Liquidity and Information-Basd Trading on th Ordr Drivn Capital Markt: Th Cas of th Pragu tock Exchang Libor 1ÀPH³HN Cntr for Economic Rsarch and Graduat Education, Charls Univrsity and Th Economic Institut of th cadmy of cincs of th Czch Rpublic Politickych vznu 7 Pragu 1, 111 21 Czch Rpublic fax: (+422) 24 22 7143 -mail: libor.nmck@crg.cuni.cz First Draft: March 3, 1997 This Vrsion: ugust 25, 1997 (CERGE-EI WP) bstract: This papr invstigats th rlation btwn liquidity and information-basd trading in th contxt of an ordr-drivn auction. modl similar in spirit to that of Easly t al. (1996) is usd to dtrmin how oftn nw information occurs and how it influncs th composition of ordrs submittd to th markt. Th risk of informationbasd trading is stimatd for a sampl of Pragu tock Exchang listd stocks. Th mpirical rsults agr with prvious findings that th risk of information-basd trading is lowr for mor activ stocks. urprisingly, information basd trading is apparntly lss common on th rcntly cratd Pragu tock Exchang than on mor wllstablishd markts. bstrakt: 7HQWR³OgQHNVH]DE YgY]WDKHPPH]LOLNYLGLWRXDREFKRGRYgQmP]DOR HQ P QDQHYHÎHMQkLQIRUPDFLYURVWÎHGmDXNFHÎm]HQkÎmND]\QDQgNXDURGHM.DQDO ]H IUHNYHQFm ÎmFKRGX QRY FK LQIRUPD³QmFK VLJQgOÖ D MHMLFK YOLYX QD VWUXNWXUX RGDQ FK REFKRGQmFK ÎmND]Ö MH RX LW PRGHO MHKR VWUXNWXUD Y\FKg]m ] ³OgQNX (DVOH\ D NRO 3RPRFm WRKRWR PRGHOX MH QgVOHGQÀ RGKDGQXWD UDYGÀRGREQRVW REFKRGRYgQm ]DOR HQkKRQDQHYHÎHMQkLQIRUPDFLURVRXERUDNFLmREFKRGRYDQ FKQD%XU]HFHQQ FK DmUÖ 3UDKD %&33 (PLULFNk Y VOHGN\ VRXKODVm V ÎHGFKR]mPL VWXGLHPL Y WRP H UDYGÀRGREQRVW REFKRGRYgQm ]DOR HQkKR QD QHYHÎHMQk LQIRUPDFL MH QL m UR OLNYLGQÀM m DNFLH 3ÎHNYDLY P ]ML WÀQmP MH H REHFQÀ UDYGÀRGREQRVW REFKRGRYgQm ]DOR HQkKRQDQHYHÎHMQkLQIRUPDFLMHQDFHQWUgOQmPWUKX%&33Y ]QDPQÀQL mqh QD ]DYHGHQ FKNDLWgORY FKWU]mFK1HZ<RUN6WRFN([FKDQJH Kywords: liquidity, information, informd trading, Pragu tock Exchang. cknowldgmnts: I am indbtd to Randall Filr and Jan Hanousk for thir usful commnts and suggstions. 1. Introduction
Th connction btwn liquidity and information basd trading has bn studid by svral authors (s, for xampl, Hasbrouck (1988, 1991) and Easly, Kifr, O Hara and Paprman (1996)) using data from dvlopd capital markts. Th main purpos of thos invstigations was to xplain th obsrvd diffrncs in sprads for activ and infrquntly tradd stocks. Easly t al. (who usd a sampl of stocks listd at th Nw York tock Exchang) found that th probability of information-basd trading is lowr for high volum stocks. Information-basd trading also xplaind, at last partially, th diffrncs in sprads for activ and infrquntly tradd stocks. I ask whthr similar conclusions hold in an mrging markt such as that of th Czch Rpublic. Th institutional structur of th Pragu tock Exchang (PE) is quit diffrnt from that of th NYE. Thr ar no markt makrs stting bid-ask sprads. Instad, trading is don through th so-calld utomatd Trading ystm, which for ach stock listd on th markt 1, clars th ordrs mad by individual brokrs. This claring is don onc a day (at about 11am), and although som additional trading latr in th day is possibl, this must b don at a pric st by th claring algorithm. Th ordrs submittd by th brokrs can b both markt (a simpl buy/sll ordr) and limit ordrs. Dspit ths major diffrncs in th institutional structur of ths markts (PE vrsus NYE), an conomtric modl similar to that usd by Easly t al. can b utilizd to xamin th importanc of information basd trading on th Pragu tock Exchang. Naturally, th purpos of this invstigation is not to study th dtrminants of a bid-ask sprad, but rathr to inspct th rol which informd agnts assum in an institutionalizd markt in an conomy whr thy also hav othr possibilitis to us thir information. Ths possibilitis can b dscribd as follows: In th U.. (or any othr country with a dvlopd capital markt), although a particular stock can b tradd on svral markts, ach of thos markts should produc a pric for th stock which is asily obsrvabl by othr agnts on th markt. Possibl arbitrag opportunitis ar thn quickly xploitd so that diffrncs in prics on diffrnt markts disappar or fall blow th lvl of transaction costs connctd with arbitrag trading. In th Czch Rpublic, thr xist thr points of stock trading: 1) th Pragu tock Exchang, whr agnts can ithr trad thir stocks on th so-calld cntral markt (dscribd abov 1 with th xcption of a vry small group of th most activ stocks which also trad continuously through th so-calld KOBO systm. 2
