) and oll (1989). Finally, rade indicaor models have been proposed by for example Glosen and Harris (1988) and Madhavan, Richardson and Roomans (1996). Hasbrouck (1988 and 1991) conribued o his field by proposing and esing a vecorised auoregressive (VAR) rade indicaor model. Among empirical research, Afflek-Graves, Hegde and Miller (1994), Jones and Lipson (1995), Lin, anger and Booh (1995), Porer and Weaver (1995) compared dealer and aucion markes. Among hose who examined repeaing ime of day, or diurnal, paerns in he bid-ask spread during a rading session, Madhavan, Richardsson and Roomans (1996) are found. Laely, Declerck (000) examined he order book from he Paris Bourse, Majois and De Winne (003) he order book from Euronex Brussels and De Winne and Plaen (003) he order book from Nasdaq Europe. In 1997 Huang and oll published a paper where hey exended Roll s model (1984), combining order processing, invenory and asymmeric informaion cos componens. Huang and oll (1997) examined 0 socks raded a he NYE, included in he Major Marke Index. ince hen, Huang and oll s (1997) model has been used in several differen empirical seings. This sudy uses Huang and oll s (1997) model for posed bid-ask spreads. The purpose is o decompose he posed bid-ask spread of 10 randomly seleced OMX sock index socks ino Huang and oll s (1997) order processing, invenory and adverse selecion componens. Following Huang and oll (1997), rades before he opening and closing call are removed. 3

4 Ineresingly, he rading mechanism a he NYE and ockholmsbörsen (B) differ. Noably here are no marke makers or specialiss a B. Also, he rading sysem a B has been compuerized since Alhough here are no formal marke makers a B, limi order rading is suppored by he exchange, susaining behavior similar o ha of marke makers. Huang and oll s (1997) model for posed bid-ask quoes is esimaed wih ordinary leas squares (OL) regressions, as well as an exended version wih diurnal probabiliy of a reversed rade. Among closely relaed empirical research, De Winne and Plaen (003) used a daase from Nasdaq Europe including marke maker idenificaion codes for rades and bidask quoes and Declerck (000) examined he limi order book a he Paris Bourse and esimaed average hourly probabiliies of reversed rades. This sudy conribues o previous research in hree ways. Firs, he iming convenion of Huang and oll s (1997) hree way decomposiion of posed bid-ask is adjused o accommodae for he way ransacions are recorded a B. For example, bid-ask quoe revisions wihou rades are no excluded from he daa se, as limi orders may change posed bid-ask quoes even if rades does no occur. econd, a version of he adjused Huang and oll s (1997) model where he probabiliy of a reversed rade is ime varying, or diurnal, is proposed and successfully esimaed. The diurnal probabiliy of a reversed rade is modeled wih polynomials. Third, a daase wih five monh of ransacions from 10 socks randomly seleced from he wedish OMX sock index have been examined. This daa se has no been widely examined before. The resuls in his sudy suppor he Huang and oll (1997) model. The probabiliy of a reversed rade ranges from 1.38 o 1.5 percen for he socks, so rade coninuaions are highly probable. All adverse selecion coefficiens are posiive, ranging from 0.31 o percen. No bunching procedure is used in his sudy, which yielded higher adverse selecion coefficiens in Huang and oll s (1997) original sudy. Also, his sudy finds a repeaing ime varying, or diurnal, paern in he probabiliy of a reversed rade. However, his does no affec he adverse selecion or invenory componens coefficiens. Bu sill, he diurnal probabiliy of a reversed rade does have an imporan implicaion for he size of he expeced changes in he mid quoe. The diurnal paern in he probabiliy of a reversed rade is consisen wih he idea of informed rading following he opening call. This should be of considerable ineres o regulaors, invesors and researchers. 4

