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1、TheBlack-LittermanModelForActivePortfolioManagementForthcominginJournalofPortfolioManagementWinter2009AlexandreSchutelDaSilvaOneofthechallengesofportfoliooptimizationisthetendencyofsmalldifferencesSeniorVicePresident,inexpectedreturninputstocreatemajorswing
2、sinportfolioweightings,sometimesQuantitativeInvestmentGroupleadingtoextremeportfolioallocations.Inourview,theBlack-Litterman(BL)modelNeubergerBermanmayplayahighlyconstructiveroleinalleviatingthisproblem,duetoitscombinationWaiLee,Ph.D.ofactiveinvestmentviews
3、andequilibriumviewsthroughaBayesianapproach.ManagingDirector,QuantitativeInvestmentGroupThisarticleexploresthedevelopmentoftheBLmodelwithinthemean-varianceNeubergerBermanportfolioefficiencyparadigm,looksatthephenomenonofunintentionaltradesBobbyPornrojnangko
4、ol,Ph.D.andadditionalrisksrelatedtothetraditionalimplementationofBLandsuggestsSeniorVicePresident,potentialremediestogetthemostoutofthisimportantinvestmentmodel.QuantitativeInvestmentGroupNeubergerBermanThemean-varianceoptimalportfoliohasbeencriticizedascou
5、nterintuitive.Often,smallchangesinexpectedreturnsinputtedintoanoptimizationsolvercanleadtobigswingsinportfoliopositions,givingrisetoextremeweightingsinsomeassets.JobsonandKorkie[1981],Michaud[1989,1998],BestandGrauer[1991],ChopraandZiemba[1993]andBritten-Jo
6、nes[1999],amongothers,arguethatthehypersensitivityofoptimalportfolioweightsistheresultoftheerror-maximizingnatureofthemean-varianceoptimization.Asaremedy,constraintsonpositionsareoftenimposedasanalternativetopreventtheoptimizationalgorithmfromdrivingtheresu
7、lttowardssome“extremecorner”solutions.Thisapproach,however,isoftencriticizedasadhoc.Moreover,whenenoughconstraintsareimposed,onecanalmostpickanydesiredportfoliowithoutgivingtoomuchattentiontotheoptimizationprocessitself.AninterestingstudybyJagannathanandMa[
8、2003],however,suggeststhatundersomespecialconditions,imposingconstraintsisequivalenttousingaBayesianshrunkcovariancematrixorexpectedreturnforecastintheoptimizationprocess.Asanalternativeremedy,Michaud[
