二級(jí)培訓(xùn)項(xiàng)目基礎(chǔ)portfoio management

TopicWeightingsinCFALevel2-Session StudySession1-Ethics&Professional10-StudySessionQuantitative5-StudySessionEconomicTopicWeightingsinCFALevel2-Session StudySession1-Ethics&Professional10-StudySessionQuantitative5-StudySessionEconomic5-StudySession5-FinancialStatement15-StudySession7-Corporate5-StudySession9-Equity15-StudySession12-FixedIncome10-StudySessionStudySessionAlternative5-StudySession16-PortfolioSS16:PortfolioManagement:Process,AssetAllocation,andRiskManagementR47TheportfolioManagementProcessandtheInvestmentPolicyStatementR48AnSS16:PortfolioManagement:Process,AssetAllocation,andRiskManagementR47TheportfolioManagementProcessandtheInvestmentPolicyStatementR48AnintroductiontomultifactormodelsR49MeasuringandManagingMarketRiskSS17:EconomicAnalysis,ActiveManagement,andTradingR50EconomicsandinvestmentR51AnalysisofactiveportfolioHigh-FrequencyTrading3-TheportfolioManagementProcessandtheInvestmentPolicyStatement4-TheportfolioManagementProcessandtheInvestmentPolicyStatement4-PortfolioInvestmentObjectivesandConstrainsManagementinvestment5-PortfolioInvestmentObjectivesandConstrainsManagementinvestment5-PortfolioPortfolioPerspective:focusontheaggregateofalltheinvestor’sPortfolioPortfolioPerspective:focusontheaggregateofalltheinvestor’sholdingstheportfolioHarryMarkowitz→ModernPortfolioTheorySomepricingsuchasCAPM,APT,ICAPM,→thesepricingmodelsareallbasedontheprinciplethatsystematicriskispriced→shouldanalyzetherisk-returntradeoffoftheportfolio6-PortfoliotheplanningIdentifyingandSpecifyingtheInvestor’sObjectiveandPortfoliotheplanningIdentifyingandSpecifyingtheInvestor’sObjectiveandCreatingtheInvestmentPolicyFormingCapitalMarketsCreatingtheStrategicAssettheexecutionTacticalAssetSecuritythefeedbackMonitoringand7-InvestmentObjectivesandInvestmentInvestmentobjectivesrelatetowhattheinvestorwantstoaccomplishwiththeportfolioObjectivesareInvestmentObjectivesandInvestmentInvestmentobjectivesrelatetowhattheinvestorwantstoaccomplishwiththeportfolioObjectivesaremainlyconcernedwithriskandreturnRiskRiskAbilitytoTakeBelowAboveAverageBelowAboveRiskmeasurement-Valueatrisk8-InvestmentObjectivesandSomespecificfactorsthataffecttheabilitytoInvestmentObjectivesandSomespecificfactorsthataffecttheabilitytoacceptRequiredspendingLong-termwealthFinancialSomespecificfactorsthataffectthewillingnesstoacceptReturnHistorical9-InvestmentObjectivesandReturnReturnsuchas:totalReturn;absoluteReturn;returnrelativetothebenchmark’s;returnnominalreturns;realreturnsinflation-adjustedInvestmentObjectivesandReturnReturnsuchas:totalReturn;absoluteReturn;returnrelativetothebenchmark’s;returnnominalreturns;realreturnsinflation-adjustedreturns;pretaxreturns;post-taxreturnsReturndesireanddesiredreturnisthatlevelofreturnstatedbytheclient,includinghowmuchtheinvestorwishestoreceivefromtheportfoliorequiredreturnrepresentssomelevelofreturnthatmustbeachievedbytheportfolio,atleastonanaveragebasistomeetthetargetfinancialobligations10-InvestmentObjectivesandInvestmentInvestmentconstrainsarethosefactorsrestrictingorlimitingtheuniverseofavailableinvestmentchoices.Liquidityrequirement:aneedforcashofInvestmentObjectivesandInvestmentInvestmentconstrainsarethosefactorsrestrictingorlimitingtheuniverseofavailableinvestmentchoices.Liquidityrequirement:aneedforcashofnewcontributionsorsavingsataspecifiedpointintime.Timehorizon:thetimeperiodassociatedwithaninvestmentobjective(shortterm,longterm,oracombinationofthetwo).Taxconcerns:taxpaymentsreducetheamountofthetotalLegalandregulatoryfactors:externalfactorsimposedbygovernmental,regulatory,oroversightauthoritiestoconstraininvestmentdecision-Uniquecircumstances:internalfactors,anindividualinvestor’sportfoliochoicesmaybeconstrainedbycircumstancesfocusingonhealthneeds,supportofdependents,andothercircumstancesuniquetothe11-awrittenplanningdocumentthatgovernsallinvestmentdecisionsfortheclientMainawrittenplanningdocumentthatgovernsallinvestmentdecisionsfortheclientMainBereadilyimplementedbycurrentorfutureinvestmentPromotelong-termdisciplineforportfolioHelpprotectagainstshort-termshiftsinstrategywheneitherenvironmentsorportfolioperformancecausepanicor12-Aclientdescriptionthatprovidesenoughbackgroundsoanycompetentinvestmentadvisercangiveacommonunderstandingoftheclient’ssituation.ThepurposeoftheAclientdescriptionthatprovidesenoughbackgroundsoanycompetentinvestmentadvisercangiveacommonunderstandingoftheclient’ssituation.ThepurposeoftheIPSwithrespecttopolicies,objectives,goals,restrictions,andportfoliolimitations.Identificationofdutiesandresponsibilitiesofpartiesinvolved.Theformalstatementofobjectivesandconstrains.AcalendarscheduleforbothportfolioperformanceandIPSreview.Assetallocationrangesandstatementsregardingflexibilityandrigiditywhenformulatingormodifyingthestrategicassetallocation.Guidelinesforportfolioadjustmentsandrebalancing.13-ThreeapproachesforinvestmentPassiveinvestmentstrategyapproach:portfoliocompositionThreeapproachesforinvestmentPassiveinvestmentstrategyapproach:portfoliocompositiondoesnotreacttochangesinexpectations,anexampleinindexingActiveapproach:involvesholdingaportfoliodifferentfromabenchmarkorcomparisonportfolioforthepurposeofproducingpositiveexcessrisk-adjustedreturnsSemiactiveapproach:anindexingapproachwithcontrolleduseofweightsdifferentfrombenchmark14-CMEandStrategicAssetCapitalmarketThemanager’sthirdtaskCMEandStrategicAssetCapitalmarketThemanager’sthirdtaskintheplanningprocessistoformcapitalmarketexpectations.Long-runforecastsofriskandreturncharacteristicsforvariousassetclassesformthebasisforchoosingportfoliosthatmaximizeexpectedreturnforgivenlevelsofrisk,orminimizeriskforgivenlevelsofexpectedreturn.StrategicAssetthefinalstepintheplanningstage,combinestheIPSandcapitalmarketexpectationstoformulateweightingsonacceptableasset15-ManagementinvestmentJustifyethicalconductasarequirementformanaginginvestmentManagementinvestmentJustifyethicalconductasarequirementformanaginginvestment theinvestmentprofessionalwhomanagesclientportfoliowellmeetsbothstandardsofcompetenceandstandardsofconduct