The Rise of the Quants

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TheRiseoftheQuants GreatMindsinFinanceSeriesEditor:ProfessorColinReadThisseriesexploresthelivesandtimes,theoriesandapplicationsofthosewhohavecontributedmostsignificantlytotheformalstudyoffinance.Itaimstobringtolifethetheoriesthatarethefoundationofmodernfinance,byexaminingthemwithinthecontextofthehistoricalbackdropandthelifestoriesandcharactersofthegreatmindsbehindthem.Readersmaybethoseinterestedinthefundamentalunderpinningsofourstockandbondmarkets;collegestudentswhowanttodelveintothesignificancebehindthetheories;orexpertswhoconstantlylookforwaystomoreclearlyunderstandwhattheydo,sotheycanbetterrelatetotheirclientsandcommunities.Titlesinclude:TheLifeCyclistsThePortfolioTheoristsTheRiseoftheQuantsTheEfficientMarketHypothesistsGreatMindsinFinanceSeriesStandingOrderISBN978–0–230–27408–2(outsideNorthAmericaonly)Youcanreceivefuturetitlesinthisseriesastheyarepublishedbyplacingastandingorder.Pleasecontactyourbookselleror,incaseofdifficulty,writetousattheaddressbelowwithyournameandaddress,thetitleoftheseriesandtheISBNquotedabove.CustomerServicesDepartment,MacmillanDistributionLtd,Houndmills,Basingstoke,HampshireRG216XS,England TheRiseoftheQuantsMarschak,Sharpe,Black,Scholes,andMertonColinRead ©ColinRead2012Allrightsreserved.Noreproduction,copyortransmissionofthispublicationmaybemadewithoutwrittenpermission.Noportionofthispublicationmaybereproduced,copiedortransmittedsavewithwrittenpermissionorinaccordancewiththeprovisionsoftheCopyright,DesignsandPatentsAct1988,orunderthetermsofanylicencepermittinglimitedcopyingissuedbytheCopyrightLicensingAgency,SaffronHouse,6–10KirbyStreet,LondonEC1N8TS.Anypersonwhodoesanyunauthorizedactinrelationtothispublicationmaybeliabletocriminalprosecutionandcivilclaimsfordamages.TheauthorhasassertedhisrighttobeidentifiedastheauthorofthisworkinaccordancewiththeCopyright,DesignsandPatentsAct1988.Firstpublished2012byPALGRAVEMACMILLANPalgraveMacmillanintheUKisanimprintofMacmillanPublishersLimited,registeredinEngland,companynumber785998,ofHoundmills,Basingstoke,HampshireRG216XS.PalgraveMacmillanintheUSisadivisionofStMartin’sPressLLC,175FifthAvenue,NewYork,NY10010.PalgraveMacmillanistheglobalacademicimprintoftheabovecompaniesandhascompaniesandrepresentativesthroughouttheworld.Palgrave®andMacmillan®areregisteredtrademarksintheUnitedStates,theUnitedKingdom,Europeandothercountries.ISBN978–0–230–27417–4Thisbookisprintedonpapersuitableforrecyclingandmadefromfullymanagedandsustainedforestsources.Logging,pulpingandmanufacturingprocessesareexpectedtoconformtotheenvironmentalregulationsofthecountryoforigin.AcataloguerecordforthisbookisavailablefromtheBritishLibrary.AcataloguerecordforthisbookisavailablefromtheLibraryofCongress.1098765432121201918171615141312PrintedandboundinGreatBritainbyCPIAntonyRowe,ChippenhamandEastbourne ContentsListofFiguresviiPrefacetotheGreatMindsinFinanceseriesviii1Introduction12ARoadmaptoResolvetheBigQuestions4PartIJacobMarschak3TheEarlyYears94TheTimes165TheTheory196Applications287LifeandLegacy35PartIIWilliamForsythSharpe,JohnLintner,JanMossin,andJackTreyner8TheEarlyYears439TheTimes5510TheTheory6111Applications6912LifeandLegacy75PartIIIFischerBlackandMyronScholes13TheEarlyYears8314TheTimes9615TheBlack-ScholesOptionsPricingTheory10916Applications11717TheNobelPrize,Life,andLegacy125PartIVRobertMerton18TheEarlyYears13519TheTimes14620TheTheory152v viContents21Applications15722TheNobelPrize,Life,andLegacy163PartVWhatWeHaveLearned23CombinedContributions17724Conclusions179Notes182Glossary188Index193 ListofFigures3.1TheMarschakfamilytree108.1TheSharpefamilytree458.2TheLintnerfamilytree508.3TheTreynorfamilytree5210.1Thecapitalallocationline6310.2Variouschoicesofriskandreturnalongthecapitalallocationline6413.1TheScholesfamilytree8413.2TheBlackfamilytree8918.1TheMertonfamilytree136vii PrefacetotheGreatMindsinFinanceseriesThisseriescoversthegamutofthestudyoffinancefromthesignificanceoffinancialdecisionsovertimeandthroughthecycleofoneslifetothewaysinwhichinvestorsbalancerewardandrisk;fromhowthepriceofasecurityisdeterminedtowhetherthesepricesproperlyreflectallavailableinformationwewilllookatthefundamentalquestionsandanswersinfinance.Wedelveintotheoriesthatgovernpersonaldecision-making,thosethatdictatethedecisionsofcorporationsandothersimilarentities,andthepublicfinanceofgovernment.Thiswillbedonebylookingatthelivesandcontributionsofthekeyplayersuponwhoseshouldersthedisciplinerests.Byfocusingonthegreatmindsinfinance,wedrawtogethertheconceptsthathavestoodthetestoftimeandhaveproventhemselvestorevealsomethingaboutthewayhumansmakefinancialdecisions.Theseprinciples,whichhaveflowedfromindividuals,manyofwhomhavebeenawardedtheNobelMemorialPrizeinEconomicsfortheirinsights(orperhapsshallbeawardedsomeday),allowustoseethefinancialforestforthetrees.Theinsightsofthesecontributorstofinancearosebecausethesegreatmindswereuniquelyabletoglimpseafamiliarproblemthroughawiderlens.Fromthegreaterinsightsprovidedbyamoreexpansiveview,theywereabletofocusupondetailsthathaveeludedpreviousscholars.Theiruniqueperspectivesprovidednewinsightsthatarethemeasureoftheirgenius.Thegiantswhohaveproducedthetheoriesandconceptsthatdrivefinancialfundamentalsshareoneimportantcharac-teristic:theyhavedevelopedinsightsthatexplainhowmarketscanbeusedortailoredtocreateamoreefficienteconomy.Theapproachtakenisonetaughtinourfinanceprogramsandpracticedbyfundamentalsanalysts.Wepresenttheoriestoenrichandmotivateourfinancialunderstanding.Thisapproachisincontrasttothetoolsoftechniciansformulatedsolelyoncapitalizingonmarketinefficiencieswithoutdelvingtoodeeplyintotheverymeaningofefficiencyinthefirstplace.Fromastrictlyaestheticperspective,onecannotentirelycondemnthetug-of-warofprofitssoughtbythetechnicians,eveniftheydolittletoenhanceandmayevendetractfromefficiency.Themathematicsandphysicsofpricemovementsviii PrefacetotheGreatMindsinFinanceseriesixandthesophisticationofcomputeralgorithmsisfascinatinginitsownright.Indeed,myappreciationfortechnicalanalysiscamefrommyuni-versitystudiestowardaBachelorofSciencedegreeinphysics,followedimmediatelybyaPhDineconomics.However,asIbegantoteacheconomicsandfinance,Irealizedthattheanalytictoolsofphysicsthatsopervadedmoderneconomicshavestrayedtoofarfromexplainingthisimportantdimensionofhumanfinancialdecision-making.Tobetterunderstandtheinterplaybetweenthescientificmethod,economics,humanbehavior,andpublicpolicy,IcontinuedwithmystudiestowardaMasterofAccountancyintaxation,anMBA,andaJurisDoctorofLaw.AsItaughttheeconomicsofintertemporalchoice,theroleofmoneyandfinancialinstruments,andthestructureofthebankingandfinancialintermediaries,IrecognizedthatmystudentshadbecomeincreasinglyfascinatedwithinvestmentbankingandWallStreet.Meanwhile,thedevelopedworldexperiencedthemostsignificantbreakdownoffinancialmarketsinalmosteightdecades.Irealizedthatthisonce-in-a-lifetimeglobalfinancialmeltdownarosebecausewehadmovedfromaneconomythatproducedthingstooneinwhich,by2006,generatedathirdofallprofitsinfinancialmarkets,withlittletoshowbutpiecesofpaperrepresentingwealththathadvalueonlyifsomestoodreadytopurchasethem.Idecidedtoshiftmyresearchfromacademicresearchinesotericfieldsofeconomicsandfinanceandtowardthecontributiontoabetterunderstandingofmarketsbytheeducatedpublic.IbegantowritearegularbusinesscolumnandabookthatdocumentedtheunravelingoftheGreatRecession.Thebook,entitledGlobalFinancialMeltdown:HowWeCanAvoidtheNextEconomicCrisis,describedtheeventsthatgaverisetothemostsignificanteconomiccrisisinourlifetime.IfollowedthatbookwithTheFearFactor,whichexplainedtheimportantroleoffearasasometimesconstructiveandatothertimesdestructiveinflu-enceinourfinancialdecision-making.IthenwroteabookonwhymanyeconomiesatfirstthriveandthenstruggletosurviveinTheRiseandFallofanEconomicEmpire.Throughout,Itrytoimparttoyou,theeducatedreader,theintuitionandtheunderstandingthatwould,atleast,helpyoutomakeinformeddecisionsinincreasinglyvolatileglobaleconomiesandfinancialmarkets.AsIdescribethetheoriesthatformthefoundationsofmodernfinance,Ishowhowindividualsbornwithoutgreatfanfarecancometoberegardedasgeniuseswithintheirownlifetime.Thelivesofeach xPrefacetotheGreatMindsinFinanceseriesoftheindividualsexaminedinthisseriesbecameextraordinary,notbecausetheymadeanunfathomableleapinourunderstanding,butratherbecausetheylookedatsomethinginadifferentwayandcausedusallthereaftertolookattheprobleminthisnewway.Thatisthetestofgenius. 1IntroductionThisbookisthethirdinaseriesofdiscussionsaboutthegreatmindsinthehistoryandtheoryoffinance.Eachvolumeaddressesthecon-tributionsofbrilliantindividualstoourunderstandingoffinancialdecisionsandmarkets.Thefirstintheseriesbeganbyestablishingaframeworkuponwhichallsubsequentdiscussionsrest.Itdiscussedhowindividualsmakedecisionsovertimeandwhythesedecisionschangeasweageandourcircumstanceschange.Theexpansionoftraditionaleconomicmodelstodecision-makingacrosstimecreatedthefoundationsoffinance.Theearlyfinancialtheorists,whichincludedIrvingFischer,FrankRamsey,JohnMaynardKeynes,FrancoModigliani,MiltonFriedman,andothers,recognizedthatthestatictime-independentmodelsofclassicaleconomicswereill-equippedtodescribehowhouseholdsbalancethepresentandthefuture.ThistopicofthefirstvolumeisvariouslycalledintertemporalchoicebymicroeconomistsandtheLifeCycleModelbymacroeconomistsandfinancialtheorists.Toyouandme,itexplainswhyweexpecttoearninterestonourinvestmentevenifwetakelittlerisk.Italsopredictswhysomeofusconcludethattheprevailinginterestrateinafinancialmarketpresentsagoodopportunitytosave,whileothersofadifferentilktakethesameinterestrateasagoodopportunitytoborrow.TheinclusionofriskanduncertaintyYet,howevervaluablewerethecontributionsoftheLifeCycliststoourunderstandingofsavingsoverourlifetime,theinclusionofriskanduncertaintyinourmodelsremainedelusive.Then,inadramaticexplo-sionoftheoryover15yearsbetween1937and1952,financetheory1 2TheRiseoftheQuantswentfromastageofinfancytoatoolthatallowedustoestablishandunderstandequilibrium.FinancebegantoincorporatetheinsightofFrankKnightthattherecanbeanunknownbutoftencalculableestimateofriskthatpervadesanentireeconomicsystem,orsystematicrisk,andriskthataffectsagivensecurity,labeledidiosyncraticorunsys-tematicrisk.ThegreatmindJohnMaynardKeyneslamented:[Underuncertainty]thereisnoscientificbasisonwhichtoformanycalculableprobabilitywhatever.Wesimplydonotknow.Nevertheless,thenecessityforactionandfordecisioncompelsusaspracticalmentodoourbesttooverlookthisawkwardfactandtobehaveexactlyasweshouldifwehadbehindusagoodBenthamitecalculationofaseriesofprospectiveadvantagesanddisadvantages,eachmultipliedbyitsappropriateprobabilitywaitingtobesummed.1Thefinanceliteraturefurtherclarifiedthattherearecalculablerisksandthatthereareuncertaintiesthatcannotbequantified.Inthe1930s,JohnvonNeumannsetaboutproducingamodelofexpectedutilitythatpermittedtheinclusionofrisk.Then,LeonardJimmieSavagedescribedhowourindividualperceptionsaffecttheprobabilityofuncertainty,andKennethArrowwasabletoincludetheseprobabilitiesofuncertaintyinamodelthatestablishedtheexistenceofequilibriuminamarketforfinancialsecurities.Withtheexistenceofequilibriumandabetterunderstandingofthemeaningandsignificanceofprobabilityathand,HarryMarkowitzthenpackageduptheseintuitionsintoatidysetofinsightswenowcallModernPortfolioTheory.Indoingso,hedemonstratedthatanefficientportfoliominimizesanddiversifiesmarketriskthroughthechoiceofsecuritiesthattakebestadvantageofthewaysinwhichtheirreturnsarecorrelatedwitheachother.Hisnotionofanefficientfrontierofsecurities,thesecuritiesmarketline,providednewinsightsintohowanoptimalfinanceportfoliocouldbedeveloped.Subsequently,JamesTobindemonstratedhowanyindividual’spreferredtrade-offbetweenriskandreturncouldbemetbyauniquecombinationofarisk-freeassetandadiversifiedmutualfund.However,whiletheseinsightswereproducedduringthe1950s,sufficientcomputingpowernecessarytoapplythemwouldnotexistforanotherdecade.Despitetheinabilityofthetransitionofthesesignificanttheoreticaldevelopmentsintopractice,thegreatmindsofvonNeumann,Savage,Arrow,andMarkowitzcreatedthesoundtheoreticalframeworkfromwhichfinancecoulddevelopandestablish Introduction3itselfonfirmfoundationsasadisciplinedistinctfromthequestionsmostoftenposedineconomics.But,whilevonNeumannconsideredhimselfaphysicistandmathematician,Savagepublishedasastatis-tician,andArrowatfirstconsideredhimselfaninsurancetheoristandthenaneconomist,theyallhelpedconstructthefoundationsoffinance.Ofthegreatmindsthatdescribedfinancialequilibria,perhapsonlyMarkowitzconsideredhimselfafinancialtheorist,atleastwhenhewasnotacomputerscientistconcentratingondevelopingcomputingalgorithmsforthesolvingoffinancialproblemsorwhenhewasnotanoperationsresearchtheorist.Thesegreatmindssharedanimportantcharacteristicwithallthegreatmindsthatcamebeforethemorwouldfollow.Theyeachlookedatafamiliarprobleminauniquewayand,throughtheiruniqueperspective,producedstunningnewinsights.Theirinsightsalsoproducedanewsetofquestions.Theyprovidedanascentfinanceliteraturewithanewsetoftheoreticaltools,butwithlittleinsightonhowpractitionerscouldusethesetools.Thenexttaskforthedisciplineoffinancewouldbetotakethesetheoreticalinsightsanddeterminehowtheycouldprofitablypriceindividualsecurities.Thisisthetopicofthethirdbookintheseries.Aswedocumentthelivesandtimesofthesegreatminds,weanswerthefollowingquestions:HowwasHarryMarkowitz’sModernPortfolioTheoryextendedtothepricingofasinglesecurity?AndhowcouldtheinsightsofMarkowitz’sPhDsupervisor,JacobMarschak,beusedtoquantifytheunknowninastandardwaysothatriskcouldbepriced?Finally,howcanonebetterleverageandhedgehisorherportfoliotoreduceriskthroughthepurchaseofoptions,theinstrumentsthatderivetheirvaluefromanunderlyingsecurity?Thesearethequestionsthatthepricinganalystssoughttoresolve. 2ARoadmaptoResolvetheBigQuestionsInthefirsthalfofthetwentiethcentury,IrvingFischerdescribedwhypeoplesave.JohnMaynardKeynesthenshowedhowindividualsadjusttheirportfoliosbetweencashandlessliquidassets,whileFrancoModiglianidemonstratedhowallthesepersonalfinancialdecisionsevolveoverone’slifetime.JohnvonNeumann,LeonardJimmieSavage,andKennethArrowthenincorporateduncertaintyintothemix,andHarryMarkowitzpackagedthestateoffinancialscienceintoModernPortfolioTheory.However,noneofthesegreatmindsprovidedasatisfactoryexpla-nationforhowthepriceofindividualsecuritiesevolveovertime.Bythe1960s,thefinancedisciplinewasbeggingforarevolutionthatcouldturnthetheoreticalintothequantitativeandpractical.Tomakethistransitionfromtheorytopracticeandtotransformfinancialmarketsrequiredasequenceofsteps.Weshalldiscusseachofthesestepsinturn.First,thedisciplinehadtoquantifyriskinapracticalway.Ourfirstgreatmindinthisvolume,JacobMarschak,proposedameasureofriskandadescriptionofthereturn/risktrade-offbasedonwhatphysiciststhencalledthefirstandsecondmomentoffinancialreturns.Physicistsusedsuchfirstandsecondmomentstodescribethecenterofgravityandtheinertiaofanobject.Thedisciplineoffinanceusedthesametechniqueinwhatwenowknowasthemeanandvarianceapproach.Withmeasuresofthemeanandvarianceathand,scholarsthendescribedhowthesemeasureswereusedtopriceanindividualsecurity.Whileweseethatfourscholarsworkedindependentlytodevelopthelinkbetweenthemeanreturnandthevarianceofasecurityanditsmar-ketprice,wewillforeverassociatethisnewmethodologyoftheCapitalAssetPricingModel(CAPM)withthegreatmindWilliamSharpe.4 ARoadmaptoResolvetheBigQuestions5However,whileSharpe’sinsightshelpedusbetterunderstandhowanindividualsecurityispriced,thegreatestneedfortherapidpricingofsecuritieswasinthederivativesmarket.Thisnewfinancialmarket,oncethesleepydomainoffarmersandfoodprocessorsconcernedaboutpricestabilityforthefuturedeliveryofagriculturalcommodities,nowrepresentsanannualmarketvaluethatrivalsthecombinedsizeoftheworld’seconomies.Thereisnowamuchgreatervolumeoftradinginthesederivatives,incommoditiesfuturesandinoptionsmarkets,increditdefaultswapsandmortgage-backedsecurities,inforeignexchangefuturesandbondfuturesthaninthetraditionalmarketforcorporatesecurities.Yet,beforethepublicationofthetheoryfromthegreatmindsFischerBlackandMyronScholes,weknewlittleabouthowtopricesuchfinancialderivatives.Meanwhile,RobertMerton,adiscipleofthegreatmindPaulSamuelson,wasrapidlyextendingtherelativelystaticmodelsoffinancetoadynamiccontextthatmoreeffectivelyincludedtime.Increatingdynamicmodelsoffinance,hewasabletomorefullydescribetheevolu-tionofmarketsovertime.Thetechniqueshedeveloped,originallywiththemarketforoptionsinmind,evenmoreclearlydelineatedfinancefromeconomics.Byitsverynature,financemustmodeltheevolutionofpricesovertimethatissimplylessrelevantwithinthetraditionalstudyofecono-mics.Consequently,financenowproducesthemostsophisticatedmodelsofdynamicdecision-makingandnecessarilyoftenrequirestheskillsofthosemostadeptatsuchdynamicmodeling,producedbyscholarstrainedasrocketscientistsorappliedmathematicians.Untilwecouldcreateascienceoutofthisfinancialart,financialderivativesmarketscouldnotdevelopfully,andmyriadriskscouldnotbehedgedandtradedefficiently.However,withtheadventoftheBlack-Scholesoptionspricingtheoryanditssubsequentextensions,theoptionsmarketburgeoned,primarilyontheChicagoBoardOptionsExchange.Inaddition,globalfinancialmarketstradedamongstthemselves,createdmammothglobalfinancecompaniesthatbecametoobigtofail,andbroughttotheforefrontconceptspreviouslyleftonlytohighfinanciers,untilthefailureofthesemarketsaffectedusallandplungedtheworldintoaglobalfinancialmeltdown.Clearly,financemarketscanbebothblessingsandcurses.However,thereisnodoubtthatthesefinancialmarketsbenefitedfromthescien-tifictoolsofanalysesandpricingthatthesegreatmindsprovided.Thegenieisoutofthebottleandfinancialworldswillnevergobacktoamoreprimitiveandsimplisticstate.Themodernquants,andtrillions 6TheRiseoftheQuantsofdollarsoffinancialinvestmenteachyear,nowrelyonthepricingtoolsprovidedbyWilliamSharpe,FischerBlackandMyronScholes,andRobertMerton,basedontheearlierfoundationalworkofJacobMarschakandathenobscurebutbrilliantFrenchPhDstudentattheturnofthetwentiethcenturynamedLouisBachelier.Inourfuture,weshallinevitablyrelyevenmoreontheproductsofthesegreatminds.Wewillnowturntohowtheconceptscameaboutandnowaffectusallsoprofoundly. PartIJacobMarschakWecanoftendiscovertheformativerootsofoneortwogreatinsightsthateventuallyculminatedinaNobelPrizeformanyofthegreatmindsdescribedinthisseries.Othersmadebrilliantobservationsoroffereduptechniquesinfinancewithwhichtheyareforeverassoci-ated.JacobMarschakwasdifferent.Hislegacyarosebecausehewasabridgeassociatedwithsomanythatcamebeforehimwhowenowrecognizeasgreatcontributorstofinance,andsomanythatheinspiredandsubsequentlybecameknownasgreatmindsthemselvesinfinanceinthe1950sand1960s.OnceonerecognizesthatJacobMarschakwasacommondenominatorbetweenthegreatmindsofpreviousvolumesthatincludeLeonardJimmieSavageandMiltonFriedman,KennethArrowandHarryMarkowitz,andevenFrancoModigliani,therootofhisinfluenceontheirworkiscompelling.WhenwediscoverthatMarschakmadediscoveriesthatweresubtleandhumblebutweresotimelyandrelatedtotheessenceoftheworkofWilliamSharpe,FischerBlack,andMyronScholes,wemustconcludethathewasmorethanamentorofothergreatminds–hewasagreatmindhimself.Wewillbeginwithhisstory. Thispageintentionallyleftblank 3TheEarlyYearsJacobMarschakwasnotatallunusualamongthecadreofgreatmindsthatformedthedisciplineoffinanceinthefirsthalfofthetwentiethcentury.LikethefamiliesofMiltonFriedman,FrancoModigliani,LeonardJimmieSavage,KennethArrow,JohnvonNeumann,andHarryMarkowitz,Marschak’sfamilytreewasoriginallyrootedintheJewishcultureandderivedfromtheintellectuallystimulatingregionofEastern,CentralandSouthernEuropeatthebeginningofthetwentiethcentury.Thisregion,comprisingwhatisnowUkraine,Hungary,Poland,Romania,andpartsofItaly,wasundertheinfluenceoftheAustro-HungarianEmpireinthelatenineteenthandearlytwentiethcenturies.TheAustro-HungarianEmpirethrivedfrom1867untiltheendoftheFirstWorldWar.Theregionwasmulti-national,culturallydiverse,andpoliticallysophisticated,asitsleaderstriedtonavigatetheobviousproblemsofpluralitycreatedbysuchageographicallyandculturallyvariedregion.Itwasperhapsthisdiversity,andthedualprideitscitizenstookintheirownregionbutalso,ratheruncomfortably,attimesintheaccomplishmentsoftheEmpireasawhole,thatfueleditsintellectualambition.Theliberal,innovative,andprogressivenationthatsuchadiversepopulationforgedexhibitedrapidgrowthandindustrialization,andspectacularintellectualization.TheEmpirewasintheshadowoftheGermanRepublicandGreatBritain,andhence,likeayoungersibling,ittriedharder.BudapestandViennaweretheintellectualcapitalsoftheAustro-HungarianEmpire.Theintellectualtradition,combinedwiththestrongbeliefineducationamongJewishfamilies,producedperhapsthegreat-estnumberofscientificgeniusesforatleasttwogenerationsintheearly1900s.JacobMarschakwasaprimeexampleofthistradition.9 