Information Sharing, Liquidity and Transaction Costsin Floor-Based Trading Systems

O verallour analysissuggeststhat inform ationsharing am ong °oor b rokersim provestheperform ance of°oor-b ased trad ingsystem s.. or d erivativesm arketslike the CB O T and the CB O E a

Inform ationSharing,Liquid ity and T ransac tionCosts

inF loor-B ased T rad ingSystem s 1

T hierry Fouc ault

HE C and CE P R 1,rue d e la Lib ¶eration

78351 J ouy enJ osas,France.

E m ail:f ouc ault@hec f r

Laurence Lesc ourret

CR E ST and Doc torat HE C 15,B oulevard G ab rielP ¶eri

9 2 2 4 5 M alako®,France.

E mail:lescourr@ensae.f r Novemb er,2 0 0 1

1 W e thank G iovanni Cespa, A sani Sarkarand seminarparticipants atCR EST , L avalU

b rokersonthe °oor ofanexc hange.W e id entify c onditionsunder w hic h the trad ersare

b etter o® sharing information W e also show that inform ationsharing im proves pric e

d iscovery, red uc esvolatility and low ersexpec ted trad ing c osts Inform ationsharing c an

im prove or im pair the d epth ofthe m arket, d epend ing onthe valuesofthe param eters

O verallour analysissuggeststhat inform ationsharing am ong °oor b rokersim provestheperform ance of°oor-b ased trad ingsystem s

K eyw ord s: M arket M ic rostruc ture,F loor-B ased T rad ingSystem s,O penO utc ry,Inf

or-m ationSharing,Inform ationSales

J E L Classi¯c ationNumb ers: G 10 ,D82

or d erivativesm arketslike the CB O T and the CB O E are °oor m arkets.2 How ever

°oor-b ased trad ing m ec hanism sare endangered spec iesasthey are progressively replac ed °oor-b y

fully autom ated trad ing system s3 G iventhistrend tow ard autom ation, it isnaturaltoask w hether °oor-b ased trad ing system sc anprovid e greater liquid ity and low er exec u-tionc oststhanautomated trad ingsystem s.T hisquestionisofparam ount importance for

m arket organizersand trad ers Infac t, it hasb eenhotly d eb ated b etw eenmemb ersof

E xc hangesw ho c onsid ered sw itc hingfrom °oor to elec tronic trad ing4.Inord er to survive

°oor-b ased trad ing m ec hanism smust outperform autom ated trad ing system salong som e

d imensions

Autom ated trad ing system sd ominate °oor-b ased trad ing systems inm any respec ts

F irst °oor m arketsare more expensive to operate (see Dom ow itz and Steil(19 99 )).Sec ond physic alspac e lim itsthe numb er ofpartic ipantsin°oor marketsb ut not inautomatedtrad ingsystem s.F inally trad ersw ithout anac c essto the °oor are at aninform ationald is-

-ad vantage c om pared w ith the tr-ad ersonthe °oor.T hisd is-ad vantage islikelyto exac erb ateagency prob lem sb etw eeninvestorsand their b rokers(Sarkar and W u (199 9))

B y d esign, °oor-b ased marketsfoster person-to-personc ontac ts Hence the ab ility of

m arket partic ipantsto share informationisgreater inthese markets.T hisfeature isoftenview ed asb eingone ad vantage,ifnot the unique one,of°oor-b ased trad ingsystem s.5 Forinstance Harris(2 0 0 0 ),p.8,pointsout that

1 O fcourse,many tradingrules have been changed since the creation ofthe N Y SE.B utithas always beena° oormarket.SeeH asbrouck,So¯anos andSosebee(1 993)foradetaileddescriptionofthetrading rules on the N Y SE.

2 In Frankfurt,the° ooroperates in parallelwith an electronictradingsystem.

3 T heM arch¶ eµ aT ermeInternationaldeFrance(M A T IF),theT orontoStockExchangeandT heL ondon InternationalFinancialFutures and O ptions Exchange (L IFFE)shutdown their° oorin 1 997,1 998 and

20 0 0 ,respectively.

4 See the Economist(July 31 st1 999):\A home grown revolutionary"and the Economist(A ugust26th

20 0 0 ):\ O utofthepits".

5 Covaland Shumway (1 998)show thatthe levelofnoise on the ° oorofCB O T ' s 30 yearT reasury

B ond futures a®ects price volatility.T his alsosuggests thatperson toperson contacts on the ° oorhave

an impacton priceformation.

`F loor-based trad ingsystem sd om inate elec tronic trad ingsystemsw henbrokers

need to exc hange informationabout their c lientsto arrange their trad es.'

