COMPETITION AMONG EXCHANGES*

TANO SANTOS AND JOSE´ A. SCHEINKMAN

Doescompetition among Ž nancialintermediaries lead to excessively low standards?To examine this question, we construct amodelwhere intermediaries designcontracts toattract tradingvolume, taking intoconsideration that traders differin credit qualityand may default. When credit qualityis observable,inter- mediariesdemand the “ right”amount of guarantees.A monopolistwould demand fewerguarantees. Private information about credit qualityhas an ambiguous effectin a competitiveenvironment. When the cost of default is large (small), privateinformation leads to higher (lower) standards. We exhibitexamples where privateinformation is present and competition produces higher standards than monopolydoes.

I. INTRODUCTION In spite ofthegeneral acceptance of the competitive mecha- nismas an allocationscheme, many observers consider Ž nancial intermediationan exception.Competition is thoughtto lead toa “raceto the bottom” in whichŽ nancial intermediariessettle for excessivelylow levels of contractualguarantees in anattemptto increasevolume. Evaluating futuresexchanges, a jointreport fromthe Treasury and theFederal Reserve Board, writtenin the wakeof the1987 crash,states that “[T]hereis sufŽcient possibil- ity that at somepoint SROs [Self RegulatoryOrganizations] mightestablish marginsthat wereinconsistent enough to present marketproblems or setthem at levelsthat mightpresent poten- tial coststo other parties that regulatoryapproval should be established in all markets.”1 In this paper weexaminethe characteristics of thecompeti- tiveequilibrium in amodelof Ž nancial intermediation,where tradersmay default and differ intheircredit quality. In particu- lar,we investigate whether competition among exchanges leads toexcessively low standards. In ourmodel, investors’ endowments have observable and

*Wethank Fernando Alvarez, Ulf Axelson, Alberto Bisin, Marcio Garcia, ChristopherCulp, Douglas Diamond, Luis Garicano, Mark Garmaise,Claudio Haddad,Robert Litterman, Robert Litzemberger, Merton Miller, Kazuhiko Ohashi, CanicePrendergast, Adriano Rampini, David Robinson, Gideon Saar, Carol Si- mons,James Stoker, Suresh Sundaresan, Kip Testwuide,and Luigi Zingales for helpfulremarks. Andreia Eisfeldt and Christopher Hennessy provided excellent researchassistance. This research was supported by grant SBR-9601920from the NationalScience Foundation. The current versiongreatly beneŽ ted from detailed writtencomments by Edward Glaeserand three referees. 1.This quote is taken from Gammill [1988].

© 2001by thePresident and Fellowsof Harvard Collegeand theMassachusetts Institute of Technology. The Quarterly Journal ofEconomics, August 2001

1027 1028 QUARTERLY JOURNALOF ECONOMICS unobservablerisks. The observable risk averages out across agents,and hencecan potentially behedged. In addition, each agenthas asmallprobability ofan unobservablenegative idio- syncraticshock. We call traderswho have a lower(higher) prob- ability ofan adverseidiosyncratic shock high (respectively,low) quality traders.These different probabilities mayresult from otherrisks already assumedby thetraders, which are left outside themodel. Traders’ quality maybe observable or hidden private information.When traders default, societyimposes a nonpecuni- ary punishmentproportional to the amount defaulted. Potentialexchanges compete by settingcollateral require- mentsand assetpayoffs. An exchange’s proŽt depends onthe payoffs promised,and onthedefaults that occur.To simplify the analysis, wepostulate that eachexchange issues a singlecon- tract,and eachagent must trade in asingleexchange. However, investorsare allowed to take any longor short position, and exchangesdemand marginsthat areproportional to the absolute sizeof positions. Whenquality is observable,competition among Ž nancial in- termediariesleads toa (constrained) optimalamount of contrac- tual guarantees.Here, our results formalize the intuition of Telser[1981] and Miller[1988], whoargue that futuresex- changeschoose margin requirements to balancethe reduced risk fromdefault against thehigher costs brought by theextra degree ofprotection. In contrast,a monopolistwould demand fewer contractualguarantees. This follows because a monopolist’s pric- ing policyinduces traders to take smaller positions. As aresult, theex post incentivesto default arelower, and this allows the monopolistto economize collateral. Westudy theeffect of theunobservability of atrader’s qual- ity onthe competitive equilibrium, and showthat this effect depends onthe level of the exogenous bankruptcy penalties. Whenthese penalties are high, if quality isobservable,low qual- ity tradersprefer the terms offered to the high quality traders.As aresult,when qualities arenot observable, the higher quality tradersface a highercollateral level than theywould if quality was observable,while the low quality tradersface exactly the sameterms that theywould faceif quality was observable.Here collateralis beingused as ascreeningdevice, and private infor- mationabout quality generatesstandards that aretoo high rela- tiveto the observable quality case.On theother hand, if the exogenouspenalties are low, the high quality agentsprefer the COMPETITION AMONG EXCHANGES 1029 termsof trade offeredto the low quality tradersin theequilib- riumwith observablequalities. As aresult,in theequilibrium with private informationabout qualities, the lower quality trad- ersface a lowercollateral level than theywould in thecompeti- tiveallocation under observable qualities, while the high quality tradersface exactly the same terms that theywould faceif qual- itieswere observable. In this case,the presence of private infor- mationresults in alowerstandard. Forintermediate levels of penalties,the equilibrium with observablequalities survivesthe presenceof private information,and thereis nodeparture from theconstrained optimality. Whencredit quality is notobservable, it is moredifŽ cult to comparethe behavior of amonopolistwith acompetitiveequilib- rium,because a monopolistmust take into account the effect that achangein acontract’s termshas onthe demand forany other contractthat heis simultaneouslyoffering. Nonetheless, as we arguein SectionIV, thereare many cases where it is possibleto establish that amonopolistwill demand fewercontractual guar- anteesthan would prevail undercompetition. Todiscuss theimpact ofliquidity in asimpleframework, we postulatethat thereis aŽxedcost to operate an exchange.These Žxedcosts assure that, ceteris paribus, exchangeswith more participants canoffer better terms. These better terms can be thoughtof as ameasureof liquidity. Weshow that whenŽ xed costsare present and competitionprevails, agents of onequality maybeneŽ t fromthe establishment of minimum collateral re- quirementsby aregulator,at theexpense of agents of the other quality, evenif theseminimum collateral requirements are bind- ing forall qualities.The agents who proŽ t fromthe establishment ofthesetougher standards areexactly those who, in theabsence ofregulation,choose to trade in theexchange with highercollat- eral.Hence, this modelprovides a candidate positivetheory to explain thefrequent demands by moreestablished exchangesfor commonstandards in Žnancial markets. In ourmodel, collateral is deposited as aperformancebond against contractualobligations. The margin requirement speci- Žesthe collateral required. This is motivatedby therole that marginsplay in futuresmarkets. Although many of ourmodeling choicesare inspired by thecharacteristics of futuresmarkets, we believethat ourapproach canbe used tounderstand thebehavior ofotherŽ nancial intermediaries.While our model is necessarily special,we argue that manyof the conclusions would survive 1030 QUARTERLY JOURNALOF ECONOMICS different speciŽcations and highlight,throughout the paper, the economicforces that drivethe conclusions. Wealso have a moreabstract motivationfor this paper— incorporatingquestions of credit quality intothe literature on securitydesign. 2 Thisliterature examines the characteristics of securitieswhen market imperfections prevent the existence of a completeset of securities. Frequently, costs of issuing securities areassumed exogenously. If asymmetricinformation is treated,it is typically assumedthat thedesigner of thesecurity has private information.Our contribution is toanalyze asituationin which securitiesare competitively designed by intermediaries,and wherethese intermediaries must consider the characteristics of theagents that theyattract. Theremainder of the paper is structuredas follows:in the nextsection we present an overviewof some of the evidence on competitionamong exchanges. Section III containsthe model and amoredetailed defenseof the assumptions. In SectionIV we presentresults for the case of no Ž xedcosts. The Ž fth section looksat theproblem of liquidity, and SectionVI containsthe conclusions.All proofsare found in theAppendix.

II. SOME EXAMPLES In this sectionwe discuss someof the evidence that motivates ourmodeling choices. A.Collateral Is Costly Whenan exchangechooses higher margins, it lowersex- pectedlosses from defaults, but increasesthe costs of trading. Facedwith highercollateral requirements, some traders will opt totrade elsewhere,others will simply trade less.As aconse- quence,the exchange becomes less liquid and losesrevenues. Hardouvelisand Kim[1995] studied theimpact ofmargin changeson volume.They examined eight metal futures contracts fromthe early 1970s toOctober 1990 —asamplethat contains over500 marginchanges. For each margin change, they con- structeda benchmarkgroup consisting of the metal contracts that donot change margins in afour-monthperiod around the

2.Some relevant references are Allen and Gale [1988, 1991], Bisin [1998], DufŽe andJackson [1989], and the February 1995 issue of the Journalof Eco- nomicTheory. Santos[1997] studied the impact of Ž nancialinnovations on the credit qualityof apreexistingbond market. COMPETITION AMONG EXCHANGES 1031 date ofthe margin change. They estimated that a10 percent increasein marginsdecreases the volume of trade by 1.4 percent and increasesthe volume of thebenchmark group by 1.8 percent. Anotherexample is reportedin Figlewski[1984]. In late1965, at therequest of thegovernment, COMEX morethan tripled margin requirementson copper futures. As aresult,the daily average numberof traded contractswent from 832 to260.