10TheRiseoftheQuantsIsrailMarschak(?1920)RussiaSpouse:JacobMarschak(18981977)Marianne(Kamnitzer)BorninUkraine,immigratedMarschak(19011993)toNewYorkSiblingLydiaMarschak(18971983)ChildrenAnnM.Jernberg(19281993)ThomasMarschak(1930)SophieFavish(Russia)Figure3.1TheMarschakfamilytreeMarschakwasborninKiev,UkraineonJuly23,1898.Hisfatherwasajewelerinanupper-middle-classfamilythatvaluededucationandintel-lectualactivism.However,unlikeFriedman,Arrow,Savage,Modigliani,vonNeumann,andMarkowitz,eachofwhomaredocumentedinthefirsttwovolumesofthisseriesandwhootherwisesharedsomeofhisheritage,Marschakwasnottheeldestson.Indeed,hewasthelastoffivechildrenand,likemanyyoungestsiblings,hehadarebelliousstreakinhisyouth.Marschak’sfamilydidnotpracticetheirreligionstrictly.Rather,theydevotedtheirenergiesmoreintosocialissues,eveniftheywerequitecomfortableeconomically.MarschaklearnedFrenchandGermanfromgovernesses,buthadtobeeducatedbothathomeandattheFirstKievSchoolofCommercewhenhisJewishheritagepreventedhimfrombeingadmittedintothelocalGymnasium.MarschakwasstillateenagerwhentheRussianRevolutionpoliti-callychargedtheregion.HehadbeenactiveintheMarxistmovementatthetimeandhadevenservedbrieflyastheMinisterofLaborintheshort-livedrevolutionarysocialdemocraticparty,theMenshevikInternationalcaucus,intheSovietrepublicofTerek.HehadbeenaherooftheRevolutionbecauseofhisyouthfulanti-Tsaristradicalismthathadcausedhimtobeimprisonedattheageof18untilhewasliberatedaftertheoverthrowoftheTsaristregime. TheEarlyYears11However,whileMarschakcouldattributehislibertytothenewBolshevikregimethatreplacedtheTsarists,hedidnotsharetherevo-lutionaryzealofthenewMoscow-centricpolitburo.HisfamilywasforcedtofleegrowingunrestinKiev,butheinsteadfoundhimselfembroiledinpoliticsintheiradoptedhomeintheNorthernCaucasus.HisactivismindefenseofanindependentanddemocraticCaucasusagainthreatenedhisfreedomasthenewSovietregimegainedstrengthandconsolidateditspowerovertheregions.Hemadethedifficultdeci-siontoleaveUkraineandcontinuehisstudiesinanotherintellectualhotbed,firsttheUniversityofBerlin,wherehewasexposedtostatisticalmethodsineconomics,andthentheUniversityofHeidelbergintheGermanRepublic.Marschakhaddiscoveredeconomicsasanoutletforhissuperioranalyticandstatisticalmind,justaseconomicswasmetamorphosingfromapoliticaleconomytoadecisionscience.HereceivedhisPhDfromHeidelbergin1922andbecameanacademicvagabondasheheldtemporaryteachingpositionsatanumberofGermanuniversities.Atthesametime,andtoearnasteadierliving,hewroteoneconomicpolicyforaleadingGermannewspaper,theFrankfurterZeitung.ItwaswhilewritingforthenewspaperthatMarschak(stillknownatthispointasJascharatherthanbyhisanglicizednameJacob)metMarianneKamnitzer.Theymarriedin1927andhadadaughter,Ann,in1928andason,Thomas,in1930.Justafewyearsafterthebirthofhisson,Marschakwasagainforcedtofleeanomnipotentandunforgivinglyideologicalregime.HehadsufferedtheinitiallysubtleoppressionofJewishintellectualsundertheHitlerregimeofhisadoptedland.OncetheNazistookpowerin1933,hesuccumbedtoacademicconsequencesbecauseofhisheritage–hecouldnotasaJewbegrantedapermanentuniversitypositionataGermanuniversity.Consequently,hemovedhisfamilytotheUniversityofOxfordinEnglandandservedasthedirectoroftheOxfordInstituteofStatisticsforfouryears,beginningin1935,undertheauspicesofthefundingoftheRockefellerFoundationbasedintheUSA.TheLauraSpelmanRockefellerMemorialFoundationwasendowedbyUSindustrialistJohnD.Rockefeller,Jr.ThepurposeoftheFoundationwastopromoteresearchinthesocialanddecisionsciences,butitwasalsoseenasawaytoexposeEuropeanscholarstoAmericanschoolsofthought.TheFoundationwasrunbyBeardsleyRuml,anexperimentalpsychologywithaPhDfromtheUniversityofChicago.Rumlespousedamoreclinicalandempiricalapproachtothesocialscienceshe 12TheRiseoftheQuantsbelievedwerebecomingincreasinglytheoreticalandesoteric.AgreaterintegrationofpragmaticstatisticsintoeconomicswashisobjectiveinfundingtheOxfordInstituteofStatisticswhichMarschakdirected.AfterfouryearsattheOxfordInstituteofStatistics,MarschakwasattractedtotheNewSchoolforSocialResearchinNewYorkCityjustastheUSAjoinedtheSecondWorldWar.HehadjoinedTheUniversityinExile,agroupofmorethan180mostlyJewishanti-fascistscholarswhowereofferedahomeattheNewSchoolfortheturbulentyearsbetween1933and1943.Marschakagainfoundhimselfinaneclecticandcross-disciplinaryframeworkforhisexpandingeconomicresearchagenda.Marschakjoinednotjustauniversitybutalsoaphilosophyandschoolofthought.TheNewSchoolforSocialResearchwasco-foundedbyAlvinSaundersJohnson(1874–1971),anAmericaneconomistfromHomer,NebraskawhohadcompletedhisPhDeducationatColumbiain1902andhadtaughtinanumberofuniversitiesacrosstheUSAbeforehereturnedtoNewYorktoedittheNewRepublicin1917.ThenextyearhehelpedstarttheNewSchoolwiththeobjectiveofprovidingarichandrigorousmulti-disciplinaryapproachtothedevelopmentofeconomictheoryandsocialsciences.AstheNewSchool’sfirstdirector,JohnsoncreatedthedivisionthatofferedrefugetoJewishscholarsinthesocialsciencesandhumanities.Marschakjoinedthiseclecticdivi-sionoftheNewSchooland,whilethere,wasinfluentialasthementorandsupervisorofFrancoModiglianiandmanyothers.ANewSchoolandbeyondWhileattheNewSchool,Marschaktransformedhisyouthfulactiv-ismintopassionateadvocacyonbehalfofotherRussianandEasternEuropeanrefugeescholars.Hewasparticularlyinstrumentalinattrac-tingintellectualrefugeesseekingrefugefromNaziGermanyduringtheNazieraandlaterontheSovietUnionduringtheColdWar.WhileattheNewSchool,Marschakwasreunitedwithotherecono-mistsinexile,includingEmilLederer(1882–1939),hisformermentoratHeidelberg,andHansNeisser(1895–1975).BoththesekindredspiritswerepoliticalandintellectualactivistsinGermany.NeisserhadbeeninstrumentalintheformationoftheinfluentialViennaColloquium,whichhelpedmotivate,hone,andpublicizesomeofJohnvonNeumann’smostsignificantworkintheearlytomid-1930s.Neisser,whotherenownedeconomistJosephSchumpeteroncedescribedas“oneofthemostbrillianteconomicminds(ofhisgeneration),”remainedattheNewSchooluntilhediedin1975.1 TheEarlyYears13LedererandNeisserweremostinfluentialinMarschak’searlywork.Theseformerparticipantsofwhatwasknownasthe“KielSchool”hadexposedMarshaktoanapproachtoeconomicsthatwasdevelopedbysomereform-orientedeconomistsintheKielInstituteofWorldEconomicsfrom1914untiltheriseoffascismforcedthemtoseekrefugeelsewhere.Thesescholars,andothers,werereunitedattheNewSchool,wheretheycontinuedtheirresearchintoeconomicgrowthandthebusinesscycle.Thisapproachtoeconomicgrowthwastimely,formanyreasons.Theworldwasexperiencingthefirstglobaldepressioninthe1930sandonlyeconomicgrowthcouldofferanysalvation.Moreover,economicswasatthispointmovingawayfromtheclassicalsimplisticandstaticmodelsofindividualmarketsandwasrecognizingtheneedtomodeleconomicsandfinancewithinarichergeneralequilibrium,multi-sectorapproachthatchangeddynamicallyovertime.ScholarsoftheKielSchoolwereleadingthequestforabetterunderstandingofhoweconomiesevolveandgrow.TheCowlesCommissionOneofMarschak’suncannyabilitieswastoassociatehimselfwithworld-classeconomicinstitutions,oftenintheearlieststagesoftheirdevelopment.AfterafewyearsattheNewSchool,hejoinedtheCowlesCommissionforResearchinEconomicsasitsdirectorin1943.Atthattime,theCowlesCommissionresidedattheUniversityofChicago,whereheremaineduntilhemovedwiththeCommissiontoYaleUniversityin1955.TheCowlesCommissionwasagrandacademicexperiment.Itsfounder,AlfredCowlesIII,wasaprominentColoradobusinessmanandfinancialadvisorwhosefinancialinstinctsconvincedhimoftheneedtoimprovethelevelofscienceandquantitativerigorinecono-micsandfinance.Hismissionwasespeciallyrelevantfollowingtheeconomicdiscipline’scolossalinabilitytopredicttheGreatCrashin1929ortosolvetheGreatDepressionduringthe1930s.Heactuallyproducedoriginalworkontherandomwalkandlamentedwhetherstockpricescouldbeforecast.2Hewasponderingtheefficientmarkethypothesisasearlyas1933,wellbeforeEugeneFamahelpedcointheexpressionandanewfinanceparadigminthe1960s.ThegrandsonofAlfredCowles,thefounderoftheChicagoTribunenewspaper,andthesonofnewspapermanandcorporateboarddirectorAlfredCowlesJr.,CowlesIII’sinsightsandhiswealthmotivatedhimto 14TheRiseoftheQuantsformtheEconometricSocietyandfunditsjournal,Econometrica.Mostnotably,healsosetuptheCowlesCommissionforEconomicResearchin1932,firstinColoradoSprings,ColoradoandtheninChicagoin1939;itnowresidesatYaleUniversity,his1913almamater,inNewHaven,Connecticut.Firstusedasaresourcetoanalyzeandmodelstockmarketindices,theCowlesCommissionpursuedtheintegrationofmathema-ticsandstatisticsintoeconomicandfinancialtheory,especiallythroughgeneralequilibriumtheoryandeconometrics.FouryearsaftertheCowlesCommissionmovedtoChicago,Marschakwasappointeditsdirector.HeheadedtheCommissionthroughtheincrediblydynamicandprogressiveperiodto1948,atwhichpointthedirectorshippassedtoTjallingKoopmans,whowasasubsequentNobellaureate.AsitsDirector,Marschakwasresponsibleforassemblingperhapsthemostaccomplishedandvisionarygroupofeconomiststhateverworkedunderoneacademicumbrella.However,bythemid-1950s,theCowlesCommission’sprogressiveandactivistpolicyprescriptionsbegantorilethetraditionalneoclas-sicalapproachoftheUniversityofChicago’seconomicsdepartment.KoopmanspetitionedtheCowlesfamilytoallowtheCommissiontomovetoYalein1955,whereitwasrenamedtheCowlesFoundation.ScholarsassociatedwiththeCowlesCommissiondevelopedanincrediblenumberoftechniquesthatweregroundbreakingatthetime.Cowlesresearchersdevelopednewmethodssuchastheindirectleastsquaresandinstrumentalvariablemethods,thefullinformationmax-imumlikelihoodestimationmethod,andthelimitedinformationmaximumlikelihoodestimationmethod.Allofthesemethodsarenowusedextensivelyinfinance.TheCowlesCommissioncolleaguesalsopioneeredsophisticatedgen-eralequilibriummodeling,asrepresentedbytheworkofCowlesscholarsKennethArrowandGerardDebreu.BeyondKoopmans,Arrow,andDebreu,eachofwhomwerehonoredwithNobelPrizes,CowlesCommissionscholarsTrygveHaavelmo,LawrenceKlein,HarryMarkowitz,FrancoModigliani,HerbertSimon,andJamesTobinwerealllikewiserecognizedwithawardsbytheNobelCommitteeforworkinitiatedatCowles.Despitehispassionanddedicationonbehalfofthoseescapingperse-cution,Marschakremainedasought-aftercolleagueandmentor.Hewasgracious,modest,andfair-minded,andcreatedanurturingenvironmentthatallowedhisPhDstudentsineconomicstoexcel.AshecontributedfirsttotheUniversityinExileattheNewSchool,andthenhelpedtofound,direct,anddefinetheresearchagendaofthoseassembledattheCowlesCommission,Marschakwasthecommondenominatorof TheEarlyYears15anewanalyticmovementand,indeed,intheformationofdecisionsciences.Marschakwasmuchmorethanalonecoginagrowingacademicmachine.Inthevariousareasofassetchoiceandportfoliotheory,theaxiomaticapproachtodecisionsciences,themodelingofuncer-tainty,andoptimalinvestmenttheory,hemadeeitherthefirstorthesecondacademicvolley.Everhumble,though,hetypicallyusedhisinsightsandinnovationstoinsteadmotivateandnurturetheworkofotheryoungerscholars.Manyofthesescholars,influencedandinspiredbyhim,wentontomakealifetimeofcontributionstofinanceandeconomics.Atleasttwoofhisstudents,ModiglianiandMarkowitz,eventuallywonNobelPrizesfortheirworkwhileattheCowlesCommission,aswouldhisCowlescollaboratorsFriedman,Arrow,Koopmans,andDebreu. 4TheTimesJacobMarschakwasaprofoundintellectualcatalystinanumberofareasinfinance.Hisinsistenceinmathematicalrigorandanaxiomaticapproach,hisdefinitionoftheproblemofassetchoiceandportfoliotheory,andhismodelingofuncertaintyandoptimalinvestmenttheorywereatonceoriginalandprofound.Whileothersaremoretypicallycreditedwithpio-neeringworkintheseareas,therootsoftheirinnovationsand,indeed,theirearlyfinanceeducationcanbetracedbacktohim.Marschak’swildlyinnovativeandsuccessfulapproacharoseaseco-nomicsandfinancewasinastateoffluxandreinvention.Histimingwasimpeccableandhisinsightswereprofound.Hetooktheseinsightstounexpectedheightsthatredefinedeconomicsandfinanceinwaysthatstillremainrelevanttoday.TheKielSchoolBeforetheFirstWorldWar,ourunderstandingofeconomicstookoneoftwoforms.Forsome,theanalysiswasrhetoricalandstraddledtheboundarybetweenpoliticsandeconomics.ThepoliticaleconomyofKarlMarx(1818–1883),JohnStuartMill(1806–1873),DavidRicardo(1772–1823),orevenAdamSmith(1723–1790)treatedsuchtopicsastrade,economicsystems,andtheownershipofresourcesandthemeansofproductionwithunsophisticatedgraphicaltoolsandwiththestrengthofphilosophicalargumentandlogic.Alternatively,others,mostnotablyLéonWalras(1834–1910),AntoineAugustinCournot(1801–1877),FrancisYsidroEdgeworth(1845–1926),andIrvingFischer(1867–1947),enhancedourunderstandingofindividualmarketsbyintroducingtothedisciplineincreasinglysophisticatedmathematicaltools.16 TheTimes17Whiletheinsightsoftheseearlygreatmindsineconomicsremainvalidtoday,theirtheorieswerenotsufficientlyrigorousandanalytictoanswerquestionsinmodernfinance.Indeed,thepersistentrecessioninEuropeintheaftermathoftheFirstWorldWar,theunexpectedGreatCrashof1929,andthestubbornGlobalDepressionin1930demon-stratedthattheprevailingfaithinasimplisticmarketequilibriumatthemicroleveldidnottranslateintoabetterunderstandingofmorecomplexandaggregatedfinancialmarkets.ThisbreakdownoftheprevailingclassicalschoolovertheGreatDepressionarosebecauseofanumberofoversimplificationsinherentinthesimplisticclassicalmodel.First,marketsmaynotbehaveinapredictablemannerifourtoolsofpredictionarebasedonrationality,buttheactorsinmarketsdonotattimesbehaverationally.Second,anelementmayevolveinisolationinawaythatdepartsfromitsevolutionwithinabroadersystem.Specifically,acomplexsystemmayreachanequilibriumthatdivergeswildlyfromthenaturalequilibriaofeachofitspartsinisolation.Forinstance,onefinancialsecuritymaynormallyconvergetowardapredictablepriceinisolation,butthispricemightoscillateovertimewhenitsmarketiscoupledwithanother.Bythe1930s,economicluminarieswerearrivingattheconclusionthattheClassicalSchoolwasinadequatetoexplainacomplexmoderneconomy.Toremedythisinadequacy,membersoftheKielSchoolandtheViennaColloquiaacknowledgedtheneedtousemuchmoresophisticatedtoolstomodeltheinteractionsbetweenmarketsandcharacterizemarketsintheaggregate.ScholarslikeMarschakandJohnvonNeumannusedtheViennaColloquiatoexpandtheirunderstandingofeconomicsandintroducetoeconomicstoolsfromphysicsandappliedmathematics.Atthesametime,thesescholarsrealizedthattheremustemergeamuchbetterunderstandingofthemotivationsanddecisionsofagentsasdiverseasindividualsandhouseholds,firmsandorganizations,andevengovern-mentandsociety.TheKielSchoolapproachshiftedtheeconomicdebateintwoimpor-tantways.Uptothatpoint,economicsatthemacrolevelwasconsideredatrivialextensionofeconomicsofthesmall,ormicroeconomics.Inthemicroeconomicsofamarket,apricethatistoohighresultsinsupplythatexceedsdemandandareductioninthepriceuntilthesurplusesinthemarketclear.Thetrivialextensiontothemacroeconomycom-mendsthatsuchsymptomsofexcesssupplyasunemploymentshouldresultinlowerwagesandmarketclearing.Inotherwords,individual 18TheRiseoftheQuantsmarketsareeitheratorconvergingtowardequilibriumatalltimes,andsomusttheaggregationofallmarketsatthemacroeconomiclevel.TheKielSchoolalsorecognizedthataggregatesofmarketsdonotbehaveassimplisticallyasclassicallytrainedmicroeconomistsmightwish.Forinstance,anaggregatemarket,suchasastockexchange,mustacknowledgeallthesubtleinteractionsbetweenitscomponentmar-ketsforindividualsecurities.Thesecomplexintersectoralinteractionsobviatethesimplicityoftheclassicalmicroeconomicapproach.Thismoresophisticatedandnuancedapproachtomarketscreatedroomformoreelaborateunderstandingsandapproachestoeconomicgyrations.Italsocalledforgreatersophisticationinthemanagementofbalancedeconomicgrowth.MarschakemergedastheintellectualleaderofhisKielSchoolcolleaguesandbroughtnewideastoanewworld,firsttotheNewSchoolforSocialResearchinNewYorkCityandthentoacadreofyoungscholarsattheCowlesCommissionatChicagoandYale. 5TheTheoryMarschakbroughtnotjustasinglenewideatoanewworld–hebroughtforthanumberofnewapproachestovexingproblemsknownornotyetunderstood,anddefinedalifelongresearchagendaforhimselfthatwouldleaveanindeliblemarkonourunderstandingoffinance.Amuchmorenuancedapproachtomarkets,withexplicitrecognitionofthewaysinwhichonemarketaffectsanother,becameahallmarkofhiswork.Hisstrongmathematicalskillsalsoallowedhimtocontributetoamovementthatbeganinthelate1920s.SoonafterhearrivedattheNewSchool,themovementtoformalizeandmathematizeeconomicswasprogressingatfullstride.Economicsbegantoincorporatethenewquantitativetoolstoresolvethenewques-tionsthatwerebeginningtoberaised.AttheNewSchool,Marschakchampionednewtoolsofmathematicsandhelpeddevelopthefieldofeconometricsthatsoonbecamethestandarddataanalytictool.Theseminarsheorganized,firstattheNewSchoolandthenattheCowlesCommission,developedabroadacademiccommunityofunparalleledpotencyandpotential.EspeciallyatCowles,Marschakbecamethecentralfigurefortheredefinitionofeconomicsand,inturn,thedevelopmentoffinanceinthepost-Warera.Abetterunderstandingofriskanduncertaintywasatitscore.AugmentingFrankKnight’streatiseonriskanduncer-tainty,Risk,UncertaintyandProfit,1MarschakandHelenMakowerin1938usedthesubjectofmonetarytheorytointroduceuncertaintytoeconomicmodeling.2Then,inMoneyandtheTheoryofAssets,hesetthestageforwhatwouldlaterbecomeModernPortfolioTheoryfollowingthesubsequentworkofhisgraduatestudent,HarryMarkowitz.19 20TheRiseoftheQuantsThemodelingofuncertaintyFrankHynemanKnight(1885–1972)wasthefirsttodifferentiatebetweentheknownprobabilitiesthatmightaffectone’sfortuneandtheunknowableuncertaintiesthatfrustrateourdecision-making.Knowablerisk,embodiedinsuchprobabilitiesastheoddsofacointurningupheadsorcomingupredonaRoulettewheel,hasbeenthesubjectofmathematicaltreatmentsasearlyasBernoulli’sresolutionoftheStPetersburgParadoxin1738.However,untilKnightdifferentiatedbetweenriskanduncertaintyinhisclassic1921book,riskhadonlybeendescribedsuperficiallyineconomicmodels,anduncertaintyhadnotevenbeendefined,muchlessincorporated.Knightianuncertaintyisdifferentiatedfromriskinthatriskinvolvesoutcomesunknownbutwithknownprobabilitydistributions.Withknowledgeoftheseknownrisks,JohnvonNeumannandOskarMorgenstern,intheir1944magnumopusTheoryofGamesandEconomicBehavior,constructedexpectedutilitiesforwhichdecision-makerscouldmaximize.Iftheseprobabilitiesareknown,itisnotdifficulttoconstructsimpledecisionrulestooptimizereturnsinfinancialmarkets.However,aseveryfinancialadvisorwarns,pastpatternsmaynotbepredictiveoffuturereturns.Thepriceoffinancialsecuritieshaslesswell-definedunknownsandoutcomesthanmaybethecasefortheflipofacoin.Therandom,andunknownorunknowable,uncertaintiesoffinancialmarketsareamuchhigherdegreethanthepredictablevagar-iesofthetossofacoin.Knightplacedintoplayamuchmoresubtleandlesstractabledefinitionoftheunknown.Ittookanothergenerationofscholars,though,tobegintoincorporateKnightianuncertaintyintodecisiontheories.Whilesomegreatminds,suchasIrvingFischerandJohnMaynardKeynes,hadthepresciencetonotetheneedtomoreformallyincorporateuncertainty,themathe-maticalintractabilityofincorporatingtheunknownintoformalmodelsvexedscholarsthen,andstilldoestothisday,toalesserdegree.Forinstance,Keynesnotedin1937:By‘uncertain’knowledge,letmeexplain,Idonotmeanmerelytodistinguishwhatisknownforcertainfromwhatisonlyprobable.Thegameofrouletteisnotsubject,inthissense,touncertainty...ThesenseinwhichIamusingthetermisthatinwhichtheprospectofaEuropeanwarisuncertain,orthepriceofcopperandtherateofinteresttwentyyearshence...Aboutthesemattersthereisno TheTheory21scientificbasisonwhichtoformanycalculableprobabilitywhatever.Wesimplydonotknow.3KnightandKeynesarewellrememberedfortheiradditiontoourunder-standingofriskanduncertainty.However,neitherscholarprovidedthewaybywhichfinancecouldsuccessfullyincorporateriskintoourmodels.Therewasonerelativelyobscureandsuccessfulexceptiontothiscombinedinabilitytosuccessfullymodeluncertainty.Anotable,butlittleknownandtooshort-lived,scholarnamedFrankPlumptonRamsey(1903–1930)contributedtoourunderstandingofuncertaintyinanunpublishedpaperentitled“TruthandProbability.”4Ramseydescribedhowoursubjectivebeliefsaboutunknownprobabilitiesinfluenceourdecisions.Hepostulatedthattherationaldecision-makerwillalignhisorherbeliefsofunknownprobabilitiestotheconsensusbetsofimpartialbookmakers,atechniqueoftencalledtheDutchBook.Thirtylater,thegreatmindLeonard“Jimmie”Savage(1917–1971)elaboratedhisconceptintoanaxiomaticapproachtodecision-makingunderuncertaintyusingargu-mentsremarkablysimilartoRamsey’slogic.TheconceptsofRamseyandSavagealsoformedthebasisforthetheoryofBayesianstatisticsandareimportantinmanyaspectsoffinancialdecision-making.Marschak’sgreatinsightWhileRamseycreatedandSavagebroadenedthelogicallandscapefortheinclusionofuncertaintyintodecision-making,itwasnotpossibletoincorporatetheirlogicuntilthefinancedisciplinecoulddevelopactualmeasuresofuncertainty.Ofcourse,modernfinancialanalysisdependscruciallyeventodayonsuchamethodologytomeasureuncertainty.Muchofwhatisnowstandardinthemeasurementoffinancialuncer-taintyoriginatedwithapaperbyMarschakin1938.Hewasthefirsttodescribeandadvocatehowtocombineassetvaluationwithuncertainty.Theapproachhedevelopedallowedustoaugmentourorderingofpreferredoutcomesinacertainworldwithameasureofuncertaintyintherealworld.Bythe1930s,scholarswerebeginningtodescribehowtoincorporateuncertaintyintodecision-makingandassetmanagement.Forinstance,in1935,NobellaureateSirJohnHicksnoted:Byinvestingonlyaproportionoftotalassetsinriskyenterprises,andinvestingtheremainderinwayswhichareconsideredmoresafe,it 22TheRiseoftheQuantswillbepossiblefortheindividualtoadjusthiswholerisksituationtothatwhichhemostprefers,morecloselythanhecoulddobyinvest-inginanysingleenterprise.5Hicks’approachcommendedanumberoffeaturesforanemergingmodelofassetpricing.Heanticipatedmodelsthatincludearisk-freereturnrf,ariskyfinancialasset,andasetofpreferencesthatincorporatebothreturnandrisk.By1938,andsixyearsbeforevonNeumannandMorgensternhadestablishedtheexpectedutilityhypothesisintheir1944bookTheoryofGamesandEconomicBehavior,Marschakproposedandexploredaordi-naltheoryofdecision-makingunderuncertainty.6Hewasalsothefirsttoproposethatthesedecisionsbemadeoverthemeanandthevariance(orstandarddeviation)oftheassetvalue.Marschak’sworktoformulatepreferencesinthenow-familiarmean-variancespaceformedthebasisformuchoffinancialassetpricingtheory.Hedidsoinhis1950paperentitled“MoneyandtheTheoryofAssets.”HeformalizedKeynes’conceptofliquiditypreferencesinhisobservation:[I]ntheactualuncertainworld,thefutureproductionsituation[technique,weather,etc.]andfuturepricesarenotknown…inthemindoftheproducer,toeachcombinationofassetstherecorrespondsoneandonlyonen-dimensionalsetofyieldcombinations…[T]oeachcombinationofassetstherecor-respondsin[thedecision-maker’s]mindandn-dimensionaljoint-frequencydistributionoftheyields[offinancialassetsandcommodities].Thus,insteadofassuminganindividualwhothinksheknowsthefutureeventsweassumeanindividualwhothinksheknowstheprobabilities[emphasisadded]offutureevents.Wemaycallthissituationthesituationofagameofchance,andconsideritasabetteralthoughstillincompleteapproximationtoreality…thantheusualassumptionthatpeoplebelievethemselvestobeprophets…7Marschak’srecognitionoftheinterplaybetweenwhatpeopleknowandbelieveandthedecisionstheymakecamewellbeforevonNeumannandMorgensternframedtheirexpectedutilityhypothesisunderrisk,Savageoutlinedanaxiomaticapproachtodecision-makingundersub-jectiveuncertainty,orKennethArrowdescribeddecision-makingundervariousstatesofnatureinfinancialmarkets.Marschakhadframedthe TheTheory23problemandindicatedthedirectionforitssolution.Mostsignificantlyforfinancialpricingtheory,hewenton:[W]ereinterpret[thedecisionvariables]tomeannotfutureyieldsbutparameters[e.g.,momentsandjointmoments]ofthejoint-frequencydistributionoffutureyields.Thus,xmaybeinterpretedasthemathematicalexpectationoffirstyear’smeatconsumption,ymaybeitsstandarddeviation,zmaybethecorrelationcoeffi-cientbetweenmeatandsaltconsumption…etc.