InformationSharing,Liquid ity and TransactionCosts infloor-basedtradingsystems. 1

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1 InformationSharing,Liquid ity and TransactionCosts infloor-asedtradingsystems. 1 Thierry Foucault HECandCEPR 1,rue de la Lib eration Jouy enj osas,france. Laurence Lescourret CRESTandDoctoratHEC 15,oulevardGabrielP eri 945Malako,France. November,001 1 WethankGiovanni Cespa,Asani Sarkarandseminarparticipants atcrest,lavaluniversity, the A FFI000 conference, the EEA 000 conference, the FM A 001 M eetings and the InternationalFinanceConference T unisie A llerrors areours.

2 Abstract InformationSharing,Liquid ity and TransactionCostsinFloor- ased Trad ing Systems. We consider informationsharingbetw eentrad ers(\ oor brokers") who possessdi erent typesofinformation,namelyinformationonthe payo ofa riskysecurityor informationon the volume ofliquid itytrad inginthissecurity.we interpret these trad ersasdual-capacity brokersonthe oor ofanexchange.we id entify conditionsunder which the trad ersare better o sharing information. We also show that informationsharing improves pric e discovery, red ucesvolatility and low ersexpected trad ing costs. Informationsharing can improve or impair the depth ofthe market,dependingonthe valuesofthe parameters. O vera lour analysissuggeststhat informationsharing among oor brokersimprovesthe performance of oor-based tradingsystems. Keywords: MarketMicrostructure,Floor-asedTradingSystems,OpenOutcry,InformationSharing,InformationSales. J E L Classi cationnumb ers: G 10,D8.

3 1 Introduction T he organiz ationoftrad ing onthe NY SE hasb eenrem arkab ly stab le sinc e its rst c onstitutionin1817.trad ingiscond ucted through openoutcry ofbid sand o ersofbrokers actingonbehalfoftheirclientsorfortheirownaccount. 1 Thistradingmechanismisnot unique to the NY SE.E quity marketslike the Frankfurt Stock E xchange and the AM E X orderivativesmarketslikethecot and thecoe are oormarkets. However oorbased trad ing mechanismsare end angered speciesasthey are progressively replaced by fulyautomated tradingsystems 3. Giventhistrend toward automation,it isnaturalto ask w hether oor-based trad ing systemscanprovid e greater liquid ity and low er executioncoststhanautomated trad ingsystems.thisquestionisofparamount importance for market organizersand trad ers. Infact, it hasbeenhotly d ebated betweenmembersof Exchangeswhoconsideredswitchingfrom oortoelectronictrading 4.Inordertosurvive oor-b ased trad ing m ec hanism smust outperform automated trad ing system salong som e dimensions. Autom ated trad ing system sd ominate oor-b ased trad ing systems inm any respec ts. First oor marketsare more expensive to operate(see Domowitz and Steil(1999)).Second physicalspace limitsthe number ofparticipantsin oor marketsbut not inautomated trad ingsystem s.f ina ly trad ersw ithout anac c essto the oor are at aninform ationald isad vantage compared w ith the trad ersonthe oor.t hisd isad vantage islikelyto exacerbate agenc y prob lem sb etw eeninvestorsand their b rokers(sarkar and W u(199 9)). y d esign, oor-based marketsfoster person-to-personcontacts. Hence the ability of market participantsto share informationisgreater inthese markets.thisfeature isoften viewedasbeingoneadvantage,ifnottheuniqueone,of oor-basedtradingsystems. 5 For instance Harris(000),p.8,pointsout that 1 Ofcourse,manytradingruleshavebeenchangedsincethecreationoftheNYSE.utithasalways beena oormarket.seeh asbrouck,so anos andsosebee(1993)foradetaileddescriptionofthetrading rulesonthenyse. InFrankfurt,the ooroperatesinparallelwithanelectronictradingsystem. 3 TheMarch eµatermeinternationaldefrance(matif),thetorontostockexchangeandthelondon InternationalFinancialFutures and O ptions Exchange(L IFFE)shutdown their oorin 1997,1998 and 000,respectively. 4 SeetheEconomist(July31st1999):\A homegrownrevolutionary"andtheeconomist(august6th 000):\Outofthepits". 5 Covaland Shumway(1998)showthatthe levelofnoise on the oorofcot's 30 yeartreasury ond futures a ects price volatility.t his alsosuggests thatperson toperson contacts on the oorhave an impacton priceformation. 1

