Peer effects and risk sharing in experimental asset markets - 1-s2.0-S0014292119300571-main

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)

UvA-DARE (Digital Academic Repository)

Peer effects and risk sharing in experimental asset markets

Gortner, P.J.; van der Weele, J.J.

DOI

10.1016/j.euroecorev.2019.04.001

Publication date

2019

Document Version

Final published version

Published in

European Economic Review

Link to publication

Citation for published version (APA):

Gortner, P. J., & van der Weele, J. J. (2019). Peer effects and risk sharing in experimental

asset markets. European Economic Review, 116, 129-147.

https://doi.org/10.1016/j.euroecorev.2019.04.001

General rights

It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)

and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open

content license (like Creative Commons).

Disclaimer/Complaints regulations

If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please

let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material

inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter

to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You

will be contacted as soon as possible.

ContentslistsavailableatScienceDirect

European

Economic

Review

journalhomepage: www.elsevier.com/locate/euroecorev

Peer

effects

and

risk

sharing

in

experimental

asset

markets

R

Paul

J.

Gortner

a

_,

_Joël

_J.

_van

_der

_Weele

b,c,∗

a Deutsche Bundesbank, Frankfurt, Germany b Tinbergen Institute, the Netherlands

c University of Amsterdam, Center for Experimental Economics and political Decision making (CREED), Department of Economics,

University of Amsterdam, Roeterstraat 11, Amsterdam 1018WB, the Netherlands

a

r

t

i

c

l

e

i

n

f

o

Article history:

Received 18 February 2018 Accepted 2 April 2019 Available online 16 April 2019 JEL classification: C92 D53 G11 Keywords: Peer effects Laboratory experiments Risk taking Asset markets

a

b

s

t

r

a

c

t

Weinvestigatethe effectofintroducinginformationabout peerportfoliosinan experi-mentalArrow–Debreueconomy.Confirmingthepredictionofageneralequilibriummodel withinequalityaversepreferences,wefindthatpeerinformationleadstoreduced vari-ationinpayoffswithinpeergroups. Informationalsoimprovesrisk sharing,as thedata suggeststhatexperiencingearningsdeviationsfrompeersinducesashifttomorebalanced portfolios.Inatreatmentwherewehighlightthehighestearner,weobserveareduction inrisksharing,whilehighlightingthelowestearnerhasnoeffectscomparedtoproviding neutralinformation.Ourresults indicatethatthe presenceofsocialinformation andits framingisanimportantdeterminantofequilibriuminfinancialmarkets.

© 2019ElsevierB.V.Allrightsreserved.

1. Introduction

Traders infinancial markets do not interactmerely through prices. The investment choicesof others are a source of informationandapotentialaspirationpointforone’sownearnings. Shiller(1993,p.167)arguesthat“Investinginspeculative assets is a social activity. Investors spend a substantial part of their leisure time discussing investments, reading about investment, orgossiping about others’ successesor failures in investing.” Modern technology facilitates peer influences: socialtradingnetworkslikeeToroorZulutradeproviderankingsofinvestorperformanceandallowinvestorstoimmediately observeandcopyothertraders’portfolios.Suchnetworksareenjoyingafastgrowingmembershipof‘socialtraders’.1

R _{The authors gratefully acknowledge financial support by the Center of Excellence SAFE, funded by the State of Hessen initiative for research LOEWE.}

Joel van der Weele gratefully acknowledges financial support from the NWO through a personal VIDI grant. We are highly indebted to Sascha Baghestanian who provided extensive feedback and commentary, and was a co-author on an early version of this paper. In addition, we thank the editor, two anonymous referees, Michael Haliassos, Michael Kosfeld, David Schindler, Oege Dijk, Jona Linde, Leonie Gerhards, Heiner Schumacher, Devesh Rustagi, Matthias Blonski, and seminar participants at the Grüneburg Seminar at the Goethe University Frankfurt, the University of California at Santa Barbara, Copenhagen University, Aarhus University and at the Labsi Workshop on Behavioral and Experimental Finance 2014 for useful comments. The views expressed in this paper are those of the authors and do not necessarily represent those of Deutsche Bundesbank.

∗ _{Corresponding author at: University of Amsterdam and Tinbergen Institute, the Netherlands.}

E-mail addresses: paul.gortner@bundesbank.de (P.J. Gortner), vdweele@uva.nl (J.J. van der Weele).

1 Between 2010 and 2016 the number of eToro-investors doubled from 1.5 to 4 million users. In roughly the same period eToro raised additional 31.5

million US Dollars to expand their businesses: financial instruments traded on eToro today range from indices, commodities, currencies and stocks to Bitcoin. Simon and Heimer (2012) show that trading on social platforms is characterized by substantial peer effects.

https://doi.org/10.1016/j.euroecorev.2019.04.001

Socialcomparisonsintraderinteractionsmayaffectequilibriuminassetmarkets.Inparticular,peoplewhoareafraidto fallbehindothersmaydisplayconformityinportfoliochoices,leadingtomultiplemarketequilibria(HeidhuesandRiedel, 2007; Schmidt, 2011). To date, there has been little empirical investigation of the impact of social concerns on general equilibriumoutcomes.Onereasonisthatequilibriumoutcomesarehardtoidentifywithobservationaldata,andsoarethe mechanismsbehindpeerinfluencesoninvestors.Inactualmarkets,peoplematchassortatively,makingithardtodistinguish socialinfluencefromselection.Controlledlaboratorystudiesthat candisentanglesucheffectshavefocussedonindividual decisionsinsteadofmarketinteractions.

Westudytheeffectofpeerinformationonrisksharinginexperimentalassetmarkets.Participants tradetwo risky as-setswithperfectlynegativelycorrelatedreturnsacrosstwoincomestates.Inasetoftreatmentsweintroduceinformation abouttheportfoliosofa“peergroup” composedofother,randomlyselectedparticipants.Exogenousvariation in informa-tionavailabilityandcontentallowsustotestitseffectonmarketoutcomes,specificallywhetherpeerinformationinduces conformity inequilibrium portfoliochoice. Indeed,we find that peerinformationreduces within-groupvariation inpeer earnings in each income state. The introduction of peerinformation also increases diversification, causingrisk takingto drop27%bytheendoftheexperiment.Thislastfindingappearstobedrivenbyaformofsociallearning:subjectsreactto being“earningoutliers” withintheirgroupbyreducingtheirexposure.

Some ofour treatments haverankings that symbolicallyhighlight eitherthehighest orlowestperformer, a featureof manytypesofinvestorinformation.2_{Inlinewiththenotionthatpositionalconcernsmatterformarketoutcomes,wefind}

that thesocial framingofpeerinformation matters.Symbolicrecognitionforthe highestearnerpartiallynegatesthe de-creaseinportfoliodiversificationthatweseeinthetreatmentswithinformationbutwithoutrankingsorintreatmentswith aspotlightonthelowestearner.

Toour knowledge, thisisthe first evidencethat peer informationaffects equilibriumoutcomesin assetmarkets, and providesasocialbenchmarkthatreducesrisktaking.Thesefindingshighlightsocialinfluencesonmarketoutcomesthrough differentchannelsthanherdingorbubbleformation,whicharethefocusofthecurrentliterature.Abetterunderstandingof thesechannelsiscrucialatatimewhenonlinetechnologymakesitevereasiertocompareourinvestmentsandoutcomes tothoseofothers.

2. Literature

Our papercontributes to severalstrands of literature in both finance and economicson the social aspects of market behavior. The design is inspired by theories about the relation betweensocial preferences and equilibrium outcomesin marketsforriskyassets(HeidhuesandRiedel,2007;Schmidt,2011).Thesetheoriespredictthatsocialpreferencescanlead to multipleequilibria, aswealso demonstrateinourmodelin AppendixA.We indeedfindevidence forconformitythat isassociated withmultipleequilibria. Toourknowledge,therehas beenlittleempiricalinvestigation oftherole ofsocial preferences inmarkets foruncertainassets,even though thereis alarge literature onsocial preferencesin markets with certainoutcomes(e.g. Dufwenbergetal.,2011;FehrandSchmidt,1999).

Thereare afewpapersthat lookattheeffectofpeerinformationinexperimental assetmarkets, buttheseareguided by differentquestions. Schoenberg andHaruvy (2012)show that seeingtheearnings ofthehighestearningindividual re-ducessatisfaction andincreasestheprevalence ofpricebubbles. Oechssleretal.(2011) enablesubjectsto chatwithone anotherduringthetradingphase,whereasubsetoftradershassuperiorinformationregardingfundamentals. Communica-tionreducesthelikelihoodofpricebubbles. MengelandPeeters(2015)findthatsocialcomparisonswithinmarketsreduce participants’willingnesstotake risksrelative toa non-market setting.Comparedto thesepapers,we investigatea differ-entsetofhypotheses.Mostimportantly,wedonotlookatbubbles:sinceportfoliosareresetineachperiod,thereislittle scopeforspeculation.Wearealsonotconcernedwithherding,i.e.,peoplediscardingtheirprivate information,asthereis noasymmetric informationinourmarkets. Instead,we focusonthe importanceof preferencesoverrelative income,and ourmainoutcomevariableisnotthepriceoftheasset,buttheamountofconformityanddiversification.

