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

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

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

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

• 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

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

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:

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

• 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)

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

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

• 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

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

• 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

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)