…Itissufficientlyrealistic,however,toconfineourselves,foreach[return]totwoparametersonly:themathematicalexpectation…andthecoefficientofvariation[“risk”].8Marschakproposedasimpleapproachtotheconsiderationoftheinterplaybetweenreturnandriskbyconfiningitsdescriptiontofirstmoments,knownasmeans,andsecondmomentsofreturns,labeledvariancesandcovariances.Healsoproposedhowthevariationofoneassetmayaffectanotherthroughtheircovariancesandtheircoefficientofvariation.MarschakalsoestablishedanewsetoftermstodescribethegeneralequilibriumofinterrelatedmarketsunderuncertaintywellbeforeArrowandDebreusubsequentlyadoptedhisvocabulary.Finally,hismean-varianceapproachemergedasthebasisofModernPortfolioTheoryatthehandsofhisPhDsuperviseeandsubsequentNobelPrizewinner,HarryMarkowitz.Markowitzlaterprofessedthathewasunfamiliarwiththisgroundbreakingworkofhissupervisor.Marschak’s1950paperalsoprecededtheworkofSavageonanaxi-omaticapproachtoutilityundersubjectiveuncertainty.Inapaperentitled“RationalBehavior,UncertainProspects,andMeasurableUtility,”Marschakexhibitedcharacteristicclarityandprescienceintheemergingtheoryofassetpricing.9Inthiswork,hemodifiedthevonNeumannandMorgensternexpectedutilityhypothesistoincludesubjectiveprobabilities.Indoingso,healsograciouslytippedhishatinafootnotetohisCowlesCommissioncolleaguesArrowandSavagefortheircommentsonhismanuscript.Inturn,thesetwogreatmindswouldtakestillfurtherMarschak’sdesiretoincorporateuncertaintyintomodelsoffinance.Inhispaper,Marschakreturnedtothemean-varianceapproachbynotingthat“theaverageamountsofgoodsarenotalonerelevanttotheman’sdecision,”andheanticipatedModernPortfolioTheorythroughcommentson“theadvantagesofdiversification.”10 24TheRiseoftheQuantsInthesameyear,Marschakproducedaseriesoflecturesonutilityandsubjectiveprobability.11Theselecturesdescribedvariousstatesofnatureinanuncertainworld,inmuchthesamewayasArrowwouldlaterincorporateinhisNobelPrize-winningworkontheexistenceofmarketgeneralequilibrium,anddescribedanapproachtotheexpectedutilityhypothesisthatwouldlaterbeemployedinMarkowitz’sNobelPrize-winningformulationofModernPortfolioTheory.HewasalsopavingthewayforhisCowlesCommissioncolleague,LeonardJimmieSavage,toproducehisseminalwork,TheFoundationsofStatistics,in1954.Thisworkestablishedasetofaxiomsbywhichfinancialmarketscanincorporateourhumansubjectivesenseofprobabilities.Evergraceful,inhislecturesMarschakevennotedtheimportantworkofFrankPlumptonRamseyaquarterofacenturyearlierandthepossi-bilitythatpersonalprobabilitiescouldbededucedbasedontheactionsofdecision-makers.Hewrote:Theprobabilitiesonwhichthesubjectbaseshisactionneednotbeidenticalwithsomeobjectivepropertiesofchancedevices(cards,dice)whichtheexperimenteruses.ThiswasobservedbytheEnglishmathematicianandlogician,F.P.Ramsey.Heshowsthatmanifestdecisionscanbethoughtofasrevealingboththesubject’sprobabili-tiesandutilities.12Marschak’sworkwasgroundbreakinginanumberofwaysandanumberoffieldsofparticularimportancetofinancetheory.Hissimpleobservationandrecommendationthatweextendthetraditionalindividualchoicemodeltoincludethevarianceofassetsandconsumptiongoodsaswellastheirmeanswasunprecedented.ItwasaprofoundextensionofKeynes’prescriptionthatmoney,assets,anduncertaintymustallbeincludedinourmodels,andhenceincorporatedintoourfundamentalapproachtoassetpricing.Marschak’scontemporaryKennethArrownoted:13IfwetaketheKeynesianconstructionseriously,thatis,asofaworldwithapastaswellasafutureandinwhichcontractsaremadeintermsofmoney,noequilibriummayexist...Fromallthis,aswellasfromourexistencediscussions,weconcludethattheKeynesianrevolutioncannotbeunderstoodifproperaccountisnottakenofthepowerfulinfluenceexertedbythefutureandthepastonthepresentandbythelargemodificationsthatmustbeintroducedintobothvaluetheoryandstabilityanalysis,iftherequisitefuturemarketsaremissing. TheTheory25Marschakestablishedafeasiblemethodologytodojustthat–totakeintoaccounttheeffectofuncertaintyonfinancialdecision-making.Bydoingso,heestablishedtheanalyticframeworkofthemean-varianceapproachthatsubsequentgreatmindsinpricinganalysishaveusedalmostuniver-sallyeversince.FundamentalPricingTheoryhadarrived.Themean-varianceapproachtoutilitytheoryWecandemonstratehowthismean-varianceapproachtranslateswealthintoutility.Whileweoftenattributethemostcommonexposi-tiontothederivationofutilityfromuncertainwealthtotheworkofHarryMarkowitz,Marschak’sstudent,andJamesTobin,hiscolleagueattheCowlesCommission,Marschakmotivatedthisfoundation.ConsiderthedecisionofaninvestorwhomustpayafeeFoutofawealthWinanticipationofanuncertainreturnR˜overtherisk-freereturn.Weknowthattheseuncertainlevelsofwealthgiverisetotheutilitythatmotivatestheinvestor’sdecisions.Then,utilitycanbewrittenas:U(WFR˜).Weretheinvestorrisk-neutral,utilitywouldbelinearlyproportionaltotheuncertainreturn-augmentedwealth.Therisk-neutralinvestorwouldremainunconcernedaboutsymmetricvariationsoftherandomreturnaboutitsmean.Wecandemonstratetheresultonexpectedutilityforthepatternofreturnsbyrepresentingutilityasaninfiniteseries.ATaylor’sseriesexpansiontakesintoaccountthedeviationofavariableanditseffectonthedependentvariablethroughthevariousderivativesoftherelationshipbetweenthetwovariables.Inthecaseofutility,aTaylor’sseriesexpansionmeasureshowdeviationsinwealthaffectsutilitythroughitsslopeandthecurvatureofutility.Itiscalculatedasfollows:U(W˜)U(WFE(R˜))/0!U'(WFE(R˜))(RE(R))/1!U"(WFE(R˜))(RE(R))2/2!U"'(WFE(R˜))(RE(R))3/3!...Ifthisinfiniteserieswerecalculatedforaninfinitenumberofterms,theseriesofmeans,first,second,third,andsoonderivativeswould 26TheRiseoftheQuantspreciselydeterminethevalueofutilityforanydeviationarisingfromtherandomreturnR.However,subsequenttermsgenerallybecomelesssignificantforfivereasons.First,noticethateachsubsequenttermincorporatesahigherlevelderivativeofutility.Ifutilityroselinearlywithincome,i.e.,U’()constant>0,thereisnocurvatureoftheutilitycurveandhencethesecondderivativeiszero.Alternatively,ifutilityisincreasingbutatasteadilydecliningrateofincrease,thenthesecondderivativeU’’()isconstantandnegative,whilethethirdderivativeU’’’()iszero.Thesethird-orderandhighereffectsarearguablyoflesssignificanceindefininghowthetranslationbetweenincomeandutilitydepartfromlinearity.Inaddition,thesehigherordertermsarezeroifweacceptthecommonlyassumedquadraticutilityfunction.Second,noticethateachsubsequenttermisdividedbyafactorialthatgrowsrapidly.Thefirsttermisdividedby0!,or1,andthesecondtermby1!,or1,whilethethirdtermisdividedby2!,or2.However,thefourthtermisdividedby3!,or6,andthefifthby4!,or24,etc.Thesefactorialsrapidlydiminishtheimportanceofhigherorderterms.Third,eachtermcontainsanexpressionofthedepartureoftheran-domreturnfromitsmean,firsttothe0power,thentothe1stpower,thentothe2ndpower,etc.Ifthesedeviationsoftherandomvariablesfromtheirmeansarecomparativelysmall,thenthesedeviationstoapowerarerelativelyevensmalleryet.Fourth,whenthepowertermsareodd,andtherandomvariableissymmetricaboutitsmean,thesehighertermscanceloutasthedevia-tioninonedirectioncounteractsthedeviationintheother.Finally,oneofthemostcommondistributionsinnatureisthenor-maldistribution.Itcanbeeasilydemonstratedthatsuchadistributioncanbedescribedcompletelybyonlyitsfirstandsecondmoments,oritsmeanandvariance.Ifoneiswillingtoassumethatinvestmentreturnsaredistributedaccordingtothiscommonnormaldistribution,theignoringofhigherorderdistributionsisnotinappropriate.Mathematiciansandphysicistscallweighteddeviationsfromacen-tralmeanvalueasthefirstmoment,suchdeviationssquaredfromthecentralvalueasthesecondmoment,etc.Usingthismathematicalvocabulary,themostimportantmeasuresoftheincreaseinutilityaris-ingfromtherandomcomponentofwealthistherateofincreaseofutilitymultipliedbythefirstmoment,orthemeanvalueoftherandomreturn,andonehalfofthesecondderivativemultipliedbythesecondmoment,alsoknownasthevarianceoftherandomreturn. TheTheory27Thesecondmomentabovecanbesimplifiedasfollows:E(RE(R))2E(R2)E(R)2Thiscalculationistypicallycalledthevarianceofreturns,ordesignateds2.Itisalsolabeledthesigma-squaredorthemeansquared.RWhenJacobMarschakproposedthatwecharacterizetherelationshipbetweeninvestmentreturnsandutilityasmostsignificantlyrepresentedbytheinvestmentreturn’sfirstandsecondmoments,hewasofferingacompactwayforfinancetheoristsandpractitionerstomeasuretheimpactofvariousdistributionsofreturns.Twoinvestmentswithequalreturnsbutwithdifferentdistributionsofthesereturnsarenotequalintheireffectonaninvestor’sutility.Becausethevarianceisalwaysapositivenumber,butenterstheTaylor’sseriescalculationasaproductwiththe(negative)secondderivativeU’’,highervarianceultimatelysubtractsfromtheresultingutility.Highvarianceisameasureofgreaterreturndeviationsfromthemean,orgreateruncertainty.Thisuncer-tainty,ascharacterizedbythevariance,detractsfromutility.Marschakproposedthatwemeasureinvestmentsbothbytheirexpectedreturnsaswellasbytheirhistoricalvarianceforthatreason.Histheoryofutil-ityunderuncertaintythenestablishedthelinkbetweenthemeanandvarianceofreturnsandtheutilityofadecision-maker.Infact,itwasMarschak’scolleaguesArrow,Tobin,Markowitz,andotherswhomorefullydescribedandextendedhissimplecharacteriza-tionofinvestment.Evenashetookgreatpainstoacknowledgeandcelebratetheworkofthosewhocamebeforehim,Marschakquietlymotivatedandnurturedothersinamosthumblemanner,withoutanyexpectationofcreditornotoriety.Suchintellectualmodestyandgener-ositymayhavebeenhismostgraciousandendearingquality. 6ApplicationsJacobMarschakproposedasimpletranslationbetweenfinanceandeconomics.Iffinancialvariablescanbedescribedbytheirmeanandvariance,then,undercertainassumptions,thesemeasurescanbedirectlyincorporatedintomeasuresofutilityandhenceacttomotivatethefinancialchoicesofhumandecision-makers.Marschakknewthatsuchasimplificationwouldpermitamuchmoretractableapproachtothedecisionsciences,justasthemeanandvarianceapproachallowedmanyphysicalprocessestobedescribedbythelawsofthermodynamics.Certainly,higherordertermsbeyondthefirstandsecondmomentsonboththefinancesideandtheutilitysidecanbeimportantinsomecircum-stances.However,themeanandvarianceisrelevantinallcircumstances.Marschakthementorinspiredstudentsandcolleaguesaliketostretchthismethodologyasfaraspossible.Forinstance,wecanusethetech-niquetodriveameasureofriskaversionamonginvestors.Toseethis,letusdetermineameasureofthecostofrisk.Letusdenotethisriskpenaltyasp.Then,theutilityadecision-makercanexpectfromwealthandanuncertainreturnisequivalenttotheutilityfromthewealthandtheexpectationofthemeanreturn,netoftheriskpenaltyp.Mathematically:EU(WR)U(WE(R)p)TakingaTaylor’sseriesexpansionoftheleft-andright-handside,andneglectinghigherorderterms,gives:U(WE(R))U'(RE(R))U"(RE(R))2/2!=U(WE(R))U'p28 Applications29Embeddedinthisexpressionisthemeasureofvarianceofreturns(R˜E(R˜))2.Wecansimplifyandsolvefortheriskpremiumptofind:p(1/2)(U"/U')Var(R)VariousmeasuresofriskaversionMarschak’scontemporariesKennethArrow1andJohnPratt2proposedsuchameasureforthecalculationofariskpremium.Inhis1965paper,Prattdenotedtheratioofthecurvaturetotheslopeoftheutilityfunc-tionU’’/U’asameasureofabsoluteriskaversion.However,henotedthathisresultswerealsocontainedwithinseminarsgivenayearbeforebyArrow.Infact,foradozenyearsfrom1952to1964,Arrowhadpublishedseminalworkonthefunctioningofsecuritiesmarketsasthewaysinwhichinvestorscouldusefinancialinstrumentstoreduceuncertainty.Inhis1964paper,heusedtheconceptofriskaversiontoexploretheoptimalinvestmentstrategyforinvestorswhocouldholdcashoranactuariallyfairsecurity.Heshowedthataninvestor’soptimalstrategydependscriticallyonhisorherlevelofriskaversion.Healsodemon-stratedthattheinvestorwillholdlessincashandpurchasemoreoftheriskyassetifthelevelofriskaversionislower.Whileheapproachedtheproblemfromtheinvestor’sperspective,hisconclusionsdovetailednicelywiththoseofPratt.Hence,wenowclassifyvariationsofmeasuresofriskaversionasflowingfromtheArrow-Prattmeasure.Themorerisk-averse,bythismeasure,themorethedecision-makerwillbewillingtopaythepremiumptoavoidtheriskofaninvestment.Iftheinvestorhasdiminishingmarginalutilityoranabsoluteaversiontowardrisk,thesecondderivativeU’’isnegativeandtheinvestorwouldbewillingtopayapositivepremiumtoavoidtherisk.Relatinghisorherdegreeofriskaversiontothevarianceoftheriskyactivitygivestheamountthedecision-makeriswillingtopaytoavoidtherisk.Ontheotherhand,onewhoisrisk-lovinghasasecondderivativeofutilityU’’thatispositiveandhenceiswillingtopayapremiumtotakearisk.Thisresulthelpsexplainwhygamblerswillpay$1.00toearnameanof$0.97orless,onaverage,ingamblinghallsthattakeatleast3percentofeachgamefor“thehouse.”ThisArrow-Prattmeasureofriskaversionisasimpleandelegantwaytobridgetheobservablesoffinancewiththedecisionsofhumansmotivatedinwaysmorecomplexthanthesimplereturnonfinancialinvestments.Theintuitiveandwidelyacceptedprincipleofdiminishing 30TheRiseoftheQuantsmarginalutility,combinedwiththeeasy-to-calculatehistoricalmeasuresofasecurity’svariability,yieldsameasureofadecision-maker’swill-ingnesstopaytoavoidthevolatility.Thisriskpremiumbehavesqualitativelyinwaysthatreinforceourintuition.However,thisintuitivelyappealingconstructstillpresentssomeproblems.First,measuresofpastvariabilitymaynotberepresentativeoffuturevolatility.Second,utilityremainsimmeasurable,evenifitsproperties–ifthesecouldbemeasured–havebeenwelldescribed.Finally,utilitytheorypredictsthatone’smeasureofriskaversionisnotaconstant.Becausetheslopeandpossiblythecurvatureofaninvestor’sutilityfunctionshoulddependonincome,sowouldboththemeasureofriskaversionandofone’sriskpremium.Indeed,largeswingsinwealthduetoequallylargevariationsinthereturnonasiz-ableinvestmentcancauseaninvestortoswingtodramaticallydifferentpositionsonriskaversion.AcursoryinspectionoftheriskpremiumpalsoshowsthattheriskpremiumtoavoidfinancialvolatilitydependsonthecurvatureoftheutilityfunctionU’’relativetoitsslope.Itiswidelyaccepted,butisnotbeyonddispute,thatinvestorshaveadecreasingmarginalutilityU’aswealthincreases.IfthemarginalutilityincreaseswithwealthmorethandoesthesecondderivativeU’’,thenthepremiumaninvestorwouldbewillingtopaytoavoidriskshouldrise.However,thewealthpartitionedtoriskyassetswillalsotypicallyincreasewithincome.Asaconsequence,abetterrelativemeasureofriskaversionmaybetheriskpremiumponewouldbewillingtopayasashareofwealth.Theresultingcalculationofwealth-adjustedrelativepreferencestowardriskavoidanceisthen:prelativew(U"/U')Var(R)/2Therecouldthenbesixpossibleregimesofriskaversion.Absoluteriskaversioncouldincrease,remainconstant,ordecreasewithincomeandassets,ascouldrelativeriskaversion.However,someofthesepos-sibilitiesdefyintuition.Increasingabsoluteriskaversionrequiresthat,aswealthincreases,anindividualchoosestoholdfewerfundsinriskyassets.Decreasingabsoluteriskaversionbetterfitsobservedbehavior.Aswealthincreases,morewealthisheldinriskyassets.Measuresofrelativeriskaversionarealsomoreorlessappealingtointuition.Increasingrelativeriskaversionpredictsthatoneholdsasmallerproportionofwealthinriskyassetsaswealthincreases.Moreappealingisthenotionofdecreasingrelativeriskaversion,inwhich, Applications31aswealthincreases,aninvestorholdsalargerpercentageofwealthinriskyassets.Anassumptionofdecreasingrelativeriskaversionhassomemacro-financialimplications.Inabullmarketoraboomingeconomy,thewealthofhouseholdsisincreasedbecausegrowthiscapitalizedinhighersecuritiesandhousingassetprices.Thewealthincreasetranslatesintoanincreasedwillingnesstoinvestinriskyassetsastherequiredrelativeriskpremiumsdecline.Theincreasinglyfavorableattitudetowardriskcontributestoaspeculativebubbleandothercharacteristicsofabullmarket.Ontheotherhand,abearmarketanditsconcomitantreductioninwealthengendersmorecautiousbehaviorandagreaterwillingnesstopaytoprotectagainstriskasashareofwealth.Thisincreaseincautious-nessreducesdemandforriskyassetsandextendsthebearmarketandeconomicdownturnstillfurther.Boomsandbusts,andbullandbearmarketsare,atleastpartially,aconsequenceofmicroeconomicbehav-iorandmicrofinancialdecisions.Atthemicro-level,too,theaxiomsofriskaversioncanproducesomesurprisingandperhapscounter-intuitiveresults.SteveRosstookacloselookatthesemeasuresofabsoluteandrelativeriskaversionandconcludedthattheyproducesomeresultsthatdefyintuitionattimes.3Considernotoneinvestorattwodifferenttimes,buttwoinvestorsofequalwealthbutdifferentlevelsofriskaversionconfrontinganidenticalchoiceofinvest-mentsorgambles.Rossshowedthatthemorerisk-averseinvestormaynonethelesschoosemoreoftheriskierassetinsomecircumstances.Healsoshowedthatalessrisk-averseinvestormayalsobewillingtopayahigherriskpremium.Thesecounter-intuitiveresultsaredrivenbyplausi-bledifferencesintheshapeofeachinvestors’utilitycurves.Rossalsopointedouttheinherentweaknessinanysuchmeasuredrivenbyunmeasurableutilityfunctions.Asanintuitivetool,andasatoolfortherationaleofriskpremiumsandthemean-varianceapproachtopricingassets,riskaversionishelpful.However,unlessutilityfunc-tionscanbemeasuredandcalculated,theoreticalcoefficientsofriskaversionhavenopracticalapplication.TheotherAchilles’heeloftheriskaversionmeasurementbridgetoriskpremiumsandassetpricingisthatitreliesdirectlyontheexpectedutilityapproachasdevelopedbyJohnvonNeumannandOskarMorgensternin1944,andgeneralizedbyLeonardJimmieSavagein1954.Onstrongerfoundationaretheprojectandportfolioinvestmentdecisionsoffirms.Unlikethenebulousutilityfunctionsoftheirhouseholdcounterparts,corporationsmeasuretheirsuccessbyprofits 