Inform ationsharing isa functionofthe °oor w hic h isd i± c ult to replic ate inelec tronictrad ing system s T hese system susually restric t the set ofm essagesthat c anb e sent b yusers(generally trad ersc anonly post pric esand quantities).Furtherm ore trad inginthesesystem sisinm ost c asesanonym ous T hisfeature preventstrad ersfrom d eveloping thereputationofhonestly sharinginform ationthrough enduringrelationships

Inform ationsharingonthe °oor c antake plac e b etw eentw o typesofpartic ipants.F irst

°oor-b rokersc anexc hange inform ationontheir trad ing motivationsw ith m arket-makers

B enveniste,M arc usand W hilelm (199 2 ) m od elthistype ofinform ationsharingand showthat it m itigatesad verse selec tion.Sec ond °oor-b rokersc anc ommunic ate w ith other °oor-

b rokers.For instance,So¯anosand W erner (1997),p.6 notic e that

`Inad d ition, by standinginthe c row d , °oor brokersmay learnabout ad d itional

broker-represented liquid ity that is not re°ec ted inthe spec ialist quotes: °oor

brokers w illoftenexc hange inform ationontheir intentions and capabilities,

espec ially w ith competitorsw ith w hom they have good w orkingrelationships.'

O ur purpose inthispaper isto analyz e thistype ofinform ationsharing.At ¯rst glance,inform ationsharing am ong °oor b rokersispuzz ling.Infac t standard m od elsw ith asym -

m etric inform ation(e.g.K yle (19 85)) show that inform ed trad ersw ant to hid e their inf

or-m ationrather thand isclose it to potentialc oor-m petitors.Furtheror-m ore,inform ationsharingreinforc esinform ationalasymetriesb etw eenthose w ho share inform ationand those w ho

d o not.It istherefore not ob viousthat it should im prove m arket quality.Hence w e ad

-d resstw o questions.F irst, isit optimalfor °oor b rokersto share inform ationw ith their

c om petitors? Sec ond, w hat isthe e®ec t ofinform ationsharing am ong °oor b rokersonthe overallperform ance ofthe m arket? Inpartic ular w e stud y the impac t ofinter-°oor

b rokersc om munic ationonstandard m easuresofm arket quality, nam ely pric e volatility,pric e d iscovery,m arket liquid ity and trad ingc osts

W e m od el°oor trad ingand inform ationsharingusingK yle (1985)'sm od elasa w orkhorse.AsinR oÄell(199 0 ),w e assum e that trad ers(°oor b rokers) have ac c essto tw o typesofin-

form ation: (i) fundamentalinform ationw hic h isinform ationonthe payo® ofthe sec urityand (ii) non-fundam entalinform ationw hic h isinform ationonthe volume ofliquid ity(non-inform ed ) trad ing.W e c onsid er the possib ility for tw o °oor b rokersendow ed w ith d i®erent

typesofinform ation(one hasfundam entalinform ationand the other hasnon-fundamentalinform ation) to share inform ation.M ore spec i¯c ally w e assum e that °oor b rokershave in-

form ationsharingagreem ents(they form a \c lique").Anagreem ent spec i¯esthe prec ision

w ith w hic h eac h b roker reportshisor her inform ationto the other b roker.After rec eiving

fundam entalor non-fundam entalinform ation,the b rokersina c lique pooltheir inform ation

ac c ord ingto the term softheir agreem ent just b efore sub m ittingtheir ord ersfor exec ution

W e estab lish the follow ingresults

²T here isa w id e range ofparam etersfor w hich it isoptim alfor °oor b rokersto sharetheir inform ation(i.e.their expec ted pro¯tsare larger w ith inform ationsharing)

²Inform ationsharing c anim prove or impair the d epth ofthe market, d epending onthe valuesofthe parameters

²Inform ationsharingalw aysred uc esthe aggregate trad ingc ostsfor liquid ity trad ers.How ever w heninform ationsharingim pairsm arket d epth,som e liquid ity trad ersarehurt

²Inform ationsharingoc c ursat the expense ofthe °oor b rokersw ho are not part tothe inform ationsharingagreem ent

²Inform ationsharingimprovespric e d iscovery and red uc esm arket volatility

Intuitively inform ationsharing intensi¯esc om petitionb etw een°oor b rokersand inthis

w ay it low ersthe totalexpec ted pro¯tsofall°oor b rokers(red uc esthe aggregate trad ing

c osts) Inform ationsharing also c hanges the alloc ationoftrad ing pro¯ts am ong °oor

b rokers.M ore spec i¯c ally the °oor b rokersw ho share inform ationc apture a larger part ofthe totalexpec ted pro¯ts, at the expense of°oor b rokersw ho d o not share inform ation

T hese tw o e®ec ts explainw hy inform ationsharing c ansimultaneously b ene¯t liquid itytrad ersand the °oor b rokersw ho share their inform ation O verallinformationsharing

b etw een°oor b rokersisanad vantage for °oor-b ased trad ingsystem ssince it resultsin(a)low er trad ingc osts, (b ) faster pric e d iscovery and (c ) low er pric e volatility.Interestingly,inline w ith our result, Venkataram an(2 0 0 0 ) ¯ndsthat trad ing c ostsonthe NY SE arelow er thanonthe P arisB ourse (anautom ated trad ingsystem ),c ontrollingfor d i®erencesinstocksc harac teristic s.6

