L2 Modern Portfolio Theory

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1、L2:ModernPortfolioTheoryAdvancedInvestmentManagementLentTerm2015Dr.ChelseaYaoNoble-Prize-WinningInsightsHarryMarkowitz–“Forhavingdevelopedthetheoryofportfoliochoice”(NobelPrize:1990)WilliamSharpe–“Forhiscontributionstothetheoryofpriceformationforfinancialassets,theso-calledCapitalAssetPr

2、icingModel(CAPM)“(NobelPrize:1990)2LectureOverview1.DiversificationandPortfolioRisk2.CovarianceandCorrelationinPortfolioConstruction3.Minimum-variancePortfolio4.PortfolioOpportunitySet5.EfficientFrontier6.SeparationProperty3PortfolioConstruction•Portfolioconstructiongenerallyhasthreestep

3、s:–Capitalallocationbetweentheriskyportfolioandrisk-freeassets(whatwedidlastlesson).•Theoptimalcapitalallocationdependsonriskaversionandtherisk-returntrade-offoftheoptimalriskyportfolio.–Assetallocationacrosswideassetclasses(stocks,internationalstocks,long-termbonds).–Securityselection.•

4、Inthislesson,wewillexaminetheriskyportfolioanddiscussthepowerofdiversification.4DiversificationandPortfolioRisk•Therearetwomainsourcesofrisksinaportfolio:–Firm-specificrisks–Economy(businesscycle,inflation,interestrates,etc.)•Consideraportfoliothathasonlyonestock:BT•Nowconsideranotherpor

5、tfoliothathastwostocks:BTandSainsbury•Withdiversification(addingmoresecuritiestoourportfolio),wecanreduceourexposuretofirm-specificrisks(portfoliovolatilityisreduced).•However,wewillstillbeexposedtothecommoneconomicfactors.5TwoTypesofRisk•Marketrisk(systematicrisk):theriskthatisattributa

6、bletoeconomywiderisksources•Uniquerisk(nonsystematicrisk):theriskthatcanbeeliminatedbydiversification6DiversificationandPortfolioRiskWhat’sonthex-axis??7PortfoliosofTwoRiskyAssets•Anefficientdiversificationaimstoreduceportfolioriskforanygivenlevelofexpectedreturn.•Consideraportfoliowithw

7、investedinabondfundand1-wDDinvestedinastockfund.Theexpectedreturnoftheportfoliois:E(r)wE(r)wE(r)PDDEE8PortfoliosofTwoRiskyAssetsThevarianceoftheportfoliois:22222ww2wwCov(r,r)PDDEEDEDEWecanexpresstheportfoliovarianceas:222wCov(r,r)wCov(r,r)2wwCov(r,r)PDDDEEEDED