Information Asymmetry in Direction and Volatility

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Permanent Link:: https://ufdc.ufl.edu/UFE0024812/00001

Material Information

Title:: Information Asymmetry in Direction and Volatility Price Process and Transaction Level Analysis
Creator:: Yoon, Joon
Place of Publication:: [Gainesville, Fla.]
Publisher:: University of Florida
Publication Date:: 2009
Language:: english
Physical Description:: 1 online resource (197 p.)

Thesis/Dissertation Information

Degree:: Doctorate ( Ph.D.)
Degree Grantor:: University of Florida
Degree Disciplines:: Industrial and Systems Engineering
Committee Chair:: AitSahlia, Farid
Committee Members:: Nimalendran, Mahendrara
Uryasev, Stanislav
Ghosh, Malay
Graduation Date:: 8/8/2009

Subjects

Subjects / Keywords:: Adverse selection ( jstor )
Bid prices ( jstor )
Efficient markets ( jstor )
Fundamental value ( jstor )
Liquidity ( jstor )
Market prices ( jstor )
Prices ( jstor )
Pricing strategies ( jstor )
Regression analysis ( jstor )
Standard deviation ( jstor )
Industrial and Systems Engineering -- Dissertations, Academic -- UF
econometrics, market, markov, stochastic
Genre:: Electronic Thesis or Dissertation
born-digital ( sobekcm )
Industrial and Systems Engineering thesis, Ph.D.

Notes

Abstract:: This dissertation develops a structural methodology for equity pricing in a semi-strong efficient market and performs an empirical study supporting the need for such a methodology. Conventional price dynamics of equities and their related options assume markets to be strongly efficient. This hypothesis however is a severe simplification ignoring liquidity risk, adverse selection effect, and the difficulty of achieving informational efficiency. The methodology proposed in this thesis categorizes equity price dynamics into 3 sub-processes: fundamental value, duration, and National Best Bid and Offer (NBBO) revisions. This approach reveals how an informed trader's knowledge is eventually incorporated into equity and option prices. Market-makers are assumed to apply Bayesian Nash-equilibrium strategies to construct rational NBBO quotes to hedge against adverse selection risk as well as to provide quotes attractive to uninformed traders. The objective of the empirical study is to find evidence of market inefficiency in both fundamental value and intra-day trades. For the former, we focus on structural breaks in direction and volatility of equity prices when new key developments are announced. Conventional event-studies only classify three sub-event windows: pre-event, event, and post-event. We propose a change-point model that allows multiple regimes in association with pre-determined key events, with variable regime lengths depending on structural breaks in direction and volatility associated with abnormal returns. Our study confirms that adjustments to key developments may begin before and end after their announcements in several stages. Furthermore, the correlation between successive key developments is found to be statistically negligible, thus supporting the uniqueness of each. For the second issue, we examine intra-day trades and NBBO data upon the announcements of new key developments. Through various statistical models, we associate with trading and NBBO two distinct sets of decision factors, depending on whether we are in a stable or a transition regime. Estimates of trade duration, NBBO duration, and realized volatility are the most distinguishable between stable and transition regimes. Overall, $R^2$s are lower for transition regimes, showing that price evolution depends more on exogenous factors than in stable regimes. Coefficient estimates differ very little between the two types of regimes, with a few exceptions. Factors of traded or NBBO exchange have limited significance, with a few exceptions. A comparison between actual empirical data and simulated results, based on uninformed limit-order traders and market-makers following Bayesian Nash-equilibrium strategies, shows that the latter are not necessarily better, except that they lead to a less volatile price discovery. ( en )
General Note:: In the series University of Florida Digital Collections.
General Note:: Includes vita.
Bibliography:: Includes bibliographical references.
Source of Description:: Description based on online resource; title from PDF title page.
Source of Description:: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:: Thesis (Ph.D.)--University of Florida, 2009.
Local:: Adviser: AitSahlia, Farid.
Statement of Responsibility:: by Joon Yoon.

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Source Institution:: University of Florida
Holding Location:: University of Florida
Rights Management:: Copyright Yoon, Joon. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:: 489236252 ( OCLC )
Classification:: LD1780 2009 ( lcc )

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Aggregations:: Institutional Repository at the University of Florida (IR@UF)
University of Florida Theses & Dissertations
University of Florida
INTERNAL UF RETRO ETDS

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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

PAGE 174

^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

PAGE 175

^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

PAGE 176

^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

PAGE 177

^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

PAGE 178

^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

PAGE 185

^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