5 The remainder of he sudy is organised as follows. ecion conains a descripion of he marke srucure a B. ecion 3 presens he mehodology and secion 4 he daa se. The sudy ends wih secion 5, empirical resuls, and secion 6, concluding remarks.. Marke srucure a ockholmsbörsen The rading sysem a ockholmsbörsen (B) was fully compuerised in ince hen, brokers ener orders for socks, converibles, premium bonds and warrans wih a rading applicaion called AXE from heir offices. Enered orders are mached agains limi orders already in he elecronic order book. If an arriving limi order is no filled i is added o he order book as anoher limi order. Order can be enered as Fill or kill ; where all shares have o be processed, or as Fill and kill ; where as many shares as possible are filled a he specified price and he res killed. There is also a division beween small and large orders. Large orders are of he magniude of EK or more. The number of shares of a large order depends on he share price, and is adjused o neares 50 or 100 shares every 6 monhs depending on he curren price. When a large order consiss of slighly more han le s say 500 shares, hen 500 are filled immediaely and he res passed o he elecronic order book for small orders. Brokers can specify he validaion ime of orders wih a maximum of eigh days, alhough some broker firm have sysems which allows hem o offer longer imes o cusomers. I is also possible o ener an order so ha i is erminaed a a cerain dae or ime of day. Prevailing limi orders are execued sricly by order of arrival, excep for rades where one broker acs boh as seller and buyer. Then inernal crossings are prioriized before ime. Price always has he highes prioriy, no rades are allowed ouside he bid-ask spread. Inside rades are allowed. On excepions, ransacions can be repored manually ouside he order book if a rade is agreed on ouside opening hours (i.e. by phone). Even ransacions ouside he bid-ask spread can be repored if an explanaion is aached, bu hen he brokers may have o explain he reasons o he exchange and he marke. AXE rading is conduced by members of he exchange; here are no formal marke makers. However, here are marke makers on B s derivaives marke, bu a B s cash marke he member who shows a limi order in he order book only pays 40 percen of he oal commission whereas he oher member pays 60 percen. The idea is o suppor liquidiy and limi order rading. Trades can be negoiaed ouside he compuer rading sysem. When 5

6 a broker acs as buyer and seller, he pays 50 percen on boh ransacions. uch a rade mus be repored o he exchange wihin a cerain ime frame. Finally, here is an opening and closing call. mall orders are no paricipaing in he price process during he morning call which sars simulaneously a 9:15 for all lised socks. A 9:30, he firs sock ges an opening price and is hereafer raded coninuously. The official opening ime is 9:30, and his holds for summer as well as winer ime. For example, on he 16 of Ocober 003, weden swiched from summer o winer ime and will swich back on he 7 of Mars 004. Meanwhile, B officially opens a 9:30 winer ime. Afer abou 7 minues, around 9:37, an opening price has been calculaed for each lised sock, and hen buyers and sellers have been mached for every sock. The closing call is enered around 17:0 and compleed 17:30, he official closing ime when official closing prices are calculaed. All socks ener he closing call simulaneously and are closed in he same order as in he opening call. 3. Mehodology In early bid-ask spread models, serial covariance in he price process played an imporan role. Roll (1984) proposed he following bid-ask spread model where he efficien bid-ask spread is a funcion of he covariance of he price process; (1) cov( p, p ) = 1 where is a consan bid-ask spread and reversed rade was assumed o be 50 percen. p he price change a ime. The probabiliy of a Roll s (1984) model assumes only order processing coss and pure bid-ask bounces, which are srong assumpions, since adverse selecion and invenory coss are likely. Laer oll (1989) proposed a model based on he idea ha he probabiliy of reverse rades would exceed 50 percen if marke makers pos bid-ask quoes in response o unwaned invenories. oll (1989) proposed ha he expeced revenue for marke makers or oher limi order invesors, on a roundrip rade, is ( π δ ), assuming ha bid-ask quoes are adjused in response o [ 1 ] is he incoming orders from liquidiy and informed invesors. The remaining ( π δ ) proporion of he bid-ask spread no earned by he marke maker. Here, is he consan bidask spread, π is he probabiliy of a reversed rade and δ he price coninuaion as a percen 6

