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CFALevel2Notes
EthicsandProfessionalstandards
Reading1:CodeofEthicsandStandardsofProfessionalConduct 6componentsoftheCodeofEthics
1. Actwithintegrity,competence,diligenceandrespect2. Placeintegrityofprofessionandclientsabovepersonalinterests3. Reasonablecareandexerciseindependentprofessionaljudgmentwhenmakinginvestment
recommendations4. Practiceandencourageotherstopracticeinethicalmanner5. Promoteintegrityandviabilityofglobalcapitalmarketsforultimatebenefitofsociety6. Maintainandimproveprofessionalcompetence
DisciplinaryReviewCommittee(DRC)responsiblefortheenforcementofCodeandStandardsProfessionalConductinquiriescomefromnumberofsources:
• Self-discloseonannualProfessionalConductStatement• WrittencomplaintsreceivedbyProfessionalConductstaffaboutinvestigation• Media,regulatorynoticesorpublicsources• Monitoredbyproctorswhocompletereportoncandidateswhoviolatedexamday
Sanctionsinclude:
• Publiccensure• MembershipsuspensionanduseofCFAdesignation• RevocationofCFAcharter
7standardsofProfessionalConduct
1. PROFESSIONALISMA. Knowledgeofthelaw(includingcodeofethicsandstandardsofprofessionalconduct)–in
theeventofaconflict,thestricterlaw,ruleorregulationapplies.B. Independenceandobjectivity–notofferoracceptgiftorcompensationthatwould
compromiseindependence/objectivityC. Misrepresentation–notmakeanyinregardstoanalysis,recommendationsoractions
§ Creditingsourcenotrequiredwhenusingstatistics,tablesandprojectionsfromrecognisedfinancialandstatisticalreportingservices
D. Misconduct–notengageinconductinvolvingdishonesty,fraud,deceit
2. INTEGRITYOFCAPITALMARKETSA. Materialnonpublicinfo–thatcouldaffectvalueofinvestment
§ Publiconceitisannouncedtothemarketplace§ Mosaictheory=reachinginvestmentconclusionthroughanalysisofpublicinfo+
non-materialnonpublicinfo§ Membersshouldmakeefforttoachievepublicdisseminationbythefirmof
informationtheypossess.Firmsshouldreviewemployeetradesandmaintainwatchlists.
B. Marketmanipulation–notdistortpricesorartificiallyinflatetradingvolumeàonlyifthereisINTENTtomislead.
3. DUTIESTOCLIENTS
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A. Loyalty,PrudenceandCare–actinbenefitofclient,placeclientsinterestbeforeemployer’s/owninterest
§ Submitatleastquarterlystatementsshowingsecuritiesincustodyandalldebits,creditandtransactions.Notvoteonallproxies.
B. FairDealing–dealingwithclientswhenmakinganalysis,recommendations,engagement§ E.g.donottakesharesofanoversubscribeIPO
C. Suitability–riskandreturnobjectives,suitableinvestments,consistentwithobjectivesandconstraintsofportfolio
§ Membersgatherinfoatbeginningofrelationshipintheformofaninvestmentpolicystatement(IPS)
D. Performancepresentation–fair,accurateandcomplete§ Includeterminatedaccountsandstatewhenterminated
E. Preservationofconfidentiality–keepinfoaboutclients(currentandpast)confidentialunless3exceptions:illegalactivities,disclosurerequiredbylaw,clientpermitsdisclosure
4. DUTIESTOEMPLOYERSA. Loyalty–actforbenefitofemployerandnotdivulgeconfidentialinfo
§ Norequirementtoputemployerinterestsaheadoffamilyandpersonalobligations§ Violationsincludemisappropriationoftradesecretsandclientlists,misuseof
confidentialinfo,solicitingemployer’sclients,self-dealing.B. AdditionalCompensationArrangements–notacceptgifts,benefitsthatmightcreateconflict
ofinterestunlessobtainwrittenconsentfromallpartiesinvolved§ Ifclientoffersbonusdependingonfutureperformance,thisisancompensation
arrangementàrequireswrittenconsentinadvance§ Ifclientoffersbonusdependingonpastperformance,thisisagiftàrequires
disclosuretoemployertocomplywithStandardI(B)IndependenceandObjectivityC. ResponsibilitiesofSupervisors–makesurepeoplecomplywithlaws,regulationandCode
andStandards
5. INVESTMENTANALYSIS,RECOMMENDATIONSANDACTIONSA. DiligenceandReasonableBasis–reasonablebasissupportedbyresearchandinvestigation
foranalysis,recommendation§ Applicationdependsoninvestmentphilosophyadheredto,members’rolesin
investmentdecisionmakingprocess,andresourcesandsupportprovidedbyemployer
§ Considerationsincludeeconomicconditions,firmsfinancialresults/operatinghistory,feesandhistoricalresults,limitationsofquantmodels,peergroupcomparisonsforvaluationareappropriate
§ Membersshouldencouragefirmtoadoptpolicyforperiodicinternalreviewofqualityof3rdpartyresearch
B. CommunicationwithClients–disclosebasicprinciplesofinvestmentprocessandconstructportfoliosandanychangesthatmightmateriallyaffectprocesses,significantlimitationsandrisks,identifyingimportantfactorsandcommunicatethem,distinguishbetweenfactandopinion.