and studid in this papr) or tak part in block or dirct trading don with largr packags of stocks; 2) th RM-ystm, a computrizd ntwork which also uss an ordr-claring mchanism, and du to its wid availability, srvs mainly small stockholdrs; and 3) th Cntr of curitis, which actually srvs as a rgistr of all scuritis and thir holdrs. ny two agnts can trad thir stocks dirctly at th countr of th Cntr of curitis at any agrd upon pric. Bfor th bginning of 1995, rcords of ths transactions wr not availabl to othr agnts. ftr this dat, wkly summaris of volums and avrag volumwightd prics wr publishd. Only rcntly (from Fbruary 1997) hav rcords on all transactions and all prics bcom availabl to th public. This mans that, for quit a long tim, informd agnts could utiliz thir information without rvaling it to othr tradrs on th (organizd) markt simply by xchanging thir shars at th Cntr of curitis rathr than on th PE or RM-ystm (providd thy thmslvs found a countrpart for this trad). mall capitalization of th PE and laggd rporting of trading at th Cntr of curitis mak rvaling of nw information through trad at th PE mor probabl than through trad at th Cntr of curitis, dspit th fact that anonymous trading is only possibl at th PE. Givn ths circumstancs, it is rasonabl to xpct that th rol of informd trading on th PE is gnrally vry low. To tst this prior xpctation, a modl xplicitly rprsnting th possibility of information-basd trading is prsntd and th probability of information vnts and informd trading ar stimatd for a subsampl of PE stocks. Th rst of th papr is organizd as follows: in ction 2, th modl is dvlopd and a liklihood function to b maximizd is drivd. In ction 3, th data ar dscribd. ction 4 provids rsults of th stimation and ction 5 concluds th papr. 3
2. Th Modl 2.1 Trading Mchanism of th PE Th structur of th modl is dtrmind by th trading mchanism of th PE and th typ of data that ar publicly availabl. It is important, thrfor, to dscrib th trading procdur in mor dtail bfor prsnting th modl. s alrady mntiond, trading is don and a pric is st by th utomatd Trading ystm (T), which clars th buy and sll ordrs 2 for ach stock. Th goal of th claring procdur is to maximiz th numbr of shars tradd. In this stting, whr shars trad via ordrdrivn auctions, th rol of th markt vrsus limit ordrs is quit diffrnt than in a continuous trading framwork. In th continuous auction, th limit ordrs waiting in th limit-ordr book of th markt makrs provid liquidity to th markt and can b matchd with th markt ordrs as th lattr arriv at th markt. Howvr, in th claring mchanism of th typ dscribd abov, th markt ordrs ar thos which, by matching any limit ordr, incras th volum of trad and liquidity of th stock. crucial fatur of th pric-stting mchanism at th PE is th uppr limit on th prcntag pric chang: for most issus, th pric can chang by at most 5% during a singl trading day (auction). Comparison of dmand and supply pattrns during th pric-stting procss can, thrfor, hav svral qualitativly diffrnt outcoms. Ths ar summarizd in th variabl (publishd by PE) calld cod of th markt, which can tak on of ight valus. Ths ar dscribd in th ppndix. Valus of this cod of th markt variabl, togthr with valus of th allocation ratio variabl (capturing th xtnt of ordr rationing) can b usd to rconstruct th numbrs of shars dmandd/supplid in a way that is discussd mor dply in th nxt sction, whr th structur of th modl is prsntd. 2.2 Th tructural tup of th Modl Th obsrvabl pics of information, namly th dgr of dmand/supply imbalanc masurd by th cod of th markt variabl and th numbr of shars dmandd/supplid at th nw markt pric, can b utilizd in th following modl to provid insights into trad and information flows. Tradrs arriving at th markt can ithr b uninformd or hav information about th valu of th stock. On ach day, prior to th bginning of th priod in which 2 Th ordr may hav a limit pric spcifid, i.., a maximum pric for buy and minimum pric for sll ordr. If th limit pric is not spcifid, it is a simpl markt ordr. 4
ordrs can b submittd to th markt, natur dtrmins whthr an information vnt rlvant to th valu of th particular asst will occur. Ths information vnts ar assumd to b indpndntly distributd and to occur with probability α. Thr ar good signals with probability 1 - δ, and bad signals with probability δ. Informd invstors know ths signals whil uninformd ons do not. s Easly t al. (1996), I assum that th arrival of uninformd buyrs and sllrs at th markt (i.., thir dcision to trad and th actual submission of ordrs to b considrd in th upcoming auction to th markt) is dtrmind by an indpndnt Poisson procss with th arrival rat ε. Th arrival of nws (signals) to th tradrs and thir subsqunt arrival at th markt ar assumd to follow a Poisson procss with th arrival rat µ. Obsrving a good (bad) signal lads to th submission of a buy (sll) ordr. This informd trading procss is also assumd to b indpndnt of th arrival procsss of uninformd tradrs. Th dscribd Poisson procsss rsult from ach agnt dciding (not having information or obsrving a signal) whthr to trad at th markt or not. Thy do not captur th dcision about th typ of ordr (markt vrsus limit) and, in th cas of a limit ordr, th dcision about limit pric. In fact, I assum that this dcision is indpndnt of th dcision on whthr or not to trad, and I thus modl it with th ad hoc construction dscribd blow. If P t-1 