7 of he spread. A reversed rade is defined as a rade a he bid (ask) followed by a rade a he ask (bid). As orders arrive, marke makers holdings may diverge from he desired invenory level. This forces marke makers o adjus posed bid-ask quoes. For example, if he holding is long, posed bid-ask quoes migh be lowered relaive o he desired invenory level. In heory, marke makers may even end up posing bid-ask quoes ha diverge from he heoreical value of he shares. On average his resuls in expeced losses, an invenory, for marke makers. In heir paper, Huang and oll (1997) proposed an exended model which added a rade indicaor, Q, which equals 1 if a ransacion is buyer iniiaed, -1 if i is seller iniiaed and 0 oherwise. Noably, i is possible o deermine wheher he ransacion is buyer or seller iniiaed by comparing he ransacion price wih he prevailing posed bid-ask quoes. Huang and oll (1997) proposed ha he underlying value is unobservable, bu ha in absence of ransacion coss i can be modeled as; () V = V 1 + α Q 1 + ε where V is he unobservable value a ime, α he percenage of he half bid-ask spread aribued o adverse selecion, he consan half bid-ask spread, Q 1 he rade indicaor a ime 1 and ε uncorrelaed public informaion shocks. Huang and oll (1997) noed ha he average of posed bid-ask quoes, he mid quoe M, can be observed, and proposed he following relaion beween he unobserved value V and he mid quoe; (3) M = V + β Q = 1 1 i where M is he mid bid-ask quoe a ime, β he percenage of he half bid-ask spread aribued o invenory holding coss, he consan half bid-ask spread, and indicaor a ime i. Q i he rade 7

8 Also, Huang and oll (1997) proposed ha mid bid-ask changes, can be prediced based on hisorical rades, condiioned o he mid bid-ask quoe a ime 1 ( M 1) and he rade indicaor a ime ( Q ); β (4) E( M ) = ( 1 ) Q π where E( M ) is expeced change in he mid quoe, π he probabiliy of a reversed rade and Q he rade indicaor a ime. Based on model (1) and (), Huang and oll (1997) proposed wo and hree way decomposiions of he bid-ask spread. The wo way bid-ask spread model separaed he order processing and invenory componens, while he hree way decomposiion separaed he adverse selecion invenory and order processing componens. Again, a reversed rade is defined as a rade a he bid followed by a rade a he ask, or vice versa. The bid-ask spread does no refer only o he posed difference beween bid-ask quoes. In Huang and oll (1997), an effecive bid-ask spread is also esimaed, which reflec he rue ransacion cos for an average sized rade. While invesors mee marke maker or indicaive bid-ask quoes on some exchanges, he posed bid-ask quoe on B represen rue bid-ask quoes. The firs difference of model (1) and model () implies ha bid-ask quoes are adjused o reflec he invenory and he informaion which was known by he ime of he las rade, and ha he mid bid-ask change can be modeled as; (5) M = ( α + β ) Q 1 + ε where is he mid bid-ask change a ime, ( β ) M α + he excess componen and ε he remaining error. All coss in excess of he order processing cos are measured by ( α + β ), where α is he adverse selecion componen and β invenory componen. Huang and oll (1997) separaed he adverse selecion and invenory componens and proposed he following model; 8

9 = α + β α π + ε (6) M ( ) Q 1 Q ( 1 ) where posiive coefficiens are expeced. Afer some rearrangemens, Huang and oll s (1997) model for posed bid-ask spreads is esimaed wih ordinary leas squares (OL): 1 (7) M = ( α + β ) Q 1 α Q ( 1 π ) + ε where 1 is he posed half bid-ask spread a ime 1. While Huang and oll esimae heir model wih GMM (as a sysem of equaions), in his sudy he fixed probabiliy of a reversed rade (π ) is simply compued as he oal number of reversed rades divided by he oal number of rades in each sample. For some socks, posed bid-ask quoes change quie frequenly wihou rades. A bid-ask quoe revision wihou a rade is recorded when a limi order is enered ino he order book which raises he prevailing bid or lowers he prevailing ask quoe wihou resuling in an immediae rade. Bid-ask quoe revisions wihou rades are kep in he daase. Therefore, posed bid-ask spreads are compued wih he laes possible quoes. Quoe revisions wihou rades are excluded from he calculaion of he probabiliy of a reversed rade. Finally, he ransaced price and quaniy a ime is recorded ogeher wih he quoes which prevail afer he ransacion, i.e. he quoes which are a resul of he ransacion. For simpliciy and clariy, his has been adjused wihou changing Huang and oll s original iming convenion, assuming ha he daa is recorded incorrecly 3. In his sudy, he following repeaing ime of day, or diurnal, version of Huang and oll s (1997) hree way decomposiion model of posed bid-ask spreads is esimaed wih OL; 1 (8) M = ( α + β ) Q 1 α Q ( 1 π ) + ε where he diurnal probabiliy of a reversed rade ( π ) depends on he ime of he day. The diurnal probabiliy of a reversed rade is esimae wih OL allowing a polynomial of up o four degrees; ˆ 3 An alernaive is o claim ha Huang and oll s iming convenion is wrong. 9