theappropriatestandardofconductisembodiedbytheCFAInstituteCodeandStandards16-Anintroductiontomultifactor17-Anintroductiontomultifactor17-ArbitragePricingTheory(APT)MultifactorModelMacroeconomicFactorFundamental?StandardizedbetaArbitragePricingTheory(APT)MultifactorModelMacroeconomicFactorFundamental?StandardizedbetaApplication：ReturnAttributionApplication:PortfolioConstruction18-ArbitragePricingTheoryassetpricingmodeldevelopedbythearbitragepricingArbitragePricingTheoryassetpricingmodeldevelopedbythearbitragepricingAfactormodeldescribesassetTherearemanyassets,soinvestorscanformwell-diversifiedportfoliosthateliminateasset-specificriskNoarbitrageopportunitiesexistamongwell-diversifiedExactlyE(RP)RFP,1(1)P,2(2)...P,k(k19-ArbitragePricingTheoryThefactorriskpremium(orfactorprice,λArbitragePricingTheoryThefactorriskpremium(orfactorprice,λj)representstheexpectedreturninexcessoftheriskfreerateforaportfoliowithasensitivityof1tofactorjandasensitivityof0toallotherfactors.Suchaportfolioiscalledapurefactorportfolioforfactorj.TheparametersoftheAPTequationaretherisk-freerateandthefactorrisk-premiums(thefactorsensitivitiesarespecifictoindividual20-ArbitragePricingTheoryArbitrageTheAPTassumestherearenoArbitragePricingTheoryArbitrageTheAPTassumestherearenomarketimperfectionspreventinginvestorsfromexploitingarbitrageopportunitiesextremelongandshortpositionsarepermittedandmispricingwilldisappearimmediatelyallarbitrageopportunitieswouldbeexploitedandeliminated21-Example-ArbitragePricingTheorySupposethattwofactors,surpriseininflation(factor1)andsurpriseinGDPgrowth(factor2),explainreturns.AccordingtotheAPT,anarbitrageopportunityexistsunlessE(RP)RFExample-ArbitragePricingTheorySupposethattwofactors,surpriseininflation(factor1)andsurpriseinGDPgrowth(factor2),explainreturns.AccordingtotheAPT,anarbitrageopportunityexistsunlessE(RP)RFβp,1(λ1)+βp,2(λ2Well-diversifiedportfolios,J,K,andL,giveninE(RJ)0.14RF1.0λ1E(RK)0.12RF0.5λ1E(RL)0.11RF1.3λ1E(RP)0.070.02βp,122-ExpectedSensitivitytoSensitivitytoGDPJKLMultifactorMultifactormodelshavegainedimportanceforthepracticalbusinessofportfoliomanagementfortwomainreasons.multifactorMultifactorMultifactormodelshavegainedimportanceforthepracticalbusinessofportfoliomanagementfortwomainreasons.multifactormodelsexplainassetreturnsbetterthanthemarketmodelmultifactormodelsprovideamoredetailedanalysisofriskthandoesasinglefactormodel.23-TypesofMultifactorMacroeconomicFundamentalfactorStatisticalfactorMixedTypesofMultifactorMacroeconomicFundamentalfactorStatisticalfactorMixedfactorSomepracticalfactormodelshavethecharacteristicsofmorethanoneoftheabovecategories.Wecancallsuchmodelsmixedfactormodels.24-MacroeconomicFactorMacroeconomicassumption:thefactorsaresurprisesinmacroeconomicvariablessignificantlyexplainequityexactlyformulaforreturnofassetbi1,b MacroeconomicFactorMacroeconomicassumption:thefactorsaresurprisesinmacroeconomicvariablessignificantlyexplainequityexactlyformulaforreturnofassetbi1,b E(R)bRii i i=returnforassetE(Ri)=expectedreturnforassetFGDP=surpriseintheGDP=surpriseinthecreditquality=GDPsurprisesensitivityofasset=creditqualityspreadsurprisesensitivityofasset=firm-specificsurprisewhichnotbeexplainedbytheSurprise=actualvalue–predicted(expected)25-………MacroeconomicFactorSupposeourforecastatthebeginningofthemonthMacroeconomicFactorSupposeourforecastatthebeginningofthemonthisthatinflationwill0.4percentduringthemonth.Attheendofthemonth,wefindthatinflationwasactually0.5percentduringthemonth.Duringanymonth,Actualinflation=Predictedinflation+SurpriseInthiscase,actualinflationwas0.5percentandpredictedinflation0.4percent.Therefore,thesurpriseininflationwas0.5-0.4=0.126-MacroeconomicFactor