6 T heissen (1 999)compares e®ective bid-askspreads in an automated tradingsystem (X etra)and the

O ur analysisisrelated to the literature oninformationsales(e.g.Ad m atiand P °eid erer(19 86), (19 88) and F ishm anand Hagerty (199 5)) Inc ontrast w ith this literature, w eassum e that the m ed ium for inform ationexc hange isinform ation, not m oney Ac tuallyinour m od el, the trad er w ho rec eivesinform ationrew ard sthe inform ationprovid er b y

d isclosinganother type ofinform ation.Hence w e c onsid er °oor-b ased system sasm arkets

for trad ingsharesand forum to b arter inform ation.Another im portant d i®erence isthat w e

c onsid er c om munic ationofinform ationonthe volum e ofliquid ity trad ing.W e show that

it m ay b e optim alto `sell'(b arter) suc h aninform ationand that salesofnon-fundam entalinform ationhave anim pac t onmarket quality

T he m od elisd escrib ed inthe next sec tion.Sec tion3 show sthat it c anb e optim alfor

°oor b rokersto share inform ation.Sec tion4 analyz esthe im pac t ofinform ationsharingonvariousm easuresofm arket perform ance.Sec tion5 c onclud es.T he proofsw hic h d o notappear inthe text are inthe Appendix

m ean¹ and a variance ¾2

v that w e norm alize to 1.T his¯nalvalue ispub lic ly revealed at

d ate 2 T rad inginthissec uritytakesplac e at d ate 1.At thisd ate,investorssub mit m arketord ersto b uy or to sellsharesofthe sec urity.T he exc essd em and (supply) isc leared atthe pric e posted b y a c ompetitive and risk-neutralm arket m aker

T he trad ing \c row d " for the sec urity isc om posed ofN + 1 °oor b rokers.7 At tim e

1, there are tw o typesof°oor b rokers: (i) N fundam entalspec ulatorsand (ii) one non

fundam entalspec ulator, B Fundam entalspec ulatorshave inform ationonthe ¯nalvalueofthe sec urity.For simplic ity,asinK yle (19 85),w e assum e that theyperfec tlyob serve this

¯nalvalue,just b efore sub m ittingtheir ord ersat d ate 1.B roker B , the non-fundamental

quoted spreads on the° oorcan belargerorsmallerthan in theautomated tradingsystem,dependingon thestockcharacteristics.O naveragethequotedspreads areequal.T his is consistentwithourresultthat theimpactofinformation sharingon marketdepth is ambiguous.

7 T hemarket-makercan alsobeconsidered as beinga° oorbrokerwhohas noinformation.

spec ulator, rec eivesord ersfrom liquid ity trad ers W e d enote ~xB the totalquantity that

b roker B m ust exec ute onb ehalfofliquid ity trad ers.Asa w hole, liquid ity trad ershave

a net d em and equalto ~x = ~x0 + ~xB shares W e assume that ~x0 and ~xB are norm allyand independently d istrib uted w ith m eans0 and variances¾2

0 and ¾2

B respec tively W enorm alize the variance ofthe ord er °ow d ue to liquid ity trad ing,¾2

B oth typesofspec ulatorsc anengage inproprietary trad ing Inpartic ular b roker B

c anac t b oth as anagent (she c hannels a frac tionofliquid ity trad ers' ord ers) and as

a principal(she sub mitsord ersfor her ow nac c ount) T hisprac tic e isknow nas`d trad ing' and isauthoriz ed insec uritiesm arkets(see Chakravarty and Sarkar (2 0 0 0 ) for a

ual-d iscussion).10M od elsw ith d ual-trad inginclud e R Äoell(19 90 ),Sarkar (199 5) or F ishm anandLongsta® (199 2 ).Inthese m od els,asinthe present artic le,b rokersengaged ind ual-trad ingexploit their ab ility to ob serve ord erssub m itted b y uninform ed (liquid ity) trad ers.11 Noneofthese m od elshasc onsid ered inform ationsharing offund am entaland nonfundam entalinform ationam ong b rokers, how ever.O ur purpose isto stud y the e®ec tsofthisac tivity.Asargued inthe introd uc tion,thistype ofinform ationexchange isa d istinctive feature of

°oor m arkets.T he spec ulatorsw ith fundam entalinformationc anb e seenasb rokersw hoexc lusively trad e for their ow nac c ount (like scalpersand loc alsind erivativesm arkets)

T hey c ould also b e seenasb rokersw ho have no c ustom ers' ord ersto exec ute at d ate 1

It isreasonab le to assume that the ord er °ow from liquid ity trad ersisindependent

ac rossb rokers (for instance b rokers have d i®erent c lients) Inc ontrast, signals onthe

fundam entalvalue ofthe sec urity are c orrelated For these reasons, w e assum ed thatonly one °oor b roker ob servesthe non-fundam entalinformation, ~xB,w hereasseveral°oor

8 In the U S, fullline brokerage houses engage in proprietary trading activities.D iscountbrokers do not,however.

9 Forinstance, on the N Y SE,orders can reach amarket-makerthrough ° oorbrokers orelectronically through asystem called SuperD ot.