is th prvious-day pric of th stock and P * t is th nw pric, dfin th pric chang p * = (P * t - P t-1 )/P t-1 and masur th pric of th stock on a givn day by th rlativ pric chang p *. Bcaus of limits on pric chang du to th trading mchanism of th PE, a trad could nvr occur at a pric outsid th admissibl (5%) intrval. W can, thrfor, think of markt ordrs as a spcial typ of limit ordr with th limit pric st 5% blow (abov) th prvious-day pric in th cas of sll (buy) ordrs. Th limit prics of particular ordrs submittd ar discrtly distributd in th admissibl intrval. This is approximatd hr by th (continuous) logistic function, which spcifis numbr of shars dmandd at pric p as B( p) = D 1+ β ( p+ s) β ( p+ s), (1) whr β and s ar paramtrs, and D is th total numbr of shars dmandd irrspctiv of possibl limit prics of corrsponding buy ordrs which was assumd abov to follow a Poisson distribution. imilarly, th numbr of shars supplid at pric p is modld as 5
( p) = β 1+ ( p s) β ( p s), (2) whr is th total numbr of shars supplid irrspctiv of th corrsponding limit prics which also follows a Poisson distribution. Dpnding on th rlativ position of B(p) and (p) (drivn by th ralization of D and ), thr ar thr possibl outcoms: a) Dmand and supply pattrns cross for p *, which lis insid th admissibl rgion. This corrsponds to cods of th markt 1, 2, and 3 in th ral data. b) Th nw pric is at th boundary and th allocation ratio is gratr or qual to 20%. This corrsponds to cods of th markt 4 and 5 in th data. c) Th allocation ratio for p * at th boundary of th admissibl rgion is lowr than 20%, or thr ar no ordrs submittd on ithr th buy or sll sid of th markt. This mans that no trad is mad and corrsponds to cods of th markt 6, 7, and 8 in th ral data. Cods 1, 2, and 3 corrspond to th situation in which th markt pric p *, proposd by th T, falls insid th admissibl intrval, and all ordrs valid at that pric ar xcutd. In that cas, th quantity (numbr of shars) dmandd, B(p * ), is qual to th quantity supplid, (p * ). If th nw pric lis at th boundary (cods 4 and 5), som ordrs may b rationd. Th xtnt of rationing is givn by th allocation ratio discussd in th ppndix and this ratio (as publishd by PE) can thrfor b usd to rconstruct th quantitis B(p * ) and (p * ) from th numbr of actually xchangd shars. Givn th paramtrs β and s, th numbr of shars dmandd/supplid at th nw pric p can b usd to comput th (unobsrvabl) total amounts dmandd ( D ) and supplid ( ). Whil it is possibl to rconstruct ths numbrs for cass a) and b) corrsponding to th cods of th markt 1,..., 5, it is not possibl to infr thm from th information publishd in th cas of no trad ( cods of th markt 6, 7, and 8). Thr ar svral ways to dal with this problm. First, on can simply condition on nonzro trad volum and rstrict onslf to th cods of th markt 1,..., 5. cond, givn th structural stup of th modl, it is in principl possibl to comput th probability of no trad (as a function of structural paramtrs) xplicitly from th assumptions on dmand/supply pattrns and to us th obsrvations with cods of th markt 6, 7, and 8 to obtain mor fficint stimats of th paramtrs of th modl. This would, howvr, involv computation of quantils of th distribution of th ratio of two Poisson random variabls, which would b xtrmly cumbrsom. 6
Th approach usd hr lis somwhr btwn th first cas of abandoning th additional information containd in obsrvations of no trad and th scond cas of xplicit (but vry complicatd) modling. Th approach utilizs th simpl implication of th modl for dmand/supply pattrns as dscribd in (1) and (2); namly, that in th cas of an information vnt, th probability of global mismatch btwn dmand and supply (rsulting in th cas of no trad) should b highr than in th cas whn no nw information occurs. Thus, if γ E is th probability of nonzro trad in th cas of a nw signal, and γ N dnots th probability of nonzro trad whn thr is no nw information, th inquality γ N γ E should hold. This rstriction is incorporatd into th modl in an attmpt to utiliz th obsrvations of no trad, particularly for bttr stimation of th probability of an information vnt, α. nothr justification for this ad hoc tratmnt of th fact that D and ar unobsrvabl in th cas of no trad is to allow mor flxibility in th Poisson-typ modl, which could b too rstrictiv with rspct to th probability of no trad. Particularly, th probability of no trad as implid by th modl spcification could b too low compard to mpirical vidnc. Thrfor, th much asir stimation and highr flxibility of th simplifid modl would sm to outwigh th possibl fficincy loss du to this simplification. Th structur of th proposd modl as discussd in th prcding paragraphs is illustratd in Figur 1. D (ε+µ) (ε) no trad 1-γ E ignal good 1-δ γ E trad Inf. vnt δ no trad occurs ignal bad D (ε) 1-γ E α (ε+µ) γ E trad 1-α Inf. vnt no trad dos not occur D (ε) (ε) 1-γ N γ N trad D, unobsrvd D, obsrvd D, unobsrvd D, obsrvd D, unobsrvd D, obsrvd 7