§ Expectationsbasedonmodeling/analysisarenotfacts§ Communicategains/lossesintermsoftotalreturns§ Explainlimitationsofmodel/assumptionsusedandoftheinvestmentitself–e.g.
liquidityandcapacityC. RecordRetention–developandmaintainrecordstosupportanalysisandrecommendation
withclients(e.g.documentingdetailsofconvo)§ Memberwhochangesfirmsmustre-createanalysisdocumentationsupporting
recommendationandmustnotrelyonmaterialcreatedatpreviousfirm§ Ifnoregulatorystandards/firmpoliciesinplace,recommends7-yearminimum
holdingperiod
6. CONFLICTOFINTEREST
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A. DisclosureofConflicts–mattersthatcouldimpairindependenceandobjectivityorinterferewithdutytoclientsandemployer
§ E.g.ownershipofstockincompanythatrecommendingB. PriorityofTransactions–clients/employerspriorityoverown
§ LimitationsonemployeeparticipationinequityIPO,privateplacement§ Blackoutperiod–nopersonalpurchase/saleofsecurityinadvanceof
client/employerC. ReferralFees–compensationreceivedorpaidtoothersforrecommendationof
products/services
7. RESPONSIBLEASACFAINSTITUTEMEMBER/CANDIDATE1. ConductasParticipantsinCFAInstitutePrograms–notcompromisereputationorintegrity
ofCFA§ e.g.examcheating,improperlyusingdesignation,notrevealconfidentialinfo
regardingCFA,misrepresentinginfoonProfessionalConductStatement(PCS)2. ReferencetoCFAInstitute,DesignationandProgram–notmisrepresentorexaggerate
meaning/implications§ MembersmustsignthePCSannually,andpayCFAmembershipduesannuallyàif
failtodothis,personwillnolongerbeanactivememberNorequirementtoreportviolationstogovtauthorities,butisadvisable
Reading3:CFAInstituteResearchObjectivityStandardsObjectivesofResearchObjectivityStandardsObjectiveistoprovidespecificmeasureablestandardsformanaginganddisclosingconflictsofinterestthatmayinterferewithanalystabilitytoconductindependentresearchandmakeobjectiverecommendations
• Clientsinterestbeforeemployeesandfirms• Minimizepossibleconflictswhichwillaffectindependenceandobjectivity• Supportselfregulation• ProvideworkenvironmentconducivetoethicalbehaviorandadherencetoCodeandStandards
Companypolicies&practicestoresearchobjectivity+changesrequiredvsrecommendedcompliance
ResearchObjectivityPolicyRequirements Recommended
• Formalwrittenindependenceandobjectivityofresearchpolicydistributedtoclients
• Supervisoryproceduresinplace• Seniorofficerattestingannuallytoclients
• Identifycoveredemployees(conductsresearch,takesinvestmentaction,abilitytoinfluencereports)
• Factorsonwhichanalystscompensationbased
• Howreportsmaybepurchasedbyclients
PublicAppearancesRequirements Recommended
• Coveredemployeesmakingpublicappearancestodiscussresearchorinvestmentrecommendationsmustdiscloseanypersonalandfirmsconflictsofinterest
• Audiencecanmakeinformedjudgement• PreparedtodiscloseallconflictsandallIB
andmarketingrelationships• Researchreportsshouldbeprovidedata
reasonablecostsReasonableandAdequateBasis
Requirements Recommended• Singleemployeeorcommitteecharged
withreviewingandapprovingallreportsandinvestmentrecommendations
• Firmsprovidingguidanceonwhatconstitutesreasonableandadequate
• Providesupportingdatatoclient
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InvestmentBanking(IB)
Requirements Recommended• SeparateresearchanalystsfromIBdept• AnalystNOTsupervisedbyIBpersonnel• PreventIBfromreviewingorapproving
researchreportsandrecommendations
• NotsharingreportwithIBuntilpublication• IBpersonnelonlyreviewtoverifyfactual
infooridentifypossibleconflictofinterest• Analystnotallowedtoparticipatein
roadshow
ResearchAnalystCompensationRequirements Recommended
• Compdirectlyrelatedtoqualityofresearchandrecommendations,andNOTlinkedtoIBorcorporatefinanceactivities
• Measurablecriteriaconsistentlyappliedtoallanalysts
• DiscloseextenttowhichcompensationisdependentonIBrevenue
RelationshipwithSubjectCompanies
Requirements Recommended• Analystnotallowsubjectcompanytosee
anypartofresearchthatmightsignalrecommendationormakepromises
• Governingr/shipwithcompanies(e.g.gifts)• Checkfactscontainedbeforepublication• Legaldeptreceivedraftbeforeshared
PersonalInvestmentandTrading
Requirements Recommended• Policiesaddressingpersonaltradingof
employees• Ensuringemployeesdonotshareinfowith
anyonewhocouldtradeahead• Prohibitemployeesandfamilyfromtrading
contrarytorecommendations
• Interestsofclientaheadofpersonal&firm• Obtainapprovalfromlegal/compliance