1 0 Forinstance, Chakravarty and Sarkar(20 0 0 )observe thatin the N Y SE potentialdualtraders are nationalfulllinebrokeragehouses andtheinvestmentbanks.

1 1

b rokersob serve the fundamentalinform ation,~v.W e have analyz ed the m od elw henthere is

m ore thanone non-fund am entalb roker (w ith independent ord er °ow ) and b rokersperfec tlyshare inform ation(inform ationsharingisd escrib ed b elow ).T he presentationofthe m od elism ore c om plex b ut the c onclusionsare qualitatively sim ilar to those w e ob taininthe

c ase w ith only one non-fundamentalb roker O ne reasonfor w hic h the m od elis more

c om plexisthat the numb er ofc liques(groupsofpaired b rokersw ith d istinct information)isendogenous Inequilib rium , thisnum b er c anb e sm aller thanthe m aximum possib lenumb er ofc liques.For instance ifthere isanequalnumb er, N , offund am entaland non-

fundam entalb rokers, the numb er ofc liquesc anb e sm aller thanN Inpartic ular, w ithperfec t informationsharing, thisisnec essarily the c ase w hen¾2

0 = 0 Inthisc ase, theaggregate ord er °ow c hanneled b y the non-fundam entalb rokersw ho are not a± liated to

a c lique playsthe role of~x0 inthe present artic le

´ = ¾2

" = 0 Sec ond there isno informationsharingif¾2

´ = ¾2

" = 1 In-b etw eenthese tw o c ases, there isinform ationsharing b ut it isim perfec t (at least onespec ulator d oesnot perfec tly d isclose hisor her inform ation) T he inform ationsetsofspec ulatorsB and S at d ate 1 are d enoted yB = (~xB; ^x;^v) and yS= (~v; ^x; ^v),respec tively.Inreality °oor b rokersare likely to exc hange inform ationw ith the b rokersw ith w homthey have enduring relationships.Inthisc ase their d ec isionto share inform ationw ith a

givenb roker must b e b ased onthe long-term (average) b ene¯tsofinformationsharing.Forthisreason,w e assum e that the spec ulatorsd ec id e to share informationb yc om paringtheirex-ante (i.e.prior to rec eivinginform ation) expec ted pro¯tsw ith and w ithout inform ationsharing.W e say that inform ationsharingispossib le ifthere existsa pair (¾2

´,¾2

") suc h thatthe expec ted pro¯tsofspec ulator S and B are larger w henthere isinform ationsharing.Insec tion3,w e id entify param eters' valuesfor w hic h inform ationsharingispossib le

R em arks

It isw orth stressingthat w e foc usonthe possib ilityofaninform ationsharingagreem ent

b ut not onitsimplementation Inpartic ular, w e d o not ad d ressenforc em ent issues Inthat, w e follow the literature oninform ationsalesw here the quality ofthe inform ation

w hich issold isassum ed to b e c ontrac tib le.12 W e also assum e that the inform ationsharingagreem ent and its c harac teristic s (¾2

´;¾2

") are know nb y allpartic ipants (includ ing the

m arket-m aker).T hisc om monknow led ge assum ptionisalso standard inthe literature oninform ationsales

2 2 T he equil ib rium ofthe F l oor M arket

Inthissec tion,w e d erive the equilib rium ofthe trad ingstage at d ate 1,giventhe c harac teristic softhe informationsharingagreement b etw eenspec ulatorsB and S.T hen,inthenext sec tion,w e analyze w hether or not it isoptim alfor B and Sto exc hange inform ation

-W e d enote b y QS(yS) and QB(yB), the ord erssub m itted b y spec ulatorsS and B , spec tively.Inthe set offundamentalspec ulators, w e assignindex1 to spec ulator S.Anord er sub m itted b y the other fundamentalspec ulatorsi= 2 ;:::;N isd enoted Qi(~v).T hetotalexc essd emand that must b e c leared b y the c om petitive m arket m aker istherefore

Asthe market maker isassum ed to b e c om petitive,he setsa pric e p(O ) equalto the asset

1 2 See A dmati and P ° eiderer(1 986),(1 988).Some papers have shown howincentives contracts can be used toinduce an information providertotruthfully revealthe quality ofhis signal(see A llen (1 990 )or

B hattacharya and P ° eiderer(1 985)) R eputation e®ects may also help to sustain information sharing agreements (seeB enabou andL aroque (1 992)).

expec ted value c onditionalonthe net ord er °ow ,i.e.