10 1 3 4 (9) ˆ π = k + k d + k d + k d + k d + η where d is he ime of he day and k he coefficiens. A polynomial of up o four degrees fis he daa well. The resul is a row vecor conaining polynomial coefficiens. In pracice, a large order migh be broken up and execued as several small orders. Also, if he size of a single arriving marke order is greaer han he firs limi order in he order book, hen ha order will be recorded as a leas wo successive rades wih he same sign by consrucion of he elecronic order book. For example his affecs he calculaion of he probabiliy of a reversed rade, defined as a rade a he bid followed by a rade a he ask or vice versa. Huang and oll (1997) proposed and esimaed models wih dummies for he rade size, bu alhough heir sample is large, some of hese resuls are insignifican. Also, wih a daa se allowing a more precise bunching procedure for rades, De Winne and Plaen (003) found ha Huang and oll (1997) probably bunched oo many rades ogeher. This analysis was possible since De Winne and Plaen (003) had access o a daa se wih marke maker idenificaion codes. Even wih deailed records of each rade, i is impossible o know he rue size of each order. For example, should he rue size be judged by he choice of he seller or he buyer? Three explanaions of posiive auocorrelaion in rade signs are probable. Firs, as menioned earlier, large orders may be broken up ino several smaller orders wih he same rade sign, where some orders also could be submied o differen brokers. econd, if he size of an arriving order is greaer han he firs order in he order book, he arriving order will be recorded as a leas wo successive orders wih he same sign. Third, uneven orders are adjused o neares 50 or 100 shares, resuling in more han one recorded rade wih he same sign. ome effecs work in opposie way wih respec o he reversed rade calculaion. For example, an opimal large orders sraegy could involve rades in he opposie direcion of he desired side, resuling in rades of he opposie sign. Trades wihin a limied ime span wih he same sign are no bunched ogeher as one rade in his sudy. 4. The daa se The daa se covers five monh of ransacions from he rading sysem a ockholmsbörsen (B) from which 10 socks included in he OMX sock index are randomly seleced, covering 10

11 he period 1 Ocober, 003 o 6 February, 004. The oal number of observaion is , of which are bid-ask quoe revisions wihou rades and reversed rades. The average sock has observaions in he daa se, of which are bid-ask quoe revisions wihou rades and reversed rades. The average fixed probabiliy of a reversed rade is From he file, rades during he opening and closing call are excluded leaving all rades execued beween 9:30 and 17:10 included. The daa se deails ransacion ime, price, volume ogeher wih posed bid-ask quoes afer each ransacion. Bid-ask quoe revisions wihou rades are preserved in he daa se. The laes available posed bid-ask spread is always used in esimaions, following he logic ha limi order invesors may adjus bid-ask quoes wihou rades. I is possible o deermine wheher he rade is buyer or seller iniiaed by comparing he price a ime wih he bes prevailing posed bid-ask quoes. 5. Empirical resuls In his sudy, Huang and oll s (1997) hree way decomposiion model for posed bid-ask spreads is esimaed using a daa se which consiss of observaions from 10 socks raded a ockholmsbörsen (B), randomly seleced from he OMX sock index. The rading mechanism a B differs in some respecs from he rading mechanism a he NYE and NADAQ. Alhough here are no formal marke makers or specialiss for socks, limi order rading is promoed by B which suppors behavior similar o ha of marke makers. The esimaed Huang and oll (1997) decomposiion model assumes hree ypes of invesors: Liquidiy invesors who rade wihou privae informaion and marke makers, or oher limi order invesors, who rade o profi from he difference beween posed bid-ask quoes, i.e. he posed bid-ask spread. The hird caegory is informed invesors who rade when hey have privae informaion 4. On average marke makers profi from rading wih liquidiy invesors and lose o informed invesors. Remarkably, Huang and oll s (1997) model encompasses earlier saisical and rade indicaor models by for example Ross (1984), oll (1989), George e al (1991), Glosen and Harris (1988), decomposing posed bid-ask spreads ino order processing, adverse selecion and invenory componens. Earlier sudies find he order processing componen o be larges, while he relaion beween he adverse selecion and 4 As his sudy is concerned wih wheher he presence of informed invesors has an effec on posed bid-ask bidask spreads, he concerned is no wheher he privae informaion is legal or illegal. 11