Thereisasizableliteraturethataimstoidentifypeereffectsinindividualfinancialdecisions.Partofthisliteratureuses field datainstockmarketparticipationcombinedwithinformationonsocialtiesorspatialdistributionoftraders.Several papersshowthatpeerschoicesmatterinstockmarketparticipation(Hongetal.,2004;KaustiaandKnüpfer,2012),trading decisions (Hackethal etal., 2014; Hong etal., 2005; Kelly et al., 2000;Shive, 2010) andrisky lifestyle choices(Card and Giuliano,2013).Thesepaperssometimesusenetworkdata,orapproximatepeersbyspatialproximity,buttypicallycannot disentanglethe mechanismsof peerinfluence.An exception is Bursztynetal. (2014),who conduct afield experimentin whichtheycandistinguishbetweenthechannelsoflearningandsocialpreferences,showingthatbothchannelsmatter.

Inaddition,arapidlygrowingnumberoflaboratoryexperimentscorroboratestheexistenceofpeereffectsinrisktaking (see TrautmannandVieider,2012,foranoverview). GantnerandKerschbamer(2018)showtheoreticallythat“convex” social preferencesleadtoconformityandconfirmthisexperimentally. LindeandSonnemans(2012)and Schwerter(2013) demon-stratethatportfoliochoicesdependona“socialreferencepoint”,theincomeofanotherparticipantintheexperiment. Dijk etal.(2014)and Fafchampsetal.(2015)findthatunder-performersstarttakingmoreriskinlaterdecisionroundstocatch

2 Social trading websites often highlight the highest earners in a given period or asset class, and so do investor magazines like Investment Week , which

Table 1

The dividend structure of the assets, expressed in experimental cur- rency.

Hot weather Cold weather Exp. Dividend Ice-cream (I) 100 0 50

Gloves (G) 0 100 50

upwiththeothers. LahnoandSerra-garcia(2015)demonstratethatbothlearningandincomecomparisonsplayan impor-tantroleindecisionmakingunderuncertainty, Baultetal.(2011)and Frydman(2015)showsimilarfindingswithadditional neurologicalevidence. Kirchleretal.(2018)showthatrankingsinducefinancialprofessionalstotakemorerisk.Bycontrast,

CorazziniandGreiner(2007)donotfindaneffectofpeerinformationinsequentialriskydecisions.Ourpapergoesbeyond thisliterature,byshowingthatpeerinfluencesaffectnotjustindividualportfoliochoices,butalsotheoutcomesofmarkets consistingofmanytraderswhointeractinrealtime.

Finally,wecontributetotheexperimentalliteraturetestinggeneralequilibriumpredictionsinassetmarkets.The litera-turefindsmixedresultsregardingthepredictivepowerofgeneralequilibriumtheory.Whetheramarketreachesequilibrium dependsontheprecisedetailsofthemarket’sdesign.Ourresultswithoutpeerinformationarecomparabletostudieswith similar market designs. Bossaertset al.(2007)look atportfolio choice in a large-scale market witha more complex as-setstructure,and,likeourpaper,findpersistentdeviationsfrompredictedequilibriumholdings.Theexperimentalmarkets in Weber etal. (2000) are almost identical to our markets without peerinformation, andwe replicatetheir findings of imperfectrisksharingandsubstantialoverpricingofassets.

3. Marketdesign

Inthissection,wedescribethedesignoftheexperiment.FullinstructionscanbeaccessedviatheonlineAppendix.3

3.1. Payoffsandmarketstructure

Weconductanexperimentalopenbook,multi-unitdoubleauction.Eachsessionconsistsofonemarketwith10traders. Allpayoffs are denotedin experimental currency (ECU) where 100 ECU = 1.50 euros. There are two equiprobable states ofnature and two tradable assets that generatedividends. Tradersare alsoendowed withcash, which pays no interest. Dividendsdepend onthe“state”, whichisrandomly determinedattheendofeach period.Thisassetstructureis similar tothatin Weberetal.(2000).Tomaketheassetstructurelessabstractandreduceconfusionamongsubjects(see Kirchler etal.,2012),assetsare framedasstocksinan “Ice-cream” (I)anda“Glove” (G)manufacturer, andthe stateofthe world isdescribedaseither“hot” or“cold” weather.Thedividendstructure givenin Table1wasalsochosentobe assimpleas possibletoavoidconfusion.

Agentstradefor10periodsthat last150seach.Shortsellingandborrowingarenotallowed. Atthebeginningofeach period,theendowmentportfolioforeachtraderisrandomlychosen(seebelow),attheendofeachperiodthestateis ran-domlydeterminedandpayoffsarerealized.Themonetarypayoff ofeachagentisdeterminedattheendoftheexperiment byrandomlyselectingasingleperiodforpayment.Inordertopreservesocialcomparisons,thisrandomizationwasdoneat thesessionlevel,sothateachsubjects’payoffsarebasedonearningsinthesameperiod.

3.2.Randomendowmentsandzeroaggregaterisk

Assetholdings were reset after each tradingperiod.At the beginning ofeach period,each traderreceived a cash en-dowmentof500ECU.Toencouragetrading,eachsubjectstartedoutwitharelativelyskewedportfolio,whichconsistedof either10Iassetsand0Gassets,orof0Iassetsand10Gassets.Intotal,fiveofeachofthosetwokindsofportfolioswere randomlyallocatedtothe traders.Thisensuredarandom compositionofendowmentsineach peergroupineach round, whilekeepingthetotalamountofassetsinthemarketfixedat50assetsofeachkind.Thusaggregateriskwaszeroineach marketandeachround.

3.3.Peerinformationandtreatments

Ineachsession,wedividedsubjectsintotwo “peergroups” of5traders,indicatedintheinstructionsasthe“red” and “blue” group.Traderscouldtradewithparticipantsfromeithergroup.Toensurethatincomecomparisonscouldtakeplace onlywithinthepeergroup,therealizationofthestatewasindependentforbothgroups,soitwaspossiblethattheweather was“hot” in onegroupand“cold” intheother.Subjectslearnedonlytheincomerealizationfortheirown groupandnot thatfortheothergroup.

Table 2

Example of peer portfolio information. This example reflects the beginning of the trading period. In the INFO-WIN treat- ment, all columns are visible. The last column’s caption reads “Highest Earnings” and signifies the number of times a trader had the highest earnings in his reference group in previous rounds. Correspondingly in the INFO-LOSE treatment, the column’s caption reads “Lowest Earnings” and shows how often a trader had the lowest earnings within the group. In the INFO treatment the last column is missing. In the PRIVATE treatment, additionally only the row marked YOU is visible. The table is updated in real time during the trading round.

ID I Assets G Assets ECU Earnings Earnings Lowest/highest

HOT COLD earnings

2 10 0 500 1500 500 ∗∗∗

5 10 0 500 1500 500

YOU 0 10 500 500 1500 ∗

3 0 10 500 500 1500 ∗∗

1 10 0 500 1500 500

Insomeofthetreatments,subjectsreceivedinformationabouttheportfoliosoftheir peergroup,whichwaspresented atthetopofthetradingscreenasin Table2.ThefirstcolumnshowsthesubjectID,thesecondandthirdshowthenumber of each assetin the portfolio, the fourth column showsthe amount of ECU held, the fifth and sixth column show the (hypothetical)payoffsofthecurrentportfolioincaseofhotandcoldweather.Thefinalcolumnshowsthehighestorlowest earnerinpreviousrounds(seebelow).

Weconductthefollowingtreatments:

PRIVATE.Subjectshadnoinformationabouttheothertraders,exceptwhattheyknewfromthegeneralinstructions,and fromthe postedbids andasks. Table 2wastherefore empty,exceptforthe rowofthe subject(YOU).Information provisionabouttheownportfoliowasthusconstantacrosstreatments.Inaddition,thelastcolumnwasmissingfrom thetable. Traders werestill assigned toone oftwo (placebo) groupsfordetermining payoffs(see above),butthey wereignorantofbeingpartofthatgroup.

INFO.Duringthetradingperiod,subjectswereinformedabouttheportfoliosoftheirreferencegroup(i.e.eithertheblue orthered group)asindicated in Table 2.Thisinformationwasupdated inrealtime so thatanynewtrade would immediatelybereflectedinthetable.Thelastcolumnwasmissingfromthistable.

INFO-WIN. Subjectsreceived the same informationasin the INFO treatment. Atthe end ofeach trading period,after thestateoftheworldhadbeendeterminedweprovidedearningsrankingswithineachpeergroup.Additionallythe “highestearning trader” received a purely symbolic‘star’. Accumulated stars were displayedin the last columnof

Table2,andcouldbeobservedbyallsubjectsinthepeergroupinallsubsequentrounds.