Anequilib rium c onsistsoftrad ing strategiesQS(:), QB(:), Qi(:);i= 2 ;:::;N and a c om petitive pric e functionp(:) suc h that (i) eac h trad er'strad ingstrategy isa b est response toother trad ers' strategiesand (ii) the d ealer'sb id d ing strategy isgivenb y E quation(1).13For givenc harac teristic s, (¾2

-´;¾2

d escrib esthe unique linear equilib rium ofthe trad inggam e

Lem m a 1 : T he trad ingstage hasa unique linear equilibrium w hic h isgivenby

¸ (¾"2;¾2´) = 6

q

¾2 v

v + (12 N + 5)¾2

v¾2

"+ 9 N ¾4

")(2 (N + 2 )¾2

v + 3(N + 1)¾2

")q

¾2 B

c reate tem porary pric e pressures B rokersw ith non-fundam entalinform ationare aw areofthese pric e pressures T hey c anpro¯t from thisknow led ge b y selling (b uying) high(low ) w henliquid ity trad ers b uy (sell) M ore form ally suppose that the fundamentalspec ulators(b ut not the market m aker) d o not expec t c hangesinthe sec urity value (i.e

°oor b rokersB and S partly ac c om m od ate liquid ity trad ers' ord ersand red uc e the ord er

°ow imb alance that must b e exec uted b y the m arket-maker.A similar e®ec t isob tainedinR Äoell(1990 ) and Sarkar (19 95)

T he previousd iscussionshow show spec ulatorsc anpro¯t b oth from fund am entalandnonfundam entalinformation Hence there isa b ene¯t to exc hange fundam ental(non-

fundam ental) inform ationfor non-fundam ental(fund am ental) information Inform ationsharing isc ostly, how ever Ac tually spec ulatorsS and B d eprec iate the value oftheirprivate inform ationw henthey share it.Consid er spec ulator B for instance.Ifshe d oesnot share inform ation(¾2

´ = +1 ), she ac c om mod ateshalfofthe ord er °ow she rec eives(since b1 = ¡1=2 ).Ifshe sharesinformationthenb rokersB and S (instead ofb roker Balone) provid e liquid ityto the ord ersc hanneled b yb roker B For instance ifthere isperfec tinform ationsharing theneac h b roker ac c om mod atesone third ofthe ord ersrec eived b y

b roker B (since b1 + b2 = ¡1=3 and a3= ¡1=3 w hen¾2

´ = 0 ).T hisc ompetitionfor theprovisionofliquid ity hastw o e®ec ts F irst, b roker B trad essm aller quantities.Sec ond,the ord er imb alance that must b e exec uted b y the m arket-m aker issm aller.Hence, for a

givenpric e sched ule (a ¯xed ¸ ), pric esreac t lessto the ord er °ow 14 Infac t spec ulator

B red uc esher trad e size w henshe sharesinform ation(b2 hasa signopposite the signof

b1) prec isely to m itigate thise®ec t.T hese tw o e®ec ts(sm aller trad e siz e/sm aller ab solutepric e m ovem ents) red uc e spec ulator'sB pro¯tsonnon-fundamentalinform ation.T hisisthe c ost ofsharingnon-fundam entalinform ation

A sim ilar argum ent holdsfor spec ulator S He d eprec iatesthe value offundam entalinform ationw henhe sharesit w ith spec ulator B Inord er to m itigate thise®ec t,he ad justshistrad ingstrategy to the message he send sto spec ulator B T hisexplainsw hy a2 hasasignopposite a1

T o sum up,inform ationsharinghasb ene¯tsand c osts.Informationsharingisa sourc eofpro¯tssince it allow seac h b roker to trad e ona new type ofprivate inform ation.B ut the

b rokersob tainnew inform ationonly ifthey d isclose allor part oftheir inform ation.T hisisc ostlysince it red uc esthe trad ingpro¯tsthat c anb e mad e onthe inform ationoriginallypossessed b y a b roker.Inthe next sec tionw e show that the b ene¯t ofinform ationsharing

c anoutw eight itsc ost

3 IsInf orm ationSharingP ossib l e?

Inthissec tion, w e id entify c asesinw hic h spec ulatorsB and S are b etter o® w hentheyshare inform ation W e start b y c onsid ering the e®ec t ofthe prec isionsw ith w hic h thespec ulatorsB and S share their inform ationonthe m arket d epth (m easured b y ¸¡1).15 Itturnsout that thise®ec t isim portant to interpret the results

Lem m a 2 : T he d epth ofthe m arket (i.e ¸¡1) isa® ec ted by the prec isionsw ith w hic hthe fundamentaland the nonfundam entalspec ulatorsshare their information

1.T he m arket d epth increasesw ith the prec isionofthe signalsent bybroker S(@¾@¸2

" > 0 ),

2 T he market d epth d ec reasesw ith the prec isionofthe signalsent by broker B (@¾@¸2

´ <

0 )

1 4 Inordertoconveytheintuitionwetake¸ as given.H owevertheslopeofthepricescheduleis a®ected

by information sharing A s shown below (L emma 2)sharing non-fundamentalinformation enlarges ¸.

T his mitigates theloss in pro¯tduetotheseconde®ect(smallerpricechanges).

1 5 T hemarketdepth is theorder° ownecessarytochangetheprice by1 unit.T helargeris the market depth,the greateris the liquidityofthe market.A ctually,when ¸ is small,the market-makeraccommo- dates largeorderimbalances withoutsubstantialchanges in prices.

Notic e that anincrease inthe quality ofthe inform ationprovid ed b y B to S enlarges¸,that isit d ec reasesthe d epth ofthe m arket T he intuitionfor thisresult isasfollow s.

