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1、CHAPTER18portfoliomanagementInthisChapter...•ModernPortfolioTheoryandtheCapitalAssetPricingModel•optimizingyourportfolio•alternativemethodologiessuchascointegration•howtoanalyzeportfolioperformance18.1INTRODUCTIONThetheoryofderivativepricingisatheoryofdeterministicreturns:Wehedgeourderiv
2、ativewiththeunderlyingtoeliminaterisk,andourresultingrisk-freeportfoliothenearnstherisk-freerateofinterest.Banksmakemoneyfromthishedgingprocess;theysellsomethingforabitmorethanit’sworthandhedgeawaytherisktomakeaguaranteedprofit.Butnoteveryoneishedging.Fundmanagersbuyandsellassets(includin
3、gderivatives)withtheaimofbeatingthebank’srateofreturn.Insodoingtheytakerisk.InthischapterIexplainsomeofthetheoriesbehindtheriskandrewardofinvestment.AlongthewayIshowthebenefitsofdiversification,howthereturnandriskonaportfolioofassetsisrelatedtothereturnandriskontheindividualassets,andhowto
4、optimizeaportfoliotogetthebestvalueformoney.Forthemostpart,theassumptionsareasfollows.•Weholdaportfoliofor‘asingleperiod,’examiningthebehaviorafterthistime.•DuringthisperiodreturnsonassetsareNormallydistributed.•Thereturnonassetscanbemeasuredbyanexpectedreturn(thedrift)foreachasset,astan
5、darddeviationofreturn(thevolatility)foreachassetandcorrelationsbetweentheassetreturns.318PartOnemathematicalandfinancialfoundations18.2DIVERSIFICATIONInthissectionIintroducesomemorenotation,andshowtheeffectsofdiversificationonthereturnoftheportfolio.WeholdaportfolioofNassets.Thevaluetodayo
6、ftheithassetisSianditsrandomreturnisRioverourtimehorizonT.TheRsareNormallydistributedwithmean√µiTandstandarddeviationσiT.Thecorrelationbetweenthereturnsontheithandjthassetsisρij(withρii=1).Theparametersµ,σandρcorrespondtothedrift,volatilityandcorrelationthatweareusedto.Notethescalingwith
7、thetimehorizon.Ifweholdwioftheithasset,thenourportfoliohasvalueN=wiSi.i=1AttheendofourtimehorizonthevalueisN+δ=wiSi(1+Ri).i=1WecanwritetherelativechangeinportfoliovalueasNδ=WiRi,(18.1)i=1wherewiSiWi=.Ni=1wiSiTheweightsWisumtoone.From(18.1)itissimpletocalculatethe
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