回归分析在股票中的应用.docx

回归分析在股票中的应用.docx

《回归分析在股票中的应用.docx》由会员分享，可在线阅读，更多相关《回归分析在股票中的应用.docx（24页珍藏版）》请在冰豆网上搜索。

回归分析在股票中的应用

MAinInternationalFinancialAnalysis

NBS8002TechniquesforDataAnalysis

AssignmentofEventStudy

Studentname:

ZHUOXUANHOU

Studentnumber:

109041249

Title:

TheAnalysisofCVRDAcquisition

Contents

Introduction1

PreparationforOLS1

TheMarketModelbenchmark1

ChoiceofData2

Sourceandvalidityofthedata2

Choiceoftestperiodandestimationperiod3

Choiceofthemarketindex3

CoefficientStabilityTest3

OrdinaryLeastSquares4

AssumptionsofOrdinaryLeastSquaresRegression5

1.Modelislinearinparameters5

2.Thedataarearandomsampleofthepopulation5

3.Theexpectedvalueoftheerrorsisalwayszero7

4.Theindependentvariablesarenottoostronglycollinear7

5.Theindependentvariablesaremeasuredprecisely7

6.Theresidualshaveconstantvariance7

7.Theerrorsarenormallydistributed11

ProceedOLSRegression12

InterpretationandDiscussionofAbnormalReturns12

Interpretationofabnormalreturnsforeachevent12

Interpretationofabnormalreturnsfortheseriesofevents16

Conclusions19

ListofReferences20

TheAnalysisofCVRDAcquisition

Introduction

ThispaperanalysestheimpactofacquisitioneventsonthestockreturnsofCVRD.Theseeventsinclude:

anannouncementthatproposedall-cashoffertoacquireIncobyCVRD;commentsonIncoBoard’sdecisiontorecommenditsOfferandannouncementofextension;extensionofitsofferforInco;CVRDacquires75.66%ofInco;CVRDpaysUS$13.3billionfortheacquisitionofInco;CVRDholds86.57%ofInco.

ThepaperusesOLSmethodtocalculatetheabnormalreturnsduringtheeventperiod,andtheninterprettheresultsgeneratedbyOLS.Atfirst,thepricedataaregainedfromYahooFinance;then,aMarketModelisset,afterwhichthedataareprocessedwithMicrosoftOfficeExcelandMinitab,usingChow-test,Durbin-watsontest,Goldfield-Quardttest,etc,totestwhetherthedataaresuitableforregression;afterwards,aregressionismadeandaMarketModelisadoptedtocalculatetheabnormalreturnsoftheeventperiod;finally,interpretationsaregiventoenclosethereasonsunderneaththeabnormalreturns.

PreparationforOLS

Inordertofocusontheimpactoffirm-specificinformationonsecurityreturns,acontrolisneededtomodeldailyreturnsconditionallyexpectedfromcontemporaneousnon-firm-specificinformation.Themarketmodelisusedasacontrol.Besides,thedatashouldbechosenproperlyonperiodandproperindexaswell.Finally,Chowtestisusedtotestcoefficientstability.

TheMarketModelbenchmark

（1）

Whereαjandβjareparametersspecifictothejthequitysecurity,Rmtisthereturnonawelldiversifiedindexportfolio（suchasNYSEComposite）duringthetthtimeperiodandεjtisthestochasticerrortermforthejthsecurityduringthetthtimeperiod.Equation

（1）partitionsRjtintoasystematiccomponentlinearlyrelatedtoRmt,andanunsystematiccomponent,εjt,whichisuncorrelatedwithRmt.Theeffectoffirm-specificeventsismeanttobefullycapturedintheunsystematiccomponent,theassumptionbeingthattheinformationsignalandRmtareindependent.Bothαjandβjmustbeestimatedhere,resultinginapredictedabnormalreturnof

（2）

Inthispaper,thereisonlyonesecurity,CVRD;thereforetheissueofjcanbeignored.Thus,equation

（1）isadaptedas

（3）

andequation

（2）isadaptedas

（4）

ChoiceofData

Sourceandvalidityofthedata

ThedatawasdrawnfromYahooFinanceadjustedclosedata.Ithasthefollowingcharacteristics:

♦Closepriceadjusteddatahavebeenadjustedfordividends,whichwouldbepartofanyrateofreturncalculation.Usually,dividendsarepaid（ifatall）everysixmonths.TheconsequenceisthatforCVRD,twoobservationswillbemeasuredwitherroreveryyear.Whenthedataareadjusted,thedividendshavebeenaddedintoprices.

♦Closepriceadjusteddatahavebeenadjustedforsplit.Withasplit,thesecuritypricewilldropremarkably,whichwillleadtoanerrorwhenthedataareprocessed.Asthedatahavebeenadjusted,thereisnothisproblemanymore.

♦YahooFinancerecordsapriceondayswhentheNYSEisclosed.Thisexcludesweekends.Andallpublicholidays（whentheydon’tfallonaweekend）willnotshowaprice.Whatthismeansisthatthesedayscanbesimplyomittedasnon-existent.

♦Thesharepricesrecordedisamid-priceandnotnecessarilyabuyorsellprice.Thiswillbeimportantintheinterpretationoftheevidence.

Thesecharacteristicswillhelpavoiderrorsstemmedfromrawdata.