4 `Floor-based tradingsystemsdominate electronic tradingsystemswhenbrokers need to exchange informationabout their clientsto arrange their trades.' Informationsharing isa functionofthe oor which isdi± cult to replicate inelectronic trad ing systems. These systemsusua ly restric t the set ofmessagesthat canb e sent by users(genera ly trad ersc anonly post pric esand quantities).furthermore trad inginthese systemsisinmost casesanonymous. Thisfeature preventstrad ersfrom developing the reputationofhonestly sharinginformationthrough enduringrelationships. Informationsharingonthe oor cantake place betweentwo typesofparticipants.first oor-brokerscanexc hange informationontheir trad ing motivationsw ith market-makers. enveniste,m arcusand Whilelm(199) modelthistype ofinformationsharingand show that it mitigatesad verse selection.second oor-brokerscancommunicate with other oorbrokers.for instance,so anosand Werner(1997),p.6 notice that Ìnad d ition, by stand inginthe crow d, oor brokersmay learnabout ad d itional broker-represented liquidity that isnot re ected inthe specialist quotes: oor brokers willoftenexchange informationontheir intentions and capabilities, especially with competitorswith whom they have good workingrelationships.' Our purpose inthispaper isto analyze thistype ofinformationsharing.at rst glance, informationsharing am ong oor brokersispuzzling.infac t stand ard mod elsw ith asymmetric information(e.g.kyle(1985)) show that informed trad erswant to hide their informationrather thandisclose it to potentialcompetitors.furthermore,informationsharing reinforcesinformationalasymetriesbetweenthose who share informationand those who do not.it istherefore not obviousthat it should improve market quality.hence we addresstwo questions.first, isit optimalfor oor brokersto share informationwith their competitors? Second, what isthe e ect ofinformationsharing among oor brokerson the overa lperformance ofthe market? Inparticular we study the impact ofinter- oor brokerscommunicationonstandard measuresofmarket quality, namely price volatility, price discovery,market liquid ity and trad ingcosts. We mod el oor trad ingand informationsharingusingkyle(1985)'smod elasa workhorse. AsinRoÄe l(1990),we assume that trad ers( oor brokers) have accessto two typesofinformation:(i) fundamentalinformationwhich isinformationonthe payo ofthe security and(ii) non-fundamentalinformationw hich isinformationonthe volume ofliquidity(non- informed) trad ing.w e consid er the possibility for tw o oor brokersend ow ed w ith d i erent

5 typesofinformation(one hasfundamentalinformationand the other hasnon-fundamental information) to share information.m ore speci c a ly we assume that oor brokershave informationsharingagreements(they form a\clique").anagreement spec i esthe precision with which each broker reportshisor her informationto the other broker.after receiving fundamentalor non-fundamentalinformation,the brokersina clique pooltheir information accord ingto the termsoftheir agreement just before submittingtheir ord ersfor execution. We establish the fo low ingresults. ²There isa wid e range ofparametersfor which it isoptimalfor oor brokersto share their information(i.e.their expected pro tsare larger with informationsharing). ²Informationsharing canimprove or impair the d epth ofthe market, d epend ing on the valuesofthe parameters. ²Informationsharingalwaysred ucesthe aggregate trad ingcostsfor liquid ity trad ers. How ever wheninformationsharingimpairsmarket d epth,some liquid ity trad ersare hurt. ²Informationsharing oc cursat the expense ofthe oor brokersw ho are not part to the informationsharingagreement. ²Informationsharingimprovesprice discovery and red ucesmarket volatility. Intuitively informationsharing intensi escompetitionb etw een oor brokersand inthis w ay it low ersthe totalexpected pro tsofa l oor b rokers(red ucesthe aggregate trad ing c osts). Informationsharing also changes the a loc ationoftrad ing pro ts am ong oor b rokers.m ore speci c a ly the oor b rokersw ho share informationc apture a larger part of the totalexpected pro ts, at the expense of oor brokerswho do not share information. T hese tw o e ec ts explainw hy inform ationsharing c ansimultaneously b ene t liquid ity tradersand the oor brokerswho share their information. O vera linformationsharing between oor brokersisanad vantage for oor-based trad ingsystemssince it resultsin(a) low er trad ingcosts,(b) faster price d iscovery and(c) low er price volatility.interestingly, inline w ith our result, Venkataraman( 00 0) nd sthat trad ing costsonthe NY SE are lower thanonthe Parisourse(anautomated trad ingsystem),contro lingfor d i erences instockscharacteristics. 6 6 Theissen(1999)comparese ectivebid-askspreadsinanautomatedtradingsystem (Xetra)andthe oorofthe FrankfurtStock Exchange forstocks thattrade in both systems. H e nds thatthe average 3