departmentinadvanceofanytrading• Restrictedperiodsforemployeetrading• Contraryinvestmentduetofinancial
hardship• Providelistofpersonalholdings
TimelinessofResearchReportsandRecommendations
Requirements Recommended• Regularlyissueresearchreportsonsubject
companiesonatimelybasis• Regularupdatesonresearche.g.quarterly• Ifcompanycoveragediscontinued,issuea
“final”researchreport
ComplianceandEnforcementRequirements Recommended
• Disciplinaryaction,monitoringeffectiveness,maintainrecordsforaudit
• Distributeclientlistofactivitieswhichareviolationsandincludedisciplinarysanctions
Disclosure
Requirements Recommended• Discloseconflictofinterestrelatedto
coveredemployeesorfirmasawhole• Disclosurescomplete&easytounderstand• Disclosevaluationmethodsforpricetgts
RatingSystem
Requirements Recommended• Musthaveratingsystemthatinvestorsfind
usefulforinvestmentdecisionthatdeterminessuitabilityofinvestment
• Avoid1-dimensionalratingsàNeedmoreinfo+descriptionofsystem
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• Absolute(buy/hold/sell)orrelative(outperform/underperform)categoriesrecommended
Reading7:TradeAllocation:FairDealingandDisclosureEvaluatetradeallocationpracticesanddetermineifcomplywithStandards
• Allocationofclienttradesonad-hocbasislendsitselftofairnessproblems:o Allocationmaybebasedoncompensationarrangements
§ E.g.allocatingdisproportionatelytradestoperformance-basedfeeaccountsàbreachesIII(A)asthisincreasesfeesatexpenseofasset-basedfeeaccounts
o Allocationmaybebasedclientrelationshipswithfirm§ E.g.allocatingdisproportionateshareofprofitabletradestofavoredclients
Describeappropriateactionstotakeinresponsetotradeallocationpracticesthatdon’trespectclientinterests
• Advancedindicationofclientinterestregardingnewissues• Distributenewissuesbyclient,notbyPM• Fairandobjectivemethodfortradeallocationsuchasproratasystem• Executionoftradesandpricefairly+inatimelyandefficientmanner• Keepingrecordsandperiodicallyreviewtoensureclientstreatedequitably
Reading8:ChangingInvestmentObjectivesEvaluatedisclosureofinvestmentobjectiveandpolicies
• Investmentactionsconsistentwithstatedobjectivesandconstraintsofthefund• MaterialdeviationfromprocessinabsenceofclientapprovalviolatesIII(C)DutiestoClients• Investmentmustfitwithinmandateorwithinrealmofinvestmentthat’sallowedaccordingtofund’s
disclosure(e.g.prospectusorPDS)Actionsneededtoensureadequatedisclosureofinvestmentprocess
• Determineclientsfinancialsituation,investmentobjectivesandlevelofinvestingexpertise• Adequacydisclosesecurityselectionandportfolioconstructionprocess• Conductregularinternalchecksforcompliancewiththeseprocesses• Sticktostatedinvestmentstrategyifmanagingspecificmandateorstrategy• Notifyinvestorsofpotentialchangeinprocessandsecuredocumentationofauthorizationfor
proposedchanges
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QuantitativeMethodsforValuationsReading9:CorrelationandRegression SamplecovarianceandsamplecorrelationcoefficientCovariancemeasuresthedegreeofhow2variablesmovetogether.
• +ve=movetogether.–ve=oppositedirections.0=norelationship
• • Limitations:
o Sensitivetoscaleoftwovariableso Rangefromnegativetopositiveinfinity
• ThereforeneedtocalculatecorrelationcoefficientCorrelationcoefficient(r)isameasureofstrengthofthelinearrelationshipbetween2variables𝜌",$ =
𝐶𝑜𝑣",$𝜎"𝜎$
=𝐶𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝑆𝐷1×𝑆𝐷2
• +1=perfectlypositivelycorrelated.-1=perfectlynegativelycorrelatedScatterplotiscollectionofpointsonagraphwhereeachpointrepresentsvaluesof2variables(X/Ypair)3Limitationstocorrelationanalysis
1. Impactofoutliersài.e.extremevalues2. Potentialforspuriouscorrelationàappearanceofr/shipwhenthereisnone(i.e.chance)3. Correlationonlymeasureslinear,doesnotcapturenonlinearrelationship
Testofhypothesisthatpopulationcorrelationcoefficient=0Needtoknowstrengthofrelationshipindicatedbycorrelationcoefficientbyusingstatisticaltestofsignificance2Tailedtest
• NullàH0:µ=µ0• AlternateàHa:µ≠µ0
ifnormallydistributedàuset-testtodeterminewhethernullshouldberejected
r=samplecorrelationcoefficient
Decision:comparetstatwithcriticalt-valueforappropriatedegreesoffreedomandsignificancelevel• REJECTH0if:
o tstat>upperCVo tstat<lowerCV
• ifrejectedàsignificantlydifferentfrom0DependentvsindependentvariablesinlinearregressionSimplelinearregressionexplainsvariationindependentvariable(predicted)intermsofvariationinindependentvariable(explanatory)6Assumptionsoflinearregression
