2100911FRM投资组合_程黄维

11金程教育FRM二级讲义RiskManagement&InvestmentManagement讲师：程黄维FRM、CFRM日期：2010年09月地点：■上海□北京□深圳上海金程国际金融专修学院上海金程国际金融专修学院专业来自百分百的投入Copyright2010ByGFEDUTHECONTENT2PortfolioManagementPerformanceManagementPortfolioVaR&RiskBudgetingHedgeFunds¾MarkowitzPortfolioTheory¾CapitalAssetPricingModel¾Marketefficiency¾ArbitragePricingTheory¾RiskMeasurement¾PerformanceMeasurement¾PerformanceAnalysis¾PortfolioVaR¾RiskBudgeting¾IntroductiontoHedgeFund¾IndividualHedgeFundStrategies¾FundsofHedgeFunds¾StyleDrifts:Monitoring,DetectionandControl专业来自百分百的投入Copyright2010ByGFEDU3SectionOnePortfolioManagement专业来自百分百的投入Copyright2010ByGFEDU4MarkowitzPortfolioTheory¾MeanVarianceModel¾Return:E(R)¾Risk:σ¾RiskAversionRisk(σ)E(R)I1I2I3MorepreferreddirectionHarryM.Markowitz（1927-）1990年诺贝尔经济学奖获得者专业来自百分百的投入Copyright2010ByGFEDU5MarkowitzPortfolioTheory¾AssumptionsaboutinvestorbehaviorofMarkowitzPortfolioTheory¾RegardE(R)asreturnandσasrisk¾Utilitymaximization¾Riskaversion专业来自百分百的投入Copyright2010ByGFEDU6MarkowitzPortfolioTheory¾PortfolioRiskandReturnComputation¾Return¾Singleasset:E(R)=ΣPiRi=1/n×ΣRi¾Two-assetportfolio:E(RP)=w1E(R1)+w2E(R2)¾Risk¾Singleasset:σ2=ΣPi[Ri-E(R)]2=1/(n-1)×Σ[Ri-E(R)]2¾Two-assetportfolio:σp2=w12σ12+w22σ22+2w1w2COV1,2=w12σ12+w22σ22+2w1w2σ1σ2ρ1,22σσ=专业来自百分百的投入Copyright2010ByGFEDU7MarkowitzPortfolioTheory¾EffectsofCorrelationonDiversificationBenefitsρ=+1ρ=+0.3ρ=-0.3ρ=-1σPE(RP)AB●●专业来自百分百的投入Copyright2010ByGFEDU8MarkowitzPortfolioTheory¾MarkowitzEfficientFrontierLowRisk/LowReturnMediumRisk/MediumReturnHighRisk/HighReturnOptimalportfoliosshouldlieonthiscurve(knowasthe“EfficientFrontier”)AportfolioabovethiscurveisimpossibleσPPortfoliosbelowthiscurvearenotefficient,becauseforthesameriskoneshouldachieveagreatreturnE(RP)专业来自百分百的投入Copyright2010ByGFEDU9MarkowitzPortfolioTheory¾OptimalPortfolio●●XYEfficientFrontierσpE(Rp)专业来自百分百的投入Copyright2010ByGFEDU10CapitalAssetPricingModel¾FromPortfolioTheorytoCapitalMarketTheory¾威廉.夏普¾Addingarisk-freeassettoportfoliotheory¾TheAssumptionsofcapitalmarkettheory¾Markowitzinvestors¾Unlimitedrisk-freelendingandborrowing¾Homogeneousexpectations¾One–periodhorizon¾Divisibleassets¾Frictionlessmarkets¾Noinflationandconstantinterest¾Equilibrium专业来自百分百的投入Copyright2010ByGFEDU11CapitalAssetPricingModel¾CapitalMarketLine¾E(RP)=(1-wM)Rf+wME(RM)=Rf+wM[E(RM)-Rf]¾σp=wMσM¾CapitalMarketLine:E(RP)=Rf+σp×{[E(RM)-Rf]/σM}●Risk(σp)E(Rp)CapitalMarketLineEfficientFrontierMRf●●BA专业来自百分百的投入Copyright2010ByGFEDU12CapitalAssetPricingModel¾SystematicandUnsystematicRisk¾Totalrisk=systematicrisk+unsystematicrisk●Risk(σp)E(Rp)CapitalMarketLineEfficientFrontierMRf●Asystematicriskunsystematicrisk¾Requiredreturnonlydependsonportfolio’ssystematicrisk,notitstotalrisk.