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1、PortfolioManagementandTrading9PortfolioSelection:“Optimizing”anError*Keywords:estimationrisk,simulation,optimization,assetallocationMarkowitzmean-variancetheory(MV)providesaclassicsolutiontotheport-folioselectionproblem.Theriskofaportfolio(asmeasuredbythevarianceofitsreturn)canbereducedb
2、ycombiningassetswhosereturnsareimperfectlycorrelated.Diversification,however,isnotboundless.Implementationofthisapproachnonethelessrequiresknowledgeofboththeex-pectedreturnsonallassetscomprisedinaportfolioandtheircovariances;aninfor-mationsetwhichbydefinitionisnotavailable.Acommonwaytocirc
3、umventthisproblemisthustousesampleestimatesofsuchmeasuresintheoptimizationpro-cedure(theso-calledplug-inapproach).Itfollowsthataprototypicalinvestorisnotonlyexposedtomarketrisk,butalsotoestimationrisk.Thelattercan,therefore,bedefinedasthelossofutilitywhicharisesfromformingportfoliosontheb
4、asisofsam-pleestimatesratherthantruevalues.Clearly,evenifthetruemomentsoftheassetreturndistributionsofaportfoliowereknownwithcertainty,MVoptimizedportfo-lioswouldnotbeatotherportfoliosineveryfutureinvestmentperiod,sincereturnrealizationsusuallydifferfromtheirexpectedvalues.However,overan
5、appropri-atelylargeinvestmentperiod,MVwouldprovideonaveragetheoptimalportfoliocomposition.Theaimofthiscaseistodiscussafewrelevantproblemscausedbytheexpo-suretoestimationriskwheninvestorsdealwithportfolioselectionandillustratetheresamplingtechniqueasoriginallyproposedbyMichaud(1998).1Byre
6、lyingonastatisticalviewofMVoptimization,thismethodleadstoabetterunderstandingofestimationriskexposure.Samplemeasuresprovidetheinitialmomentestimatetoa∗withGiovannaBoi,RiccardoGrassiandAlessandraPalmieri.1ResampledEfficiencyoptimizationwasco-inventedbyRichardMichaudandRobertMichaud,U.S.pat
7、ent6,003,018,worldwidepatentspending.NewFrontierAdvisors,LLC(NFA)isexclusiveworldwidelicensee.2749PortfolioSelection:“Optimizing”anErrormultivariatenormaldistributionwhichisusedtogenerateassetreturns.Anumberofindependentdrawsarethensortedoutofthismultivariatepopulationofr