E xc hange ofnon-fund am entalinform ationincreasesthe role of°oor b rokers(B and S) inthe provisionofliquid ity.T o see thispoint, let QT = QB + QSb e the totaltrad e siz e ofspec ulatorsB and S and c onsid er their expec ted totaltrad e siz e c ontingent on~xB = xB

W e ob tain

E(QT j~xB = xB) = (b1+ b2 + a3)(xB) = ¡(1

2 +

¾2 B

6(¾2

B + ¾2

T he sm aller is¾2

´,the larger isthe frac tion(jb1+ b2+ a3j) ofthe ord ersrec eived byb roker B

w hich isac c omm od ated b y spec ulatorsSand B Asa c onsequence the d ealer partic ipateslessto liquid itytrad es.Inthissense the exc hange ofnon-fund am entalinform ation`siphons'uninform ed ord er °ow aw ay from the m arket-m aker.T husthissiphone® ec t increaseshisexposure to inform ed trad ingand the pric e sched ule b ec om essteeper.16

Interestingly anincrease inthe quality ofthe inform ationprovid ed b y S to B hasexac tly the opposite e®ec t: it im provesthe d epth ofthe m arket.Inthisc ase, the e®ec tofinform ationsharingisto increase c ompetitionam ongfundam entaltrad ers.Hence theyscale b ack their ord er siz e (a1 and a0d ec rease w hen¾2

" d ec reases).T hise®ec t red uc esthe

m arket-m aker'sexposure to inform ed trad ing and thereb y m akesthe pric e sched ule lesssteep

W e d enote spec ulator j'sex-ante expec ted pro¯t (i.e.b efore ob servinginform ation) b y

´, the expec ted trad ingpro¯ tsfor spec ulatorsB

1 6 In equilibrium informed traders scale backtheirordersize when ¸ increases.B utthis is insu±cient tocompensatethereduction in uninformed tradingdue tothe siphone®ect.

E ach spec ulator'sexpec ted pro¯tshastw o c om ponents: (i) the expec ted pro¯t she or he

ob tainsb y trad ing onfundam entalinform ation(¦jf) and (ii) the expec ted pro¯t she or

he ob tainsb y trad ing onnon-fundam entalinform ation(¦jnf) Aninform ationsharingagreem ent isviab le ifand only ifb oth spec ulatorsB and Sare b etter o® w henthey shareinform ation.Hence aninform ationsharingagreem ent ispossib le ifand only ifthere exists

T he ¡s' m easure the expec ted surplusassoc iated w ith the inform ationsharingagreem ent

for spec ulatorsB and S

P roposition1 : T he set ofparametersfor w hic h spec ulatorsB and S share informationisnon-empty

W e estab lish the result b y provid ing 3 num eric alexam ples For eac h exam ple, w ereport inT ab les1, 2 and 3 b elow the b reak-d ow nofthe trad ing pro¯tsfor the d i®erentpartic ipantsw ith and w ithout inform ationsharing W e also c ompare the m arket d epth

w ith and w ithout inform ationsharing T he exam ples have b eenc hosenb ec ause theyillustrate d i®erent phenom ena that w e w illd iscussinthe rest ofthe paper.T he trad ingpro¯tsare scaled b y ¾2

v and ¾2

x that w e norm aliz e to 1 throughout the paper

P ro¯tsand Depth Inform ationSharing No Inform ationSharing(N ¡1)£¦i

¡S= ¦Sf+ ¦Sn f¡¦S(1 ;1 ) = 0 :0 114 ;and

¡S= ¦Sf+ ¦Sn f¡¦S(1 ;1 ) = 0 :0 0 0 3;

¡B = ¦B

nf¡¦B(1 ;1 ) = 0 :0 155

O b serve that the totalsurplusfor spec ulatorsB and Sispositive and equalto ¡S+ ¡B =

0 :0 158.T he totalsurplusfor allspec ulatorsisnegative and equalto ¡0 :0 134 :

Inallthe exam ples, the joint expec ted pro¯tsofspec ulatorsB and S increase w henthey share inform ation.Notic e that thisisa nec essary c onditionfor inform ationsharing

Ac tually E quations(7) and (8) im ply that

¦B(¾´2;¾"2;N ) + ¦S(¾´2;¾2";N ) > ¦S(1 ;1 ;N )+ ¦B(1 ;1 ;N ):

At the sam e tim e, there isa d ec line inthe joint expec ted pro¯tsofthe spec ulatorsw ho

d o not share information.E ventually the totalexpec ted pro¯tsfor allthe spec ulatorsarelow er inallthe exam ples(thisisalw aysthe c ase; see P roposition5 inSec tion4 ).Insuminform ationsharingisa w ay for spec ulatorsB and S to sec ure a larger part ofa sm aller

`cake'.T he fallintotalpro¯tsisnot surprising: inform ationsharingincreasesc om petition

b etw een°oor b rokers.T he surprisingpart isthat the joint expec ted pro¯tsofspec ulators