6 Our analysisisrelated to the literature oninformationsales(e.g.ad matiand P eid erer (1986), (1988) and Fishmanand Hagerty (1995)). Inc ontrast w ith this literature, w e assume that the medium for informationexchange isinformation, not money. Actua ly inour model, the trader who receivesinformationrewardsthe informationprovider by disclosinganother type ofinformation.hence we consider oor-based systemsasmarkets for trad ingsharesand forum to barter information.another important di erence isthat we consider communicationofinformationonthe volume ofliquid ity trad ing.we show that it may be optimalto `se l'(barter) such aninformationand that salesofnon-fund amental informationhave animpact onmarket quality. The mod elisd escrib ed inthe next section.sec tion3 show sthat it canb e optimalfor oor brokersto share information.section4 analyzesthe impact ofinformationsharing onvariousm easuresofmarket performance.section5 conclud es.t he proofsw hic h d o not appear inthe text are inthe Appendix. TheModel.1 InformationSharingAgreements The TradingCrowd. We consid er a mod eloftrad inginthe market for a riskysecurityw hich isbased onk yle (1985). T he nalvalue ofthe security, w hich isd enoted ~v, isnorma ly d istributed w ith mean¹andavariance ¾ v thatwenormalizeto1.this nalvalueispubliclyrevealedat d ate.trad inginthissecuritytakesplace at d ate 1.At thisd ate,investorssubmit market ord ersto buy or to se lsharesofthe security.t he excessd emand (supply) iscleared at the price posted by a competitive and risk-neutralmarket maker. The trading\crowd"for the securityiscomposed ofn +1 oor brokers. 7 At time 1, there are two typesof oor brokers: (i) N fundamentalspeculatorsand (ii) one non fundamentalspeculator,.fundamentalspeculatorshave informationonthe nalvalue ofthe security.for simplicity,asink yle(1985),w e assume that theyperfectlyobserve this nalvalue,just before submittingtheir ord ersat d ate 1.roker, the non-fund amental quoted spreads on the oorcan belargerorsmallerthan in theautomated tradingsystem,dependingon thestockcharacteristics.o naveragethequotedspreads areequal.t his is consistentwithourresultthat theimpactofinformation sharingon marketdepth is ambiguous. 7 Themarket-makercanalsobeconsideredasbeinga oorbrokerwhohasnoinformation. 4

7 speculator,receivesordersfrom liquiditytraders. Wedenote ~x the totalquantitythat broker must execute onbehalfofliquidity trad ers.asa whole, liquidity trad ershave a net demand equalto ~x = ~x 0 + ~x shares. We assume that ~x 0 and ~x are normaly and independentlydistributed with means0 and variances¾0 and ¾ respectively. We normalizethevarianceoftheorder owduetoliquiditytrading,¾ x,to1,i.e.: ¾ x=¾ +¾ 0=1: Inthisway,¾ canbeinterpretedasbroker'smarketshareofthetotalorder owfrom liquid ity trad ers.t he rem ainingpart ofthe ord er ow c anb e seenasb einginterm ed iated b y oor b rokersw ho d o not trad e for their ow nac c ount or asb eing routed elec tronic a ly tothe oor. 8, 9 oth typesofspeculatorscanengage inproprietary trad ing. Inparticular broker c anac t b oth as anagent (she channels a frac tionofliquid ity trad ers' ord ers) and as a principal(she submitsordersfor her ownaccount). Thispractice isknownas`dualtrad ing' and isauthorized insecuritiesmarkets(see Chakravarty and Sarkar( 000) for a discussion). 10 Modelswithdual-tradingincludeRÄoel(1990),Sarkar(1995)orFishmanand Longsta (199).Inthese mod els,asinthe present article,brokersengaged ind ual-trad ing exploittheirabilitytoobserveorderssubmittedbyuninformed(liquidity)traders. 11 None ofthese mod elshasc onsid ered inform ationsharing offund am entaland nonfund amental inform ationamong b rokers, how ever.o ur purpose isto stud y the e ec tsofthisac tivity. Asargued inthe introd uction,thistype ofinformationexchange isa d istinctive feature of oor markets.the speculatorswith fund amentalinformationcanbe seenasbrokerswho exclusively trad e for their ownaccount (like scalpersand localsind erivativesmarkets). T hey could also b e seenasb rokersw ho have no customers' ord ersto execute at d ate 1. It isreasonable to assume that the order ow from liquidity tradersisindependent ac rossb rokers(for instanc e b rokers have d i erent c lients). Inc ontrast, signals onthe fundamentalvalue ofthe security are correlated. For these reasons, we assumed that onlyone oorbrokerobservesthenon-fundamentalinformation,~x,whereasseveral oor 8 IntheU.S,fulllinebrokeragehousesengageinproprietarytradingactivities. Discountbrokersdo not,however. 9 Forinstance,ontheNYSE,orderscanreachamarket-makerthrough oorbrokersorelectronically through asystem called SuperD ot. 10 Forinstance,Chakravartyand Sarkar(000)observethatin the NYSE potentialdualtraders are nationalfulllinebrokeragehouses andtheinvestmentbanks. 11 SeealsoMadrigal(1996). Weborrowthedistinctionbetween`fundamental'vs. ǹon-fundamental' speculators from this author. 5