INFO-LOSE. This treatment wasidentical to the INFO-WINtreatment, except that the “lowest earning trader” was an-nouncedandgotastarinsteadofthehighestearningtrader.

DifferencesinoutcomesbetweenthePRIVATEandINFOtreatmentallowustoidentifytheimpactofpeerinformationon market outcomes.The INFO-WINandINFO-LOSEtreatment identifytheadditionaleffectsofperformance rankings,where the former provides a symbolicreward for high earnings andthe lattera symbolicpenalty forlow earnings. Note that instructionswerethesameforallparticipantswithinagiventreatment,andallparticipantshavefullinformationaboutthe marketstructureandfundamentalvalueoftheassetstoruleoutherdingorinformationcascades.

3.4. Elicitationofriskpreferencesandbackgroundinformation

Aftermarkettradinghadconcluded,weelicitedsomefurtherinformationaboutthepreferencesandbackgroundofthe participants.

Riskpreferences. We measured risk preferencesusing the bombrisk elicitation task(BRET) developedby Crosetto and Filippin(2013).Subjectshadtochoosehowmanyboxestocollectfromapileof36boxes.Witheachcollectedbox, subjectsearneda monetary paymentof10ECU (=15 eurocents).One randomlychosen boxcontainedabomb.The participantdidnotknowinwhichboxthe bombwaslocated,andifshecollectedit sheearnednothing.Thus,the risk ofearning nothingincreases exponentially witheach collectedboxwhile payoffsincrease linearly,so that the decisionwhentostopcollecting isa goodproxyforsubjects’risk preferences(CrosettoandFilippin,2013). Another reasontochoosethistaskisthatitiseasytoexplaintosubjects.

Strategyquestionnaire.Weaskedsubjectsdirectlyabouttheirtradingstrategies,includingwhethertheyengagedin spec-ulationortried toequalizethenumberofbothassetsintheir portfolio,and,intheINFO treatments,whetherthey wereinfluencedbyothertraders’portfolios.Answerweremadeonathree-pointscale(‘Yes’,‘Sometimes’,‘No’). Finally,we askedsome standard control questionssuch asgender, field ofstudies, andprevious participationin asset marketexperiments.4

4 In the first wave of sessions we elicited a measure of social value orientation based on _{Murphy et al. (2011) at the end of the experiment. We did not}

have a clear hypothesis on these variables. We found that these data were noisy and did not have any explanatory power. Since the elicitation was rather time consuming we did not elicit them in the second wave (see Footnote 5_).

3.5.Procedures

Allsessions wereconductedat theFrankfurt LaboratoryforExperimental EconomicResearchatthe GoetheUniversity Frankfurt,thefirst20inthespringof2014,additionaleightsessionsinthewinterof2017.Treatmentswerebalancedover time.5 _{Subjectswere recruited usingORSEE(Greiner,2003).Ineach treatment, weconducted7 sessions/marketswith10}

traderseach.OnesessionintheINFOtreatmentwasrunwith8insteadof10subjects,soatotalof278subjectsparticipated intheexperiment. The experimentlastedapproximately90min.Averageearningswere 22.86euros,witha minimumof 10.34eurosandamaximumof33.82euros.

After the experimenter hadread the instructions out loud at the beginning of the experiment, subjects answered a numberofcontrol questionstotestunderstandingandplayedapracticeroundtofamiliarizethemselveswiththetrading environment.Instructionsfortheelicitation ofrisk preferencesandquestionnaireswere providedonscreen.Programming wasdoneinz-Tree (Fischbacher, 2007). Atthe endoftheexperiment, subjectswere calledforwardone byone andpaid privately.

4. Hypotheses

The PRIVATEtreatment functions asa baseline against whichwe evaluate the effectsof peer information.Under the assumptionthatalltradersareself-interestedandriskaverse,acommonassumptioninassetpricingmodels(e.g. Bossaerts etal., 2007), Arrow-Debreu generalequilibrium theory predicts that the unique competitive equilibriumin the PRIVATE treatment features full risk sharing. We verify this in our theoretical model in Appendix A. We expect the risk sharing strategyto be salientsincethe assetstructureis simple.Sinceall investorshavethe sameinformationthere isno scope forherding(inthesense of Bikhchandanietal.,1992).Furthermore,asendowmentsareresetineachperiod,thereisvery littlescope forspeculation.Becausethereisnoaggregatemarketrisk,bothassetpricesshouldbeequaltoexpectedvalue toavoidtheexistenceofarbitrageopportunities.

Despite these considerations, earlier research on similar markets has found imperfect risk sharing. Weber et al. (2000)studyasimilarmarketdesignandfindthattheexistenceofan endowmenteffectresultsinoverpricingand under-diversification ofportfolios. Bossaertset al.(2007)look atportfolio choice ina large-scale market witha more complex assetstructure,andalsofindpersistentdeviationsfrompredictedequilibriumholdings. Ackertetal.(2016)lookatportfolio choiceoutsideamarketcontext,andshowthatbehavioralbiasesleadpeopleawayfromportfoliodiversification.

4.1. Theeffectofpeerinformation

Onewell-established resultinthe social preferenceliterature is that people dislike earninglessthan their peers (e.g.

BoltonandOckenfels,2000;Fehr andSchmidt,1999;ZizzoandOswald,2001). In AppendixA,wemodelsuchpreferences inthecontextofageneralequilibriumsettinginafinancialmarketlikeours,andshowthatsuchpreferencestranslateinto adesireforconformity.Specifically,holdingaportfoliothatdivergesfromthatoftheothergroupmemberscreatesasocial riskofearninglessthantheothers.Ifsubjectsare sufficientlyconcerned aboutthisrisk,multipleequilibriaexistinwhich alltradersinapeergroupholdthesameportfolio.Some equilibriafeatureimperfect risksharing,eveniftradersarerisk averseovertheirown monetaryoutcomes.When tradersareapproximatelyriskneutralovertheir ownmonetarypayoffs, asmaybethecaseinourmarketswithrelativelysmallstakes,equilibriamayfeaturearbitrarylargeamountsofrisktaking. Toinvestigatetheseissues,theINFOtreatmentintroducespeerinformation,andthusthepossibilitytocompareone-self toothers.ThetradingscreenintheINFOtreatmentnotonlygaveareal-timeoverviewofallportfoliosinthegroup,butit alsoshowedthepayoffsofeachgroupmemberineachstateoftheworld forthecurrentportfolios.Thisallowedan easy comparisonofpayoffsinbothstateswiththoseofothersubjects.

Hypothesis1. Thewithin-groupvarianceofearningsineach stateoftheworldwillbe lowerintheINFOtreatment than inthePRIVATEtreatment.

4.2.Theeffectofsymbolicrewards

Performance rankings forfinancial professionals are commonplace in the finance industry (Kirchler et al., 2018). For instance,the socialtrading websites mentionedin theintroduction oftenhighlight thehighest earnersin a givenperiod orassetclass.To simulatetheseconditions,we conduct twotreatments in whichwe provide payoff rankingsat theend ofeach tradingperiod, and providesymbolic, non-financial recognition for eitherthe best or the worst performer.6 _We

5 We ran these extra sessions in order to investigate a curious, non-hypothesized pattern: the first 20 sessions showed that risk aversion was significantly

higher after the INFO treatments compare to the PRIVATE treatment. To investigate more deeply whether this change was due to the different market experiences in these treatments, the sessions in 2017 featured an additional risk aversion task before the markets started. The risk aversion effect appeared not to be robust in our new sessions. Specifically, we did not run these sessions to improve p -values, as all the same differences between our four treatments were present and statistically significant in the original sessions (see Baghestanian et al., 2014 ).

6 Our focus on symbolic recognition distinguishes our setup from the literature on tournament incentives and asset market bubbles ( _{Cheung and Coleman,}

4.61 4.69 4.01 3.72 4.03 3.69 4.13 4.29

0

.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Average Exposure

PRIVATE

INFO

INFO-LOSE

INFO-WIN

Full Sample

Last 5 Periods

Fig. 1. Mean exposure for all periods and for the last five periods in each of the four different treatments. Exposure is defined as the absolute difference between holdings of the two assets. It is a measure of the riskiness of a trader’s portfolio.

hypothesizethatintroducingsymbolicrewardsforthehighestearnerwillincreaseaggregateexposure,becausetakingmore riskincreasesthechanceofearningthemost.7

Whenit comestotheeffectsofhighlightingthelowestearner,there isevidencethatpeopledislikeoccupying thelast placeinearningsranking(Kuziemkoetal., 2014), andgenerallydislikeearninglessthan others(FehrandSchmidt,1999). Participants inourmarketscanavoidbeingthelowestearnerby choosingalessextremerisk exposurethanothers.Over time,competitionforincomerankswillthereforeleadtoincreasingdiversification,comparedtothecasewhereno perfor-mancerankingsweregiven.