32TheRiseoftheQuantsdenominatedineasy-to-measurecurrency.Thesecorporatefinancedecisionsmaybebasedonexternalinvestmentsinotherfirms,oruponthevariousprojectsthatareproposedwithinthefirm.Eachcomeswithrisksthatmaypervadetheorganization,theindustrysector,orthemacroeconomy.Evenwithinafirm,theserisksmayimposeotherrisksonthefirmwellbeyondthescopeoftheproject.Forverylargeprojects,thesolvencyofthefirmcouldevenbechallenged.Thesearethetypesofriskswithwhichcorporatefinanciersmustcontend.However,espe-ciallyforcomparativelysmallchangesincorporatefortunes,profitswillbeaffectedsomewhatlinearlywiththeupsideanddownsiderisksofcorporateopportunities.Consequently,firmsaretypicallyassumedtonotsufferthenon-linearitiesofhouseholdswhofacediminishingmarginalreturnsarisingfromutilityfunctionsthataretypicallynon-linear.Similarly,banksdonotneedtotakesuchnon-linearitiesandaversionsintoaccountsolongastheyarewelldistancedfrominsolvencyandtheirportfolioofposi-tionscontainsadiversifiedmixofwinnersandlosers.However,theownersoftheserisk-neutralcorporationsarehumans.Whileinvestorscanusediversificationtoensuretheirportfoliostakebestadvantageofthecovariancesbetweentheunderlyingassets,theypricesecuritiesbasedonhowtheyaffecttheinvestor’squalityoflife.Hence,investorsremainconcernedaboutriskaversionandthemeanandvarianceofthesecuritiesthatconstitutetheirportfolios.ThescientificanalysisofsecuritiespricingBy1950,Marschakhadintroducedtofinancetheoryamethodtopricerisk,throughhismean-varianceapproach.Muchlater,however,wediscoveredthathewasnotthefirsttoofferameasureofthecostofvolatilityoffinancialinstruments.Attheturnofthetwentiethcentury,theFrenchmathematicianLouisBachelier(1870–1946)pro-ducedaPhDthesiswiththetitle“TheTheoryofSpeculation.”Inthisrevolutionarythesis,BachelierwasthefirsttoapplythemathematicalmodelofBrownianmotiontothemovementofsecurityprices.HedidsofiveyearsbeforeAlbertEinsteinappliedthesamemodeltothemove-mentofsmallparticles.EinsteinandBachelierbothnotedthat,beyondacommondriftele-ment,themovementofaparticleorastockfromoneperiodtothenextisuncorrelated.Wenowknowthisphenomenonastherandomwalk.WereturntoBachelier’smodellaterinourdiscussionofoptionspricingtheory,andmorefullyinthenextvolumeofourserieson Applications33therandomwalkandtheefficientmarkethypothesis.Withoutfullyanticipatingtheprofoundimpact,henonethelesscreatedawaveofscientificinnovationinfinance.Otherscontinuedthetraditionthathehelpedtoestablish.InBritain,theFinancialReviewofReviewsbegananalyzingthepricesandvolatil-ityofvariousstocksandbonds.TheprecursorsoftheratingsagenciesStandard&Poor’s,Fitch,andMoody’sbeganresearchingandanalyzingthefundamentalprofitabilityofcompaniesasawayofassuringinves-torsthatcorporatebondsweresound.Infact,USbanksduringthe1910sand1920sremainedlessregulatedbyastill-nascentFederalReserveandhadinvestedheavilyinsecuritiesofdubioussoundness.Followingthebankfailuresofthe1920sandthe1930s,theFederalReserverequiredbankstoinvestonlyinAAA-ratedbondsasdeterminedbythesethreeratingsagencies.Anindustryforthescientificquantificationofriskwasborn,aswasanear-monopolyinthegrantingofthesefirmsastheonlyapprovedratingsagencies.Inthecontextofincreasedawarenessoftheneedforgreaterscienceinfinance,bythe1930sMarschak’svisionofmeasurementoffinancialsecuritiesbasedontheirmeanandvariancewasjustrightforthetimes.IntheaftermathoftheRoaring(andperhapsdecadent)Twenties,andthetroubledThirties,investmentbecameviewedasaterriblegambleratherthanathoughtfulopportunitytosecureafuture.Ittookalmost25years,fromthelate1920stothemid-1950s,forthestockmarkettoreturntoitsRoaringTwentiespeakandformarketconfidencetoreturn.Beforeitcould,scientificallybaseddecision-makinghadtoreplacetheemotionoflesssophisticatedmarkets.AnanalysisofnecessityOverthisturbulentperiod,achemistrygraduateandinvestmentadvi-sornamedJohnBurrWilliamswentbacktoHarvardtocompleteaPhDandresearchandwriteabookonthescienceofinvestment.Heappliedscientificprinciplestosecuritiespricinganddevelopedwhatwenowknowasfundamentalsanalysis,inwhichthevalueofasecurityisbasedonitsdiscountedflowoffutureprofits.CombinedwithMarschak’srecognitionthatvariability,inadditiontoreturns,isnecessarytounder-standsecuritiesprices,withWilliams’TheTheoryofInvestmentValue,4thetheoryoffinancewasbeginningtotakeshape.BythetimeWilliamswrotehistheory,inthemidstofthestockmarketlullofthe1930s,themostsophisticatedandacademicanalystswerealreadyadoptingsomemeasuresofmarketvolatilityintotheir 34TheRiseoftheQuantsfinancedecision-making.Forinstance,in1909,HenryLowenfeldcommented:ItissignificanttoseehowentirelyalltherestoftheGeographicallyDistributedstocksdifferintheirpricemovementsfromtheBritishstock.Itisthisindividualityofmovementonthepartofeachsecurity,includedinawell-distributedInvestmentList,whichensuresthefirstgreatessentialofsuccessfulinvestment,namely,CapitalStability.5Notonlywereboththeexpectedmeanandvarianceofreturnsofastocksignificantdeterminantsofitsprice;howonestockvariesincor-relationwithanotheralsobecamepartofthemix.WhileMarschakfirstrecognizedthescientificsignificanceofthesefirstandsecondmoments,itwashisgraduatestudentHarryMarkowitzwhowouldtaketheseideasstillfurtherinhisconstructionofoptimalinvestmentportfoliosthattakeadvantageofthewaysinwhichthesecondmomentsbetweensecurities,orcovariances,canbeusedtotheinvestor’sadvantageinreducingoverallportfoliorisk.Markowitz’sModernPortfolioTheorywasdescribedmorefullyinthesecondvolumeofthisseries6andrevolutionizedfinance.WiththeadoptionofModernPortfolioTheoryasfinance’smostfundamentaltool,mean-varianceanalysis,anditscoincidentassumptionofquadraticutility,forwhichthirdandhighermomentsareirrelevant,wasfirmlyestablishedinthefinanceliterature.Inremainsfirmlyentrenchedtoday.Whilesomemayquarrelovertheperfectionoftheseassumptions,themean-varianceapproachMarschakdevelopedforsecuritiespricingremainsimportantnonetheless,andcontinuestobethemostcommonlyappliedandintuitivelyunderstoodpracticaltooloffinancialanalysis. 7LifeandLegacyTodaythereisperhapsnopersonwhowasattheepicenterofandmoresubstantiallyinfluencedthepost-SecondWorldWarfinancialrevolutionwhoislesswellknownthanJacobMarschak.However,thetestimoniesofgreatmindsinfinance,fromMiltonFriedmantoKennethArrow,LeonardJimmieSavage,andHarryMarkowitz,demonstratehislastinglegacythroughacombinationofhisideasandhisgenerousmentor-ingofthesefutureNobelPrizewinners.AndeachhaspaidtributetoMarschakasamajorforceinmotivatingtheirNobelPrize-caliberwork.FollowingMarschak’smostproductiveyears,firstatColumbiacon-ductingstatisticalresearchinthewareffortandthenasDirectoroftheCowlesFoundationatChicago,theFoundationwasmovedtoYaleinNewHaven.Withthismove,MarschakalsoacceptedapositionasProfessorofEconomicsatYale.HeheldthispositionuntilhewasrecruitedbytheeconomicsdepartmentattheUniversityofCalifornia,LosAngeles(UCLA)in1960.HeremainedatUCLAfortherestofhisacademiccareer.Inadditiontohisworkonthemean-varianceapproachtosecuritiespricing,Marschakwasaprofoundintellectualcatalystinanumberofotherareasinfinance.Hisinsistenceonmathematicalrigorandanaxiomaticapproachforthefundamentalsoffinance,hisdefinitionoftheproblemofassetchoiceandportfoliotheory,andhismodelingofuncertaintyandoptimalinvestmenttheorywereatonceoriginalandprofound.Whileothersaremoretypicallycreditedwithpioneeringworkintheseareas,therootsoftheirinnovationsand,indeed,theirearlyfinanceeducationcanbetracedbacktoMarschak.WhileMarschakworkedtointerjectgreaterscienceandstatisticsintofinance,hewasactuallyaguidinghandforthefirstcoupleofgenera-tionsoffinancialtheory.Wehavedocumentedhowheadvocatedfor35 36TheRiseoftheQuantsamean-varianceapproachandhowheencouragedhisstudentHarryMarkowitztodolikewise.TheyoungMarkowitzwassearchingforathesistopic,anditwasMarshak,hissupervisor,whoencouragedhimtotakeupthemeanandvarianceapproach.HeinfluencedMiltonFriedmanandLeonardJimmieSavageintheirworkonriskaversion,andmentoredKennethArrowonhistheoryofgeneralequilibriuminsecuritiesmarkets.Healsoinfluencedanotherstudent,RoyRadner,inhisgroundbreakingincorporationofinformationanduncertaintyingeneralequilibriumtheory.ContributionstoeconometricsMarschak’sprofoundinfluencearoseinlargepartbecauseofhisworkinestablishingstatisticsandeconometricsastoolsineconomicsandfinance.HebeganthisworkwhileattheNewSchoolandcementedhiscontributionandnetworkwhileattheCowlesCommission.WhileatCowles,heworkedtodevelopabridgebetweenstatisticsandeconomicsthathehadbegunwhileinNewYorkattheNewSchoolandtheNationalBureauofEconomicResearch.Hisinfluenceovertheincorporationofstatisticsintoeconomicswasperhapswithoutparallelinthisperiodduringthe1940s,whenhecreatedabridgebetweenestablishedstatisticaltechniquesandusefulmethodologiesindecision-making.Marschak’scontributiontothedevelopmentofthefieldofeconome-tricswasequallyprofound.Econometricsisthetoolofchoiceinthedeterminationofpatternsindata.Ifonedoesnotknowthedeterministicrelationshipthatgeneratesdata,econometricscanbeusedbothtoidentifystatisticalpatternsandtomeasurejusthowwellananalyticmodelcanreplicateobserveddata.Whilethetoolsofeconometricsinitiallycamefrommathematicsandstatistics,theyneededtobeadaptedandexpandedtotheuniqueneedsofdecisionsciencessuchaseconomicsandfinance.Toassistintheestablishmentofthisnewbranchineconomicsandfinance,hehelpedfoundtheEconometricSocietyandwaslaterelecteditspresident.Ofcourse,iftheworldwerenotfraughtwithuncertainties,correla-tionsandcausalitywithinthedatawouldbeamuchsimplermattertoinvestigate.However,uncertainty,incompleteinformation,random-ness,andperhapsevennon-rationalityareallinevitablehallmarksofhumandecision-making.Todelvemoredeeplyintothecharac-terizationofdecision-making,Marschakhadtofirstparameterizethedata,ashedidwithhismean-varianceapproach,andthenconstruct LifeandLegacy37modelsofrationaldecision-makingwithinaparametricmodelofuncertainty.Marschakwasalsoparticularlyinterestedintheconsistencyofhumandecision-making.Certainly,itisdifficulttoarguethathumansmakerationaldecisionsifonecannotverifywhethertheirdecisionsareconsistentovertime.However,anobserverofhumandecisionscannotknowallthevariousfactorsthatinfluencesuchdecisions.Assuch,itisdifficulttodetermineconsistencythroughobservation.Inthislight,Marschak’sworkonthedeterminationofconsistencywasgroundbreak-inginitstime.TheoryofinformationMarschakwasanearlydeveloperofthetheoryofinformationwellbeforetherewasabroadappreciationoftheimportanceofmodelinginformation.Inthelate1940sandearly1950s,communicationsengi-neerswereworkingonthetheoreticallimitsofinformation-carryingcapacities.SuchtheoristsasWilliamShannonandJohnvonNeumannweredoingsoatthecuspofthecreationofcomputersandthedevelop-mentofnewmethodsforwirelesscommunication.Theydemonstratedthatthetheoreticalabilityforsystemstocarryandconveyinformationfollowscertainscientificandstatisticalprinciples.However,whiletheirapproachwasdesignedtoremoverandomnessanduncertaintyfrominformationsystems,Marschakwasinterestedinaparallelproblem.Hewantedtoknowhowdecisionsaremadeinuncertainenvironments.Hedifferentiatedbetweenthequalityofinformationthatmightconcernanengineerandthevalueofinformationthatmightconcernoneneedingtomakeaconsistentandefficientdecision.Marschakwasexploringdecision-makinginfuzzyinformationalenvironmentsjustasvonNeumannandOskarMorgensternwereestablishingtheanalogybetweendecision-makingandthetheoryofgamesintheirlandmarkbookTheoryofGamesandEconomicBehavior.MarschakwasinterestedinhowtogeneralizetheworkofFrankRamseyandLeonardJimmieSavagebyextendingthevonNeumannexpectedutilityparadigmtodecisionsmadeinanenvironmentofuncertainty.Heconstructedaresearchagendainhoworganizationsincorporateuncertaintythatbothdrewuponandinformedrelateddisciplinesfromengineeringtostatisticsandpsychology.Indemonstratingthatmanyseeminglydistinctdisciplinesareallunitedthroughuncertaintyandtheeconomicproblem,hestrengthenedhislegacyasabridgebetweenthedecisionsciencesandabridgebetweenscholars. 38TheRiseoftheQuantsAninspirationtoanewgenerationoftheoristsMarschak’sgroundbreakingworkcanbetracedthroughthesuccessofthosehementoredandthecolleaguesheinspired.Inthismeasure,andintheaccumulatedNobelPrizesfromthoseheinspireddirectly,hemaybewithoutpeer.Certainly,theinfluenceofonewhodevelopswholenewandproductiveareasofresearch,suchasJohnvonNeumann,hasprofoundreachandinfluence.Marschak’sinfluencewasmuchmoreintimate,though.Thisintimacyinthedirectinspirationofothersmakesitlessobviouswherehisgeniusendedandthatofothersbegan.Forinstance,Marschak’sworkoninformationandontheconsistencyofdecision-makinghelpedinspirehisstudentRoyRadnertoproducehisgroundbreakingworkonrationalexpectationsequilibria.In1967RadnerfurtherdevelopedMarschak’sintuitionbydemonstratingtheinformationalroleofpricesthatisnowacornerstoneofmodernfinancetheory.Inhispaperonthesubject,“CompetitiveEquilibriumunderUncertainty,”healsodeterminedthesignificanceofwhatwenowknowasarationalexpectationsequilibrium.1Radnerwentontoestablishequilibriumunderuncertaintyin1968,andtherebyprovedanassertionthatKennethArrowhadmadebuthadnotprovedmorethanadecadeearlierthatacompetitivemarketcouldstillbeefficienteveniftherangeoffuturesinstrumentsdoesnotspanallpossiblestates.2Indeed,MarschakandRadnerwouldgoontocollaborateintheextensionoftheirmodelsofinformationanduncertaintytothetheoryofteamsandofdecision-makingwithinorganizations.ThisworkbetweenMarschakandRadneritselfspawnedanewliteratureonorganizationaltheoryandontheprincipal-agentproblemthatiscrucialtoourunderstandingoffinancialmarkets.WhentheirworkculminatedintheseminalbookEconomicTheoryofTeams,publishedbyYaleUniversityPressin1972,Marschakwasinhisseventy-fourthyear.3Hiscareerhadspannedsixdecadesandhehadsavedsomeofhismostsignificantworkforlast.Overamostdiverse,productive,active,andinspirationalcareer,Marschakwaselectedtopresideovertwolearnedsocietiesandhadbeenappointedafellowin1963totheRoyalStatisticalSocietyandadistin-guishedfellowin1967totheAmericanEconomicsAssociation.HehadalsobeennamedfellowtotheAmericanAcademyofArtsandSciencesandtotheInstituteofMathematicalSciences,andwasawardedwithhonorarydegreesfromtheUniversityofBonnin1968,theUniversityofCaliforniain1971,hisalmamatertheUniversityofHeidelbergin LifeandLegacy391972,andNorthwesternUniversityin1977,justacoupleofmonthsbeforehedied.Throughouthiscareer,Marschakwasanextraordinaryscholarlybridge.Hisacademichallmarkwasintheorganizationofnetworksofscholars,throughacademicsinexiletohisInterdisciplinaryColloquiumonMathematicsintheBehavioralSciencesatUCLA,whichcontinuestothisdayandisnamedinhishonor.MarschakwasoneofonlyafewpeopletobeelectedtopresideoverboththeEconometricsSocietyandtheAmericanEconomicsAssociation.However,beforehecouldtakehispositionattheAmericanEconomicsAssociation,hediedofastrokeinLosAngelesonJuly27,1977,justfourdayspasthisseventy-ninthbirthday.Hewasremem-beredasamanwhocouldspeakadozenlanguages,onewhobefriendedandmentoredscholarsfromaroundtheworld,andonewhowasbusyatworkuptothedayhediedinnewcapacities.Atthetimeofhispassing,MarschakwassurvivedbyhiswifeMarianneandhisdaughterAnnJernberg,byason,ThomasMarschak,andbysixgrandchildren.AnnpassedawayinJuly1993andMariannediedlessthanamonthlater.BothofMarchak’schildrenobtainedPhDsandcelebratedhighlyproductivecareers.AnnwasanotedpsychologistandThomaswasaprofessorattheUniversityofCaliforniaatBerkeleyintheBusinessAdministrationdepartment.Mostsignificantly,though,isthesimpleyetprofoundlegacyMarschakleftforallthosewhofollowedhim.Financialinstrumentscanbecharacterized,inlargepart,bythemeanandvarianceoftheirreturns.Themathematicsofthisproposi-tionwasuncomplicatedandthecharacterizationoffinancialsecuritiespricesbytwoparameterswasmostprofound.Forthat,Marschakisbestremembered. Thispageintentionallyleftblank PartIIWilliamForsythSharpe,JohnLintner,JanMossin,andJackTreynorPractitionersrecognizedit,SirJohnHickssurmisedit,JacobMarschakproposedit,andHarryMarkowitzincorporateditintoModernPortfolioTheory.ButitwasnotuntilWilliamForsythSharpe,JohnLintner,JanMossin,andJackTreynortransformeditintotherealmofapplicationthatthemean-varianceapproachallowedustopriceindividualsecurities.WhatwenowknowastheCapitalAssetPricingModelhassincebecomethefoundationofsecuritiespricingtheory. Thispageintentionallyleftblank 8TheEarlyYearsJacobMarschakandSirJohnHickspioneeredtheconceptofamean-varianceapproach,alsoknowntomathematiciansandphysicistsasthefirstandsecondmomentapproach,totheriskrewardtrade-offinthe1930sand1940s.However,itwasnotuntilHarryMarkowitzformallyincorporatedriskanduncertaintyintofinancialdecision-makinginhisdescriptionofthemean-varianceapproachtoportfoliodesigninthe1950sthatamoregeneraltheoryoffinancebegantofoment.FollowingMarkowitz’sModernPortfolioTheory,thedisciplineoffinancehadtoruminateontheseideasforadecade.Suddenly,fourresearchersindependentlyarrivedatthesamerevolutionaryinsightataboutthesametime.Ifwecandesignaportfoliobasedonthemeanandvarianceofsecurities,perhapswecanalsopriceindividualsecuri-tiesbasedontheirhistoriclevelofvariability.Thisadjustmentforuncertaintyallowedsecuritiestoyieldacompeti-tivereturnthatwascommensuratewiththeirrisks.Theirinsightshavebecomethestandardmethodandintuitionforsecuritiespricingeversince.ThegreatinsightsofWilliamForsythSharpe,JohnLintner,JanMossin,andJackTreynorforeverratchetedupthedegreeofanalyticrigornowcommonlyemployedinfinance.Theyalsoheraldedintheeraofthequants.Whilethesefourscholarsarrivedatasimilarconclusionataboutthesametime,theintellectuallandscapehadbeeninthemakingforadecade.FinancescholarswerewellawareofMarkowitz’sinnovativeModernPortfolioTheoryintheearly1950s.However,hisformalizationofhistoricvariabilityanditsinfluenceonreturnsrequiredadvancesincomputingpowerthatwassufficientlyrapidtoenablethemyriadcalculationsthatwouldturntheoryintopractice.Untilthesecalculationscouldbeperformedroutinelyandatlowcost,ModernPortfolioTheory43 44TheRiseoftheQuantswouldremainanintellectuallysatisfyingresultbutonedevoidofeasyapplication.ItwasintheareaofcomputeralgorithmsthatMarkowitzincreasinglydevotedhistime.Inthe1950s,otherswereteasingaddi-tionaltheoreticalresultsoutofhisnewportfolioframework.However,followingasuggestionfromMarkowitzhimself,ayoungscholardiscoveredawaytoprovideasimpleinterpretationandmethodofapplicationtoModernPortfolioTheorythatwouldallowthepractitionertopriceindividualsecurities.Mostcloselyassociatedwiththerevolution-arynewapproachtosecuritiespricingisWilliamForsythSharpe.WilliamForsythSharpeThefirstandforemostofthegreatmindsmostidentifiedwitharevolutioninthepricingofsecuritiesisWilliamForsythSharpe.HeisalsothefirsttofollowtheinspirationofMarkowitzandModernPortfolioTheory.Inturn,MarkowitzandSharpeunknowinglyinitiatedanewschoolofquantitativefinancialmethodsandanalysisthatforevertransformedthedisciplineoffinance.ItisfittingthatSharpe’sfamilyrootsarealsoasdistinctlyAmericanaswashistheorythatembodiedanemergingAmericantheoreti-calpragmatismthatframedthefoundationoffinanceinthe1960s.WilliamForsythSharpeisthesonofRussellThornleySharpe(1905–1992)andEvelynForsythJillson(1908–2007).Thesefamilynamescanbetracedbackforcenturies.HisfatherwasthegrandsonofMarySharpeofRhodeIsland.HerSharpefamilydatedbackintoearlyAmericaevenfurther.TheoriginalSharpesandJillsonshadbothekedoutapioneerexistenceinthesouthernMassachusettsandRhodeIslandregionforthefirstcenturiesoftheNewWorld,withancestorsdatingbacktothetimeofthePilgrims’arrivalontheMayfloweranditssisterships.Almostthreecenturieslater,WilliamForsythSharpe’smother,EvelynForsythJillson,wasfromafamilywellestablishedinRhodeIsland,withsufficientresourcestosendtheirdaughtertoBrownUniversity’swomen’scollegeintheearly1920s.Inherlifeandtimes,Evelynwasanaccom-plishedsciencemajoratatimewhenfewwomenstudiedscience.Equallyaccomplishedwasherfuturehusband,RussellThornleySharpe,agraduateofhighestSummaCumLaudehonorsfromthenearbyIvyleaguecompetitor,HarvardUniversityinCambridge,Massachusetts.RussellwasfromEastGreenwich,RhodeIsland,justashortridefromhisfuturebride’shomeinProvidence.FollowinghisgraduationfromHarvard,RussellSharperemainedathisalmamaterasAssistantSecretaryforStudentServices.Thisacademicpositionwasthebeginningofanillustriouscareer.Soonafterhis TheEarlyYears45WilliamT.Sharpe(1878–?)RussellT.Sharpe(1905–1992)FloraSharpe(1878–?)Spouse:WilliamForsythRobertaRuthSharpeJamesJillson(1610–?)Sharpe(1934–)BorninScotland,Children:immigratedtoDeborahAnnSharpeMassachusettsGeraldEltonJillsonJonathanF.Sharpe(1873–?)Spouse:KathrynDorothyPeckEvelynForsythJillson(1908–2007)HarrietyF.Jillson(1873–?)Figure8.1TheSharpefamilytreegraduation,RussellandEvelynhadonechildtogether,WilliamForsythSharpe,bornonJune16,1934.RaisedincomfortbutinthemidstoftheGreatDepressionandtheonsetoftheSecondWorldWar,youngWilliamwasnonethelessexposedtoarichacademicenvironment.Bythen,hismotherwasaschoolteacherandhisfatherwasanacademic,firstatHarvardbuteventuallyasthe8thPresidentatMonticelloCollege,inGodfrey,MadisonCounty,Illinoisfrom1953to1958.BythetimeRussellSharpehadreachedthepinnacleofhisacademicadministrationcareer,hewasalreadyanotedauthorineducationadministration.HisPhDthesisin1956fromStanfordUniversitydealtwithadministrativeleadership.EvenbeforehecompletedhisPhD,hehadwrittenabookonfinancialassistanceforcollegestudentsthathadalreadyestablishedhisacademiccredentials.However,beforeRussellSharpefirmlyestablishedhisacademiccareeratthehighestlevelofacademicadministrationfollowinghisstintatHarvard,hewasforcedtomovehisfamily.JustafteryoungWilliamturnedseven,theUSAenteredtheSecondWorldWar.RussellhadbeenamemberoftheNationalGuard.Hisunithadbeenactivatedandhis 46TheRiseoftheQuantsfamilywasrequiredtomovetoTexasjustasWilliamwasbeginninggradeschool.Soonthereafter,thefamilymovedtonorthernCaliforniaandthentosouthernCalifornia.WhileyoungWilliamhadtoattendanumberofschoolsinhisearlyyearsduetotheserelocations,heeventuallywasabletosettleintheschoolsysteminRiverside,California.WilliamfoundschoolstimulatingandthecurriculumrichinRiverside.Heexcelledinscienceandmathematics,andwasdrawn,orperhapsdirected,towardscienceandpre-medicalstudiesattheUniversityofCaliforniaatBerkeley.Likemanyothergreatminds,Williamwasacademicallyprecocious.BerkeleyintheyearsfollowingtheSecondWorldWarwasgarneringareputationasoneofthetoppublicuniversitiesinthecountry.WilliamenteredBerkeleyattheyoungageof17.However,hesoondiscoveredthathischosenfieldofsciencewasnotforhim.Attheageof18,hemoveddownthecoasttoUCLAanddeclaredhismajorinbusinessadministration.Twoofthefoundationcoursesforallbusinessstudents,thenandnow,areaccountingandeconomics.WhileWilliamfoundaccountingtediousandnotparticularlychallengingintellectually,hewasattractedtotheloftierideasofeconomics.Hesoonchangedhismajortoeco-nomicsandearnedaBachelor’sdegreeineconomicsin1955andaMaster’sdegreeoneyearlaterattheageof21.WhileatUCLA,Sharpewasprofoundlyinfluencedbytwoofhisprofessors.Thefirst,thenotedeconomistArmenAlchian,actedashiseconomicsmentor.ThesecondinfluencewasFredWeston,aprofessoroffinancewhohadsharedwithSharpeapieceofgroundbreakingfinancetheorythathadjustbeenpublishedbyHarryMarkowitz.SharpebegantoponderthebroaderimplicationsofMarkowitz’sbigidearegardingtheoptimalrisk–rewardtrade-offinthenewModernPortfolioTheory.WithaMaster’sdegreeineconomicsinhand,SharpetookajobwiththeRANDCorporationinSantaMonica,California,justafewminutes’drivefromUCLA.ThisjobopportunitypermittedhimtobecomeimmersedinanintellectuallystimulatingenvironmentwhilehealsopursuedaPhDatUCLAunderthecontinuedmentorshipofProfessorAlchian.ItalsoallowedhimtocrosspathswithHarryMarkowitzhimself.TheRANDCorporationWhileatRAND,Sharpehadtheopportunitytorubshoulderswithsomeofthegreatestmindseverassembledtoaddressthesciences,mathematics,andsocialsciencesdemandedintheColdWar-immersedUSA. TheEarlyYears47RAND’smissionwas“tofurtherandpromotescientific,educational,andcharitablepurposes,allforthepublicwelfareandsecurityoftheUnitedStatesofAmerica.”1Eventoday,itremainsathinktankdevotedtoresearchanddevelopmentthathelpstosecuretheleadershipoftheUSAinsecurity-relatedstudies.AspartofthewareffortduringtheSecondWorldWar,underthedirec-tionoftheCommandingGeneraloftheArmyAirForceH.H.