8 brokersobserve the fundamentalinformation,~v.we have analyzed the mod elw henthere is more thanone non-fundamentalb roker(with independent ord er ow) and brokersperfectly share information(informationsharingisd escribed below).the presentationofthe mod el ismore complex but the conclusionsare qualitatively similar to those we ob taininthe case w ith only one non-fund amentalbroker. O ne reasonfor w hich the mod elis more complexisthat the number ofcliques(groupsofpaired brokerswith distinct information) isendogenous. Inequilibrium, thisnumber canbe sma ler thanthe maximum possible number ofcliques.for instance ifthere isanequalnumber, N, offundamentaland nonfundamentalbrokers, the number ofcliquescanbe sma ler thann. Inparticular, with perfect informationsharing,thisisnecessarilythe case when¾0 = 0. Inthiscase,the aggregate ord er ow channeled by the non-fundamentalbrokerswho are not a± liated to acliqueplaystheroleof~x 0 inthepresentarticle. InformationSharing. W e mod elinformationsharing asfo low s.w e assume that the nonfund am entalspeculator,, hasanagreement to share informationwith one fundamentalspeculator, S. Accord ing to thisagreement, before trad ing at date 1, the non-fundamentalspeculator sendsa signal ^x=~x +~ ; to the fundamentalspeculator.inexchange,the fundamentalspeculator sendsa signal ^v=~v+~"; to the nonfund amentalspeculator.t he rand om variab les~ and ~" are ind epend ently and normalydistributedwithmeanzeroandvariances¾ and¾ ",respectively.werefertothe inverseof¾ (resp.¾ ")astheprecisionofthesignalsentbybroker(s).thelargeris¾ (¾" ),thelesspreciseisthesignalsentbyspeculator (speculators)andhencethelower isitsinformative value.two polar casesare ofparticular interest.first there isperfect informationsharingif¾ =¾ " =0.Secondthereisnoinformationsharingif¾ =¾ "=1. In-b etw eenthese tw o c ases, there isinformationsharing b ut it isimperfect (at least one speculator doesnot perfectly disclose hisor her information). The informationsetsof speculators and Satdate1aredenoted y =(~x ;^x;^v)and y S =(~v;^x;^v),respectively. Inreality oor brokersare likely to exchange informationw ith the brokersw ith w hom they have end uring relationships.inthisc ase their d ec isionto share informationw ith a 6

9 givenbroker must be based onthe long-term(average) bene tsofinformationsharing.for thisreason,w e assume that the speculatorsdecid e to share informationbycomparingtheir ex-ante(i.e.prior to receivinginformation) expected pro tswith and without information sharing.wesaythatinformationsharingispossibleifthereexistsapair(¾,¾ ")suchthat the expected pro tsofspeculator S and are larger whenthere isinformationsharing. Insection3,we id entify parameters' valuesfor which informationsharingispossible. Remarks. It isw orth stressingthat we focusonthe possibilityofaninformationsharingagreement but not onitsimplementation. Inparticular, we do not addressenforcement issues. In that, we fo low the literature oninformationsaleswhere the quality ofthe information whichissoldisassumedtobecontractible. 1 Wealsoassumethattheinformationsharing agreement and itscharacteristics(¾ ;¾ ") are knownby alparticipants(including the market-maker).thiscommonknowledge assumptionisalso standard inthe literature on informationsales.. The equilibrium ofthe Floor M arket Inthissection,we derive the equilibrium ofthe trad ingstage at date 1,giventhe characteristicsofthe informationsharingagreement betweenspeculators and S.Then,inthe next section,we analyze whether or not it isoptimalfor and Sto exchange information. WedenotebyQ S (y S )and Q (y ),the orderssubmitted byspeculatorssand,respectively.inthe set offundamentalspeculators, we assignindex1 to speculator S.An ordersubmittedbytheotherfundamentalspeculatorsi=;:::;n isdenoted Q i (~v).the totalexcessd emand that must be cleared by the competitive market maker istherefore O= i=n X i= Q i (~v)+q S (y S )+Q (y )+~x: Asthemarketmakerisassumedtobecompetitive,hesetsapricep(O)equaltotheasset 1 SeeAdmati andp eiderer(1986),(1988).somepapershaveshownhowincentivescontractscanbe used toinduce an information providertotruthfully revealthe quality ofhis signal(see A llen(1 990)or hattacharya and P eiderer(1 985)). R eputation e ects may also help to sustain information sharing agreements(see enabou andl aroque(1 99)). 7

10 expected value cond itionalonthe net ord er ow,i.e. p(o)=e(~vjo): (1) Anequilibrium consistsoftradingstrategiesq S (:),Q (:),Q i (:);i= ;:::;N and a competitive price functionp(:) such that(i) eac h trad er'strad ingstrategy isa best response to othertraders'strategiesand (ii)thedealer'sbiddingstrategyisgivenbyequation(1). 13 For givencharacteristics,(¾ ;¾ "),ofaninformationsharingagreement,the next lemma describesthe unique linear equilibrium ofthe trad inggame. Lemma 1 : The tradingstage hasa unique linear equilibrium which isgivenby p(o) = ¹+ O; () Q S (y S ) = a 1 (~v ¹)+a (^v ¹)+a 3^x; (3) Q i (~v) = a 0 (~v ¹);i=;:::;N (4) Q (y ) = b 1 ~x +b ^x+b 3 (^v ¹), (5) wherecoe±cientsa 1 ;a ;a 3 ;a 0 ;b 1 ;b ;b 3 and are a 1 = 3(¾ v+¾ ") ((N+)¾ v+3(n+1)¾ ") ; ¾ v a = ((N+)¾v +3(N+1)¾ " ); a 3 = ¾ 3 ; ¾ +¾ a 0 = ¾ v+3¾ " ((N+)¾ v+3(n+1)¾ ") ; b 1 = 1 ; b = b 3 = ¾ 6 ; ¾ +¾ ¾ v ((N+)¾ v +3(N+1)¾ " ); 13 Moreprecisely,weconsiderthePerfectayesianEquilibriaofthetradinggame. 8