Hypothesis2. ComparedtotheINFOtreatment,theintroductionofrankingsandsymbolicrecognitionleadsto (a) higheraverageportfolioriskintheINFO-WINtreatment,wherewehighlightthehighestearner. (b) loweraverageportfolioriskintheINFO-LOSEtreatment,wherewehighlightthelowestearner. 5. Marketoutcomes

Beforewe testourhypotheses,we provideagraphicaloverviewofthe primarymarketoutcome – risktaking– across treatments. Ourmeasure is theabsolutedifference betweenthe numberof Iandthe numberof G assetsinthe end-of-periodportfolio.Werefertothismeasureofriskinessofindividualportfoliosas“exposure”.Anexposureofforexample4 impliesapayoff differenceof400ECU(6 Euros)betweenbothstatesoftheworld.Welookatendofperioddataonly,as thesereflecttheresultoftradinginthesessionaggregatedoveragivenperiod.

Exposureacrossallsessionswasonaverage4.2. Fig.1showsaveragesbytreatmentoverallperiodsandforthelastfive periods,wherebehaviormayhaveconvergedmorecloselytoequilibrium.Inaddition, Fig.2showsthedynamicsofmean exposurebytreatmentoverthe10tradingperiods. AppendixBprovidesthedescriptivestatisticsin TableB.1and TableB.2, aswellasgraphsofthetimeseriesindividualsessionsin Fig.B.1.

Inthefirstperiod,meanexposurelevelsarecomparableacrosstreatments.Afterthat,exposureinthePRIVATEtreatment staysroughlyconstant,whilethereisadropinexposureintheINFOtreatment,see Fig.2(a).Similarly, Fig.2(b)showsthat exposureintheINFO-LOSEtreatmentdropsinitiallyandstabilizesinthelastfiveperiods.TheINFO-WINtreatmentdisplays quitesomevolatilityinexposurelevels,withapronouncedupwardjumpinthelastperiod.

7_{Roussanov (2010) shows theoretically that a desire to get ‘ahead of the Joneses’ may lead to less diversified portfolios. Fafchamps et al. (2015) , Dijk}

et al. (2014) and Kirchler et al. (2018) show experimentally that low earners in the early part of their respective experiments adopt more risky strategies to catch up with those who are performing better. Bault et al. (2008) show that gains loom larger than losses when in competition with others, and people take more risk if they can get ahead of a prudent opponent. A strategy of “imitate the luckiest” may also lead to a proliferation of risk taking ( Offerman and Schotter, 2009 ). Symbolic awards for the highest earner also have important effects on effort outside financial markets ( Kosfeld and Neckermann, 2011 ).

3 4 5 6 Exposure 2 4 6 8 10 Period PRIVATE INFO

(a) Mean exposure PRIVATE vs INFO.

3 4 5 6 2 4 6 8 10 Period

INFO INFO-LOSE INFO-WIN

(b) Mean exposure INFO treatments.

Fig. 2. Time series of exposure. The panel on the left, (a), shows mean end of period exposure for the PRIVATE and the INFO treatment. Each time series corresponds to one treatment mean. Panel (b) on the right hand side plots the treatment average for all INFO treatments. INFO-treatments give traders information on the portfolios of their exogenous reference group. INFO-WIN and INFO-LOSE, in addition, give a symbolic reward to either the best or the worst performer in each period respectively. In the PRIVATE treatment, traders do not have information about other traders.

Giventhat eachtraderstartedwithan initialexposureof10,it isclearthatmarkets areusedto reduceportfoliorisk. However, perfectrisk sharingis not achieved inany singleperiod. Thisfailure tofully diversify is in linewithprevious evidenceof Weberetal.(2000)and Bossaertsetal.(2007).Thepresenceofriskseekingtraderswhodriveexposureupwards maybe a reasonwhyourmarkets fail to achieve perfectdiversification.8 _{Anotherreasonmaybe that tradersdisplay an}

endowmenteffect,asdemonstrated in Weber etal. (2000).This last explanation isconsistent withmarket prices inour experiment,which aresubstantially abovethe fundamentalvalue of50. AppendixC providesa morein-depthanalysisof prices.

Wenowturntoamoredetaileddiscussionofourhypotheseswiththeassociatedstatisticaltests. Section6discussesin detailthenon-hypothesizeddropinexposureintheINFOtreatment.

5.1. Conformityinassetmarkets

Hypothesis1predictsthatduetopreferencesoverrelativepayoffs,peerinformationinducesconformityandreducesthe variationin grouppayoffsin eachstate. Toinvestigatethis hypothesis,we usewithin-groupvariance ofearnings ineach payoff stateasa measureof conformity.9 _{Forevery peergroup offivetraders, wecalculate thewithin-groupvariance of}

earnings(GVar)inperiodtasfollows: GVart:=  i∈K



xH i,t− ¯xHi,t



2 +



xC i,t− ¯xCi,t



2 . (GVar)

Here,Kisthesetofgroupmembers, ¯xa

i,t istheaveragepayoff ofthisgroupifthestateoftheworldisa∈{H,C},andxai,t is thecorrespondingpayoff ofanindividuali.

WefindthatGVarishigherinthePRIVATEcomparedtotheINFOtreatment,butthiscouldsimplybeduetothehigher levelofexposureinthesesessions.Tocontrolforthis,wenormalizethegroupvariancebydividingwiththegroup’sshare oftotalvariancewithinasession(TVar).Tocalculatethelatter,weusethefactthattheaveragepayoff ineachperiodisthe startingvalueofeachportfolio,namely1000unitsofexperimentalcurrency:

TVart:=  i∈K



xHi,t− 1000



2 +



xC_i,t− 1000



2. (TVar)

Thus,our measureof conformityGVar/TVar doesnot dependon theoverall variance inexposure within thesession. We average over all periods for a session, leavingus withone observationper peergroup (2 observations per session,and

8 Indeed in the BRET, 30% of traders make risk seeking choices. Consistent with this line of reasoning, we find a modest, although statistically insignificant

rank-correlation between average session exposure and average session risk tolerance ( ρ= 0 . 30 and p = 0 . 12 ).

9 We use earnings rather than portfolios or exposure, because the social preferences models we use to derive our hypotheses (see _{Appendix A ) are}

defined over payoffs. Measures based on portfolio holdings may not neatly map into payoffs due to differences in cash holdings and/or intra-period gains and losses. The design facilitated payoff comparisons, as the trading screen in the INFO treatments showed the (virtual) earnings of each group member in each state of the world, which were updated in real time.

.5

1

PRIVATE

INFO

GVar/TVar

.5

1

PRIVATE

INFO

Fig. 3. Conformity measure (GVar/TVar) by treatment averaged over all periods (two leftmost panels) and over the last five periods (two rightmost panels). Each panel shows means with 95% confidence intervals and distribution of individual observations.

14 observationsper treatment). Theobservations inboth thePRIVATE andINFOtreatment are representedgraphicallyin

Fig.3.

Wetestfortreatmentdifferencesstatisticallyusingnon-parametricWilcoxonrank-sumtest(alsocalled Mann–Whitney-U-testorMWU),andfindthat thedistributionofGVar/TVarissignificantlydifferentintheINFOcomparedtothePRIVATE treatment(p=0.033,one-sidedMWUtest;averagesare0.89and0.85forPRIVATEandINFO,respectively).Becauseweare testingequilibrium predictions,we should allow foran initial convergenceperiod. Indeed, Fig. 2(a)showsthat there are trendsinexposure inthe INFOtreatment.Therefore,weperformthesameanalysisforthesecond halfofthe experiment only(i.e.,thelast5periods),andfindthatthesignificanceoftheresultincreases(p=0.022,one-sidedMWUtest;averages of0.90and0.81forPRIVATEandINFO,respectively).Thefindingthat conformitybecomesmorepronounced overtimeis consistentwiththeideathatthisisanequilibriumphenomenon.10

Howdoesconformitycomeabout?Asderived in AppendixA,intheINFO-treatment equilibriamightobtainwhereall groupmembersholdmoreofoneassetthantheother.Thus,intheseequilibriaparticipantsshouldskewtheiracquisitions towardsoneofthetwoassets.InthePRIVATEtreatment,thereisnoreasonforgroupmemberstoholdthesameportfolio, andhencewe should notexpect skewedpatternsofacquisition. Totest whethersuch asymmetrictradeflows doindeed characterizeourINFOtreatment,we define“risktransfer” betweengroupsastheamountbywhicheithergroupincreased itspayoff intheHOTorCOLDstate:



xt:=







 i∈K

(

x_i,t− yi,t

)







(RiskTransfer)

wherexdenotesstock-holdingattheendofaperiodandyatbeginningofaperiod,ttheperiod,andiisasubjectingroup K.



xt isameasureofthenetincreaseinagivenassetinagroupduringthetradingperiodunderconsideration.Wetake theabsolutevalue inordertogetameasurethatisthesameforbothgroups,sothereisonlyoneobservationper period andsession.