12 invenory componen vary. Mos researcher repor posiive adverse selecion coefficiens, for example 1 sudies quoed in Chueh and Yen (1999) repor posiive coefficiens. Ineresingly, Majois and De Winne (003), who examine he elecronic order book a Euronex Brussels, find 16 ou of 19 adverse selecion coefficiens negaive. They acknowledge ha he probabiliy of a reversed rade is a criical parameer, and argue ha low probabiliies of reversed rades conribue o heir unreasonable resuls, unreasonable because in heir sudy privaely informed invesors are a posiive hing for marke makers and limi order invesors. Majois and De Winne (003) argue ha he Huang and oll (1997) model migh no be suiable for markes wih elecronic order books. This sudy however, srongly suppors Huang and oll s (1997) model, when he iming convenion is adjused o mach he elecronic order book a B. A close review of he daa se revealed ha he ransaced price and quaniy is recorded ogeher wih posed bid-ask quoes prevailing afer he ransacion in quesion. Also, in his sudy bid-ask quoe revisions wihou rades are kep in he daa se for he purpose of an accurae calculaion of he posed bid-ask spread which prevailed before he ransacion of ineres. Bid-ask quoe revisions wihou rades were excluded from he calculaion of he probabiliy of a reversed rade. For he adjused Huang and oll model, he resuls are ha he fixed probabiliy of a reversed rade range from 1.38 o 1.5 percen (Table a). This is consisen wih he idea ha rade coninuaions are highly probable. Also, posiive adverse selecion cos coefficiens range from 0.31 o percen. The mean of he adverse selecion coefficiens is 5.0 percen, which is consisen wih relaively infrequen informed rades a B, alhough here is some variaion. One sock has an adverse selecion cos coefficien which is no significan a common significance levels, consisen wih he idea ha he informaion abou Invesor (INVE-B) is symmeric. In he case of kanska (KA-B), he adverse selecion cos coefficien is no significanly differen from zero a he five percen level. Invenory coefficiens range from 5.15 o 7.8 percen, wih a mean of percen. No bunching procedure is used in his sudy, which yielded higher adverse selecion coefficiens in Huang and oll (1997), as he adverse selecion coefficien was correlaed posiively wih he rade size. 5 I is emping o repor he cos of adverse selecion for a sock by muliply he average spread wih he number of raded shares and he adverse selecion cos coefficien. However, his would be oo simplisic. 1