11 and (¾ ";¾ )= q 6 ¾v ¾ +¾ (4(N+1)¾ 4 v +(1N+5)¾v¾ "+9N¾ ") 4 ((N+)¾v +3(N+1)¾ " q¾ ) 4¾ +9¾ +36¾ 0 ¾ +¾ : Trad erspurchase (se l) the security whentheir estimationofthe asset value isabove (below)theunconditionalexpectedvalue.hence,thecoe±cientsa 1,a 0 andb 3 arepositive. Nonfund amentalinformationisalso a source ofpro t.intuitively liquid itytrad ers'ord ers create temporary price pressures. rokerswith non-fundamentalinformationare aware ofthese price pressures. They canpro t from thisknow led ge by se ling(buying) high (low) whenliquidity tradersbuy (sel). More formaly suppose that the fundamental speculators(but not the market maker) do not expect changesinthe security value(i.e. ~v = ¹).Suppose also that and S perfectly share informationand that liquidity trad ers submit buyord ers.t hese ord erspush the price upward because the market maker cannot d istinguish liquid ity ord ersfrom informed ord ers.speculatorsand Show ever know that the correct value ofthe securityis¹.inanticipationofthe upward pressure onthe clearing price,theysubmit se lord ers. ysymmetry,theysubmit buyord erswhenliquiditytrad ers submitselorders.thisexplainswhycoe±cientsb 1 and a 3 arenegative.thismeansthat oor brokers and S partly accommod ate liquidity trad ers' ord ersand red uce the ord er ow imbalance that must be executed by the market-maker.a similar e ect isobtained inräoe l(1990) and Sarkar(1995). The previousdiscussionshowshow speculatorscanpro t both from fundamentaland nonfundamentalinformation. Hence there isa bene t to exchange fundamental(nonfundamental) informationfor non-fundamental(fundamental) information. Information sharing iscostly, how ever. Actua ly speculatorss and depreciate the value oftheir private informationwhenthey share it.consid er speculator for instance.ifshe does not shareinformation(¾ = +1),sheaccommodateshalfoftheorder ow she receives (since b 1 = 1=).Ifshesharesinformationthenbrokers and S(instead ofbroker alone) provide liquid ityto the ord erschanneled bybroker.for instance ifthere isperfect informationsharing theneach broker accommod atesone third ofthe ord ersreceived by broker (since b 1 +b = 1=3and a 3 = 1=3when¾ =0).Thiscompetitionfor the provisionofliquid ity hastwo e ects. First, broker trad essma ler quantities.second, theorderimbalancethatmustbeexecuted bythemarket-makerissmaler.hence,fora 9

12 givenprice schedule (a xed ),pricesreact lessto the order ow. 14 Infact speculator reduceshertradesizewhenshesharesinformation(b hasa signoppositethesignof b 1 )preciselytomitigatethise ect.thesetwoe ects(smalertradesize/smalerabsolute price movements) reduce speculator's pro tsonnon-fundamentalinformation.thisis the cost ofsharingnon-fundamentalinformation. A similar argument holdsfor speculator S. He depreciatesthe value offundamental informationw henhe sharesit with speculator.inord er to mitigate thise ect,he ad justs histradingstrategytothemessagehesendstospeculator.thisexplainswhya hasa signopposite a 1. To sum up,informationsharinghasbene tsand costs.informationsharingisa source ofpro tssince it a low seach broker to trad e ona new type ofprivate information.ut the brokersob tainnew informationonly ifthey disclose a lor part oftheir information.t his iscostlysince it red ucesthe trad ingpro tsthat canbe mad e onthe informationorigina ly possessed by a broker.inthe next sectionw e show that the bene t ofinformationsharing canoutweightitscost. 3 IsInformationSharingPossible? Inthissection, we identify casesinw hich speculators and S are better o whenthey share information. We start by consid ering the e ect ofthe precisionswith which the speculatorsand Ssharetheirinformationonthemarketdepth(measuredby 1 ). 15 It turnsout that thise ect isimportant to interpret the results. Lemma : The depthofthe market (i.e. 1 ) isa ected bythe precisionswithwhich the fundamentaland the nonfundamentalspeculatorsshare their " < 0). 14 Inordertoconveytheintuitionwetake asgiven.howevertheslopeofthepricescheduleisa ected by information sharing. A s shown below(l emma )sharing non-fundamentalinformation enlarges. T his mitigates theloss in pro tduetotheseconde ect(smallerpricechanges). 15 Themarketdepthistheorder ownecessarytochangethepriceby1 unit.thelargeristhemarket depth,the greateris the liquidityofthe market.a ctually,when is small,the market-makeraccommodates largeorderimbalances withoutsubstantialchanges in prices. 10

