Asset Pricing Under Endogenous Expectations in an

AssetPricingUnderEndogenousExpectationsinanArtificialStockMarketbyW.BrianArthur,JohnH.Holland,BlakeLeBaron,RichardPalmer,andPaulTayler*Dec12,1996*AllauthorsareaffiliatedwiththeSantaFeInstitute,whereArthurisCitibankProfessor.Inaddition,HollandisProfessorofComputerScienceandEngineering,UniversityofMichigan,AnnArbor;LeBaronisAssociateProfessorofEconomics,UniversityofWisconsin;PalmerisProfessorofPhysics,DukeUniversity;andTayleriswiththeDept.ofComputerScience,BrunelUniversity,London.2AssetPricingUnderEndogenousExpectationsinanArtificialStockMarketAbstractWeproposeatheoryofassetpricingbasedonheterogeneousagentswhocontinuallyadapttheirexpectationstothemarketthattheseexpectationsaggregativelycreate.AndweexploretheimplicationsofthistheorycomputationallyusingourSantaFeartificialstockmarket.Assetmarkets,weargue,havearecursivenatureinthatagents’expectationsareformedonthebasisoftheiranticipationsofotheragents’expectations,whichprecludesexpectationsbeingformedbydeductivemeans.Insteadtraderscontinuallyhypothesize—continuallyexplore—expectationalmodels,buyorsellonthebasisofthosethatperformbest,andconfirmordiscardtheseaccordingtotheirperformance.Thusindividualbeliefsorexpectationsbecomeendogenoustothemarket,andconstantlycompetewithinanecologyofothers’beliefsorexpectations.Theecologyofbeliefsco-evolvesovertime.Computerexperimentswiththisendogenous-expectationsmarketexplainoneofthemorestrikingpuzzlesinfinance:thatmarkettradersoftenbelieveinsuchconceptsastechnicaltrading,“marketpsychology,”andbandwagoneffects,whileacademictheoristsbelieveinmarketefficiencyandalackofspeculativeopportunities.Bothviews,weshow,arecorrect,butwithindifferentregimes.Withinaregimewhereinvestorsexplorealternativeexpectationalmodelsatalowrate,themarketsettlesintotherational-expectationsequilibriumoftheefficient-marketliterature.Withinaregimewheretherateofexplorationofalternativeexpectationsishigher,themarketself-organizesintoacomplexpattern.Itacquiresarichpsychology,technicaltradingemerges,temporarybubblesandcrashesoccur,andassetpricesandtradingvolumeshowstatisticalfeatures—inparticular,GARCHbehavior—characteristicofactualmarketdata.AcknowledgmentsWearegratefultoKennethArrow,LarryBlume,BuzBrock,JohnCasti,StevenDurlauf,DavidEasley,DavidLane,RamonMarimon,TomSargent,andMartinShubikfordiscussionsoftheargumentsinthispaper,andofthedesignoftheartificialmarket.Allerrorsareourown.AssetPricingUnderEndogenousExpectationsinanArtificialStockMarketbyW.BrianArthur,JohnH.Holland,BlakeLeBaron,RichardPalmer,andPaulTaylerIntroductionAcademictheoristsandmarkettraderstendtoviewfinancialmarketsinstrikinglydifferentways.Standard(efficient-market)financialtheoryassumesidenticalinvestorswhosharerationalexpectationsofanasset’sfutureprice,andwhoinstantaneouslyandrationallydiscountallmarketinformationintothisprice.1Itfollowsthatnoopportunitiesareleftopenforconsistentspeculativeprofit,thattechnicaltrading(usingpatternsinpastpricestoforecastfutureones)cannotbeprofitableexceptbyluck,thattemporarypriceoverreactions—bubblesandcrashes—reflectrationalchangesinassets’valuationsratherthansuddenshiftsininvestorsentiment.Itfollowstoothattradingvolumeisloworzero,andthatindicesoftradingvolumeandpricevolatilityarenotseriallycorrelatedinanyway.Themarket,inthisstandardtheoreticalview,isrational,mechanistic,andefficient.Traders,bycontrast,oftenseemarketsasofferingspeculativeopportunities.Manybelievethattechnicaltradingisprofitable2,thatsomethingdefinableasa“marketpsychology”exists,andthatherdeffectsunrelatedtomarketnewscancausebubblesandcrashes.Sometradersandfinancialwritersevenseethemarketitselfaspossessingitsownmoodsandpersonality,sometimesdescribingthemarketas“nervous”or“sluggish”or“jittery.”Themarketinthisviewispsychological,organic,andimperfectlyefficient.Fromtheacademicviewpointtraderswithsuchbeliefs—embarrassinglytheveryagentsassumedrationalbythetheory—areirrationalandsuperstitious.Fromthetraders’viewpoint,thestandardacademictheoryisunrealisticandnotborneoutbytheirownperceptions.3Whilefewacademicswouldbewillingtoassertthatthemarkethasapersonalityorexperiencesmoods,thestandardeconomicviewhasinrecentyearsbeguntochange.Thecrashof1987damagedeconomists’beliefsthatsuddenpriceschangesreflectrationaladjustmentstonewsinthemarket:severalstudiesfailedtofindsignificantcorrelationbetweenthecrashandmarketinformationissuedatthetime1FortheclassicstatementseeLucas(1978),orDibaandGrossman(1988).2ForevidenceseeFrankelandFroot(1990).3Toquoteoneofthemostsuccessfultraders,GeorgeSoros(1994):“this[efficientmarkettheory]interpretationofthewayfinancialmarketsoperateisseverelydistorted.…Itmayseemstrangethatapatentlyfalsetheoryshouldgainsuchwidespreadacceptance.”2(e.g.Cutleretal.1989).Tradingvolumeandpricevolatilityinrealmarketsarelarge—notzeroorsmall,respectively,asthestandardtheorywouldpredict(Shiller,1981,1989;LeroyandPorter,1981)—andbothshowsignificantautocorrelation(Bollerslevetal.,1990;GoodhartandO’Hara,1995).Stockreturnsalsocontainsmall,butsignificantserialcorrelations(FamaandFrench,1988;LoandMackinlay,1988;Sum