专业来自百分百的投入Copyright2010ByGFEDU13CapitalAssetPricingModel¾Riskvs.NumberofPortfolioAssets(TotalRisk=unsystematicrisk+systematicrisk)σ(risk)Marketrisk(σmkt)SystematicRiskUnsystematicRiskNumberofsecuritiesintheportfolio≈30专业来自百分百的投入Copyright2010ByGFEDU14CapitalAssetPricingModel¾CapitalAssetPricingModel¾E(Ri):expectedreturnonriskyasset¾Rf:riskfreerate¾E(Rmkt)-Rf:priceofrisk,marketportfolioriskpremium¾βi:quantityofrisk,systematicalriskofasseti¾βi×[E(Rmkt)-Rf]:beta-adjustedmarketriskpremiumi,mktifimktfi2mktCovE(R)=R+[E(R)-R],(=)ββσ专业来自百分百的投入Copyright2010ByGFEDU15CapitalAssetPricingModelExample:capitalassetpricingmodel1.Theexpectedreturnonthemarketis15%,therisk-freerateis8%,andthebetaforstockAis1.2.Computetherateofreturnthatwouldbeexpected(required)onthisstock.Answer：E(RA)=0.08+1.2(0.15-0.08)=0.164note:βA1soE(RA)E(Rmkt)2.Theexpectedreturnonthemarketis15%,therisk-freerateis8%,andthebetaforstockBis0.8.Computetherateofreturnthatwouldbeexpected(required)onthisstock.Answer：E(RB)=0.08+0.8(0.15-0.08)=0.136note:βB1soE(RB)E(Rmkt)专业来自百分百的投入Copyright2010ByGFEDU16CapitalAssetPricingModel¾SecurityMarketLine(SML)●E(Ri)E(Rmkt)RfSecurityMarketLine(SML)MarketPortfolioβmkt=1SystematicRisk(βi)·B·A·C专业来自百分百的投入Copyright2010ByGFEDU17·D·DCapitalAssetPricingModel¾ComparingtheCMLandtheSML·A·BCML·E·C·DRfE(RM)·A·BSML·E·C·DRfE(RM)E(R)βM=1ββ=1σσM·A·BCML·CRfE(RM)β=1σσM·A·BCML·CRfE(RM)E(R)β=1σσMβ=1β=1专业来自百分百的投入Copyright2010ByGFEDU18CapitalAssetPricingModel¾RelaxingtheCAPMAssumptions¾Differentborrowingandlendingrates¾Zero-betaversionoftheCAPM●TotalRisk(s)E(r)Rflending●BARfborrowingstockzerobetaportfoliostockmarketzerobetaportfolioE(R)=E(R)+(Beta)[E(R)-E(R)]专业来自百分百的投入Copyright2010ByGFEDU19CapitalAssetPricingModel¾RelaxingtheCAPMAssumptions¾Transactioncosts:theSMLisaband.¾Heterogeneousexpectationsandplanningperiods:theSMLisaband.专业来自百分百的投入Copyright2010ByGFEDU20Marketefficiency¾Marketefficiency(有效市场)¾Marketefficiencyisthesimpleststatementthatsecuritypricefullyreflectsallavailableinformation.¾CAPMassumesthatthemarketsarestrongefficientbecauseitisassumedthatallinvestorshavethesameexpectations.WeakEfficiencyinformationinpastpricepatternsisincorporatedintothecurrentprices.StrongEfficiencyallinformationincludingprivateandpublicSemistrongEfficiencyallpublicinformationincludingthatinpastpricepatterns专业来自百分百的投入Copyright2010ByGFEDU21Arbi