B.TradersCare aboutthe Risk ofNonperformance In theUnited States theCommodity Exchange Act expressly precludesthe CFTC fromimposing minimum margin require- mentsfor futures transactions. Nonetheless, futures exchanges havealways demanded positivemargins. As acounterpartyto everytrade, an exchangeassumes a riskwhen it allows atrader topost lessthan 100 percentcollateral. 3 Thespeculation in silver by Bunkerand HerbertHunt, and associates,from September 1979 toApril 1980, provided an experimentthat showsthat tradersare willing topay todo business in an exchangewith less performancerisk. In thelate 1970s theHunt brothers established largelong positions in silverfutures at theChicago Board of Trade(CBOT) and NewYork’ s COMEX. Starting in October 1979, theCBOT tooka seriesof actions,including positionlimits, that causedthe Hunts to move most of theirtrades toNew York. Sellersof futures in NewYork had reasonto worry about the possibility ofa default by theHunt brothers, while those selling in Chicagowere insulated fromthis risk.Bailey and Ng[1991] showedthat spreads betweenthe COMEX and theCBOT in- creasedtoward theend of theHunt episode, when it was evident that thebrothers were facing Žnancial distress.They also argued that evidenceof a deteriorationin theHunts’ Ž nancial conditions canbe matchedto positivechanges in theCOMEX-CBOT spread, and that this spread fell with positiveannouncements about the Hunts.

3.In reality, it is the clearinghouses that guarantee deliveries. Clearing- housescollect margins, set capital requirements, and other Ž nancialstandards. Theymay also establish rules to assess members to cover defaults. All trades that areguaranteed by the clearinghouse must go through a clearingmember— other brokersmust trade through a member.Traders in turn gothrough a broker. Clearinghousesand exchanges also set minimum margins that brokers must charge.In this paper we ignore the distinction between clearinghouses and exchanges,and omit the brokers from the picture. 1032 QUARTERLY JOURNALOF ECONOMICS

C.ExchangesCompete on Contractual Guarantees Competitionamong Ž nancial intermediariesinvolves many dimensionsof product differentiation.In somecases exchanges introducenearly identical instruments.Two examples are the one-monthDeutschmark futures contracts which started trading onboth Frankfurt’ s DTBand London’s LIFFEin late1996, and thecompetition between Singapore’ s SIMEX and Osaka’s OSE in theNikkei futures. In othercases, exchanges create new con- tractsthat theyhope will betterŽ ttheneeds of potential traders. Tomakethe problem tractable, we concentrateon theguarantees demanded fromtraders to insure contract performance, even though,in reality,product differentiationoccurs simultaneously alongseveral dimensions, only one of which is theseguarantees. Exchangesuse several devices to guarantee contract perfor- mance,including markingto market, trading limits,and capital requirements.However, in this paper weuse margin require- mentsas aproxyfor all ofthese instruments. Themost notorious recent case of competition among ex- changesproduced thedemise of Barings PLC,the oldest mer- chantbank in GreatBritain. In thefall of1988, theOsaka Stock Exchange(OSE) launcheda Nikkei225 futurescontract which mimickeda contractthat theSingapore International Money Exchange(SIMEX) had beentrading fortwo years. Trading quicklymoved to Japan, and by theend of 1990, theOSE had a marketshare that exceeded90 percent.From January 1990 until August 1993, theOSE increasedmargins on four occasions, while theSIMEX decreasedmargins Ž vetimes and increasedmargins twice.Ito and Lin[1996] documentedthat eachmargin increase led tolost volume in favorof thecompeting exchange. In Decem- berof 1993 marginrequirements in theSIMEX were15 percent ofacontract’s facevalue, versus 30 percentin Japan, and SIMEX had regained30 percentof the Nikkei contracts. Among those movingtheir business to Singapore was Barings. NicholasLee- son,who was simultaneouslyBarings’ proprietary trader and head ofsettlements in Singapore,accumulated large losses in futuresand onoptions on futures on the Nikkei index, and hid theselosses from the London ofŽ ce. Like most futures exchanges, SIMEX had apolicyof limiting“ speculative”positions to prevent largelosses, but Barings had assured theSingapore exchange that theirposition was hedgedby an oppositeposition in Osaka. Nonetheless,SIMEX failed totake measures to verify Barings’ COMPETITION AMONG EXCHANGES 1033 positionat theOSE, as it would normallydo. Gerard Pfaudwadel, chairmanof MATIF,the French futures exchange, said that,“ It’s clearthat abig part oftheproblem with Barings was dueto the battle fornew business between Singapore and Osaka ...ex- changesshouldn’ t competeby reducingthe amount of security theyrequire, because as soonas theydo, it increasesthe risk for everyoneinvolved.” 4 In someinstances, competition among exchanges is actually competitionamong regulators. Commenting on the competition betweenthe Singapore and HongKong exchanges, Euromoney [February,1997] wrote:“ ...Theregulators in HongKong and Singapore. ..want toensure standards highenough to attract mainstreaminternational investors and yetto encourage less sophisticated regionalplayers too. ...Thejoint distinction of HongKong and Singaporeis that theyare tier one, or nearlytier one,regimes. To maintain that distinction theymust not be temptedinto a racefor regulatory leniency.” This remark also illustratesthat exchangesmust bear in mind distinct potential clienteleswhen choosing contractual guarantees. In ourmodel, weconsider two sets of agents, distinguished by their“ credit quality.”Exchanges take into account the impact ofcollateral requirementson the demand by eachof these qualities, for the exchange’s products.

D.Intermediaries’Assessment of Counterparty Risk Is Imperfect An importantaspect ofour model is that wedo not allow exchangesto use nonlinear prices. We assume that exchanges cannotprice discriminate as afunctionof the size of trades becausewe believe that, in actual Žnancial markets,intermedi- arieshave difŽ culties in assessingthe total risk of counterparties. TheBarings case,and theLTCM debaclethat involvedthe over- the-countermarket, illustrate this inability whentraders are simultaneouslydealing with severalcounterparties. However, thereare also examples involving a singlemarket. In 1977 the CFTC had alimiton positionsin thesoybean futures markets of threemillion bushels, approximately 5 percentof theannual U.S. soybeanoutput. Nonetheless, Bunker and HerbertHunt suc- ceededin acquiring alongposition of 26.9 millionbushels at the CBOT, using thename of family members.Among these, Houston BunkerHunt, a nineteen-yearold freshman,“ borrowed”2 million

4.Quoted by Suzanne McGee in The Wall Street Journal, March 17,1995. 1034 QUARTERLY JOURNALOF ECONOMICS dollars fromhis fatherto pay forthe margins on a positionof threemillion bushels that heboughtby placing his ordersfrom a public phonebooth at the F KA fraternityhouse at theUniversity of Tulsa.5 Pirrong[1996] relatesa cruderincident at theCBOT, in whichtwo traders sold thousands ofT-bond futurecontracts and boughthundred ofputs onthese futures. They were eventually caught,but notbefore imposing severe losses on their clearing Žrm.

III. THE MODEL

A.Descriptionof the Economy Consideran economywith twoperiods. In theŽ rstperiod onlyasset trading occurs;all endowmentrealizations and con- sumptiontake place in thesecond period. In this secondperiod thereare two equally probable observablestates of the world, s1 and s2 .Thereare a largenumber of agents.In eachstate, exactly half ofthe agents receive an endowmentof x units ofthe con- sumptiongood. The other half “typically”receives a largerendow- ment y.However,each of theseagents has asmallprobability of receiving z < x instead ofthe larger endowment y. The occur- renceof this bad draw is private informationand independent acrossagents. We call theprobability ofthe bad draw, z, the “quality”of the agent. Formally, each agent is characterizedby membershipin agroup i [ {1,2}, and aquality p [ { p,q}. Within eachgroup a fraction a p is ofquality p .Thetable belowdescribes thedistribution ofendowments of an agentof quality p [ { p,q}.

group endowment ins 1 endowment ins 2

1 x y withprobability p z withprobability 1 2 p 2 y withprobability p x z withprobability 1 2 p

Sinceeach group is themirror image of theother, aggregate endowmentis constant.Agents maximize the expected utility of consumption,and havea commonutility function u[ with u0 <

5.See Fay [1982]. The episode did not cost the brothers much. The Hunts settledout of court in1981,paying $500,000 and agreeing to stay out of soybean futuresfor two years. COMPETITION AMONG EXCHANGES 1035

0, and u9 (0) = ` .Sincewe want tointroduce the possibility of default, weŽ xparametersso that, in equilibrium,an agentwould buy assetsthat transferconsumption to the state where they receivethe certain endowment x.Thatis, we assume

