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IamdeeplyappreciatedtoallthehelpIhavereceivedinresearch.Mydeepestgratitudeistomyadvisor,Dr.FaridAitSahlia.Hegavemenotonlythetremendousfreedomtoexploreonmyownbutalsotheconstructivecriticismwhenmyresearchwentpointlessly.Hetaughtmehowexpressideasandexaminethefeasibility.Myco-advisors,Dr.Nimalendran,Dr.Karceski,Dr.Ghosh,andDr.Uryasevhavebeeninspiringmewithnewideas.WithouttheirgiantstepsontheirresearchareaIcouldnothavecouragetodigintosuchintricateelds. 4
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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 7 LISTOFFIGURES .................................... 9 ABSTRACT ........................................ 11 CHAPTER 1INTRODUCTION .................................. 13 1.1FundamentalProblem ............................. 13 1.2AsymmetricInformationinEquityandOption ................ 15 1.3LiquidityMeasuresofEquityandOption ................... 20 1.4AnalysisonFundamentalValue:EventStudy ................ 25 1.5AnalysisofIntradayPriceProcesses ...................... 27 1.6Contributions .................................. 28 2EVENTSTUDY:ACHANGE-POINTMODELAPPROACH .......... 29 2.1Methodology .................................. 29 2.1.1AbnormalReturn ............................ 29 2.1.2EstimationofStructuralBreakPoints ................. 30 2.1.3EstimationofDirectionandVolatilityChanges ............ 33 2.1.4ModelSelectionviaBayesFactor ................... 35 2.2EmpiricalAnalysis ............................... 36 2.2.1Data ................................... 36 2.2.2AbnormalReturns ............................ 38 2.2.3KeyDevelopmentAnnouncements ................... 40 2.2.4EstimatingStructuralBreakPoints,Direction,andVolatility .... 42 2.2.5SelectingtheBestChange-PointModel ................ 44 2.2.6EstimatingtheLengthofEachRegime ................ 47 2.2.7StatisticalPropertiesinStructuralBreaks .............. 47 3ANALYSISOFINTRADAYPRICEPROCESS .................. 57 3.1AModelofEquityPriceDiscovery ...................... 57 3.1.1EvolutionofFundamentalValue .................... 57 3.1.2DurationsofTradesandNationalBestBidandOerRevisions ... 60 3.1.3EvolutionofBidandAskPrices .................... 64 3.1.4PerformanceMeasures ......................... 67 3.2EmpiricalAnalysis ............................... 69 3.2.1Data ................................... 69 3.2.2TheEmpiricalSpecication ...................... 84 5
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.............................. 89 3.2.4NBBOProcess .............................. 94 3.3SimulationResults ............................... 113 4CONCLUSION .................................... 120 4.1LimitationandFutureResearch ........................ 120 4.2Summary .................................... 122 APPENDIX ADERIVATIONOFEQUATIONS .......................... 124 A.1DerivationofEquation( 3{18 ) ......................... 124 A.2DerivationofEquation( 3{19 ) ......................... 125 A.3DerivationofEquation( 3{21 ),( 3{22 ) ..................... 126 BSUMMARYOFEXCHANGEFACTORS ..................... 127 B.1TradeSummaryofExchangeFactors ..................... 127 B.2NBBOSummaryofExchangeFactors ..................... 134 CFULLTABLESOFCHAPTER 2 .......................... 143 REFERENCES ....................................... 193 BIOGRAPHICALSKETCH ................................ 196 6
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Table page 1-1LiquidityDimensionsandTheirComponentsinEquityandOption ....... 24 2-1Direction,Volatility,andAR(1)TestforAbnormalReturnsbyIndustry .... 39 2-2Direction,Volatility,andAR(1)TestforAbnormalReturnsbyMarketCapitalizationandBook-to-MarketRatio .............................. 41 2-3AR(1)Test,StationarityTest,andDistributionFittingforInterarrivalTimesofKeyDevelopments ................................. 43 2-4SelectionoftheBestChange-PointModel:Example ................ 46 2-5TheBestChange-PointModels ........................... 46 2-6TheBestChange-PointModelforAllFirms .................... 48 2-7LengthsofRegimesintheBestChange-PointModels ............... 49 2-8DirectionandVolatilityDierencesinConsecutiveRegimes ........... 50 2-9CorrelationandAutocorrelationofDirectionsandVolatilities .......... 52 3-1TradeSummarybyExchange ............................ 71 3-2TradeSummarybyTradeTimeInterval ...................... 75 3-3TradeSummarybyIndustrySectors ........................ 77 3-4NBBOSummarybyAskandBidExchanges .................... 80 3-5NBBOSummarybyTradeTimeInterval ...................... 84 3-6NBBOSummarybyIndustrySector ........................ 85 3-8SummaryofRegressions ............................... 92 3-9SummaryofRegressions ............................... 103 3-10SummaryofSimulationResults ........................... 115 3-11SummaryofPerformanceofPricingStrategies ................... 119 B-1SummaryofExchangeFactors ............................ 127 B-2SummaryofExchangeFactors ............................ 134 C-1BestChange-pointModelsonAbnormalReturns ................. 144 C-2LengthsofRegimesinEachChange-PointModel ................. 152 7
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................... 159 C-4ConsecutiveDierencesinMLEofVolatilities ................... 165 C-5CorrelationandAutocorrelationofDirectionsandVolatilities .......... 170 8
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Figure page 1-1ASchematicModelofSemi-strongEcientMarket ................ 16 2-1TransitionDiagramofRegimeChange ....................... 30 2-2PosteriorProbabilitiesofThree-RegimeModelinanEventPeriod ........ 44 2-3MLEConvergenceofsandsinMCEM ..................... 45 3-1SamplePathsofFundamentalValue(left)and(ontheright)AssociatedDirection,Volatility,andPriceJumpsatKeyDevelopments ................. 59 3-2ARealizationofNBBOrevision ........................... 64 3-3RealizationsofNBBOPriceEvolutions ....................... 67 3-4EvolutionofMeanandStandardDeviationofTradeDurationinEventWindows 87 3-5EvolutionofMeanandStandardDeviationofRealizedVolatilityinEventWindows 87 3-6EvolutionofMeanandStandardDeviationofBid-AskSpreadinEventWindows 88 3-7EvolutionofMeanandStandardDeviationofBid-AskSpreadAfterTradeinEventWindows .................................... 88 3-8EvolutionofMeanandStandardDeviationofLog-ScalePriceinEventWindows 88 3-9EvolutionofMeanandStandardDeviationofTradeSizeinEventWindows .. 89 3-10EvolutionofMeanandStandardDeviationofR2inModellog(ITi) ....... 91 3-11EvolutionofMeanandStandardDeviationofR2inModelDi 92 3-12EvolutionofMeanandStandardDeviationofR2inModelA+iPi 92 3-13EvolutionofMeanandStandardDeviationofR2inModelPiB+i 93 3-14EvolutionofMeanandStandardDeviationofR2inModelPi 93 3-15EvolutionofMeanandStandardDeviationofR2inModelSTi 93 3-16EvolutionofRegressorsinModellog(ITi) ..................... 95 3-17EvolutionofRegressorsinModelDi 96 3-18EvolutionofRegressorsinModelA+iPi 97 3-19EvolutionofRegressorsinModelPiB+i 98 3-20EvolutionofRegressorsinModelPi 99 9
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100 3-22EvolutionofMeanandStandardDeviationofR2inModellog(INj) ....... 103 3-23EvolutionofMeanandStandardDeviationofR2inModelNDj 104 3-24EvolutionofMeanandStandardDeviationofR2inModelAjBj 104 3-25EvolutionofMeanandStandardDeviationofR2inModelBj 104 3-26EvolutionofMeanandStandardDeviationofR2inModelAj 104 3-27EvolutionofMeanandStandardDeviationofR2inModelSNBj 105 3-28EvolutionofMeanandStandardDeviationofR2inModelSNAj 105 3-29EvolutionofRegressorsinModellog(INj) ..................... 106 3-30EvolutionofRegressorsinModelNDj 107 3-31EvolutionofRegressorsinModelAjBj 108 3-32EvolutionofRegressorsinModelBj 109 3-33EvolutionofRegressorsinModelAj 110 3-34EvolutionofRegressorsinModelSNBj 111 3-35EvolutionofRegressorsinModelSNAj 112 10
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Thisdissertationdevelopsastructuralmethodologyforequitypricinginasemi-strongecientmarketandperformsanempiricalstudysupportingtheneedforsuchamethodology.Conventionalpricedynamicsofequitiesandtheirrelatedoptionsassumemarketstobestronglyecient.Thishypothesishoweverisaseveresimplicationignoringliquidityrisk,adverseselectioneect,andthedicultyofachievinginformationaleciency.Themethodologyproposedinthisthesiscategorizesequitypricedynamicsinto3sub-processes:fundamentalvalue,duration,andNationalBestBidandOer(NBBO)revisions.Thisapproachrevealshowaninformedtrader'sknowledgeiseventuallyincorporatedintoequityandoptionprices.Market-makersareassumedtoapplyBayesianNash-equilibriumstrategiestoconstructrationalNBBOquotestohedgeagainstadverseselectionriskaswellastoprovidequotesattractivetouninformedtraders. Theobjectiveoftheempiricalstudyistondevidenceofmarketineciencyinbothfundamentalvalueandintra-daytrades.Fortheformer,wefocusonstructuralbreaksindirectionandvolatilityofequitypriceswhennewkeydevelopmentsareannounced.Conventionalevent-studiesonlyclassifythreesub-eventwindows:pre-event,event,andpost-event.Weproposeachange-pointmodelthatallowsmultipleregimesinassociationwithpre-determinedkeyevents,withvariableregimelengthsdependingonstructuralbreaksindirectionandvolatilityassociatedwithabnormalreturns.Ourstudyconrmsthatadjustmentstokeydevelopmentsmaybeginbeforeandendafter 11
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Forthesecondissue,weexamineintra-daytradesandNBBOdataupontheannouncementsofnewkeydevelopments.Throughvariousstatisticalmodels,weassociatewithtradingandNBBOtwodistinctsetsofdecisionfactors,dependingonwhetherweareinastableoratransitionregime.Estimatesoftradeduration,NBBOduration,andrealizedvolatilityarethemostdistinguishablebetweenstableandtransitionregimes.Overall,R2sarelowerfortransitionregimes,showingthatpriceevolutiondependsmoreonexogenousfactorsthaninstableregimes.Coecientestimatesdierverylittlebetweenthetwotypesofregimes,withafewexceptions.FactorsoftradedorNBBOexchangehavelimitedsignicance,withafewexceptions. Acomparisonbetweenactualempiricaldataandsimulatedresults,basedonuninformedlimit-ordertradersandmarket-makersfollowingBayesianNash-equilibriumstrategies,showsthatthelatterarenotnecessarilybetter,exceptthattheyleadtoalessvolatilepricediscovery. 12
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Thischapterpresentsathoroughintroductionofthisdissertation.Section1.1denesandsetskeyassumptionsofthemarket,participants,andtheadverseselectioneect,andthenraisesthefundamentalproblem.Section1.2consistsofaliteraturereviewonrationalequityandoptionpricinginasemi-strongmarket,highlightingthelackofconsensusregardingoption-relatedadverseselection.Section1.3reviewstheliteratureonmarketmicrostructurerelatedtoinformedtradinginequitiesandoptionsandshowshowliquiditymeasurescaneectivelyrevealadverseselection.Section1.4introducesanalternativepricediscoveryprocessthatincorporatesliquiditymeasures,whichwillbeextensivelydevelopedinthenextchapter.Section1.5givesabriefoverviewoftheempiricalstudy,withSection1.6summarizingitscontributions. FamaandFrench ( 1993 ).Wealsoassumethatallinformedtradersplacemarket-orders,sincetheiradvantagedependsontiming,andalllimit-ordertradersareuninformed,withalltradesoccurringatmarketprices.Hencemarket-ordertraderscanbeinformedoruninformed,butalllimit-ordertraders,includingmarketmakers,areuninformed.Therearemanymarket-makersandpublic(uninformed)limit-ordertraders,whooerliquiditythroughholdinginventorybyimposingbid-askspreadtomarketordertraders.Tosimplifythemodel,weassumeanimaginarymonopolisticmarket-makerwhoalwaysoersequilibrium 13
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Firm-orindustry-specicinformationcumulativelyresetarm'sfundamentalvalueupontheoccurrenceofeachkeydevelopment,suchasanearningsannouncement,amergeroracquisition,anewresearchdiscovery,theappearanceofanewcompetitor,downsizingandsoon.Informationitselfisuncertainuntilitiseective.Thusitsimpactonexpectedreturns(direction)andstandarddeviation(volatility)makestradersmoreactivetoadjustthecurrentequityandoptionprices.Whenkeyeventshappen,directionalorvolatilityinformationisknownrstonlytosomeinformedtraders,thenismadepublic,followedbyitsreectionintheequityprice.Whetherknownonlytoinformedtradersormadetopublic,informationmaystillbeuncertain,butitsincorporationintotheequitypriceindicatesalesseningofthisuncertainty. Aninformedtradermaybenetfromheradvancedknowledgeinoneoftwoways.Ifshegetspositivedirectionalinformation,shetakesalongequitypositionandtakesabullishoptionstrategy,whichisgoinglongonthecallandshortontheput.Withnegativedirectionalinformation,shetakesashortequitypositionandabearishstrategy,goingshortonthecallandlongontheput.Ifshehaspriorknowledgeofaforthcominghighvolatility,shetakesalongstraddleposition,goinglongoncallandput.Ontheotherhand,herpriorknowledgeofaforthcominglowvolatilityleadshertoashortstraddleposition,shortonthecallandput.Oncetheinformationispubliclyavailable,bothinformedanduninformedtradershaverealizeddirectionalandvolatilityinformation.For
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Easley,O'Hara,andSrinivas ( 1998 ),thatisonewhotradesforliquidity-basedreasons,hencebuyingandsellingequityandoptionsatthesamerate,irrespectiveoftheinformationalcontentinthemarket.Amarket-makerrevisesbid-askquotesonthebasisofpubliclyavailableinformationandwhenmarketordersarrive.Weassumethereisnoherdingorblung:neitheruninformedtraderisherdedbyanymarkettrend,nordoesaninformedtrader\blu"uninformedtraderstoconcealinformation.Figure 1-1 isaschematicmodelillustratinghowdirectionalandvolatilityinformationowbetweenequityandoption,andhowamarket-makermeasuresprivateinformationandincorporatesitintoequityandoptionprices.2Amarket-makerfacesanadverseselectionproblemfromdirectional-andvolatility-informedtradersfromequityandoptiontrade.Sinceanoptionisaderivativesecurity,informationincorporatedintheunderlyingequityisreectedintheoptionpriceaswell.Inasemi-strongecientmarket,aninformedtradercantradeoptionstotakeadvantageofequity-relatedpriorinformation.Therefore,themainproblemiswhetheramarketmakercansetrationalpricesandspreadsofequityandoptionunderadverseselectionriskfromdirectional-andvolatility-informedtraders.Thesignicanceofthisproblemishighlightedinthereviewsectionbelow. Easley,O'Hara,andSrinivas ( 1998 )and CherianJ.A. ( 1998 ).
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ASchematicModelofSemi-strongEcientMarket 16
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Duetotheunprecedentedgrowthinoptionsmarketsandgiventheconsensusthatnancialmarketsarenotecientbecauseofinformationasymmetryamongtraders,agrowingnumberofresearchershavebeeninterestedintheconsequencesofinformationtradinginequityandoptionmarkets.However,theoreticalandempiricalstudiesaresplitonwhetherornotaninformedtraderwouldusethisadvantagetotradeoptions.OneschoolofthoughtsuggestsasocalledLeverageHypothesisandclaimsthataninformedtraderwouldfavoroptiontradingbecauseofanoption'shighleverage,itslowtransactioncosts,lessstringentmarginconditions,absenceofuptickruleforshorting,built-indownsideprotection,andtheopportunitytobetonvolatility.3Empiricalevidenceshowsthatoptionvolumecontainsinformationaboutfuturestockprices,4optionpricescontributeanaverageof17%totheequitypricediscovery5.optionvolumeisrelatedtopublicannouncement,6andoptionstrategieswithVegaexposureconveyinformationaboutfuturevolatility.7Evidenceofinformedtradinginoptionwasfoundinexaminingliquidityofoptionmoneyness.Researchersshowedthatanout-of-the-money(OTM)optionoersagreatleverageadvantage.Anat-the-money(ATM)optionprovidesvolatility Black ( 1975 ), Chakravarty,Gulen,andMayhew ( 2004 ), CherianJ.A. ( 1998 ), Back ( 1993 ),Busi-nesssnapshot10.2,p235of Hull ( 2000 ).4 ( 1998 )suggestedmultimarketsequentialtrademodel,Iextendedthemodeltoincorporatetradingstrategiesandtolinktospreaddecompositionmodelfrom Madhavan,Richardson,andRoomans ( 1997a ). Chen,Lung,andTay ( 2005 )usedoptiontradingvalueratiotoex-tractinformationinoptiontrading.5 ( 2004 )appliedHasbrouck'sinformationsharingapproach.6 ( 2006 )focusedonlinkingproxiesbetweeninformedtradingandnews.7 ( 2006 )focusedonoptionstrategiesthatarepackagedforvolatilitytrading.
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Empiricalevidenceshowsthatoptionbid-askspreadspositivelydependondelta-hedgingcostsandthebid-askspreadsofunderlyingequity.Furthermore,optiontradingvolumereducesbid-askspreads,whichisoppositethebid-askspreadofequity,andoptionliquidityhasaverysmalladverseselectioncomponent,becausetheoptionmarketusuallyhasbigdepth.Finally,optiontradingstrategieswithdeltaexposuredonotappeartocontaininformationaboutfuturereturns,whichimpliesoptionorderowanddirectionaltradingarenotquiterelated.11Evidencefrombothschoolsofthoughtrevealsthattheoptionmarketisavenueforinformedtrading.As Back ( 1993 )mentioned,theexistenceofanoptionimpliesthatricherclassofinformationsignalscanbereceived,howeverinformedtradingofoptionsdoesnothaveaclearadvantagefromanadverseselectionperspective. ( 2004 ), Chen,Lung,andTay ( 2005 ), Blasco,Corredor,andSanta-maria ( 2006 )givealmostthesamendings.9See Vijh ( 1990 ).10See ChoandEngle ( 1999 ).11See Vijh ( 1990 ), ChoandEngle ( 1999 ), Landsiedl ( 2005 ),and RudigerFahlenbrach ( 2006 ).
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Back ( 1993 )and Easley,O'Hara,andSrinivas ( 1998 ).13See BiaisandHillion ( 1994 )14See ChoandEngle ( 1999 )15See Dumas,Fleming,andWhaley ( 1996 )16See Ross ( 1976 )
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From Bagehot ( 1971 )'sessay,aresearcheldcalledmarketmicrostructure,whichexaminestheeectsofprivateinformationontheliquidityofanancialsecurity,hasthrived.Inanancialmarket,aprimarycauseofilliquidity,thecostofimmediacy,isadverseselection,whicharisesfromthepresenceofprivatelyinformedtraders.20Bagehotdescribedhowliquidityinamarketisinverselyrelatedtothespread.Thesmallestspreadamarketmakercanmaintainandstillsurviveisinverselyrelatedtoaverageowrateofnewinformationaectingthevalueoftheasset,andisdirectlyrelatedtothevolumeofliquidity-motivatedtransactions.Thereareinfactthreedimensionsofliquiditytocaptureadverseselection:(i)Tightness(orinverselybreadth)iscostofturningaroundatrade BiaisandHillion ( 1994 )18 ( 1998 )explainsself-fulllingprophecy.19See BiaisandHillion ( 1994 ).20See BrennanandSubrahmanyam ( 1996 ).
