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1、THEJOURNALOFFINANCEVOL.LVIII,NO.1FEB.2003AMonteCarloMethodforOptimalPortfoliosJE?RO?MEB.DETEMPLE,RENE?GARCIA,andMARCELRINDISBACHERnABSTRACTThispaperproposesanewsimulation-basedapproachforoptimalportfolioallocationinrealisticenvironmentswithcomplexdynamicsforthestatevari-ablesandl
2、argenumbersoffactorsandassets.Afirstillustrationinvolvesachoicebetweenequityandcashwithnonlinearinterestrateandmarketpriceofriskdynamics.Intertemporalhedgingdemandssignificantlyincreasethedemandforstocksandexhibitlowvolatility.Wethenanalyzesettingswherestockreturnsarealsopredictedb
3、ydividendyieldsandwhereinvestorshavewealth-dependentrelativeriskaversion.Large-scaleproblemswithmanyassets,includingtheNasdaq,SP500,bonds,andcash,arealsoexamined.Thequestionofoptimalportfolioallocationhasbeenoflong-standinginterestforacademicsandpractitionersinfinance.Whilethemean-
4、varianceanalysisofMarkowitz(1952)isstillcommonlyusedamongportfoliomanagers,ithasbeenwellunderstood,sinceMerton(1971),thatlong-terminvestorswouldpreferport-foliosthatincludehedgingcomponentstoprotectagainstfluctuationsintheirinvestmentopportunities.PromptedbytheseminalpapersofMerton
5、(1969,1971)andSamuelson(1969),studieshaveexploredvariousaspectsofthedynamicportfolioproblemwhenassetpricesfollowdiffusionprocesses(e.g.,Richard(1975)).Thisliteraturehasrelied,forthemostpart,onadynamicprogrammingapproachtotheproblem.MorerecentcontributionsbyPliska(1986),Karatzas,Leh
6、oczky,andShreve(1987),andCoxandHuang(1989)haveproposedanalter-nativeresolutionmethodbasedonmartingaletechniques.Inthecontextofthisapproach,anoptimalportfolioformulawasderivedbyOconeandKaratzas(1991).ThisexpressioninvolvesexpectationsofrandomvariablesdependingonnJe¤ro“meB.Detempleis
7、atBostonUniversity,SchoolofManagementandCIRANO;Rene¤GarciaisatUniversite¤deMontre¤al,DepartmentofEconomicsandCIRANO;andMarcelRindisbacherisatUniversityofToronto,RotmanSchoolofManagementandCIRANO.ThepaperwaspresentedatBostonUniversity,BostonCollege,CIRANO,McMasterUniversity,MIT,NYU(
8、Stern),NYU(Courant),Univer