Figur 1: Tr diagram of th trading procss. α is th probability of an information vnt, δ is th probability of a bad signal, ε is th arrival rat of uninformd tradrs, µ is th arrival rat of informd tradrs, γ E is th probability of nonzro trad in th cas of an information vnt, and γ N γ E is th probability of nonzro trad whn no nw information occurs. D (ω) ( (ω)) indicats that th total numbr of shars dmandd (supplid) follows a Poisson procss with th arrival rat ω. Ths valus ar unobsrvd if thr is no trad and can b rconstructd (using (1) and (2)) from th data on shars dmandd/supplid at th nw pric, othrwis. Th paramtrs to b stimatd for a givn stock ar α, δ, ε, µ, γ E, γ N, β and s. Th primary goal of th papr is, howvr, to stimat th xtnt of information basd trading. Basd on th branch of th tr prvailing on a givn day, buy and sll ordrs follow diffrnt arrival procsss. Th avrag arrival rat of informd tradrs is α((1- δ)µ + δµ) + (1-α)*0 = αµ. Th avrag arrival rat of all tradrs is α((1-δ)(µ+2ε) + δ(µ+2ε)) + (1-α)*2ε = αµ+2ε. Th ovrall probability of informd trading is givn by th ratio of ths two xprssions, so that αµ PI = αµ + 2 ε. (3) 2.3 Th Liklihood Function In th proposd modl buy and sll ordrs follow on of thr Poisson procsss on ach day. Whthr or not nw information occurs is not dirctly obsrvabl. It is, howvr, rflctd in th data so that mor buy ordrs ar xpctd on good-signal days, and mor sll ordrs ar xpctd on bad-signal days. On no-vnt days, thr ar no informd tradrs arriving at th markt and fwr trads can b xpctd. Th probabilitis of ths cass ar dtrmind by th probability of nw information occurring and th typ of information. To construct th liklihood function for th whol modl, th liklihood of ordr arrivals on a day of known typ is drivd first. Considr a good-signal day. Th buy ordrs arriv at rat µ + ε as both uninformd and informd tradrs submit ths ordrs. Th sll ordrs arriv at rat ε as only uninformd tradrs sll. Th distributions of th total numbr of shars supplid/dmandd ar indpndnt Poisson distributions. Thn, th liklihood of obsrving th total of D buy ordrs and sll ordrs submittd on a good-vnt day, conditional on nonzro trad, is D ( µ ε) ( µ + ε) εε D!! + 8. (4)
imilarly, on a bad-vnt day, this conditional liklihood is and for a no-vnt day, it is D ε ( ) ( µ ε) D!! ε µ + ε + ε, (5) D ε ε ε D!!. (6) Lt D NT dnot th no trad 0-1 indicator variabl, which is 1 if thr was no trad with th stock on a givn day (cod of th markt qual to 6, 7 or 8), and 0, othrwis. Th probabilitis of a good-vnt day, bad-vnt day, and a no-vnt day ar α(1-δ), αδ, and 1-α, rspctivly. Th ovrall liklihood function for a givn day, thrfor, is [ 1 1 1 ] D L((, ) θ) = D α( γ ) + ( α)( γ ) NT E N D ( µ ε) ( µ + ε) ε + ε α( 1 δ) D!! (7) + ( 1 DNT ) D ε ε ( µ ε) ( µ + ε) ε ε αδ ( α ) ε ε + + + 1 D!!!! Th valus of D and ar not dirctly obsrvabl and ar modld hr by (1) and (2), from which w can writ [ 1 β ( + )] [ 1 β ( )] = B + D p s = + p s, (8), (9) whr B and ar th numbr of shars dmandd/supplid at th nw markt pric, and x dnots th narst intgr to x; this rounding is mployd as D and ar assumd to follow (discrt) Poisson distribution. ubstituting from (8) and (9) into (7), w gt th liklihood L((B,) θ) in trms of obsrvabl variabls. s days ar indpndnt, th liklihood of obsrving th data (B i, i ) I i=1 ovr I days is th product of daily liklihoods, I L = L( θ ( Bi, i)) This function is thn maximizd to stimat th paramtr vctor θ. i= 1. (10) 3. Th Data Th modl drivd in th prvious sction is stimatd for a subsampl of stocks tradd on th PE. ll data availabl from th introduction of a givn stock on th 9
markt 3 until Novmbr 30, 1996 ar usd. For ach stock in th sampl, w nd to stimat th paramtrs of th trad procss. If th stock is tradd too infrquntly, thr may not b nough data for this stimation. lso, th pric lvl of a givn stock can influnc th trading procss. Ths issus ar discussd blow whr I dscrib th sampl slction critria. Th sampl of all joint stock companis tradd on th PE was first sortd on th avrag probability of nontrading (probability of no trad in a givn day). Th sampl is thn dividd into dcils, whr th first dcil contains th most frquntly tradd stocks. lthough thr wr mor than 1,750 firms listd on th PE in 1996, most of thm did not trad vry frquntly (s 1ÀPH³HN (1996) for dtails). Trading frquncis and volums dcras rapidly across dcils. To b abl to judg th rol of trading activity, and at th sam tim to b abl to stimat th modl 4, I us stocks from th first through th fifth nontrading dcils. To liminat th possibl ffcts of th stock pric lvls, I construct a matchd sampl of stocks with th sam prics but diffrnt trading frquncis. This matching is vry similar to th on usd by Easly t al.: th avrag pric of th stock ovr th whol priod was usd to sort th stocks within th nontrading dcils. Th adjacnt pairs of stocks from diffrnt dcils ar thn matchd into groups. This yilds 175 