ASSUMPTION 1. u9 ( x) > (1 2 p )u9 ( z) + p u9 ( y). Noticethat this assumptionis onlyplausible if p is closeto 1. FordeŽ niteness we assume that p > q,and this meansthat the “unlucky”draw ( z)is relativelymore likely for quality q agents. Werefer to agents of quality p(q)as high (low) quality agents. Each agentknows his ownquality. Exchangescompete for customers by issuing contracts. 6 SinceŽ rst-period endowmentsare zero, exchanges are limited to issuing forwards.To focus on the ability ofthe marketed con- tractsto spread risksamong investors, we assume that exchanges mustbreak even in eachstate of the world. 7 In this paper we assumethat investorsare precluded fromparticipating in more than oneexchange. In addition, weidentify eachcontract with an exchange.8 Each exchangeincurs a Žxedcost s $ 0. Weconcentrate our analysis oncontracts that treatgroups (but notqualities) symmetrically.The forward is normalizedso that theparty that is longmust deliver one unit oftheconsump- tiongood in state s2.Agentsmay potentially default. ToŽ nance thecosts of operation and defaults, theexchange pays lessthan oneunit foreach unit ofthe claim; it deliversto an agentthat is longone unit ofthecontract, K < 1units ofthegood in state s1 . Theexchange is alsoallowed torequire collateral from traders. Whena traderdeposits collateral C,this amountis takenfrom his second-periodendowment and deliveredto the exchange with probability oneto satisfy any claimsthe exchange has onthe

6.We model exchanges as competitive Ž rms,even though until recently manyexchanges were organized as “mutualnonproŽ t organizations.”Here “ mu- tual”refers to the fact thatthe Ž nancialintermediaries who trade in theexchange alsocontrol it. The term “ nonproŽt” should not be equated to “ charitable.”Pre- sumablythe objective function of theseexchanges was to maximize the surplus of itsmembers, but there could be somedivergence between this objective and proŽ t maximization.We choose here to assume proŽ t maximizationdirectly because it avoidsthe explicit modeling of the member Ž rms,and because there is a clear trendamong exchanges to organize as for-proŽt Žrms. 7.We mayassume that any agent can set up an exchange. Since each agent isan inŽ nitesimal portion of theeconomy, he is not able to sustain Ž nitelosses, andthis justiŽ es theassumption that exchanges must break even in each state of the world. 8.Hahn [1978] discusses the role of this assumption in the Rothschild- Stiglitzmodel. 1036 QUARTERLY JOURNALOF ECONOMICS agent.This requires that C doesnot exceed the minimum endow- mentthat thetrader receives in astatewhere he is requiredto deliverto the exchange. There is nocost of setting up collateral. Consistentwith oursearch for a symmetricoutcome, and tomake themodel robust to splitting and poolingorders, we assume that eachexchange chooses a marginrate F $ 0and demands that a traderwith apositionof u contractssecures at least F u u u as collateral.Investors are allowed totake any longor shortposition in themarketed asset. However, an agent’s default triggersan examinationof that agent’s trades,and his positionsare netted beforesettlement. Since K < 1,agents would neversimultaneously takea longand ashortposition. The two assumptions we make— that tradersuse a singleexchange and that exchangescannot pricediscriminate as afunctionof the size of positions—partially canceleach other. Still left in themodel is amoral-hazard prob- lemthat, as weargued in SectionII, affects Žnancial inter- mediation,and it is valuable toexamine the effect of theinability ofexchanges to control the risk of their counterparties in this particularly simplecase. 9 Sincewe assume a largenumber of traders,the default risk that eachtrader represents is averagedout and an asset’s quality is representedby thescalar K.Hence,in themodel, there is no riskassociated with trading in aparticular exchange—an agent simply facesdistinct termsof trade in different exchanges.One possiblereinterpretation of themodel that allows fordifferences in riskacross exchanges is toassumethat thereare “ risky”times in whichthe idiosyncratic risk ( z instead of y)is presentand “quiet”times in whichthis riskis absent.Agents have to choose an exchange,before it is knownwhether they are in ariskyor quietperiod. However, the portfolio of eachagent is chosenafter it is knownwhether the idiosyncratic risk is present.Exchanges that pay alower K in riskytimes can be rightly regarded as riskier.For simplicity, we do not pursue this interpretationhere. As wealready discussed,our assumptions guarantee that, in equilibrium,agents take positions that areout of the money in thestate where they face a lottery.The presence of individual uninsurableshocks (receiving z instead of y)makesit undesir-

9.In contrast, in Bisin and Guaitoli [1998] agents can simultaneously buy contracts fromseveral insurance companies, and each insurer can monitor the positionof an agent in their own contract. Bisinand Gottardi [1999] discuss existenceof equilibrium,in a modelwhere agents can purchase several different contracts andface linear prices. COMPETITION AMONG EXCHANGES 1037 ableto require that agentsdeliver fully ontheir commitments, sincein this casethey would notbe able totransfer much to the statewhere they receive the endowment x.Allowing fordefault is welfareimproving. Default is essentiallya methodto make pay- offs covary,albeit imperfectly,with theidiosyncratic shock. We Žndit particularly convenientto borrow the default technologyof Shubik and Wilson[1977], whichwas alsoused by Diamond [1984] and Dubey,Geanakoplos, and Shubik [1996]. This amountsto introducing a penalty that is imposeddirectly on the utility oftheindividual and measuredin utility units.If in period 2an agentis committedto deliver an amount w $ 0 in the observedstate, and deliversinstead D $ 0,he suffers apenalty, l max (w 2 D,0),in utility units.That is, if anagent’s deliveries meethis commitments,he suffers nopenalties, otherwise the penalty is proportionalto the amount that hefails todeliver. Noticethat, in conformitywith ourearlier assumption concerning therobustness to the splitting and poolingof trades,penalties are linearfunctions of theamount an agentcomes short. Theparameter l should beunderstood as theeconomywide bankruptcy code,and exchangescannot alter it. Since default is introducedto allow forsome relief when z is obtained,it is natural toassume that u9 ( z) > l .Wewill alsoassume that the penalty is nottoo small. More exactly, we assume

ASSUMPTION 2. u9 ( z) > l > p u9 ( y) + (1 2 p )u9 ( z).

In addition, toeliminate one multiplier, we assumethat z is sufŽciently small, so that agentsthat obtain y will always deliver in excessof collateral.

ASSUMPTION 3. u9 ( y 2 z) < l .

Weareready nowto describe the investor’ s problem.Suppose that thedefault penalty parameteris l ,and that theagent is trading in an exchangethat demands collateralof F (per unit) and pays in themoney contracts K (per unit). An agentwho trades in this exchangehas todecidehow many contracts to buy and howmany units todeliverwhen he isoutof themoney. In the Appendix wewrite down thedecision problem of the agent pre- ciselyand showthat theagent’ s maximizationproblem has a uniquesolution. Furthermore, the symmetry present in our modelguarantees that theposition chosen by an agentof group2 is exactlyequal to the negative of theposition taken by an agent 1038 QUARTERLY JOURNALOF ECONOMICS ofgroup 1. Lemma 1 in theAppendix conŽrms that group1 agentstake long positions in theforward contract. Each agentalso has todecide how much to deliver. Since u9 ( z) > l ,an agentwho receives z will makeno deliveries in excessof collateral. When endowed with y,theinvestor will equatethe marginal utility ofconsumptionto the marginal pen- alty, l . Let u * solve u9 ( y 2 u *) = l .Agroup1 agentwho is long u p contracts,and receivesendowment y,will fully deliverif u p # u *.Otherwise,he will deliver D = max{u *,F u p } = u *, since F u p < z,and fromAssumption 3, z # u *.Thedelivery decision depends onthe investor’ s quality onlythrough the position. Hence, given theparameters l , F , and K,asolutionto the optimization prob- lemfaced by an agentof group 1 and quality p canbe parame- terizedby twopositive numbers ( u p ,Dp ).TheŽ rstelement is the positionhe takes, and thesecond the amount he chooses to deliverwhen his endowmentrealization is y. In theAppendix weshow that theŽ rst-orderconditions for theagents problem deŽ ne a function u p (F ,K)that is smooth exceptperhaps forthe (measure zero) set of values of the pa- rametersfor which u p = u *.

B.Equilibrium In viewof the results in theprevious subsection, it sufŽces to makereference to group 1 agentswhen discussing equilibria. Write Vp (F ,K)forthe expected utility achievedby group1 agents of quality p trading inan exchangethat demands collateralof F (per unit) and pays in themoney contracts K (per unit). Sincewe assumethat theparameter l is Žxed,we do not make any explicit referenceto l in thedeŽ nition of V orin theother quantities that follow.We will concentrateon either pooling or separating equi- libria. Thereis nolossin generalityin assumingthat all agentsof agivenquality trade in thesame exchange. Hence, in apooling equilibriumthere will bea singleexchange, while in aseparating equilibriumthere will betwo exchanges. If (u p ,Dp )solvesthe maximization problem for group 1 when facing thecontract ( F ,K), we write

1 (1) P p (F ,K) º 2 a p [p Dp 1 (1 2 p )F p u p 2 Ku p ] 2 s , forthe per capita proŽt generatedby acontract( F ,K), if it attracts all agentsof quality p and noagentsof theother quality.