InthePRIVATEtreatment,weexpectbothgroupstoholdthesameportfolioonaverage.Sincetheaveragegroup endow-mentconsistsofbothassetsinequalproportion,risktransfershouldbezero.IntheINFOtreatmenthowever,membersof one groupmightaccumulate moreofoneasset, resultinginapositive risktransfer. Wetest thishypothesis withaMWU testusing14observations,forboththecompletesample(averagingallperiods)andthelastfiveperiods.Despitethe rela-tivelylowpowerofthetest,wefindsuggestiveevidenceofincreasedrisktransferintheINFOtreatment,with(one-sided) p-valuesclosetoorjustbelowconventional significancelevels(p=0.056 forthe completesampleand p=0.042 forthe lastfiveperiods).

Summary1. InlinewithHypothesis 1,wefindevidenceforconformity:Comparedtothe PRIVATEtreatment, thewithin groupvariation ofincomeineachpayoff stateislowerintheINFOtreatment.Wefindsuggestiveevidencethat increased conformityisachievedbyanincreasedrisktransfer(skewedtradingpattern)betweengroups.

10 These results are robust to running an OLS regression instead of a non-parametric test that allows us to additionally control for risk aversion, the share

Table 3

INFO treatments only. The dependent variable is average end of period exposure in a given period. Column (1) shows the results of a fixed effect regression. The independent variables are a period variable and an interaction of the treat- ment dummy and the period variables. Columns (2) and (3) show results of random effect regressions. Column (2) introduces a treatment dummy, column (3) the share of male participants and average choice in the BRET. Period 10 is the base period. Standard errors, clustered on session level, in parentheses. Significance levels on two-sided tests are denoted by ∗_{p < 0.10,} ∗∗_{p < 0.05,} ∗∗∗_{p < 0.01.} (1) (2) (3) FE RE1 RE2 Period X INFO −0.137 ∗∗∗ _−0.137 ∗∗∗ _−0.137 ∗∗∗ (0.0336) (0.0321) (0.0322) Period X INFO-WIN 0.213 ∗∗∗ _0.213 ∗∗∗ _0.213 ∗∗∗ (0.0635) (0.0606) (0.0609) Period X INFO-LOSE 0.00186 0.00186 0.00186 (0.0663) (0.0633) (0.0636) INFO-WIN 1.047 ∗∗ _0.999 ∗∗ (0.470) (0.417) INFO-LOSE 0.0 0 0519 −0.0310 (0.525) (0.492) Share Male 0.629 (1.082) Bombchoice 0.0700 (0.0720) Constant 3.774 ∗∗∗ _3.424 ∗∗∗ _2.079 ∗∗ (0.128) (0.225) (1.018) Observations 210 210 210 R 2 _{0.102 0.069 0.098}

In Section6,weinvestigatetherelationbetweenconformityandexposurelevels.

5.2.Theeffectofexplicitrankings

Wenowturn toatest ofHypothesis 2,abouttheeffectofintroducing explicitrankings.Tothisend, we comparethe INFOtreatmentwiththeINFO-WINandINFO-LOSEtreatmentinwhichthehighestandlowestearnerineachperiodwere highlightedwithastar.

Figs.1and 2(b)show thatthedifferencesinaverageexposurebetweentheINFOtreatmentsaremodestatmost. How-ever,therearesometrends,withexposureintheINFO-WINtreatmentstayingflatorevengoingup,whileitgoesdownin theotherINFOtreatments.Themostconservativestatisticaltestistocomparethedistributionofexposurebetweenthese treatments non-parametrically, collapsingall 100 individual observations per session(10 periods times10 traders) intoa singlemean,yielding 7observationspertreatment.UsingMWUtests,wefindnosignificantdifferencesbetweentheINFO treatments,eitherforthefullsampleorforthelastfiveperiods.

Obviously,takingsessionaverages neglects alotofinformationandreducesthepowerofthetest,leadingtothe pos-sibilityof type II errors. Toincrease statisticalpower andto be able to control forthe trends apparent inthe graphical analysis,weconductpanel regressionsusingperiodaverages,yielding10observationspersession.Afixed-effect specifica-tionispresentedincolumn(1)of Table3,whichallowsustocontrolforsession-specificunobservablessuchasendogenous differencesinsessionpricesorunobserveddifferencesingroupcomposition.Weinteracttreatmentdummieswiththe pe-riodvariabletocapturethetimetrendsapparentin Fig.2(b).Wefindevidenceforahighlysignificantnegativetrendinthe INFOandINFO-LOSEtreatments,whilethereisnocleartrendintheINFO-WINtreatment.11

Columns(2)and(3)showtheresultsofrandomeffectsestimationsinordertomoredirectlytesttheeffectofthe treat-mentmanipulations.Tobestcapturetheconvergencethroughouttheexperiment,wechooseperiod10asabaseperiod,so thetreatmentdummiescapturelastperiodaveragesofexposure.TheyshowthatintheINFO-WINtreatment,subjectshave onaverage1unithigherexposurethanintheINFOtreatment.Thesedifferencesemergeoverthecourseoftheexperiment, asevidenced bythesignificantlydifferenttime trendsbetweentreatments.Theresultsare robusttoincludingcontrolsin column(3).12

ThestatisticaldifferencebetweentheINFO-WINtreatment andtheotherINFO treatmentsis largelydrivenby thelast period.When thisperiodisexcluded,theresultsbecomestatisticallyinsignificant.Perhapssubjectsaimto“win” thefinal period,whichmayhavemoresignificanceforthemthan theother periods(wethankan anonymousrefereeforpointing thisout).However,intheabsenceofmoreinformationaboutsubjects’thoughtprocesses,wehavenowayofconvincingly

11 This result is echoed by a two-sided non-parametric Jonckheere–Terpstra test applied to the session means in each period. This test shows a significant

downward trends for both INFO and INFO-LOSE ( p = 0 . 025 and p = 0 . 004 respectively), but not for INFO-WIN (or PRIVATE).

testingthistheory.In AppendixD,wedofurthertestthepresenceofpositionalconcernsexploitingthevariationinstarting portfolios.WefindevidenceforadesiretocomeoutontopofothersintheINFO-WINtreatment.

Summary2. ContrarytoHypothesis2(b),therearenosignificantdifferencesinexposurebetweentheINFOandINFO-LOSE treatments onanyofourtests.Bothtreatments displayasignificantnegativetrendinexposure.There isnosuch trendin theINFO-WINtreatment,andwe findevidencethat inlinewithHypothesis2(a),exposure intheINFO-WINtreatmentis higherthanintheINFOtreatmentbytheendoftheexperiment.

6. Peerinformationanddiversification

The previous section showedthat introducing peer informationincreasesdiversification over time, atleast aslong as the highest earner is not highlighted. Fig. 2(a) showsno such trend in the PRIVATE treatment, leadingto a substantial differenceinexposurebytheendoftheexperiment.Wedidnothypothesizethisresult,butitisofinterestnevertheless.It presentsacontrasttomuchoftheexperimentalfinanceliterature,inwhichpeerinfluencesareoftenassociatedwithmore volatilepayoffsduetospeculationorherdingbehavior.However,thesemotivescannot playarolehere:thelackofprivate informationin oursettingminimizesscope forherding orinformationcascades,andbecause portfoliosare reset ineach period,speculationisnotattractive.Inthissectionwetakeacloserlookatthesedynamics.Thereadershouldkeepinmind thatalltheanalysesinthissectionarepost-hoc,i.e.conceivedafterthedataweregathered.

Asastartingpoint, Fig.1showsthemeanexposureinthePRIVATEandINFOtreatment,demonstratingthatthe differ-enceincreasesovertime.Followingthestatisticalapproachoutlinedin Section5.2,wefirsttakethemostconservativetest tocomparetheINFO andPRIVATEtreatment,by collapsingeach sessionintoasingleobservation,yielding7observations per treatment.Wefind nosignificantdifference ona two-sidedMWUtest forall periods(p=0.48)orthelast 5periods (p₌0_.20).

Asintheprevioussection,weareconcernedwiththelowpowerofthesetestsandthelackofcontrolsfortimetrends andpersonal characteristics.In Table 4, wethereforereport panel regressionsusingperiodaverages with10observations per session. A fixed-effect specificationis presented incolumn (1)of Table 4. We interacttreatment dummies withthe period variableto capturethe time trendsapparent in Fig.2(a). It showsa highlysignificant negativetrendin theINFO treatments,whichisabsentinthePRIVATEtreatment.

In columns(2)and(3) we presenttheresults ofrandom effectsestimations. Sinceperiod 10is chosen asa base pe-riod,thetreatmentdummiescapturelastperiodaveragesofexposure.TheyshowthatintheINFOtreatment,subjectshave on average 1 unit lower exposure than in the INFO treatment, a drop of 27% that is significant at the 5% level. These differences emerge over the course of the experiment, as evidenced by the significantly different time trends between treatments.