13 Notice that anincrease inthe quality ofthe informationprovid ed by to S enlarges, that isit decreasesthe depth ofthe market. The intuitionfor thisresult isasfo lows. Exchange ofnon-fund amentalinformationincreasesthe role of oor brokers( and S) in theprovisionofliquidity.to seethispoint,let Q T = Q +Q S bethetotaltradesizeof speculators and Sandconsidertheirexpectedtotaltradesizecontingenton~x = x. Weobtain E(Q T j~x =x )=(b 1 +b +a 3 )(x )= ( 1 + ¾ 6(¾ +¾ ))(x ): (6) Thesmaleris¾,thelargeristhefraction(jb 1 +b +a 3 j)oftheordersreceivedbybroker which isac commod ated by speculatorssand.asa consequence the d ealer participates lessto liquid itytrad es.inthissense the exchange ofnon-fundamentalinformation`siphons' uninformed ord er ow aw ay from the market-maker.thusthissiphone ect increaseshis exposuretoinformedtradingandthepriceschedulebecomessteeper. 16 Interestingly anincrease inthe quality ofthe informationprovided by S to has exactly the opposite e ect: it improvesthe depth ofthe market.inthiscase, the e ect ofinformationsharingisto increase competitionamongfundamentaltrad ers.hence they scalebacktheirordersize(a 1 and a 0 decreasewhen¾" decreases).thise ectreducesthe market-maker'sexposure to informed trad ing and thereby makesthe price sched ule less steep. We denote speculator j'sex-ante expected pro t(i.e.before observinginformation) by j (¾ ;¾ ";N).UsingLemma1,weobtainthefolowingresult. Lemma3:For givenvaluesof¾ " and ¾,theexpected tradingpro tsforspeculators 16 Inequilibrium informedtradersscalebacktheirordersizewhen increases.utthisisinsu±cient tocompensatethereduction in uninformed tradingdue tothe siphone ect. 11

14 and Sare S (¾ ;¾ ²;N) = Ã ¾v (¾ v +¾ " )(4¾ v +9¾ " ) + ((N+)¾v +3(N+1)¾ " ) ¾ 4! 9 ¾ +¾ and; (¾ ;¾ ";N) = def = S f(¾ ;¾ ";N)+ S nf(¾ ;¾ ";N); Ã 4¾v(¾ 4 v+¾ ") + ¾ 4¾ +9¾! ((N+)¾v+3(N+1)¾ ") 36 ¾ +¾ def = f(¾ ;¾ ";N)+ nf(¾ ;¾ ";N): E ach speculator'sexpected pro tshastwo components:(i) the expected pro t she or he obtainsbytradingonfundamentalinformation( j f )and (ii)the expected pro t she or he obtainsby tradingonnon-fundamentalinformation( j nf ). Aninformationsharing agreement isviab le ifand only ifb oth speculators and Sare better o whenthey share inform ation.henc e aninform ationsharingagreem ent ispossib le ifand only ifthere exists apair(¾ ;¾ " )suchthat and ¾ ;¾ " ;N def = (¾ ;¾ " ;N) (1;1;N)>0; (7) S ¾ ;¾ " ;N def = S (¾ ;¾ " ;N) S (1;1;N)>0: (8) The s' measure the expected surplusassociated with the informationsharingagreement for speculators and S. Proposition1 : The set ofparametersfor which speculators and S share information isnon-empty. We establish the result by providing 3 numericalexamples. For each example, we report int ab les1, and 3 b elow the b reak-d ow nofthe trad ing pro tsfor the d i erent participantswith and without informationsharing. We also compare the market depth w ith and w ithout informationsharing. T he examples have b eenchosenb ec ause they ilustrate di erent phenomena that we wildiscussinthe rest ofthe paper.the trading pro tsarescaledby¾ v and ¾ x thatwenormalizeto1throughoutthepaper. 1

15 Proof: Example1: ¾0 =0,¾" =0,¾ ==3,N =. Pro tsand depth InformationSharing No InformationSharing (N 1) i f i6=s; 0:0589 0:1178 S f 0:0589 0:1178 S nf 0: f nf 0:1767 0:357 TotalExpected Pro ts 0:44 0:4714 M arket Depth( ) 1:0607 0:948 Table1 Inthiscase we obtainthat S = S f+ S nf S (1;1)=0:0589+0:0707 0:1178=0:0118; and = f + nf (1;1)=0:0589+0:1767 0:357=0: O bserve that the totalsurplusfor speculators and S ispositive and equalto S + =0:0118; but that the totalsurplusfor a lspeculatorsisnegative and equalto (N 1) i + S + =(0:0589 0:1178)+0:0118= 0:0471: ( i denotesthedi erenceintheexpectedpro twithandwithoutinformationforaspeculator d i erent from S or.) Example: ¾ 0 =0:6,¾ " =0,¾ =0,N =10. 13

16 Pro tsanddepth InformationSharing No InformationSharing (N 1) i f i6=s; 0:1815 0:165 S f 0:00 0:041 S nf 0: f nf 0:0153 0:0344 TotalExpected Pro ts 0: M arket Depth( ) Table Inthiscase we obtainthat S = S f + S nf S (1;1)=0:0114; and = f + nf (1;1)=0:0011 Observe that the totalsurplusfor speculators and S ispositive (0:015) but that the totalsurplusfor a lspeculatorsisnegative( 0:04:) Example3: ¾ 0 =0:6,¾ " =0,¾ =1:3,N =10. Pro tsand Depth InformationSharing No InformationSharing (N 1) i f i6=s; 0:1874 0:165 S f 0:008 0:041 S nf 0: f nf 0:090 0:0344 TotalExpected Pro ts 0:615 0:749 M arket Depth( ) Table3 Inthiscase we obtainthat S = S f + S nf S (1;1)=0:0003; 14