“Hap”Arnold,theprojectassembledtheverybestscientists,mathematicians,andstrategists.SuchgreatmindsasJohnvonNeumann,KennethArrow,andHarryMarkowitzhadbeenassociatedwithRANDduringorimmediatelyfollowingtheSecondWorldWar.AftertheWar,theCorporationbecameseparatefromtheArmy,andbroadeneditsscopetovariousscientificandsocialissues,includingeconomics,healthcare,poverty,andeducation.RANDquicklyestablisheditselfduringtheWarandpost-Waryearsasoneofahandfulofhotbedsforbothgametheoryandcomputing.By1948,itemployed200people,manyofwhomhadPhDsintheareasofmathematics,engineering,physics,aerodynamics,chemistry,psychol-ogy,computing,andeconomics.VonNeumannworkedonateamthatdevelopedthecomputingpowerandthealgorithmsthatwouldhelptorapidlysolvestrategicgamesandotheriterativeproblemsinphysicsandmathematics.WhilevonNeumanndiedbeforeSharpehadanopportunitytoobservehisbrilliantmindinaction,SharpewasfortunateenoughtomeetanotherRANDfellow,Markowitz,whowasstillatRANDwhenhearrived.MarkowitzwassevenyearsSharpe’sseniorandhadjoinedRANDin1952,justfouryearsearlier,freshoutofgraduateschoolhimself.TheRANDInstitutewasalsoinstrumentalinMarkowitz’sintellectualdevelopment.Soonafterhisarrival,MarkowitzmetGeorgeDantzig(1914–2005),amathematicianandanearlydeveloperofoperationsresearchandcomputerscience.OneofthemajorchallengestakenonbyRANDwasthedevelopmentofcomputeralgorithmsthatcouldsolvenumericallysuchproblemsasoptimaltrajectoriesandpathswhentravelofballisticmissilesisbuffetedbyrandomforces.Applicationtoproblemsinphysics,weaponry,andspaceflightwereobvious.Lessobviouswastheapplicationofsuchtechniquestosecuritiespricingandoptimalfinancialportfoliodesignunderuncertainty.Dantzigwasabrilliantmathematicianandcomputerscientist.Hisbrilliancewasrevealedearlyinhisuniversityschooling.In1939,whilestudyingattheUniversityofCaliforniaatBerkeley,hearrivedlateforclass.OntheboardProfessorJerzyNeymanhadjustwrittentwo 48TheRiseoftheQuantsperplexingproblemsthathaddefiedsolutionamongthegreatmindsinstatistics.HistardinessmeantDantzigdidnothearthepreambletotheproblemontheboard.Hehadassumedthetwoquestionswereahome-workassignment.Thateveninghebegantotrytosolvetheassignment,butfounditunusuallydifficult.Afterafewdays,hemanagedtosolvethequestions.Whenhehandedinthe“assignment,”Neymanwasastounded.HehelpedDantzigpublishthesegreatinsightsashisfirstpublication.Hewasfurtherrecognizedwhenthefamousmathemati-cianAbrahamWaldseparatelysolvedthesecondproblemyearslater.2ThisscenewasstylizedandimmortalizedintheopeningofthepopularmovieGoodWillHunting.3IntheyearthatMarkowitzjoinedRANDandbeganworkingwithDantzig,Markowitzpublishedthemostinfluential15pagesofhislifeintheMarch1952editionoftheJournalofFinance.4Thearticle,simplyentitled“PortfolioSelection,”definedModernPortfolioTheoryandwasdocumentedinthesecondvolumeofthisseries.However,whileheexplicitlydefinedtheoptimalcreationofafinancialportfoliobasedonhistoricmeanreturnsandvariances,ashissupervisorJacobMarschakhadsuggested,Markowitzimmediatelydiscoveredthatsufficientcom-putingpowerdidnotexisttoperformthecalculationsnecessarytodeterminethenecessarysolutionsinatimelymanner.Assuch,heandDantzigsetouttoworkonthedevelopmentofcomputeralgorithmsthatwouldallowpractitionerstosolvethisimportantquestioninfinance.WhileMarkowitzandDantzigdevelopedothercomputingalgorithmsnecessarytosolvefinanceproblems,SharpepursuedhisPhDstudieswithProfessorAlchianashisofficialsupervisor,butwithhisnewcolleagueHarryMarkowitzashisshadowmentor.Withthesetwogreatmentors,SharpecompletedaPhDthesisatUCLAfiveyearslater,in1961,thatproducedasinglefactormodelofsecuritiesprices.Hiswork,asanaturalextensionofMarkowitz’sModernPortfolioTheory,producedaprelimi-naryversionofthesecuritymarketlinethatisnowcommonlyemployedintheapplicationofMarkowitz’soptimalfinancialportfoliotheory.WithaPhDinhand,SharpetookajobasanassistantprofessorattheUniversityofWashingtonin1961.Hisresearchagendafocusedongeneralizinghisthesisresults.In1962hesubmittedapaperforpublica-tionintheJournalofFinance.Thispaperdescribedanewapproachtothepricingofanindividualsecurity,whichwenowcalltheCapitalAssetPricingModel(CAPM).WhilethefinancedisciplineregardsSharpe’sCAPMideaasoneofthemostprofoundandessentialconceptsinfinancetheory,theeditoroftheJournalofFinancein1962atfirstrefusedtopublishthepaper. TheEarlyYears49Hewouldhavetowaittwomoreyearsforachangeinjournaleditorshipbeforehecouldfinallygethisgroundbreakingworkpub-lished.Meanwhile,threeotherresearchersindependentlyproducedpapersdescribingthesamemethodologyandinsights,butinverydifferentways.However,whenhisworkwasawardedaNobelPrizein1990jointlywithhismentor,HarryMarkowitz,onlySharpewassingledoutforcreditfortheCAPMbytheNobelPrizeCommittee.Despitehisdelaysingettinghisworkpublished,heisnowrecognizedasthefirsttooriginatetheCAPMframework.However,thesethreeotherscholarsalsodeservecredit.WewilldescribenextthefirstoftheseotherCAPMscholars:JohnVirgilLintner.JohnLintnerItisrareinacademiaforasoleandisolatedscholartoappreciateaproblemthatnoothersees.Studentsandpractitionersstudyanddiscusssolutions.Theacademicworldsometimesbandiesaboutproblemsforyearsordecades.Often,theyframetheirproblemsfromwildlydifferingperspectivesandcontexts.TheCAPMisbutoneexample,andJohnLintnerwasbutonesuchinvestigatorwhowasexploringitsimplica-tionswithinthecontextofassetvaluationwithinacorporation.Yearslater,scholarswoulddiscoverthatbothLintnerandSharpewerepursuingthesameproblemfromverydifferentangles.Thatisnotalltheyhadincommon.FewfamiliescantracetheirpioneerAmericanrootsbacktotheCivilWareraofSharpe’snamesakeortothepre-USAeraofSharpe’smother’sfamily.Certainly,nopreviousgreatmindinthisseriescoulddoso.However,theLintnernamecanalsobetracedbacktobeforetheCivilWar,toJohnLintner’sgreat-grandfather,CasperHenryLintner.Lintner’sgreat-grandfather,Casper(Chaspna)Lintner,wasborninStuttgart,Germanyin1828andemigratedtotheUSAintimetofightasaprivateinthe133rdOhioRegimentoftheNationalGuardInfantryontheUnionsideoftheAmericanCivilWar.Alreadybythattime,CasperhadmarriedJohnLintner’sgrandmother,MargaretHibbits,whoseancestorshadlivedinOhiosincebeforetheUSAwasacountry.Margaretwasborntwoyearsbeforeherfuturehusband,onSeptember11,1830,inMt.Valley,Ohio.SoonafterCasperandMargaretLintnermet,theymarried,onMay4,1851.Together,theyhadeightchildrenover14yearsfrom1853to1867.CasperandMargaretLintner’sfirstchildtogether,JamesMartinLinter(1853–1929),wasJohnLintner’sgrandfather.JamesandhiswifeHannahhadthreechildren:Arthurin1883,Robertin1892,and,inbetween,Virgil,JohnLintner’sfather,in1885. 50TheRiseoftheQuantsCaspierHenryLintner(1828–1915)BorninGermany,immigratedtoKansasJamesMartinLintner(1853–1929)MargaretHibbits(1830–1917)VirgilLintner(1885–?)HannahLintner(1856–?)JohnVirgilLintnerSpouse:(1916–1983)SylviaChanceJohnDaily(1820–1887)Spouse:EleanorJ.HodgesDavidGrayDaily(1857–1939)Children:JohnH.LintnerMaryB.DailyNanceC.L.Molvig(1832–1908)PearlC.Daily(1887–1965)EvaL.Daly(1867–?)Figure8.2TheLintnerfamilytreeBythetimeJohnLintnerarrived,theLintnerfamilywaswellestablishedinElm,Kansas.VirgilLintnerandhiswifePearlhadtwochildrenwhilelivingthere:first,JohnVirgilwasbornonFebruary9,1916,followedbyRobertin1919.JohnattendedtheUniversityofKansasandgraduatedwithaBachelor’sdegreein1939attheageof23andaMaster’sdegreeayearlater.DuringhisyearstudyingforhisMaster’s,hewasofferedhisfirstteachingappointment,attheUniversityofKansascampusinLawrence.WithhisMaster’sinhand,hemovedtoNewYorkCitytoworkforthepres-tigiousNationalBureauofEconomicResearchin1940–1941.WiththeadditionalmotivationtocontinuewithhisschoolingwiththeonsetoftheSecondWorldWar,JohnattendedHarvardUniversityforasecondMaster’s,whichhecompletedin1942.HeearnedaPhDinbusinessadministrationfromHarvardin1946.Byallaccounts,HarvardwasimpressedwithLintner.UponreceiptofhisPhD,hewasaskedtoremainattheuniversityunderathree-yearpaidmembershiptotheHarvardSocietyofFellowstopursuearesearchagendaashesawfit.AsaHarvardfellow,hefollowedinthefootsteps TheEarlyYears51ofthegreatmindPaulSamuelson,whoisdocumentedinthefourthbookofthisseries.Followinghisfellowship,LintnerwasofferedanassistantprofessorshipinbusinessadministrationatHarvardBusinessSchoolin1946,anasso-ciateprofessorshipin1951,afullprofessorshipin1956,andtheGeorgeGundProfessorofEconomicsandBusinessAdministrationfrom1964untilhisuntimelydeathin1983.Hediedbeforethe1990awardingoftheNobelPrizefortheCAPM.Inhisseminalwork,Lintnerlookedatthecapitalassetpricingproblemfromauniqueperspective.WhileSharpeandothersweretakingMarkowitz’sinspirationinthedirectionofindividualsecuritiespricing,Lintnerlookedattheproblemfromthecorporatestockissu-anceperspective.Buriedwithinhisorganizationalframework,hehadtreatedthepricingofriskysecuritiesinawaythatwasstrikinglysimi-lartoSharpe’smorestandardapproach,butwasdisguisedandhenceunder-appreciatedforatime.ResearchershavesinceremarkedontheequivalenceofLintner’sandSharpe’sapproach,andLintner’sparallelcontributionhassinceearnedgreaterappreciation.FollowinghisCAPMworkintheearly1960s,Lintnercontinuedtoundertakeresearchincapitalmarkettheory.However,whileheremainedafixtureatHarvard,hispublicationrecordwasunspectacular.Nonetheless,someassertthathiscontributiontoCAPMtheoryandhismoretimelypublicationdeservedrecognitionbytheNobelPrizeCommittee,alongwithSharpe.However,NobelPrizesarenotgivenposthumously.LintnerdiedofanapparentheartattackwhiledrivinginhishometownofCambridge,MassachusettsonJune8,1983,morethannineyeasbeforetheNobelCommitteerecognizedtheworkofWilliamSharpe.JanMossinTwootherscholarsarealsonowcreditedwithoriginalcontributionstotheCAPM.Oneremainedinrelativeobscurity,primarilybecausehereturnedalmostimmediatelyfollowinghisCAPMthesisintheUSAtohishomeschoolinNorway,offthebeatenpathofacademicfinanceresearch.JanMossinwasborninOsloin1936.In1959hecompletedaBachelor’sdegreeineconomicsattheNorwegianSchoolofEconomicsandBusinessAdministration.Followinghisdegree,heworkedinindustryforacoupleofyearsbeforehecametotheUSAtocompleteaMaster’sdegreeatCarnegieMellonUniversity(thentheCarnegieInstituteofTechnology).FollowinghisMaster’sin1964,heremainedattheCarnegieInstitutetoearnaPhDin1968. 52TheRiseoftheQuantsMossin’sintellectualproductionwasprodigiousinhisyearsatCarnegieMellon.Bythetimeofhisgraduation,hewasconsideredanoutstandingstudent,alreadywithalonglistofpublicationsintopjournals.ItwashisdissertationworkontheCAPMforwhichheremainsbestknown.However,hisintensescholarshipattheCarnegieInstituteevolvedintomoreregionallyrelevantresearchoncehereturnedtohishomecountry.JackLawrenceTreynorThereisoneadditionalnamethatmanynowassociatewiththeCAPM.Thislastnameislesscommonlyheardinthecirclesoffinancialtheo-rists,butisoneofgreatinfluenceamongfinancepractitioners.And,likeSharpeandLintnerbeforehim,hisheritageisdistinctlyAmerican.JackTreynoristhechildofJackVernonTreynorandAliceTreynor.Jacktheyoungertookhisfirstnamefromhisfatherandhismiddlenamefromhisgrandfather’smiddlename.IthadbeenthetraditionintheTreynorfamilyforsonstotakethenamesoftheirfathersandgrandfathers.ThomasP.Traynor(1833–?)EmigratedfromEnglandtolowaVernonLawrenceTreynor(1866–?)MaryF.Smith(1829–)JackVernonTreynor(1897–1966)SusanClark(1870–1949)JackLawrenceSpouse:Treynor(1930–)BetsyTreynorAliceCavin(1896–1992)Figure8.3TheTreynorfamilytree TheEarlyYears53VernonLawrenceTreynorandhiswifeSusanClarkTreynorwereJackLawrence’spaternalgrandparents.Vernon’sfatherwasbornin1832inEngland.UponhisimmigrationtotheUSA,hemarriedMaryF.Smith,borninIowain1829.TheTreynorlineagehadsettledintheareaofCouncilBluffs,Iowa.WhenJackwasbornonFebruary21,1930,hisfamilylivedindown-townCouncilBluffs,at2045thAvenue.Hisfamilywaswell-to-do,withaservant,FannieHarris,tendingtotheirneeds.Infact,youngJackwasbuckingthefamilytrendwhenhetookupthestudyoffinance.Hehadtwogenerationsofheritagenodoubtinfluencinghiscareerchoice.HisfatherandhisgrandfatherwerebothphysiciansinPottawattamieCounty,Iowa.Jackwasanintellectuallyprecociousstudentwhoexcelledinmath-ematics.AtHaverfordCollege,hewasamemberoftheMathClub,theVarsityClub,andtheGleeClub,playedguardinAmericanfootball,andmaintainedtheIowatraditionbyletteringinwrestling.Hisclassmatesatcollegecalledhima“corn-fedIowaisolationist.”Healsoclaimedhewouldearnhisfirstmillionbytheageof30andthenhewouldmarrywell.YoungJackwasanall-Americanboy.AfterTreynorgraduatedfromHaverfordCollegewithamajorinmathematics,hewentontostudyattheHarvardBusinessSchool.HegraduatedfromHarvardin1955,butremainedaftergraduationatHarvardforanadditionalyearasaresearchassociate.WhileatHarvard,Treynorponderedtheappropriatemethodtodiscountthestreamofincomethatanespeciallylong-livedinvestmentprojectmightyieldtoacompany.Herealizedsomethingeverystudentoffinancenowknows.Suchpresentvaluecalculationsarehighlysensitivetothechoiceoftheinterest(ordiscount)rate.Hearguedthatthisdiscountrateshouldsomehowbeadjustedtoreflecttheriskinessanduncertaintiesoftheproject.Thisprobleminducedhimtopondertherelationshipbetweenriskandreturn,whichgaverisetohisuniqueversionoftheCAPM.TreynorwasexploringthisconceptastimepermittedwhileonhisfirstjoboutofcollegeattheprestigiousArthurD.Littleconsultingfirm.Thefirmappointedhimtoitsnewoperationsresearchdepartmentin1956becauseofhisstrongmathematicsandbusinessbackground.Hisofficialdutiesdidnotpermithimtopursuetheoreticalworkoncompanytime,sohecontinuedonhisprojectdiscountingprojectinhissparetime.Afteryearsoflittleprogress,hedevotedaprolongedthree-weekvacationinEvergreen,Coloradoin1958tothedevelopmentofhispetproject,Forthenexttwoyears,hecontinuedhistheoreticalfascinationnightsandweekendsatArthurD.Little.By1961,wewaspreparedtobegincirculatingtheworkunderthetitle“Market,Value,Time,andRisk.” 54TheRiseoftheQuantsCrossingofpathsAsanalumnioftheHarvardBusinessSchool,TreynorsoughtoutcommentonhisnewpaperfromProfessorJohnLintner.Lintnerofferedlittlefeedbackorinterestinthepaper.5However,oneofhiscolleaguesatArthurD.LittlesentacopyofhisanalysistoMertonMiller.MillerwasthenteachingatNorthwesternUniversityinIllinois,buthadco-authoredwiththegreatmindinfinanceFrancoModiglianisomeseminalworkontheoptimaldebtandequitystructureofafirm.Bythen,ModiglianihadmovedtohispermanenthomeoftheMassachusettsInstituteofTechnology(MIT),justacrosstownfromHarvard.MillersuggestedthatTreynorcontactModigliani.Modigliani,knownasagraciousandsupportivementortoyoungtheorists,invitedTreynortovisitanddiscusshiswork.Modiglianialsoencouragedhimtocontinuehisstudies,atMIT,ineconomics.Modigliani’ssupportinducedTreynortotaketemporaryleavefromArthurD.LittletoembarkonaPhDstudyatMIT.TakingModigliani’sadvicestillfurther,Treynordividedhisthesisworkupintotwoparts.Thefirstresultedinapaperentitled“TowardaTheoryoftheMarketValueofRiskyAssets,”presentedinthefallof1962,andafollow-uppaper,“ImplicationsfortheTheoryofFinance,”afewmonthslater.Ultimately,Treynorneverpublishedhisfirstpaperuntilaretrospectivewasconstructedin1999.However,hehadbeguntoexchangeworkwithWilliamSharpewho,atthesametime,wastryingtogethissimilarworkpublishedintheJournalofFinance.BackatworkatArthurD.Little,Treynorbegantoapplyhisinsightsandtechniquesinthedevelopmentofmeasuresthatmighthelppracti-tionerstovaluesecurities,basedonhisvaluationofriskyassetstheory.ThisworkeventuallyresultedinaseriesofHarvardBusinessReviewpub-lications,including“HowtoRateManagementofInvestmentFunds”6and,withKayMazuy,“CanMutualFundsOutguesstheMarket?”7Treynorobviouslyhadthetalenttosucceedintheoreticalwork.However,whilehedabbledinscholarship,wasassociatedwithanumberofuniversitiesduringhiscareer,andwastheeditororreviewerforvarioustheoreticalandpractitionerjournalsinfinance,heremainedaguruprimarilyamongpracticingmoneymanagers.HewentontoformTreynorCapitalManagement,basedinPalosVerdesEstates,California.Whilehedidnotearnhisfirstmilliondollarsbytheageof30,hehasmademanytimesoverthisamountduringhiscareer.PerhapsheevenwaiteduntilheearnedhisfirstmillionbeforehemarriedElizaGlassmeyerRoyonAugust29,1968,attheageof38. 9TheTimesOverathree-decadeperiodfromtheearly1930s,financetheoryhadfollowedanesotericandelegantpaththatbroughtittothecuspofaflourishofactivityinthe1960s.Ithadadvancedonlythroughaseriesofmathematicalinnovations,mostlyatthehandsofscholarsassociatedwiththeUniversityofCambridgeandPrincetonUniversityandtheCowlesCommission,firstattheUniversityofChicagoandthenatYale.ThealumniofthesefourivorytowersincludedthefinancialluminariesIrvingFischer,JohnMaynardKeynes,FrankPlumptonRamsey,FrancoModigliani,MiltonFriedman,JohnvonNeumann,LeonardJimmieSavage,KennethArrow,HarryMarkowitz,andJacobMarschak.Eachofthesescholarswhohadbroughtfinancetothisbreakoutpointhadatleastonefootinthestudyofmathematics.Atleastfourofthemwouldconsiderthemselvesappliedortheoreticalmathematiciansratherthanfinancialtheorists.AndallbutFischerwereeitherfromEuropeorwerebutoneortwogenerationsremovedfromEurope.ThisEuropeanpedigreeissignificantbecausethesepioneerseachbroughttofinanceaninsistenceofscientificstyleoverpragmaticsub-stance,withthepossibleexceptionoftheever-pragmaticFriedman.Thisisnottosaytheirtheories,whichactasthefoundationofmodernfinance,didnotcontainwithinthemenduringconceptsandbroadutility.However,thetheoriesoftheEuropeanschoolproponentswerealsocompactandbeautiful,andthetheoristswerewillingtosacrificesomepracticalityanddetailintheinterestofscientificbeautyandaxio-maticgenerality.Thisemergingaxiomaticapproachwasinacademicvoguebythe1940sandhasremainedcommonamongeconomistsandfinancialtheoristseversince.However,thesimplisticmodelingwasalsooftenahallmarkoftheoreticianswhoareoftenonestepremovedfromthereal-worldmarketstheirtheoriesaredesignedtoaddress.55 56TheRiseoftheQuantsBythe1960s,though,thefinanceliteraturetookonadistinctlyAmericanpragmatismthathasheldswayinfinanceeversince.Theoreticalconceptsremainedimportant,butpracticalandtestablehypotheses,andmeasuresusefultopractitionersbecametheorderofthefinancialday.Theoriesandtechniquesweredevelopedthatcouldmakepeoplemoneyorreduceinvestors’risk.Anewgroupofgreatmindsinfinance,whosefamilytreehadalmostuniversallybeenrootedintheAmericasformanygenerationsorevenmanycenturies,becamethecarriersofthefinancialflame.Inthe1960stherebegananewschooloffinancialtheory.Initswake,itleftnewtoolsthatallowedfortheriseofthequantitativeschooloffinance.Gonewastheerainwhichfinancialanalysiswasconsideredanartform.Financetheoryhadgivenrisetothequants.ModernPortfolioTheoryBythe1960s,thescienceoffinancehadcomealongwayinjustashortperiodoftime.Thenatureofsavingsandfinancialinvestmentwerenotfullydescribeduntilthe1940s.Theconditionsforacompetitiveequilib-riuminfinancemarketswasestablishedintheearly1950s,asweretheanalyticfoundationoffuturesmarketsandmarketportfolios.However,therewaslittlereasontodetermineanalyticallyanoptimalportfolioatanymomentintimeifthesolutionrequiredateamofpeopletomakethethousandsofcalculationsthatweperformalmostinstantaneouslyasamatterofcoursetoday.JustasvonNeumannoncequipped,itdoesnotmakesensetotakeaweektorunananalysisforafive-dayweatherforecast.Whilethetheoreticaladvancementsbythelate1950swereinteresting,theyimposedhugedemandsforrapidcalculationsthattherelativelyprimitivecomputersinthateracouldnotmeet.VonNeumannrecognizedthisproblem,atleastinthecaseofphysicsandmathematicsproblems,anddevotedmuchofhisenergyinhislateryearstothenewfieldofcomputerprogramming.Modigliani,too,recognizedboththegreatpotentialandalsothegreatdistancetogoincomputinganditsapplicationtofinanceandeconomics.Consequently,immediatelyfollowingthedevelopmentofModernPortfolioTheoryin1952,whileatRAND,Marschak’smenteeHarryMarkowitzbegantodevoteallofhistimetoalgorithmsthatcouldquicklysolvetheprob-lemsintheemergingfinancialanalytics.Bytheearly1960s,becauseoftheworkofvonNeumann,Markowitz,andDantzig,amongothers,thecomputingbottleneckshadmostlybeenovercome.Algorithmsandprogramswerebeingdevelopedthat TheTimes57couldquicklysolvethematrixalgebraproblemsnecessarytodeterminehistoricalreturnsandvariancesoflargenumbersofsecurities.By1964,thenecessaryalgorithmsandprogramswereinplace,WilliamSharpewasfinallyabletopublishhispaperoncapitalassetpricing,andIBMbegansellingarevolutionarynewcomputer,theIBM360.Thiscomputerfilledaroom,costhundredsofthousandsofdollars,requiredtechnicianstooperateit,andperformedupto34,000instructionspersecond.1Toputthiscomputingpowerinperspective,amodernsmartphonecancalculatetensofthousandsoftimesfaster.Nonetheless,withthetheoretical,software,andhardwaretoolssuddenlyavailable,quan-titativefinanceanalystscouldfinallygettoworkinpricingsecuritiesanddeterminingtheextentthatsecuritiespricemovementseitherfitordepartfromourintuition.First,ModernPortfolioTheoryand,soon,theCAPMledtheway.TheCAPMhasdefinedfinancetheoryandrevo-lutionizedpracticeeversince.ThebigideaIn1936and1937twoscholarshadpresentedtwowildlydivergentpicturesofthepricingoffinancialsecurities.OneinspiredMarkowitztodevelophisModernPortfolioTheory.Theothermorecynicalmodel,fortunately,didnot.KeynespublishedhismagnumopusTheGeneralTheoryofEmployment,InterestandMoneyin1936asthefirstsuccessfulexplanationofstablemacroeconomicequilibriawellbelowtheoptimalequilibriumdescribedbyclassicaleconomists.Heofferedarathercynical,butattimescertainlynotunreasonable,pictureofhumanpsychologyandthewaysinwhichwecanconfoundevenourownbestinterests.Whilehehadinmindanexplanationforwhythemacroeconomycanunderperform,healsoofferedexplanationsastowhyafinancialmarketcandepartfromrationality.Inhisfamousbeautycontestanalogy,hedescribedacontestinwhichpeoplearenottojudgethecontestantwhomtheybelieveisthemostbeautiful,butratherwhotheybelieveisregardedbyothersasthemostbeautiful.Henoted:Itisnotacaseofchoosingthose[faces]that,tothebestofone’sjudgment,arereallytheprettiest,noreventhosethataverageopiniongenuinelythinkstheprettiest.Wehavereachedthethirddegreewherewedevoteourintelligencestoanticipatingwhataverageopinionexpectstheaverageopiniontobe.Andtherearesome,Ibelieve,whopracticethefourth,fifthandhigherdegrees. 