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GlostenandMilgrom ( 1985 )showhowbreath,orbid-askspread,becomeswiderastheadverseselectioneectishigher.Intheirsequentialtradingmodel,throughBayesianNashEquilibriumpricing,amarketmakerlearnsprivateinformationthroughtheowofbuy-initiatedorsell-initiatedtrades,andthentransfershislosstoanuninformedtraderthroughawidenedspread.Besidesadverseselectioncosts,thespreadincludesoperationandinventorycoststooerimmediacy.Howeverthesearetransitoryandareusuallyverysmallinacompetitivemarket. Inhisanalysisofacompetitiveauctionmarket, Kyle ( 1985 )showedhowmarketdepthisdeterminedbyinformedtrading,andhowaninformedtradersetsherstrategyaccordingly.Amarketmakergathersallordersforanauctionperiod,andsetarationalexpectationequilibriumprice.Thelatterisapricethatmaximizestheinformedtrader'sprotwhilethemarketmakerstaysrisk-neutralbytransferringlosstotheuninformedtrader.Sinceamarketmakercannotdistinguishwhethereachorderowcomesfromaninformedtraderoranuninformedtrader,hesetspricesproportionaltotheimbalanceoforders,whichindicatesthedegreeofinformedtrading.Theoptimalslopeoforderimbalance,whichshowshowmuchpriceschangetothedegreeoforderimbalance,iscalledthepriceimpact,inverselyrelatedtodepth.Ontheotherhand,aninformedtraderknowsthatthereisalimittotradeinindividualauctions,becausethepricewillgouptothetruevalueofherinformationifshetradesuptoalimit.Henceshestrategically\hides"in Black ( 1971 ),andorganizedby Kyle ( 1985 ).
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Thelastliquiditydimensionispricereversal,orresiliency.Accordingto Llorente,Michaely,Saar,andWang ( 2001 ),ifinformedtradingisrelativelyinsignicant,returnsaccompaniedbyhighvolumeshavetendencytoreversethemselvesinsubsequentperiods,becauseanecientmarketpullspricesbacktoequilibriumpricebytraderswhobelievethatcurrentpricesaretoofarfromthetrueprice.However,ifinformedtradingissignicant,asexpressedthroughhightradevolume,thenreturnsarelesslikelytoreverseandcancontinueinsubsequentperiods. Llorente,Michaely,Saar,andWang ( 2001 )suggeststhatpricereversalexpectationisnegativelyproportionaltopastreturnsandcurrentvolume,togetherwithuncertaintyofprice,dividends,andprivateinformation. Inadditiontoequityliquiditydimensionsandtheiradverseselectioneect,examinationofoptionliquiditydimensionsandtheiradverseselectioneecthasbecomeanimportantissueonthebasisofempiricalevidenceregardingincompletemarkets.Optionliquidityhasthreemorecharacteristicsthanequityliquidity.First,ithasmoneynessandtimetomaturity.Thesetwocontingenciestopriceandtimerangeallowtraderstochoosetobeexposedtoortobeprotectedfromriskimposedinthoseranges.Howevertheselimittheliquidityoftheoption,whichmakesitdicultfortheoptionmarketmakertondrationalprices.Second,byitsderivativenature,anoptionliquiditydependsontheliquidityofunderlyingequityandotherenvironmentalvariables.Theoptionprice'ssensitivitiesonthosevariablesarerepresentedbyGreekletterssuchasDelta,Gamma,Vega,Theta,andRhoinchapter15of Hull ( 2000 ).Hencetheadverseselectionimpactonoptionliquidityistransferredfromtheunderlyingequity,buttheoptionliquiditymayhaveitsownadverseselectioncomponenttransferringtotheunderlying.Sinceoptionisonlyavolatilityvehicle,theimpliedvolatilityforecastillustrateshowoptionaectstheliquidityoftheunderlyingasset.Third,optionliquiditycanbeaectedbyitsownhedgingstrategy.Anoptionwritermaychoosetohedgeshort 22
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Merton ( 1990 ).Theaskspreadofoptionisthecostofhedgingashortoption,whichistheexpectedvalueofaccumulatedhedgingcostsuptomaturity,thehedgingcostisthehalfspreadoftheunderlyingequity.Inotherwords,itisthemarketordercostforeverytradeofhedgingstrategy.Similarly,thebidspreadisthecostofhedgingalongoption,ortheexpectedvalueofaccumulatedhedgingcost,whichisthenegativeofthemarketordercostofhedging.Therefore,theGlosten-Milgrom'sBayesianNashEquilibriumcannotbedirectlyusedinthissetupbecausetheexpectedhedgingcostsalreadyaccountforadverseselectionintheunderlying.Moreover,ithasthemarket'sexpectedadverseselectionuptomaturityatallpossiblepriceevolutions.Itisinfacttheexpectedvalueofhedgingcostsinrisk-neutral(onlyneutralinasenseofpublicinformationrisk)probability. Thereisstrongempiricalevidencetosupporttherelationshipbetweenadverseselectionandbid-askspreads.AdverseselectioncostsaresignicantinOTMoption,sinceOTMoptionshavebiggerspreads,arelessfrequentlytraded,andhavebiggertradesizepertransactionthanATMoption,aslowpricelureinformedtradersintoseekleverageeects.HedgingcostissignicantinATMandOTMoptionsinlongdurations,sincemarketmakersshouldhedgetheiroptioninventory.Iftheunderlyingmarketishighlyliquid,thenthewholespreadisdeterminedbytheliquidityintheunderlyingsecuritymarketandhedgeratio.BecausethisisnotthecaseinthedierencebetweenATMandOTMoptionspreads,itisevidencethatamarketmaker(orequivalentlyoptionwriter) Martellini ( 2000 ).
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Kyle ( 1985 )'smodeltodirectionalinformationandoptionpricechangecouldnotbefound. Thelastdimensionispricereversal.Iwasnotabletondanyliteraturethatexaminespricereversaleectinoptionmarkets.Similartotheequityprice,anoptionpricemaytendtoreversewhenuninformativeshockoccur.AlthoughIexpectthatthedirectionaleectwillbemuchlessthroughhedging,uninformativevolatilityshockwillhaveasignicanteectonoptionpricereversal.Table1.1isasummaryofliquiditydimensionsandpropertiesinequityandoptionmarkets. Sofar,wehaveexaminedliquiditymeasuresofequityandoption.Nowamarketmakercanwatchthosemeasurestodetectanyinformedtradingpossibilitiesintheorder ChoandEngle ( 1999 ), BiaisandHillion ( 1994 ), Bollen,Stoll,andWhaley ( 2003 ),and Fontnou-velle,Fishe,andHarris ( 2003 ).24See Fontnouvelle,Fishe,andHarris ( 2003 ).25See Easley,O'Hara,andSrinivas ( 1998 ).26See ChoandEngle ( 1999 ).
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LiquidityDimensionsandTheirComponentsinEquityandOption Breadth(Bid-askspread)AdverseselectioncostHedgingcostOperatingcostAdverseselectioncostInventorycostOperatingcostCompetitioncost PriceimpactOrderimbalanceSignofordervolumeUncertaintyofuninformedvolumeNotmuchdirectionalimpactUncertaintyofpricedistributionvolatilityimpact PricereversalOrderowNotclearUncertaintyofpriceUncertaintyofprivateinformationUncertaintyofdividends 25
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InChapter 2 ,weinvestigatetheempiricalevidenceofstructuralbreaksinpricedynamicsofequitypriceswhennewkeydevelopmentsaectingfundamentalvalueareannounced.Weshowtheexistenceofatransitionregimethatcanbeattributedtoactivitiesperformedbyinformedtraders.Wefocusonstructuralbreaksduetofundamentalvaluechangesspecictoindividualrms,thusexcludingcasesofliquidityormarket-widechanges.Liquiditychangesnecessarilyinvolvemeasurementsofliquiditysuchasadverseselection,depth,andresiliency.Furthermore,theyrequireananalysisofintradaytradesandquotesdata.Market{orindustry{widechangescanberegardedsimilarlyifweconsiderthemarketorindustryportfolioasasingleequity.Fromanempiricalpointofview,amarket-widekeydevelopmentislikelytobeincorporatedinthereturnofthemarketportfolio.Thereforeitseectonaspecicequityreturncanbelteredoutbyusingabnormalreturnsrelativetomarketbenchmarks,suchasthosegeneratedbytheCAPMandtheFama-Frenchthree-factormodel. Themethodologyforthisresearchisbasedon Chib ( 1998 )'schange-pointmodel,whichhashadnumerousapplicationsintheanalysisofequitypricedynamics.Webrieydiscusstwopapersthatareclosesttothepresent. PastorandStambaugh ( 2001 )investigatewhetheralongreturnhistoryisusefulinestimatingthecurrentequitypremiumevenifthehistoricaldistributionhasexperiencedstructuralbreaks.Theirapplicationisbasedonachange-pointmodelonavalue-weightedportfolioofNYSE 26
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PastorandStambaugh ( 2001 )showthatachange-pointmodelenablesustouselonghistoricaldatawithhighprecision. LiuandMaheu ( 2008 )researchstructuralbreaksinrealizedvolatilityoftheS&P500indexfromJanuary1993toMarch2004.Becausetheinstabilityofthevolatilityprocesshasimportantimplicationsfordecisionsinriskmanagement,portfoliochoice,andderivativepricing,theseauthorsuserealizedvolatilityasitprovidesanaccurateestimateofexpostvolatilityandbecauseofitsabilitytobeincorporatedinabroadclassofcontinuous-timemodels.TheyuseaHAR-GARCH27modelforestimationandachange-pointmodeltodeterminestructuralbreaksinrealizedvolatility.Theyndstrongevidenceofstructuralbreaksinlog-realizedvolatilitybutweakerevidenceforchangesinboththeregressionparametersandvarianceoftheHAR-GARCHmodel.
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InChapter 3 ,weconstructbidandaskequitypricingstrategiesinasemi-strongecientmarketandevaluatetheirempiricalperformancewithtradeandquotedata.Throughthisanalysis,ourgoalistodetectpatternsdistinguishingtransitionfromstableregimes. 2 ,ourresearchfocusesonrm-specickeydevelopmentscontainedinannouncementdatesfromnancialmediaandrelatedabnormalreturndata. PastorandStambaugh ( 2001 )and LiuandMaheu ( 2008 )provideempiricalevidenceofanexpectedequitypremium,whichcorrespondstothedirectionofanindividualequity.Theirstudiesalsosupporttheexistenceofstructuralbreaksinrealizedvolatilityovertime.Insteadofanalyzingonelongtime-seriesastheydo,weconsiderseveral,witheachcontainedinatimewindowassociatedwithakeyevent.Ourmajorcontributionfromthissetupistonotonlyidentifysignicantstructuralbreaksaroundkeydevelopmentannouncements,butalsotoprovideanalternativetoconventionaleventstudies.Thisisduetothefactthatourmethodenablesustoestimatevariousregimelengths,detectnewdirectionsandvolatilities,andassessthecorrelationbetweenconsecutiveregimes. Anothercontributionofourresearchistoprovidesomegroundworktolinkfundamentalanalysis,liquidity,andpricedynamics.Thisisparticularlyimportantforpopularoptionpricingmodelsbasedonjump-diusionsandstochasticvolatility. InChapter 3 ,themethodologywedevelopisanextensionofthesequentialtradingmodelsof GlostenandMilgrom ( 1985 ), Easley ( 1996 ), CherianJ.A. ( 1998 ), Easley,O'Hara,andSrinivas ( 1998 ),tonameafew.Themaincontributionofthispaperisthatourmethodologyextendsthosesequentialtradingmodelsintoacontinuoustimeframework,whichcansimulaterealpricedynamicsdirectlycomparablewithspread 28
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Roll ( 1984 ), George,Kaul,andNimalendran ( 1994 ), Madhavan,Richardson,andRoomans ( 1997b ).Althoughourempiricalstudydoesnotfollowtheframeworkofspreaddecompositionmodels,itfocusesonhowintradaytradesandNBBOdatamayactdierentlybetweentransitionandstableregimes.Furthermore,thestudyprovidesparameterstosimulatestrategiesofbidandaskpricing. 29
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Thischapterisorganizedasfollows.InSection 2.1 ,wepresentanapplicationof Chib ( 1996 )'schange-pointmodel.Section 2.2 containsourempiricalresults. Chib ( 1998 )'schange-pointmodel.OurmodelestimatesthelengthofeachregimebyGibbssampling,ndsmaximumlikelihoodestimatorsofdirectionandvolatilityforeachregimebytheMonte-Carloexpectation-maximization(MCEM)method,andproducesthemarginallikelihoodofeachmodel(associatedwithaspecicnumberofregimes)tondaBayesfactorthatevaluatesthemodel'sperformancerelativetotheothers.Thestatisticalmethodsusedtoanalyzeestimatesofthechange-pointmodelaredescribedmorefullyinSection 2.2 FamaandFrench ( 1993 )togeneratenormalreturns.Thepredictionsforthelatterarethevalue-weightedmarketreturn(denotedrn),theaveragereturnonasmallmarket-capitalizationportfoliominustheaveragereturnonalargemarket-capitalizationportfolio(SMB),andtheaveragereturnonahighbook-to-marketportfoliominustheaveragereturnonalowbook-to-marketportfolio(HML).Abnormalreturn,anktforrmnonitskthkeydevelopmentattimetisdenedasthedierencebetweenrnktandpredictedequityreturn,^rnktbasedontheFama-Frenchthree-factormodel: 30
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TransitionDiagramofRegimeChange where ^rnkt:=^n+^nrmkt+^snSMBkt+^hnHMLkt;(2{2) wherermkt,SMBmkt,andHMLmktare,respectively,thevaluesofrm,SMB,andHMLfortthdateofkeydevelopmentk.Theregressionestimates^n,^n,^sn,and^hnaregeneratedbytheEVENTUSsoftware,throughaWRDSinterface Cowan ( 2007 ).Theyarebasedon\normal"returndataconsistingofobservationsoutsideeventwindows(eachoflengthT).TheestimationmethodwechoseisthatofEGARCH(1,1),whichaccountsforthepossiblecorrelationbetweenchangingreturnsandvolatilityaswellasmodelstochasticvolatility.Sincethereareusuallyatmostonekeyeventonanyday,ourentirestudyisbasedondailydata. Letf(atjs;2s)denotethedensityoftheabnormalreturnwhentheregimestattimetiss.ThevariablestisassumedtofollowaMarkovchain,st+1canstaythecurrentvalueofstorjumptothatofst+1.Figure 2-1 showsatransitiondiagramofregimechanges, 31
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Let=(s;2s)fors21;:::;S.Forourmodelweneedtoestimatethejointposteriordistributionoftheparameterset=s;1sSandtransitionprobabilitymatrixP,denoted(;PjAT),whereAT=a1;a2;:::;aT,aswellastheposteriorprobabilitiesp(stjAT),1tT,fortheregimesetST=s1;s2;:::;sT.Sincethelatterisunobservable,weadopttheBayesianparadigmbyspecifyingconjugatepriors.Moreexplicitly,usinggivenhyper-parameterstobedetailedlater,weemploythefollowingdistributions: ByBayestheorem,(;PjAT)/(;P)f(ATj;P).Sincedependsontheunobservedregimesfs1;s2;:::;sTg,weaugmenttheposteriordensityto(ST;;PjAT).WethenuseaGibbssamplertogenerateposteriorrealizationsoftheparameters,(P;;ST)asfollows: 1. GenerateP(PjST) 2. Generate(jST;AT) 3. GenerateST(STj;AT;P) 32
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wherem:=mss,m=0 mas,m=0+m,m=0+m,2m=20+(m1)S2s+0 whereSt:=fst;:::;sTg.Weomitthe(sTjAT;;P)and(s1jAT;S2;;P)termsbecausep(sT=S)=1andp(s1=1)=1byconstruction.ThengeneratingposteriordistributionofSTreducestogeneratingf(stjAT;St+1;;P)g,t=T1;:::;2,recursivelytakingtheirproduct. Chib ( 1996 )showedthat wherest+1isknownfromthepreviousiteration.GivenST=sT=S,sT1;sT2;:::;s2aregeneratedthrough(2.8)asfollows: 33
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Asshownin(2.7),therighthandsideof(2.6)requiresnding(st=kjAt;;P)and(st+1jst;P).ThelattercanbefoundthroughtheconditionalMarkovtransitionprobabilitygivenSTfromStep1.Tondtheformer,weconsideranotherrecursivecalculation.Becauseweknow(s1=1jA1;;P)=p(s1=1)=1,wecancalculate where Byconstruction,wehave(s1=1jA0;;P)=p(s1=1)=1. ThroughtheGibbssampler,wecansimulatetheposteriordistributionofregimesas: whereMisthenumberofiterationsoftheGibbssamplerandsuperscriptisusedforsampleidentication. 34
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WendthemaximumlikelihoodestimatorsofdirectionandvolatilityofaregimebyapplyingtheMonteCarloexpectation-maximization(MCEM)algorithm,sincethelikelihoodfunctionisintractablewithunobservableregime RobertandCasella ( 2005 ).TheMCEMalgorithmproceedsasfollows: Ineachiteration(i),i=1;:::;IwegenerateMsampleregimesetsS(1)T;S(2)T;:::;S(M)Twhereform=1;:::;M,S(m)Tisgeneratedaccordingto(STjAT;(i)).Wethenobtainthefollowingexpectationestimate: Thesecondtermf(S(m)TjP)isxedbecausef(s(m)1=1jP)=f(s(m)T=TjP)=1and ^pss=PMm=1m(m)ss wherem(m)ssistheexpectednumberofdatesthesystemremainsinregimesduringthemthiteration. =argmax1 Itisnowstraightforwardtondthemaximumlikelihoodestimatorbecauseweknowtheposteriordistributionsofdirectionandvolatility.TheMLEofmeandirectionforthe 35