The resultsarerobust toincludingcontrolsincolumn(3),whereinlinewiththeliterature,the shareofmaletraders increasesrisktaking(EckelandFüllbrunn,2015).Itiscuriousthattheshareofmalesdoesnothaveasimilarlystrongeffect intheINFOtreatments,see Table3.Toexplorethisfurther,weextendtheregressionmodelin Table4,column(3),withan interactiontheINFOtreatmentdummyandShareMale.WefindthatthedropintheINFOtreatmentisalmostentirelydue tothebehavior ofmale subjects.While wehavenoclearexplanationforthisfinding,itisan interestingobservationthat couldbeaddressedinfutureresearch.

Table 4

PRIVATE and INFO treatment only. The dependent variable is average end of period exposure in a given period. Column (1) shows the results of a fixed effect regression. The independent variables are a period variable and an interaction of the treatment dummy and the period variables. Columns (2) and (3) show results of random effect regressions. Column (2) introduces a treatment dummy, column (3) the share of male participants and average choice in the BRET. Period 10 is the base period. Standard errors, clustered on session level, in parentheses. Significance levels on two-sided tests are denoted by ∗_{p < 0.10,} ∗∗_{p < 0.05,} ∗∗∗_{p < 0.01.} (1) (2) (3) FE RE1 RE2 Period 0.00918 0.00918 0.00918 (0.0410) (0.0392) (0.0395) Period X INFO −0.146 ∗∗ _−0.146 ∗∗∗ _−0.146 ∗∗∗ (0.0533) (0.0509) (0.0513) INFO −1.225 ∗∗ _−1.062 ∗∗ (0.534) (0.447) Share Male 3.484 ∗∗ (1.628) Bombchoice −0.00153 (0.0355) Constant 4.037 ∗∗∗ _4.650 ∗∗∗ _2.980 ∗∗∗ (0.120) (0.483) (0.785) Observations 140 140 140 R 2 _{0.083 0.084 0.189}

Table 5

Panel regressions of exposure on lagged deviations from group payoffs. columns (1) and (2) include fixed effects, columns (3) and (4) report Arellano–Bond estimators for exposure in t − 1 . To explore learning, columns (2) and (4) use data from the first half of the experiment only. Standard errors, clustered for columns (1) and (2), robust for (3) and (4), in parentheses. Significance levels on two-sided tests are denoted ∗_{p < 0.10,} ∗∗_{p < 0.05,} ∗∗∗_{p < 0.01}

(1) (2) (3) (4) FE FE5 AB AB5 IndVar t−1 0.0 0 0806 −0.0 0 0742 0.0 0 0 0587 0.0 0 0 0357 (0.0 0 0611) (0.00182) (0.00178) (0.00199) IndVar t−1 X INFO −0.00161 ∗ −0.00398 ∗∗ −0.0 040 0 −0.00397 ∗∗ (0.0 0 0928) (0.00194) (0.00255) (0.00201) Exposure t−1 1.042 ∗∗∗ 0.793 ∗ (0.263) (0.468) Exposure 2 t−1 −0.0860 ∗∗∗ −0.0798 ∗∗ (0.0213) (0.0337) Constant 4.231 ∗∗∗ _4.713 ∗∗∗ _2.872 ∗∗∗ _3.688 ∗∗∗ (0.0755) (0.157) (0.613) (1.114) Observations 1242 552 1104 414 R 2 _{0.003 0.039}

6.1. Conformityandsocialreinforcement

We now explore whether the drop in exposure in the INFO treatment is linked to the conformity documented in

Section5.1.One reasontothinkthatthismaybethecaseisaformofsocialreinforcement learning:subjectsintheINFO treatmentswhosepayoffsdeviatestronglyfromtheir peergroupmaylearnfromthisexperience,andtrytoavoidextreme payoffsinthenextperiod.Todoso,they wouldhavetoreduceexposure,thusexplainingthegradual dropinexposurein theINFOtreatments.

Toinvestigate whether such “social reinforcement” explains the results, we propose a measure of individual earning deviationsthatissimilartothewithin-groupdeviationmeasure(GVar)definedabove.Again,weusedeviationsinearnings ratherthanexposure,becausesocialpreferencemodelsaredefinedoverpayoffs(seeFootnote9_{).Ourmeasureofindividual}

variation(IndVar)isgivenby IndVari,t=



xHi,t− ¯xHi,t



2

+



xC_i,t− ¯xC i,t



2

. (IndVar)

IndVaris thesquared deviationof(virtual) earnings xi,t fromthe average ofperson’s i’s group ¯xi,t summed over both statesinperiodt.Thisvariablealsocapturesourtheoreticalmodelwithv(· )asasquarefunction.13

Followingthereasoningabove,wehypothesizethat exposureisinfluencednegativelybythedisutilityofbeinga social outlier (as measured by IndVar) in the previous period t− 1. We therefore regress exposure on lagged levels of IndVar, includingfixed effects foreach subject. The random variationin startingportfolios combined withrandom resolution of uncertaintyprovidesvariationinIndVarthatallowsouridentification.Sincethelearningeffectshouldbemorepronounced inearlyperiods,wepresentresultsbothforallperiodsandforthefirsthalfoftheexperimentonly.

Column(1)in Table 5showsthat individualsinthe INFOtreatment reduce theirexposure afterhavinga highIndVar, i.e.,afterhavingdissimilar(potential)payoffscomparedtotheir peers,wherethedummyissignificant atmarginal levels. Column(2)presentsresultsforthefirsthalfoftheexperimentonly.In linewitha learninginterpretation,thecoefficient becomeslargerandnowreachessignificanceatthe5%level.Sinceindividualexposurepotentiallyfollowsanautoregressive process,fixedeffectpanel regressionmightbe biased.Wethereforealsousedynamicpanel methods(Arellano andBond, 1991) to control for lagged exposure as well asits squared value in columns (3) and (4).The results demonstrate that laggedexposureindeedhassignificant explanatoryvalue. Thecoefficientforthepresenceofpeerinformationforthefirst fiveperiodsisofsimilarsize,butreachessignificanceatthe5%level.

Whilemoreresearchisneededtoconfirmthesenon-hypothesizedfindings,wefindevidencethatpeerinformationhelps subjectsinlearningtodiversify.Sucha“socialreinforcement” channelcan explain bothincreased conformityand decreasing exposureintheINFObutnot inthePRIVATEtreatment.Italsoexplainswhyexposureshouldstabilizeaftersomeperiods, aswithin-groupdeviations shrink overtime and theimpetus forlearningdiminishes. A back-of-the-envelopecalculation suggeststhatquantitatively,thesocialoutliereffectislargeenoughto(morethan)explainthedropinexposureintheINFO treatment.14

13 Note that our theory in _{Appendix A focuses on a reference group of higher earners. However, as we point out, this is merely a simplification, and the}

theoretical results are robust to including a disutility of earning more than others. In the following, average group exposure is used. The results are also robust to instead using the average exposure of other group members.

14 For instance, the average level of IndVar equals about 170 in the first round. If we take the Arellano–Bond estimate from _{Table 5 , we find that this}

should imply a drop in exposure of 170 ∗ 0 . 004 = 0 . 68 in the second round of the INFO treatment. This is somewhat smaller than the actual drop in the second round, but quite a bit larger than the average drop over all periods, estimated in Table 4 . These calculations should be taken with a large grain of salt, as they contain strong simplifying assumptions regarding the linearity of the effect and the use of average exposure among other things.

0

.1

.2

.3

.4

.5

Fraction

Yes

Sometimes

No

Did others' portfolios affect your trading behavior?

INFO INFO-WIN INFO-LOSE

0

.1

.2

.3

.4

Fraction

Yes

Sometimes

No

Did you try to avoid/obtain the lowest/highest payoff?

INFO-WIN INFO-LOSE

a

b

Fig. 4. Distribution of post-trading questionnaire answers by treatment.

Summary3. AsaresultofadownwardtrendintheINFOtreatment,exposureattheendoftheexperimentissignificantly lower than that inthe PRIVATEtreatment. We findevidence that subjectsin the INFOtreatments reduce exposureafter havingpayoffsthatdeviatefromtheirpeers.

6.2. Self-reportedsocialinfluence

To better understandsubjects’ decisions,we look atthe self-reported assessments ofsocial influence gathered inthe questionnaire. Since thesereports were made at the endof the experiment anddo not refer to particular situations or periods,theresultscanatmostbeindicativeofthetradingstrategy.Also,thereportswouldnotcapturesubconsciouspeer influences.

Fig.4(a)showstheanswertothequestionwhethertheportfoliosofothersinfluencedtheir tradingbehavior.Answers were providedon athree-pointscale. Morethanhalf ofthesubjectssaythey were influencedatleastsometimes,which indicates that people didpayattentionto theportfolios ofothers.There islittle differencebetweenthe threeconditions withpeerinformation.