SlopecoefficientsarenaturallyinterpretedasthefactorMacroeconomicFactor SlopecoefficientsarenaturallyinterpretedasthefactorsensitivitiesoftheAfactorsensitivityisameasureoftheresponseofreturntoeachunitofincreaseinafactor,holdingallotherfactorsconstant.Thetermεiisthepartofreturnthatisunexplainedbyexpectedreturnorthefactorsurprises.Ifwehaveadequatelyrepresentedthesourcesofcommonrisk(thefactors),thenεimustrepresentanasset-specificrisk.Forastock,itmightrepresentthereturnfromanunanticipatedcompany-specific27-FactorSensitivitiesforaTwo-StockSupposethatstockreturnsareaffectedbytwocommonfactors:surprisesininflationandsurprisesinGDPgrowth.Aportfoliomanagerisanalyzingthereturnsonaportfoliooftwostocks,Manumatic(MANM)andNextech(NXT),ThefollowingequationsdescribethereturnsforFactorSensitivitiesforaTwo-StockSupposethatstockreturnsareaffectedbytwocommonfactors:surprisesininflationandsurprisesinGDPgrowth.Aportfoliomanagerisanalyzingthereturnsonaportfoliooftwostocks,Manumatic(MANM)andNextech(NXT),Thefollowingequationsdescribethereturnsforthosestocks,wherethefactorsFINFL.andFGDP,representthesurpriseininflationandGDPgrowth,respectively:One-thirdoftheportfolioisinvestedinManumaticstock,andtwo-thirdsisinvestedinNextechstock.Formulateanexpressionforthereturnontheportfolio.StatetheexpectedreturnontheCalculatethereturnontheportfoliogiventhatthesurprisesininflationandGDPgrowthare1percentand0percent,respectively,assumingthattheerrortermsforMANMandNXTbothequal0.5percent.28-FactorSensitivitiesforaTwo-Stock29-CorrectAnswer1Theportfolio'sreturnisthefollowingweightedaverageofthereturnstoFactorSensitivitiesforaTwo-Stock29-CorrectAnswer1Theportfolio'sreturnisthefollowingweightedaverageofthereturnstothetwostocks:Rp=(1/3)(0.09)+(2/3)(0.12)+[(1/3)(-I)+(2/3)(2)]FINFL+[(1/3)(1)+(2/3)(4)]FGDP+(1/3)εMANM+(2/3)=0.11+1FINFL+3FGDP+(1/3)εMANM+(2/3)CorrectAnswer2Theexpectedreturnontheportfoliois11percent,thevalueoftheinterceptintheexpressionobtainedinPart1.CorrectAnswer3Rp=0.11+1FINFL+3FGDP+(1/3)εMANM+(2/3)εNXT=0.11+1(0.01)+3(0)+(1/3)(0.005)+(2/3)(0.005)=0.125or12.5percentFundamental求出FP/ERiNoeconomicAsseti'sattributvalue-averageattributeb(attributeFundamental求出FP/ERiNoeconomicAsseti'sattributvalue-averageattributeb(attribute(P/E)1-P/30-sectionaldata)………Standardized31-Suppose,forexample,thataninvestmenthasadividendyieldStandardized31-Suppose,forexample,thataninvestmenthasadividendyieldpercentandthattheaveragedividendyieldacrossallstocksbeingconsideredis2.5percent.Further,supposethatthestandarddeviationofdividendyieldsacrossallstocksis2percent.Theinvestment'ssensitivitytodividendyieldis(3.5%-2.5%)/2%=0.50,orone-halfstandarddeviationaboveaverage.StandardizedThescalingpermitsallfactorsensitivitiestobeinterpretedsimilarly,StandardizedThescalingpermitsallfactorsensitivitiestobeinterpretedsimilarly,despitedifferencesinunitsofmeasureandscaleinthevariables.Theexceptiontothisinterpretationisfactorsforbinaryvariablessuchasindustrymembership.Acompanyeitherparticipatesinanindustryoritdoesnot.Theindustryfactorsensitivitieswouldbe0-1dummyinmodelsthatrecognizethatcompaniesfrequentlyoperateinmultipleindustries,thevalueofthesensitivitywouldbe1foreachindustryinwhichacompanyoperated.32-StatisticalFactorStatisticalfactorInastatisticalfactormodel,statisticalmethodsareappliedtohistoricalreturnsofagroupofsecuritiestoextractStatisticalFactorStatisticalfactorInastatisticalfactormodel,statisticalmethodsareappliedtohistoricalreturnsofagroupofsecuritiestoextractfactorsthatcanexplaintheobservedreturnsofsecuritiesinthegroup.Instatisticalfactormodels,thefactorsareactuallyportfoliosofthesecuritiesinthegroupunderstudyandarethereforedefinedbyportfolioweights.Twomajortypesoffactormodelsarefactoranalysismodelsandprincipalcomponentsmodels.FactoranalysismodelsbestexplainhistoricalreturnPrincipalcomponentsmodelsbestexplainthehistoricalreturnAdvantageandMajoradvantage:itmakeminimalMajorweakness:thestatisticalfactorsdonotlendthemselveswelltoeconomicinterpretation33-ArbitragePricingTheoryTherelationbetweenAPTandmultifactor34-Multifactorcross-sectionalequilibriumpricingmodelthatexplainsthevariationacrossassets’expectedreturnstime-seriesArbitragePricingTheoryTherelationbetweenAPTandmultifactor34-Multifactorcross-sectionalequilibriumpricingmodelthatexplainsthevariationacrossassets’expectedreturnstime-seriesregressionthatexplainsthevariationovertimeinreturnsforoneassetequilibrium-pricingmodelthatassumesnoarbitrageadhoc(i.e.,ratherthanbeingderiveddirectlyfromanequilibriumtheory,thefactorsareidentifiedempiricallybylookingformacroeconomicvariablesthatbestfitthedata)risk-freeexpectedreturnderivedfromtheAPTequationinmacroeconomicfactormodelArbitragePricingTheoryComparisonCAPMand35-Allinvestorsshouldholdsomecombinationofthemarketportfolioandtherisk-freeasset.Tocontrolrisk,lessriskaverseinvestorssimplyholdmoreofArbitragePricingTheoryComparisonCAPMand35-Allinvestorsshouldholdsomecombinationofthemarketportfolioandtherisk-freeasset.Tocontrolrisk,lessriskaverseinvestorssimplyholdmoreofthemarketportfolioandlessoftherisk-freeasst.APTgivesnospecialroletothemarketportfolio,andisfarmoreflexiblethanCAPM.Assetreturnsfollowamultifactorprocess,allowinginvestorstomanageseveralriskfactors,ratherthanjustone.Theriskoftheinvestor’sportfolioisdeterminedsolelybytheresultingportfoliobeta.maydrivetheinvestortoholdportfoliostitledawayfromthemarketportfolioinordertohedgeorspeculateonmultipleriskfactors.Application：ReturnMultifactormodelscanhelpusunderstandindetailtheApplication：ReturnMultifactormodelscanhelpusunderstandindetailthesourcesofmanager’sreturnsrelativetoaActivereturn=Rp?Withthehelpofafactormodel,wecananalyzeaportfolioactivereturnasthesumoftwoThefirstcomponentistheproductoftheportfoliomanager’sfactortilts(overweightorunderweightrelativetothebenchmarkfactorsensitivities)andthefactorreturns;wecallthatcomponentthereturnfromfactortilts.Thesecondcomponentofactivereturnreflectsthemanager’sskillinindividualassetselection(abilitytooverweightsecuritiesthatoutperformthebenchmarkorunderweightsecuritiesthatunderperformthebenchmark);wecallthatcomponentsecurityselection.36-Application：ReturnActivereturn=factorreturn+securityselectionFactor- kApplication：ReturnActivereturn=