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bythevirtueofthefactofthenormalposteriordistributionofthedirectionparameter.Similarly,giventhatgammaposteriordistributionofthevarianceofabnormalreturnthevarianceforthesthregimeis: wherea(m)sisdenedin(2.15).Forthesimulation,thesamplesizeMandIaresetlargeenoughsothedierencebetweentwosuccessiveestimateisnegligible. Chib ( 1996 ),themarginallikelihoodforabnormalreturnsinachange-pointmodelMrwithrregimescanbeexpressedas: wherethedensitiesareaspreviouslydenedwithnowanexplicitreference.Theoreticallysettinganyvaluesinf;Pgdoesnotaecttheresult,butpracticallyweuseMLEestimatesfromtheprevioussection.WiththismarginallikelihoodwecancomparetwomodelsMrandMsbyusingtheBayesfactordenedas: orsimplytakeadierencebytakinglogforbothmarginallikelihoodsas: lnBrs:=lnm(ATjMr)lnm(ATjMs):(2{19) 36
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Jereys ( 1961 ),alargevalueoflnBrsindicatesthatthedatasupportsMroverMs.Wecanfurtherexpressthelog-scalemarginallikelihoodasfollows: lnm(AT)=lnf(ATj)+ln()+ln(P)ln(jAT)ln(PjAT;):(2{20) NotethatwhenthereisnoriskofconfusionwesuppressthemodeltermMinournotation.Thersttermontherightsidecanbemademoreexplicitasfollows: lnf(ATj)=TXt=1lnf(atj)=TXt=1lnSXs=1f(atj;st=s)(st=sjAt1;)!;(2{21) where(st=sjAt1;)isgivenin(2.8).Thesecondandthirdtermsin(2.20)canbeeasilyfoundbypluggingMLEestimatesofdirectionandvolatility.Forfourthterm,weagainusesimulationestimates: whereS(g)Tisthegthdrawfrom(STjAT),asdescribedattheendofSection2.1.1.Thefourthtermissimilarlyestimated: whereS(g)Tisthegthdrawfrom(STjAT;),asdescribedabove.Ineachcase,wehave 2.2.1Data 37
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Basedonthesampledrms,weused ReutersKnowledge ( 2006 )tosearchfor'High'signicantdevelopmentsreportedfrom2004to2006.Asaresult,273rmshaveononeormoresignicantdevelopments,26rmshadmorethan30signicantdevelopmentsfromatotalof4,114developments.TheReutersKnowledgewebsitegivesthespecictimeofeachannouncementandsomeexpresstheinterarrivaltimeofkeydevelopmentsinminutesforeachrm. EventstudydataareobtainedfromEVENTUSatWRDS.Eacheventdateisselectedfromakeydevelopment,andbasicFama-FrenchDailyeventstudyisperformedwiththissoftware.TheindexforthemarketfactorisCRSPvalue-weightedreturn. Foreverykeydevelopment,61daysofabnormalreturnsarecollected:30beforetheeventdate(asreportedinEVENTUS),30after,andthereturnontheeventdate.Thecorrespondingeventwindowsaretheintegerscountingthedaysbeforeandaftertheeventdateintheinterval[30;30],with0correspondingtotheeventdates.Associatedsub-intervalsarethepre-eventwindow[30;2],eventwindow[1;0],andpost-eventwindow[1;30].ForetheFama-Frenchparameterestimationperiod,themostonecanusein3255daysintheyears2004-2006,fromwhichthelast46tradingdaysareremoved.Fromwhatremains,setsof61daysareremovedwheneveranassociatedeventoccurs. AllmethodologyandbackgrounddataprocessingareimplementedthroughthestatisticalsoftwareRandtheMySQLdatabase.InsomecasesRproducesvalueofzeroforthenormaldensity.Theyarereplacedbythenumber1010.Furthermore,caseswherethelog-likelihoodfunctionyieldsverylargenegativevaluesaredeleted. 38
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Chib ( 1998 ),theprioreectofchoosingdierentexpecteddurationsforeachmodelisminimalinpractice. TheGibbssamplertondbreak-pointsisiterated500timesafter150transientiterations,andtheMCEMalgorithmtondmaximumlikelihoodestimatorsisiterated150times,witheachiterationtaking50,100and200sub-iterationstondthesamplemeanin(2.15)andvariancein(2.16). Campbell,Lo,andMacKinlay ( 1997 ).Aweaker,butstillindicativeoftheindependenceassumptionistherejectionofanAR(1)modelforthetimeseriesofabnormalreturnsaswedonext.Inthiscase,thenullhypothesisstatesthat IfisinsignicantorthecorrespondingR2isnearzero,ourindependenceassumptionisempiricallysound.Table 2-1 reportssummariesofkeydevelopmentsandcorrespondingabnormalreturnscategorizedbyindustrysectors.Wecanseethatthestandarddeviation 39
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Direction,Volatility,andAR(1)TestforAbnormalReturnsbyIndustry FirmsEventsMarketCap.BTMEventAbnormalReturn^ Materials2814.18.520.47(30;2)0.0311.809-0.04810.0065(1;0)0.1193.138-7.42930.0000(1;30)0.0281.8420.0023 Industrials2313.39.110.41(30;2)0.0052.085-0.03010.0074(1;0)0.074.087-4.07410.0000(1;30)-0.012.1370.0009 ConsumerDiscretionary2617.77.080.42(30;2)0.0251.711-0.01900.0060(1;0)0.2193.345-3.15380.0016(1;30)0.0211.8060.0004 ConsumerStaples2514.727.690.43(30;2)-0.0061.7840.00410.0067(1;0)-0.0023.6680.60660.5441(1;30)0.0431.8750.0000 HealthCare2521.218.330.43(30;2)-0.0072.283-0.01720.0056(1;0)-0.1654.195-3.06890.0022(1;30)-0.022.4460.0003 Financials268.54.950.41(30;2)-0.0131.5070.02770.0087(1;0)0.1712.3133.19930.0014(1;30)0.0031.6530.0008 InformationTechnology2517.86.820.47(30;2)-0.0222.418-0.03730.0061(1;0)0.1413.504-6.10050.0000(1;30)-0.0072.6330.0014 TelecommunicationServices2018.752.970.49(30;2)0.0111.8720.03410.0067(1;0)0.0082.5325.12370.0000(1;30)0.0311.9290.0012 Utilities2018.79.430.46(30;2)-0.0080.968-0.01250.0067(1;0)0.0881.534-1.87930.0602(1;30)0.0110.9820.0002
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2-2 presentsthesamedatabutcategorizedbybig/smallmarketcapitalization,andvalue/mid/growthbook-to-marketratio.Thesmallmarketcapitalizationshowsabout10timesbiggerjumponaveragesabnormalreturns.Theabnormalreturnsinthevaluebook-to-marketcategorydrop0:04%onaverage,whereasforthegrowthcategorytheyjump0:07%onaverage.AsinTable 2-1 ,the^andR2valuesareindicativeoflowornoserialcorrelationforeverycategory. log(ki)=+log(k(i1))+i;i=1;:::;K;(2{26) whereiiswhitenoise.Weuselog-scaleinterarrivaltimessincetheyonlyallowpositivevalues.ThestationarityofinterarrivalcanbeassessedwiththeKwiatkowski-Phillips-Schmidt-Shin(KPSS)test Kwiatkowski,Phillips,Schmidt,andShin ( 1992 ).The 41
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Direction,Volatility,andAR(1)TestforAbnormalReturnsbyMarketCapitalizationandBook-to-MarketRatio Thistablepresentssummarystatisticsforabnormalreturnsfromatotal237rms,categorizedbybig/smallmarketcapitalizationandValue/Mid/Growthbook-to-marketratiosfrom2004to2006,followingthecategorizationruleinSection2.2.1.ColumnlabelsareidenticaltoTable 2-1 FirmsEventsMarketCap.BTMEventAbnormalReturn^ Small1019.81.080.45(30;2)0.0032.23-0.01840.0041(1;0)0.1613.889-4.48890.0000(1;30)0.022.3340.0003 Value8214.97.940.71(30;2)0.0061.8-0.03220.0037(1;0)-0.0423.304-8.75140.0000(1;30)-0.0121.9290.0010 Mid8316.426.710.4(30;2)0.0011.736-0.02490.0035(1;0)0.133.025-7.10850.0000(1;30)0.0261.7820.0006 Growth7214.615.170.19(30;2)0.0052.240.00540.0040(1;0)0.0723.6371.37070.1705(1;30)0.0032.3710.0000
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Table 2-3 reportsresultsonautocorrelation,stationarity,distributiontforkeydevelopmentinterarrivaltimescategorizedbyindustrysectors,marketcapitalization,andbook-to-marketratios.Overallestimatesof^areverysmall,nearzeroforallrmsandtheR2ofthemodelshowstheeectof^tobeweak.Hencewecanconcludethattheinterarrivaltimeseriesthroughoutallthecategoriesarenotlikelytobeseriallycorrelated.Theresultallowstoassumethatinterarrivaltimesaredistributedindependently.IntheKPSStest,wecompareKPSSlevelandKPSSvalueasinTable1atpage166in Kwiatkowski,Phillips,Schmidt,andShin ( 1992 ).Ifweconsidercategoriesaccordingtoindustryandmarketcapitalization,thenweseethatKPSSlevelvaries.However,forcategoriesalongbook-to-marketratiosshowssubstantialstationarityby5%criticallevel.Theseresultsimplythatthebook-to-marketratioofarmisabetterindicatorofnewkeyarrivalthanothertwofactors.FromtheKStest,wendthattheDstatisticsofexponentialdistributionareclosertozerothanthoseofthenormaldistribution,Hencewecanarmthatinterarrivaltimedistributionofkeydevelopmentfollowsindependentexponentialdistribution,andthatdistributionislikelytohaveastationaryparameter. 2-2 showsthemarginalposteriorprobabilityPssgivenfanktgduringaneventperiod.TheeventdateisApril6th,2006,andthermisJ.C.Penny.Wehavetwokeydevelopmentsonthatday:oneisthatJ.C.PenneyreiteratedQ1EPSguidanceandtheotheristhatS&PraisedJ.C.Penney'screditrating.Clearly,theRegime2probabilitiesshowthatinformationmayhavebeenknowntoinvestorsabout15daysbeforetheannouncement.ThemostrecentkeydevelopmentaboutJ.C.Pennywas 43
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AR(1)Test,StationarityTest,andDistributionFittingforInterarrivalTimesofKeyDevelopments 2-1 and 2-2 .TheestimatefortheinterceptoftheAR(1)modelisomitted. ^KPSSKS-EKS-N Energy1620.190.063.170.000.060.120.10.080.310.180.00Materials3530.220.063.860.000.040.190.10.070.100.190.00Industrials3390.200.053.890.000.040.690.00.070.050.200.00ConsumerDiscretionary4930.240.054.950.000.050.350.10.070.010.150.00ConsumerStaples3470.170.053.190.000.030.220.10.070.050.160.00HealthCare5660.220.045.240.000.050.230.10.070.010.210.00Financials2190.230.064.060.000.070.580.00.080.140.190.00InformationTechnology4280.230.045.160.000.060.510.00.100.000.100.00TelecommunicationServices4070.260.046.720.000.101.090.00.100.000.220.00Utilities3800.200.053.990.000.040.100.10.080.020.110.00 Big27130.250.0214.380.000.070.170.10.050.000.170.00Small9810.170.035.860.000.030.120.10.090.000.180.00 Value12900.260.0310.490.000.080.820.00.050.000.180.00Mid13470.230.038.670.000.050.780.00.060.000.190.00Growth10570.240.039.030.000.070.520.00.060.000.170.00
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PosteriorProbabilitiesofThree-RegimeModelinanEventPeriod announcedonMarch2nd,morethanamonthprior.Thereforeitisnotlikelythatregime2isaresultofthepreviousnews.Figure 2-3 presentsasetofconvergencegraphsofMLEestimatesforfsgandfsgfromMCEM,withthesamedataasinFigure 2-2 ,Therstrowplotsfsgandsecondrowplotsfsg,fors=1;2;3,consecutively.InthiscasewecaneasilynoticethatMLEestimatesconvergequickly.Weidentifythatinregime2,directionisnegativeandeventhoughobviouslygoodnewswasannounced,directioninregime3isalmost50%lowerthanthatinregime1.Volatilityinregimes1and2areverysimilar.However,inregime3,itjumpsupto80%thevalueinregimes1and2.Thisresultimpliesthatthemarketovervaluedtheequitybeforetheannouncementandthatthepost-announcementperiodshowshighervolatilitywithadropindirectioncomparedtothepre-announcementperiod. 45
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MLEConvergenceofsandsinMCEM whichhasthehighestBayesfactorrelativetoalltheothers.Thisapproachisempiricalandisonlymeanttosuggestgood,plausibleregime-switchingmodels.Togetstatisticallymeaningfulresults,werestrictourdatatothe30mostrecentkeydevelopmentsandtheirassociatedabnormaldatafor26rmsintheyear2004to2006. LetBrsdenotetheBayesfactorofamodelwithrregimesrelativetoanotherwithsregimes.Achange-pointmodelwithrregimewillbethebestifitattainsthelargestvalueoflnBrsforallvaluesofsinf1;2;3;4g.Sincethiscomparisonsmustaccountforall30eventsinvolved,thecriterionisinfacttheaverageoveralltheseevents,denoted lnBrs. Jereys ( 1961 )suggeststhatamodelMrwithrregimesmustsatisfy lnBrs>2forallsinordertobeconsideredamongthebest. Table 2-4 reportstwoexamplesofselectingthebestchange-pointmodel.FirmAA,Alcoa,hasfourcompetingchange-pointmodelsfrom1regimeto4regimes.ObservingthesamplemeanofBayesianfactor lnBrs>2on30keydevelopments,wecanidentify 46
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SelectionoftheBestChange-PointModel:Example ThetablereportsGibbssamplerresultdescribedinSection2.1.2.26rmshaving30ormorekeydevelopmentareselected,andlnBrsiscalculatedbychange-pointmodelhavingrregimes.Therstfourcolumnsshow lnBrs(>2)tocompareMrwithMs.Thenextfourcolumnsshow95%uppercondencelimitfromone-sidedttest. ComparedModelUpperCondenceLimit TickerModelM1M2M3M4M1M2M3M4 JCPM10.0030.6328.7112.44NA67.5957.2230.92M2-30.630.00-1.92-18.196.32NA33.2323.93M3-28.711.920.00-16.27-0.2137.07NA11.13M4-12.4418.1916.270.006.0360.3143.68NA Table2-5. TheBestChange-PointModels Numberforeachtickeristhebestnumberofregimesinchange-pointmodel,whichisselectedbythebiggestsumofpvalues TickerMrTickerMrTickerMrTickerMr thatM4hasthebiggest lnB4soveralls=1;:::;4.Thereforeweselect4-regimechange-pointmodelforAlcoa.ThesecondexampleofJ.C.Pennyalsoshowsthatover30samples,one-regimemodelispreferred.FollowingthewayintroducedinTable 2-4 ,Table 2-5 reportsthebestchangepointmodelsbyallrms.Among26rms,14rmspreferone-regimemodel,hencetheydoesnotshowspecicpatternofregimenumbers.Theresultmayimplythatoverahalfofallsamplermsmayhaveexperiencednosignicantimpactinabnormalreturnfromanykeydevelopment.Otherimplicationisthatnoonechange-pointmodelisdominantthroughout30events.Forexample,someeventsprefer3-regimemodel,andothereventsprefer4-regimemodel,sothat1-regimemodelmay 47
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2-6 showsthatonlyoneregimemodelispreferredwhenwetakesamplefromallrms.Oneinterpretationofthisresultispossible.Equitymarkethasaconstantowofnewdevelopmentfromvariousrms.Therefore,ifwetakeaverageonabnormalreturnofallrms,approximatedabnormalreturnofmarketisnotsensitivetoindividualrm'skeydevelopmentarrival. 2-2 ,regime2islikelytobeginabout15daysbeforethenewsisannounced,andregime3beginsrightafterthenewsisannounced.Wecansuspectupto15daysbeforetheannouncements,priceadjustmentsinthemarketmayhavealreadystarted.Table 2-7 reportslengthsofregimesinthebestchange-pointmodels,excludingone-regimemodel.AtM2,therstregimelengthisalwayslessthan30days,implyingtherstregimeisnishedbeforeannouncement.Itmaybeinterpretedthatatthesecondregimekeydevelopmentisincorporatedinequitypricebeforetheannouncement.AtM3,thesecondregimetendstoendrightbeforetheannouncementdate.AtM4,3rdregimehasannouncementdateinmostcases.Theseobservationsindicatethatpriceisnotadjustedinstantlyateventdate,butgraduallyadjusted,eitherbyreachingconsensusatnewpricelevelorbyadverseselectioneectcausedbyinformedtrader.Therefore,wedenotearegimehavingannouncementdateisatransitionregime. 48
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TheBestChange-PointModelforAllFirms ThetablereportsGibbssamplerresultdescribedinSection2.1.2.26rmshaving30ormorekeydevelopmentareselected,andlnBrsiscalculatedbychange-pointmodelhavingrregimesfromall26rms.Nextfourcolumnsshow lnBrs>2tocompareMrwithMs.Thenextfourcolumnsshow95%uppercondencelimitfromone-sidedttest.Thelastfourcolumnsshowpvaluesdeterminingwhethernullhypothesisisrejected. ComparedModelUpperCondenceLimitpvalue ModelM1M2M3M4M1M2M3M4M1M2M3M4
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LengthsofRegimesintheBestChange-PointModels Tablereportssampleaverageofmssanditscondencelimitssampledfrom30keydevelopmentsbyeachrms.mssisthenumberofone-steptransitionsstayingthesameregimes.Thisvaluecanbeinterpretedasthenumberofdaysinregimes.Firsttwocolumnsindicatetickersymbolsandchange-pointmodelhavingrregimes.Thenextfourcolumnsoftherstrowshowstheaveragelengthofregimes,^mssinaneventperiodof61days.Thesecondrowshows95%condencelimitoftwo-sidedttest. TickerMr^m11^m22^m33^m44 2-3 ,inthatvolatilityintransitionregimemaybehigherthanthatinstableregime.Table 2-8 reportssamplemeansandWelch 50
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DirectionandVolatilityDierencesinConsecutiveRegimes 2-5 ,excludingrmspreferoneregimemodel.FirstpanelshowsthesamplemeanofMLEofdirections,^s,on30samplesbyeachregime,and95%condencelimitandpvaluefromWelchtwosamplet-test.Nullhypothesisonthetestisthatthedierencebetweenmeansofthedirectionsonconsecutiveregimesarezero.ThesecondpanelpresentssamplemeanofMLEvolatilities^s,andt-testresults.^sand^sareestimatedbyMCEMdescribedinSection2.1.3. WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr ^1
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Anotherissueisthepossibilityofrelationsamongdirectionandvolatilityoncurrentandpreviousregimeswhenstructuralbreakoccurs.Asimplepairoflinearautoregressivepaneldatamodelscanbeusedtoestimatetherelations: ^j=10+11^i+12^i+13^j+1j; ^j=20+21^i+22^i+23^j+2j; wherei=1;:::;S1,j=2;:::;S,andtheindexofeventsamplenkaresuppressed.Table C-5 showsautoregressivepaneldatamodelestimationresultsontheprevailingchange-pointmodels. 52