Wewill alsowrite P p ,q (F ,K) º P p (F ,K) + P q (F ,K) + s for the COMPETITION AMONG EXCHANGES 1039 proŽt generatedby acontract( F ,K),if it attracts all agentsof bothqualities. A poolingequilibrium is

(a) acontract( F ,K) such that P p,q (F ,K) $ 0; (b) thereis noother contract ( F 9 ,K9 )that whenoffered in addition tothe contract ( F ,K)makespositive proŽ ts.

(a) guaranteesthat, in state s1 ,thesum of theŽ xedcosts of theexchange plus theamount it deliversto the parties that are longthe asset (group 1) doesnot exceed the amount delivered by theout-of-the-money positions (held bymembersof group 2). By symmetrywe do not need to write the equivalent equation for state s2 .(b) reects free entry. We also do not need to include marketclearing among our equilibrium conditions because group 2always takesthe negative of theposition taken by group1. A separatingequilibrium, whenqualities areobservable, is (a) for each p [ { p,q}acontract( F p ,Kp ) such that P p (F p ,Kp ) $ 0; (b) thereis noother contract ( F 9 ,K9 )that whenoffered in

addition tothe contracts ( F p ,Kp )p [ { p ,q } makespositive proŽts. Whenqualities arenot observable, we must add tothe deŽ - nitionof aseparating equilibrium: (c) For each p [ { p,q}, Vp (F p ,Kp ) $ Vp (F p 9 ,Kp 9 ) for any p 9 Þ p . Condition (c) statesthat agentsof each quality preferthe contractassigned tothat quality tothe other contract.

IV. COMPETITION WITH COSTLESS EXCHANGES In this sectionwe study theequilibrium when s = 0. In our setup,because agents can vary the size of their positions, the zero-proŽt combinationsdo not form a straight lineas in the originalRothschild and Stiglitz [1976] model.Proposition 1 de- scribesthese zero-proŽ t lines.Proposition 2 characterizesequi- libria whenqualities areobservable. In this case,an exchangeis createdfor each quality. Typically,but notalways, theexchange that requiresa highercollateral serves the high quality agents. Wethendiscuss theoptimality propertiesof this equilibriumand comparethe equilibrium allocation with themonopoly outcome. Theremainder of thesection deals with thecase in whichan agent’s quality is private information.When an equilibriumex- ists,we show that, unlike the Rothschild-Stiglitz model,the in- 1040 QUARTERLY JOURNALOF ECONOMICS centiveconstraints may bind forany ofthe two qualities and asa resultthe default ratemay be higher, lower, or exactlythe same as in thecase of observable qualities. Wewill assumethat collateralis expensivewhen compared with penalties.More precisely, Assumption 4statesthat it never pays toextractcollateral from the unlucky agents to distribute to theagents who receive x,evenafter accounting for the reduced penalties.This assumption is used tosimplify proofsand to characterizein amoreexplicit mannerthe equilibrium when qualities areobservable.

ASSUMPTION 4. u9 ( x) 2 [u9 ( z) 2 l ] # 0.

Theproperties of equilibria will depend onthe level of the exogenouspenalties, l .Suppose that l *p and u *p solvethe follow- ing systemof equations:

(2) p u9 ( x 1 u *p p ) 5 u9 ( y 2 u *p ),

(3) l *p 5 u9 ( y 2 u *p ).

That is, l *p is theminimum level of penalties such that, when thereare no collateral requirements and exchangesset K = p , agentsof quality p takea position u *p whichleads themto fully deliver,when they obtain thehigh endowment y.Sincethere is no collateralposted, agents deliver nothing if theyobtain z and the realizeddefault ratefrom quality p is exactly 1 2 p . Thenext proposition describes the zero-proŽ t linesfor an exchangethat onlyattracts agentsof quality p .

PROPOSITION 1.(i) Forany F [ [0,1], thereexists exactly one K(F ,p ) > 0 such that P p (F , K(F ,p )) = 0 and u p > 0. The function K is increasingin F . (ii) Suppose that l # l *p and u * solves u9 ( y 2 u *) = l . Let [F *p ,K*p ]bethe unique solution to

(4) u9 (x 1 u *K*p ) K*p 2 (1 2 p )F *p [u9 (z 2 u *F *p ) 2 l ] 2 l 5 0

(5) K*p 2 (1 2 p )F *p 2 p 5 0

if asolutionexists with 0 # F *p # 1.Otherwise set F *p = K*p = 1. Then,

K(F ,p ) , (1 2 p )F 1 p , for all 0 # F , F , F *p

K(F ,p ) 5 (1 2 p )F 1 p , for all F $ F *p . COMPETITION AMONG EXCHANGES 1041

Proposition1 (i) establishesthat forany collateralrequire- mentthere exists precisely one value of K = K(F ,p )suchthat if an exchangeis theonly one serving quality p and usesparame- ters (F ,K)then(a) agentsof quality p takea nonzeroposition in that exchange,and (b) theexchange makes zero net revenue from theagents of quality p .Notethat (1 2 p )F + p is theexpected deliveryrate of traders of quality p ,conditionalon full deliveryby thosewho obtain y (and nodeliveries above collateral for those that obtain z).Part(ii) statesthat thereis acollaterallevel F *p with thefollowing property: for any F ,thecorresponding zero- proŽt K(F ,p )is lessthan this expecteddelivery rate if and only if F # F *p .Theequations in part (ii) oftheproposition also have asolutionif l > l *p .However,in this case F *p < 0. That is, exchangescould demand negativecollateral and still obtain full deliveryfrom those who obtain y.In this case,exogenous penal- tiesare high enough,and collateralis notneeded to guarantee delivery.In fact, exchangescould deliver a positiveamount to agentswho claimed to have received z.Sincewe want tostress therole of collateral, we assume

ASSUMPTION 5. l # l *p , for each p [ { p,q}. Whenqualities areobservable, costless entry guarantees that, in equilibrium,each exchange attracts asinglequality and the termsoffered by theexchange maximizes the utility ofthat quality subjectto the constraint that individuals canchoose to default and sufferthe penalties. If collateralis setabove F *p ,loweringthe collateralrequirement by an inŽnitesimal amount would notlead to any defaults by agentsthat receiveendowment y.Themarginal gain in theexpected utility ofa group1 agentwould be (6) (1 2 p )u [u9 ( z 2 F u ) 2 l ]. On theother hand, tomaintain proŽts constant,the exchange would haveto lower deliveries proportionately. The marginal loss in expectedutility foran agentof group 1, conditional on being long,would be(1 2 p )u u9 ( x + u K).Assumption 4guarantees that this amountis smallerthan theexpression in (6). Hence,in equilibrium,the collateral charged by theexchange serving qual- ity p cannotexceed F *p . Increasingcollateral requirements when F < F *p penalizes thetraders who obtain endowment z,but allows exchangesto increase K.Theincrease in K is Žnancedby twosources. The Žrst,exactly as in thecase where F > F *p ,is theincrease in 1042 QUARTERLY JOURNALOF ECONOMICS deliveriesfrom the agents who receive endowment z, and is proportionalto 1 2 p .As wejust argued above, Assumption 4 guaranteesthat this increasein collateraland deliverieshas a negativenet effect on expected utilities. Here, however, there is alsoa secondsource to Žnancethe increase in K.Toeconomizeon collateral,agents respond by loweringthe absolute value of their positions.When F > F *p ,this has noeffect on the share of each agent’s obligationsthat is fulŽlled. However, when F < F *p , lowering u reducesthe default rateand allows exchanges,holding proŽts constant,to increase K.In theAppendix weshow that, when F < F *p ,theelasticity of thetrading position u with respect tothe collateral requirement F is largeenough to guarantee an increasein expectedutility whenevercollateral is raised.The nextproposition formally states these results.

PROPOSITION 2.If qualities areobservable, there exists a unique equilibrium.In this equilibriumthere is onetraded contract foreach quality p [ { p,q}, [F *p , (1 2 p )F *p + p ],and agents whoobtain endowment y deliverfully. In this equilibrium,if penaltiesare low, positive collateral is usedas asubstitutefor penalties. 10 Asocialplanner who could decideon the amount transferred to each player as afunctionof amessagesent by theplayer concerningtheir endowment could dobetter. The social planner would typically makepositive trans- fersto agents who claimed to have received z.However,if sucha schemewere in place,individual agentswould havean incentive toclaim more than one“ name,”just as in any rationingscheme. In otherwords, to decentralize such an allocationwould require placing limitson traders’ positions, something our exchanges cannot do.11 Suppose that thecentral planner is restrictedto linearschemes, and that hecannot avoid theimposition of pen- altieson traderswho fail todeliver.A standard argumentshows that thecentral planner would choosethe competitive allocation describedin Proposition2. In this sense,the equilibrium under symmetricinformation is aconstrainedoptimum. We also show, in theAppendix, that amonopolistwould demand zerocollateral. Hencethe default ratethat amonopolistwould facefrom traders

10.Indeed, it is possible to prove that the equilibrium margin requirement F *p isa decreasingfunction of the penalties in place.See Santos and Scheinkman [1998]. 11.See the story ontheHunts’ speculation on soybeansdescribed in Section II above. COMPETITION AMONG EXCHANGES 1043