B and S c anincrease d espite the d ec line inthe totaltrad ing pro¯tsfor the spec ulators

T hisiskey since thisisa nec essary c onditionfor informationsharing.W e now provid e anexplanationfor thisob servation.T he explanationisquite c om plexb ec ause severale®ec tsinterplay

Consid er the follow ingratio

r1(¾2

";¾2

T j~v = v)E(QT j~v = v;¾2

" = 1 ;¾2

T hisratio c om paresthe expec ted totaltrad e size (QT) ofthe c lique form ed b y spec ulators

B and Sc ond itionalonfundamentalinform ationw ith and w ithout aninform ationsharingagreem ent.U singLem m a 1,w e c anw rite thisratio as

Hence r1 > 1 m eans that the c lique form ed b y B and S trad es m ore aggressively on

fundam entalinform ationw henthere isinform ationsharingthanw henthere isnot.U sing

the expressionsfor a1,a2 and b3giveninLem m a 1,w e eventually ob tain

w here (N ¡1)Qiisthe totaltrad e siz e ofspec ulatorsd i®erent from B and S.U singLem m a

2 ,w e d ed uc e that r2 increasesw ith ¾2

U singthe expressionsfor ¸(1 ;1 )and ¸(¾2

²;1 ) giveninthe proofofLem m a 2 ,w e ob tain17

w hich d erive from trad ing onfundam entalinform ation.18 For thisreason, inform ationsharing enlargestheir joint expec ted pro¯t onfundam entalinform ation.T hisisthe c ase

for instance inE xamples2 and 3

Now c onsid er the e®ec t ofinform ationsharing onthe pro¯tsw hich d erive from

non-fundam entalinformation.O nthe one hand,there are m ore spec ulatorsw ho ac c om m od atethe ord er °ow b rokered b y B T hise®ec t d ec reasesthe levelofexpec ted pro¯t onnon-

fundam entalinformation.O nthe other hand the exc hange ofnonfundam entalinform ation

1 7 T heproofrequires straightforward manipulations and is availableupon request.

1 8 N oticethatspeculators inourmodelarelikeCournotcompetitors.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.

d ec reasesthe market d epth and thise®ec t increasespro¯tsfrom non-fundam entalspec ulationasc anb e seenfrom Lem m a 3 It turnsout that there are c ases(for instance

-E xam ple 1) inw hic h the sec ond e®ec t d ominatesand the joint expec ted trad ingpro¯tsofspec ulatorsS and B onnon-fund am entalinform ationare larger w henthere isinform ationsharingor

¦Bn f(¾´2;¾2";N ) + ¦Sn f(¾2´;¾"2;N )¡¦Bnf(1 ;1 ;N ) ¸0 ; for ¾2´ < 1 and ¾"2 < 1

O b serve that thisc anoc c ur onlyw heninform ationsharingim pairsm arket d epth (increases

¸).InE xam ple 3,inform ationsharingim provesm arket d epth and the joint expec ted pro¯tonnon-fundam entalinform ationd ec reases

T o sum up, there are tw o reasonsw hy inform ationsharing c anincrease the joint pec ted pro¯tsofspec ulatorsB and S:

ex-²Sharingfundamentalinformationallow sthe c oalitionform ed b y b rokersSand B totrad e m ore aggressively onfundam entalinformationand to c apture thereb y a largershare ofthe totalpro¯tsfrom spec ulationonfundam entalinformation

²Sharingnon-fundam entalinform ationc anred uc e the m arket d epth.T hisim pliesthatpric esreac t m ore to ord er imb alances.Larger totalexpec ted pro¯tsfrom spec ulationonnon-fundam entalinform ationfollow s

T he prec isionsw ith w hic h the spec ulatorsshare their inform ationd etermine how thesurplus (¡S + ¡B) c reated b y inform ationsharing is split b etw eenb rokers B and S.For instance, c onsid er E xam ples2 and 3 T he value of¾2

´ islarger inE xam ple 3, b utotherw ise the valuesofthe param etersare id entic alinthe tw o exam ples.T he surplusforspec ulator B (S) islarger (low er) inE xam ple 3 thaninE xam ple 2 Inline w ith intuition,

for a ¯xed value of¾2

",spec ulator B (S) prefersto provid e (rec eive) aninform ationoflow(high) quality Hence spec ulatorsB and S have c on°ic ting view sover the inform ationsharingagreem entsw hic h should b e c hosen.It isalso w orth stressingthat the siz e ofthesurplusc reated b y inform ationsharingd epend sonthe prec isionsw ith w hic h trad ersshareinform ation For instance the joint surplusissm aller inE xam ple 2 thaninE xam ple 3.Inthispaper, w e d o not stud y how trad ersselec t the c harac teristic softheir inform ationsharing agreem ent (¾2

² and ¾2

´) T hisisnot nec essary b ec ause our statem entsregard ing

m arket perform ance (next sec tion) only d epend sonthe existence ofinform ationsharing

W e now c onsid er inm ore d etailsinform ationsharingagreementsinw hich spec ulatorsBand Sperfec tly share information(¾2