groups out of which 25 groups ar randomly slctd. Tabl.1 in th ppndix lists th group statistics for th slctd stocks, thir avrag probabilitis of nontrading, book valus of th firms (numbr of shars outstanding tims thir fac valu), avrag prics, and th numbr of obsrvations (numbr of days on th markt). Th individual stock data (not shown, availabl from author) show clarly that th xtnt of nontrading, as wll as th avrag pric of th stock, is closly rlatd to th siz of th firm. Largr firms hav a much highr liquidity and a highr avrag pric. 4. Estimation In sction 2, th liklihood function for th structural modl was drivd. This liklihood function can b maximizd, conditional on trad data for a givn stock, to obtain th stimats of th trad procss and information flow for that stock. Th 3 Jun 22, 1993 and March 1, 1995 for most of th stocks offrd in th first and scond wav of th vouchr privatization, rspctivly. Th vast majority of stocks ntrd th markt on on of thos two dats. 4 Th stimation procss oftn dos not convrg for infrquntly tradd stocks. 10
probability paramtrs α, δ, γ E, and γ N wr rstrictd to (0,1) by a logit transformation of th unrstrictd paramtrs. To nsur that γ N γ E, as prdictd by th modl, γ N was xprssd as γ E + γ, and this summation was also rstrictd to (0, 1). Th arrival-rat paramtrs ε and µ wr rstrictd to (0, ) by a logarithmic transformation. Th liklihood function xprssd in trms of ths unrstrictd paramtrs was thn maximizd using th ML procdur of th TP packag. tandard rrors for th conomic paramtr stimats wr calculatd from th asymptotic distribution of th unrstrictd paramtrs using th dlta mthod. Bcaus of thir lngth, dtaild rsults of th stimation ar not prsntd hr. Howvr, to illustrat th individual-firm rsults and complt th pictur as prsntd by group statistics rportd in Tabl 1 and discussd blow, th stimatd paramtrs and corrsponding standard rrors for ach stock in th middl-nontrading group C of th sampl ar providd in Tabl.2 of th ppndix. Th valus of t-statistics rportd in Tabl.2 show that th paramtrs of th modl ar, in most cass, stimatd quit prcisly; this is tru spcially for th arrival rats of uninformd (ε) and informd (µ) tradrs. Not that th stimats of paramtrs β and s of th dmand and supply functions ar not rportd. Th rason is that ths paramtrs wr nvr significantly diffrnt from zro. Thr ar svral possibl xplanations for this obsrvation. First, if th limit prics of all ordrs lay at th boundaris of th admissibl nw-pric intrval so that ths ordrs wr valid throughout th whol intrval (and thy wr, in fact, quivalnt to th markt ordrs with no limit pric spcifid), th dmand and supply pattrns would b flat, justifying an stimat of β qual to zro. Howvr, this dos not sm to b an accurat account. scond xplanation is that th modl chosn for th shap of dmand and supply pattrns insid th admissibl rgion (th logistic function) may not b appropriat. I hav, thrfor, trid a simplr modl using a linar structur for ths pattrns. Th stimats of this linarizd modl in no way diffr from thos rportd. Th third, and most probabl, xplanation is that th modl as dsignd rquirs simply too much from th data, and thrfor, it is not possibl to rliably stimat th shap of th dmand and supply pattrns from th aggrgat numbr of buy and sll ordrs on any givn day. Having som spcial information about th typ of day (whthr nw information occurrd and what typ of information it was) could hlp. If thr ar signals that ar not purly firm-spcific but influnc svral 11
firms simultanously, thn th application of panl data tchniqus could hlp to rsolv this problm. I will rturn to this point in th conclusion. 12
Tabl 1: ummary statistics on stimatd paramtrs by group 3DUDPHWHU 3,7 ε µ α δ $)LUVWGHFLOH 0HDQ 0HGLDQ 6WGGHY 6WDWVLJQDW %6HFRQGGHFLOH 0HDQ 0HGLDQ 6WGGHY 6WDWVLJQDW &7KLUGGHFLOH 0HDQ 0HGLDQ 6WGGHY 6WDWVLJQDW ')RXUWKGHFLOH 0HDQ 0HGLDQ 6WGGHY 6WDWVLJQDW ()LIWKGHFLOH 0HDQ 0HGLDQ 6WGGHY 6WDWVLJQDW To s th diffrncs in stimatd paramtrs among th groups, group statistics wr computd (Tabl 1). Bsids th man, mdian, and standard dviation, this tabl shows a prcntag of firms in a givn group, for which an stimat of a givn paramtr is statistically significant at th 5% significanc lvl. Though th ranking of th stimats of probability of informd trading and arrival rats across dcils is consistnt with prior xpctations, th variability of th stimats suggsts that thr ar no significant diffrncs in mans of th paramtrs across groups 5. Lik Easly t al., I, thrfor, comput nonparamtric statistics to compar th distributions of stimatd variabls across groups. pcifically, th Kruskal-Wallis tst and th Wilcoxon rank sum tst ar usd. Th Kruskal-Wallis tst srvs to chck whthr th fiv population distribution functions ar idntical against th altrnativ that at last on of thm is diffrnt. Th Wilcoxon tst is usd for a pairwis comparison of ths distribution functions and tsts whthr th valus for on sampl 5 This fully agrs with th findings of Easly t al., who also find a similar ranking of not significantly diffrnt group mans. 13