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WereportOLSestimatesofsimpleautoregressivepaneldatabetweendirectionandvolatilityofcurrentregimeandofthelastregime.Nullhypothesesoncoecientsares=0,s=1;:::;S.Explanatoryvariableisspeciedatcolumn^=^,andcomparingpairofregimesis(i;j),jiscurrentregimeandiispastregime.Superscriptsdistinguishexplanatoryvariablesin(2.28)and(2.29)aresuppressed. ^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 BIIB3(1;2)^-0.13080.5223-0.32948.4220.00590.8230.81230.00960.2365^0.01070.00230.09590.027400.98650.21930.00960.3512(2;3)^00.0224-0.09760.42610.99430.18960.66250.26090.0725^0.0131-0.02680.0210.113400.00090.85580.26090.4035 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 CAT3(1;2)^-0.0157-0.03710.20231.02980.11140.92960.71450.15050.0823^0.0106-0.0988-0.22980.075600.38280.11670.15050.1682(2;3)^0.00130.0005-0.08810.0280.73190.99390.71040.92180.006^0.00970.02180.02160.013500.64140.89550.92180.0115 CELG4(1;2)^-0.01570.13412.8711-0.39830.2710.80220.010.37710.2377^0.01290.43130.4765-0.07560.0320.05540.35330.37710.1649(2;3)^0.026-0.31910.1685-1.08870.16510.17880.74690.18150.1033^0.0175-0.1189-0.0052-0.062100.03110.96650.18150.1919(3;4)^-0.01670.0450.14520.65380.0260.51180.59490.00930.24^0.0213-0.0265-0.1350.356200.60050.50240.00930.2404 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 KFT2(1;2)^-0.00450.01950.0140.52520.00010.37160.833300.5771^0.0091-0.0364-0.0611.093100.24510.522300.5903 PTRY4(1;2)^-0.00710.07780.6055-0.13460.73340.87810.52820.88420.0201^0.0157-0.0276-0.1959-0.006200.79930.33830.88420.0423(2;3)^0.0125-0.0921.2469-1.1230.52460.69510.24620.07670.1731^0.0175-0.086-0.0632-0.10290.00110.21990.84810.07670.1713(3;4)^0.0248-0.0406-0.3579-1.026900.30080.01020.00020.477^0.0201-0.0048-0.2149-0.412300.84740.01560.00020.473 TMO4(1;2)^-0.0084-0.195-1.29891.17270.42010.78380.2180.11490.1537^0.00880.0338-0.02350.07920.00030.85480.93260.11490.1021 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 UNH2(1;2)^-0.00640.05710.16330.2490.03190.61550.19260.13020.1264^0.01480.1012-0.15720.344700.44760.28890.13020.1882 VZ3(1;2)^0.0069-0.0979-0.2916-0.44440.03130.76480.43260.1960.1065^0.00570.03770.1338-0.14270.0010.8390.5260.1960.0964(2;3)^-0.0008-0.03440.06810.16750.77430.79010.77210.54820.0171^0.00760.0611-0.21210.083800.50260.1950.54820.1109 WYE2(1;2)^-0.0041-0.04680.07120.30160.01430.67240.53350.01140.2363^0.0117-0.0248-0.06620.735700.88610.71140.01140.2273
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Fromtheattempttoanalyzestatisticalpropertiesfromthesampleofeventperiods,wefoundthatdirectionandvolatilitymightbedrawnfromthesamedistribution,andtheyareseeminglyuncorrelatedbetweenregimes.Thesefacts,andthendingfromSection2.2.2,provideajusticationofdesigningstochasticprocessofkeydevelopmentarrivalwithindependentandidenticallydistributeddirectionandvolatilityrandomvariables,hencewecandeneitasaMartingaleprocess. Wecanthinkoftwopossibleissuesfromtheseresults.Oneisthatapossibilityofimpactsofsamplekeydevelopmentsaresimilarenoughtobesummarizedasonedistribution.Ifkeydevelopmentaboutsomecataclysmicdamagetothermexistsbutisnotincludedourmodel,themodelparametersestimatedbygivensamplecannotbesaidtorepresentallpossiblekeydevelopment.Theotherissueisthatthelackofstatisticalpropertyisduetosmallsamplesize.Bothissuesrequirelongertimehorizonwithvarioustypesofkeydevelopments,anditmaybesubjecttothefutureresearch. 57
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Thischapterisorganizedasfollows.InSection 3.1 ,weconstructthebidandaskpricingstrategy.Section 3.2 illustratestheempiricalanalysisontradeandquotedata.Section 3.3 showssimulationresultscalculatedbythemodelinSection 3.1 3.1.1EvolutionofFundamentalValue Theannouncementofakeydevelopmentcreatesatransitiontimeinterval,whichwecalltransitionregime.Informedtradersacquireinformationearlierthanthepublicandtheirtradescauseadverseselectioneectsonuninformedtradersuntiltheinformationisfullyincorporatedintotheequityprice.Itmaytakeareasonableamountoftimetointerprettheimplicationofakeydevelopmentwithpricesadjustingtonewlevelsofdirectionandvolatility.Wecallthistimeintervalatransitionregime.Whenthetransitionregimeends,weassumenewlevelofdirectionandvolatilitythatpersistuntilthenextkeydevelopmentoccurs,whichagainbreaksthefundamentalvaluestructurallyfromitspast.Welabelthisintervalstableregime. Thefundamentalvalueprocessinthepresentworkisdenedasapairofprocessesoffundamentalvaluecompoundingdirectionsandvolatilitiescontinuously.Weassume 58
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Followingtheannouncementofthenthkeydevelopment,theresultingchangeinfundamentalvalueleadstovaluesSnandSn2,ofdirectionandvolatility,respectively,forthenextregimedrawnfromthedistributionbelow: Theabovedistributionsarealsoassumedtobeindependentacrossregimes.ApricejumpJnmayalsooccurwhenthereisagapbetweenitsmarketexpectationandthepricefollowingthekeydevelopment.WeparameterizethejumpwiththedirectionTnandvolatilityTn2forthetransitionregimeas where Wefurtherassumethattheabovedistributionsareindependentacrossregimes.Theparametersforstableregime(S;S2;S;S)andforthetransitionregime(T;T2;T;T)canbeobtainedthroughtheofeventstudymethodologywithhistoricalpricedata.DirectionalandvolatilityinformedtradersobtaintheactualvalueSnandSn2,respectively,whereasuninformedtradersandmarketmakersonlyknowtheircorrespondingdistributionsgivenabove. ThekeydevelopmentarrivalprocessI(t)isofPoissontypewithconstantrateI,andisknowntoinformedtraders.Thedurationofthenthtransitionregime,LIn,followsanexponentialdistributionwithconstantrateL.WithTInmeasuring(indays)thelength(orduration)ofthenthkeydevelopment,thecorrespondingalternatingstableand 59
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SamplePathsofFundamentalValue(left)and(ontheright)AssociatedDirection,Volatility,andPriceJumpsatKeyDevelopments transitionregimeintervalsaredenedrespectivelyas: and Obviously,thebeginningofatransitionregimecoincideswithastableregime'sending. Informedtradersestimatethelog-scalereturndirectionofanequity,wI(t),bycontinuouslycompoundingSn,anditsvolatilityvI(t)bycontinuouslycompoundingSn2: Figure 3-1 displayssamplepathsofafundamentalvalueprocessandassociateddirection,volatility,andpricejumpprocessesatkeydevelopments.Theleftsidegraphshowsa1-yearevolutionoffundamentalvaluewith3standarddeviationslimits.Directionaltradersbelievethatthepricewillcompoundataconstantdirectionuntilthearrivalof 60
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Oneofthekeyassumptionsinthispaperisthatprivateinformationcontainseitherdirectionorvolatilityaboutthenextstableregime,notacertainpricelevel.Thereforeunlikein Kyle ( 1985 )and Easley ( 1996 ),informedtradersdonottradefrominformationonapricelevel.Instead,theytradedynamicallyfollowingmarketaction.Volatilitytraderscannottakeanyadvantageinequitytradingwithoutreferringtoassociatedoptionprices.Hence,weruleouttheirroleinthissetup.Asweassumethatallinformedtradersplacemarketorders,theyhavenoabilitytochoosethesizeofthetrade.Insteadtheycantrademoreintensivelytoaccumulatethemaximumprot.Thereforethestrategyofmarket-ordertradersandthequoterevisionsofmarket-makersarebasedonthetradingintensity.WhenNBBOisrevisedbyeitheratrade,publicinformation,orkeydevelopmentannouncement,allthemarketparticipantsinitializetheirstrategyonthe 61
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Adirectionaltrader'straderateisproportionaltothespreadswI(t)a(t)andb(t)wI(t)asfollows: wherex+;xrefertomax(x;0);min(x;0)respectively.DB(t)andDB(t)arethetradingratesofdirectionaltraderforbuyingandsellingattimet,respectively,andcDBandcDSarecoecientsrepresentingsensitivitiestothosespreads.Basedonthisrate,directionaltradersplaceordersbyfollowingthedurationdistributionsas Alltradeandquotedurationsaremeasuredinseconds. Anuninformedtrader'straderateisbasedonarelationshipbetweenthebuyingandsellingdurationsTB;TS,andthespreadsa(t)w(t)andw(t)b(t).Inestimatingtradedirection,wemayhavecaseswherewecannotdetermineasideoftradewhenthebidoraskpricedoesnotchangeafteratrade,oriftwoormoresubsequenttradesoccuratthesameprice.Wecallthiscaseasindeterminatetrade,withdurationTI.EmpiricalidenticationoftradingdirectionB;I;SismentionedinSection 3.2.2 .Log-scaledurationlogTandthespreadsa(t)w(t)orw(t)b(t)canbeexpressedaslinearmodelssuchas:logTB:=cUB0+cUB1(a(t)w(t))+B;logTI:=cUI0+I;logTS:=cUS0+cUS1(w(t)b(t))+S;
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3.3 .RatesofuninformedtraderbytradedirectionsareUB(t)=1=exp(UB(t)+UB2=2);UI(t)=1=exp(UI(t)+UI2=2);US(t)=1=exp(US(t)+US2=2); AmarketmakerrevisesNBBOquotesinthreecases:afteratrade,newpublicmarketinformation,orannouncementofakeydevelopment.Whenatradeoccurs,amarketmakersetsthenextbidandaskquotesincorporatinganyinformationrevealedbythelasttrade.Accordingto GlostenandMilgrom ( 1985 ),amarketmakersetsbid-askspreadtohedgeagainsttheadverseselectionriskfrominformedtrades.NewpublicinformationrevisesNBBOquotesinarealmarketbecausemultiplemarketmakersandpubliclimit-ordertradersconstantlyupdateNBBOquotesforliquidityorfromindustry-wideinformationoracompetitor'skeydevelopment.Whenakeydevelopmentisannounced,amarketmakershouldreviseNBBOquotestoincorporatethenews;otherwiseitcancauseasignicantadverseselectionriskforanytraderagainstthemarketmaker. 63
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WealsoassumetherateofNBBOrevisionwithouttradeorkeydevelopment,NWOTisconstant.ItcanbefoundempiricallybysubtractingtraderatefromthetotalNBBOrate,ignoringtherateofkeydevelopmentdurationbecauseitisalotlongerthenatradeoranNBBOrevision. Fromthememorylesspropertyoftheexponentialdistribution,thenextarrivalmayhavethesmallestdurationsofar.DenotebyNBBO(t)thecountingprocessofNBBOrevisions.ThenthedurationofnextNBBOrevisionis Fortheremainderofthispaper,wesuppressthesubscriptNBBO(t)+1.ThentherateofNBBOarrivalattimetis Finally,letX(t)beacauseofNBBOrevisionattimet,thenX(t)istheoneoffUB,UI,US,DB,DS,NWOT,Ig.ThentheprobabilitythatthenextNBBOrevisioniscausedbyX(t)=xis 3-2 presentssamplecountprocessesofeachtypeofNBBOrevisionsontheleftandshowsdurationdensitiesforeachtypeontheright.Thetimehorizonis30minutes. 64
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ARealizationofNBBOrevision 3.1.2 ,therevisionofbidandaskpriceswithouttradeincorporatespublicinformationorannouncementofkeydevelopments.Inthiscaseweassumethatadverseselectionriskisresolvedbynewinformation,sothatthemarketmakerrevisesbid-askspreadwithahistoricalaverage.NBBOrevisionsasaresultoftrade,however,containadverseselectionriskthattradersmaybemoreinformedthanmarketmakers.Thereforemarketmakerrevisebidandaskpricesaswellasbid-askspreadstocompensateforthepotentiallosstoinformedtraders. Wesuggestthreepossiblebid-askspreadsettingstrategies.First,aconstantbid-askspreadstrategytosimplykeepthebid-askspreadconstantandonlychangeoccursatnextbidandprices.Second,aBayesianNashequilibriumstrategywithpartialmomentthatisadirectextensionof GlostenandMilgrom ( 1985 ),whereamarketmakercalculatestheexpectedvalueoffundamentalvaluegiventhenexttradedirection.Estimationofpartialmomentsisbasedonhistoricaldurationofkeydevelopment,direction,andvolatilitydata.Third,aBayesianNashequilibriumstrategywithorderimbalancethatincorporates 65
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SupposethenextNBBOrevisionoccursattimetandthecurrenttimeist0.DenotebyD(t)thejumpprocessoftradedirectiongiventhattradeoccursattimet.ThenDi=8>>>>>><>>>>>>:1;Ifbuy-initiatedtradeoccurs,0;Iftradedirectioncannotbedetermined,1;Ifsell-initiatedtradeoccurs. WerecallthattheestimationoftradingdirectionisaddressedinSection 3.2.2 Thenthelasttradedpriceisw(t)=8>>>>>><>>>>>>:a(t0);IfD(t)=1;a(t0)+b(t0) 2;IfD(t)=0;orNBBOrevisionwithouttradeoccurs,b(t0);IfD(t)=1 IfanNBBOrevisioniscausedbynthannouncementofkeydevelopment,thenw(t)=w(t0)+Jn: 66
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ABayesianNashequilibriumpricestrategywithpartialmomentsapproximatesaninformedtrader'sbuying,DB(t)andsellingDS(t)as Unfortunately,amarketmakerhaslittlemeantoestimatethecoecientscDBandcDSdirectlyfromtradeandquotedata.Instead,themarketmakerperformsasimulationofthepricedynamicstosearchthosecoecientsoptimizingperformancemeasuresdescribedinSection 3.1.4 .Belowaretheformulasoftwospreads: 67
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RealizationsofNBBOPriceEvolutions Then, (3{21) 3{18 ),Eq.( 3{19 ),Eq.( 3{21 ),andEq.( 3{22 )aregiveninAppendix??.Figure 3-3 presentsthreesamplepathsofNBBOpriceevolutionsfollowingthethreestrategies.Theupperpanelshowsthepriceevolutionofask,lasttraded,andbidprices.Thelowerpanelshowstheorderimbalanceofeachstrategy. 68
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NBBO(T)NBBO(T)Xn=1(w(Sn)wI(Sn)); NBBO(T)1NBBO(T)Xn=1(jw(Sn)wI(Sn)jME(T))2; whereSnisthesumofdurationsofNBBOrevisionsdenedas Amarketmaker'snetprotsconsistsofprotsfromuninformedtradesandlossesfrominformedtrades.Amarketmakermakesaprotfrombid-askspreadsforeachsharewhenaround-triptradehappens.WeextractthetradecountingprocessT(t)fromNBBO(t).T(t)consistsofoneoffUB(t);US(t)DB(t);DS(t)g,whichareprocessescountingthenumbersofuninformedbuy,uninformedsell,directionalbuy,anddirectionalselltradesuptotimet,respectively.Amarketmaker'sprotPM(T)uptotimeTcanbeexpressedas DecisionvariablesforselectingbidandaskpricingstrategiesarethecoecientscDBandcDSthatweuseincalculatingthebid-askspreadintheBayesianNashequilibrium 69
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3.2.1Data KeydevelopmentsdataforselectedrmsareobtainedfromThomsonReuters''High'signicantdevelopmentreportsduringtheyear2004-2006.273rmshaveoneormoresignicantdevelopments,26rmshavemorethan30signicantdevelopmentsfromtotal4114signicantdevelopments. IntradayquoteandtradedataareacquiredfromconsolidatedtradeandquotedatafromTAQdatabaseforselectedrmsin2006.SinceconsolidatedquotedatasuppliedbyTAQretainwholelimitorderbookdata,weextractNBBOdatabyrunningPerlscriptontheWRDSUNIXserver.FromtheresultingdataweonlyselectdistinctNBBOquotes.WelterconsolidatedtradedatabyselectingonlythoseindicatorCORRequaltoeither0;1or2,toruleoutcanceledtransactionaswellastradeswithsize0.Incaseofmultipletradesorquotesinasecond,wedistinguishthoserecodesbyaddingnumbersgeneratedfromuniformdistributionintheinterval(0;1).Forexample,ifthreetradesorquotes 70
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Todeterminethetradedirection,D(t)ofeachtrade,weuseanalgorithmof Ellis,Michaely,andO'Hara ( 2000 ).First,wesplitbidandaskquotesinNBBOandinterweavewithtradedata,orderingbytime.ThenwelagtheNBBOdataby1secondtoadjustwiththetimelagoftradereporting.Second,weperformpricematchingfromeachtrade.IfthemostrecentNBBOrecordbeforeatradehasanaskpriceidenticaltothattrade,thensetdirectionofthetradeto1.IfthemostrecentNBBOrecordhasbidpriceidenticaltothattrade,thensetdirectionofthetradeto-1.Third,iftradepricesandNBBOpricesdonotmatchthenweperformatick-testbysimplysettingdirectionto1whencurrenttradepriceishigherthanthepreviouslytradedpriceand-1otherwise.Ifneitherpricematchingnortick-testdeterminesatradedirection,thenwesetthedirectionto0,implyingthatthedirectionisindeterminate.FromTable 3-1 toTable 3-3 ,wesummarizethetradedatabyexchanges,tradetimeintervals,andindustrysectors,respectively.InTables 3-4 to 3-6 ,wesummarizeNBBOdatabyexchanges,tradetimeintervals,andindustrysectors. Rosenthal ( 2008 ),andisaconsequenceofthepropertyofthePoissonprocessusedinmodelingNBBO(t).