1. Linearrelationshipexistsb/wdependentsandindependentvariable2. Independentvariableuncorrelatedwithresiduals3. Expectedvalueofresidualtermiszero[E(ε)=0]4. Varianceofresidualtermisconstantforallobservations
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5. Residualtermindependentlydistributedàresidualnotcorrelatedwithanyotherobservations6. Residualtermnormallydistributed
SIMPLELINEARREGRESSIONMODEL:Yi=b0+b1Xi+εi,
b1istheslopecoefficientà • Predictedchangeindependentfor1unitchangeinindependent• i.e.betaàmeasuressystematicrisk
b0isintercepttermà • i.e.ex-postalphaàmeasuresexcessrisk-adjustedreturn
Errorterm(εi)representsportionofdependentvariablethatcannotbeexplainedbyindependentvariableRegressionisalineofbestfit.Itisthelineforwhichestimatesofb0andb1aresuchthatsumofsquareddifferencesbetweenestimatedY-valuesandactualY-valuesisminimizedàSumofsquarederrors(SSE)
• Simplelinearregression=ordinaryleastsquares(OLS)regressionNote:HypothesistestorconfidenceintervalneededtoassessimportanceofvariableStandarderrorofestimate,coefficientofdetermination,andconfidenceintervalforregressioncoefficientStandarderrorofestimate(SEE)measuresthedegreeofvariabilityoftheactualY-valuesrelativetotheestimatedY-values
• Measureshowwellregressionmodel“fits”thedataàthesmallertheSEthebetterthefit• SEEistheSDoferrortermsinregressionàalsoreferredtoas“standarderrorofregression/residual”• SEEwillbeLOWifr/shipb/wdependentandindependentisSTRONG(e.g.r/shipb/wtreasuryyield
bondandmortgagerates)
• SEE CoefficientofDetermination(R2)isthe%oftotalvariationindependentexplainedbyindependent
• R2of0.63meansvariationofindependentexplains63%ofvariationindependentvariable• R2maybecomputedbysquaringcorrelationcoefficient(r)foraregressionwith1variable
o R2=r2• Note:correlatedb/betweenpredictedandactualvaluesissquarerootofR2• Ifmorethan1variableàmultipleregressiontechniquesneeded(e.g.ANOVA)
o E.g.𝑅$ = 789:;<=7>?;@<;A<B=ABA;:?;@<;A<B=
= 1 − D=789:;<=7>?;@<;A<B=ABA;:?;@<;A<B=
Confidenceintervalforregressioncoefficient
• ài.e.CoefficientEstimate±t*SEo tc=criticaltwotailedt-valueànote:n-2o sb1=standarderrorofregressioncoefficient
• SEE=sb1=widerconfidenceintervalNullandalternativehypothesisaboutpopregressioncoefficientandappropriateteststatistic
t-testfortrueslopecoefficient(b1)isequaltohypothesizedvalue: • RejectH0ift>CVorift<-CV
o Ifrejectàslopecoefficientdifferentfromhypothesist-stat=Coefficientestimate/SEPredictedvaluefordependentvariablePredictedvalues–valuespredictedbyregressionequation,givenanestimateofindependentvariable
• PredictedvalueofY:
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o Y=predictedvalueofdependento Xp=forecastedvalueofindependent
ConfidenceIntervalforpredictedvalueofdependentvariable
• Confidenceinterval: o Sf=SEofforecast
§ ànote:willmostlikelybegivenSfinexamAnalysisofvariance(ANOVA)inregressionanalysis,andcalculateF-statisticsAnalysisofvariance(ANOVA)–statisticalprocedurefordividingtotalvariabilityofvariableintocomponentsthatcanbeattributedtodifferentsources.Analysingtotalvariablesofdependentvariable
Totalsumofsquares(SST)measurestotalvariationindependentvariableàsumofsquareddifferencesbetweenactualandmeanvalueofY
Regressionsumofsquares(RSS)measuresvariationindependentvariableexplainedbyindependentàsumofsquareddistancesbetweenpredictedYandmeanofY
Sumofsquarederrors(SSE)measuresunexplainedvariationindependentvariableà(akasumofsquaredresiduals)àsumofsquaredverticaldistancesbetweenactualYandpredictedYonregressionline
Note:memorizingformulanotimportant.NeedtoknowwhattheymeasuretoconstructANOVATotalVariation=explainedvariation+unexplainedvariationàSST=RSS+SSER2=EBA;:?;@<;A<B= FFE –D=789:;<=7>?;@<;A<B=(FFI)
EBA;:?;@<;A<B=(FFE)= I89:;<=7>?;@<;A<B=(KFF)
EBA;:?;@<;A<B=(FFE)
• R2isthecorrelationsquared
SEE= 𝑀𝑆𝐸 = FFI=N$
• MSE=meansquarederror• SSEissumofsquaredresiduals.SEEistheSDoftheresidual
F-testassesseshowwellsetofindependentvariables,asagroup,explainsvariationindependentvariable
• Testswhetherallslopecoefficientsareequalto0• Usedtotestwhetheratleastoneindependentvariableexplainssignificantportionofvariation• F-statistic:F=OFK
OFI= KFF/Q
FFI/=NQN"
MSR=meanregressionsumofsquaresALWAYS1TAILEDTESTkisnumberofslopeparametersestimated(i.e.df=k)k(numerator)=1k(denominator)=n-2
