paul wilmott on quantitative finance portfolio management

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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,thenourportfoliohasvalue
N=wiSi.i=1Attheendofourtimehorizonthevalueis
N+δ=wiSi(1+Ri).i=1Wecanwritetherelativechangeinportfoliovalueas
Nδ=WiRi,(18.1)i=1wherewiSiWi=.Ni=1wiSiTheweightsWisumtoone.From(18.1)itissimpletocalculatethe