tnd to b highr or lowr than for th scond sampl. Th valus of th tst statistics ar givn in Tabl 2. Considr first th paramtrs capturing th arrival rats of uninformd and informd tradrs. Tabl 1 shows larg diffrncs in both ε and µ across groups. Naturally, th arrival rat of uninformd tradrs falls dramatically whn going from th most activ stocks to lss liquid ons. Th Kruskal-Wallis tst rjcts th hypothsis that ths arrival rats ar qual across groups; th Wilcoxon tst supports this obsrvation by showing that th distribution of ε for th most activ stocks () diffrs significantly from that of othr groups B, C, D and E. Only th diffrncs btwn th adjacnt groups B and C, C and D, and D and E ar not significant. Tabl 2: Nonparamtric tsts Th Kruskal-Wallis tst is usd to dtrmin whthr th fiv populations (groups of stocks) from which th paramtr valus ar drawn ar idntical against th altrnativ that at last on of thm diffrs. Th Wilcoxon rank sum tst compars two populations and indicats whthr on of thm tnds to yild highr valus. Dcils ar dnotd by (most frquntly tradd stocks) through E (fifth nontrading dcil). 3DUDPHWHU 3,7 ε µ α δ.uxvndo:doolv7hvwv $V\PWRWLFDOO\GLVWULEXWHGDVχ &ULWLFDOYDOXHIRUα LV :LOFR[RQUDQNVXPWHVW $% $& $' $( %& %' %( &' &( '( $V\PWRWLFDOO\GLVWULEXWHGDV1 &ULWLFDOYDOXHIRUα LV Th distributions of arrival rats of informd tradrs also xhibit th xpctd pattrns. ccording to Tabl 1, th arrival rat of informd tradrs incrass whn going from mor activ to lss activ stocks, not only in rlativ trms (compard to th arrival rat of uninformd tradrs), but also in absolut valus. 6 gain, both th Kruskal-Wallis tst and Wilcoxon tst confirm this ranking and show significant diffrncs btwn most of th dcils. Th hypothsis of idntical distribution is not 6 This is diffrnt from th obsrvation of Easly t al., who find that (in absolut trms) th arrival rat of informd tradrs is highr for mor activ stocks. 14
rjctd for pairs B and C, C and D, C and E, and D and E, i.., primarily for th groups of lss tradd stocks. Unlik in Easly t al., th stimats of th information vnt paramtrs α and δ ar not linarly rlatd to th stocks liquidity. Whil th probability of an information vnt occurring on a givn day has a man of 13.53% for th first dcil, it incrass to 30.80% for th scond dcil and falls back to 19.29% for th fifth dcil. Thus, only th low man probability of an information vnt occurring for th first dcil dos not conform to th pattrn of dcrasing frquncy of information vnts for lss activ stocks found in Easly t al. lso, th magnituds of ths frquncis ar significantly lowr than thos found for NYE stocks (about 50% for th first and 35% for th ighth dcil). Morovr, th pattrn of good/bad signals is rvrsd th probability of a bad signal falls from 20.75% for th most activ stocks to 9.41% for th fourth group and incrass to 18.67% for th fifth dcil of PE stocks; it incrass from about 35% for th first dcil to 50% for th ighth dcil of NYE stocks. 7 s for th statistical significanc of ths obsrvations, th Kruskal-Wallis tst lads to rjction of th hypothsis of an idntical distribution of paramtr α across groups; this tst also finds (at 5% lvl) significant diffrncs in th distributions of typs of signals (paramtr δ) across th fiv groups. Th Wilcoxon rank sum tst finds statistically significant diffrncs in th distributions of paramtr α for almost all pairs of groups th only xcption is th pair B and C, i.., th scond and third nontrading dcils. Th tst also supports th hypothsis of a highr probability of a bad signal (δ) for th most activ stocks, compard to othr groups. Finally, considr th paramtr which is of highst intrst th ovrall risk of informd trading. Th group mans rportd in Tabl 1 show an incras in this paramtr whn going from mor activ to lss activ stocks. Both th Kruskal-Wallis and Wilcoxon tsts indicat significant diffrncs in th distributions of th probability of informd trading across groups. Only whn th bottom thr dcils ar compard dos th Wilcoxon tst not rjct th hypothsis of idntical distributions. This again 7 Thr is no clar xplanation of th rlativly low probabilitis of th bad signals on th PE. On possibility is, howvr, that bcaus of th concntration procss, th bad signals ar rflctd mor in a dcras in th trading activity than in an incras in th supply of shars (invstors who want to acquir a highr portion of th firm will b mor rluctant to sll its shars whn obsrving a bad signal). This would man that arrival rats of informd tradrs in th cas of an information vnt ar diffrnt for good and bad signals. Th modl as stimatd did not allow for such a possibility. 15
