Portfolio Optimization with TE Constraints

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1、PortfolioOptimizationwithTracking-ErrorConstraintsPhilippeJorionThisarticleexplorestheriskandreturnrelationshipofactiveportfoliossubjecttoaconstraintontracking-errorvolatility(TEV),whichcanalsobeinterpretedintermsofvalueatrisk.Suchaconstrainedportfolioisthetypicalsetupforactivemanagerswhoaregi

2、venthetaskofbeatingabenchmark.Theproblemwiththissetupisthattheportfoliomanagerpaysnoattentiontototalportfoliorisk,whichresultsinseriouslyinefficientportfoliosunlesssomeadditionalconstraintsareimposed.ThedevelopmentinthisarticleshowsthatTEV-constrainedportfoliosaredescribedbyanellipseonthetradi

3、tionalmean–varianceplane.Thisfindingyieldsanumberofnewinsights.Becauseoftheflatshapeofthisellipse,addingaconstraintontotalportfoliovolatilitycansubstantiallyimprovetheperformanceoftheactiveportfolio.Ingeneral,plansponsorsshouldconcentrateoncontrollingtotalportfoliorisk.ntypicalportfoliodelegat

4、ion,theinvestorGiventheseproblems,whydoestheindustryassignsthemanagementofassetstoaportfo-maintainthiswidespreademphasisoncontrollingIliomanagerwhoisgiventhetaskofbeatingtracking-errorrisk?2Rollconjecturedthatdiversify-abenchmark.Whentheinvestorobservesingamongmanagerscouldmitigatetheinherento

5、utperformancebytheactiveportfolio,theissueisflawinTEVoptimization,butasIwillshowlater,itwhethertheaddedvalueisinlinewiththerisksdoesnot.undertaken.ThisissueisparticularlyimportantInthisarticle,Iinvestigatewhethertheagencywhenperformancefeesareinvolved.Performanceproblemcanbecorrectedwithadditi

6、onalrestric-feesinduceanoption-likepatterninthecompensa-tionsontheactiveportfoliowithouteliminatingthetionofthemanager,whomayhaveanincentivetousualTEVconstraint.Thus,becausetheTEVcon-takeonmorerisktoincreasethevalueofthestraintissowidelyusedinpractice,ItaketheTEVoption.1Tocontrolthisbehavior,i

7、nstitutionalconstraintasgiven,eventhoughthisrestrictionisinvestorscommonlyimposealimitonthevolatilitynotoptimal.Iderivetheconstant-TEVfrontierinofthedeviationoftheactiveportfoliofromthetheoriginalmean–variancespace.benchmark,whichisalso