" = ¾2

´ = 0 ).P erfec t inform ationsharingisofinterest

b ec ause it isrelatively easy to im plement.Ac tually,ifthere isperfec t inform ationsharing,

B know s w hich quantity S should trad e and vic e versa (inour m od elthey optimallytrad e the sam e quantity).Consequently, one spec ulator c and etec t cheating b y the otherspec ulator b y ob servinghisor her trad e size

P roposition2 : For N ¸ 2 , there exist tw o c ut-o® values (i) ¾2

0(N ) and (ii) ¾¤2

0 (N )suc h that perfec t informationsharingispossible ifand only if¾2

0 2 [¾2

0(N );¾¤20 (N therm ore the c uto® valuesincrease w ith N and are suc h that 0 < ¾2

)].Fur-0(N ) < ¾¤2

0 (N ) < 1

T he propositionshow s that perfec t inform ationsharing ispossib le ifb roker B d oesnot c hannela too large or a too sm allfrac tionofthe ord er °ow from liquid ity trad ers

O b serve that pro¯tsm ad e onnon-fund am entalinform ation(¦jn f) are proportionalto the

am ount ofliquid itytrad ingb rokered b yB (¾2

0).Hence ¾2

0 d eterm inesthe value ofnon-fundam entalinform ation.P erfec t inform ationsharingc antake plac e w henthisvalueisneither too large, nor too sm all Ifthe value ofnon-fundamentalinform ationislarge(¾2

0 < ¾2

0(N )),the c ost ofd isclosingher inform ationperfec tlyfor B (sm aller

pro¯tsonnon-fundam entalinform ation) islarge c om pared to the b ene¯t (the possib ility to pro¯t from

fundam entalinform ation).Inord er to attenuate thisc ost,B must therefore send a noisysignalto S.W henthe value ofnon-fund am entalinform ationissm all(¾2

0 > ¾¤2

0 (N )), the

b ene¯t ofperfec t informationsharing issm allfor the fund am entalspec ulator.T herefore

he refusesto perfec tly d isclose hisinform ation

T he larger isthe numb er offundam entalspec ulators, the sm aller must b e the frac tionofliquid ity trad ers' ord er °ow b rokered b y B to sustaina perfec t inform ationsharingagreem ent (¾2

0(N ) increasesw ith N ).Ac tually the pro¯tsfrom fund am entalinform ation

d ec rease w ith the numb er offundamentalspec ulators.T he value offund am entalinform tionistherefore sm allw henN islarge.Hence b roker B ac c eptsto perfec tly d isclose herinform ationonly ifthe value ofnon-fundam entalinform ationisitselfsm all.T he last partofthe propositionim pliesthat for allvaluesofN ,there exist valuesof¾2

a-0 < 1 such that aperfec t inform ationsharingagreem ent c anb e sustained F igure 1 plots¾2

R em ark.Inthe mod elw e assum e that b rokers' rolesare ¯xed : one hasfundamentalinform ationand the other hasnon-fundam entalinform ation.Another possib ility isthatthe rolesare random ly alloc ated b efore trad ingand unkw now nat the tim e b rokersd ec id e

to share inform ation.For sim plic ity, assum e that eac h b roker inthe c lique hasanequalprob ab ility to b e the b roker endow ed w ith non-fundamentalinform ation Inthisc ase,

b rokersagree to share inform ationi®

¯xed ,it isstillpossib le w henb rokers' role are randomly c hosen

4 Inf orm ationSharin g and M arket P erf orm ance

Inthissec tion, w e analyze the e®ec tsofinform ationsharing ontrad itionalm easuresof

m arket quality: (1) the inform ationale± c iency ofpric es(m easured b y V ar(~v jp)), (2 )pric e volatility (measured b y V ar(~v¡p)),(3) m arket d epth (m easured by ¸) and (4 ) theexpec ted trad ingc ostsb orne b y liquid ity trad ers(i.e.their expec ted losses,E(~x(p¡~v)))

T hese aspec tsofm arket performance play a prom inent role inthe d eb atesregard ing the

d esignoftrad ingsystem sand have attrac ted c onsid erab le attentioninthe literature (see

M ad havan(19 96) or Vives(19 95) for instance)

P rop osition3 : P rices are more inform ative (V ar(~v j p) smaller) and less volatile(V ar(~v¡p) smaller) w henthere isinformationsharing

T he intuitionb ehind thisresult issim ple.W henspec ulatorsSand B share inform ation,the numb er ofspec ulatorstrad ing onfundam entalinform ationincreases.It follow sthatthe aggregate ord er °ow ism ore informative For thisreason, pric esare m ore ac c uratepred ic torsofthe ¯nalvalue ofthe sec urity and pric e d iscovery isim proved

W e now examine the im pac t ofinform ationsharing onthe d epth ofthe m arket Asshow nb y Lem m a 2 , anincrease inthe prec isionw ith w hic h spec ulator S transm itshisinform ationim proves market d epth How ever, anincrease inthe prec isionw ith w hich