MultipleregressionàF-stattestsallindependentvariablesSimplelinearregressionàonly1independentvariableRejectnullifF(test-statistic)>Fc(criticalvalue)àindependentvariablesigndifffrom0àmakessigncontributiontoexplanationofdependentvariableLimitationsofregressionanalysis
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• Linearrelationshipscanchangeovertimeàparameterinstability:estimationfromspecifictimeperiodmaynotberelevantforforecastsinanotherperiod(e.g.economicandfinancialvariables)
• Usefulnesslimitedifothermarketparticipantsareawareandactonthisevidence• Ifassumptionsnothold,theinterpretationandtestsofhypothesesmaynotbevalid
o E.g.ifdataisheteroskedastic(non-constantvarianceoferror)orexhibitsautocorrelation(errortermsnotindependent)àthenregressionresultsmaybeinvalid
Reading10:MultipleRegressionandIssuesinRegressionAnalysisMultipleregressionisregressionanalysiswithmorethan1independentvariable
• Usedtoquantityinfluenceoftwoormoreindependentvariablesonadependentvariable• E.g.variationinstockreturnsintermsofbeta,firmsize,equity,industryclassificationetc…
Yi=b0+b1X1i+b2X2i+…+bkXki+ei
• EstimatesinterceptandslopecoefficientssuchthatSSEisminimized• Residual(ei)isthedifferencebetweenobservedvalueandpredicatedvaluefromregression:
o ei=yi–ŷiInterpretestimatedregressioncoefficientsandtheirp-valuesInterpretationofestimatedregressioncoefficientsformultipleregressionissameassimplelinearregressionforintercepttermBUTsignificantlydifferentforslopecoefficient:
• Intercepttermisvalueofdependentvariablewhenindependentvariablesareequalto0• Eachslopecoefficientisestimatedchangeindependentvariablefor1unitchangeinindependent
variable,holdingotherindependentvariablesconstantàpartialslopecoefficientP-valueisthesmallestlevelofsignificantforwhichnullhypothesiscanberejected
• Alternativetohypothesistestingofcoefficientsistocomparep-valuestothesignificancelevelo p-value<significancelevelàREJECTNULLàSIGNIFICANTDIFFERENTto0o p-value>significancelevelàDONOTREJECTNULL
InterpretresultsofhypothesistestsofregressioncoefficientsNeedtodetermineifindependentvariablemakessignificantcontributiontoexplainingvariationindependent
T-statisticà Degreesoffreedomisn–k–1
• Kisthenumberofregressioncoefficientsintheregression.1isfortheintercepttermConfidenceintervalforpopulationvalueofregressioncoefficient
Sameassimplelinearregression: àcoefficient±(criticalt-value)*(coefficientSE)• Twotailedvaluewithn–k–1
Assumptionsofmultipleregressionmodel
• Sameassimplelinearregressionassumptions(justwithmorethan1variable)
𝐹 =𝑅𝑆𝑆/𝑘
𝑆𝑆𝐸/(𝑛 − 𝑘 − 1) = 0.17230/3
0.8947/(156 − 3 − 1)
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F-statisticandhowitusedinregressionanalysis• F-testassesseshowwellsetofindependentvariablesexplains
variationindependent• i.e.whetherat-leastoneindependentvariableexplains
significantportionofvariationindependent• Sameformulaassimplelinearregression:F=OFK
OFI= KFF/Q
FFI/=NQN"
• RejecthypothesisifF(test-stat)>F(criticalvalue)o Rejectionàatleastonecoefficientsignificantly
differentàatleast1independentvariablesmakessignificantcontributiontoexplanationofdependentvariable
R2vsadjustedR2inmultipleregressionCoefficientofdetermination(R2)usedtotestoveralleffectivenessofentiresetofindependentvariablesinexplainingthedependentvariableSamecalcassimplelinearregression:R2=EBA;:?;@<;A<B= FFE –D=789:;<=7>?;@<;A<B=(FFI)
EBA;:?;@<;A<B=(FFE)= I89:;<=7>?;@<;A<B=(KFF)
EBA;:?;@<;A<B=(FFE)
UnfortunatelyR2maynotbereliablemeasureofexplanatorypowerofmultipleregressionmodelàbecauseR2almostalwaysincreasesasvariablesaddedtothemodelàhighR2mayreflectimpactoflargesetofindependentvariablesratherthanhowwellsetexplainsdependentvariableàoverestimatingregression
• R2ofatleast30%isconsideredreasonablefitToovercomeproblem,recommendusedadjustedR2à𝑹𝒂𝟐 = 𝟏 − 𝒏N𝟏
𝒏N𝒌N𝟏× 𝟏 −𝑹𝟐
nis#observations.Kis#independentvariables
• 𝑹𝒂𝟐£R2àaddingnewindependentvariableswillincreaseR2butmayeitherincreaseordecrease𝑹𝒂𝟐
o ifnewvariablehassmalleffectonR2,valueof𝑹𝒂𝟐maydecrease• 𝑹𝒂𝟐maybelessthan0
MultipleregressionequationusingdummyvariablesWhenindependentvariableisbinary(onoroff),theyarecalleddummyvariablesàusedtoquantityimpactofqualitativeevents
• assignedvalueof0or1• ifwanttodistinguishnclassesàusen-1dummyvariables