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ThistablesummarizesconsolidatedtradedataincludingdirectionanddurationfromTAQin2006from293rmsintheRussell3000set.Thedataarecategorizedbyexchanges.DuetothedataerrorsinTAQ,weexcludedtradedataofsomermswithexchangecode1and8,whichisabout882,590trades.Exchangecodes:`A':AmericanStockExchange,`B':BostonStockExchange,`I':ISE,`M':MidwestExchange(Chicago),`D'NASDADFandTRF,`Q'and`T'NASDAQ-NMSStockMarket,`N'NewYorkStockExchange,`C'NSX,`P'PacicExchange,`X':PhiladelphiaExchange.During2006,NASDAQexchangecodehasbeenchangedfrom\T"to\Q".Wepresentsummaryoftwocodesseparately.Price,spreads,andtradedurationaremeasuredbylog-scale.B-Aisanaveragepercentagebid-askspread.A-LTisanaveragepercentagespreadbetweenaskpriceandlasttradedprice,andLT-Bisanaveragepercentagespreadbetweenlasttradepriceandbidprice. ExchangeFirmsTradeTradesSizePriceA-LTLT-BA-LTLT-BTradeCodeDir.atTrd.atTrd.afterTrd.afterTrd.Dur. A16Total6569315273.2040.00080.00180.00080.00122.56Buy3383155103.2060.00010.00190.00020.00162.59Indet.583315383.2610.00130.00480.00080.00162.14Sell2602855463.1880.00170.00100.00160.00062.60 Continuedonnextpage
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ExchangeFirmsTradeTradesSizePriceA-LTLT-BA-LTLT-BTradeCodeDir.atTrd.atTrd.afterTrd.afterTrd.Dur. B235Total4745273983.6920.00050.00080.00030.0003-0.03Buy1936894093.6800.00000.00060.00000.00040.10Indet.644643473.7270.00230.00380.00050.0006-1.17Sell2163744023.6930.00040.00000.00040.00000.20 I51Total6931963.1020.00040.00040.00040.0004-0.99Buy2891863.0170.00000.00070.00000.0007-0.90Indet.963143.4130.00050.00040.00030.0004-1.08Sell3081683.0840.00070.00000.00070.0000-1.04 M219Total9475539343.6060.00100.00220.00040.00050.14Buy41814210723.5930.00000.00080.00000.00070.37Indet.1342876343.6680.00470.01320.00100.0014-0.96Sell3951248893.6000.00080.00010.00070.00000.27 D273Total256782084583.4850.00040.00070.00050.0007-0.69Buy124077514583.4810.00010.00070.00020.0008-0.64Indet.21005325363.5260.00140.00420.00120.0019-1.27 Continuedonnextpage
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ExchangeFirmsTradeTradesSizePriceA-LTLT-BA-LTLT-BTradeCodeDir.atTrd.atTrd.afterTrd.afterTrd.Dur. Sell111699254433.4830.00070.00010.00070.0003-0.63 Q115Total292314982913.1950.00040.00050.00050.0005-1.41Buy124467252883.2060.00000.00090.00020.0008-1.24Indet.50270583363.1340.00030.00030.00050.0005-2.28Sell117577152763.2100.00090.00000.00080.0002-1.22 T257Total342711103943.3150.00050.00060.00060.0007-0.94Buy153274934013.3170.00000.00100.00020.0011-0.81Indet.46878013923.2980.00070.00110.00080.0010-1.92Sell142558163873.3180.00100.00010.00100.0003-0.76 N148Total624699025913.6580.00030.00040.00030.00030.70Buy308249545903.6540.00000.00060.00010.00050.71Indet.42923727683.7280.00040.00060.00030.00040.30Sell273525765653.6520.00050.00010.00050.00010.74 C256Total30737762783.2880.00040.00040.00040.0004-1.34Buy12938902823.2990.00000.00080.00010.0007-1.21 Continuedonnextpage
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ExchangeFirmsTradeTradesSizePriceA-LTLT-BA-LTLT-BTradeCodeDir.atTrd.atTrd.afterTrd.afterTrd.Dur. Indet.5180722873.2510.00030.00030.00030.0003-1.99Sell12618142703.2920.00080.00000.00070.0001-1.22 P273Total389882222433.3530.00040.00040.00040.0004-1.28Buy167714332413.3770.00000.00080.00010.0008-1.14Indet.57798582733.2950.00030.00030.00030.0003-2.11Sell164369312343.3480.00080.00000.00070.0001-1.13 X99Total2001502153.6660.00020.00030.00020.00031.01Buy1117543413.678-0.00030.0007-0.00020.00070.94Indet.149363613.7190.00030.00030.00030.00031.13Sell735467533.6360.0009-0.00040.0009-0.00031.10
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ThistablesummarizesconsolidatedtradedataincludingdirectionanddurationfromTAQin2006from293rmsinRussell3000.Thedataiscategorizedbytradetimeintervals. TradeFirmsTradeTradesSizePriceA-LTLT-BA-LTLT-BTradeIntervalDir.atTrd.atTrd.afterTrd.afterTrd.Dur. Continuedonnextpage
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TradeFirmsTradeTradesSizePriceA-LTLT-BA-LTLT-BTradeIntervalDir.atTrd.atTrd.afterTrd.afterTrd.Dur. Buy267589443993.4550.00000.00070.00010.0006-0.16Indet.63072193583.3630.00020.00020.00030.0003-1.40Sell248246873793.4440.00070.00000.00060.0001-0.17
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ThistablesummarizesconsolidatedtradedataincludingdirectionanddurationfromTAQin2006from293rmsinRussell3000.ThedataiscategorizedbyindustrysectorclassiedbyGICS. IndustryFirmsTradeTradesSizePriceA-LTLT-BA-LTLT-BTradeSectorDir.atTrd.atTrd.afterTrd.afterTrd.Dur. Consumer29Total220276423193.6370.00030.00040.00040.0006-0.45DiscretionaryBuy99725583263.6450.00000.00070.00020.0007-0.30Indet.28314463143.6140.00050.00080.00050.0007-1.50Sell92236383123.6350.00060.00010.00060.0003-0.29 Consumer26Total175327354723.4750.00040.00060.00050.0006-0.10StaplesBuy85166224783.4430.00000.00090.00010.0009-0.01Indet.15163184953.6190.00070.00140.00070.0009-0.98Sell74997954603.4830.00090.00000.00080.0002-0.02 Energy27Total165417904163.6980.00040.00070.00040.00060.10Buy80839304183.6940.00000.00080.00020.00070.15Indet.14484894723.7440.00100.00290.00080.0014-0.53Sell70093714043.6920.00070.00010.00070.00020.17 Financials29Total152477513273.4470.00040.00050.00040.0005-0.37 Continuedonnextpage
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IndustryFirmsTradeTradesSizePriceA-LTLT-BA-LTLT-BTradeSectorDir.atTrd.atTrd.afterTrd.afterTrd.Dur. Buy68233003313.5000.00000.00080.00020.0008-0.16Indet.20623873243.2360.00050.00090.00060.0007-1.54Sell63620643243.4590.00070.00010.00070.0002-0.22 Health30Total253395264223.4490.00040.00050.00050.0005-0.63CareBuy114985004263.4520.00000.00080.00020.0008-0.53Indet.27818464253.4530.00050.00080.00070.0007-1.41Sell110591804173.4440.00080.00000.00080.0002-0.54 Industrials29Total161426423323.5200.00050.00050.00050.0005-0.01Buy75253633323.5440.00000.00080.00020.00080.08Indet.15954293703.4630.00080.00130.00080.0008-0.85Sell70218503253.5080.00080.00000.00080.00020.09 Information26Total294367582773.3130.00030.00030.00040.0004-1.69TechnologyBuy120810652833.3000.00000.00070.00010.0007-1.53Indet.54702662603.3790.00020.00030.00030.0004-2.46Sell118854272793.2970.00080.00000.00070.0001-1.50 Continuedonnextpage
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IndustryFirmsTradeTradesSizePriceA-LTLT-BA-LTLT-BTradeSectorDir.atTrd.atTrd.afterTrd.afterTrd.Dur. Materials29Total177034753743.7190.00040.00050.00040.00040.29Buy85326453743.7120.00000.00070.00010.00060.34Indet.14845514113.7590.00080.00130.00060.0008-0.32Sell76862793663.7190.00060.00010.00060.00020.36 Telecommunication25Total254072828352.8650.00050.00060.00050.0005-1.26ServicesBuy118964928502.9330.00000.00100.00010.0009-1.14Indet.27917609872.4120.00070.00130.00060.0007-2.34Sell107190307792.9070.00090.00000.00090.0001-1.11 Utilities23Total112968283993.6030.00030.00040.00030.00030.78Buy54934634013.6040.00000.00050.00010.00050.81Indet.7799235033.6300.00080.00150.00050.00060.23Sell50234423793.5970.00050.00000.00050.00010.84
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ThistablesummarizesNBBOquoteswithdurationfromTAQin2006categorizedbyexchangesofnationalbestaskpriceandnationalbestbidprice.Sincebidandaskpricesarenotreasonablesometimesbeforeandaftertradinghourswhentradingisrare,someofthedatamayshowextremelylargespreads. AskBidFirmsNBBOAskAskBidBidNBBOB-AEx.Ex.RevisionPriceSizePriceSizeDur.Spread AA1614695813.3911373.399921.0810.0017C54033603.815203.811050-1.5990.0003D143143362.9315882.9329790.5090.0019M7265532.0225392.0138111.5300.0027P1613112873.368923.36818-0.3270.0016T159679293.707013.701620-1.8380.0005X3313.887873.961000.853-0.0771 BB139101188.85137-4.191415.59613.0373C59148933.8610073.861252-0.5320.0012D29434943.7513623.752691-1.6200.0005M234573.6610413.661966-0.1410.0009N351308683.7313413.733019-0.4770.0005P59492933.8211503.821217-1.0530.0010T6288073.8511383.841141-0.8780.0162X114.193004.18100-0.7650.0064 CA54104203.8111383.81521-1.5500.0003B138183234.0311953.35845-0.2250.6860C252185882623.4116553.391663-0.7890.0121D2433979113.5343513.531306-1.2060.0006 Continuedonnextpage 81
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AskBidFirmsNBBOAskAskBidBidNBBOB-AEx.Ex.RevisionPriceSizePriceSizeDur.Spread M87371343.8410843.841382-0.3810.0008N14271788583.768793.761374-0.5210.0007P258211765113.4012503.401030-1.1050.0030T252313586103.3122243.302268-1.2420.0053X321203.723433.72100-0.8470.0053 DA152312392.9715262.9711260.6210.0021B30418203.7531643.751133-1.5930.0011C2413828623.6111713.613790-1.2240.0006D272100625383.7024083.662270-1.6810.0381M911449023.6525743.651773-1.1490.0007N148305703353.6719453.672176-1.0560.0006P27280944883.6919573.691226-1.5540.0036T1144861773.0015703.007030-1.2300.0009X484883.863913.85107-1.1530.0047 MA5202281.9431541.9325851.5400.0030B265043.6317213.621136-0.2710.0008C89358243.7915313.791150-0.4230.0008D961832323.6322693.632595-1.1330.0007M7039862.9219832.9221150.6980.0090N996665613.5823003.582208-0.0810.0007P1052100693.6318203.621172-0.7090.0010T84219603.3526013.352352-0.3800.0013 Continuedonnextpage 82
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AskBidFirmsNBBOAskAskBidBidNBBOB-AEx.Ex.RevisionPriceSizePriceSizeDur.Spread X12183.689503.67100-1.0390.0108 NB361842063.7248203.721222-0.4510.0005C14281825293.7418543.74900-0.5210.0007D148367325413.6629673.661937-1.0720.0006M1007279083.6031443.604167-0.0770.0007N1481674750763.5625793.561909-0.1890.0007P148407454533.6422553.641014-0.7040.0009T13934200303.6526513.651284-0.3850.0007X8487623.738423.72101-0.5130.0046 PA1612702603.407243.40807-0.4030.0017B63615363.8217503.82978-1.0030.0010C258222139563.3811493.381342-1.0540.0029D27087929063.7013023.691817-1.5270.0128M1092125813.6516613.651599-0.7180.0009N148376129093.6610063.661666-0.6830.0009P273231267983.479533.45940-0.8900.0261T264313684303.3115253.301855-1.0710.0060X8723253.816983.79100-0.6820.0172 TA159125793.7214643.71708-1.9410.0005B90104243.969013.37825-0.5460.5942C252294837873.3220853.312098-1.2610.0051D1135550622.8678472.862052-1.1710.0009M84232793.4716573.471988-0.3640.0013 Continuedonnextpage 83
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AskBidFirmsNBBOAskAskBidBidNBBOB-AEx.Ex.RevisionPriceSizePriceSizeDur.Spread N13929729543.6811233.681795-0.3730.0007P264279182733.3317883.331412-1.1110.0038T264413596433.2541513.244245-1.2820.0102X311014.085734.071000.2290.0095 XA21124.071004.074791.6950.0022B243.721003.713750.3500.0061C281773.721003.72261-0.7600.0054D527503.781023.78379-0.9030.0052M6133.621773.61846-1.1600.0068N8790903.721153.72578-0.5640.0050P8127243.721193.72316-0.6910.0067T31873.841923.83613-0.7570.0058X24853.651003.41100-0.2910.2316 84
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NBBOSummarybyTradeTimeInterval ThistablesummarizesNBBOquoteswithdurationfromTAQin2006categorizedbytradetimeintervals. IntervalFirmsNBBOAskAskBidBidNBBOB-ARevisionPriceSizePriceSizeDur.Spread Weadaptaregressionmethodologyandanotherobjectiveofthisstudyistodeterminewhetherthecoecientsassociatedwiththeabovefactorsdiersignicantlybetweenstableandtransitionregimes.Amarketmakerwhonoticeschangesinthesecoecientswouldadjusthisbid-askspreadscorrespondingly. Atrader'smotivationforherdecisionscanbeassessedthroughvariousvariables,amongwhichtradedurationanddirectionarethemosttelling.Forexample,ifthepriceismorefavorabletobuy-initiatedtraders,theywilltrademoreintensively.Hencethedurationwillbeshortandtheorderimbalancewillincrease.Thespreadbetweentheaskpriceandthelasttradedpriceafteratrade,andthespreadbetweenthelasttradedpriceandthebidpriceaftertradeindicateamarketmaker'sreactiontothebuy-andsell-initiatedtrades,respectively.Tradepriceandsizemayalsorevealatrader'sintentions. Amarketmaker'sdecisiononNBBOrevisionscanbeassociatedwithquoterelatedvariables.Theirinteractionscanalsobeusefultodierentiatethedegreestowhichinformationisincorporatedbetweenrevisionwithtradeandthosewithout.NBBO 85
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NBBOSummarybyIndustrySector ` ThistablesummarizesNBBOquoteswithdurationfromTAQin2006categorizedbyindustrysectorclassiedbyGICS. SectorFirmsNBBOAskAskBidBidNBBOB-A(%)RevisionPriceSizePriceSizeDur.Spread Energy27641409913.6611443.66921-0.8430.0040ConsumerDiscretionary29662014353.689213.68779-0.5580.0041ConsumerStaples29560135503.577543.56731-0.5960.0063Financials29722075773.659223.64800-0.8240.0046HealthCare26597360693.5233473.522541-0.6580.0035Industrials30691075473.4713383.471294-0.8760.0052InformationTechnology29539022623.5911363.581012-0.5550.0070Materials26729455553.2516963.241685-1.5220.0035TelecommunicationServices25572879353.0899843.088714-1.0060.0050Utilities23489188173.5810273.58847-0.2410.0047
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TradeindexofintradaytradingITi= Tradeduration,timeintervalbetween(i1)standithtradesPi= Log-scaletradedpriceonithtradeAi;Bi= Themostrecentlog-scaleaskandbidpricesbeforetrade,followingalgorithmof Ellis,Michaely,andO'Hara ( 2000 )AiPi1= SpreadbetweenaskandlasttradedpricesPi1Bi= SpreadbetweenlasttradedandbidpricesDi= Tradedirection(ordinal)A+i;B+i= RevisedlogscaleaskandbidpricesrightaftertheithtradeSTi= TradesizeonithtradeNNi= NumberofNBBOrevisionsinatradedurationofITiNTi= NumberoftradessincethelasttradewiththesamedirectionasthatoftheithETi= Exchangecodeofithtrade(categorical)j= NBBOrevisionindexofintradaytradingINj= NBBOduration,timeintervalbetween(j1)standjthNBBOquotesAj;Bj= LogscaleaskandbidpricesofjthNBBOquoteNDj= DirectionofNBBOrevision(-1:bidpricechanged,0:indeterminate,1:askpricechanged)SNAj;SNBj= SizeofaskandbidquotesENAj;ENBj= Exchangecodeinaskandbidquotes(categorical) 87
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EvolutionofMeanandStandardDeviationofTradeDurationinEventWindows Figure3-5. EvolutionofMeanandStandardDeviationofRealizedVolatilityinEventWindows Ifweweretoperformastatisticalanalysisforeachrmandtradedatainthesamplewewouldneedtohandleamassivedatasetofintradaytradesandquotes2.Asisconventionalinanevent-study,weneedtorelyonsomeaggregation,withthegoalofndingsignicantresultsonthebasisof61daywindows(30dayspriortotheannouncementand30followingit). Figure 3-4 toFigure 3-9 showtheevolutionofaverageandstandarddeviationofselectedvariablessuchastradeduration,realizedvolatility,bid-askspread,bid-askspreadaftertrade,log-scaleprice,andtradesizeinaggregatedeventwindow.Realizedvolatility 3.2.1 has196,867,860rows,andatablecontainingconsolidatedquotedatahas620,461,738rows.
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EvolutionofMeanandStandardDeviationofBid-AskSpreadinEventWindows Figure3-7. EvolutionofMeanandStandardDeviationofBid-AskSpreadAfterTradeinEventWindows Figure3-8. EvolutionofMeanandStandardDeviationofLog-ScalePriceinEventWindows 89
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EvolutionofMeanandStandardDeviationofTradeSizeinEventWindows wherePiisthelog-priceontheithtrade. Foramodelhavingtradedurationlog(ITi)asresponsevariable,weproposethefollowingregression: log(ITi)=0+1Di+2STi+3Pi+4ETi+5(AiPi1)+6(Pi1Bi)+7log(ITi1)+8Di1+9STi1+10ETi1+11NNi+12NTi+i; whereiiswhitenoise. ForamodelhavingtradedirectionDiasresponsevariableweproposeanorderedlogitmodel.Thelatterisjustiedonthegroundsthatdecisionstotradeondirectionwhetheritisbuy,indeterminate,orsellwouldberankedaccordingtothetrader's 90
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whereDiisalatentobservationsatisfyingDi=8>>>>>><>>>>>>:1ifDi<1;0if1Di<2;1if2Di: Modelshavingotherresponsevariablessuchasspreadbetweenaskandlasttradedpricesaftertrade,A+iPi,spreadbetweenlasttradedpriceandbidpriceaftertrade, 91
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EvolutionofMeanandStandardDeviationofR2inModellog(ITi) FromTable 3-8 ,regressionmodelsPiorSTihaverelativelylowR2onaverage.Thereforetransactionpriceortradesizearenotlikelytobeexplainedbyanyregressor.Modelsforlog(ITi),A+iPi,andPiB+ihavehigherR2.Figure 3-10 to 3-15 illustratetheevolutionofR2inaggregatedeventwindows.Fromallgraphs,wecanseethatthemeanR2valuesareremarkablylowernearthekeyannouncementdatesthan 92
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SummaryofRegressions ThistableisasummaryofOLSandorderedlogitregressionresultsofmodelsspeciedinSection 3.2.1 .Nisthenumberofregressionsforeachmodel./RSSisaconstantstandarddeviationofi,exceptitisaresidualsumofsquaresforthemodelforDi.Forthelatter,R2iscalculatedbyMcFadden'spseudoR2method.DFrefertodegreesoffreedomforeachregression. ResponseVariablesN/RSSR2DF log(ITi)62865Mean1.7640.413108Std.Dev.0.4250.096168Di44084Mean410130.106326Std.Dev.410150.0812961A+iPi62647Mean0.0020.533112Std.Dev.0.0100.226175PiB+i62647Mean0.0020.543112Std.Dev.0.0120.226175Pi62865Mean0.0060.133108Std.Dev.0.0050.146168STi62865Mean13970.123108Std.Dev.31920.166168 Figure3-11. EvolutionofMeanandStandardDeviationofR2inModelDi EvolutionofMeanandStandardDeviationofR2inModelA+iPi
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EvolutionofMeanandStandardDeviationofR2inModelPiB+i EvolutionofMeanandStandardDeviationofR2inModelPi Regressorsineachmodelsmaybesignicantforsomermsandtradedaysbutnotalways.Inparticular,ifthesignicanceofsomeregressorsaredierentbetweenstableregimeandtransitionregime,theresultmightgivesomeinsightsintoaninformedtrader'sstrategy.InOLSregressions,wedenearegressorassignicantwhenthepvalueislessthan0.001andcollectthesignicantregressions.InorderedlogitregressionformodelDi, Figure3-15. EvolutionofMeanandStandardDeviationofR2inModelSTi