FIGURE I Overcollateralization The q agentsare indifferent between trading contract (0, q)andtrading con- tract (F *p ,K*p).Thedashed line is the indifference curve of q agents. of quality p is at least 1 2 p ,while,in thecompetitive equilib- rium,the default ratefrom traders of quality p is (1 2 p )(1 2 F *p ) # 1 2 p . Weturn next to the case where an agent’s quality is private information.In this case,the equilibrium constructed in Propo- sition2 is notnecessarily sustainable. In theexample displayed in Figure I, l = l *q < l *p.Whenqualities areobservable, the q agentswould trade thecontract ( F *q ,K*q ) = (0,q),whereasthe p agentswould trade thecontract ( F *p,K*p ).Bothqualities prefer thecontract offered to the p agents.In this examplethe single crossingproperty holds. Since the net revenue contributed by agentsis acontinuousfunction of the contract terms, ( F ,K), whenquality is notobservable, any equilibriummust be separat- ing.In suchan equilibrium,the q agentsmust get at leastas muchutility as theywould obtain in theequilibrium with observ- ablequalities. Otherwise, an entrantwould offera contractclose to (0,q),attract all the q agents,and makea proŽt fromthe q agents.An application ofthe implicit functiontheorem shows that at zerocollateral p agentsdeliver at ahigherrate than q agents.Hence the entrant gains fromany p agentsthe contract attracts.On theother hand, since(0, q)is thebest separating 1044 QUARTERLY JOURNALOF ECONOMICS contractfor the q agentsthat breakseven, in equilibrium,the q agentscannot get more utility than in thecase of observable qualities.To determinethe contract offered to the p agents,Ž rst noticethat thesingle-crossing property implies that, along any q indifferencecurve, the utility ofthe p agentsincreases with F . Hence,if aseparating equilibriumexists, the contract offered the p agentsmust be at theintersection of the p zero-proŽt lineand the q agents’indifference curve that passes through(0, q). Such a point (F p,Kp)mustnecessarily satisfy F p > F *p ; i.e., the p exchangeis “overcollateralized.”In this equilibrium,collateral is beingused as ascreeningdevice. 12 Lemma2 in theAppendix, establishesthat the p quality agentstake a largerposition than the q quality agentsin the preferredcontract, ( F *p ,K*p ).Hencea minimumcontract size would serveto ameliorate the screening problem. Frequently, contractsizes in exchangeare considerable, although this may simply reect Ž xedcosts of trading. In theRothschild-Stiglitz model,the high quality agents neverprefer the allocation proposed to the low quality agents. Thepresence of moral hazard changesthis outcome.In our model,when qualities areobservable, it is possiblethat, in equi- librium,the p agentsprefer the contract offered on the q ex- 13 change. If themargin differential, F *p 2 F *q ,is largeenough, althoughthe delivery rate in the q exchangeis lower,the p agents mayprefer to trade in that exchangebecause the lower margins would allow themto take a largerposition. In this case,the equilibrium,when qualities cannotbe observed, involves the p quality agentsgetting the same allocation as in thecase where qualities areobservable, and the q quality agentstrading in an exchangewith sufŽciently low collateral (and consequentlylow deliveryrate) to deter the p agentsfrom trading. Here,since the p quality agentswould takea largeposition in the q exchange, positionlimits can help solvethe adverse selection problem. In thenext example we Ž xall parametersexcept for the penalty rate l and examinethe equilibria whenan agent’s quality is private information.We show that if l is high enough,in equilibrium,the q agentsget the same contract and p agents face ahighercollateral than theywould if quality was observable.On

12.Bester [1985, 1987] uses collateral as a screeningdevice in a different context. 13.Results with a similar avorcan be foundin Chassagnonand Chiappori [1997].However, their model and ours cannot be nested. COMPETITION AMONG EXCHANGES 1045

FIGURE II Theplot shows the optimal collateral rate, under full information, as a function ofthe default penalty. There are three regions. In region A thefull information equilibriumis not incentive compatible: agents of quality p wouldmigrate to the q exchangeif the full information contracts wereoffered. In region B the full informationequilibrium is incentivecompatible. In region C thefull information equilibriumis againnot incentive compatible, but now the q agentswould migrate to the p exchangeif the full information contracts wereoffered.

theother hand, if l is low,we obtain “undercollateralization”— the p agentsface exactly the same contract as theywould if quality was observablewhile the q agentstrade in an exchange with alowercollateral than thecollateral they deposit in the equilibriumwith observablequalities. For intermediate penalty valuesthe equilibrium with observablequalities is incentivecom- patible. Intuitively,when penalties are low, moral hazard is important,and whenquality is observable,the collateral require- mentthat is imposedon agents of quality p, F *p,is muchlarger than thecollateral imposed on the quality q agents, F *q . Hence the p quality agentswould preferthe exchange that servesthe q quality. On theother hand, whenpenalties are high, F *p is not muchbigger than F *q . Hence the q agentsprefer to trade onthe p exchange,to beneŽ t fromthe higher delivery rate. For inter- mediatevalues the collateral requirements differential is enough to deter the q agentsfrom migrating to the p exchange,but not high enoughto encourage the p agentsto move to the q exchange. FigureII showsthese equilibrium margin requirements as a functionof the penalty rates. 1046 QUARTERLY JOURNALOF ECONOMICS

Example. In this example u(c) = 2 c2 1 ,and endowmentsare { x,y,z} = {.75, 2.2,. 625}. Each quality representshalf ofthe population, p = .985, and q = .916.Thesevalues imply that l *p = .4596 and l *q = .4588. In this example,there are no Ž xed costs;that is, s = 0.Assumptions 1–5 aremet provided that .4043 < l # .4588. If thedefault penalty l $ .4550, theincentive compatibility constraintthat is binding isthat ofthelow quality agents,as in standard adverseselection models. On theother hand, if l [ (.4230,.4550), theequilibrium when quality is ob- servableis alsoan equilibriumfor the private informationcase. Finally,if .4043 < l # .4230, theincentive compatibility con- straint ofthe high quality agentis theone that binds—the high quality agentsprefer to trade in thelow quality exchange. Toillustrateundercollateralization, we computethe equilib- rium for l = .4051. If quality is observable,the equilibrium contractsare ( F *p,K*p) = (.57,.9936) and ( F *q ,K*q ) = (.29,.94). Theutility the p agentsobtain in equilibriumis lowerthan the onethey would obtain by migratingto the q exchange.The p agentswould takea largerposition in the q exchangethan they would takein theirown exchange ( u p(F *q ,K*q ) = .774 and u p(F *p ,K*p ) = .6288). FigureIII showsthe equilibrium when quality is private information.Since the single-crossing property holds, the equi- libriumis necessarilyseparating. Compared with thecase where quality is observable,the q agentsface a lowercollateral require- ment (F q = .26) and consequentlya lowerdelivery rate ( Kq = .9013), whilethe contract that the p agentstrade doesnot change.14 Thislower quality contractdeters the p agents from migratingto the q exchange.This undercollateralization is typi- cal whenthe moral-hazard problemis substantial; i.e.,where low penaltiesrequire high collateralrates to deter traders from tak- ing excessivelylarge positions. In thesecases the q agents,since theyare more likely to obtain thelow endowment z, are more affected bycollateralrequirements. As aconsequence,when qual- ity is observable,they face a muchlower collateral requirement than that faced by the p agents.

14.This separating equilibrium would involve (partial) default by the q agentswhen they obtain endowment y.Thisis aconsequenceof thefact thatwe haveonly two possibleendowments in thestate where endowment is uncertain.If wehad more than two possibleendowments, the decrease in quality in the asymmetricinformation equilibrium would be associatedwith an increase in the fractionof endowments where default occurs. COMPETITION AMONG EXCHANGES 1047

FIGURE III Undercollateralization Thezero proŽ t linescross several times. In equilibrium the p agents are indifferentbetween trading contract ( F *p ,K*p )andtrading contract ( F q ,Kq ).

In contrastwith thesituation where qualities areobservable, it is noteasy to compare the contracts offered by amonopolist with theones that would prevail undercompetition, when a trader’s quality is private information.Nonetheless, there are severalsituations where one can establish acomparison.The Ž rst is whena largefraction of tradersis ofagivenquality p . In this case,since a monopolistsuffers aŽrst-orderloss when he raises collateralabove zero, he would always choosezero collateral for thecontract chosen by quality p .Thesecond is whenit isoptimal forthe monopolist to offer a singlecontract. Here, the reasoning in Lemma5 in theAppendix canbe used to establish that this contractwould requirezero collateral.