58TheRiseoftheQuantsKeyneswasanalogizingthatthosewhoinvestinthestockmarketarenotinvestinginarationalwayregardingthefundamentalvalueofasecurity;rather,investorsareanticipatinghowothersmightvaluethesecurity.Thisrathercircularlevelofstrategizing,notunlikeaSherlockHolmesandMoriartyexamplesuggestedbyvonNeumann’scollabo-ratorOskarMorgensternafewyearsearlier,interjectsstrategyintowhatmightotherwisebeasimplematteroffundamentalsanalysis.Ayearlater,in1937,JohnBurrWilliamspublishedabookinwhichhedescribedamorerationalapproach.AsafinancialadvisorhimselfbeforehereturnedtocompleteaPhDatHarvard,Williamswasfamiliarwiththosewhopricesecuritiesnotinanticipationoftheirvaluationbythemarket,butratherbasedoncompanyandprojectfundamentals.Hedevelopedhistechniqueforfundamentalsanalysisbasedonthediscountedvaluationofexpectedfutureearnings.Hisapproachlinkedpricesdirectlytoexpectedearningsandtotheexpectedrateofreturnonalternativeassetsasabenchmarkfortheappropriatediscountrate.ThisapproachhaddefinedfundemantalsanalysiseversincefinancepractitionersabsorbedWilliam’smethodology.AcceptanceofWilliams’approachwouldsuggestthattheprice/earningsratioforasecurityshouldremainrelativelyconstantunlessearningschangeortheprevailinginterestratechanges.WilliamsdidnothavethestatisticaltoolsofMarschak,whohadataboutthesametimerecommendedthedescriptionofsecuritiesbasedonboththeirmeanpatternofreturnsandtheirvariance.However,WilliamsdidimpressMarschak’sstudent,HarryMarkowitz,whorecognizedthatastableandpredictablecovariancebetweensecuritiescanbeusedtoreducetheriskandvariabilityofaportfolioofsecurities.Markowitzwasdescribingwhatwenowknowofasportfoliotheory.WhilewaitingtomeetwithMarschakattheUniversityofChicagotoformulateapossiblethesistopic,hetookpartinaconversationwithanotherpersonwhowasalsowaitingtovisitMarschak.Fromthischanceencounter,Markowitzwasintroducedtothepossibilityofthestudyofstockmarketreturns.HeseizedupontheideaandsubsequentlyspoketoMarschakaboutit.Marschak,inhischaracteristicstyle,wasmostsupportiveofthisyoungresearcher’sagenda,but,asMarkowitzlaterrelated,didnottellMarkowitzthathehadindeedthoughtandwroteaboutsecuritiesreturns,derivedtheappropriatenessofameanandvariancedescriptionofthem,andevencommentedonthesignificanceoftheconceptofcovariancebetweensecurities.MarkowitzquicklyrealizedwhatMarschakhadcontemplatedforyears.Twostocksthattendtoriseandfluctuatelooselywiththeoverall TheTimes59marketmayalsobenegativelycorrelatedwithoneanother.Insuchacase,ifthereisapatterninwhichonestockisrisingabitmorethanaverageandtheotherisnotrisingasquicklyastherestatagiventime,thisnegativecovariance,orsecondmoment,betweenthetwostockscanbeusedsothatthesupernormaltemporaryreturnsofonecanoffsetthesubnormaltemporaryreturnsoftheother.Atanothermomentintime,eachofthesestocksmayreversetheirrelationshipstothemean,butstilloffseteachother.Consequently,aportfoliothatholdsthispairofstocksinjusttherightproportionsmayofferanaveragereturn,butbelow-averagecombinedvolatility.Withthebudofanewconceptathand,MarkowitztrackeddowntheoriginalworkofWilliamsoncompanyfundamentalsasapredictorofastockpriceandaddedhistwist.Ifthereturnwerecombinedwithameasureofrisk,thenhecouldhelpfillinaglaringholeintheemer-gingliterature.Markowitztookthisconceptstillfurtherbynotingthataportionofthevarianceinasecuritypricecanbereducedifthesecurityiscom-binedwithanothersecuritythathasanegativecorrelationwithit.Then,asthetwosecuritiesmoveupwiththerisingtideofthestockmarket,theirvariationsthatmoveinoppositedirectionscanoffseteachother.Fromthis,hedevelopedthetheoryofoptimalportfolioselectionandcontributedtoourunderstandingofportfoliodiversification.Ofcourse,portfoliodiversificationwasnotanewsubject.Keyneshaddescribedtheimportantroleofassetmixesinhismonetarytheoryof1936.Henotedthatcashisalsoaninvestmentassetandhaddescribedhowindividualsholdtheirassetsinmanyforms,ofvaryingliquidity.Hepostulatedthattherelativeproportionoftheseholdingsinanindi-vidualportfoliowillvarybasedontheprevailinginterestrate,investorconfidence,andotherfactors.FollowingMarschak,JamesTobin(1958)mergedMarkowitz’soptimalportfolioselectionwithKeynes’theoryofmoneytoproducewhatwenowknowasthetwo-fundseparationtheorem.TobintookMarkowitz’sconceptsandsimplifiedthemtodemonstratethatanyindividualcanproduceanoptimalportfolio,basedontheiruniqueattitudetowardrisk,usingarisk-freeasset,suchasmoneyortreasurybonds,andaMarkowitzportfolioofriskyassets.Peoplewoulddifferonlyintheirrelativeshareoftherisk-freeandtheriskyassetportfolio.MarkowitzwentontoincorporateTobin’smoreeloquentandelegantinterpretationintoasubsequentbookayearlater.ItisthisdefinitionbyTobinoftheassetportfolioproblemthatwenowcoverinourfinanceclasses. 60TheRiseoftheQuantsThepracticalchallengeofMarkowitz’sapproachwasthatitrequiredafinancialpractitionertocalculatethevarianceofeachpotentialsecu-rityinaportfolioorinthemarket,anditscovariancewitheveryothersecurity.Onlyfromthesecouldonepickasetofsecuritiesthatwouldoffertheoptimalrisk–rewardmixwithminimalcombinedvarianceforagivenreturn.Thecomputingpowerrequiredtoperformsuchcalculationswasfarbeyondthestateoftheartin1952whenMarkowitzdevelopedtheconcept.ThischallengepreoccupiedhisresearchagendaatRANDforyears,butalsoyieldedsomeimportantinsightsandalgorithmstosolvetheproblem.However,evenbytheearly1960s,withnewalgorithmsathandandemergingnewcomputersthatwerecheaper,althoughnotyetafford-ableforanybutthelargestfinancialhousesorresearchcenters,thereemergedonceagainasimplerinterpretationthattookMarschak’sideaofameanandvarianceapproach,Markowitz’stheoreticaldesignofanoptimalportfoliothatminimizedvarianceforagivenreturn,andTobin’sseparationtheorem,andproducedasimplerandevenmoreintuitivewaytodescribeessentiallythesamething,butinawaythatwasmucheasierforpractitionerstoapply.WenowknowthisfreshandproductiveinterpretationastheCAPM. 10TheTheoryBeforewedescribethebrilliantinsightthatprovidedatoolforsecuritiespricingthatwassosimpleandpracticalthatwestilluseittoday,letustakeamomenttoreviewJamesTobin’ssimplification.Inthe1950s,TobinwasaCowlesCommissioncolleagueatthesametimewithJacobMarschakandHarryMarkowitz,MiltonFriedmanandLeonardJimmieSavage,KennethArrowandGerardDebreu,andnumerousotherCowlesscholarsandfellowswhoweredelvingintotheroleofuncertaintywhileadvancingthetoolsofeconomictheoryandeconometrics.Tobinwasappointedforthesamereasonaswerehiscolleagues.ThegoaloftheCommission’sfounder,AlbertCowles,wastofurtherthestate-of-the-scienceinourunderstandingofmarkets,especiallyfinancialmarkets.Cowlesproducedperhapsthemostintellectuallyrichsocialsciencesacademythathaseverbeenassembledwiththebeliefthatthecross-pollinationofintellectamongitsparticipantscouldcreatemyriadgreatinsights.Inthe1950s,thisgrandacademicexperimentresultedintheArrow-Debreuproofoftheexistenceofmarketequilib-rium,andTobin’sextensionofMarkowitz’sModernPortfolioTheory,whichmotivatedthecreationoftheCAPM.TounderstandTobin’sinterpretation,letusbrieflyrecalltheMarkowitzmodelfromthesecondvolumeofthisseries.AssumptionsMarkowitzbeganwithanumberofsimpleassumptionsthatwererelativelyinnocuous.Heassumedthatrisk-averseinvestorswouldonlytakeonadditionalriskifcompensatedbyahigherreturn.Heassumedthatthisriskcanbedescribedasanormallydistributedvarianceinreturnsandthateachassetiinaportfoliocanbedescribedbyits61 62TheRiseoftheQuantsreturnR,itsstandarddeviationandvariance2,andisweightediniIIaportfolioasashareωi.Healsodescribedthecorrelationbetweenanyonesecurityiinaportfolioandanothersecurityjasij.Theseassump-tionsallowustocalculatetheexpectedreturnoftheportfolioRpbysummingacrossallsecurities:ER()pi=∑wER()iiandtheportfoliovariance:sw22pi=+∑∑si2∑wiwjsisjrijiij≠iNoticethatallofthecoefficientsontheright-handsideoftheportfoliovarianceexpressionarenecessarilypositive,exceptforthecorrelationcoefficient.Wecanreadilyseethatportfoliovarianceisminimizedifthecorrelationcoefficientij1.WecangeneralizethisriskminimizationprocedurethroughthematrixalgebraforwhichMarkowitzdevelopedefficientsolutionalgorithmsthatweremoreeasilycomputable.ThismatrixalgebraapproachthatminimizesvarianceforagivenreturnRandwealthwbecomes:mins2T=∋minXVXr=−X1r.+XR()WfXXwherethewealthconstraintr(X1=−W.)rX+RaffirmsthatwealthisfinvestedinariskyportfolioRthatreturnsRandarisk-freeassetthatreturnsrf.TheLagrangianoptimizationisthen:LX=+VTTλ(r−()W−+X1rX.R)fThiscanbereadilysolvedas:*1rw−rf−.XV=−(r1r)V(r1r)−−.T1−.(r1rf)ffwheretheexpressionrequiresustoinvertthe(ratherlarge)matrixofcovariancesV1ofallassets.Fromthis,wecandeterminethematrixofoptimalassetreturns:wRVT−1()R−⋅1rfr=11TVRr−1()−⋅f TheTheory63andtheoptimalportfoliomix:WXV*1=−−(r1.r)1V(r1r)T1−−.ffJamesTobinofferedanadditionalinsightbyaddingarisk-freeassetintothemix.TheMarkowitzoptimizationdeterminesapointontheupperlocusofagraphthatmapstheriskandreturnofallpossiblesecurities.Thisupperlocusyieldsthehighestreturnrforanystandarddeviationorvariance,andisnowcalledtheMarkowitzbullet,withanoptimalcapitalallocationlinesuperimposedbetweentherisk-freereturnandtheefficientportfoliofrontier.Tobin’sinsightwastoofferinvestorstheopportunitytoincludeintheirportfolioarisklessassetoranycombina-tionoftheoptimalsecurityportfolioandtherisklessasset.Fromthisframework,aninvestorisofferedarangeofinvestmentopportunitiesthateachyieldthebestpossiblereturnforanylevelofrisk,accordingtoeachinvestor’sriskreturnpreferences.Whilethemodelassumesthatallwouldrequireagreaterreturntotakeongreaterrisk,someinvestorsmaynonethelessresideatalowlevelofriskandreturn,whileothersmayacceptahighercombinationofriskandreturn.ThesequalitiescanbesuperimposedontheMarkowitzbulletandthecapitalallocationline.Markowitz’smodelismostprofoundifweaccepttheassumptionsthatasecuritycanbepricedbasedonitsmeanhistoricreturnanditsExpectedreturnCapitalallocationlineEfficientportfoliofrontierRisk-freereturnRiskFigure10.1Thecapitalallocationline 64TheRiseoftheQuantsExpectedreturnHighrisktoleranceCapitalallocationlineEfficientportfoliofrontierLowrisktoleranceRisk-freereturnRiskFigure10.2Variouschoicesofriskandreturnalongthecapitalallocationlinevarianceorstandarddeviation.However,italsoactedasaspringboardtoanequallyelegantinterpretationfromoneofMarkowitz’sassociates,WilliamForsythSharpe.TheSharpeinsightBythetimeWilliamForsythSharpeintroducedhimselftoMarkowitzin1960attheRANDCorporation,atthebehestofamentor,FredWestonatUCLA,ModernPortfolioTheorywasstillarelativelytheoreti-calinsight.Computationalchallengespreventedapowerfultheoreticaltoolfrommakingtheleapfromacademiaintopractice.Serendipitywasrepeatedwhen,followingachancemeetinginthewaitingroomofJacobMarschakadecadeearlierthatgaverisetoModernPortfolioTheory,thespeculativeknockontheofficedoorofMarkowitzchangedSharpe’sacademicfortunesandwouldestablishanewtheoryasthefoundationaltoolofsecuritiespricing.JustasMarkowitzwasfishingforathesistopicintheearly1950s,sowasSharpeintheearly1960s.SharpehadleftUCLAwithaMaster’sdegreeandwithakeenintuition,andwasanxioustocompleteaPhDthesiswhilehesimultaneouslysupportedhimself.HisnewlydiscoveredRANDcolleagueMarkowitzsuggestedtohimthathemighttakealookatportfoliotheoryonthemargin.Thistermofartinfinanceisusedtoexploretheimplications TheTheory65whensomefinancialoreconomicrelationshipischangedasmallamountormarginally.Inthiscase,whatwouldbetheimplicationsoftheaddi-tionofasingleassettoanoptimalportfolio?Sharpe’sexplorationofthissimplequestionwasobviouslyrelevanttofinancialpractitionerswhoneededamethodologytovaluetheriskofanindividualsecurity.Sharpe’sresolutiontoMarkowitz’squestionalsoforeverdemocratizedfinancialmarketsthroughitscreationofasimpletoolthatfinancepractitionerscanintuitivelyunderstandandemploytopriceindividualsecurities.ThefinanceworldhadtowaitforawhiletowitnessSharpe’sresolu-tion,though.Hepublishedhisnovelapproach,firstin19631andtheninitsseminalformin1964oncethemostprestigiousJournalofFinancefinallypublishedthenow-famous1962submission.Thislatterworkwasdelayeduntilaneweditorfinallyagreedtopublishtheground-breakingpaper.Thereferee’scriticismthatinitiallydelayedthepaper’spublicationregardedthehomogenityassumptionofthemodel.IntheCAPMapproach,itwasassumedthatinvestorshaveidenticalinforma-tionandestimationsofrisk,eveniftheydifferintheirindividualriskaversion.Acoupleofyearsofback-and-forthappealsandachangeineditorshipoccurred,andthepaperwasfinallyaccepted.However,afewyearslater,JamesTobin,whohadoriginallyofferedthemotivationoftheusefulnessofarisk-freeassetasabasicelementoftheCAPM,alsoexpressedhisreservationsoverarelatedissue–therepresentativeagentapproach.FromeconomicstofinanceThisrepresentativeagentframeworkwasemployedbySharpeasaneffectivetoolinthedeterminationofwhatwouldhappenifoneaddedanewriskyassettothemix.LetusassumethereisaportfolioMandwewanttodeterminetheresultoftheadditionofariskyassetA,wheretherelativeweightingsarewMandwArespectively.Thenthenewportfoliovarianceissimplyaweightedaverageofvariancesofthetwocompo-nents,withanappropriateadjustmentforthecomponentcovariance:ws22MM++ww22AA2wwrssMAAMAMNotethatarelativelysmalladditiontotheportfolioimpliesthatw2A≈0whilew2M≈1.Then,theincrementtoportfolioriskis2wwrssMAAMAMandtheexpectedmarketreturniscalculatedas:wwMMAAE(R)+E(R) 66TheRiseoftheQuantsTheinvestorpurchasesanincreasedreturn(wM1)E(RM)wAE(RA)wAE(RA)atacostofincreasedvariance2wMwArAMsAsM.Thediversifica-tionisefficientiftheadditionalriskispricedconsistentwiththeriskpremiumintherestoftheefficientportfolio.Accordingly:wwAAf()E(R−=R)/2MAAwrMAMsswwA()E(RMf−R)/2MAAMwsswhichcanberearrangedtoyieldthebasicresultoftheCAPM.ItisasimplerelationshipbetweentheexpectedvalueofafinancialassetE(RA),therisk-freerateofreturnRf,theexpectedmarketreturnE(RM),andameasureofrelativestandarddeviationsinthemarketandtheasset:E(R)R+(E(R)R)Af=−MfrssssAMAM/MM=Rf+(E(R)R)Mf−ssAM/MMTheexpressionssAM/MMissimplythestandarddeviationbetweenthenewassetandthemarketrelativetothemarketstandarddeviation.EversincethisformulationoftheCAPM,wecallthisrelativevariancethebeta,andinterpretitasarelativemeasureoftherequiredreturnoftheassetoverthemarketreturn,commensuratewithitsrisk.Embeddedinthiselegantapproachtopricinganindividualsecurityareanumberofassumptions.First,weassumethatthemarketisper-fect.Bythiswemeanthattherearenotransactionscostsortaxes,thatnotraderhasthepowertoinfluencepricesandallareequallyandcost-lesslyinformed,thatassetscanbetradedininfinitelydivisibleamounts,andthatexpectationsarehomogenouswhileinvestorsarerationalmaximizersinthedomainofsecuritymeansandvariances.Inaddition,themarketportfoliomustcontainallsecuritiesinpro-portiontotheirrelativecapitalization,andeachsecurityisefficientlypricedaccordingtoitsrisk.Ifweacceptthesepremises,thereisanimportantconsequence.Anindividualinvestorisfreedfromanalyzingtheentiremarketandcansimplyholdamarketportfolio,oranefficientindexfund.Theinvestorcanpriceadditionstotheportfoliobysimplyconsideringthesecurity’sbeta.Thenthemarketactsasapooloftheriskaversionofallparticipants,weightedbytheirholdings,andeachindividualsecurityissimplypricedrelativetoitscovariancerelativetothemarketvariance.Allsecuritiespriceriskefficientlyandhencethecombinationofanytwosecuritiescouldreplicatethemarketportfolio.LetustakealookatthemarketportfoliofromtheperspectiveoftheCAPMfromanempiricalperspective.Weknowthattheexpected TheTheory67returnofanefficientportfolioisbasedontherisk-freerateofreturnrfplusariskpremiumbasedonthemarketvariance.Thisriskpremiumperunitofriskissimplytheslopeofthecapitalallocationline.Ifwecompareanactualsecurityinasimilarway,wecouldrunaregressionoftheincrementtoreturnri–rfforanalternativeassetrelativetotherisk-freereturnasfollows:rirfii(rMrf)εi,whererMisthemarketreturnandεiisthenormallydistributedrandomerror.Thentheintercepttermi,nowknownasJensen’salpha,isthedegreetowhichtheassetisunderpriced,basedontheassumptionsoftheCAPM,andtheestimatedslopeIistherelativeriskpremiumfactor.SystematicandunsystematicriskThecapitalassetpricingapproachallowsustointerprettwocomponentsofrisk.Ifaregressionshowsthattheasset’sreturnishighlycorrelatedwithmarketreturns,thenitsriskmoveswiththesystematicriskofthemarket.If,ontheotherhand,thecorrelationwiththemarketisrelativelysmall,thenitsriskisunsystematicorlesscorrelatedwithmarketrisk.Suchunsys-tematicriskcanbereducedthroughdiversificationandthelawoflargenumbers,astheserandomcomponentstendtobeoffsetting.However,sys-tematicriskaffectsallmarketassetsandthuscannotbediversifiedaway.Sharpe’smotivationwasthataportfolio’sexpectedreturncanbemeasuredbasedonitsbeta,oritsriskinessvis-à-vistheoverallmarket.Thebetathenrepresentsacompactproxyforthesecurityprice,asameasureofthereturnthatcanbeexpectedforaninvestmentinsecuritycommensuratewithitsriskrelativetotheriskofthemarketoverall.SimultaneousdiscoveriesOtherswerepursuingdifferentapproachesthatwouldnonethelessdrawthesameconclusionsashadSharpe.TwoyearsafterSharpehadman-agedtogethistreatiseontheCAPMpublished,JanMossinsignificantlyextendedhisCAPMresults.Mossin’smostimportantextension,motivatedaspartofhisPhDthesisattheCarnegieInstituteofTechnology,broughtSharpe’ssingle-periodanalysisintoamulti-perioddynamicsetting.Mossin’s1966paper,andafurther1968extensionintheJournalofBusiness,demonstratedthatinvestorswhoexhibitconstantrelativeriskaversionact,ineffect,asiftheyaremyopic.Undersuchmyopia, 68TheRiseoftheQuantsaninvestor’sdecisionscanbehandledasiftheyareindependentofthefuturetimehorizon.Aninvestormayrebalancetheoverallsizeoftheportfolio,butneednotrebalancethesameportfolioproportions.Suchageneralization,underconstantrelativeriskaversion,avoidsacommoncriticismofthestaticnatureofSharpe’sapproach.Meanwhile,JohnLintner,thenatHarvardUniversity,continuedtoexploretheoptimalchoiceofprojectsbyafirmtobestmatchitsriskandreturnprofile.Lintner,too,reliedextensivelyfirstonMarkowitz’sModernPortfolioTheoryandthenonTobin’sseparationtheoremtodrawalmostidenticalresultsashadSharpefromtheindividualsecuritiesapproach.Indeed,thestrengthandsophisticationofhisresultsmayactuallyhaveexceededSharpe’ssophisticationintheJournalofFinance.AmodernreaderofhispaperwillnoticeremarkablesimilaritiestoLintner’sgraphicalexpo-sitions,andourmoderntextbookexpositionoftheCAPM,withreturnontheverticalaxisandriskonthehorizontalaxis,ratherthanSharpe’sapproachwiththeaxesreversed.Certainly,ifLintnerhadlivedlonger,hemighthaveearnedthesamelevelofrecognitionashadSharpe.Finally,JackTreynor,whohadponderedthesameissueforyearsandthendevotedavacationtoanintenseperiodofwritingtorecordhisversionoftheCAPM,hadalsoarrivedatthesameconclusions.NotunlikeLintner’sapproach,TreynorusedMarkowitzandTobinasaspringboardtoexplorehowdebt,orrisk-freeborrowing,andequitythroughprofitsfromretainedearningswillyieldreturnsonreinvest-mentinnewprojectsforthefirm.HewasalsoawareofModigliani’sandMertonMiller’sresultsthatdemonstratedtheneutralityofvalu-ationofthefirm,whetheritisfundedthroughborrowingorthroughtheissuingofshares.2Treynor,too,describedriskonthehorizontalaxisandreturnontheverticalaxis.However,heapproachedtheproblemfromanentirelydifferentperspective.Hisapproach,anexpansionoftheModigliani-Millertheoremtouncertainty,obscuredforyearshiscontributiontothecapitalassetpricingmodelingofindividualmar-ketsecurities.Inretrospect,wenowunderstandtheparallelnatureofhisworkandtheCAPMaswenowknowit.Consequently,hisroleinthedevelopmentoftheCAPMandhisrecordingofhisresultsin1962shouldstandinparalleltothedraftofSharpeinthesameyear.Similarly,JanMossin’scontributiontotheCAPMbeganatraditioninfinancethatwentunderappreciateduntilRobertMertonpopular-izedthenewapproachintheearly1970s.ByextendingSharpe’sstaticCAPMmodeltothetimedynamicsetting,hewouldbeginatraditioninfinanceofexplicitlyincludingthedynamicsoftime.Afewyearslater,MertonwouldlaterextendBlackandSchole’soptionspricingtheorytothedynamiccontextfollowingintheMossintradition. 