17 and = f + nf (1;1)=0:0155 Observethatthetotalsurplusforspeculators and Sispositiveandequalto S + = 0:0158.The totalsurplusfor a lspeculatorsisnegative and equalto 0:0134: Ina lthe examples, the joint expected pro tsofspeculators and S increase when they share information.notice that thisisa necessary conditionfor informationsharing. ActualyEquations(7)and(8)implythat (¾ ;¾ ";N)+ S (¾ ;¾ ";N)> S (1;1;N)+ (1;1;N): At the same time, there isa decline inthe joint expected pro tsofthe speculatorswho d o not share information.e ventua ly the totalexpected pro tsfor a lthe speculatorsare low er ina lthe examples(thisisalw aysthe case; see P roposition5 insection4).insum informationsharingisa w ay for speculators and S to secure a larger part ofa sma ler `cake'.the fa lintotalpro tsisnot surprising: informationsharingincreasescompetition between oor brokers.the surprisingpart isthat the joint expected pro tsofspeculators and S caninc rease d espite the d ec line inthe totaltrad ing pro tsfor the speculators. T hisiskey since thisisa nec essary cond itionfor informationsharing.w e now provid e an explanationfor thisobservation.the explanationisquite complexbecause severale ects interplay. Consider the fo lowingratio r 1 (¾";¾ def ) = E(Q T j~v=v) E(Q T j~v=v;¾ " =1;¾ =1): Thisratiocomparestheexpectedtotaltradesize(Q T )ofthecliqueformedbyspeculators and Scond itionalonfund amentalinformationw ith and w ithout aninformationsharing agreement.usinglemma 1,we canwrite thisratio as r 1 (¾";¾ )= a 1(¾" ;¾ )+a (¾" ;¾ )+b 3(¾ " ;¾ ) : a 1 (1;1) Hence r 1 > 1 meansthat the clique formed by and S tradesmore aggressively on fund amentalinformationwhenthere isinformationsharingthanwhenthere isnot.using 15

18 theexpressionsfor a 1,a and b 3 giveninlemma1,weeventualyobtain r 1 (¾";¾ )=( (1;1) (¾²;¾ ) )( (4¾v+3¾ ²)(N+1) ): (N+)¾v+3(N+1)¾ ² As (1;1)> (0;1)(Lemma),itisimmediatethat r 1 (0;1)>1.ycontinuity,this inequalityalso holdstrue for other valuesof¾ ² and ¾. Hence there exist information sharingagreementsw hich ind uce the clique formed by and Sto trad e more aggressively. Inturnthisforcesspeculatorswho are not part ofthe clique to shade their totaltrade size.to see thispoint consid er the fo lowingratio r (¾² def ;¾ ) = E((N 1)Q i j~v=v) =( (1;1) E((N 1)Q i j~v=v;¾ " =1;¾ =1) (¾²;¾ ) )( (¾v+3¾ ²)(N+1) ); (N+)¾v+3(N+1)¾ ² where(n 1)Q i isthetotaltradesizeofspeculatorsdi erentfromands.usinglemma,wededucethat r increaseswith¾.thisimpliesthat r (¾ ² ;¾ ) r (¾ ² ;1): Usingtheexpressionsfor (1;1)and (¾ ² ;1)givenintheproofofLemma,weobtain17 r (¾ ² ;1)<1 8¾ ² <1: Weconcludethatr (¾ ² ;¾ )<1.Thismeansthatinformationsharingagreementsforcethe speculatorsw ho are not part ofthe clique to trad e lessaggressively ontheir information. Hence the speculatorsw ho share informationappropriate a larger share ofthe totalpro ts which derive from tradingonfundamentalinformation. 18 For thisreason, information sharing enlargestheir joint expec ted pro t onfund am entalinform ation.t hisisthe c ase for instance ine xamples and 3. Now consid er the e ect ofinformationsharing onthe pro tsw hich d erive from nonfund amentalinformation.o nthe one hand,there are more speculatorsw ho accommod ate the ord er ow brokered by. T hise ect d ecreasesthe levelofexpected pro t onnonfund amentalinformation.o nthe other hand the exchange ofnonfund amentalinformation 17 Theproofrequiresstraightforwardmanipulationsandisavailableuponrequest. 18 NoticethatspeculatorsinourmodelarelikeCournotcompetitors.InCournotcompetition,each rm would like to committo trade a largersize than itdoes in equilibrium. T his commitmentwould force other rms totradeinsmallersizes.inthis waythecommitted rm cancapturealargershareofthetotal pro ts. Intuitively sharing fundamentalinformation is a way to make this commitmentcredible. T his e ecthas been pointedoutbyfishman and H agerty(1 995)in amodelofinformation sale. 16