V. LIQUIDITY Liquidity is acomplexphenomenon that canonly be properly discussed inadynamic model.However, in this paper weareonly interestedin oneaspect ofliquidity—that tradersprefer, ceteris paribus, totrade in amarketwith highervolume. We postulate Žxedcosts because in thepresence of Ž xedcosts trading is 1048 QUARTERLY JOURNALOF ECONOMICS

FIGURE IV Impactof Minimum Margin Requirements

cheaperin exchangeswith morevolume. As in thecase of noŽ xed costs,it is straightforward toshow that, when qualities areob- servable,the equilibria areconstrained efŽ cient. It is alsoeasy to seethat, in thepresence of these economies of scale, pooling equilibria mayexist, whether quality is observableor not. Hold- ing otherparameter values constant, pooling equilibria occurfor highervalues of s . In this sectionwe show that, by imposingminimum margin requirements,regulators may cause the equilibrium to shift to- ward apoolingequilibrium that beneŽts tradersof onequality at theexpense of traders of the other quality. In theexample illus- trated in FigureIV quality is observable,and in theabsence of minimummargin requirements, quality p trades thecontract

(F *p,K*p),and quality q agentsthe contract ( F *q,K*q ). In this 15 pool example F *q < F *p . To each F weassociate a K (F ) such that pool 0 (F ,K (F ))is onthe zero-proŽ t poolingline. Let Fp denote the setof all marginrequirements F suchthat theutility ofa p quality agentfacing theterms ( F ,K pool(F ))is greaterthan the utility the p agentsobtain whenfaced with ( F *p ,K*p ). These are

15.The parameters used to generate this example are the same as in the exampleof SectionIV withthe exception that s = .017. and l = .435. COMPETITION AMONG EXCHANGES 1049 thecandidate poolingequilibria that would deliverto the p qual- ity agentsan allocationthat theyprefer to the allocation they get 0 in theseparating equilibrium.Similarly, let Fq denotethe set of all marginrequirements F such that a q quality agentprefers to pool facethe terms ( F ,K (F ))tofacing ( F *q ,K*q ).Sincethe equilib- 0 0 riumis separating, Fp ù Fq is empty.For if F is apoint in the intersection,an entrantoffering terms slightly worsethan (F ,K pool(F ))would attract everyoneand makea proŽt. In fact, 0 themargin levels that belongto Fp arelarger than themargin 0 levelsthat belongto Fq . Nowsuppose that theregulator sets a minimummargin m requirement F = (1 2 m )F *q + m F *p, m > 0.Theseminimum marginrequirements are never binding onthe p quality ex- change. The q quality exchange,on the other hand, mustset a highermargin requirement. Using reasoning similar to the proof ofProposition2, we can show that, if thereis aseparating equi- librium,the q exchangewill setits marginrequirement at the minimumlevel allowed. To check whether this is actually an equilibrium,we must examine whether there are points onthe zero-proŽt poolingline that arepreferred by bothqualities. Let m Fq denotethe set of all marginrequirements F such that a q quality agentprefers to face the terms ( F ,K pool(F )) instead of facing theterms prescribed in thecandidate equilibrium.Since theutility that the q quality agentscan obtain by themselves, whenthe minimum margin requirements are imposed, is lower than theutility theyobtain whenthese requirements are absent, m 0 thereare points in Fq that arenot in Fq .In particular, the m 0 maximummargin in Fq is largerthan themaximum F in Fq . For theparameter values used here, we Žrstreach a m I < 1 for which m m thereis acommonpoint between Fq and Fp .At this point there aretwo equilibria— one separating, another pooling. The pooling equilibriuminvolves a marginrequirement F > F m I .If theregu- # latorincreases the margin requirements beyond F m I ,thereexists acontinuumof poolingequilibria. The most favorable equilibrium for the q agentshas amarginrate of exactly F .All otherequi- # libria treatthe p agentsbetter than theyare treated in the absenceof marginrequirements, at theexpense of the q agents. Oncethe regulator sets a minimummargin requirement greater than F ,all equilibria treatthe p agentsbetter than theyare # treatedin theabsence of margin requirements, again at the expenseof the q agents. The p agentsstrictly prefer any mini- mummargin requirement in theinterval ( F ,F # )tono margin # 1050 QUARTERLY JOURNALOF ECONOMICS requirements.This interval contains margin requirements above

F *p,themargin rate that the p agentswould facein theabsence ofregulation. In this examplethe p quality agentsbeneŽ t fromthe estab- lishmentof minimumstandards, at theexpense of the q agents.

Theroles are reversed when F *q > F *p .In any case,the quality that faceshigher margin requirements in theabsence of regula- tionmay beneŽ t fromminimum margin requirements.

VI. CONCLUSIONS In this paper weconstructed a simplemodel where ex- changesdesign contractsto attract trading volume,while simul- taneouslytaking into consideration that potentialcustomers dif- ferin creditquality and maychoose to default. Whenquality is observable,we showed that competition amongexchanges leads toa constrainedefŽ cient outcome, and a monopolistwould demand smallerguarantees than competitors demand in equilibrium. In this model,adverse selection interacts in subtleways with moralhazard. Adverseselection may result in higher,lower, or exactlythe same amount of guarantees as in thepure moral hazard case,depending onthe intensity of the moral hazard problem.That moral hazard mayserve to mitigate adverse selec- tionproblems is an interestingand novelaspect ofthis model. Theoften heard assertion that competitionamong exchanges leads necessarilyto low standards is notveriŽ ed in this model, and doesnot seem to have empirical support. There is norecorded majorincident of default by an Americanfutures exchange. The Barings episode,that has generatedmuch of the more recent criticismsof exchange competition, did notresult in lossesfor anyonebut thecreditors, stockholders, and employeesof the merchantbank. The margins deposited by Barings provided SIMEX with amplefunds tomeet the costs incurred in liquidat- ing thepositions. 16 Nonetheless,exchanges continue to use the threatof a “raceto the bottom” as ajustiŽcation for common marginpolicies. 17

16.Szala, Ginger, D. Nusbaum,and J. Reerink,“ BaringsAbyss,” Futures, XXIV(May 1995), 68 –74. 17.Ecofex, a group of27 European futures and options exchanges, coordi- natespolicy on marginand its members agree not to compete with each other on margins.(See Suzanne McGee in The Wall Street Journal, March 17,1995.) COMPETITION AMONG EXCHANGES 1051

Weshowedthat minimummargin requirements can be used tobeneŽ t agroupof tradersat theexpense of another.Since we postulated freeentry, and an inŽnite supply ofidentical potential exchanges,the zero-proŽ t conditionwould still hold in equilib- rium.However, if an exchangehas anatural advantage in serv- ing thegroup of traders that gains fromthe regulation, it would proŽt fromthe introduction of minimum margin requirements. Althoughwe limit the capacity ofexchanges to control posi- tions,we do not allow agentsto trade in morethan oneexchange, orexchangesto issue more than onecontract. In theliterature on incentives,it is wellestablished that nonexclusivecontracts af- fectthe nature of equilibria. 18 Similarly,in themodel in this paper, if exchangescannot enforce exclusivity, the equilibrium in Proposition2 is nolonger necessarily a Nashequilibrium. How- ever,in Santosand Scheinkman[2001] weshow that, when qualities areobservable, exchanges are restricted to issue a single contract,and agentscan trade simultaneouslyin severalex- changes,the equilibrium in Proposition2 is an “anticipatory equilibrium”in thesense of Wilson [1977]. If an exchangeoffers thecontract described in Proposition2, [ F *p , (1 2 p )F *p + p ], to agentsof quality p ,any entrantwho makes a proŽt will causethe incumbentexchange to make losses. In addition, oncethe incum- bentexchange exits, the entrant will losemoney. That is, the constrainedoptimum can beimplemented as an anticipatory equilibrium.In this sense,allowing agentsto trade simulta- neouslyin morethan oneexchange does not lead toexcessively lowstandards. In themodel in this paper thereare no shocks to the aggre- gateendowment. It is easyto accommodate such shocks, provided that exchangescan make the contract terms contingent on the aggregatestates. Bernanke [1990] arguesthat in practiceit may bedifŽ cult for an exchangeto make terms contingent in all possibleaggregate states, and that thegovernment has arolein protectingthe clearing and settlementsystems when rare, large, aggregateshocks occur. Bernanke contends that in October1987 theFed intervened to redistribute risks from the exchange clear- inghousesto the money center banks, and avoided asystemic crisis.If themonetary authorities need to intervene in extreme events,it maybe desirableto set standards forexchanges. How-

18.E.g., Bizer and deMarzo [1992], Arnott andStiglitz [1993], or Kahn and Mookherjee[1998]. 1052 QUARTERLY JOURNALOF ECONOMICS ever,these standards would haveto be dictated bythenature of thecontingencies that lead tothe monetary authorities’ intervention.