TypesofheteroskedasticityandhowserialcorrelationaffectsstatisticalinferenceHeteroskedasticityoccurswhenvarianceofresidualsisnotthesameacrossallobservationsinthesample.Thishappenswhentherearesubsamplesthataremorespreadoutthantherestofthesampleài.e.varianceoferrorsincreasesmagnitude(i.e.asxincreases,variancesincrease)
• Unconditionalheteroskedasticity:notrelatedtolevelofindependentvariables(functionofx)àdoesn’tsystematicallyincrease/decreasewithchangesinvalueofindependentvariables
o Violationofequalvarianceassumption.Usuallycausesnomajorproblemswithregression• Conditionalheteroskedasticity:relatedtolevelofindependentvariable(dependsonx)
o E.g.varianceofresidualtermincreasesasvalueofindependentvariableincreaseso Createssignificantproblemsforstatisticalinferenceo Chi-squareusedastestàift>cvrejectnull
Note:homoscedasticityisifvarianceofresidualsstaysthesame.EffectsofHeteroskedasticityonregressionanalysis:
• F-testforoverallsignificantofregressionisunreliable• Coefficientestimatesarenotaffected• StandardErrors(SE)areunreliableestimates
o IfSEisunderstatedàT-statoverstatedàproblemthatwillincorrectlyrejectnullhypothesis
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Detectingheteroskedasticity2methodstodetect:
1. Examiningscatterplotsofresiduals2. BreuchPagantestàMorecommon
o Callsforregressionofsquaredresidualsonindependentvariableso Ifconditionalheteroskedasticitypresentàindependentvariableswillsignificantly
contributetotheexplanationofthesquaredresidualsCorrectingheteroskedasticity
• CalculaterobuststandarderrorsàcorrectsSEoflinearregressionmodelàthenusedtorecalculatet-statusingoriginalregressioncoefficients
o PREFERREDMETHOD• Generalizedleastsquaresàmodifiesoriginalequationinattempttoeliminateheteroskedasticity
SerialCorrelation(akaautocorrelation)referstosituationsinwhichresidualtermsarecorrelatedwithoneanother
• Commonproblemwithtimeseriesdata• Positiveserialcorrelation–existswhenpositiveregressionerrorin1timeperiodincreases
probabilityofobservingpositiveregressionerrorfornexttimeperiod• Negativeserialcorrelation–existswhenpositiveregressionerrorin1timeperiodincreases
probabilityofobservingnegativeregressionerrorfornexttimeperiodEffectofserialcorrelationonregressionanalysis
• PositiveserialcorrelationresultsincoefficientSEthataretoosmallàcausedt-stattobeoverstatedàcausingtoomanytype1errors(rejectionofnullwhenactuallytrue)
• F–testunreliablebecauseMSEwillbeunderestimatedDetectingserialcorrelationà2methods:
• Residualplotsàlookingatscatterplotofresidualsovertime• Durbin-Watsonstatistic(morecommon)
o DW=2(1-r)rissamplecorrelationb/wsquaredresidualsfromoneperiodandthosefrompreviousperiod
§ DW=2iferrortermsarehomoskedasticandnotseriallycorrelated(r=0)§ DW<2iferrortermspositivelyseriallycorrelated(r>0)§ DW>2iferrortermsnegativelyseriallycorrelated(r<0)
o DecisionruleàcompareDWtoupperandlowercriticalDWvalues(duanddl)CorrectingSerialCorrelation
• AdjustcoefficientSEsusingtheHansenmethod(recommended)o AdjustedSEsusedinhypothesistesting
• Improvespecificationofmodelo Incorporatetime-seriesnatureofdataànote:canbetricky
MulticollinearityanditscausesandeffectsinregressionanalysisMulticollinearityreferstoconditionwhen2ormoreindependentvariablesinmultipleregressionarehighlycorrelatedwitheachotherEffectsofmulticollinearityonregressionanalysis
• Coefficientsbecomesunreliable• SEofslopecoefficientsareartificiallyinflatedàgreaterprobabilityoftype2error(thevariableis
notstatisticallysignificant)• HighR2• Interpretingregressionbecomesproblematic
Detectingmulticollinearity
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• Wheret-testsindicatenoneofindividualcoefficientsissignificantlydifferentthanzero,whileF-testisstatisticallysignificantandR2ishigh
• ifabsolutevalueofsamplecorrelationb/w2independentvariablesinregressionisgreaterthan0.7àmulticollinearityisaproblem
• LinearcombinationsofmultiplevariablesCorrectingmulticollinearity
• Omit1ormorecorrelatedindependentvariablesànotaneasytasktoidentify
• Statisticalproceduressuchasstepwiseregressionàsystematicallyremovesvariablesfromregressionuntilmulticollinearityisminimized
Modelmisspecificationaffectonregressionanalysis+howtoavoidcommonformsofmisspecificationModelspecificationistheselectionoftheindependentvariablestobeincludedintheregressionandthetransformations(ifany)ofthosevariables3broadcategoriesofmodelmisspecification
1. Functionalformcanbemisspecifiedo Importantvariablesomittedo Variablesshouldbetransformed(e.g.bytakingnaturallogarithmofvariable,orbysquare