19 decreasesthe market depth and thise ect increasespro tsfrom non-fundamentalspeculationascanbe seenfrom Lemma 3. It turnsout that there are cases(for instance Example 1) inw hich the second e ect dominatesand the joint expected trad ingpro tsof speculatorss and onnon-fund amentalinformationare larger whenthere isinformation sharingor nf(¾ ;¾ ";N)+ S nf(¾ ;¾ ";N) nf(1;1;n) 0; for ¾ <1 and ¾ " <1 O bserve that thiscanoccur onlyw heninformationsharingimpairsmarket d epth(increases ).InE xample 3,informationsharingimprovesmarket d epth and the joint expected pro t onnon-fundamentalinformationdecreases. To sum up, there are tw o reasonsw hy informationsharing canincrease the joint expectedpro tsofspeculators and S: ²Sharingfund amentalinformationa low sthe coalitionformed b y b rokerssand to trad e more aggressively onfund amentalinformationand to c apture thereb y a larger share ofthe totalpro tsfrom speculationonfundamentalinformation. ²Sharingnon-fund amentalinformationcanred uce the market d epth.t hisimpliesthat pricesreact more to ord er imbalances.larger totalexpected pro tsfrom speculation onnon-fundamentalinformationfo lows. The precisionswith which the speculatorsshare their informationdetermine how the surplus( S + ) created by informationsharing issplit betweenbrokers and S. For instance,consider Examples and 3. The value of¾ islarger inexample 3,but otherwise the valuesofthe parametersare identicalinthe two examples.the surplusfor spec ulator (S) islarger(low er) ine xample 3 thanine xam ple.inline w ith intuition, fora xedvalueof¾",speculator (S)preferstoprovide(receive)aninformationoflow (high) quality. Hence speculators and S have con icting view sover the information sharingagreementsw hich should be chosen.it isalso worth stressingthat the size ofthe surplusc reated b y inform ationsharingd epend sonthe prec isionsw ith w hich trad ersshare information. For instance the joint surplusissma ler ine xample thanine xample 3. Inthispaper, w e d o not stud y how trad ersselect the characteristicsoftheir information sharingagreement (¾ ² and ¾ ). Thisisnot necessarybecause our statementsregarding market performance(next section) only d epend sonthe existence ofinformationsharing agreements,notonthespeci cvalueschosenfor ¾ " 17 and ¾.

20 We now consid er inmore detailsinformationsharingagreementsinw hich speculators and Sperfectlyshareinformation(¾" =¾ =0).Perfectinformationsharingisofinterest because it isrelatively easy to implement.ac tua ly,ifthere isperfect informationsharing, knowswhich quantity S should trade and vice versa (inour modelthey optimaly trad e the sam e quantity).consequently, one speculator cand etect cheating by the other speculator by ob servinghisor her trad e size. Proposition : For N, there exist two cut-o values(i) ¾ 0 (N) and (ii) ¾ 0 (N) suchthatperfectinformationsharingispossibleifand onlyif¾0 [¾ 0(N);¾ 0 (N)].Furthermore the cuto valuesincrease with N and are suchthat 0 < ¾ 0(N) < ¾ 0 (N) < 1. T he propositionshow s that perfec t informationsharing ispossib le ifb roker d oes not channela too large or a too sma lfractionofthe ord er ow from liquid ity trad ers. Observethatpro tsmadeonnon-fundamentalinformation( j nf )areproportionaltothe amountofliquiditytradingbrokeredby(¾ =1 ¾ 0 ).Hence¾ 0 determinesthevalueof non-fundamentalinformation.perfect informationsharingcantake place whenthisvalue isneither too large, nor too sma l. Ifthe value ofnon-fundamentalinformationislarge (¾ 0 <¾ 0(N)),thecostofdisclosingherinformationperfectlyfor(smalerpro tsonnonfund amentalinformation) islarge compared to the b ene t (the possibility to pro t from fundamentalinformation).inorder to attenuate thiscost, must therefore send a noisy signalto S.Whenthevalueofnon-fundamentalinformationissmal(¾ 0 > ¾ 0 (N)),the b ene t ofperfec t informationsharing issm a lfor the fund am entalspec ulator.t herefore he refusesto perfectly d isclose hisinformation. The larger isthe number offundamentalspeculators, the sma ler must be the fraction ofliquidity traders' order ow brokered by to sustaina perfect informationsharing agreement (¾ 0(N)increaseswith N).Actualythepro tsfromfundamentalinformation d ecrease with the number offund amentalspeculators.the value offund amentalinformationistherefore sma lw henn islarge.hence broker acceptsto perfectly d isclose her informationonly ifthe value ofnon-fund amentalinformationisitselfsma l.t he last part ofthepropositionimpliesthatforalvaluesofn,thereexistvaluesof¾ 0 <1suchthata perfectinformationsharingagreementcanbesustained.figure1plots¾ 0(N)and¾ 0 (N) fordi erentvaluesofn andshowswhenperfectinformationsharingispossible Thecuto values¾ 0(N)and¾ 0 (N)areimplicitlyde nedin theproofofp roposition. 18

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