APPENDIX Investor’s Problem Suppose that an agentof group 1 is trading in an exchange with parameters( F ,K);that is,the exchange demands collateral of F (per unit) and pays in themoney contracts K (per unit). If D(w)denotesthe amount delivered to the exchange, by an agent whoreceives endowment w [ { x,y,z},wemay write the optimi- zation problemof agroup1 agentas 19

Problem p (F ,K) 1 [u(c(x)) 2 m max{( 2 u 2 D(x)),0}] 2 p max + [u(c( y)) 2 l max{(u 2 D( y)),0}] , {u ,D} 2 1 2 p + [u(c(z)) 2 l max{(u 2 D(z)),0}] 5 2 6 subject to c( x) 5 x 2 D( x) 1 max{u ,0}K c( y) 5 y 2 D( y) 1 max{ 2 u ,0}K c( z) 5 z 2 D( z) 1 max{ 2 u ,0}K z $ max{u ,0}F and x $ max{2 u ,0}F D( y), D( z) $ max{F u ,0} and D(x) $ max{2 F u ,0}. TheŽ rstthree constraints deŽ ne the income of the agent who buys u units oftheasset and choosesto deliver D(w) in state w [ { x,y,z}.Thefourth constraint expresses the fact that,if an agent goeslong (short), the collateral must not exceed z (respectively, x).Thelast constraintstates that deliveriesare nonnegative, and that if an agenthas an obligationto deliver to the exchange, he will haveto deliver at leasthis collateral. 1 Problem p (F ,K)has auniquesolution. Write ( u p ,

19.Implicit in this formulation is the fact thatagents never post excess collateral,and that in each state agents spend all their income. COMPETITION AMONG EXCHANGES 1053

[Dp (w)]w [ { x,y,z})forthe solution to p (F ,K).Sincethe optimiza- 2 tionproblem for group 2 is themirror image of p (F ,K), u p = 1 2 u p .Hence,the market clearing condition in themarket for the assetis automaticallysatisŽ ed. Equilibrium will depend onlyon 2 thesupply ofcontracts by exchanges.Further, Dp (w) = Dp (w), justifying themissing superscript. The next lemma establishes formallythat agentsof group1 want togo long.

1 LEMMA 1.Assumptions 1and 2imply that, u p ,theoptimal posi- tionfor an agentof group 1 and quality p ,is nonnegative.

1 Proofof Lemma1. Suppose in fact that u p < 0. Let D* solve 1 u9 ( x 2 D*) = l .AssumeŽ rstthat 0 > u p # 2 D*.In this case, 1 1 Dp ( x) = 2 u p and using theŽ rst-ordercondition that u p must satisfy, weobtain

1 u9 ( x) , u9 ( x 1 u p ) 1 1 5 K[p u9 ( y 2 u p K) 1 (1 2 p )u9 ( z 2 u p K)] , p u9 ( y) 1 (1 2 p )u9 ( z), acontradictionto Assumption 1. 1 1 Next,assume that u p < 2 D* < u p F .In this case Dp ( x) = 1 D*,and again using theŽ rst-ordercondition that u p mustsatisfy, we obtain u9 ( x) , u9 ( x 2 D*) 5 l 1 1 5 K[p u9 ( y 2 u p K) 1 (1 2 p )u9 ( z 2 u p K)] , p u9 ( y) 1 (1 2 p )u9 ( z), again acontradictionto Assumption 1. 1 Finally considerthe case D* # 2 u p F .In this case, Dp ( x) = 1 1 2 u p F ,and oncemore using theŽ rst-ordercondition that u p must satisfy, weobtain

1 l 5 u9 ( x 2 D*)F 1 l (1 2 F ) # u9 ( x 1 u p F )F 1 l (1 2 F ) 1 1 5 K[p u9 ( y 2 u p K) 1 (1 2 p )u9 ( z 2 u p K)] , p u9 ( y) 1 (1 2 p )u9 ( z), acontradictionto Assumption 2. h 1 Noticethat since u p $ 0, Dp ( x) = 0.Assumption 1also guaranteesthat Dp ( z) = F u u p u ;that is,an agentwho receives the endowment z will deliveronly the collateral. This justiŽ es writing thesolution to problem p (F ,K) as a pair (u p ,Dp ),wherethe Ž rst elementis theposition of an agentof group 1 quality p , and the secondone is theamount delivered in state y. 1054 QUARTERLY JOURNALOF ECONOMICS

Let u *bethe solution to u9 ( y 2 u *) = l .Assumption 3,and thefact that u9 (0) = ` ,guaranteethat u * > z > F u . When receivingendowment y, if u p # u *,theagent fully delivers;while if u p > u *,theagent delivers only u *.By Assumption 2, u * > 0. Let u > u 1[u p > u *] bethe indicator function taking thevalue 1 if p * and

0otherwise,and similarlyfor 1 [u p # u *].ThenLemma 1 allows usto writethe consumption of an agentof group 1 and quality p as

(7) cp ( x) 5 x 1 u p K

(8) cp ( y) 5 y 2 Dp 5 y 2 (1[u p # u *]u p 1 1[u p > u *]u *)

(9) cp ( z) 5 z 2 u p F , where [u p ,Dp ]is theunique solution to problem p (F ,K). For each u $ 0, let D = 1[u # u *]u + 1[u > u * ]u * and

(10) gp (F ,K,u )

u9 ( x 1 u K) K 2 p 1[ ]u9 ( y 2 D) º u # u * . F 2 (1 2 p )F u9 ( z 2 u F ) 2 l [p 1[u > u *] 1 (1 2 p )(1 2 F )]G Thefunction g deŽnes the Ž rst-orderconditions for the optimal choice u p > 0.This choice must satisfy

(11) gp (F ,K,u ) # 0, with equality if u p > 0.These Ž rst-orderconditions deŽ ne the functions u p (F ,K) for p [ { p,q}.Sincewe assumedthat u0 < 0, and for u large, gp (F ,K,u ) < 0,thefunctions u p arewell deŽ ned. Further,these functions are smooth whenever they are positive, exceptfor the (measure zero) set of values of theparameters for which u p = u *,wherethe right-hand-side derivativesmay differ fromthe left-hand-side derivatives. Thenext lemma establishes that, when both types aretrad- ing in thesame contract, p agentsalways takelarger positions than q agents.

LEMMA 2.For any contract( F ,K), u p $ u q ,with strictinequality if F > 0 and u q > 0. Proofof Lemma 2. Thisfollows from equation (11), thecon- cavity of u,and Assumption 2. h

Exchange’s ProŽt Function Thenext lemma establishes that thezero-proŽ t lineis well deŽned. Recall that theproŽ t function P p (F ,K)was deŽned in equation(1) above. COMPETITION AMONG EXCHANGES 1055

LEMMA 3. For each 0 # F # 1,thereexists at mostone K such that u p (F ,K) > 0 and P p (F ,K) = 0. Proofof Lemma 3. Fix a F [ [0,1]. Thederivative of g with respect to u is deŽned for every u > 0, except at u *, and this derivativeis strictlynegative. Hence the function u p (F ,z) is Lip- schitz (see,e.g., Mas-Colell [1985], page 32) at any K where it is strictlypositive. The derivative ­ u p /­ K (that existsunless u p = u *, where ­ u p /­ K+ Þ ­ u p /­ K2 )satisŽes for each K > 0:

­ u p u p (12) . 2 . ­ K K Also,

1 P p (F ,K) 5 2 a p [p (u *1[u p (F ,K)> u *] 1 u p (F ,K)1[u p (F ,K)# u *])

1 (1 2 p )F u p (F ,K) 2 u p (F ,K) K].

Hence, P p (F ,z)is aLipschitz functionat any K such that u p (F ,K) > 0.Suppose nowthat K satisŽes P p (F ,K) = 0 and u p (F ,K) > 0.Clearly, 0 < K # 1. If u p (K) Þ u *equation(12), impliesthat ­ P p /­ K < 0.On theother hand, if u p (F ,K) = u *, thenwe may calculate the derivative of P p (F ,K)with respectto K using either ­ u p /­ K+ or, ­ u p /­ K2 .In any case,the derivative is negative.Since P p is Lipschitz, and has anegativederivative wheneverit is zero,it canonly cross zero once. h Lemma3 allows usto deŽ ne the zero-proŽ t lineas theset of (F ,K) such that u p (F ,K) > 0 and P p (F ,K) = 0.Notice that, in principle,for some F theremay exist no K with (F ,K) in the zero-proŽt line,but such K,ifit exists,is unique.

Equilibrium In orderto characterize the equilibrium for a givenmargin requirementwe set

(13) hp (F ,K,u ) º Ku 2 [p (1[u > u *]u * 1 1[u # u *]u ) 1 (1 2 p )u F ].

For a given F , if (K,u p )aresuch that gp (F ,K,u p ) = 0 and hp (F ,K,u p ) = 0,thenagents of group1 and quality p trading in an exchangewith terms( F ,K) will buy u p contracts,and make deliverychoices that will producezero proŽ ts forthe exchange.