agrs with th obsrvation of Easly t al. that probability of informd trading incrass with dcrasing liquidity. 5. Conclusions Rcnt discussions about th connction btwn liquidity and th informational rol of stock markts yild important insights into th markt makrs dcision on th bid-ask sprads in th framwork of continuous-tim dalr markts. clar conclusion of mpirical studis is that low liquidity nhancs th risk of information-basd trading and that widr sprads for infrquntly tradd stocks do at last partially rsult from markt makrs insuring thmslvs against losss from trading with an informd agnt. This papr tris to accss th sam problm in th stting of ordr-drivn auction markts. For a sampl of Pragu tock Exchang stocks, th bhavior of activ and infrquntly tradd stocks was invstigatd. modl, similar in spirit to that of Easly t al., but taking into account th limits of data availability and othr spcifics of th PE, was proposd and th probability of information-basd trading was stimatd for ach stock in th sampl. Whil it was not possibl to stimat th undrlying shaps of th dmand and supply pattrns, th arrival rats of uninformd and informd tradrs and probabilitis of information vnts wr stimatd with rasonabl prcision. Th analysis confirms th a priori xpctation that th probability of information-basd trading is lowr for activly tradd stocks than it is for inactiv stocks. Th rlativ pattrns and obsrvations on th rol of liquidity in dtrmining th xtnt of information-basd trading, rportd abov for th cas of th ordr drivn (auction) stock trading at th PE, ar in full accord with th findings of Easly t al. for th pric drivn (continuous auction) trading at NYE. Th xtnt of informd trading, howvr, diffrs substantially. Whil Easly t al. rport avrag probabilitis of informd trading of about 20% 8, th avrag risks of information-basd trading found hr ar just 0.19%, 1.39%, and 2.01%, rspctivly, for th corrsponding thr groups (dcils) of PE stocks. Thr ar svral factors that could xplain this diffrnc. First, as discussd in th introduction, th situation in th Czch Rpublic in th analyzd priod was spcial in th sns that informd tradrs had many opportunitis to utiliz thir information outsid th pric-making markt. This could also xplain why th arrival rats of informd tradrs for activ stocks ar lowr in magnitud than 16
th arrival rats of informd tradrs for inactiv stocks it is asir for an informd tradr to find anothr party for a transaction that involvs activly tradd stocks than it is to find on for trading an illiquid stock. Howvr, whn an informd agnt trads dirctly with anothr party (outsid th markt), othr agnts may mor asily idntify him as bing informd. In th cas of a dvlopd markt, whr all agnts ar prictakrs on th markt, an informd tradr is mor likly to trad in th markt than outsid bcaus of th risk of rvaling his typ. Th PE, howvr, is a markt with quit small capitalization, on in which ordrs submittd by on agnt may substantially influnc th auction pric of th particular stock. t th sam tim, thr was (during th priod studid in this papr) a substantial tim lag in rporting of th transactions mad at th Cntr of curitis and th rporting rquirmnts wr vry wak. Furthr, th transaction costs of th transfr at th countr of th Cntr of curitis wr ngligibl compard to th costs of trading on th markt this diffrnc in trading costs was, of cours, largst for th most activ stocks (which hav, at th sam tim, th highst prics). Ths facts ar likly to hav ld th informd agnt to trad primarily outsid th markt. nothr argumnt xplaining th low avrag probabilitis of informd trading coms from th work of Pagano and Rqll (1996), who show, in a stylizd nvironmnt, that gratr transparncy of th trading mchanism rducs trading costs and th ability of informd tradrs to profit from thir information. In this rspct, th ordr-drivn auction of th PE ranks abov th continuous auction of th NYE. This also supports th lowr risk of informd trading on th PE. To conclud, th proposd modl documnts that th risk of informd trading dcrass with incrasing liquidity of a stock. Th xtnt of information-basd trading at th PE is vry low in magnitud, which can b xplaind by th othr opportunitis informd tradrs hav to utiliz thir privat information and by th institutional structur of th markt. Th shaps of dmand and supply pattrns which could not b idntifid in this modl may, hopfully, b rvald whn panl data tchniqus ar applid to nhanc th modl and to utiliz information carrid by signals that ar not purly firm-spcific. 8 16.4%, 20.8%, and 22.0% for th thr groups thy us 17
REFERENCE Diamond, D. W., Vrrcchia, R. E. (1991). Disclosur, Liquidity, and th Cost of Capital, Journal of Financ 46(4): 1325-1359. Easly, D., Kifr, N. M., O'Hara, M. (1996). Cram-kimming or Profit-haring? Th Curious Rol of Purchasd Ordr Flow, Journal of Financ 51(3): 811-833. Easly, D., Kifr, N. M., O Hara, M., and J. B. Paprman (1996). Liquidity, Information, and Infrquntly Tradd tocks, Journal of Financ 51: 1405-1436. Hasbrouck, J. (1988). Trads, Quots, Invntory, and Information, Journal of Financial Economics 22: 229-252. Hasbrouck, J. (1991). Masuring th Information Contnt of tock Trads, Journal of Financ 46: 179-207. 1ÀPH³HN, L. (1996). Expctd Rturns Whn hars r ubjct to Infrqunt Trading: Evidnc from th Czch and lovak tock Markts, unpublishd. Pagano, M. and. Rqll (1996). Transparncy and Liquidity: Comparison of uction and Dalr Markts with Informd Trading, Journal of Financ 51: 579-611. 18