The INFO-WINandINFO-LOSEtreatments potentially induce positionalconcerns. Therefore,we askedwhethertraders inthese treatments aspiredtohavethe highestpayoff intheINFO-WIN treatmentandto avoidthelowest payoff inthe INFO-LOSEtreatment.Panel(b)of Fig.4showsthatmorethanhalfofthesubjectstriedtoobtainthehighestpayoff atleast someofthetime,whereasalmostthree-quarterssaytheytriedtoavoidearningthelowestpayoff atleastsomeofthetime. Thus, our symbolicawards appear to havemotivated atleast some ofthe participants in their tradingbehavior. Indeed, subjects who self-report an inclination to pursue the highest payoff within their group at least sometimes, havehigher averageexposure relativeto their groupmembers (two-sidedMWU, p=0.037).Thisis inlinewith Kirchleretal.(2018), whoshowthatsymbolicrankingaffectrisktakingbehavioramongfinancialprofessionals,aswellaswiththeliteratureon positionalpreferencescitedintheliteraturesection.Wefindnosuchcorrelationforsubjectswhosaidtheywantedtoavoid havingthelowestpayoff.

7. Conclusion

Ourfindings show that social influences are importantdeterminantsof equilibriuminassetmarkets. In linewiththe predictionsofageneralequilibriummodelwithsocialpreferences,wefindevidencethatinformationaboutpeers’portfolios reducesthevarianceofincomeinpeergroups.Wealsoobservethatinformationabouttheportfoliosofothersincreasesrisk sharingandreducesthevarianceofearnings inourexperimental markets,exceptwhenthehighestearnerishighlighted. Ourresultsareconsistentwiththeideathatpositionalconcernsareanimportantdriverofrisksharinginfinancialmarkets, andprovideanimpetusformodelsthatincorporatesuchconcerns.

The effectofearningcomparisonshighlightsa differentkindofsocialinfluencethan ispresentintheexisting (exper-imental)finance literature.Infact,the lackofprivateinformationin oursettingminimizesscopefortraditionallystudied peereffectssuchas“informationcascades” orherding.Also,becauseportfoliosareresetineachperiod,speculationisnot attractive.The experimentdemonstratesthatpeereffects mattereveninthe absenceofthesemotives,andsuggestspeer portfoliosprovidea socialbenchmarkagainstwhichsubjectslearntoconform anddiversify.Futureresearchshouldverify theseeffectsbothinthelabandinthefield.Replicationeffortsbyotherresearchersareparticularlyimportant,sincesome ofourcomparisonsyieldstatisticalsignificanceinparametricanalysisbutnotonthemostconservativetests.

Generally,thereisa needtoinvestigatetheimpactofavailabilityofpeerinformationinitsincreasingly diverseforms. Forinstance, weknow verylittle abouttheeffect ofdifferenteconomic “narratives” onmarket equilibriumandstability.

Furthermore,tradingplatforms often emphasizesuccess stories andspectacularprofits, whichwill likelyresultin higher aggregate exposure.15 _{A more detailed understanding of thesocial side of markets may help the design of morestable,}

betterfunctioningmarkets.

AppendixA. Generalequilibriumwithsocialpreferences

Herewemodelaneconomythatresemblesourexperimentalsetup.Consideranendowmenteconomywithtwoequally probablestatesoftheworlds∈{1,2},andtwostate-contingentcommoditiesxs,wherex1pays1instateoneand0instate two,andviceversaforx2.

There isa continuum of agentsdistributed on [0,2]. Eachagenti belongsto eitherone of two peergroups ‘red’and ‘blue’, definedas r=

{

i:i∈[0,1

)

}

andb=

{

i:i∈[1,2]

}

, wherewe denote the peergroup of agenti by gi∈{r, b}. Every agentrandomlyreceivesaninitialendowmentofeither

ω

=

(

1,0

)

or

ω

=

(

0,1

)

,whereeachisequallylikely.Wedenoteby x_i=

(

x_1i,x_2i

)

thestatecontingentcommodityvectorofagenti.

Theutilityofagentiwhobelongstogroupgiisgivenby Vi=E[u

(

xsi

)

]−

α

Es



v



 gi

(

xs j− xsi

)

1xs j>xsidj

, (A.1)

whereu(_{· )}istheutilityderivedfromtheownmonetarypayoffs,andv(_{· )}representssocialpreferences:agentsareenvious whentheirex-postincomeislessthantheincomeoftheir peersxjwithintheirgroup,i.e.,otherredorblueagents,while theydonotcareabouttheirconsumptionrelativetothegrouptheydonotbelongto.Inotherwords,agentswantto“keep upwiththe Joneses”,wheretheJoneses consistofa subset ofsociety,i.e.immediateneighbors,colleagues oradifferent referencegroupofinterest.Wewillassumethatu(· )isincreasingandconcave.Moreover,weassumev(· )tobeincreasing, strictlyconcaveanddifferentiable,withpositivederivativeattheorigingivenby dv

dx_si





v=v(0)

:=

v

0>0.

Thisutility functionimpliesthatan agentfacestwo kindsofrisk.First,shefaces‘consumptionrisk’,whichstemsfrom variance in the payoff xi and the assumption that the u is concave. Agents can minimize consumption risk to zero by choosing a balanced portfolio andconsumingthe same in each state ofthe world. Second, she faces ‘social risk’, which occurswhenshedeviatesfromtheportfolioheldbyothergroupmembers,whichimpliesapositivevarianceofthesecond termoftheutilityfunction.Theagent’soptimalportfoliochoicemayrequirehertotradeoff thesetwokindsofrisk.

Notethatwe makeseveralsimplifyingassumptions.First,we assume thatall agentshavethe samesocialpreferences. Second,weabstractfromdisutility fromexperiencingadvantageous inequality,i.e.ourutility functionisequivalenttothe inequalityaversion modelby Fehr andSchmidt (1999), wheretheguilt parameter

β

isset tozero.Notethat all theoret-ical results would continueto holdif people (also)experienced such disutility, as it would be an additional source for conformism.16

Equilibrium

Suppose now that agents can trade assets for prices p=

(

p1,p2

)

. Each agent i in the economy solves the following problem: max x1i,x2i 1 2u

(

x1i

)

−

α

2

v



 gi

(

x1j− x1i

)

1x1j>x1idj

+1 2u

(

x2i

)

−

α

2

v



 gi

(

x2j− x2i

)

1x2j>x2idj

s.t pxi≤ p

ω

i.

Weconsidercompetitiveequilibria(CE)oftheeconomy:

Definition1. ACEconsistsofanallocation

{

x∗_i

}

i∈[0,2] andasystemofpricesp=

(

p1,p2

)

,suchthat: 1.Foreveryi,x∗_i maximizesutilityinthebudgetset

{

xi∈R2+

|

pxi≤ p

ω

i

}

2.Marketsclear:₀2x∗_idi=2 0

ω

idi.

15 eToro provides salient rankings of the most successful traders. _{Simon and Heimer (2012) show that best short-term performers in their (undisclosed)}

trading site actively and successively promote their portfolios among members of the social trading site under study via the built-in chat interface. Hence, even if the corresponding platform does not highlight the best short-term performer directly but simply enables peers to communicate with one another, the effects of social trading on risk sharing can be undermined. Interestingly, Han and Hirshleifer (2016) argue that the social transmission of investment ideas is biased. People rather communicate their investment successes than losses. This bias in communication can explain the social transmissions of more risky investment strategies ( Kaustia and Knüpfer, 2012 ).

16 There are also other ways to model social preferences in the presence of uncertainty. Specifically, consistent with a concern for procedural fairness,

utility can be defined over expected levels of inequality, rather than the expected utility of inequality in each state of the world. Our results do not hold if agents care about inequality purely procedurally, but will hold qualitatively if their utility is a mixture of procedural and inequality concerns, as proposed by Saito (2013) .

Furthermore,we definea “symmetricequilibrium” asaCE inwhichall agentsinthesamepeergroup havethesame portfolioallocationxsi= ¯xsrforalli∈[0,1)andxsi=¯xsbforalli∈[1,2].Feasibilityimpliesthatinsuchanequilibrium,agents fromtheothergroupholdthemirroredportfolio ¯xsb=1− ¯xsr.

Weobtainthefollowingresult

Proposition 1. For any z∈[−

αv

0,

αv

0], theeconomy has a symmetric CE characterized by p2=p1=1 suchthat u

(

x∗2r

)

− u

(

x∗_1r

)

=u

(

1− x∗

1b

)

− u

(

1− x∗2b

)

≤

|

z

|

.

ProofofProposition1. Considerthecandidatesymmetricequilibriuminwhichall redagentsconsumexs=¯xrs andblue agentsconsumexsb=1− ¯xsr instates,andp2=p1.