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Trade-relatedregressorsmayhavedistincteectsandtheirsignicanceratiosmayvary,dependingonwhethertheyapplytoastableregimeoratransitionregime.Asignicantratioisthefractionofregressionswithsignicantregressorsoverthetotalnumberofregressions.Ineachpanelofthesegures,theuppergraphisfortheaverageestimateofthecoecientandthelowerisfortheproportionofregressionsinwhichthecoecientissignicant(i.e.withp-value<0:001inOLSandwith3
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EvolutionofRegressorsinModellog(ITi)
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EvolutionofRegressorsinModelDi
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EvolutionofRegressorsinModelA+iPi
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EvolutionofRegressorsinModelPiB+i
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EvolutionofRegressorsinModelPi
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EvolutionofRegressorsinModelSTi
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log(INj)=0+1Bj+2Aj+3ENAj+4ENBj+5SNBj+6SNAj+7NDj+8Bj1+9Aj1+10ENBj1+11ENAj1+12SNBj1+13SNBj1+j: TheNBBOdirectionNDjindicatesthesourceofapricechangeinanNBBOrevision.IfNBBOisrevisedduetoanaskpricechange,thenNDj=1,andifitisduetoabidpricechange,thenNDj=1.Ifitisindeterminate,thenNDj=0.AnindeterminatecasemayincluderevisionswiththesamebidandaskpriceasinthelastNBBObutwithadierentsize,orrevisionswherebothbidandaskpriceshavechanged,orrevisionswiththesamebidandaskpricesbutwheretheaskorbidexchangehaschanged.ThevariableNDjhasimportantimplicationsinthatitshowsthedirectionofincorporationofpublicinformation,whethertheinformationispositiveornegative. AmodelthathasNBBOdirectionNDjasresponsevariablecanbespeciedasorderedlogitmodelsincethedecisionofNBBOdirectionwhetherask,indeterminate,orbidwouldberankedbypreference.ENAjandENBjimplynorankorpreferenceandarethusdenedascategoricaldata. whereNDjisalatentvariablesuchasNDj=8>>>>>><>>>>>>:1ifNDi<1;0if1NDi<2;1if2NDi;
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Modelshavingbid-askspreadAjBj,bidpriceBj,askpriceAj,andbidsizeSNBj,andasksizeSNAjasresponsevariablescanbespeciedasOLSregressionsasfollows: FromTable 3-9 ,regressionmodelswithlog(INj)haveverylowR2onaverage.ThedurationofanNBBOrevisionisnotlikelytobeaectedmuchbyanyothermarketinformation.ModelswithAjBj,Bj,orAjhavehigherR2thantheothers.ThehigherR2saremainlyduetothepersistencebetweenresponsevariablesandlaggedresponsevariablesinregressors.TheSNBjandSNAjmodelsalsohavepersistinglaggedresponse 103
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SummaryofRegressions ThetablesummarizesOLSandorderedlogitregressionresultsondatadescribedinSection 3.2.2 .Nisthenumberofregressions./RSSisaconstantstandarddeviationofj,exceptthatitisaresidualsumofsquaresforthemodelNDj.ForthemodelNDj,R2iscalculatedbyMcFadden'spseudoR2method.DFisthedegreesoffreedomofeachregression. ResponseVariablesN/RSSR2DF log(INj)64010Mean1.7820.076410Std.Dev.0.2820.077285NDj41489Mean1:21090.18113182Std.Dev.3:410100.06815001AjBj64010Mean0.0670.736411Std.Dev.0.1590.277285Bj64741Mean0.0280.886422Std.Dev.0.0790.207337Aj64741Mean0.0200.896422Std.Dev.0.0710.197337SNBj64741Mean7710.576422Std.Dev.252790.187337SNAj64741Mean7140.596422Std.Dev.12620.197337 Figure3-22. EvolutionofMeanandStandardDeviationofR2inModellog(INj) variables,whichimpliesthatthemajorityofthebidandasksizesarepassedontothenextNBBOduetothepricerevisionwithouttrade. Figures 3-22 to 3-28 showtheR2evolutiononaggregatedeventwindows.Fromallgraphs,wecanseethatthemeanR2valuesareremarkablylowerduringtransitionregime,implyingthatNBBOrevisionsaremoreaectedbyexogenousinformationduringtransitionregime. 104
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EvolutionofMeanandStandardDeviationofR2inModelNDj EvolutionofMeanandStandardDeviationofR2inModelAjBj EvolutionofMeanandStandardDeviationofR2inModelBj EvolutionofMeanandStandardDeviationofR2inModelAj
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EvolutionofMeanandStandardDeviationofR2inModelSNBj EvolutionofMeanandStandardDeviationofR2inModelSNAj 3.2.3 ,regressorsaresignicantwhentheirpvaluesarelessthan0.001inOLSandabsolutetvaluesarebetween3and100fororderedlogitregression.Weclassifyregressorsintotwocategories.OneconsistsofNBBOrevision-relatedregressorssuchaslog(INj),Bj,Aj,SNBj,SNAjandNDj.Theotherconsistsofexchange-relatedregressors,suchasENAj,andENBj. Figures 3-29 to 3-35 displaytheevolutionofregressorsinmodelsforlog(INj),AjBj,Bj,Aj,SNBj,andSNAj.Ineachpanelforaregressor,uppergraphrepresentstheevolutionoftheaverageestimateofthecoecientovertheeventwindow,andthelowergraphshowsthepercentageofregressionswherethiscoecientissignicant.AsinSection 3.2.3 ,exchange-relatedregressorsareaggregatedacrossallrmsandtradetimes.Table B-2 inAppendix B.2 reportscoecientestimatesofexchangefactors. 106
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EvolutionofRegressorsinModellog(INj)
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EvolutionofRegressorsinModelNDj
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EvolutionofRegressorsinModelAjBj
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EvolutionofRegressorsinModelBj
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EvolutionofRegressorsinModelAj
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EvolutionofRegressorsinModelSNBj
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EvolutionofRegressorsinModelSNAj
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3.1.3 ,amarketmakerhas3typesofbid-askspreadstrategies,whichcanbeevaluatedonthebasisofexplicitperformancemeasures.Thelattermayproducedierentoutcomes,dependingonwhetherthepricedynamicsevolveinastableregimeortransitionregime.Bystrictlyfollowingthesestrategies,characteristicsofpricedynamicscanbeverydierentfromthoseofrealpriceevolution.Thekeypointofthesimulationistoassesswhetherthesestrategiesresultinmoreecientpricedynamics. Sincepricedynamicsevolverandomly,wesimulate30samplepathsforeachrmin30minutestimeintervals.Althoughthelengthofthepricedynamicsisrathershort,thesimulatednumbersofNBBOrevisionsandtradesarelargeenoughtocapturemostofaspectsofpricedynamics.Thetimeintervalmayhavedistinctiveattributesdependingonwhetherwehaveastableregimeoratransitionregimeandthereforesimulatebothcases.Finally,wehavethreetypesofbid-askspreadstrategies,hencethetotalnumberofsimulationscomprisingallthosecasesis180foreachrm. Allestimablecoecientsinpricedynamics,namelycUB0,cUB1,cUI0,cUS0,cUS1,UB,UI,USarearchivedintwosets,oneforstableregimesandtheotherfortransitionregimes.Standarddeviationsofuninformedbuying,UB,indeterminate,UI,andselling,US,oftradedurations,arefromthesummarydatain 3-1 andin 3-3 .ProportionalcoecientscUB1andcUS1arederivedfromtheestimates^5and^6inregressionmodellog(ITi).InndingcUB0,cUI0,andcUS0,wecannotuse0ofmodellog(ITi)becausethisvaluealldefaultfactorsofexchangesETi,ETi1,andtradedirectionDiandDi1.HencewendthembyindirectwaysuchascUB0= log(ITi)B^5 log(ITi)I;cUS0= log(ITi)S^6 114
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3-10 summarizesthesimulationresultsbyregimeandbid-askspreadstrategy. 115
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Thetablereportsasummaryofsimulationresultsfor27rms,bidandaskpricestrategies,andforthetworegimes(\transi-tion"and\stable").InthecolumnPricingStrategy,`1'indicatesconstantbid-askspread,`2'Bayesian-Nashequilibriumstrategywithpartialmoments,and`3'Bayesian-Nashequilibriumstrategywithorderimbalance.Intherevisiontypecolumn,NBBOWOTmeansNBBOrevisionwithouttradebymarketmaker.Uninf.andInf.meanuninformedandinformedtrading.Meansandstandarddeviationsofrevisionduration,ask,bid,andbid-askspreadaremeasuredonlog-scale. RegimePricingRevisionNMeanStdev.MeanStdev.MeanStdev.MeanStdev.MeanStdev.StrategyTypeDur.Dur.AskAskPricePriceBidBidB-AB-A Stable1Inf.Buy105.029.042.121.022.121.022.121.020.00290.0012Inf.Sell165.485.433.521.663.521.663.521.670.00240.0013NBBOWOT.9168132.123.443.901.193.901.193.901.190.00090.0012Uninf.Buy1013701.472.453.841.033.841.033.841.030.00050.0006Uninf.Indet.256590.731.223.870.903.870.903.870.900.00040.0003Uninf.Sell887481.442.443.841.023.841.023.841.020.00050.0006 2Inf.Buy128.426.463.671.383.231.993.661.380.01030.0067Inf.Sell173.203.062.801.662.851.842.691.770.11290.1168NBBOWOT.8184632.253.514.101.293.931.123.771.200.33071.0954Uninf.Buy2322710.621.873.851.033.691.093.761.070.08200.2667Uninf.Indet.176000.941.555.671.184.270.522.860.922.80381.9039 Continuedonnextpage
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RegimePricingRevisionNMeanStdev.MeanStdev.MeanStdev.MeanStdev.MeanStdev.StrategyTypeDur.Dur.AskAskPricePriceBidBidB-AB-A Uninf.Sell2030130.631.903.171.123.331.153.151.140.01780.0415 3Inf.Buy184.805.512.790.792.740.862.770.790.02260.0526Inf.Sell132.952.213.631.663.931.763.601.690.03330.0404NBBOWOT.6965142.523.813.821.123.821.123.811.120.00430.0686Uninf.Buy2390240.541.763.571.373.431.383.551.380.02560.0733Uninf.Indet.50351.552.313.900.773.890.853.821.020.07740.6678Uninf.Sell2250610.491.682.961.313.071.392.931.340.02880.0774 Transition1Inf.Buy816.6530.043.852.353.842.353.842.350.00220.0010Inf.Sell1923.1642.013.791.913.781.913.781.910.00240.0009NBBOWOT.5403322.666.593.781.413.781.413.781.410.00130.0019Uninf.Buy1109993.439.543.821.073.821.073.811.070.00060.0007Uninf.Indet.421091.444.223.670.943.670.943.670.940.00030.0004Uninf.Sell1052523.288.493.771.063.771.063.771.060.00050.0006 2Inf.Buy1014.7918.194.711.343.361.994.711.340.00860.0106Inf.Sell915.8528.263.980.954.451.673.970.960.01090.0174NBBOWOT.3721222.916.884.191.534.101.474.001.500.18750.7345 Continuedonnextpage
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RegimePricingRevisionNMeanStdev.MeanStdev.MeanStdev.MeanStdev.MeanStdev.StrategyTypeDur.Dur.AskAskPricePriceBidBidB-AB-A Uninf.Buy940982.498.284.581.394.391.313.971.300.60561.4170Uninf.Indet.226922.946.875.881.104.330.612.700.833.18011.7121Uninf.Sell850022.427.853.971.233.681.213.231.180.73871.3417 3Inf.Buy343.2223.114.222.093.582.404.182.050.03830.0464Inf.Sell515.4319.101.540.681.510.911.480.710.05600.0457NBBOWOT.1539942.998.043.641.333.601.333.571.360.06740.3820Uninf.Buy312173.3910.413.701.033.671.033.294.690.40964.7738Uninf.Indet.32313.3718.203.790.843.750.863.254.760.54494.7460Uninf.Sell345692.959.483.939.583.600.913.570.940.35319.7082
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FromTable 3-11 ,wenoticedierencesinperformancemeasuresbetweenthetworegimes.Inastableregime,wherenokeydevelopmentisannounced,theBayesian-NashequilibriumstrategywithorderimbalancedominatesintermsofmeanME(T)andPM(T).Theconstantbid-askstrategyhasabetterperformanceinSE(T).Inthetransitionregime,theconstantbid-askspreadstrategyuniformlyprevailsovertheothertwoBayesianNash-equilibriumstrategies.Welchtwo-samplet-testsareperformedtondstatisticallysignicantdierencesbetweenthe3setsofperformancemeasuresinpricingstrategiesatthe95%condencelevel.p-valuesofallpairwisetestsfailtorejectthenullhypothesisthatthedierencebetweenthemeansofthetwosamplesarezero.Thereforeinthissimulation,wecannotconcludethatoneofthethreebid-askpricingstrategiesispreferabletotheother.However,wewillneedtohavemorepreciseparametersetuptorenethoseresults. 119
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SummaryofPerformanceofPricingStrategies Thetablereportsperformancemeasures,ME(T),SE(T),andPM(T)fromsimulationresultsfor27rms,bidandaskpricestrategies,andregimes.Inthecolumnofpricestrategy,`1'indicatesconstantbid-askspread,`2'Bayesian-Nashequilibriumstrategywithpartialmoments,and`3'Bayesian-Nashequilibriumstrategywithorderimbalance.Thelast4columnscontaintheWelchtwo-samplet-testresults.Indexescolumnshowstheindexesoftwosamplesofpricingstrategies. RegimePricingRealizedp-valuesofWelch2samplet-test StrategyReturnVolatilityME(T)SE(T)PM(T)IndexesME(T)SE(T)PM(T) Stable1Mean0.051.011.930.35-0.07(1,2)0.871:181075:191033Std.Dev.1.110.491.970.230.862Mean-0.027.341.920.4264.12(2,3)0.762:011050.61Std.Dev.0.847.91.920.33145.793Mean05.541.890.3659.14(1,3)0.640.483:061012Std.Dev.0.718.631.930.29237.73 Transition1Mean01.141.850.39-0.07(1,2)0.029:7310226:601045Std.Dev.1.430.761.530.30.822Mean-0.049.522.020.6244.76(2,3)0.0046:021083:171042Std.Dev.1.2811.541.440.685.163Mean-0.032.751.810.481.5(1,3)0.562:641061:301034Std.Dev.0.332.331.450.443.37
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BallandTorous ( 1988 ).However,knowingthecontentofnewscangiveuscausalitytonewdirectionandvolatility.Itcanhelpclassifytransitionregimesmoreclearlythanuncertainevent-datemodelduetothefactthatthesetupofuncertaineventdatealsomakesusassumeuncertaintransitionregimesimilarto PastorandStambaugh ( 2001 ).Thelatterrestrictsourabilitytodeterminemultipletransitionregimesineventperiodsorperformadetailedanalysisoftheregimecontainingtheeventdate.Finallysincethesamenewscanbeinterpretedinmanyways,whichmaybereectedinchangesofdirectionandvolatilityleadingtonewregimes. Asfurtherstudywecanextendouranalysistoliquiditychanges.Inrelationtothekeydevelopmentannouncement,onecananalyzeintradaydataineventperiods,inamannersimilartoobservingtheadverseselectioncomponentinbid-askspreadsasin KrinskyandLee ( 1996 ),orobservingregimechangesinrealizedvolatilityasin LiuandMaheu ( 2008 ). InChapter3,themethodologysimulatesmarketquoteandtraderevisions,closelyimitatingrealmarketpricedynamics.Sincethepricedynamicsispath-dependentaswellastime-dependent,wedonotdevelopaclosedformorparametricmodelofpricedynamics.ClosedformpricedynamicsmaybedevelopedbyinvestigatingconvergencetogeometricBrownianmotionasinchapter3of Merton ( 1990 )undersomeconditionsofconvergence. 121
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Themainreasonwedonotapplyspreaddecompositionmodelsisthatthemodelsfocusondecomposingbid-askspreadintoseveralcomponentstondevolutionofadverseselectioncomponentovertime,butdonotfocusontherelationshipbetweentradedurationandbid-askspread.Combinationofspreaddecompositionmodelsespecially Madhavan,Richardson,andRoomans ( 1997b )and Easley ( 1996 )wouldgivemoreinsight,howeverbothmodelsdoesnotconsidertradeandquotedurationsboth. AlgorithmforextractingNBBOfromconsolidatedquotedatashouldbemoreprecise.MostofempiricalpapersanalyzingquotedatausesPerlscriptprovidedbyWRDStoextractNBBOusesonlyforNYSElistedquote,notforNASDAQ,AMEXandothers.Werunthescriptforalldatawearchived,hencetheremightbesomeissuesasmentionedbyauthorsofthepapers. Insimulation,theperformanceofsimulationisanissue.In30minutesofsimulation,thesimulationtakesconsiderabletimetogenerateallquoteandtradedata.WemayneedtoreprogramwithC++toimproveperformance,ordevelopingapproximationmethod. Anotherissueisthatvolatilityinthisintervalishugefor30minutesoftrading.Inarealdata,wecouldidentifythattransactionpricerevolutiondoesnotfollowthelatestbidoraskpricesnecessarily,norfollowingbidoraskpricesdiscountedbyoperatingcost 122
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Insimulationresults,wecanidentifyexplodingnumberofinformedtrading,becauseofabiggapbetweenwI(t)andw(0).Wecalculatedw(0)fromhistoricalaverageofw(t)inentiretimehorizon,henceitisquitedierentfromevolutionofwI(t).Couplingw(0)equalswI(0)insteadofaveragepricewouldgivemoreprecisecomparisonamongbidaskpricestrategies. InChapter3,weachievedtheobjectives. First,webuildastructuredmethodologyofbidandaskpricedynamicsofmarketmakerbasedonsequentialtradingmodelsundercontinuoustimeframework,directlyreplicatingintradaytradingandquotedata.Themethodologyconsistsoffundamentalvalueprocess,durationprocess,andNBBOrevisionprocess.InNBBOrevisionprocess,wesuggested3possiblebid-askspreadpricingstrategies. Second,weperformempiricalstudyinvestigatingthesignicantdeterminantsaectingdecisionsoftradesandNBBOrevisions.Theempiricalstudyconsistsofvarious 123
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Finally,wesimulatedatawiththemethodologybasedonempiricaldata.Theresultsgivesdierentpreferencesonbidandaskpricingstrategiesbetweeninstableregimeandtransitionregime,howeverthedistinctionisnotstatisticallysignicant. 124
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3{18 ) wherep(D=1jw)=8>><>>:p(D=1jw>0)=DBdt+UBdt;p(D=1jw0)=UBdt: A{1 )andorganizeit,then Foranyoftworealnumberst,s,weknowlimt!0lims!0t s=1; 3{6 ),E(wI(t))=wI(0)+E0@I(t)Xi=1SiTIi1A+E0@Si0@tI(t)Xi=1TIi1A1A:
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Ross ( 1996 ),wecanndE0@I(t)Xi=1SiTIi1A=E0@I(t)+1Xi=1SiTIi1AESI(t)+1TII(t)+1=(I+1)S PluggingEq.( 3{20 )inDBandEq.( A{3 )inE(w),wehave 3{19 ) A{5 )andorganizeit,then PluggingEq.( 3{20 )inDSthenwehave
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3{21 ),( 3{22 ) 3{21 )isidenticaltoderivingEq.( 3{18 ),exceptplugginginDB(t):=cDBI+(t)insteadofDB(t):=cDB(wI(t)w(t))+.AlsoderivationofEq.( 3{22 )isthesameasthatofEq.( 3{19 ),exceptplugginginDS(t):=cDS(wI(t)w(t))insteadofDS(t):=cDSI(t). 127