11ApplicationsMarkowitz’sModernPortfolioTheoryspawnedcontributionsfromindividualsecuritiespricingtoprojectanalysis,multi-periodportfoliomodelingandoptimalcapitalstructureforcorporations.ThesevariousbranchesallstemmedfromthesameseedplantedbyJacobMarschakandSirJohnHicks–themeanandvariancedescriptionofreturnssubjecttouncertainty.NoneoftheseextensionscouldhaveoccurredwereitnotforthemicroeconomicfoundationscreatedbythoseassociatedwiththeCowlesCommissioninthe1940sand1950s.Thisapproachhasformedthebasisforthepricingoffinancialsecuritieseversince.Ofcourse,thefirstandsecondmomentapproachthatMarschakoriginatedinthe1930sand1940sisaccurateonlyifsomequiterestrictiveassumptionsaremade.Theseare,especially,thesymmetryofvariabilityofreturns,ofwhichthenormaldistributionisacommonspecialcase.Sincetheseinnovations,anumberoffinancialtheoristshaverelaxedtheassumptionofnormaldistributions.Forinstance,ithasbeennotedthatthenormaldistributionisbutoneofafamilyofdistributionscalledellipticaldistributionfunctions.Itturnsoutthatthemean-varianceapproachisapplicableforthisentirefamilyofvariabilitydistributions.1Someofthesubsequentextensionshaveallowedfinancialtheoriststorelaxtheassumptionofrisklesslendingandborrowing,forinstance,inBlack’szeroBetamodel,andthreedifferentclassesoftheCAPM–theoriginalCAPM,andthemoregeneralizedCCAPMandICAPM.WeshalldescribetheseCAPMextensionstoincludeconsumptionandintertem-poralchoicelaterinthischapter.OneproblemwiththeCAPMthattroubledoneofitsinspirations,JamesTobin,wasthattheinvestorwasassumedtoberepresentative.Inotherwords,investorswerehomogenouswithoutanymarketpowerand69 70TheRiseoftheQuantsoptimizemeanversusvarianceforsecuritieswithnormallydistributedreturns.Consequently,HarryMarkowitz,JamesTobin,WilliamForsythSharpe,andtheothersdiscoveredalinearpricingrelationshipinwhichexpectedreturnswereafunctionofthedegreeofsystematicriskinthefinancialmarket.Ifasecuritydepartsfromthislinearrelation-ship,rationalinvestorswillallsimultaneouslymakedecisionstorealignthepriceofasecurity.Thisapproachsharesobviousimplicationswiththeefficientmarkethypothesis,asthenextvolumeofthisserieswilldescribe.Inessence,investmentinagivensecuritybecomessomewhatirrelevant,then,ifeachsecurityispricedefficientlyaccordingtoitsrisk.Arisk-freeassetandanysingleassetcanthenprovideanyrisk-returntrade-offifbothlongandshortpositionsarepermitted.Theneedforabroadermarketportfolioisobviated.WeaknesseswiththeCAPMmodelAmodelbasedonthemeanandvarianceapproachisaccurateonlyifweacceptanumberofrestrictiveassumptions.First,wemustassumeassetreturnsarenormallydistributedor,moregenerally,ellipticallydistributed.Theassumptionofnormallyorellipticallydistributedassetreturnspredictsthatrelativelylargeswingsinassetpricesgreaterthantwostandarddeviationsshouldoccurextremelyinfrequently.However,individualsecuritiesoftenexhibitsurprisinglylargeswings.Second,shareholdersmustnotbeaffectedbymomentsbeyondthefirstmoment,orthemeanofthereturn,andthesecondmoment,itsvar-iance.Thisconditionimpliesthatshareholderscanbefullyrepresentedbyaquadraticutilityfunction.Thisratherrestrictiveassumptionmeetsmanyofthereasonablerequirementsforutilityfunctions,butassumesthatthemarginalutilityofincomediminishesataconstantrate.Sincethe1960s,financialtheoristshavebecomemuchmoresophis-ticatedintheirtreatmentofrisk.Theemphasisonsecondmomentswasamathematicalconvenienceinthe1930s.Secondmomentshadanimportantandaccurateanalogyamongphysicistsinthecalculationofmomentsofinertiaforrotatingbodies.Theycouldalsobecalculatedreadilyusingmatrixalgebraandsimplecalculatingmachines.Forthesesamereasons,thetechniqueofordinaryleastsquareslinearregressionwaswidelyadopted.Boththesecondmomentvariancecalculationandtheleastsquareserrorcalculationattachesanerrorpenaltyproportionaltothesquareofthedeviation.Usingthetechniqueofmatrixalgebratocalculateasecondmomentsimplyrequiresarowmatrixoferrortermstobemul-tipliedbyitstranspose.Thesquarefunctionhastheconveniencethatthe Applications71squareofallerrortermsarepositive,soeachcontributestothetotalerrormeasureratherthancancelsitout.Fromaperiodwhenallcalculationshadtobemadebyhand,theeminentphysicistCarlFriedrichGauss(1777–1855)recognizedthepragmaticbenefitsofthisapproachearlyinthenineteenthcentury.Beyondthisconvenientproperty,though,thereisnobehavioraljustificationthaterrorsshouldimpingeuponourdecision-makingbasedontheminimizationoftheirsquaredvalue.Withtheinventionofmoderncomputing,wecannowattachanysortoferrorfunctiontoourcalculations.Forinstance,behavioralfinancialthe-oristssuggestwemaywanttoattachadifferentmeasuretosecuritieslossesthangainsbecausemanystudieshavedemonstratedthatlossesnegativelyaffectshareholdersmorethangainsbenefitthem.Forinstance,withaggressivemarginingofstocks,shareholderscanbecomeverysensitivetolosses.Financialtheoristshaveproposedalternativeerrorfunctionsthatbetterfitreasonableassumptionsandobservationsofhumanbehavior.TheCAPMmodelalsoassumesfullinformationamonghomogenousagentsandperfectmarkets.Whiletherehavebeensomerelaxationsoftheseassumptions,itiscertainthattheseassumptionsarenotheldupinnormalmarkets.Thereexistasymmetriesininformationandshare-holdersdonotshareidenticalbeliefsandexpectations.Infact,thereislikelytobeadifferentsetofexpectationsofprobabili-tiesbetweencurrentandfutureshareholders.ThisasymmetryhasbeentreatedbyfinancialbehavioristswhohavedevelopedpsychologicallybasedassetpricingmodelsasanalternativetotheCAPM.2ExtensionsoftheCAPMMorecomplicatedversionsoftheCAPM,includingthesubsequentworkbyJohnLintner,includedtaxesandtransactionscoststhatwereoriginallyomittedfromtheCAPMmodel.PerhapslessproblematicisthattheCAPMmodelalsoassumesthatsharescanbeinfinitelydivisible,evenifthereareoftenpremiumstobepaidwhensecuritiesarepurchasedinlotssmallerthan100,andtherecannotbefractionalshares.TheCAPMwasinitiallydevelopedasastaticmodel,notanintertem-poralanddynamicmodel,withasecuritiespricedeterminedateachinstantoveradynamictimepath.JanMossinmadecontributionstosuchanintertemporalmodelwiththeresultsoftheCAPMemergingasaspecialcase.Later,anintertemporalCAPMmodel(ICAPM)wasfurtherdevelopedbyRobertMerton(seebelow),whohadextendedintothedynamiccontexttheBlack-Scholesoptionspricingtheory.Inaddition,theabilitytorebalanceaportfoliobydrawingdownassetvalueto 72TheRiseoftheQuantsconverttoconsumption,andviceversa,isextendedthroughtheconsumptionCAPM(CCAPM)modeldevelopedbyMarkRubensteinin19763andDouglasBreedenin1979.4Thisapproachmodelshowshareholdersoptimizetheutilityfromdiscountedlifetimeconsumptionbypermittingarebalancingoftheirconsumptionandassetdecisionsateachpointintime,dependingontheavailableopportunitiesforinvestmentreturns.Finally,anadditionalextensionofsuchanapproachcanincludeotherassetformsincludedinwealth,suchasrealestate,collectables,andpension,socialsecurity,andmedicalcareprograms.Theseformsofwealthhaveimportantimplicationsonbothconsumptionandinvest-ment.Demographic,social,andeconomicchangescanlikewiseaffectthisrebalancingandshiftsecuritiespricingovertimeinotherwisesimilarmarkets.ThebeginningsofanefficientmarkethypothesisThedifficultiesinobservingthetruewealthportfolioofinvestorsgaverisetowhatisknownasRoll’scritique,firstdescribedbyRichardRollin1977.5Inhis1977paper,Rollalsoofferedatautologythatismoredamningtoourmodelingofsecuritiesprices.LetusrecallthattheCAPMbetaisameasureofthesecurity’spremiumnecessarytocompensateforthegreaterriskofthesecurity.Inherentinthismeasureistheriskprofileoftheinvestor,whoisassumedtobehomogenous.Commentsonthenecessityofincludingheterogenousinvestorsandacompositionofinvestmentandconsumptionovertimearedulynoted.However,thereremainsamorefundamentalproblem,whichwillbethesubjectofthenextvolumeinthisseries.Ifthemarketisassumedtobemean-varianceefficient,thentheCAPMmodel,whichisalsoderivedfromtheassumptionofmean-varianceefficiency,simplybecomesare-statementoftheefficiencymarkethypothesis.Perhapsmostsignificantly,justasMarkowitz’sModernPortfolioTheorywastheinspirationforCAPM,CAPMmotivatedthemorepowerfulBlack-Scholesoptionspricingtheory.Inafatefulcollabora-tion,FischerBlackandMyronScholes,describedlaterinthisbook,andMichaelJensennotedthatvariationsinsecuritiesreturnsdonotseemtofollowtheCAPMmodel.Inparticular,low-riskandlow-betastocksseemtoofferhigherreturnsthanthemodelwouldpredict.Iffinancewishestopreservethebeliefthatmarketsareefficient,thentheCAPMmodeldoesnotseemtowork.Ontheotherhand,iftheCAPMmodelispreserved,thentheefficientmarkethypothesisdoesnothold,despite Applications73thenotionthattheCAPMmodelistautologicallysimilartotheefficientmarketapproach.6Theefficientmarkethypothesiswillbedescribedingreaterdetailinthenextvolumeinthisseries.Thesevariousauthorsproposedaplotbetweenreturnsagainstbetas,orriskpremiummeasures.Thereshouldbeastrongcorrelationbetweenthetwo,withanintercepttermofzerothatsignifiesthatazerobetaisequivalenttotherisk-freeasset.Whenempiricalstudiesofreturnsandbetaswerecompared,itwasdiscoveredthatthiscorrelationisnoisy,meaningthatthereisrandomnessinthecorrelations,especiallyforindividualsecurities.Inaddition,theydiscoveredthatboththeslopeoftherelationshipanditsinterceptweredifferentfromthosepredictedbytheCAPMbyastatisticallysignificantamount.ThiswaspreciselythemeasureofJensen’salphanotedearlier.Tobin’sregretAlltheCAPMcontributorsreliedcriticallyonTobin’sadditiontoMarkowitz’sModernPortfolioTheory.TobinhadtakenModernPortfolioTheoryintotherealmofKeynesianmonetaryeconomicsbysupplyingnuancetothetheoryofliquiditypreferenceandtheassetmixofhouse-holds.Hecouldnothaveanticipatedthatthissinglecontribution,incombinationwithModernPortfolioTheory,wouldcreatethepointwhentheoreticalfinancedivergedfromeconomics.Hadheanticipatedthisdeparture,hemighthaveframedhis1958paperquitedifferently.Tobin’spaperfitsintothecategoryofmicroeconomicfoundationsofmacroeconomictheory.Likethefinanceoftheentiremarket,themacroeconomyisincrediblycomplexandnuanced.Manyofthesub-tletiesofthemarketconstitutethenoisethatsimpletheoriescannotexplainwithoutsomuchcomplexitythattheirconclusionsbecomeinconclusive.Consequently,microeconomicfoundationscreatesimplerepresentationsandthenexploretheseabstractionswithinamacroeco-nomiccontext.Onesuchassumptionthatiscommoninsuchmodelsisthecreationofarepresentativeagentasatoolforanalysis.Thisoversimplificationishelpfulbecauseitallowsthemodeltofocusononeaspectofthequestion.SuchanoversimplificationwasincrediblyusefulforTobin’sinquiryin1958.However,theassumptionofarepresentativeagentmakeslittlesensewhenthemodelistakenfrommicroeconomicstothemacrofinanceofmodernmarkets.Hugevolumesoftrades,eachfromsomeonewhobelievesthatsellingisoptimalandanotherwhobelievesthatbuyingisoptimal,whileothersliquidatetheirpositions, 74TheRiseoftheQuantsperhapsfortheiruniqueconsumptionneedsorexpectations,allcastintodoubttheassumptionofasinglemonolithicinvestor.Tobinrecognizedthiscriticismhimselfandstatedthattherepresentativeagentassumption,asappliedtofinancemarkets,wasoneofhismostregrettablestatements.7Tobinevennotedthatthenotionofequilibriumseemstostandinstarkoppositiontoobservedmarketbehavior.Ifamarketisinequilibrium,thereisnoneedtotrade.Assumptionsofequilibriumseemtomakelittlesensewhenmarketstradehundredsoftimesoverinshortperiodsoftime.Despiteitslimitationsandstrongassumptions,theCAPMmodelhasenduredandflourishedeversinceitscreationinthe1960s.Everyfinancestudentlearnsthemodelfromitsfoundations,anditmotivateshowgenerationsoffinancialtheoristsandpractitionersthinkaboutandspeakofthepricingofsecurities.ItsenduringsuccessisthatitovercamethedifficultiesofMarkowitz’sModernPortfolioTheory,asaugmentedbyTobin.Theoriginaltheoryrequiredafinancialpractitionertocalcu-lateacovariancematrixofarankequaltothenumberofassets.Eveniftheanalysiswererestrictedtosecurities,anddangerouslyomittedotherassetsthathouseholdshold,therankofthematrixisbetween10,000and100,000forpubliclytradedcompaniesalone,dependingonthedegreeofglobalizationassumed.However,Sharpe,Lintner,Mossin,andTreynordemonstratedtechniquesthatcouldbereadilyappliedtoonesecurityatatimebycomparingthatsecurity,orthatprojectinthecaseofTreynor,totheoverallmarket.ThissimplicitypotentiallybroughttheCAPMintothecomputerprocessorofeveryfinancialpractitioner. 12LifeandLegacyThepracticalityandintuitiveappealoftheCAPMhasallowedittoendure.Certainly,noonewoulddenythatpastobservedmeasuresofriskoughttoinfluenceexpectedreturns,evenifonecanimagineotherforcesthatcouldimpingeaswell.Ofcourse,expectedreturnsarenotanobservablevariable.Ourregressionsarebasedonrealizedreturns,withalltheirattendantnoisefromotherunrelatedfactors.Indeed,theCAPMhasconstantlyevolvedtoincludeotherfactors.Taxes,dividendyields,transactionscosts,andintertemporalversionshaveallaugmenteditsconceptualusefulness.Certainly,theCAPM’sprincipalambassador,WilliamSharpe,andtheonlysurvivingacademicianofitsfoundingfourdevelopershasalwaysheldfaithintheutilityofhismodel.Whenaskedifhethoughtthemodelwassomethingbig,heresponded:Ididn’tknowhowimportantitwouldbe,butIfigureditwasprobablymoreimportantthananythingelseIwaslikelytodo.IhadpresenteditattheUniversityofChicagoinJanuary1962,andithadagoodreactionthere.Theyofferedmeajob.Thatwasagoodsign.IsubmittedthearticletotheJournalofFinancein1962.Itwasrejected.ThenIaskedforanotherreferee,andthejournalchangededitors.Itwaspublishedin1964.ItcameoutandIfiguredOK,thisisit.I’mwaiting.Isatbythephone.Thephonedidn’tring.Weekspassedandmonthspassed,andIthought,rats,thisisalmostcer-tainlythebestpaperI’mevergoingtowrite,andnobodycares.Itwaskindofdisappointing.Ijustdidn’trealizehowlongittookpeopletoreadjournals,soitwasawhilebeforereactionstartedcomingin…EugeneFamacalledittheCapitalAssetPricingModel.That’swherethenamecamefrom.175 76TheRiseoftheQuantsTheCAPMmodelstandswithMarkowitz’sModernPortfolioTheoryasthetwomostenduring,albeitimperfect,intuitivemodelsofsecuritiespricinginprimaryfinancialmarketsforsecuritiesthatareassumedtobeefficient.Bothscholarsprovidedtheoreticaljustificationfortheintuitivenotionsthatreturnscompensateforriskanddiversificationreducesrisk,respectively.ThePrizeTheSverigesRiksbankPrizeinEconomicSciencesinMemoryofAlfredNobel,oftenknownastheNobelPrizeinEconomics,wasawardedin1990tothreescholarsfor“theirpioneeringworkinthetheoryoffinan-cialeconomics.”MertonMillerwontheawardforhisworkonfinancialleverageandinrecognitionofhiscontribution,withFrancoModigliani,fortheequivalencyofdebtandequityfinancingincorporatefinance.ModiglianihadpreviouslywontheawardforhisworkontheLifeCycleHypothesisofconsumptionandsavings,andthusdidnotsharethelaterNobelPrizein1990withhiscollaborator.TheCommitteedoesnotmakeanawardtomorethanthreepeopleinagivencategoryeachyear,rarelyofferstheawardagaintoapreviousrecipient,anddoesnotgiveawardsposthumously,unlesstherecipientdiedbetweentheannouncementandtheawardingofthePrize.Onlyontwooccasions,toJohnBardeeninPhysicsin1956and1972,andFrederickSangerin1958and1980inChemistry,hastheNobelPrizeCommitteeawardedasingleindividualtwiceinagivendiscipline.Giventhattwootherscholarshadseparatelyprovidedthedisciplineofpersonalfinancewithitstwomostintuitivetools,itisfittingthatMarkowitzandSharpetogetherwontheawardfortheirworkonsecuri-tiespricing.JamesTobin,theintermediarywhogeneralizedandmadeMarkowitz’sModernPortfolioTheorymoreusefulandaccessible,andactedasthespringboardforWilliamSharpe’sCAPM,hadnotbeenpassedover,though.TobintoohadwontheNobelPrizein1981forhisworkonfinancialeconomies,inpartforhiscontributiontoport-foliotheoryin1958withinthecontextofhisinterestintheliquiditypreferencesofhouseholds.WhileTobincertainlystoodshouldertoshoulderwithMarkowitzandSharpeinthecreationoftheCAPM,andwasprominentintheiraddressesinStockholm,itwasunlikelythathewouldagainberewarded.NorwouldJohnLintner,whodiedsuddenlyin1983,orJanMossin,whoalsodiedprematurelyinNorwayin1987,berecognizedbyacom-mitteethatdidnotgiveposthumousawards.Finally,whileJackTreynor LifeandLegacy77arrivedatsimilarconclusionsashadhisCAPMcolleagues,albeitfromadifferentperspective,hepursuedacareerasafinancialpractitionerandexecutiveanddidnothavethelifetimecontributionofworkwhichtheNobelCommitteetypicallychoosestoreward.LatercareersFollowinghisencounterwithMarkowitzashisinformalPhDmentorandhissuccessfulthesisdefenseatUCLAin1961,Sharpesecuredaposi-tionasanassistantprofessorattheUniversityofWashington.ItwasinhisfirstyeartherethathecompletedandhonedhisinfluentialCAPMpapers,especially“CapitalAssetPrices–ATheoryofMarketEquilibriumUnderConditionsofRisk”intheJournalofFinance,submittedin1962andpublishedin1964.2By1968,hehadmovedagain,just30minutesfromhishometownattheUniversityofCaliforniaatIrvine,and,finally,twoyearslatertoStanfordUniversity’sGraduateSchoolofBusiness.Inthelate1960s,followingthesuccessfulpublicationofhisCAPMpaper,Sharpewasdrawnintoconsultingbyanotherfuturegreatmind,FischerBlack.Thiswork,inwhichBlackalsoinvolvedMichaelJensenofChicagoforanearlyproject,andthenhisfuturecollaboratorMyronScholes,helpedtoinspireBlacktoseeyetanotherextensionoftheCAPMintooptionspricingtheory.In1973SharpewasnamedtheTimkenProfessorofFinanceatStanford,whichhehelduntilheretiredastheStanco25ProfessorEmeritus.WhileatIrvineandStanford,hecontinuedhisresearchinfinance.Heremainedkeenlyinterestedinportfoliochoiceinfinancialmarketequilibrium.Hewroteaprominenttextbook,calledInvestment,nowinitssixthedition,withGordonAlexanderandJeffreyBailey,andFundamentalsofInvestments,alsowithGordonAlexanderandJeffreyBailey,andnowinitsthirdedition.Sharpealsobegantostudypensionsinthepost-CAPMportionofhiscareer.Inhisresearch,hecontinuedtolookintowaysinwhichtheore-ticalconceptscanbereducedtomethodologiesthatcanbeappliedbypractitioners.Forinstance,heproducedadiscrete-timebinomialoptionpricingprocedurethatofferedareadilyapplicableprocedureforBlack-Scholessecuritiespricing,whichwillbecoveredinthenextpartofthisbook.HealsodevelopedtheSharperatio,ameasureoftheriskofamutualorindexfundversusitsreward.Sharpecontinuedtoworktomakefinancialconceptsmoredemocraticandmoreaccessible.HehelpeddevelopFinancialEngines,anInternet-basedapplicationtodeliverinvestmentadviceonline. 