Foranyredagentitisoptimalnottoswitchconsumptionfromstate1tostate2if:

1 2u

(

¯x2r

)

− 1 2u

(

¯x1r

)

−

α

2

v

0≤ 0

Converselyitisnotoptimaltoswitchconsumptionfromstate2tostate1if:

1 2u

(

¯x1r

)

− 1 2u

(

¯x2r

)

−

α

2

v

0≤ 0

Soeveryequilibriumsatisfies:

−

αv

0≤ u

(

¯x1r

)

− u

(

¯x2r

)

≤

αv

0 (A.2)

Analogous reasoningholds forblue agents.Feasibilityimpliesthat x_1b=1_{− x}1r.If we definez:=u

(

¯x1r

)

− u

(

¯x2r

)

,we findthatu

(

¯x1b

)

− u

(

¯x2b

)

=u

(

1− ¯x1r

)

− u

(

1− ¯x2r

)

=u

(

¯x2r

)

− u

(

¯x1r

)

=−z.Sincez∈[−

αv

0,

αv

0]implies−z∈[−

αv

0,

αv

0], anyallocationthatsatisfies (A.2),satisfiestheanalogueconditionforblueagents.

Finally,sincex∗_idi₌

ω

_idi_,excessdemandiszeroforeachmarketandpricesp1=p2 clearbothmarkets. 

Proposition1saysthatthereisarangeofsymmetricequilibria,whereeach agentholdsthesameportfolioasallother agentsinherpeergroup.Thismultiplicityiscausedbytheexistenceofsocialpreference,whichcauseakinkintheagent’s utilityfunctionsatthelevelofthepeergroup’sconsumption,sotheoptimalportfoliodependsontheportfoliooftheothers. Inparticular,sincezmaybedifferentfrom0,thereexistequilibriawheretheredagentsconsumemoreinstate1and theblueagentsinstate2orviceversa,sothatrisksharingisimperfecteventhoughu(· )isconcave.Theseequilibriaoccur becauseanagentwhodeviatestowardsamorebalancedportfoliowillreducehisincomerisk,butwillincrease hersocial risksinceshenowfacesthepossibilitiesoffallingbehindhispeersinatleastoneoftheincomestates.Thelargerthesocial concerns

α

,thelargeristhedeviationfromthebalancedportfoliothatcanbesustainedasanequilibrium.Notethat equi-libriathatfeatureimperfectinsuranceareinefficient:all(risk-averse)agentsarebetteroff ex-ante(haveahigherexpected utility)intheperfectrisksharingequilibrium.Notealsothatwithoutsocialpreferences

(

α

₌0

)

_,multiplicitydisappearsand onlyaCEwithperfectrisksharingremains.

Ifagentsare(approximately)riskneutralovertheirmonetarypayoffs,wecanprovidesomefurtherresults: Proposition2. Ifagentsareriskneutralovermonetarypayoffs,

(a) allcompetitiveequilibriaaresymmetric.

(b) anysymmetricallocationthatsatisfiesfeasibilityandtheindividualbudgetconstraintsisaCE.

Proof. Proof of (a). Assume an asymmetric equilibrium exists. For now assume that in equilibrium, within the red peer grouponlytwodifferentconsumptionvectors ¯x1

gand ¯x2g areconsumedbyanon-emptysubsetoftraders,suchthat∪2j=1

{

i: xi=¯xgj

}

=[0,1

)

.Thereisnoaggregateriskinthemarket,hencep1=p2.Soforanytraderintheredpeergroupconsuming alinearcombination

γ

x1

i+

(

1−

γ

)

x 2

i

γ

∈

(

0,1

)

isfeasible.Becausev(· )isstrictlyconcave,suchalinearcombinationyields highersocialutilitythanthevectorsitiscomposedof.MoreoverE[u(x)]isconstantforanyportfoliothatsatisfiesthebudget constraint. Sothereexistfeasibleconsumptionvectorswhichyielda higherutility thantheinitially proposedasymmetric equilibrium. Sincethisargumentgeneralizestothebluegroupandtoinstancesofthreeormoresubsetsofagentswithin onepeergrouphavingdifferentconsumptionvectors,wearrivedatacontradiction.

Proof of (b). Risk neutrality implies that u(x) is constant, so u

(

x∗_2r

)

− u

(

x∗_1r

)

=u

(

1− x∗

1b

)

− u

(

1− x∗2b

)

=0. Thus,

Proposition1issatisfiedforanyz. 

Proposition2(a)showsthatwhenagentsare(approximately)riskneutralovertheir ownpayoffs,socialpreferences al-wayslead groupstocoordinateupon onlyone allocation.Because agentsare indifferentbetweenall allocations that give themthesameexpectedpayoffs,considerationsofsocialriskmeansthathavingdifferentportfoliosfromotherscannever beoptimal. Proposition2(b)isasimplecorollaryof Proposition1,andshowsthatriskneutralityimpliesthatsocial prefer-encescanleadtoportfolio’sthatarearbitrarilyskewed.

Table B.1

This table reports various summary statistics for all sessions as a total and each treatment individually. Variables reported are number of sessions, number of par- ticipants, number of male participants, average end of period exposure, standard deviation of end of period profits as well as average Bomb Choice.

All PRIVATE INFO INFO-WIN INFO-LOSE

Sessions 28 7 7 7 7

Participants 278 70 68 70 70

Male 133 34 30 32 37

Avg. Exposure 4.20 4.67 3.74 4.30 3.69 Sd. Profits 291.16 331.77 259.79 302.90 263.35 Avg. Bomb Choice 15.30 16.84 15.33 14.92 14.00

Table B.2

Average end-of-period exposure by period and treatment. Period PRIVATE INFO INFO-WIN INFO-LOSE 1 4.89 4.82 3.94 5.27 2 4.23 3.97 4.34 4.63 3 4.25 4.62 3.57 4.09 4 4.29 3.97 3.26 3.94 5 5.00 4.12 4.74 4.00 6 5.31 4.47 4.06 3.57 7 4.46 3.59 4.51 3.66 8 4.51 3.50 3.77 3.74 9 4.66 3.88 3.89 3.37 10 4.49 3.18 5.22 4.09

1

2

3

4

5

6

7

8

Exposure

2

4

6

8

10

Period

Treatment Mean Session Mean

PRIVATE

1

2

3

4

5

6

7

8

Exposure

2

4

6

8

10

Period

Treatment Mean Session Mean

INFO

1

2

3

4

5

6

7

8

Exposure

2

4

6

8

10

Period

Treatment Mean Session Mean

INFO-LOSE

1

2

3

4

5

6

7

8

Exposure

2

4

6

8

10

Period

Treatment Mean Session Mean

INFO-WIN

Fig. B.1. Time series of exposure. Exposure is defined as the absolute difference between holdings of the two assets. The figure plots treatment means alongside session means. Each line corresponds to an individual session. INFO-treatments give traders information on the portfolios of their exogenous reference group. INFO-WIN and INFO-LOSE, in addition, give a symbolic reward to either the best and the worst performer in each period respectively. In the PRIVATE treatment, traders do not have information about other traders.

AppendixC. Prices

Inequilibrium,weexpectbothassetstobeequallypriced.Wedoindeedfindstrongsupportforthisprediction,asprices ofassetG andIarestatisticallyindistinguishable(two-sided Wilcoxonsigned rankteston bothmedianandmeanprices p=0.86and0.57,respectively),sointheremainder,wepoolpricesforbothassets.

Inaddition, becausethereis noaggregate riskin themarket,prices oftheassetsshould be equaltothe fundamental value. Fig.C.1showsaveragetransactionpricesoverall 10tradingperiods,and Appendix Bcontainsdisaggregatedgraphs

50 60 70 Price 2 4 6 8 10 Period

PRIVATE INFO Fundamental Value

(a) Mean prices across treatments.

50 60 70 2 4 6 8 10 Period INFO INFO-LOSE

INFO-WIN Fundamental Value

(b) Mean prices by treatment and session.

Fig. C.1. Time series of transactions prices. Data are pooled between asset I and G. The panel on the left (a), shows mean transaction prices for the PRIVATE and INFO treatment. Panel (b) on the right hand plots prices from the INFO treatments. The pointed line corresponds to the fundamental value (FV).

40

60

80

100

Price

2

4

6

8

10

Period

Treatment Mean Session Mean

Fundamental Value

PRIVATE

40

60

80

100

Price

2

4

6

8

10

Period

Treatment Mean Session Mean

Fundamental Value

INFO

40

60

80

100

Price

2

4

6

8

10

Period

Treatment Mean Session Mean

Fundamental Value

INFO-LOSE

40

60

80

100

Price

2

4

6

8

10

Period

Treatment Mean Session Mean

Fundamental Value

INFO-WIN

Fig. C.2. Time series of transactions prices. Data are pooled between asset I and G. The plot shows treatment means alongside session means. Each dashed line corresponds to an individual session, the pointed line to the fundamental value (FV), and the connected black squares to the treatment mean.