PPENDIX Dscription of th variabl cod of th markt publishd by th PE: Cod = 1... prfct balanc Numbr of scuritis supplid and numbr of scuritis dmandd at th nw pric ar qual. Th nw pric is within th allowd sprad margin. Cod = 2... local xcss on supply sid Numbr of scuritis supplid at th nw pric is highr than th numbr of scuritis dmandd at that pric. Th nw pric is within th allowd sprad margin. ll buy ordrs with limit pric highr or qual to th nw pric will b satisfid. ll ordrs with limit pric lowr or qual to th nw pric will b rationd 9. Cod = 3... local xcss on dmand sid Numbr of scuritis dmandd for purchas at th nw pric is highr than th numbr of scuritis supplid at that pric. Th nw pric is within th allowd sprad margin. ll sll ordrs with limit pric lowr or qual to th nw pric ar satisfid. Buy ordrs with limit pric highr or qual to th nw pric will b rationd 3. Cod = 4... global xcss on supply sid Numbr of scuritis supplid at th nw pric is highr than th numbr of scuritis dmandd at that pric. Th nw pric quals th lowr limit of th allowd pric sprad margin. ll buy ordrs with limit pric highr or qual to th nw pric will b satisfid. ll ordrs with limit pric lowr or qual to th nw pric will b rationd according to th allocation ratio, which is th ratio of shars actually sold to th numbr of shars supplid. Cod = 5... global xcss on dmand sid Numbr of scuritis dmandd at th nw pric is highr than th numbr of scuritis supplid at that pric. Th nw pric quals th uppr limit of th allowd pric sprad margin. ll sll ordrs with limit pric lowr or qual to th nw pric will b satisfid. Buy ordrs with limit pric highr or qual to th nw pric will b rationd according to th allocation ratio, which is th ratio of shars actually sold to th numbr of shars dmandd. Cod = 6... total xcss on supply sid Numbr of scuritis supplid at th nw pric is highr than th numbr of scuritis dmandd at that pric. Th nw pric quals th lowr limit of th allowd pric sprad. Th allocation ratio is lowr than 20 %, and thrfor no trad will tak plac. Cod = 7... total xcss on dmand sid Numbr of scuritis dmandd at th nw pric is highr than th numbr of scuritis supplid at that pric. Th nw pric quals th uppr limit of th allowd pric sprad. Th allocation ratio is lowr than 20 %, and thrfor no trad will tak plac. Cod = 8... not quotd No sll or buy ordrs wr placd, or such ordrs wr placd, but th limit prics of sll ordrs do not ovrlap with th limit prics on th dmand sid. Th prvious pric rmains valid. No trad taks plac. 9 This could happn du to th discrt natur of th distribution of ordrs actually submittd. In th modl, th stpwis non-incrasing (non-dcrasing) functions dscribing cumulativ numbrs of shars dmandd (supplid) at a givn pric wr modld by th smooth logistic functions so that rationing occurs only at th boundaris of th admissibl pric intrval. 19
Tabl.1: Data on groups of PE stocks includd in th sampl This tabl prsnts group statistics of th data on stocks includd for stimation. Book valu is masurd in thousands of CZK. Prob. of nontrading Book valu vrag pric # of obs. $)LUVWGHFLOH 0HDQ 7.31% 2320094 1045.64 596 0HGLDQ 6WGGHY 2.56% 2852227 1201.57 96 %6HFRQGGHFLOH 0HDQ 22.37% 528341 479.04 541 0HGLDQ 6WGGHY 5.73% 305027 603.04 112 &7KLUGGHFLOH 0HDQ 41.03% 343051 364.92 550 0HGLDQ 6WGGHY 4.60% 281362 400.05 112 ')RXUWKGHFLOH 0HDQ 57.32% 183022 290.50 543 0HGLDQ 6WGGHY 3.05% 157732 262.28 111 ()LIWKGHFLOH 0HDQ 67.06% 116531 205.36 548 0HGLDQ 6WGGHY 2.28% 91529 166.04 114 Tabl.2: Paramtr stimats for th middl-nontrading group C This tabl prsnts th stimats of th paramtrs of th modl for ach stock includd in th middlnontrading group C of th sampl. BIC stands for Bohmian Idntification Cod, an official tag usd by th PE authoritis for a givn firm. PIT givs th probability of informd trading as drivd from th othr paramtrs: ε, arrival rat of uninformd tradrs, µ, arrival rat of informd tradrs, and α, probability of an information vnt. δ givs th probability of a bad signal; γ E (γ N ) th probability that thr will b trad, conditional on an information vnt occurring (not occurring). Valus of t-statistics ar givn in parnthss blow th paramtr stimats. maximum liklihood stimation was prformd using th ML procdur of TP packag. - marks th cass whr th stimation algorithm faild to provid stimats of standard rrors. %,& 3,7 ε µ α δ γ ( γ 1 *URX&7KLUGQRQWUDGLQJGHFLOHVWRFNV %$$76/+. %$$%8=8/ %$$$9,$% %$$3(*$ %$$)$6$' %$$/,*5$ %$$2'.2/ %$$81&8. %$$75,2' 20
%,& 3,7 ε µ α δ γ ( γ 1 %$$-,+/( %$$+2727 %$$58%(1 %$$*(126 %$$2%7,6 %$$06/= %$$&$'&% %$$6.5%5 %$$&$/2) %$$-$/7$ %$$&.'.+ %$$35$*/ %$$353/< %$$.28=( %$$65287 %$$==135 21