factorreturn+securityselectionFactor- kkpk=factorsensitivityforthekthfactorintheactive=factorsensitivityforthekthfactorinthebenchmark=factorriskpremiumforfactorSecuritySecurityselectionreturn=activereturn–factorThesecurityselectionreturnisthentheresidualdifferencebetweenactivereturnandfactorreturn.37-Application：RiskActiveDefinition:thestandarddeviationofactiveExactly(RRactiverisk(RPApplication：RiskActiveDefinition:thestandarddeviationofactiveExactly(RRactiverisk(RPRBtInformationDefinition:theratioofmeanactivereturntoactivePurpose:atoolforevaluatingmeanactivereturnsperunitofactiveExactIRs(R 38-Example:Information39-Toillustratethecalculation,ifaportfolioachievedameanreturnof9percentduringthesameperiodthatitsbenchmarkearnedameanreturnof7.5percent,andtheportfolio'strackingriskExample:Information39-Toillustratethecalculation,ifaportfolioachievedameanreturnof9percentduringthesameperiodthatitsbenchmarkearnedameanreturnof7.5percent,andtheportfolio'strackingriskwas6percent,wewouldcalculateaninformationratioof(9%-7.5%)/6%=0.25.Settingguidelinesforacceptableactiveriskortrackingriskisoneofthewaysthatsomeinstitutionalinvestorsattempttoassurethattheoverallriskandstylecharacteristicsoftheirinvestmentsareinlinewiththosedesired.Application：RiskWecanseparateaportfolio'sactiverisksquaredintoApplication：RiskWecanseparateaportfolio'sactiverisksquaredintotwoActiverisksquared=s2 R Activefactorriskisthecontributiontoactiverisksquaredresultingfromtheportfolio'sdifferent-than-benchmarkexposuresrelativetofactorsspecifiedintheriskmodel.Activespecificriskorassetselectionriskisthecontributiontoactiverisksquaredresultingfromtheportfolio'sactiveweightsonindividualassetsasthoseweightsinteractwithassets'residualrisk.Activerisksquared=Activefactorrisk+Activespecific40-SteveMartingale,CFA,isanalyzingtheperformanceofthreeactivelymanagedmutualfundsusingatwo-factormodel.Theresultsofhisriskdecompositionareshownbelow:ActiveSizeFactorStyleSteveMartingale,CFA,isanalyzingtheperformanceofthreeactivelymanagedmutualfundsusingatwo-factormodel.Theresultsofhisriskdecompositionareshownbelow:ActiveSizeFactorStyleWhichfundassumesthehighestlevelofactiveWhichfundassumesthehighestpercentagelevelofWhichfundassumesthelowerpercentagelevelofactivespecific41-CorrectAnswerThetablebelowshowstheproportionalcontributionofvariousresourcesofactiveriskasaproportionofactiverisksquared.StyleFactorSizeCorrectAnswerThetablebelowshowstheproportionalcontributionofvariousresourcesofactiveriskasaproportionofactiverisksquared.StyleFactorSizeTheGammafundhasthehighestlevelofactiverisk(6.1%).Notethatactiveriskisthesquarerootofactiverisksquared(asgiven).TheAlphafundhasthehighestexposuretostylefactorriskasseenby56%ofactiveriskbeingattributedtodifferencesinstyle.TheAlphafundhasthelowestexposuretoactivespecificrisk(15%)asaproportionoftotalactiverisk.42-Application:PortfolioPassivemanagement.Analystscanusemultifactormodelstomatchanindexfund'sfactorexposurestothefactorexposuresApplication:PortfolioPassivemanagement.Analystscanusemultifactormodelstomatchanindexfund'sfactorexposurestothefactorexposuresoftheindextracked.Activemanagement.Manyquantitativeinvestmentmanagersrelyonmultifactormodelsinpredictingalpha(excessrisk-adjustedreturns)orrelativereturn(thereturnononeassetorassetclassrelativetothatofanother)aspartofavarietyofactiveinvestmentstrategies.Inevaluatingportfolios,analystsusemulti-factormodelstounderstandthesourcesofactivemanagers'returnsandassesstherisksassumedrelativetothemanager'sbenchmark(comparisonportfolio).Rules-basedactivemanagement(alternativeindexes).Thesestrategiesroutinelytilttowardfactorssuchassize,value,quality,ormomentumwhenconstructingportfolios.43-Application:PortfolioTheCarhartfour-factormodel(fourfactorERP=RFApplication:PortfolioTheCarhartfour-factormodel(fourfactorERP=RF+β1RMRF+β2SML+β3HML+Accordingtothemodel,therearethreegroupsofstocksthattendtohavehigherreturnsthanthosepredictedsolelybytheirsensitivitytothemarketreturn:Small-capitalizationstocks:SMB=ReturnofSmall–ReturnofLowprice-tobook-ratiostocks,commonlyreferredtoasstocks,HMLStockswhosepriceshavebeenrising,commonlyreferredto―momentum‖stocks:WML=ReturnofWinner–returnof44-MeasuringandManagingMarket45-MeasuringandManagingMarket45-UnderstandingTheConfidenceHistoricalMethodMonteUnderstandingTheConfidenceHistoricalMethodMonteCarloSimulationMethodExtensionsofVaROtherKeyRiskMeasuresApplicationsofRiskMeasuresUsingConstraintsinMarketRisk46-UnderstandingVaRstatesatsomeprobability(often1%or5%)theexpectedlossduringaspecifiedtimeperiod.ThelosscanbestatedUnderstandingVaRstatesatsomeprobability(often1%or5%)theexpectedlossduringaspecifiedtimeperiod.Thelosscanbestatedasapercentageofvalueorasanominalamount.VaRalwayshasadualinterpretation.Ameasureineithercurrencyunits(inthisexample,theeuro)orinpercentageterms.AminimumAstatementreferencesatimehorizon:lossesthatwouldbeexpectedtooccuroveragivenperiodoftime.47-UnderstandingAnalysisshouldconsidersomeadditionalissueswithTheVaRtimeperiodshouldrelatetothenatureofthesituation.AtraditionalstockandbondportfoliowouldlikelyfocusonalongermonthlyorquarterlyVaRUnderstandingAnalysisshouldconsidersomeadditionalissueswithTheVaRtimeperiodshouldrelatetothenatureofthesituation.AtraditionalstockandbondportfoliowouldlikelyfocusonalongermonthlyorquarterlyVaRwhileahighlyleveragedderivativesportfoliomightfocusonashorterdailyVaR.ThepercentageselectedwillaffecttheVaR.A1%VaRwouldbeexpectedtoshowgreaterriskthana5%VaR.Theleft-tailshouldbeexamined.Left-tailreferstoatraditionalprobabilitydistributiongraphofreturns.Theleftsidedisplaysthelowornegativereturns,whichiswhatVaRmeasuresatsomeprobability.Butsupposethe5%VaRislosing$1.37million,whathappensat4%,1%,andsoon?Inotherwords,howmuchworsecanitget?48-Understanding49-Understanding49-50-GivenaVaRof$12.5millionat5%foronemonth,50-GivenaVaRof$12.5millionat5%foronemonth,whichofthefollowingstatementsiscorrect?Thereisa5%chanceoflosing$12.5millionoveroneThereisa95%chancethattheexpectedlossoverthenextmonthislessthan$12.5million.Theminimumlossthatwouldbeexpectedtooccuroveronemonth5%ofthetimeis$12.5million.Estimating3methodstoestimateAnalyticalmethod(variance-covariance/deltanormalHistoricalEstimating3methodstoestimateAnalyticalmethod(variance-covariance/deltanormalHistoricalMonteCarlo51-UnderstandingTheanalyticalmethod(orvariance-covariancemethod)isbasedonthenormaldistributionandtheconceptofone-tailedconfidenceintervals.Example:AnalyticalTheexpectedUnderstandingTheanalyticalmethod(orvariance-covariancemethod)isbasedonthenormaldistributionandtheconceptofone-tailedconfidenceintervals.Example:AnalyticalTheexpectedannualreturnfora$100,000,000portfoliois6.0%andthehistoricalstandarddeviationis12%.CalculateVaRat5%significance.ACFAcandidatewouldknowthat5%inasingletailisassociatedwith1.645,orapproximately1.65,standarddeviationsfromthemeanexpectedreturn.Therefore,the5%annualVaRis:VaRRpz6%1.6512%$100,000,$13,800,52-TheConfidence[,[1.65,1.65][TheConfidence[,[1.65,1.65][1.96,1.96[2.58,2.5868%confidenceintervalis90%confidenceintervalis95%confidenceintervalis99%confidenceintervalμ-μ-μ-μμ-53-Forthe5%VaRis1.65standarddeviationsbelowtheForthe5%VaRis1.65standarddeviationsbelowthe1%VaRis2.33standarddeviationsbelowtheVaRforperiodslessthanayeararecomputedwithreturnandstandarddeviationsexpressedforthedesiredperiodoftime.FormonthlyVaR,dividetheannualreturnby12andthestandarddeviationbythesquarerootof12.Then,computemonthlyVaR.ForweeklyVaR,dividetheannualreturnby52andthestandarddeviationbythesquarerootof52.Then,computeweeklyVaR.Foraveryshortperiod(1-day)VaRcanbeapproximatedbyignoringthereturncomponent(i.e.,enterthereturnaszero).ThiswillmaketheVaRestimateworseasnoreturnisconsidered,butoveronedaytheexpectedreturnshouldbesmall.54-Theexpectedannualreturnfora$100,000,000portfoliois6.0%andtheTheexpectedannualreturnfora$100,000,000portfoliois6.0%andthehistoricalstandarddeviationis12%.CalculateweeklyVaRat1%.Thenumberofstandarddeviationsfora1%VaRwillbe2.33belowthemeanreturn.Theweeklyreturnwillbe6%/52=0.1154%.Theweeklystandarddeviationwillbe12%/521/2=1.6641%VaR=0.1154%-2.33(1.6641%)=-WhichofthefollowingstatementsisnotA1%VaRimpliesadownwardmoveofAonestandarddeviationdownwardmoveisequivalenttoa16%A5%VaRimpliesamoveof1.65standarddeviationslessthantheexpectedvalue.55-Analytical(variance-covariance)AdvantagesoftheanalyticalmethodEasytocalculateAnalytical(variance-covariance)AdvantagesoftheanalyticalmethodEasytocalculateandeasilyunderstoodasasingleAllowsmodelingthecorrelationsofCanbeappliedtoshorterorlongertimeperiodsasDisadvantagesoftheanalyticalmethodAssumesnormaldistributionofSomesecuritieshaveskewedVariance-covarianceVaRhasbeenmodifiedtoattempttodealwithskewandoptionsinthedelta-normalmethod.Manyassetsexhibitleptokurtosis(fatThedifficultyofestimatingstandarddeviationinverylarge56-HistoricalAdvantagesofthehistoricalmethodVeryeasytocalculateHistoricalAdvantagesofthehistoricalmethodVeryeasytocalculateandDoesnotassumeareturnsCanbeappliedtodifferenttimeperiodsaccordingtoindustryTheprimarydisadvantageofthehistoricalmethodistheassumptionthatthepatternofhistoricalreturnswillrepeatinthefuture(i.e.,itisindicativeoffuturereturns).57-58-Youhaveaccumulated100dailyreturnsforyour$100,000,000portfolio.Afterrankingthereturnsfromhighesttolowest,youidentifythelowerfivereturns:58-Youhaveaccumulated100dailyreturnsforyour$100,000,000portfolio.Afterrankingthereturnsfromhighesttolowest,youidentifythelowerfivereturns:-0.0019,-0.0025,-0.0034,-0.0096,-CalculatedailyVaRat5%significantusingthehistoricalSincethesearethelowestfivereturns,theyrepresentthe5%lowertail