Choiceoftestperiodandestimationperiod

Thereturnshistoryforeachsecurityisusuallydividedintoanestimationperiod（EP）andatestperiod（TP）.TheEPisusedforestimatingtheparametersofthebenchmarkexpectedreturn.ThisallowsapredictedabnormalreturntobecalculatedwithintheTP.（Strong,1992）

Inourcase,EPissetfrom01/08/2002to31/07/2006,andTPissetfrom01/08/2006to06/11/2006.AlthoughTPissetupasthisperiod,itwillbemodifiedaccordingtosomeconditions.Thiswillbediscussedlaterinthepaper.Thefirsteventdateis11/08/2006.Theformofthisprocedureisillustratedschematicallybelow:

Choiceofthemarketindex

Inthispaper,NYSECompositeisselectedasthemarketbenchmark.Theindexisweightedusingfree-floatmarketcapitalizationandcalculatedonbothpriceandtotalreturnbasis.ItiscomposedtomeasuretheperformanceofallordinarysecuritieslistedontheNYSE,containingover2,000U.S.andnon-U.S.securities.TheNYSECompositeIndexhasbeenadjustedtoeliminatetheeffectsofcapitalizationchanges,newlistingsanddelistings.Thus,itisasuitablemarketindextobethebenchmarkforCVRD.

CoefficientStabilityTest

Chowtestisusedtotestthecoefficientstability.TheChowtestisastatisticalandeconometrictestofwhetherthecoefficientinonelinearregressionisequaltothecoefficientontheotherdifferentdataset.Itisusuallyusedintimeseriesanalysistotestforthepresenceofastructuralbreak.Inprogramevaluation,theChowtestisoftenusedtodeterminewhethertheindependentvariableshavedifferentimpactsondifferentsubgroupsofthepopulation.

TheChowteststatisticis

（5）

WhereSc,S1andS2areSSRfromthecombineddata,thefirstgroupandthesecondgrouprespectively. N1 and N2 arethenumberofobservationsineachgroupand k isthetotalnumberofparameters（inthiscase,k=2）

Werunthetestasfollows:

Ourmarketmodelis

Rit=α+βRmt+εt

Wesplitourdataintotwogroups,two-yearperiodforeach.Thenwehave

Rit=α1+β1Rmt+εt

Rit=α2+β2Rmt+εt

Sethypothesis

H0:

α1=α2,β1=β2;

H1:

anyofthemarenotequal.

Summarizingtheregressionresults,wehave

Value

Sc

0.417398653

S1

0.197546678

S2

0.18040653

N1

502

N2

504

K

2

Chow

5.20788E-05

Theteststatisticfollowsthe Fdistribution.CheckingFtablewithP=0.05,both500degreesoffreedom,wehavecriticalFis1.16.Chowteststatistichereissmallerthan1.16,soH0cannotberejected.Therefore,coefficientαandβarestable.

OrdinaryLeastSquares

instatisticsandeconometrics,ordinaryleastsquares（OLS）isalsoknownaslinearleastsquare.Itisamethodwithwhichestimateunknownparametersinalinearregressionmodel.Thismethodminimizesthesumofsquaredverticaldistancesbetweentheobservedresponsesinthedataset,andtheresponsespredictedbythelinearapproximation.Theresultingestimatorcanbeexpressedbyasimpleformula,especiallyinthecaseofasingleregressorontheright-handside.

（6）

isalinearregressionmodelwithasingleregressor,Rmt;Ritistheregressand.αandβareconstantstobeestimated.Weareparticularlyinterestedintheinterceptαandslopecoefficientβandtoknowtherelationshipbetweensecurityreturnandmarketreturnduringthetestperiod.Afterwards,theyarepluggedintotheequationfortheeventperiod.WiththedataofRitandRmtineventperiod,tcanbeobtained,knownastheabnormalreturn.

（7）

andcumulativeabnormalreturnis

（8）

AssumptionsofOrdinaryLeastSquaresRegression

TheassumptionsaretherequirementofaneffectiveOLSregression,thatiswithouttheseassumptions,theresultofOLSregressionwillprobablybedistortedandnotbeabletoshowarealisticsituation.Theassumptionsare:

1.Modelislinearinparameters

Withasimilarstructureoftheformula,MMissuitableforthisassumption.AscanbeseeninEquation

（1）,RtandRmtareassumedtobelinearrelated.

2.Thedataarearandomsampleofthepopulation

Ifthedata,AR,arestatisticallyindependentfromoneanother,wecanarguethattheyarerandom.Durbin-Watsontestisusedtotestwhetherthedatahaveanauto-correlationproblem.

TheDurbin-WatsonTestforserialcorrelationassumesthatthetarestationaryandnormallydistributedwithmeanzero.Theteststatisticis

（9）

Wehaved≈2（1-ρ）,whereρmeasuresthelevelauto-correlation.Iftheerrorsarewhitenoise,dwillbecloseto2.Iftheerrorsarestronglyauto-correlated,dwillfarfrom2.Ifρ=0andd=2,thereisnoauto-correlation.Ifρ=-1andd=0,thedataareperfectlypositivelycorrelated.Ifρ=+1andd=4,thedataareperfectlynegativelycorrelated.

Involvingdand4-d,theinterpretationoftheresultmaybecomplicated.InDraperandSmith（1998）,Page184-190.Insomecases,thetestcanbe"inconclusive,"i.e.,H0ofuncorrelatedisneitheracceptednorrejected.

Steps:

（1）Calculatethelogarithmicreturnsforeachday.Theequationis

Rt=ln（Pt/Pt-1）（10）

（2）InExcel,clickData|DataAnalysis|Regression,andchoose‘displayresiduals’toobtaintheresidualsdata.Andthen,theresidualsdataarepluggedintoth