2011年11月融仕国际教育FRM一级--CAPM模型讲义

SectionThree:PortfolioManagementTheory•TopicOne:Markowitz’sPortfolioSelectionTheoryHarryMarkowitz,“PortfolioSelection,”JournalofFinance7,no.1(March1952):77–91;HarryMarkowitz,PortfolioSelection—EfficientDiversificationofInvestments(NewHaven,Conn.:YaleUniversityPress,1959)SectionThree:PortfolioManagementTheory•假设条件•1.关于市场效率的假设——StrongEfficiency；•2.关于交易行为的假设——smooth&unlimited；•3.关于交易者行为的假设——sameinformation;以上三个假设可以概括为：理性经济人在强有效市场中进行不受限制的、“光滑”的交易。是一组非常强的假设，因此理论的现实可操作性较差。SectionThree:PortfolioManagementTheory•Marketefficiency(有效市场)Marketefficiencyisthesimpleststatementthatsecuritypricefullyreflectsallavailableinformation.CAPMassumesthatthemarketsarestrongefficientbecauseitisassumedthatallinvestorshavethesameexpectations.•StrongEfficiency:allinformationincludingprivateandpublic;•Semi-strongEfficiency:allpublicinformationincludingthatinpastpricepatterns;•WeakEfficiency:informationinpastpricepatternsisincorporatedintothecurrentprices.SectionThree:PortfolioManagementTheory•ExpectedRateofReturn•TheexpectedreturnrateforaportfolioNpi=1Portfolioexpectedreturn=E(R)=()iiERω∑AExample:4种资产构成的投资组合SectionThree:PortfolioManagementTheory•Correlationcoefficient•correlationcoefficientbetweenthereturnsofsecurities1and2:121212(,)()()CovRRRRρσσ=×NOTES:(1)Acorrelationcoefficientof+1meansthatreturnsalwaysmovetogetherinthesamedirection.Theyareperfectlypositivelycorrelated.(2)Acorrelationcoefficientof-1meansthatreturnsalwaysmoveinthecompletelyoppositedirection.Theyareperfectlynegativelycorrelated.(3)Acorrelationcoefficientofzeromeansthatthereisnorelationshipbetweenthetwostock’sreturns.Theyarelinearlyuncorrelated.SectionThree:PortfolioManagementTheory•Thevolatility(StandardDeviation)ofReturns•VarianceandstandarddeviationofReturnsarecommonmeasuresofinvestmentrisk.•Supposeforportfoliowithtwoassets,22221112111212(1)2(1)Pσωσωσωωρσσ=+−+−Thinkabout:相关性系数的几个特殊取值（-1，0，1）时，公式是怎样的？SectionThree:PortfolioManagementTheory•EfficientFrontier(有效边界)Example(CombiningStockswithDifferentReturnsandRisk)Wenowconsidertwoassetswithdifferentexpectedratesofreturnandindividualstandarddeviations.请大家以相关性系数等于0为条件，计算casef以及caseg的组合期望及方差。SectionThree:PortfolioManagementTheorySupposethecorrelationcoefficientoftwostocksiszero,theexpectedreturnandvolatilityoftheportfolioisdescribedinthefollowingtable.SectionThree:PortfolioManagementTheoryPortfoliorisk-returnplotsfordifferentweights：Thelowerthecorrelationbetweenthereturnsofthestocksintheportfolio,thegreaterthediversificationbenefit.Theefficientfrontieristheenvelopecurvethatcontainsthebestofallthesepossiblecombinationsandrepresentsthesetofportfoliosthatwillgivetheinvestorsthehighestreturnateachlevelofrisk.(有效边界是与所有可能的投资组合相对应的组合线的一条包络线，而有效边界表示了在不同风险条件下能够给投资者带来的最高期望收益，或者在不同期望收益条件下能够给投资者带来的最低风险。)SectionThree:PortfolioManagementTheoryFeasibleSet&efficientFrontier:SectionThree:PortfolioManagementTheory•CapitalMarketLine(资本市场线)TheportfoliocomposedoftheriskfreeassetandriskyassetportfolioatpointAontheefficientfrontier.SectionThree:PortfolioManagementTheory•Thestraightlinefromtherisk-freerate(RFR)tangenttotheefficientfrontierofriskyassetsatpointMisreferredtoasthecapitalmarketline(CML).•Sobothreturnandriskincreaseinalinearfashionalongcapitalmarketline.•Formula:()()[]MFMERRpFpERRσσ−=+SectionThree:PortfolioManagementTheory•SystematicandunsystematicriskUnsystematicrisk(oruniqueriskordiversifiablerisk)istheriskthatdisappearsintheportfolioconstructionprocess.Sincethemarketportfoliocontainsallriskyassets,itmustrepresenttheultimateindiversification.Alltheriskthatcanbediversifiedawaymustbegone.(随着投资组合的构建而逐步消失的风险被称为可分散的风险（亦称“非系统风险”或“特定风险”），而市场组合则代表了最终的风险分散化结果，即可分散的风险全部消失了；)Systematicrisk(alsocallednondiversifiableriskormarketrisk)istheriskthatisleftcannotbediversifiedawaysincethereisnothinglefttoputintotheportfolio.(无分散的风险而留存在投资组合中的风险就被称为了系统风险（亦称“无可分散风险”或“市场风险”）)SectionThree:PortfolioManagementTheory•TopicTwo:Sharpe’sCapitalassetPricingModelWilliamF.Sharpe,“CapitalAssetPrices:ATheoryofMarketEquilibriumunderConditionsofRisk,”JournalofFinance19,no.3(September1964):425–442.SectionThree:PortfolioManagementTheory•Assumptions(EightPoints)(1)AllinvestorsareMarkowitzefficientinvestorswhowanttotargetpointsontheefficientfrontier.(所有投资者都是马考维茨有效投资者)(2)Investorscanborroworlendanyamountofmoneyattherisk-freerateofreturn.(投资者可以按照无风险收益率借入或借出任意的金额)(3)Allinvestorshavehomogeneousexpectations;thatis,theyestimateidenticalprobabilitydistributionsforfutureratesofreturn.(投资者具有一致的预期，即投资的收益率的概率分布都相同)(4)Allinvestorshavethesameone-periodtimehorizonsuchasonemonth,sixmonths,oroneyear.(投资者具有相同的投资期限，如一个月、六个月或一年，也就是说投资者持有某只股票或某个投资组合的期限都是相同的)SectionThree:PortfolioManagementTheory(5)Allinvestmentsareinfinitelydivisible,whichmeansthatitispossibletobuyorsellfractionalsharesofanyassetorportfolio.(所有的投资可以无限的细分，即可以投资任意份额的资产或投资组合)(6)Therearenotaxesortransactioncostsinvolvedinbuyingorsellingassets.(买卖资产无税收和无交易费用)(7)Thereisnoinflationoranychangeininterestrates,orinflationisfullyanticipated.(无通胀或利率变化，或者通胀被完全预计到)(8)Capitalmarketsareinequilibrium.(资本市场处于均衡状态，也就是说对于某个资产而言，其承担的系统风险可以得到补偿，而非