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Thetablerecordsallcoecientestimatesofexchangefactors.Exchangetypehavefourpossiblevalues.`E':exchangewherethetradeoccurredfromETi,`L':exchangecodewherethelasttradeoccurredfromETi1,`A':exchangecodewheretheaskquotehasbeenpostedfromENAi,and`B':exchangecodewherethebidquotehasbeenpostedfromENBi.Signicantcountrepresentsthenumberofregressionsthathastheexchangefactorwithpvalueislessthan0.01atOLSorabsolutevalueoftvalueisbetween3and100atorderedlogit.Signicantratioistheratiobetweensignicantcountsandallcounts. ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. log(ITi) EA13%-4.12411.5609B89%-2.34001.98800.71820.6211C142519%-1.02611.70740.29940.3288D324020%-0.25163.44160.25930.2648I43%-4.50042.42711.41060.8212M14858%0.30523.73170.50780.8908N694923%-3.6731360.96850.15620.2387P1298825%-3.2350273.52430.25380.3370Q413130%16.62061157.01670.29271.4207T397316%0.096316.11970.22130.3363X554%-5.748311.55832.11311.7017 LA13%-5.56211.4111B1113%2.094610.67071.11270.8293C180624%-0.97051.23930.27860.2711 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. D317720%-0.12578.88820.25880.2919I43%-2.05902.75510.85540.7157M180010%0.72882.34930.44350.5068N611320%-0.131719.49270.16990.1952P1505828%-1.085116.88340.27602.7425Q494236%-1.18754.53310.27920.3107T390416%-0.492118.25850.31155.3704X544%-0.692310.51892.20362.0857 LB33.5%0.6261.2350.3280.150C2773.7%0.1631.5200.3220.250D5413.4%0.0031.2230.2680.177I54.2%-2.8862.6320.8940.313M1831.0%0.0341.8860.4340.298N13924.6%-0.1480.7740.1670.122 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. P15743.0%-0.0401.9780.2470.201Q6254.6%-0.0420.9640.2040.152T7483.0%0.4053.0430.2180.220 LA25%-0.00130.00080.00030.0001B67%-0.00090.00370.00040.0001C4977%0.00390.08920.00070.0105D7965%0.00050.01610.00050.0040I43%-0.00030.00170.00030.0001M16569%-0.00170.05810.00050.0072N15965%-0.00030.00370.00020.0006P30116%0.00050.02920.00050.0037Q9457%0.00020.04700.00110.0058T12355%0.02290.93610.00050.0045 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. X12810%-0.00040.00570.00050.0012 AC189054%-0.330718.02600.06081.2508D243724%-0.12260.85230.00090.0122M201020%-0.00800.18070.00090.0145N939032%-0.00030.00500.00010.0004P1639427%-0.04846.13730.00750.4252T914325%-0.08918.20750.01340.5694X119184%0.00410.00430.00050.0005 BC108729%0.253412.20780.07431.1547D151015%-0.07780.58570.00080.0073M118913%0.00360.11860.00060.0089N338512%0.00110.05270.00010.0019P955815%0.02494.14600.00870.3900T591116%0.03925.27140.01390.4958X25019%-0.00010.00350.00030.0003 BC166445%1.8106101.72480.08632.5736D249525%-0.07171.41670.00250.0825 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. M199121%-0.01320.30340.00040.0070N905931%-0.00110.07450.00010.0013P1606626%0.182232.73450.00920.8285T863624%0.340144.64820.01701.1300X115386%0.00420.01080.00060.0035 EA1541%-0.00020.00170.00030.0001B1416%0.00220.00410.00050.0006C77710%0.00010.00410.00020.0007D14019%0.03071.12640.00060.0068I87%-0.00060.00350.00020.0001M272815%-0.00030.00720.00030.0013N371412%-0.00020.01440.00020.0028P598011%0.00000.02950.00050.0048Q172513%-0.00630.26610.00080.0051T267511%0.00130.05710.00060.0123X28422%-0.00030.00510.00040.0005 LA38%0.00120.00090.00030.0001B56%0.00060.00380.00040.0001C5227%-0.00210.05100.00070.0112D8545%0.00320.04770.00110.0108I33%0.00000.00240.00040.0000M179010%-0.00240.09730.00050.0057N16706%-0.00030.01020.00030.0031P30806%-0.00020.02280.00050.0044Q9267%0.00010.03270.00100.0064 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. T12835%0.00360.12240.00060.0049X13410%0.00090.01490.00070.0023 LA25%-0.01300.01010.00440.0035B1011%0.00250.01010.00250.0015C108615%-0.00320.11150.00190.0211D209713%0.00060.04840.00150.0091I98%0.00210.01690.00340.0023M178110%-0.00550.27000.00340.0663N466115%-0.00010.00740.00070.0011P737414%-0.00010.01400.00100.0029Q182613%0.00070.02060.00120.0052T369615%-0.00020.01270.00090.0015 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. X464%0.02690.08190.00990.0158 LA13%408171525B45%5458710732847356285C2483%218151146771262D4963%-13010940445881I22%4462612715822173M8835%109208188991677N13765%-6666585266672P22224%-2842126066267575Q8376%-30749885234135311T7243%-255739565352672X14111%-105132868427323551
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Thetabledisplaysallcoecientestimatesofexchangefactors.Exchangetypetakesfourpossiblevalues.`A':exchangecodewheretheaskNBBOhasbeenpostedfromENAj,`B':exchangecodewherethebidNBBOhasbeenpostedfromENBj,`LA':exchangecodewherethelastbidNBBOoccurredfromENAj1,and`LB':exchangecodewherethelastaskNBBOoccurredfromENBj1. ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. log(INj) AC167225%6.592.22.923.3D158514%-1.559.11.717.7M4474%1.22.50.60.6N982633%0.41.40.10.4P1617725%2.6920.33.8262.3T906226%-670.065406.111.8698.3X1406%-1.66.71.20.8 BB4879%-1691.92650.5228.9152.6C218031%181.8728.580.2114.7D202218%58.4433.015.660.7M4765%10.7203.16.642.2N977233%0.030.40.25.5P1803628%1113.0146871.312.7250.4T1055527%-327.239585.123.0109.5X1397%2.247.12.516.3 LAC69618%1.769.11.415.2D137512%0.849.11.114.8M3544%3.040.81.415.3 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. N1140939%0.57.30.12.7P1526524%-5.4830.42.8265.5T897524%-23.02150.99.2690.9X1526%-4.520.91.44.9 LBB4767%-1582.82591.7219.4165.1C76719%211.4697.051.8116.1D157814%13.7161.05.038.1M3494%15.1142.14.133.6N1179840%0.43.90.10.5P1663126%9.1163.22.829.6T854822%20.4352.47.374.5X1517%-7.258.12.115.1 BC3148.5%-43.894459.49926.97498.443D150214.4%-11.575203.9434.50742.316M5185.8%-1.2150.6850.3210.190N550619.4%-0.3010.6990.0860.162P1141719.6%-0.34991.6681.17320.930 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. T575416.6%25.620560.06810.171133.778X50.3%4.5723.6621.1360.773 LAC2487.7%4.37160.3750.8217.453D140813.6%-1.16843.5310.74210.194M6486.8%7.085144.0691.78536.099N626322.0%1.16148.3250.28711.932P1078518.5%0.19859.4770.43412.282T605917.6%6.865286.8493.33685.143X30.1%-2.9630.8680.7690.393 LBC2848.6%10.238112.3543.17626.763D174316.7%3.09889.4481.13221.279M6507.3%-1.3130.6250.3320.184N695524.5%-0.4130.4800.0940.106P1258821.6%-0.61274.5970.37514.586T576216.6%-27.164524.0167.374125.853X30.1%3.8153.4381.0650.974 BB61100%13.4130.2930.0030.010 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. C451864%-9.8965.4450.0800.309D352931%-1.8034.8010.0430.231M8749%-0.2922.0070.0030.024N683423%0.0100.6170.0110.064P2245635%-2.51854.3650.0360.777T1520539%-3.0696.8370.0410.322X78841%0.0041.0530.0090.095 LAC70318%0.1942.2930.0210.159D284526%0.3171.6520.0370.180M94310%-0.0040.1900.0040.021N784227%-0.0810.4650.0150.068P1617426%-0.53664.0920.0260.891T958325%-1.522166.7580.0542.353X73531%-0.1340.8070.0260.159 LBB70100%-9.5975.4250.0810.312C121730%5.6169.2750.1740.624D310228%0.5752.3440.0410.176M8189%0.0901.0690.0040.032N773826%-0.0910.6090.0160.103P1706027%0.3753.0480.0310.214T1068628%0.6506.6360.0450.455X72333%-0.1541.4440.0390.275 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. M6056%0.0230.3550.0030.015N433715%-0.0500.8540.0110.124P1331521%-0.0472.3340.0200.446T871324%0.1064.6000.0220.450X46121%-0.0390.6510.0150.085 BB101100%-5.6016.1110.0390.036C494367%2.45711.5150.1670.605D408736%0.7943.3420.0400.161M177419%0.0122.0610.0020.035N946732%-0.0150.5660.0060.074P2539340%0.5125.3600.0430.303T1828046%0.6906.3770.0550.348X97549%-0.0410.8890.0120.111 LAC84521%0.1836.4020.0140.236D182516%-0.1331.6630.0320.281M5015%-0.0190.3390.0030.014N515517%0.0460.3990.0080.047P1179018%0.0410.7390.0110.073T827722%-0.0851.9970.0110.136X41517%0.1130.6590.0200.096 LBB8196%3.5146.7820.0450.046C178542%-1.2366.7100.0790.338D375334%-0.1651.7430.0220.153M169518%-0.0220.4050.0010.012N899930%0.0300.4570.0060.055 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. P2049832%-0.0952.1360.0150.130T1502638%-0.1144.4610.0230.604X93042%0.0591.1210.0190.156 BB10099%4.1644.0970.0410.039C447561%-1.73211.2710.2011.021D233621%-1.0704.7960.0580.362M5135%-0.2201.2040.0040.021N327411%-0.0220.5350.0070.077P1414122%0.187175.7480.0901.123T1240331%0.987176.9600.0940.791X42021%-0.2474.5230.0220.231 LAC144236%0.0150.6460.0050.036D345131%-0.1086.5830.0220.630M189519%0.0030.1170.0010.018N880630%0.0020.1580.0020.024P2007031%-0.38356.8990.0100.708T1516639%-1.048130.7890.0191.629 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. X103442%0.0040.1330.0020.019 LBB8298%-2.8684.5650.0390.037C135232%1.25310.5290.1370.756D182816%0.3513.7730.0350.331M4595%0.0620.5720.0020.010N396713%0.0000.3240.0040.036P1006016%-0.19630.1350.1146.897T836421%0.1327.7050.0350.374X36417%0.2504.6110.0270.246 BB8685%-868623411443480172176109857C286539%557415566079034980199143D513145%201876416804410238161149M313433%303811381114197572517N2109071%222465477825P3620956%440841600378309958204T2313858%640782007869552376725 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. X43822%-4586552516514204 LAC3218%444523696363432D6786%387488552132511216M4535%5699476591407N16366%-26059781701258P36306%229710270889313605T26227%-47360521593587351262X964%1835160936392482 LBB6881%828060010892217162934114048C137233%-28332528532151564871708D419938%-410031552101255682373M250727%-17166760643215082253N1593654%-145341175738P2971446%-1268261927788017364T1814546%-15240804912229437805X30314%5938668418204963 BB9594%-64658479827280180304141196 Continuedonnextpage
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ExchangeExchangeSignicantSignicantMeanStd.Dev.MeanStd.Dev.TypeCodeCountRatioEstimateEstimateStd.Err.Std.Err. C194826%869770725739252295262160D10259%1068600985854953659356650M4355%30121307110299915227N307110%574783100262P53268%300376447721721977203420T511113%322536455050123627208490X985%81884856813807050 LAC129232%-1380139673962338D419938%1238273084082717M289329%-7786584429700N1547152%-195290088282P2910246%9708062426914497T1792347%218689944199045X34514%6197922574902689 LBB7286%662594510431994164696137985C63815%-629818513812638897261777D8087%-239285435630012572229038M4345%-49806511113438702N15575%-1712738166384P38216%-10476721112636833108096T29147%-143574242258810828130081X1226%-61224216311036121
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2 144
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Firsttwocolumnsindicatetickersymbolofrmsandchange-pointmodelhavingrregimesthatwewanttocompare.Nextfourcolumnsshows lnBrs>2withcomparedmodelhavingsregimes.Thenextfourcolumnsshows95%uppercondencelimitduetotheone-sidedttest.Thelastfourcolumnsshowsthepvaluesdeterminingnullhypothesisisbeingrejected. ComparedModelUpperCondenceLimitpvalue TickerModelM1M2M3M4M1M2M3M4M1M2M3M4 AEP10.0017.4336.8620.25NA37.4474.7544.420.000.900.940.90AEP2-17.430.0019.432.832.59NA63.9930.760.050.000.740.52AEP3-36.86-19.430.00-16.611.0325.12NA31.000.050.210.000.26AEP4-20.25-2.8316.610.003.9225.1164.22NA0.060.390.700.00 BIIB10.009.18-1.837.64NA51.1013.6531.710.000.610.340.65BIIB2-9.180.00-11.01-1.5432.73NA31.6648.990.330.000.300.45BIIB31.8311.010.009.4717.3153.69NA34.600.490.640.000.69 Continuedonnextpage
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ComparedModelUpperCondenceLimitpvalue TickerModelM1M2M3M4M1M2M3M4M1M2M3M4 BSX10.0011.59-3.5232.32NA37.677.2477.400.000.730.200.87BSX2-11.590.00-15.1120.7314.49NA12.5271.680.190.000.150.73BSX33.5215.110.0035.8514.2842.75NA81.820.590.790.000.89BSX4-32.32-20.73-35.850.0012.7630.2210.13NA0.100.230.090.00 CAT10.0022.49-13.4839.02NA53.7422.5683.810.000.860.240.91CAT2-22.490.00-35.9716.538.77NA-9.6567.120.100.000.010.69CAT313.4835.970.0052.5049.5262.28NA107.680.700.980.000.93CAT4-39.02-16.53-52.500.005.7734.062.68NA0.070.270.050.00 CELG10.00-1.82-1.79-23.25NA-0.5120.82-6.500.000.000.390.01CELG21.820.000.02-21.433.12NA22.37-4.620.410.000.440.01CELG31.79-0.020.00-21.4524.4122.32NA3.900.490.440.000.06CELG423.2521.4321.450.0040.0038.2446.80NA0.980.970.900.00 EGN10.0026.3055.1483.04NA59.2697.81148.280.000.890.980.98EGN2-26.300.0028.8456.746.66NA58.47115.760.080.000.930.94 Continuedonnextpage
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ComparedModelUpperCondenceLimitpvalue TickerModelM1M2M3M4M1M2M3M4M1M2M3M4 FDX10.002.20-2.8461.01NA17.8313.86106.920.000.510.310.98FDX2-2.200.00-5.0458.8113.43NA6.32103.650.330.000.150.98FDX32.845.040.0063.8519.5416.39NA112.300.530.670.000.98FDX4-61.01-58.81-63.850.00-15.10-13.97-15.39NA0.010.010.010.00 FL10.0016.0416.96111.55NA41.4845.29172.440.000.820.811.00FL2-16.040.000.9295.519.41NA25.59148.680.120.000.471.00FL3-16.96-0.920.0094.5911.3723.74NA153.400.130.420.000.99FL4-111.55-95.51-94.590.00-50.66-42.34-35.77NA0.000.000.000.00 GCO10.0020.8932.469.58NA47.0772.6938.450.000.880.900.67GCO2-20.890.0011.57-11.325.29NA48.8011.100.070.000.670.16GCO3-32.46-11.570.00-22.897.7625.65NA15.430.080.270.000.14GCO4-9.5811.3222.890.0019.3033.7361.21NA0.250.760.820.00 JCP10.0030.6328.7112.44NA67.5957.2230.920.000.900.940.83 Continuedonnextpage
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ComparedModelUpperCondenceLimitpvalue TickerModelM1M2M3M4M1M2M3M4M1M2M3M4 KFT10.00-2.8714.8714.06NA-0.1942.6944.900.000.000.780.74KFT22.870.0017.7316.935.54NA45.0947.150.710.000.830.80KFT3-14.87-17.730.00-0.8012.969.62NA41.820.160.110.000.46KFT4-14.06-16.930.800.0016.7813.2943.42NA0.190.150.480.00 MGM10.0015.8413.8146.57NA44.5230.9098.120.000.790.880.92MGM2-15.840.00-2.0330.7212.83NA32.1191.700.150.000.420.78MGM3-13.812.030.0032.763.2836.18NA87.100.060.500.000.83MGM4-46.57-30.72-32.760.004.9930.2521.58NA0.060.180.140.00 MON10.0054.188.7966.35NA99.8429.10122.650.000.970.710.97MON2-54.180.00-45.3912.16-8.52NA5.8181.680.020.000.060.60MON3-8.7945.390.0057.5611.5296.59NA120.410.190.920.000.93MON4-66.35-12.16-57.560.00-10.0457.355.30NA0.020.370.060.00 Continuedonnextpage
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ComparedModelUpperCondenceLimitpvalue TickerModelM1M2M3M4M1M2M3M4M1M2M3M4 PG10.0011.8137.7239.99NA36.9972.7273.980.000.740.950.97PG2-11.810.0025.9128.1813.37NA52.1972.050.180.000.930.84PG3-37.72-25.910.002.27-2.710.38NA44.450.030.040.000.50PG4-39.99-28.18-2.270.00-6.0015.7039.91NA0.020.130.430.00 PLCE10.002.1526.1274.97NA10.5858.41121.670.000.510.890.99PLCE2-2.150.0023.9772.826.28NA58.04119.440.210.000.860.99PLCE3-26.12-23.970.0048.856.1710.10NA106.870.070.100.000.91PLCE4-74.97-72.82-48.850.00-28.27-26.209.17NA0.000.010.070.00 PTRY10.0011.4314.69-0.68NA30.7137.948.370.000.790.820.31PTRY2-11.430.003.26-12.127.85NA19.0711.800.120.000.550.16PTRY3-14.69-3.260.00-15.388.5512.55NA12.150.120.290.000.15 Continuedonnextpage
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ComparedModelUpperCondenceLimitpvalue TickerModelM1M2M3M4M1M2M3M4M1M2M3M4 QCOM10.003.7927.0028.14NA18.0857.4665.980.000.580.910.87QCOM2-3.790.0023.2224.3610.51NA49.8065.030.250.000.910.82QCOM3-27.00-23.220.001.143.453.36NA37.850.060.060.000.48QCOM4-28.14-24.36-1.140.009.7016.3135.58NA0.090.140.440.00 S10.0013.291.3134.61NA36.6017.7784.510.000.790.470.86S2-13.290.00-11.9821.3110.02NA16.4277.300.140.000.200.72S3-1.3111.980.0033.2915.1440.38NA82.400.370.720.000.86S4-34.61-21.31-33.290.0015.3034.6715.82NA0.110.240.120.00 T10.0029.0431.9930.31NA73.2075.5561.140.000.850.870.94T2-29.040.002.961.2715.12NA8.5254.580.120.000.610.49T3-31.99-2.960.00-1.6811.562.61NA51.520.100.070.000.45T4-30.31-1.271.680.000.5252.0454.89NA0.040.460.500.00 TMO10.000.40-2.94-19.88NA8.9113.5912.510.000.380.310.13TMO2-0.400.00-3.33-20.288.12NA14.9212.470.320.000.310.13 Continuedonnextpage
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ComparedModelUpperCondenceLimitpvalue TickerModelM1M2M3M4M1M2M3M4M1M2M3M4 TSN10.009.7414.8027.11NA45.3945.1459.940.000.640.760.90TSN2-9.740.005.0617.3725.91NA23.8166.650.290.000.610.70TSN3-14.80-5.060.0012.3115.5413.69NA55.630.180.260.000.66TSN4-27.11-17.37-12.310.005.7131.9031.00NA0.070.250.290.00 UNH10.00-1.881.5134.26NA0.438.6969.080.000.000.450.94UNH21.880.003.3936.154.20NA10.4771.230.470.000.630.95UNH3-1.51-3.390.0032.755.673.68NA66.570.210.100.000.93UNH4-34.26-36.15-32.750.000.55-1.061.07NA0.040.040.050.00 VZ10.0010.62-14.6713.69NA24.221.2034.510.000.850.040.83VZ2-10.620.00-25.293.072.97NA-5.0515.130.060.000.010.56VZ314.6725.290.0028.3630.5445.54NA53.340.910.970.000.96VZ4-13.69-3.07-28.360.007.139.00-3.38NA0.110.240.020.00 WYE10.00-2.117.4614.52NA0.2223.5034.050.000.000.720.86 Continuedonnextpage
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ComparedModelUpperCondenceLimitpvalue TickerModelM1M2M3M4M1M2M3M4M1M2M3M4
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Firsttwocolumnsindicatetickersymbolsandchange-pointmodelhavingrregimes.Thenextfourcolumnsoftherstrowshowstheaveragelengthofregimes,^mssinaneventperiodof61days.Thesecondrowshows95%condencelimitoftwo-sidedttest. TickerMr^m11^m22^m33^m44 AEP223.1637.84(18.82,27.49)(33.51,42.18)AEP318.2513.1829.57(14.5,22)(11.25,15.1)(25.97,33.17)AEP414.3211.6811.5223.48(12.35,16.29)(10.57,12.78)(10.62,12.42)(20.8,26.17) BIIB218.9842.02(15.39,22.58)(38.42,45.61)BIIB316.0711.7333.2(12.47,19.68)(9.32,14.14)(29.47,36.93)BIIB414.299.3810.7226.61(10.47,18.11)(7.18,11.57)(8.92,12.52)(22.7,30.52) BSX216.8344.17(14.42,19.24)(41.76,46.58) Continuedonnextpage 153
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TickerMr^m11^m22^m33^m44 CAT221.4539.55(18.91,24)(37,42.09)CAT319.7611.5529.7(17,22.52)(9.09,14)(26.68,32.71)CAT414.1711.9510.6224.27(11.98,16.35)(10.42,13.48)(8.4,12.83)(21.24,27.29) CELG228.2732.73(23.93,32.61)(28.39,37.07)CELG322.7513.724.55(19.18,26.32)(10.44,16.96)(20.35,28.75)CELG417.5811.2111.7820.43(14.37,20.79)(9.43,12.99)(9.09,14.47)(16.37,24.49) EGN216.9644.04(14.92,19)(42,46.08)EGN314.2113.3833.4(12.54,15.88)(12.38,14.38)(31.5,35.31)EGN412.8111.7911.0625.34(11.27,14.36)(10.7,12.87)(10.37,11.76)(23.45,27.22) FDX219.1741.83(16.08,22.27)(38.73,44.92) Continuedonnextpage 154