13 This sudy idenifies repeaing ime of day, or diurnal, paerns in he probabiliy of a reversed rade. Figure 1 is consisen wih he idea ha he probabiliy of a reversed rade is lowes righ afer he opening call. This is especially visible for socks where he adverse selecion cos coefficien (Table a) is significan and relaively large. An anonymous sock broker 6 a a major bank described he informaion siuaion in he morning as a fully se dinner able. The sock broker rades he banks accoun on his informaion, which was considered privae. According o he broker, he bes ime o uilize privae informaion is righ afer he opening call. The reason for waiing unil afer he opening call is ha hen i is also possible o observe and inerac wih oher invesors. This does no rule ou oher inerpreaions. ome socks exhibi simple diurnal paerns, while hose wih a relaively high adverse selecion coefficien end o have more complex paerns. This is consisen wih he idea ha when he adverse selecion coefficien is high more coefficiens in he polynomial are significan. For socks wih a high adverse selecion cos coefficien, he probabiliy of a reversed rade is low righ afer he opening call, which is consisen wih he idea ha his period exhibi srong dependency in he order flow. While his makes i easy o predic he order flow, a direcional order flow also makes i difficul for marke makers o manage he invenory. If marke makers and limi order invesors are risk averse, following a rade a he bid quoe hey will revise he posed ask quoe downwards, and vice versa for a rade a he ask quoe. When he order flow is direcional, he probabiliy of being able o offse a rade wih a limi order will be low. When he diurnal version of he adjused Huang and oll model is esimaed, he coefficiens for adverse selecion or invenory componens remain unchanged. Even so, he diurnal probabiliy of a reversed rade has an imporan implicaion for he expeced change in he mid quoe, i.e. he average of posed bid-ask quoes. As he probabiliy of a reversed rade approaches zero, he erm ( 1 π d ) in Model (8) approaches one. Therefore, for mos sock in he daa se he half bid-ask spread wo rades ago ( ) affecs expeced changes in he mid quoe relaively more righ afer he opening call. While one can argue ha his effec also can be capured wih ime varying parameers for invenory and asymmeric informaion componens, here he impac of he las rade ( 1 ) is sable hroughou he day. 6 Telephone inerview 3 epember,

14 Besides Model (8) being parsimonious, diurnal paerns in he probabiliy of a reversed rade are empirical facs. Also, he probabiliy of a reversed rade can be considered exogenous 7. Using diurnal probabiliies of reversed rades seems more reasonable han o use diurnal coefficiens for invenory and adverse selecion componens. In conjuncion wih earlier noions of larger bid-ask spreads righ afer he opening call, his should be of considerable ineres o marke makers and liquidiy invesors who wan o minimize losses o informed invesors. I is difficul o generalize abou he resuls. However, he resuls in his sudy are consisen wih he idea of informed rading a B, alhough adverse selecion cos coefficiens are relaively small. Also, he diurnal paern in he probabiliy of a reversed rade is consisen wih informed rading righ afer he opening call. This should be of considerable ineres o regulaors, invesors and researchers. 6. Concluding remarks In he marke microsrucure lieraure, hree ypes of invesors frequenly reappear. Marke makers, or oher limi order invesors, are assumed o have an informaion disadvanage relaive o so called informed invesors. In addiion, liquidiy invesors rade randomly while so called informed invesors profi from rading wih marke makers and liquidiy invesors. To marke makers, informed and liquidiy invesors are indisinguishable. To compensae for rading wih informed invesors, marke makers pos wider bid-ask quoes. In addiion o he obvious cos of order processing, marke microsrucure models which incorporae invenory coss have been proposed by for example oll (1978), Amihud and Mendelson (1980, 198), Ho and oll (1981). In hese models, in addiion o he order processing cos, marke makers are compensaed for holding unwaned invenories. Also, marke microsrucure models of he bid-ask spread which accommodaes asymmeric informaion coss has been proposed by Copeland and Galai (1983), Glosen and Milgrom (1985), Easley and O Hara (1987) and Foser and Viswanahan (1994). In addiion o his, various saisical models have been proposed by for example Roll (1984), oll (1989) and George, Kaul and Nimalendran (1991) and so called rade indicaor models by for example Glosen and Harris (1988) and Madhavan, Richardson and Roomans (1996). 7 In his case he probabiliy of a reversed rade can be considered srongly exogenous, which implies ha curren and lagged changes in he mid quoe rades does no explain he probabiliy of a reversed rade. 14

