金融学概论讲义(北大光华管理学院)lecture05

1PrinciplesofFinanceLecture05CapitalAssetPricingModel2AquickreviewofportfoliochoiceGiveneachsecurity’sexpectedreturn,standarddeviation,thecorrelationbetweenthesesecurities,andtheweightsofthesesecuritiesintheportfolio,wecancalculatetheexpectedreturnandstandarddeviationoftheportfolio:12(1)prwrwr222221121222(1)(1)p3OurapproachHowdowedecideontheweightsofthesetwosecurities?Wetake3steps:A.analyzethecombinationofonerisklessassetandoneriskyasset.B.analyzethecombinationoftworiskyassets.C.analyzetheportfolioofonerisklessassetandacombinationoftworiskyassets.Wefindoutthebestcombinationoftworiskyassetshere!4PortfolioofOneRiskySecurityandOneRisklessAssetPortfolioofaRiskyandaRisklessSecurity00.050.10.150.20.2500.10.20.30.4StandardDeviationExpectedReturn5PortfolioofTwoRiskySecuritiesTheRisk-ReturnTrade-OffCurve0.000.020.040.060.080.100.120.140.1600.050.10.150.20.25StansardDeviationExpectedReturn6EfficientPortfolio&EfficientFrontierEfficientportfolio:theportfoliothatoffersthehighestexpectedreturnataspecifiedlevelofrisk(standarddeviation)orthelowestdegreeofriskforaspecifiedexpectedreturnEfficientfrontier:theboundarylineVSdefinestheefficientsetofportfolios7TheRisk-ReturnTrade-OffCurve0.000.020.040.060.080.100.120.140.1600.050.10.150.20.25StansardDeviationExpectedReturn8Difficultiesinthemean-varianceanalysisGivennsharesintheportfolio,weneedtoestimate:1.nmeans.2.nstandarddeviations3.n(n-1)/2correlations!Foraportfolioof2000securities,weneedmorethan2,000,000parameterstoestimate!Afterwehaveestimatedtheseparameters,findingtheoptimalportfoliorequiresquadraticprogramming,andthisneedsheavyuseofcomputing.9SomesimplificationprinciplesWeneedtocreateequationsthatcapturethekeyfactorsparsimoniously.Weneedtodevelopsimplemodels:linearmodelsarethenpreferredtoquadraticmodels.Inthelastlecture,wehaveobservedthattherearetwokindsofrisk:diversifiableandnon-diversifiablerisk.Assumethereturnofacompany’sshareconsistsoftwoparts:oneassociatedwithmarketreturn(non-diversifiablerisk),theotherassociatedwithcompany-specificfactors(diversifiablerisk).Thisgreatlysimplifiestheproblem.10AssumptionsofCAPMInvestorsevaluateportfoliosbylookingattheexpectedreturnsandstandarddeviationsoftheportfoliooverasingleperiodInvestorshavehomogeneousexpectationswithrespecttotheexpectedreturns,standarddeviationsandco-variancesoftheriskysecuritiesInvestorsarerisk–averseandprefermorethanlessPerfectmarkets:notaxes,notransactioncosts,securitiesareinfinitelydivisible,sameborrowingandlendingrates,informationfreelyavailabletoallinvestors11TheEfficientFrontierofRiskyAssetsPrP12TheMarketPortfolioMfrMrMCMLPPr13TheMarketPortfolioEveryinvestor’srelativeholdingsoftheriskyassetisthesametangentportfolioSinceeveryinvestor’srelativeholdingsoftheriskysecurityisthesame,theonlywaytheassetmarketcanclearisifthoseoptimalrelativeproportionsaretheproportionsinwhichtheyarevaluedinthemarketplacei.e.inequilibrium,thetangentportfoliomustbethemarketportfolioDependingontheirriskaversions,differentinvestorsholdportfolioswithdifferentmixesofrisklessassetandthemarketportfolioThemarketportfolioisanefficientportfolio14TheMarketPortfolioAsimpleexampletounderstandthemarketportfolioSupposethereexistonly2assetsintheworld.AssetAisworth$2m,assetBisworth$4m.Ifinvestorsholdthesamecompositionintheirportfolios,theirportfoliomustconsistsof1/3inAand2/3inB.Imaginethereareonly3investors,eachcaninvest$1m,$2mand$3mrespectively.Marketclearance(supplyoffundsequalsdemandoffunds)meansthattheywillallsplittheirwealthbetweenAandBsuchthat1/3isinvestedinAand2/3isinvestedinB.15TheCapitalMarketLine(CML)Supposeweinvestwproportionofourwealthintothemarketportfolio,1-wintoarisklessasset.22222222(1)(1)mmfmffmmw(1)(1)mfmfmmrwrwrrr()mffmrrrr16TheCapitalMarketLine(CML)CMLdescribetherelationshipbetweenexpectedreturnandrisk(standarddeviation)forefficientportfoliosCapitalMarketLinemffmrrrrRewardperunitofrisk(priceofrisk)mfmrr17AnExampleofApplyingCML%15Mr,%21M,and%7fr%6.16pr(Efficientportfolio),?pAnswer:P21.007.015.007.0166.0P25.2%18EquilibriumpriceofindividualassetCMLdepictstheequilibriumreturn-riskrelationshipofefficientportfolios.Whataboutindividualassetsandinefficientportfolios?SupposewehaveaportfolioPwhichconsistsofwinariskyassetand1-winthemarketportfolio.Itsexpectedreturnandstandarddeviationisgivenby:1/2222(1)(1)2(1)pimpimimrwrwr19EquilibriumpriceofindividualassetAswchanges,theexpectedreturnandstandarddeviationofportfolioPchange.Incalculus,weusethefirstorderderivativestodepictsuchchanges:1/222222221(1)2(1)222224pimpimimimmimimdrrrdwd20EquilibriumpriceofindividualassetTheinsightofCAPMissuchthatinequilibrium,everyinvestorholdsamarketportfolioplussomeriskfreeinvestment.Therefore,inequilibrium,wmustbezero!Atw=0,wehave:1/22221222pimpmmimimmmdrrrdwddw21EquilibriumpriceofindividualassetTherisk-returnrelationshipofportfolioPisgivenbyppdrd,whichisequalto//ppdrdwddw.2///ppimppimmmdrdrdw