DynamicAssetAllocationwithLiabilities

Electroniccopyavailableat:http://ssrn.com/abstract=20499501DynamicAssetAllocationwithLiabilities∗DanielGiamouridis1,AthanasiosSakkas2,NikolaosTessaromatis3Currentversion:April2012(Firstversion:December2011)AbstractWedevelopananalyticalsolutiontothedynamicmulti-periodportfoliochoiceproblemofaninvestorendowedwithpowerutilitydefinedoverthefundingratio(theratioofAssetsoverLiabilities)atafinitehorizon,undertime-varyinginvestmentopportunities.Ourmodelproducesdifferentassetallocationsrelativetoadynamicassetallocationmodelthatdoesnotaccountforinvestors’liabilitiesandalsorelativetoamyopicmodelthataccountsforinvestors’liabilities.ThedifferencesinassetallocationstranslatetolargeeconomicbenefitsforinvestorspursuingAssetLiabilityManagementwiththeproposedmodel.Wearguethatthesebenefitsarisebecauseourmodelexplicitlyincorporatesinvestors’liabilitiesbutalsobecauseitexploitsthepredictabilityofinvestmentopportunities’variation.JELClassification:G11,G12,G23Keywords:StrategicAssetAllocation;DynamicAssetAllocation;Asset–LiabilityManagement∗Wearegratefulforfinancialsupportfromthe‘Dauphine-AmundiChairinAssetManagement’.DanielGiamouridisalsogreatlyacknowledgesfinancialsupportfromtheAthensUniversityofEconomicsandBusinessResearchCenter(ΕΡ-1681-01).Anyremainingerrorsareourownresponsibility.1DanielGiamouridisisanAssistantProfessorofFinance,DepartmentofAccountingandFinance,AthensUniversityofEconomicsandBusiness,Athens,Greece.HeisalsoSeniorVisitingFellowatCassBusinessSchool,CityUniversity,London,UK,and,ResearchAssociateatEDHEC-RiskInstitute,EDHECBusinessSchool,Nice,France.E-mailaddress:[e-mail].2AthanasiosSakkasisaPhDcandidateattheDepartmentofAccountingandFinance,AthensUniversityofEconomicsandBusiness,Athens,Greece.HeisalsoaResearchAssistantatALBAGraduateBusinessSchool,Athens,Greece.E-mailaddress:[e-mail].3NikolaosTessaromatisisanAssociateProfessorofFinance,ALBAGraduateBusinessSchool,Athens,Greece.HeisalsoCEOandCIOofEDEKTAssetManagement,Athens,Greece.E-mailaddress:[e-mail]t:http://ssrn.com/abstract=20499502DynamicAssetAllocationwithLiabilitiesAbstractWedevelopananalyticalsolutiontothedynamicmulti-periodportfoliochoiceproblemofaninvestorendowedwithpowerutilitydefinedoverthefundingratio(theratioofAssetsoverLiabilities)atafinitehorizon,undertime-varyinginvestmentopportunities.Ourmodelproducesdifferentassetallocationsrelativetoadynamicassetallocationmodelthatdoesnotaccountforinvestors’liabilitiesandalsorelativetoamyopicmodelthataccountsforinvestors’liabilities.ThedifferencesinassetallocationstranslatetolargeeconomicbenefitsforinvestorspursuingAssetLiabilityManagementwiththeproposedmodel.Wearguethatthesebenefitsarisebecauseourmodelexplicitlyincorporatesinvestors’liabilitiesbutalsobecauseitexploitsthepredictabilityofinvestmentopportunities’variation.JELClassification:G11,G12,G23Keywords:StrategicAssetAllocation;DynamicAssetAllocation;Asset–LiabilityManagementElectroniccopyavailableat:http://ssrn.com/abstract=204995031.IntroductionOneofthemostimportantdecisionsmanypeoplefaceisthechoiceofaportfolioofassets.Inhisseminalwork,Markowitz(1952)pioneeredsingle-periodportfoliochoicewiththeconceptofmean-varianceoptimization.Samuelson(1969)andMerton(1969,1971,1973)showed,however,thatsincelong-terminvestorsjudgerisksverydifferentlyfromshort-terminvestors,theiroptimalportfoliosneednotbethesame.AlthoughMerton(1971,1973)developedananalyticalframeworkforunderstandingtheportfoliodemandsoflong-terminvestors,empiricalworkhaslaggedfarbehindduetothedifficultyofsolvingMerton’sintertemporalmodel(CampbellandViceira,2002).Abrieftaxonomyofthedevelopmentsintheempiricalliteratureofmulti-periodportfoliochoiceisprovidedinJurekandViceira(2011,JVhereafter).JVidentifythreetypesofapproaches.First,optimalportfolioscanbeobtainedasexactanalyticalsolutionsforspecialcasesofthemulti-periodportfoliochoiceprobleminacontinuoustimesetting(KimandOmberg,1996,Wachter,2002,BrennanandXia,2002,ChackoandViceira,2005,Liu,2007).Second,optimalportfolioscanbedeterminedwithnumericalmethods(Brennan,SchwartzandLagnado,1997,Brandt,1999,Barberis,2000,Lynch,2001,Dammon,Spatt,andZhang,2001,Detemple,GarciaandRindisbcher,2003,Brandtetal.,2005,Koijen,NijmanandWerker,2009).Third,optimalportfolioscanbecomputedinclosed-formthroughapproximateanalyticalmethods(CampbellandViceira,1999,2001,2002,Campbell,ChanandViceira,2003).InthesamearticleJVdiscussshortcomingsoftheseapproachesandproposeananalyticalrecursiveapproachwhichresultsinaclosed-formsolutionforthedynamicmulti-periodportfoliochoiceproblem.Multi-periodportfoliochoiceisparticularlyrelevantforinvestorswhodeterminetheirholdingssuchthattheywillbeabletofinancealong-termstreamofliabilities.Examplesofsuchinvestorsareprivateaswellasinstitutionalinvestorslikepensionfunds,foundations,andendowmentfunds.Inthispaperwestudytheportfoliochoiceproblemofthistypeofinvestors,aproblemthatisgenerallyreferredtoasAssetLiabilityManagement(ALMhereafter).ThemorecomplexdecisionthatALMinvestorsfacehasbeeninitiallystudiedinasingle-period