FRM知识点：Markowitz Efficient Frontier

《FRM知识点：Markowitz Efficient Frontier》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、frm.gfedu.comFRM知识点：MarkowitzEfficientFrontier1IntroductionMarkowitzefficientfrontier,brieflyefficientfrontier,containsallportfoliosofriskyassetsthatarational,risk-averseinvestorwillchoose.Theportfolioonthecurveprovidesaninvestorwiththehighestreturnunderagivenstandard

2、deviation.2UnderlyingassumptionsofMarkowitzEfficientFrontier2.1Investorsattempttomaximizetheirutilities.Utility()fromaninvestmentstrategyisafunctionoftwovariables-theanticipatedreturn()andrisk.Theriskfrominvestmentcanbemeasuredbythestandarddeviation()oftheexpectedretu

3、rnadjustedwithariskaversioncoefficient(A)whichreflectstheuniquerisktoleranceofaspecificindividual..2.2Investorsarerisk-adverseandrational.Arationalinvestortriestomaximizehisreturnwithgivenrisksandminimizehisriskwithcertainreturns.2.3Theexpectedreturnsareassumedtobenor

4、mallydistributed.Thisassumptionmitigatesthepossibilityofextremecases(fattail)inthedistributiontofurtherreinforcethecreditabilityofusingstandarddeviationasameasurementofinvestmentrisk.frm.gfedu.com1.1Themarketisefficient.Theefficiencyinthecapitalmarketreferstothecondit

5、ionthatpricesreflectalltheinformationavailable.2DerivingEfficientFrontier2.1InvestmentOpportunitySetInvestmentopportunitysetincludesallpossiblecombinationsofdifferentportfoliosavailableforinvestors.Itcanbecreatedwithanytwofeasibleriskyassets.Byalteringweightsbetweenth

6、esetwoportfolios,wecancreatenewportfoliosserveasadditionalcornerportfoliosforfurthercombinationprocess.Withpermutationandcombinationofnewlycreatedportfolios,wecanplotnumerousscatteredspotsonthegraph(sourcefrom:2017CorporateFinanceandPortfolioManagement).Eachofthesespo

7、tsmarksacorrespondingattainableportfoliointheopportunityinvestmentset.frm.gfedu.comWheninvestorsgetaccesstoforeignassetclasses,theopportunitysetwillextendfurthertonorthwestwhererisksislowergivenexpectedreturn,becausethediversificationaffectarousingfromlowcorrelationsb

8、etweenforeignassetsanddomesticassets.1.1DerivingMinimum-VarianceFrontierGenerally,insteadofinfiniteoptionsintheinvestmentopp