rootingvariable)àaimingtostandardisevariableàcommon-sizefinancialstatemento Dataimproperlypooledfromdifferentsamples
2. Independentvariablescorrelatedwitherrortermintimeseriesmodelso Laggeddependentvariable(frompriorperiod)usedasindependentvariableo Functionofdependentvariableusedasindependentvariableà“forecastingthepast”o Independentvariablesmeasuredwitherror(e.g.actualinflationusedasaproxyforexpected
inflation)3. Othertime-seriesmisspecificationsthatresultinnonstationary
o Variablesproperties(e.g.meanandvariance)arenotconstantthroughtimeModelswithqualitativedependentvariables
• Dummyvariablesusedwhenqualitativedependentvariable(e.g.ifbondissuerwilldefault)• Ordinaryregressionmodelofleastsquaresnotappropriate,butseveraltypesofmodelsthatuse
qualitativedependentvariables:o ProbitandLogitmodels
§ Probitmodelbasedonnormaldistribution§ Logitmodelbasedonlogisticdistribution§ Maximumlikelihoodmethodologyusedtoestimatecoefficientsàprobabilityof
occurring(e.g.merger,bankruptcyordefault)o Discriminantmodels
§ Resultinlinearfunctionwhichgeneratesscore/rankingforobservation§ E.g.makesuseoffinancialratiosasindependentvariabletopredictqualitative
dependentvariablebankruptcyEvaluateandinterpretamultipleregressionmodelanditsresults
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Reading11:Time-SeriesAnalysis Calculatepredictedtrendvaluefortimeseries,modeledaseitherlinearorlog-lineartrendTimeseriesisasetofobservationsforvariableoversuccessiveperiodsoftime.Serieshasatrendifconsistentpatternseenbyplottingdata.Lineartrendisatimeseriespatternthatcanbegraphedusingstraightline
• Yt=b0+b1(t)+eio Downwardslopingline=negativetrendo Upwardslopingline=positivetrend
• Ordinaryleastsquares(OLS)regressionusedtoestimatecoefficientintrendline:
o àpredictedvalueofy=estimatedintercept+estimatedslopecoefficient• Residualerror=actualvalue–predictedvalue
Timeseriesoftendisplaysexponentialgrowth(continuouscompounding)
• PositiveexponentialgrowthàdataincreasesatconstantrateàConvexcurve• NegativeexponentialgrowthàdatadecreasesatconstantrateàConcavecurve• yt=e
b0+b1(t)o Takenaturallogofbothsidestoarriveatlog-linearmodel
ln(yt)=ln(eb0+b1(t))àln(yt)=b0+b1(t)
• Useoftransformeddataproduceslineartrendlinewithbetterfitandincreasespredictiveabilityofmodel
Factorsthatdeterminewhetherlinearorlog-lineartrendshouldbeused+limitationsoftrendmodels
• Linearappropriateifdatapointsequallydistributedaboveorbelowregressionline• Logappropriateifnon-linearshape
o Ifresidualsfromlinearmodelareseriallycorrelatedàlogappropriateo E.g.financialdata(stockprices)
• ifvariablegrowsatconstantrateàuselog• ifvariablegrowsatconstantamountàuselinear
Limitationoftrendmodels=Serialcorrelation(Autocorrelation):ifresidualspersistentlypositiveornegativeforperiodsoftime
o CanuseDurbinWatsontodetectRequirementfortimeseriestobecovariancestationaryandsignificanceofseriesthatisnotstationaryWhendependentvariableisregressedagainst1ormorelaggedvaluesofitself,themodeliscalledanautoregressivemodel(AR)
• Xt=b0+b1xt-1+ei• Pastvaluesusedtopredictcurrentandfuturevalue(e.g.salesoffirmregressedagainstsalesoffirm
inpreviousmonth)• StatisticalinferencedbasedonOLSestimatesmaybeinvalidunlesstimeseriesbeingmodelledis
covariancestationaryàifitsatisfies3conditions:i. Constantandfiniteexpectedvalueàexpectedvalueoftimeseriesconstantovertimeii. Constantandfinitevarianceàvolatilityarounditsmeandoesnotchangeovertimeiii. Constantandfinitecovarianceb/wvaluesatanygivenlag
Structureofautoregressivemodeloforderpandcalculate1and2periodaheadforecastsSecond-orderautoregressivemodel(AR2):Xt=b0+b1xt-1+b2xt-2+eiARmodeloforderp(ARp):Xt=b0+b1xt-1+b2xt-2+…+bpxt-p+ei
• pindicatesnumberoflaggedvaluesthatARmodelwillincludeasindependentvariablesForecastingwithARmodel
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• sinceindependentvariableisalaggedvalueofdependentvariableàcalculate1-step-aheadforecastBEFORE2-step-aheadforecast
o akaChainruleofforecasting• 1-period-aheadforecastforAR(1)model:
• 2-period-aheadforecastforAR(1)model:
• Multi-periodforecastsmoreuncertainthansingleperiodforecasts
HowautocorrelationsofresidualsusedtotestwhetherARmodelfitstimeseriesWhenARmodelcorrectlyspecified,residualtermswillnotexhibitserialcorrelation.ProceduretotestwhetherARtimeseriesmodeliscorrectlyspecifiedinvolves3steps:
1. EstimateARmodelbeingevaluatedusinglinearregressiona. Startwith1storderARmodel
2. Calculateautocorrelationsofmodel’sresidualsa. Levelofcorrelationbetweenforecasterrorsfrom1periodtothenext
3. Testwhetherautocorrelationsaresignificantlydifferentfromzeroa. T-testusedàt=estimatedautocorrelation/SE
𝑆𝐸 = "A,wheretisthenumberofobservations
Ifmodelcorrectlyspecified,noneofautocorrelationswillbestatisticallysignificantMeanreversionandcalculatemean-revertinglevelTimeseriesexhibitsmeanreversionifhastendencytomovetowarditsmeanàdeclinewhencurrentvalueisabovemean,andrisewhencurrentvalueisbelowmean
• Ifmean-revertinglevelàmodelpredictsnextvaluewillbesameascurrentlevel• 𝑥A =
de("Ndf)
o ifcurrentlevel>xtàexpectedtofallinnextperiod
• Allcovariancestationarytimeserieshaveafinitemean-revertinglevelo AR1willhavefinitemean-revertinglevelwhenabsolutevalueoflagcoefficient<1
In-samplevsout-of-sampleforecasts+comparingforecastingaccuracybasedonrootmeansquarederrorcriterion
• In-sampleforecasts(Ŷt)arewithinrangeofdatausedtoestimatemodelo Comparinghowaccuratemodelisinforecastingactualdatausedtodevelopmodelo Mostpublishedresearchemploysin-sampleforecastsonly
• Out-of-sampleforecastsaremadeoutsidesampleperiodo Comparehowaccuratemodelisinforecastingyvariablefortimeperiodoutsideperiodused
todevelopmodelo MOREVALUABLEàImportantbecausetheyprovidetestsofwhethermodeladequately
describestimeseriesandwhetherithasrelevance(predictivepower)inrealwork• Rootmeansquarederror(RMSE)criterionisusedtocompareaccuracyofARmodelsinforecasting
out-of-samplevalues.Usedtoshowwhichmodelwillproducebetter(moreaccurate)forecastso Squarerootoftheaveragesquaredforecasterror
§ STEPS:Squareerror,sumsquarederrors,divide#offorecasts,squarerootaverageo ModelwithlowestRMSE=lowerforecasterroràexpectedtohavebetterpredictivepower
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Instabilityofcoefficientsoftime-seriesmodels• Financialandeconomicconditionsdynamicàestimatedregressioncoefficientin1periodmaydiffer
toanotherperiod• Modelswithshortertimeseriesaremorestable• Modelsarevalidonlyforcovariance-stationarytimeseries
Characteristicsofrandomwalkprocessandcontrastthemtocovariancestationaryprocess
• Iftimeseriesfollowsrandomwalkprocess,thepredictedvalueofseriesin1periodisequaltovalueofseriesinpreviousperiodplusarandomerrorterm
o Expectedvalueoferrortermis0.Varianceoferrortermsisconstant.Noserialcorrelation.o xt=xt-1+et
• Iftimeseriesfollowsrandomwalkwithadrift,intercepttermisnotequalto0o Timeseriesexpectedtoincrease/decreasebyconstantamounteachperiodo xt=b0+b1xt-1+et
b0istheconstantdrift
• Randomwalkandrandomwalkwithadriftwillexhibitnocovariancestationarityo Why?Becauseisexhibitsunitroot
UnitrootsIfcoefficientlagvariableis1theseriesifnotcovariancestationary.Iflagcoefficient=1àtimeseriesissaidtohaveaunitrootandwillfollowarandomwalkprocess.ModellingthisinanARmodelcanleadtoincorrectreferences.
• i.e.aunitrootisatimeseriesthatisnotcovariancestationaryUnitroottestingfornonstationary2teststodeterminewhethertimeseriesiscovariancestationary:
1. RunARmodelandexamineautocorrelationso Statisticalsignificanceofautocorrelationsatvariouslagsexaminedo Stationaryprocessifresidualautocorrelationinsignificantlydifferentfrom0o Stationaryprocessifresidualautocorrelationsthatdecayto0asnumberoflagsincrease
2. PerformDickeyFullerTesto Moredefinitivetesto TransformsARmodeltorunsimpleregressionàthentestwhethertransformedcoefficient
isdifferentfrom0usingamodifiedt-testFirstDifferencing
• Firstdifferenceprocessinvolvessubtractingvalueoftimeseries(dependentvariable)inprecedingperiodfromcurrentvalueoftimeseriestodefinenewdependentvariable(y)
o i.e.anapproachthatmayworkinthecaseofmodelingatimeseriesthathasaunitrootHowtotestandcorrectforseasonalitySeasonalityinatime-seriesisapatternthattendstorepeatfromyeartoyear(e.g.Monthlysalesdataforaretailer)
• ModelwouldbemisspecifiedunlessARmodelincorporateseffectsofseasonality• TocorrectforseasonalityàadditionallagofdependentvariableisADDEDtooriginalmodelas
anotherindependentvariableAutoregressiveconditionalheteroskedasticity(ARCH)ARCHexistsifvarianceofresidualsin1periodisdependentonvarianceofresidualsinapreviousperiod
• IfARCHexists,SEofregressioncoefficientsareINVALID• ARCHmodelusedàsquaredresidualsfromestimatedtime-seriesmodelregressedonfirstlagof
squaredresiduals
o Ifcoefficient(a1)statisticallydifferentfrom0àtimeseriesisARCH(1)