LEMMA 4.If Assumption 4holds,there exists exactly one K(F ) such that P p (F ,K(F )) = 0 and u p (F ,K(F )) > 0. Further, K(F )is increasing,and u p (F ,K(F ))is decreasing. 1056 QUARTERLY JOURNALOF ECONOMICS

Proofof Lemma4. Suppose that F # [ (0,1) is suchthat ( F # ,K# ) # is in thezero-proŽ t line,and u p > 0is theassociated position. A simplecomputation shows that theLipschitz map G = ( g,h) : (0,1) 3 (0,1) 3 (0,` ) ® R2 satisŽes theconditions of theimplicit functiontheorem (see, e.g., Mas-Colell [1985], page 32), and # # # hence,there is aneighborhood W of F and U of (K,u p ), and a Lipschitz function H : W ® U such that G(F ,K,u ) = 0 with

(F ,K,u ) [ W 3 U if and onlyif K = H1 (F ) and u = H2 (F ). # Further,for u p Þ u *,thefunctions H1 and H2 aresmooth, and one canshow, using Assumption 4,that H92 < 0.We will provethe resultstarting fromvalues of F near1 and apply theimplicit functiontheorem to extend the construction of H2 to the whole interval.Let K(F ) = p + (1 2 p )F ,and noticethat K9 > 0. If F is closeenough to 1, Assumption 1guaranteesthat u p (F ,K(F )) > 0,and Assumption 3insuresthat u p (F ,K(F )) < u *. Hence, (F ,K(F ))is in thezero-proŽ t lineand, by theunique- nessestablished in Lemma3, K(F ) = H1 (F ), and u p (F ,K(F )) = H2(F ).Usingthe implicit functiontheorem, and thefact that H92 < 0,we can extend this constructionuntil eitherwe reach F = 0orwe reach a F * such that u p (F *,p + (1 2 p )F *) = u *. If thelatter occurs, the implicit functiontheorem guarantees that we can deŽne H2 in aneighborhoodof F *.In this neighborhood, if F < F *,themonotonicity of H2 insuresthat H2 (F ) $ H2 (F *) = u *. If H2 (F ) = u *, H1 (F ) = p + (1 2 p )F ,and, fromthe Žrst-ordercondition, we obtain

(14) u9 ( x 1 u *H1(F )) H1(F ) 2 (1 2 p )F u9 ( z 2 F u *) 2 l (1 2 p )(1 2 F ) 5 0. Notethat equation(14) alsoholds for F = F *.However,using Assumption 4,we can show that theleft-hand side ofequation

(14) is strictlydecreasing in F ,acontradiction.Hence, H2 (F ) > u *,and by uniqueness H1 (F ) = p u */H2 (F ) + (1 2 p )F , an increasingfunction of F . Since l > 0,we can establish aglobal bound for u p (F ,K)and, consequentlyfor H2 and H1 . We can use themonotonicity of H2 toextend the construction for any F $ 0. h Proofof Proposition 1 (i) Thisis established in Lemma4. (ii) By solvingfor K*p in equation(5), wemay rewrite (4) in the form, M(F *p ) = 0.Assumption 4impliesthat M9 < 0,and henceuniqueness follows. COMPETITION AMONG EXCHANGES 1057

Suppose Žrstthat asolutionexists to (4) and (5) with 0 #

F *p # 1. If 0 < F < F *p ,fromequations (4) and (5) weknow that thecontract [ F *p ,p + (1 2 p )F *p ]is onthe zero-proŽ t line.By Lemma4 weknowthat theposition u associatedwith thecontract (F ,K(F ,p ))is greaterthan u *. Hence,

p u * 1 (1 2 p )u F K(F ,p ) 5 , p 1 (1 2 p )F . u

On theother hand, if F $ F *p ,Lemma4 guaranteesthat the positiontaken by agentsalong the zero-proŽ t lineis lessthan u * and agentswho receive y will notdefault. Finally supposethat nosolution exists to equations (4) and

(5) in [0,1]. Since, l # l *p , u *p $ u *, where u *p is deŽned by equation (2). Hence,

M(0) 5 u9 ( x 1 u *p )p 2 l $ u9 ( x 1 u *p p )p 2 l *p 5 0, and, sinceno solution to (4) and (5) with F *p # 1 exists, M(F ) > 0 for each 0 # F # 1. Since K(F ,p ) # (1 2 p )F + p , and M(F ) > 0, K(F ,p ) < (1 2 p )F + p for all F < 1. h

Proofof Proposition 2. Takingthe derivative of the utility functionof an agentof quality p with respectto F along the zero-proŽt linewe obtain

dV dK 5 u u9 (c ( x)) 2 (1 2 p )[u9 (c ( z)) 2 l ] dF H p dF p J

5 u (1 2 p )(u9 (cp ( x)) 2 [u9 (cp ( z)) 2 l ]) p u * du 2 u9 (c (x)) 1 . p S u D dF [u > u *]

Firstconsider F > F *p $ 0.By Lemma4, 1 [u > u *] = 0, and hence using Assumption 4weobtain dV/dF < 0.Therefore,it is opti- malto lower the collateral requirement.

Secondconsider 0 < F < F *p . Then,

dV (1 2 p )u (u9 (cp (x)) 2 [u9 (cp (z)) 2 l ]) 1 du 5 u9 (cp (x))p u * 2 dF H u9 (cp (x))p u * u dF J

u9 (cp ( x))p u * 5 B F 1058 QUARTERLY JOURNALOF ECONOMICS where

(1 2 p )F u9 (cp (z)) 2 l 2 u9 (cp (x)) (15) B 5 eF (u ) 2 H K 2 (1 2 p )F S u9 (cp (x)) D J and F du e (u ) 5 2 . 0. F u dF eF (u )is theelasticity of the position with respectto the margin requirement.We next show that B > 0. Let

A 5 (1 2 p )F u [u0 (cp ( z))F 1 u0 (cp ( x)) K] , 0. Adirectapplication ofthe implicit functiontheorem yields

(1 2 p )F [u9 (cp ( x)) 1 l 2 u9 (cp ( z))] 1 A eF (u ) 5 . 2 u9 (cp (x))(K 2 (1 2 p )F ) 1 A Substituting theformula for the elasticity in equation(15) and manipulating theresulting expression, we obtain

A[u9 (cp (x)) K 2 (1 2 p )F (u9 (cp (z)) 2 l )] B 5 . [2 u9 (cp (x))(K 2 (1 2 p )F ) 1 A](u9 (cp (x))(K 2 (1 2 p )F )) Recalling theŽ rst-ordercondition for u $ u *,

u9 (cp ( x)) K 2 (1 2 p )F (u9 (cp ( z)) 2 l ) 2 l 5 0, we can write Al B 5 . 0. [2 u9 (cp (x))(K 2 (1 2 p )F ) 1 A](u9 (cp ( x))(K 2 (1 2 p )F )) h

Monopoly Assumethat qualities areobservable and s = 0. A monopo- list will maximizethe proŽ ts it canextract from each quality:

P p (F ,K) 5 a p 3 [p (1[u p # u *]u p 1 1[u p > u *]u *) 1 (1 2 p )u p F 2 u p K]. Thenext lemma shows that themonopolist sets margins equal to zero.

LEMMA 5.The optimal solution for the monopolist’ s problemis F *p = 0, for all p [ { p,q}.

Proofof Lemma 5. Thecontinuity of the function u p (F , K) guaranteesthat themonopolist has an optimal choice.If u p Þ u *, let m I and m # bethe positive, possibly inŽnite, multipliers associ- COMPETITION AMONG EXCHANGES 1059 ated with therestrictions that F $ 0 and F # 1,respectively. The Žrst-orderconditions of the monopolist are given by

dP p du p (16) } [p 1[ ] 1 (1 2 p )F 2 K] 2 u 5 0 dK u p # u * dK p

dP p du p (17) } [p 1 1 (1 2 p )F 2 K] dF [u p # u *] dF

1 (1 2 p )u p 1 (m I 2 m # ) 5 0. WeŽrstprove that, under the optimal contract, the agent takes a position u p # u *.Suppose that u p > u *.By combining(16) and (17), weobtain (18) [(1 2 p )F 2 K]

u0 (cz(p ))u p F 1 u0 (cx(p ))u p K 1 [u9 (cx(p )) 2 (u9 (cz(p )) 2 l )] 3 2 2 H u0 (cz(p ))F 1 u0 (cx(p )) K J m I 2 m # 5 . 1 2 p If (1 2 p )F 2 K < 0,thenthe left-hand side of(18) isnegative, whichnecessarily implies that m # > 0 and m I = 0; that is F = 1. But by Assumption 3,

(19) u9 ( y 2 u p ) , u9 ( y 2 z) , l 5 u9 ( y 2 u *), and hence u p mustbe smaller than u *,acontradiction.On the otherhand, if (1 2 p )F 2 K $ 0,thenthe Ž rst-ordercondition ofthe agent and Assumption 4showthat u p > u *cannever be optimal.It followsthat, under the optimal monopoly contract, u p # u *.Next,once again combining(16) and (17), weobtain a relationbetween K and F that canonly be met if either m I Þ 0 or m # Þ 0: # 2 2 m I 2 m u0 (cx(p )) K 1 p u0 (cy(p )) 1 (1 2 p )u0 (cz(p ))F 3 S 1 2 p D F p 1 (1 2 p )F 2 K G

5 u0 (cz(p ))u p F 1 u0 (cx(p ))u p K 1 [u9 (cx(p )) 2 (u9 (cz(p )) 2 l )]. GivenAssumption 4,it is immediatethat this equationcan only hold if m I > 0;that is,if F = 0. If u p = u *,considerthe function F o(K) deŽned by u p (F o(K),K) = u *.Theimplicit functiontheo- remguarantees that this functionis welldeŽ ned in an openset

U.UsingAssumption 4,it isimmediatethat (1 2 p )dF o/dK < 1, and hencethat themonopolist’ s proŽts aremaximized at k = inf U. Obviously k = 0isnota candidate. Thus,it mustbe true 1060 QUARTERLY JOURNALOF ECONOMICS that F o(k) [ {0,1}. But as equation(19) aboveshows, if F = 1, u p < u *. h

UNIVERSITY OF CHICAGO PRINCETON UNIVERSITY

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