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1、SummaryThehistoryofquantitativeriskmanagementisclearwhenviewedthroughthelensofModernPortfolioTheory.Manyofthemostimportantdevelopmentsinriskmanagementandmanyofourmostchallengingproblemsarereadilyapparentwithinthisframework.AbouttheAuthorMichaelB.MillerstudiedeconomicsattheAmericanUniversit
2、yofParisandtheUniversityofOxfordbeforestartingacareerinriskmanagement.HeisamemberofGARP’sFRMExamCommitteeandtheauthorofMathematicsandStatisticsforFinancialRiskManagement.TheHistoryofQuantitativeRiskManagementandModernPortfolioTheory1In1952,TheJournalofFinancepublished“PortfolioSelection”by
3、HarryMarkowitz.ThearticleintroducedtheworldtoModernPortfolioTheory(MPT).Forthisandrelatedwork,MarkowitzwouldgoontowintheNobelPrizeinEconomics.ThecentralinsightofMPTissimple,elegant,anddifficulttodispute.Puttingthissimpleideaintopractice,however,requiresustomakethreebasicassumptions.Thehist
4、oryofquantitativeriskmanagementcanbeviewedasacontinuingefforttorefinetheseassumptions.ThecentralinsightofMPTisthatinvestorsaretryingtogetthehighestreturnswiththeleastamountofrisk.Giventwoportfolioswiththesamelevelofrisk,butdifferentexpectedreturns,arationalinvestorwillprefertheportfoliowit
5、hthehigherexpectedreturn.Similarly,giventwoportfolioswiththesameexpectedreturn,butdifferentrisklevels,arationalinvestorwillpreferthelessriskyportfolio.Thatthisseemsobvious—thatitseemsnaturaltoframeinvestingintermsofriskandreturn—isatestamenttotheprofoundimpactthatMPThashadonfinanceandriskm
6、anagement.1ThispaperispartofaseriesofpapersbyMichaelB.Miller,whichcanbefoundatwww.risk256.com.Pleasedonotreproducewithoutpermission.Torequestpermission,ortoprovidefeedback,youcancontacttheauthor,mike@risk256.com.ThisversionofthepaperwaslastupdatedMay17,2012.Asstated,thecentralinsightofMPTi
7、shardtodispute.Allelsebeingequal,rationalinvestorswilltrytomaximizereturnsandminimizerisk.Therealproblemsarisewhenwetrytoputthissimplestatementintopractice.Markowitzhimselfmadetwokeyassumptions:1.Thatriskcanbeequatedtostandarddeviation.2.Thattherelationshipbet