15 In his sudy, Huang and oll s (1997) hree way decomposiion model of posed bid-ask spreads is esimaed using a daa se which consiss of 10 socks raded a ockholmsbörsen (B), randomly seleced from he OMX sock index. The Huang and oll (1997) model decomposes posed bid-ask spreads ino hree ypes of coss and ness several oher models, and feaures from hem. The daase consiss of observaions, and is ineresing as he rading mechanism a B differs from he NYE and NADAQ. Noably B has had an elecronic order book since 1989, and here are no marke makers or specialiss for socks. Alhough here are no formal marke makers, limi order rading is promoed by B, supporing rading behavior similar o ha of marke makers. This sudy conribues o previous research in hree ways. Firs, he iming convenion of Huang and oll s (1997) hree way decomposiion of posed bid-ask is adjused o accommodae for he way ransacions are recorded a B. econd, a version of he adjused Huang and oll s (1997) model where he probabiliy of a reversed rade is ime varying, or diurnal, is proposed and successfully esimaed. The diurnal probabiliy of a reversed rade is modeled wih polynomials. Third, a daase wih five monh of ransacions from 10 socks randomly seleced from he wedish OMX sock index is examined. This daa se has no been widely examined before. The resuls are ha he fixed probabiliy of a reversed rade range from 1.38 percen o 1.5 percen. Trade coninuaions are highly probable. Even so, his sudy suppors he Huang and oll (1997) model. The signs of esimaed adverse selecion coefficiens are posiive for all socks ranging from 0.31 o percen. No bunching procedure is used in his sudy, which probably yielded higher adverse selecion coefficiens in Huang and oll s (1997) sudy. Also, his sudy finds diurnal paerns in he probabiliy of a reversed rade. However, his does no change he coefficiens for adverse selecion or invenory componens. Bu diurnal probabiliies of reversed rades do have an imporan implicaion for he size of he expeced changes in he mid quoe. Noably, he diurnal paern in he probabiliy of a reversed rade is consisen wih he idea of informed rading following he opening call. This should be of considerable ineres o regulaors, invesors and researchers. 15

16 References Affleck-Graves, J.,. Hedge, and R. Miller, 1994, Trading Mechanisms and he componens of he bid-ask spread, Journal of finance, 49, Amihud Y, and H. Mendelson, 1980, Dealership marke: Marke making wih invenory, Journal of Financial Economics, 8, Copeland, T. C., and D. Galai, 1983, Informaion effecs on he bid-ask spread, Journal of Finance, 38, Declerck, F. 000, Trading coss on a limi order book marke; Evidence from he Paris Bourse, Working paper, Universié de Lille. De Winne, R., and I. Plaen, 003, An analysis of marke maker s behaviour on Nasdaq Europe, Working paper, Caholic Universiy of Mons. Easley, D., and M. O Hara, 1987, Price, rade size, and informaion in securiies markes, Journal of Financial Economics, 19, Engle and Russel, 00, Analysis of high frequency daa. Working Paper. Foser, F. and. Viswanahan, 1994, raegic rading wih asymmerically informed invesors and longed-lived informaion, Journal of Financial and Quaniaive Analysis, 9, George, T. J., G. Kaul, and M. Nimalendran, 1991, Esimaion of he bid-ask spread and is componens: a new approach, Review of Financial udies, 4, Glosen, L. R., and L. E. Harris, 1988, Esimaing he componens of he bid-ask spread, Journal of Financial Economics, 1, Glosen, L. R. and P. R. Milgrom, 1985, Bid, ask and ransacion prices in a specialis marke wih heerogeneously informed raders, Journal of Financial Economics, 14, Hasbrouck, J., 1988, Trades, quoes, invenories and informaion, Journal of Financial Economics,,

17 Hasbrouck, J., 1991, Measuring he informaion conen of sock rades, Journal of Finance, 46, Ho, T., and H. R. oll, 1981, Opimal dealer pricing under ransacions and reurn uncerainy, Journal of Financial Economics, 9, Huang R. D., and H. R. oll, 1997, The componens of he bid-ask spread: A general approach. The Review of Financial udies 10, Jegadeesh, N., and. Timan, 1995, hor-horizon reurn reversals and he bid-ask spread, Journal of Financial Inermediaion, 4, Jones, C., and M. Lipson, 1995, Coninuaions, reversals, and adverse selecion on h Nasdaq and Nyse/Amex, Financial Research Cener Memorandum, 15, Princeon Universiy. Lin, J-C., G. anger, and G. Booh, 1995a, Exernal informaion coss and he adverse selecion problem: A compairson of Nasdaq and NYE socks. Madhavan, A., M. Richardson, and M. Roomans, 1996, Why do securiy prices change? A ransacion-level analysis of Nyse socks, Working paper, Universiy of ouhern California. Majois, C., and R. De Winne, 003, A compairson of alernaive Bid-ask spread decomposiion models on Euronex Brussels, Working paper, Caholic Universiy of Mons. Roll, R., 1984, A simple implici measure of he effecive bid-ask spread in an efficien marke, Journal of Finance, 39, en, A. (1993), Money and Value. On he Ehics and Economics of Finance. Economics and Philosophy 9, oll, H., 1978, The supply of dealer services in securiy markes, Journal of Finance, 33, oll, H., 1989, inferring he componens of he bid-ask spread: heory and empirical ess, Journal of Finance, 44,

18 Company Number of observaions Table 1. Descripive saisics Bid-ask quoe revisions wihou rades Reversed rades In beween rades Fixed probabiliy of a reversed rade ALIV ATCO-B DROT-B ENRO FPA-A HOLM-B INVE-B KA-B TE-R WMA Average Table 1 presens descripive saisics of he daa se which covers five monh of ransacions from he rading sysem a ockholmsbörsen (B) from where 10 socks included in he OMX sock index are randomly seleced. The daase covers he period from 1 Ocober, 003 o 6 February, 004. From he file, rades during he opening and closing call are excluded. The daa se deails ransacion ime, price, volume and posed bid-ask quoes righ afer he ransacion. 18

19 Table a. Fixed probabiliies; adverse selecion and invenory holding componens Adverse elecion, α Invenory Holding, β Company Coefficien d. Error Coefficien d. Error ALIV ATCO-B DROT-B ENRO FPA-A HOLM-B INVE-B KA-B TE-R WMA Average Table a presens resuls from esimaing model (7) of posed mid bid-ask quoes, decomposing he posed bidask spread ino order processing, adverse selecion and invenory holding componens. In model (7) he probabiliy of a reversed rade is fixed. Table b. Diurnal Probabiliies; adverse selecion and invenory holding componens Adverse elecion, α Invenory Holding, β Company Coefficien d. Error Coefficien d. Error ALIV ATCO-B DROT-B ENRO FPA-A HOLM-B INVE-B KA-B TE-R WMA Average Table b presens resuls from esimaing model (8) of posed mid bid-ask quoes, decomposing he posed bidask spread ino order processing, adverse selecion and invenory holding componens. In model (8) he probabiliy of a reversed rade is diurnal, which is depends on he ime of he day. 19

20 Table 3. Diurnal Probabiliies; polynomial coefficiens Company k 0 k 1 k k 3 k 4 ALIV E E-10 ( ) ( ) (5.96E-07) (1.51E-10) ATCO-B E-05.14E E-1 ( ) ( ) (6.07E-06) (3.08E-09) (5.79E-13) DROT-B E E E-1 ( ) ( ) (1.4E-05) (7.8E-09) (1.38E-1) ENRO E E E-1 ( ) ( ) (1.48E-05) (7.55E-9) (1.43E-1) FPA-A E-05 ( ) (7.1E-06) HOLM-B E-05.51E E-1 (.730) ( ) (1.00E-05) (5.1E-09) (9.71E-13) INVE-B E E E-1 ( ) ( ) (1.00E-05) (5.14E-09) (9.77E-13) KA-B E-05 (0.0109) (8.11E-06) TE-R E E-08-07E-1 ( ) ( ) (9.8E-06) (5.03E-09) (9.56E-13) WMA E-07 ( ) ( ) (4.44E-08) In model (9), polynomials of up o four degrees are used o fi he probabiliy of a reversed rade o he ime of he day, such ha; (9) ˆ π = k + k d + k d + k d + k d where d is he ime of he day and k he coefficiens. The resul is a row vecor conaining he polynomial coefficiens. 4 η 0

21 Figure 1. Diurnal probabiliy of a reversed rade as a funcion of ime of day 0.3 ALIV DROT-B FPA-A INVE-B TE-R ATCO-B ENRO HOLM-B KA-B WMA In model (8) he probabiliy of a reversed rade is diurnal, which is depending on he ime of he day. Figure 1 presens he resuls from fiing polynomials of four degrees o he proporion of reversed rades during each minue of he day. The figure shows he probabiliy of a reversed rade as a funcion of he ime of he day. 1