the intuition behind b-l model portfolios

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1、THEINTUITIONBEHINDBLACK-LITTERMANMODELPORTFOLIOSbyGuangliangHeGoldmanSachsAssetManagement32OldSlip,24thFloorNewYork,NY10005guangliang.he@gs.comRobertLittermanGoldmanSachsAssetManagement32OldSlip,24thFloorNewYork,NY10005bob.litterman@gs.comAbstractInthisarticlew

2、edemonstratethattheoptimalportfoliosgeneratedbytheBlack-Littermanassetallocationmodelhaveaverysimple,intuitiveproperty.TheunconstrainedoptimalportfoliointheBlack-Littermanmodelisthescaledmarketequilibriumportfolio(reflectingtheuncertaintyintheequilibriumexpected

3、returns)plusaweightedsumofportfoliosrepresentingtheinvestor’sviews.Theweightonaportfoliorepresentingaviewispositivewhentheviewismorebullishthantheoneimpliedbytheequilibriumandtheotherviews.Theweightincreasesastheinvestorbecomesmorebullishontheview,andthemagnitu

4、deoftheweightalsoincreasesastheinvestorbecomesmoreconfidentabouttheview.1IntroductionSincepublicationin1990,theBlack-Littermanassetallocationmodelhasgainedwideapplicationinmanyfinancialinstitutions.Asdevelopedintheoriginalpaper,theBlack-Littermanmodelprovidesthefl

5、exibilityofcombiningthemarketequilibriumwithadditionalmarketviewsoftheinvestor.TheBlack-Littermanapproachmaybecontrastedwiththestandardmean-varianceoptimizationinwhichtheuserinputsacompletesetofexpectedreturns1andtheportfoliooptimizergeneratestheoptimalportfoli

6、oweights.Becausethereisacomplexmappingbetweenexpectedreturnsandtheportfolioweights,andbecausethereisnonaturalstartingpointfortheexpectedreturnassumptions,usersofthestandardportfoliooptimizersoftenfindtheirspecificationofexpectedreturnsproducesoutputportfolioweigh

7、tswhichdonotseemtomakesense.IntheBlack-Littermanmodeltheuserinputsanynumberofviews,whicharestatementsabouttheexpectedreturnsofarbitraryportfolios,andthemodelcombinestheviewswithequilibrium,producingboththesetofexpectedreturnsofassetsaswellastheoptimalportfoliow

8、eights.AlthoughBlackandLittermanconcludedintheir1992article[BlackandLitterman,1992]:“...ourapproachallowsustogenerateoptimalportfoliosthatstartatasetofneutralweightsandthent