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TickerMr^m11^m22^m33^m44 FL219.3541.65(16.6,22.09)(38.91,44.4)FL316.6811.9332.39(13.8,19.56)(10.23,13.63)(29.8,34.99)FL413.9311.410.8124.86(11.93,15.93)(10.25,12.55)(9.71,11.91)(22.88,26.84) GCO220.2940.71(16.14,24.43)(36.57,44.86)GCO321.229.7929.99(17.43,25.01)(8.05,11.53)(26.08,33.9)GCO415.4612.169.4823.91(13.25,17.66)(10.79,13.52)(7.62,11.34)(20.74,27.07) JCP217.8543.15(15.01,20.69)(40.31,45.99)JCP315.1212.733.18(12.99,17.24)(11.63,13.77)(30.37,36)JCP412.6811.910.6325.79(10.79,14.57)(10.7,13.1)(9.82,11.43)(23,28.59) KFT220.6240.38(16.75,24.48)(36.52,44.25) Continuedonnextpage 155
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TickerMr^m11^m22^m33^m44 MGM216.9244.08(14.39,19.44)(41.56,46.61)MGM315.6112.1533.24(12.97,18.25)(10.87,13.43)(30.87,35.6)MGM412.9611.7410.6425.66(11.26,14.66)(10.6,12.88)(9.58,11.71)(23.71,27.61) MON21942(16.37,21.64)(39.36,44.63)MON317.5811.8631.56(14.61,20.55)(10.37,13.36)(28.33,34.79)MON414.8312.169.6424.36(12.59,17.07)(10.84,13.49)(8.73,10.56)(21.45,27.28) PDX223.4937.51(19.78,27.21)(33.79,41.22)PDX320.610.3730.03(16.97,24.23)(8.72,12.01)(26.51,33.55)PDX414.9411.699.3825(12.7,17.18)(9.87,13.5)(8.38,10.37)(21.83,28.17) PG214.5946.41(12.66,16.52)(44.48,48.34) Continuedonnextpage 156
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TickerMr^m11^m22^m33^m44 PLCE218.8242.18(16.19,21.45)(39.55,44.81)PLCE317.611.3732.03(14.6,20.6)(9.4,13.35)(29.08,34.98)PLCE413.712.510.6224.18(11.82,15.57)(10.58,14.41)(9.13,12.11)(21.68,26.69) PTRY220.8640.14(17.99,23.72)(37.28,43.01)PTRY317.7212.6130.67(14.8,20.63)(10.82,14.41)(28.09,33.25)PTRY414.0712.719.8724.36(12.41,15.72)(11.03,14.38)(8.77,10.97)(21.72,26.99) QCOM222.2238.78(17.9,26.54)(34.46,43.1)QCOM319.210.1331.67(14.89,23.51)(8.49,11.76)(27.73,35.61)QCOM413.5511.159.9826.32(11.37,15.72)(9.42,12.88)(8.69,11.28)(22.99,29.66) S221.8939.11(18.02,25.77)(35.23,42.98) Continuedonnextpage 157
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TickerMr^m11^m22^m33^m44 T218.6442.36(16.76,20.52)(40.48,44.24)T316.9212.7531.33(14.44,19.4)(11.23,14.27)(28.3,34.36)T413.5512.1410.9524.35(11.84,15.27)(10.86,13.43)(9.94,11.97)(21.62,27.08) TMO222.2538.75(19.84,24.66)(36.34,41.16)TMO318.5512.4629.99(15.68,21.42)(11.06,13.85)(27.25,32.74)TMO415.0711.8910.0524(12.76,17.38)(10.6,13.17)(8.94,11.15)(21.79,26.2) TSN220.1140.89(17.3,22.92)(38.08,43.7)TSN317.9912.5930.41(15.21,20.78)(10.88,14.31)(27.39,33.43)TSN414.3111.1210.7724.79(12.18,16.45)(9.97,12.26)(9.81,11.74)(21.99,27.6) UNH217.4843.52(15.07,19.89)(41.11,45.93) Continuedonnextpage 158
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TickerMr^m11^m22^m33^m44 VZ220.1640.84(17.62,22.69)(38.31,43.38)VZ317.5312.6130.85(14.42,20.65)(11.68,13.55)(27.92,33.79)VZ414.7210.7710.4225.09(12.08,17.35)(10,11.53)(9.55,11.3)(22.73,27.46) WYE222.5138.49(18.88,26.14)(34.86,42.12)WYE318.3314.9527.73(15.64,21.01)(13.32,16.58)(24.36,31.1)WYE414.413.2111.9821.41(12.8,16)(11.97,14.44)(10.81,13.14)(18.86,23.97) 159
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Tablereportsmeandirectionson30samplesbyeachregime,and95%condencelimitandpvaluefromWelchtwosamplet-test.Nullhypothesisonthetestisthatthedierencebetweenmeansofthedirectionsonconsecutiveregimesarezero. WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr Continuedonnextpage
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WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr Continuedonnextpage
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WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr Continuedonnextpage
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WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr Continuedonnextpage
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WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr Continuedonnextpage
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WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr
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Tableshowsmeanvolatilitieson30samplesbyeachregime,and95%condencelimitandpvaluefromWelchtwosamplet-test.Nullhypothesisonthetestisthatthedierencebetweenmeansofthevolatilitiesonconsecutiveregimesarezero. WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr Continuedonnextpage
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WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr Continuedonnextpage
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WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr Continuedonnextpage
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WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr Continuedonnextpage
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WelchTwoSamplettest(CondenceLimit)(pvalue) TickerMr
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WereportsOLSestimatesofsimpleautoregressivepaneldatabetweendirectionandvolatilityofcurrentregimeandofthelastregime.Explanatoryvariableisspeciedatcolumn^=^,andcomparingpairofregimesis(i;j),jiscurrentregime. ^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 AEP2(1;2)^-0.0019-0.0050.17320.3240.28260.96910.31150.0370.1686^0.00830.0904-0.26760.48400.5680.19790.0370.19913(1;2)^0.0038-0.32310.5824-0.78040.38240.46310.22890.16120.1175^0.0055-0.11680.2081-0.094900.44670.21730.16120.1217(2;3)^-0.00380.00570.05240.59330.06850.91380.76940.0010.4073^0.0093-0.0165-0.41540.585300.7530.01310.0010.53364(1;2)^0.0062-0.00160.2019-0.91910.22340.99730.75290.07310.1233^0.0065-0.0194-0.0267-0.12880.00010.9090.91140.07310.1208(2;3)^0.00760.14410.3417-1.85990.28190.64480.68710.12710.0952^0.0030.00170.1263-0.04690.00420.97340.34460.12710.12(3;4)^-0.004-0.02030.03860.57460.08650.71390.91060.03450.1646^0.00660.01320.01930.279600.73190.93580.03450.1624 BIIB2(1;2)^0.0119-0.0939-0.0645-0.40250.00590.64150.49420.01680.2094 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 BSX2(1;2)^0.0007-0.0162-0.0098-0.05320.79980.74250.89750.68060.0106^0.0174-0.0117-0.1715-0.124500.87670.13260.68060.0923(1;2)^-0.00390.09210.1874-0.05350.80420.83470.78360.93320.0052 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 CAT2(1;2)^0.0043-0.0280.0594-0.45950.0060.71590.34340.00020.5118^0.0107-0.1512-0.067-0.912700.15530.44950.00020.53833(1;2)^-0.0157-0.03710.20231.02980.11140.92960.71450.15050.0823^0.0106-0.0988-0.22980.075600.38280.11670.15050.1682(2;3)^0.00130.0005-0.08810.0280.73190.99390.71040.92180.006 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 CELG2(1;2)^-0.0294-0.48590.40930.91280.00070.4660.10630.00020.4283^0.02830.1042-0.30970.448100.82430.07970.00020.43663(1;2)^-0.0188-0.16230.18520.90490.01090.73130.49060.00060.3758^0.01970.0309-0.12840.409500.92260.47740.00060.3746(2;3)^-0.008-0.01180.10590.34430.46620.96460.79050.35620.0335^0.0206-0.016-0.1570.095300.90870.45190.35620.06954(1;2)^-0.01570.13412.8711-0.39830.2710.80220.010.37710.2377 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 EGN2(1;2)^-0.00440.12680.12060.34590.20820.39910.54090.14470.087^0.0127-0.2245-0.37810.231300.06060.01320.14470.27693(1;2)^-0.00330.17990.18140.00560.50550.47290.57260.98680.0234^0.0118-0.0929-0.27440.001900.52320.13390.98680.0853(2;3)^-0.0040.04530.05340.41580.04650.53170.64820.01570.2141^0.0092-0.11180.01160.491500.14910.92780.01570.25924(1;2)^-0.01060.1147-0.40690.99590.15240.74530.56760.11790.0991^0.0068-0.02760.15680.09180.0010.79680.46720.11790.1048(2;3)^-0.0109-0.0897-0.42581.08350.02480.41420.22320.01460.2163 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 FDX2(1;2)^-0.00160.0007-0.01460.25490.38740.99250.90720.0730.1215^0.01-0.0303-0.05730.464300.77560.73370.0730.13023(1;2)^0.0031-0.050.0669-0.31410.25370.71020.67540.18140.0788^0.0089-0.0773-0.0523-0.215300.48610.69270.18140.0958(2;3)^0.00210.10280.1192-0.43430.57060.6920.69530.05470.155^0.0091-0.17480.02-0.31010.00120.42320.93820.05470.1714(1;2)^0.0205-0.66180.9649-2.52640.13160.2870.47820.03410.26^0.0088-0.1065-0.3941-0.063900.28140.06070.03410.3595(2;3)^-0.00180.0406-0.07950.20050.8080.7390.91030.72630.0111^0.0081-0.0302-0.0240.02390.00050.4710.92160.72630.026(3;4)^-0.0018-0.0295-0.04380.28450.35980.52690.73220.15960.0787 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 FL2(1;2)^-0.0020.0028-0.18190.20550.56730.97730.16170.31550.1142^0.01440.07330.05590.188500.4380.6590.31550.07783(1;2)^-0.0007-0.05540.10410.02120.93520.89230.83450.9670.0018^0.01410.2531-0.050.003200.09960.79450.9670.1236(2;3)^-0.0012-0.01070.04580.06290.73530.88990.81480.72710.0101^0.0109-0.01050.29340.07570.00210.90160.16320.72710.08064(1;2)^0.0255-0.49320.3778-2.28790.00510.34190.51550.00070.3667^0.0078-0.22770.2173-0.15930.00080.09010.14980.00070.4175(2;3)^0.0098-0.1077-0.8424-0.09970.39540.64050.32450.87190.0423^0.0085-0.00750.2107-0.01020.01480.91940.44290.87190.0446(3;4)^-0.0007-0.00790.05070.02910.81580.85610.71120.85680.007^0.01460.0486-0.15980.043800.36170.33740.85680.0698 GCO2(1;2)^-0.00750.07410.05450.47480.0050.56570.695500.598 Continuedonnextpage
PAGE 179
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 JCP2(1;2)^-0.0009-0.0661-0.02160.07380.73370.36220.75170.7070.0362^0.01340.05810.0070.074900.42770.91880.7070.02663(1;2)^-0.0099-0.5708-0.17310.7530.04060.04380.58970.04110.2812 Continuedonnextpage
PAGE 180
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 KFT2(1;2)^-0.00450.01950.0140.52520.00010.37160.833300.5771^0.0091-0.0364-0.0611.093100.24510.522300.59033(1;2)^0.00350.0084-0.0371-0.35190.70340.97680.96650.71740.0052^0.00660.0519-0.058-0.014600.37110.74680.71740.0423(2;3)^-0.001-0.00650.04210.220.58290.85160.80830.14170.0819 Continuedonnextpage
PAGE 181
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 MGM2(1;2)^0.0205-0.0041-0.0863-1.0620.00190.98510.63030.00270.3027^0.0162-0.0289-0.0174-0.279200.79870.85010.00270.29913(1;2)^0.0115-0.34760.022-0.5690.20130.51080.95890.25170.0633^0.0105-0.18540.197-0.08820.00130.37140.23470.25170.1105(2;3)^-0.00310.0125-0.06950.32320.28730.75660.49770.03730.2055^0.0150.002-0.09590.483800.96760.44380.03730.20424(1;2)^-0.0005-0.3174-0.0290.27440.92570.15920.89410.39830.0994 Continuedonnextpage
PAGE 182
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 MON2(1;2)^-0.0089-0.056-0.04790.57080.22590.78940.86430.13930.1115^0.0171-0.01-0.29860.143900.92430.02610.13930.273(1;2)^0.0189-0.2162-0.4077-1.21270.01010.50180.28740.01530.2415^0.0116-0.0172-0.0552-0.169800.88690.70280.01530.207(2;3)^0.0051-0.0794-0.39060.01350.34620.44590.19720.95660.0738^0.0168-0.0615-0.40740.008600.45980.08790.95660.11744(1;2)^-0.00320.30830.44080.16160.60340.29870.23050.71690.0752^0.0107-0.0589-0.09330.031800.65720.57170.71690.0171(2;3)^0.0166-0.3753-1.2178-0.33010.07080.16950.06370.37060.1789 Continuedonnextpage
PAGE 183
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 PDX2(1;2)^0.0064-0.1949-0.2585-0.39940.0170.68260.08860.00030.4307^0.0154-0.5942-0.3881-1.02060.00010.43340.11090.00030.42373(1;2)^0.0067-0.03160.3975-0.64630.47660.96170.51030.02420.2132^0.0177-0.1938-0.2329-0.27920.00190.65330.55760.02420.2152(2;3)^0.004-0.04860.0004-0.5370.00440.16130.99300.7142^0.0085-0.0842-0.0109-1.326800.1210.892700.71784(1;2)^0.0031-0.69520.5735-0.52340.74940.52490.39750.07710.158^0.0116-0.07670.2954-0.22020.05740.91420.50280.07710.1212(2;3)^0.0155-0.0882-0.1525-0.91040.03430.58520.5470.0030.2927^0.0157-0.0875-0.1145-0.320.00010.35810.44480.0030.3088(3;4)^0.0042-0.06360.059-0.56570.00430.08550.323500.7091 Continuedonnextpage
PAGE 184
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 PG2(1;2)^-0.0022-0.01470.03030.21790.01330.73220.59720.04960.1598^0.0074-0.0160.00830.643700.82830.93320.04960.14823(1;2)^0.0007-0.2185-0.0459-0.08160.85810.18770.89720.84370.0671^0.0072-0.1074-0.1231-0.018700.17560.46690.84370.0792(2;3)^0.0001-0.0654-0.19840.24280.96420.62580.47770.47480.0503^0.0065-0.0047-0.01820.081600.95240.9110.47480.02234(1;2)^0.0018-0.2968-0.45780.42810.58610.1080.18560.42490.1213^0.00440.11830.19830.057600.07940.11550.42490.1525(2;3)^-0.0019-0.0572-0.36440.85310.79410.87440.71340.21720.0738^0.006-0.0068-0.26770.06790.00120.94720.33520.21720.1015(3;4)^-0.0018-0.0305-0.06850.1880.24850.47870.6470.33540.0677^0.00660.029-0.05330.190100.50360.72350.33540.0508 PLCE2(1;2)^-0.0140.08240.18370.49930.17150.6790.58250.12350.0939 Continuedonnextpage
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^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 PTRY2(1;2)^-0.00140.09570.115-0.02570.75780.47390.41030.86680.0558^0.0253-0.1231-0.3887-0.042900.47560.02470.86680.1993(1;2)^0.01850.3221-0.1872-0.71630.02310.40710.67080.03480.1847 Continuedonnextpage
PAGE 186
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 QCOM2(1;2)^0.0101-0.0328-0.0943-0.65050.00610.870.52030.00090.3538^0.0147-0.0964-0.1318-0.542500.59730.32250.00090.38043(1;2)^0.01970.43070.0404-0.8220.15530.7110.96830.10260.1101^0.0106-0.21740.2599-0.12070.04130.62520.50320.10260.1232(2;3)^-0.00520.0567-0.09210.38320.2170.38820.58710.10740.1415 Continuedonnextpage
PAGE 187
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 S2(1;2)^0.0066-0.0255-0.2231-0.37060.00150.7970.057300.5318^0.0181-0.1449-0.4743-1.403700.44960.036500.54953(1;2)^-0.0056-0.2033-0.27720.59910.00860.01590.04150.00030.4852^0.00940.1640.29520.66400.07140.0390.00030.4301(2;3)^0.0039-0.2794-0.3433-0.23970.30490.29860.20730.11120.256^0.0109-0.28940.1415-0.39490.01880.40330.68960.11120.12084(1;2)^0.0041-0.0546-0.2525-0.17110.40210.79690.51760.61010.036 Continuedonnextpage
PAGE 188
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 T2(1;2)^0.0009-0.0068-0.1291-0.01580.71020.9430.44850.93870.0271^0.00980.0218-0.4177-0.014700.81030.00660.93870.26423(1;2)^0.00570.20990.3598-0.80840.28940.5180.48560.13510.1015^0.00770.0880.0411-0.103700.44850.8250.13510.0979(2;3)^-0.00240.04710.02540.25370.18530.40770.87210.13930.0982^0.0074-0.0427-0.01140.323700.50730.94880.13930.08984(1;2)^0.0036-0.5964-0.95650.34390.48830.28210.14540.5960.0872^0.00420.12390.27050.03190.00410.46570.17740.5960.07(2;3)^-0.0050.0390.63590.21140.31950.81680.260.71930.0535 Continuedonnextpage
PAGE 189
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 TMO2(1;2)^0.0013-0.0669-0.0534-0.04680.34730.52090.4690.62310.0344^0.01240.023-0.2257-0.201500.91550.13380.62310.09633(1;2)^0.0091-0.37030.4115-0.85830.35460.62770.67670.14030.0912^0.0071-0.13580.2059-0.09520.02310.59320.53020.14030.1049(2;3)^-0.0001-0.0099-0.10860.09360.93270.5840.06330.44710.1846^0.0108-0.0126-0.11590.239500.66410.22410.44710.11924(1;2)^-0.0084-0.195-1.29891.17270.42010.78380.2180.11490.1537^0.00880.0338-0.02350.07920.00030.85480.93260.11490.1021(2;3)^0.0059-0.15770.1665-0.48380.35010.12810.67420.3460.1542^0.00940.0469-0.175-0.070700.24060.24240.3460.1436(3;4)^0.0027-0.0777-0.0441-0.1580.24130.24160.79820.40910.0838 Continuedonnextpage
PAGE 190
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 TSN2(1;2)^-0.0042-0.03420.03070.20440.14340.72930.76810.19720.0661^0.01580.0433-0.14160.308800.72150.26370.19720.10613(1;2)^0.0081-0.17410.5603-0.47240.44540.78140.4270.33440.0659^0.01360.2723-0.1208-0.07590.00030.27390.67060.33440.0864(2;3)^0.00060.0484-0.1111-0.10240.77590.20830.23010.46940.1324^0.01130.0683-0.0671-0.198400.20220.60670.46940.08154(1;2)^-0.0017-0.0876-0.0239-0.1770.87130.89850.97380.76570.0057^0.01090.19280.1076-0.01960.00070.39580.65620.76570.0637(2;3)^-0.0070.07240.72330.16930.4820.68680.18850.6690.0697^0.01680.0179-0.38720.04220.00010.84180.15740.6690.0793(3;4)^-0.0039-0.106-0.03820.45760.14580.12120.77990.06950.1582^0.00680.10780.20470.26470.00020.03450.04060.06950.3315 UNH2(1;2)^-0.00640.05710.16330.2490.03190.61550.19260.13020.1264 Continuedonnextpage
PAGE 191
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 VZ2(1;2)^0.00490.0238-0.0711-0.42940.06770.92630.72840.09060.1078^0.0089-0.0662-0.1841-0.247300.7340.22960.09060.15153(1;2)^0.0069-0.0979-0.2916-0.44440.03130.76480.43260.1960.1065 Continuedonnextpage
PAGE 192
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2 WYE2(1;2)^-0.0041-0.04680.07120.30160.01430.67240.53350.01140.2363^0.0117-0.0248-0.06620.735700.88610.71140.01140.22733(1;2)^0.0099-0.2579-0.4412-1.02070.02380.51960.32490.00020.4582^0.0082-0.0221-0.0877-0.40220.0020.93020.75730.00020.4215(2;3)^-0.0032-0.1116-0.07560.36270.05290.11090.5030.04150.1975 Continuedonnextpage
PAGE 193
^j=^0+^1^i+^2^i+^3^j^j=^0+^1^i+^2^i+^3^jpvalues TickerMr(i;j)^=^^0^1^2^3^0^1^2^3R2
PAGE 194
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Joon-HuiYoonisadoctorofphilosophyofquantitativenanceconcentrationinindustrialandsystemsengineeringattheUniversityofFlorida.HereceivedhisPh.D.degreeinquantitativenanceforhisdissertationon\InformationAsymmetryinDirectionandVolatility:PriceProcessandTransactionLevelAnalysis."HealsoholdsmasterofsciencedegreefromtheTexasA&MUniversityandisaholderofCertiedinProductionandInventoryManagement.Hehadworkedforfouryearsininformationtechnologyindustrybeforepursuingacademia.Heisinterestedincombininginformationtechnologyandnancialtheoriestomakenancialmarketmoreecient. 197
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