78TheRiseoftheQuantsEverconcernedaboutthepractitioner’ssideoffinance,Sharpebegantoconsultwithinvestmenthouses,firstMerrillLynchandthenWellsFargo.AtMerrillLynch,hehelpedsetuptheirCAPManalysiscapacity.AtWellsFargo,hehelpeddevelopmethodologiesforthecreationofindexfundsandtheassessmentofportfoliorisk.In1986SharpecollaboratedwiththeFrankRussellCompanytoestablishtheSharpe-RussellResearchfirm.ThiscompanycapitalizedonSharpe’sacademicinterestinpensionsandportfolioallocations,andoffereditsexpertiseprimarilytofoundations.By1989,hefoundhimselfretiringfromfull-timeacademiatofocusonhisconsultingfirm,whichhassincebeenrenamedWilliamF.SharpeAssociates,onthecuspofthereceiptofhisNobelPrize.Overhisacademiccareer,SharpewasatrusteeofEconomistsforPeaceandSecurity,andwasawardedtheDoctorofHumaneLettersfromDePaulUniversity,theDoctorHonorisCausafromtheUniversityofAlicanteinSpain,andtheDoctorHonorisCausafromtheUniversityofVienna.HealsoreceivedUCLA’shighesthonor,theUCLAMedal,andwaselectedPresidentoftheAmericanFinanceAssociationin1980.Sharpehastwochildren,DeborahAnnandJonathanF.Sharpe,fromhisfirstmarriagetoRobertaRuth,andispresentlymarriedtoKathryn,whoisbothanaccomplishedpainterandartstudioownerandaprofes-sionalcollaboratorathiscompany.HeremainsactiveintheStanfordUniversitycommunity.JohnLintnerJohnLintneremergedasoneofthemosthighlyrespectedmembersatHarvardUniversity.Harvardhasbeenknownforitsemphasisoninstitu-tions,andLintner’sworksubsequenttohisCAPMcontributionwasinthisvein.Helookedattheroleoftaxesandoftransactioncostsonthepricingofthesecurity,primarilyfromatheoryofthefirmperspective.However,hisacademicbibliographyremainedrathermodest,withmanyofhiscontributionsconfinedtoHarvardUniversityworkingpapers.Overhiscareer,LintnerwasappointedasafellowoftheAmericanAcademyofArtsandSciences,andwasamemberoftheAmericanEconomicAssociation,theAmericanStatisticalAssociation,theAmericanAssociationfortheAdvancementofScience,andtheEconometricsSociety.LikeWilliamSharpeandmanyothergreatmindslikeFischerBlack,MyronScholes,andRobertMerton(whofollowedhim),andFrancoModiglianiandWilliamSharpe(whoprecededhim),hepresidedovertheAmericanFinanceAssociation(in1974)andheearnedthedistinctionofmembershiptothe LifeandLegacy79SocietyofFellowsofHarvardUniversity.HealsoservedthegovernmentonthePresident’sCouncilofEconomicAdvisorsandtheFederalHomeLoanBoard.Inaddition,Lintnerservedonnumerouscorporateboards,includingtheCambridgeSavingsBank,theUSandForeignSecuritiesCorporation,andChaseofBostonMutualFunds,andwasaconsultanttosuchgroupsastheUSCensus,theSecretaryoftheTreasury,andvariousotherprivatecorporations.HediedsuddenlyofaheartattackwhiledrivingonJune8,1983inCambridge,Massachusetts.JanMossinFollowinghisgraduationfromtheCarnegieInstituteofTechnology,JanMossinreturnedtohisnativeNorwayandgarneredastrongnationalreputationprimarilyasaneconomistwhofocusedonmoreregionallyrelevanteconomicissuesforhishomecountry.Healsomadecontribu-tionstootherareasbeyondthetheoryoffinance.Hisworkdelvedintotheeconomicsofuncertainty,operationsresearch,laboreconomics,andoptionspricing.HisworkalsotookhimtotheUniversityofCaliforniaatBerkeleyin1969–1970,NewYorkUniversityin1973–1974,ColumbiaUniversityin1976,theUniversityofTexasin1978–1979,andtheUniversityofWashingtonin1983–1984.Beforemanyothersinthediscipline,Mossinemployedthetoolsofgametheorywellbeforetheybecameastandardtoolineconomics.WhilepursuinghisteachingcareerinEurope,hepresidedovertheEuropeanFinanceAssociationandwaselectedaFellowoftheEconometricSociety.Hetoodiedprematurely,notlongafterhisfiftiethbirthday,in1987,threeyearsbeforehisCAPMcolleagueswereawardedtheNobelPrize.JackTreynorJackTreynorwasanall-Americanboy,determinedtomakehisfirstmillionby30andthentomarrywell.OfalltheCAPMcolleagues,hemostlikelyeasilyachievedthisloftygoal.Treynor’sfinancialsuccessdivertedhisattentionandhenevercompletedhisMITPhD.HeleftwithhisMaster’sforworkinindustry,wherehedevelopedhisconceptoftheCAPMmodelasamethodologyforafirmtoassessthereturn,netofrisk,ofaninternalproject.HewroteafewarticlesforpractitionerjournalssuchastheJournalofInvestmentManagementandtheCFAInstitute’sFinancialAnalystsJournal,where 80TheRiseoftheQuantshewasalsotheeditor.HeisalsoaSeniorDistinguishedFellowfortheInstituteforQuantitativeResearchinFinance(theQgroup).WhilehecontinuestoserveontheadvisoryboardsoftheFinancialAnalystsJournalandtheJournalofInvestmentManagement,andhastaughtcoursesatColumbiaUniversityandtheUniversityofSouthernCalifornia,hehaddevotedmuchofhiscareertothecorporatesector.Overhiscareer,hehasamassedmorethan70directorships,trusteeships,andgeneralpartnerships.Treynor’sdedicationtothefluidintegrationbetweentheoryandpracticewonhimtheInternationalAssociationofFinancialEngineers(IAFE)awardasthe2007IAFE/SunGardFinancialEngineeroftheYear(FEOY).ThisawardisinrecognitionofhiscontributionstotheCAPM.TreynorremainsPresidentofTreynorCapitalManagementandlivesinPalosVerdesEstates,California.Heturned81in2011.InadditiontohislegacyasoneoftheoriginatorsoftheCAPM,TreynorinspiredanotherNobelLaureateinawayremarkablysimilartotheinspirationthatHarryMarkowitzofferedWilliamSharpe.HewashiredbyMerrillLynchin1966byDonaldRegan,whowouldeventuallygoontobecometheUSA’s66thSecretaryoftheTreasuryandthenPresidentRonaldReagan’schiefofstaffinthe1980s.BeforemovingfromArthurD.Little,TreynoroverlappedtherewithayoungFischerBlackforayear.HiscolleagueBlackcontinuedtheresearchagendahebeganwithTreynorafterthelatter’sdeparture,andco-authoredthreeacademicpaperswithTreynorin1972,1973,and1976.Treynor’stremendousfinanceintuitionwasmostinfluentialonBlackandmanyothers.HisinsightsintotheprocessoffinancialsecuritiespricinginspiredBlacktomakeperhapsthemostprofound,insightful,andelegantdiscoveryinsecuritiespricing.ItistheworkofBlack,Treynor’syoungcollaborator,andhisco-consultantWilliamSharpeatArthurD.Littletowhichwenowturn. PartIIIFischerBlackandMyronScholesTheprogressionoffinancehasbeenremarkable.FromthedescriptionbyIrvingFischerastowhypeoplesavetothedeterminationbyJohnMaynardKeynes,HarryMarkowitz,andJamesTobinoftheoptimalmixofassets,financehasconsistentlyandsteadilybuiltuponever-broadeningfoundations.EversinceJohnBurrWilliamsdevelopedhisanalysisandthepresentvaluemethodologyofthevaluationofprojectsandoffirms,andJohnLintnerextendedthepresentvaluemethodologyincorporatefinancetoincorporaterisk,themodelshavenotdivergedbutratherhavebeenemployedtomorefullydescribethereturn–risktrade-off.ThismethodologyinthepricingofindividualstocksculminatedintheCAPM.Finally,thereemergedatoolthatthepractitionercouldusetodeter-minetheappropriatepriceofastock,givenitshistoricalpatternofrisk.However,onefurtherextensionwasbeggingtobediscovered.HowcouldapractitionerextendtheconceptsoftheCAPMtoalsodeterminethefairpriceforahedgetoinsureasophisticatedinvestoragainstmarketmovements?Therecouldnotbethreemoredifferentgreatmindsthatwouldresolvethesequestions.Thesethreecompletedtheanalysisofourpricingofsecuritiesandthederivativesthatinsurethem.While,uptothispoint,thegreatmindsdocumentedhereworkedwithindependence,andattimesinparallelwithoutknowledgeoftheother’swork,thenextsetofgreatmindsworkedinclosecollaborationandwillforeverbelinkedthroughtheculminationoftheirworkintheBlack-Scholesoptionspricingmodel. Thispageintentionallyleftblank 13TheEarlyYearsThetwonamesoftheoriginalformulatorsoftheBlack-Scholesoptionspricingmodelwillbeforeverassociatedwitheachother.However,haditnotbeenforthetheorythatlinkedthemforfinancialeternity,itwouldbedifficulttoevenimaginethemarecollaborators.Onewasatallall-Americanboy,withafamilytreethatdatesbacktowellbeforetheUSAwasanation,whiletheotherwasthegrandsonofRussianandPolishimmigrantsandgrewupinthebrawlingfrontierminingtownsofCanada.Webeginwiththesecondstoryfirst.MyronSamuelScholesCanadaattheturnofthetwentiethcenturywasmuchlikeitisnow,atleasteconomically.Then,theworldwasonthegoldstandard,andCanadahadsetitssightsonbecomingthesecondlargestgold-miningnationintheworld,justintimetofueltheglitteroftheGildedAgeinAmerica.Now,Canadaisstilltheworld’ssecondlargestproducerofthenewcommodityofinternationalcachet,oil,theblackgold.TheserichresourcesattractedCanadiansandimmigrantsaliketothefrontiersthatcontainedvastnaturalresources.DuringtheGildedAge,theKlondikeandCaribougoldrushesattractedpeoplefromallaroundtheworldwhoforgedadifficultpathtowardwhatsomeperceivedaseasyriches.Immigrantsrealizedthattheoddswerelongbutthattherewardwouldcompensatethemfortherisk.Othersundertookasteadier,low-riskbuttypicallylow-returnstrategyofservicingtheneedsofthosewholivedhardandfastandoftendiedthesameway.Thegreat-grandparentsofMyronSamuelScholestookthislatterroute.Hismother’sgrandparents,JohnerandBerthaChormaninoff,83 84TheRiseoftheQuantsMarkSchlossberg(1886–?)JessScholes(1905–?)EsterBorensterMyronSamuelScholesSpouse:(1941–)BarbaraScholesChildren:AnneH.ScholesM.VernerSaraL.ScholesSpouse:AnneH.VernerJanBlaustein(1910–1956)BucovetskyFigure13.1TheScholesfamilytreewereborninTsaristRussiain1855and1856,respectively,butescapedtheturmoilofthatcountryandbroughttheirdaughter,Fanny,andherhusband,SamuelMorrisBucotevskyofPoland,totheNipissingminingregionofNorthernOntario,Canada.Afewyearsbeforetheirarrivalin1910,therehadbeenamajorfindofcobaltinthetownnamedafterthemineraldiscovery.Samuelalmostimmediatelystartedworkasaself-employedmerchantanddiscoveredthathewasinpreciselytherightplaceattherighttime.Hissmallstoreexpandedtobecomeadepartmentstorethatcateredtothevariedneedsofarapidlygrowingminingtown.Infact,hisbusinessmodelwaswelladaptednotonlytoCobalt,Ontario,buttomanyotherlikecommunitiesinNorthernOntariothathaddiscoveredmineralsfromgoldtonickel,bariteandzinc.Amongthesecommunitieswasaclose-knitRussianJewishcommunity,andSamuelreliedonthenetworkofhisextendedfamilytofuelthedra-maticgrowthofhisdepartmentstoresallacrossNorthernOntario.ThewaveofRussianimmigrantstotheminingtownsinandaroundTimmins,OntarioalsobroughttheVerners,andAnneH.Vernerasaveryyounggirl,inthefirstdecadeofthetwentiethcentury.Anne’smotherwasmarriedtoSamuelBucovetsky’sbrother.AsSamuelbegantobuildhisretailempire,hequicklyenlistedhisniece,Anne,tohelp TheEarlyYears85builduptheirflagshipoperationinTimmins,justafewmilesfromherfamily’shomeinthegoldrushtownofSouthPorcupine.JustafewyearsbeforetheVernersarrivedinCanada,anothersonofPolishJewishimmigrantsarrivedinNewYorkCitywithhiswifeEsterandaveryyoungsonHerman.UpontheirarrivalinAmerica,theychangedhisfamily’snametoSchlossberg.Later,theirsons,JessandHerman,shortenedthefamilynamestillfurthertoScholes.Asayoungadult,theolderbrotherHermanventuredfromNewYorkCitytoHamilton,Ontarioinsearchofopportunity.Hisbrother,whowasfiveyearsyounger,soonfollowedhimtoseekalivelihoodduringtheGreatDepression.JessarrivedfirstinthetownofHamiltontolivewithhisbrother.MiningtownswerethrivingintheGreatDepressionandJessimaginedthathecoulddevelopalivelihoodinthoseleantimesinhisvocationofdentistryforafewyearsintheminingtownofTimmins,almost500milestothenorth.DuringtheGreatDepression,JesstendedtohisdentistrypracticeandAnneVernerassistedinthegrowthoftheBucovetskyDepartmentStorechain.AstheGreatDepressioncametoanend,JessmarriedAnne.Theyhadtheirfirstchild,MyronSamuelScholes,ayearlater.Theiryoungerson,David,wasbornfiveyearslater.ThefirstcoupleofyearsofmarriageandofMyron’slifewererathertumultuous.OnatraintriptoTorontoin1941,theBucovetskyDepartmentStorespatriarchSamuelBucovestskydied.Hispassingcreatedyearsoflegalwranglingasthehusbandsofhisdaughtersviedtotakeoverabusinessthathadgrowntoemploymorethan1,000peopleatitspeak.BecausetheownershipstakebelongingtothenewlymarriedAnneScholeshadnotbeenfullyestablished,shewaseffectivelyexcludedfromthecompany.Itbecamedifficulttoseethedepartmentstoresinherhometownthatshehadhelpedbuilduprunbyothers.Inaddition,itwasapparenttoherandherlearnedhusbandthatyoungMyronandDavidneededmoreintellectualstimulationthantheycouldfindinTimmins.TheScholesfamilymovedtoHamiltonbeforeMyronpreparedtoenterhighschool.OnceMyronenteredhighschool,hebecamewellawareofhisprecociousacademicskillsandespeciallyhisacumenformathematics,physics,computing,andfinance.Fortunately,hishighschool,WestdaleSecondarySchool,hadbeenfoundedinHamiltontoactasacollegiatepreparatoryschoolnotlongbeforethearrivaloftheScholesfamilyinthetown.There,Myronfoundgreateracademicstimulation,andhethrived.Hecamenearthetopofhisclassinhiseveryyear.Hisprowessinphysicsearnedhimascholarshipatthepublicuniversityin 86TheRiseoftheQuantsHamilton,McMasterUniversity.Andhisemerginginterestinfinancewasencouragedbyhismotherandfatherastheypermittedhimtomakehisowninvestmentsinthestockmarket.ThispenchantforinvestmentevenallowedyoungMyrontohelpsubsidizehiscollegeattendanceandprovideforanotherflowofincomeearlyinhisacademiccareers.HerelatedtotheOttawaCitizennewspaperhissomewhatriskyandoverconfidentinvestmentstrategy:‘‘Iwouldtakemysalaryandinvestitinthestockmarket.ThenI’dusethesecuri-tiestoborrowfromthebanktolive.Ialwaystoldmywifethatwewereinvesting,notborrowing.’’1However,asevereplungeinthemarketintheearly1970sthreatenedhisveryfinancialsurvival.Wereitnotforaskepticalbutsympatheticbanker,hemighthavebeenruined.Aroundthetimeofhisgraduationfromhighschool,twotragediesbefellMyronScholesandhisfamily.Hismotherdiedofcancerjustafewdaysafterhissixteenthbirthday.Ataboutthesametime,aconditioncalledkeratoconuscausedtheformationofscartissueinMyron’seyes.Whilehewasabletocurehiseyesightproblemsthroughanoperationtenyearslater,hewasforcedtorelyonabstractthoughtandmentalreasoningtogethimthroughhissenioryearinhighschoolandhisyearsatcollege.Scholesfoundhimselfineconomicsandfinanceonlybychance,despitehiswell-establishedinterestinpolitics,economics,finance,andmarketsevenbeforeheenteredcollege.Upongraduationfromhighschool,hetookasummerjobwithhismother’sbrother’smagazinepublishingcompany.There,hetookgreatprideinthedevelopmentofapuzzleforoneofthecompany’smagazinesmarketedatteenagegirls.Despitetheabstractbeautyofhisdesign,theeditorialboardpannedit.Throughthispainfullesson,herealizedthathepreferredtosolveproblemswhichhumanswouldappreciateratherthanthoseoftheesotericvarietythatappealedtotheoreticalphysicists.TheentrancecommitteeatMcMasterUniversityanticipatedthatyoungScholeswouldentertostudyphysicsorengineering.However,heenrolledineconomicsandliberalstudies.Hisdecisionturnedouttobeagoodone.BecauseMcMasterinthosedayswasstillarelativelysmallschool,hehadtheopportunitytogettoknowProfessorMcIver.ProfessorMcIverhadgraduatedfromtheUniversityofChicagoandwaswellversedinthemarket-orientedChicagoSchoolasespousedbyMiltonFriedmanandGeorgeStigler.HisChicagoSchooleconomicphilosophymadeastrongimpressiononMyron.ScholesgraduatedwithaneconomicsdegreefromMcMasterin1962,justbeforehistwenty-firstbirthday.Hehadtomakeachoicefrom TheEarlyYears87threealternatives.Hecouldgoontostudyeitherlaworeconomics,orhecouldrejoinhisuncle’spublishingbusiness,ashismotherwouldhavepreferred.Indeferencetothememoryofhismother,hedecidedtopursuebothhisacademicavocationandindulgehismother’swishesbyenrollingattheUniversityofChicago.Theyoungmanwhogrewupinafrontierminingtownof25,000people,mostlymen,foundhimselfinAmerica’ssecondcityandwithinthehallsthatwouldsoonberecog-nizedforspawningmoreNobelPrizesinEconomicsthananyotherplaceintheworld.Scholes’miningtownscrappinessandCanadianpolitenesswasaninterestingcombinationattheurbaneChicagoivorytower.AnewtoolforthefacultyLikehismother,Scholeswasendearinglyentrepreneurial.Hehadforsakensummeremploymentathisuncle’spublishinghousetoinsteadworkattheUniversity’scomputercenter.ThiswasintheerajustbeforeandduringthereleaseoftheIBM360computeranditsaccel-erationofmoreaffordableandsophisticatedcomputinginacademia.ProgrammingwasdoneinCOBOLandFORTRANatthetime,andreliedoncomputerpunchcardsforthestorageandorganizationoflinesofcomputercodeanddata.Thedisciplineofcomputerscienceswasstillnew,andnewapplicationsofcomputingpoweroutstrippedcomputersciencesgraduatesbyawidemargin.Giventhedemandforprogrammers,itwasnotdifficultforScholestotalkhimselfintoajobatthecomputercenteratChicago.However,becausehismoreseniorcolleaguesweretoobusy,hehadtoteachhimselfprogramming.Liketheotherendeavorstowhichheturned,hefoundhisnicheandcultivatedhistalenttomaximumadvantage.Soon,awho’swhooffinanceprofessorsbutcomputerneophyteswereseekinghimouttohelpintheirprogrammingneedsforvariousdata-orientedresearchprojects.EugeneFamaandMertonMillersoughthimout,asdidLesterTeslerandPeterPashigian.Scholesfoundhimselfinhighdemandamongsomeoftheworld’sfinancialelite.Scholes’hardwork,innateintelligence,andrelationshipswiththefaculty,arisingespeciallyfromtheactiveencouragementhereceivedfromChicagoprofessorMertonMiller,earnedhimtheappreciationandrespectofhisnew-foundcolleagues.HewasencouragedtostayonatChicagotocompleteaPhDinfinance.Notsurprisingly,hisPhDthesiswasacleveranalysisofsecuritiespricing,basedontherisk–rewardtrade-offandthenewtooloftheCAPM,whichwashighlydata-andcomputing-intensive. 88TheRiseoftheQuantsInthemiddleofthe1960sandonlyjustaspapersontheCAPMwerebeginningtocirculate,Scholes’thesissharedcharacteristicsofthesameapproachthathadinspiredWilliamSharpe,JohnLintner,andJackTreynorintheirCAPMexplorations.Atthemicro-level,inLintnerandTreynor’sapproach,hewonderedhowwouldthevalueofafirmchangewithchangesintheprospectsofaproject.SharpeandScholestookthemacro-approach.Howwouldtheprofitabilityofasinglestockbeincorporatedintoitsstockpricerelativetotheentiremarket?Sharpe’sapproachgaverisetotheCAPM.Asanaturalextension,Scholesexploredhowtheinformationdeducedfromthelargesalebyaninformedtraderwouldbeincorporatedintothestockprice.Hehadimmersedhimselfintheliteratureonriskandreturn,andonsignalingandinformationtheory.Theseunderstandingswouldleadtohissubse-quentgroundbreakingworkonthevalueofstockoptions.ScholesdefendedhisPhDin1968.IntheUSuniversitysystemitisextremelyrareforthegraduateofaPhDprogramtotakeupapositionatthatuniversity.IfonehadtoforsaketherichintellectualheritageoftheUniversityofChicago,withthegreatconcentrationofsubsequentwinnersoftheNobelPrize,whichwasfirstawardedtheyearafterScholesgraduated,thentheMassachusettsInstituteofTechnology(MIT)wouldbethenextchoice.ScholessecuredapositionatMITasanassistantprofessor.Earlyon,youngProfessorScholescastanauraofacademicbrilliance.FromhiscolleaguesattheSloanSchooltothoseathissubsequentposi-tionsattheUniversityofChicagoandStanfordUniversity,everybodyhasaScholesstory,usuallyinvokingsomesenseofbrashconfidencebutalsogentlegraciousness.CharacteristicofthisisthestoryofferedbyCarolLevenson,agraduatefromtheUniversityofChicago.Shecom-mentedthat“Prof.Scholeswasverycharismatic.Hewassofaroverourheadsthatnobodywassmartenoughtohaveanyinteractionwithhim.WefeltlikewewerestudyingwithEinstein.’’2AtMIT,thefreshlyPhD-mintedScholeshadtheopportunitytoworkwiththeearlyNobelPrizewinnerFrancoModigliani,whowasdiscussedinthefirstvolumeofthisseries,andRobertMerton,anotheryoungjuniorprofessorwhowouldalsosubsequentlywinaNobelPrize.ScholesalsohadtheopportunitytomeetandtoworkcloselywithFischerBlack.FischerBlackThesecondhalfoftheBlack-Scholescollaborationcouldnotbemoredifferentfromthefirst.Indeed,FischerBlackdistinguishedhimself TheEarlyYears89WilliamBlack(1770–1860)StanleyWarrenBlack(1876–1965)SarahStevens(1774–1850?)FischerBlackFreidrichFischer(1911–1999)born1802Germany,died1855Missouri,andLouisePieperborn1810,GermanyMariannaFischer(1874–1960)JosephineFischer(1841–1926),bornShiloh,ILCatherineTawes,FischerSheffyspouseFrantzYochisZempBlack(1938–1995)(1787–1824),Son:TerryLintonEntlebuchSwitzerlandJamesBlakeneyZempMiriamMimiAllen,(1886–1940)spouseDr.GeorgeSinclair,immigratedtoSouthChildren:Carolina,1710s,Ashleydied1730ElizabethClarkeMelissaZemp(1913–2000)PaigeRalphLenoir,bornAlethea1640England,immigratedtoNewYorkColonyAlbertusMooreLenoir(1890–1972)JohnandSaraOldfield,Jamaica,NewYork,1639Figure13.2TheBlackfamilytreefrommosteverygreatscholarinfinanceandeconomicsinthemodernerafollowingModernPortfolioTheoryandArrowandDebreu’sgeneralequilibrium.HesharedmanyqualitieswithJackTreynor,butalsoman-agedtonavigatetheivorytower,theworldofhighfinance,andfinanceimmortality.Andyethedidsowithouttheextensiveformaltrainingineconomicsandfinancethatistheuniversalnormandthepriceofadmissiontotheworldofscholarship.Inonerespect,Blacksharedmuchwithsomeotherswhopopulatethisvolumeofgreatmindsthatestablishedthequantschooloffinance.LikethefamiliesoftheCAPMpioneersWilliamSharpe,Treynor,andJohnLintnerbeforehim,Black’sfamilynameintheUSAdatedbacktopre-revolutionarydayswhenanothertypeofpioneerforgedalifeinanewworld.TheBlackfamilyhadmigratedacrossthepioneerUSAduringthe1800sastheymadetheirwayfromtheeasternseaboardtowardtheIllinoisfarmland.ItwastherethattheyremainedforgenerationsuntiltheopportunitytopracticelawbroughtFischerBlack’sfather,StanleyBlack,whohadrecentlyearnedalawdegreefromVincennes 90TheRiseoftheQuantsUniversityinIndiana,tojoinStanley’ssister,Amy,ShehadmovedtoNorthCarolinaandhadmarriedThadBryson,whowasanattorneyandthesonofthetown’sfounder.There,AmyintroducedherbrothertoherfriendMarianna.StanleyandMariannasoonmarried,and,fromthenon,theBlacknamebecamerootedinthesmallbutgrowingtownnestledintheNantahalaNationalForestabout50milessoutheastofKnoxville,Tennessee.SoonaftertheBlackfamilymovedtoBryson,thesizeofthetownalmosttripledtojustunder1,500residents.ThefamilyquicklyestablisheditselfinBrysonintheturnofthetwentiethcentury.StanleyBlacksetupalawpracticeandlatersteppedintosavetheBrysonCityBank,anenterprisethathepassedontohiseldestson,StanleyWarrenBlackJr.Fischer’sfatheralsohadtwooldersisters,EllenEnglemanBlack,whoearnedaPhDinsociologyfromtheUniversityofChicagoandlaterbecameNorthCarolina’sCommissionerofWelfare,andLouiseBrysonBlack,whomarriedOscarCox,anattorneywiththeUSTreasurywhohadauthoredtheLend-LeaseActandthemilitarycommissionthattriedWorldWarIIenemycombatants.Theyoungestboy,FischerSheffeyBlack,wasbornin1911,13yearsaftertheBlackfamilybecamewellestablishedintheiradoptedstateofNorthCarolina.FischertrainedtobeanengineerandmovedearlyinhiscareertoWashington,DCtotakeupthejobasamanagerandengineerwiththePotomacElectricPowerCompany.Followinginhisfather’sfootsteps,hequicklyobtainedalawdegreebystudyingevenings.ItwasinWashingtonthathemetElizabethClarke(Libby)Zemp.LiketheBlackclan,Libbytoocouldtraceherrootsonhermother’ssidetopre-Revolutionarytimes,alsoanthesideoftheSouth.LibbyhadlefthernativeSouthCarolinatofindworkinWashingtonfortheRoosevelt-eraWorksProgressAdministration.Theysoonmarried,andLibbyemergedasemotionalandspiritualcenterofthefamily,thesamerolethatFischer’smotherMariannahadservedwhenFischerwasachild.FischerSheffeyBlackJr.wasthefirstchildofthemarriage.WhenhewasbornonJanuary11,1938,inWashington,DC,hisyoungfamilywasenjoyinganalmostrurallifeonfouracresoflandinFallsChurch,notfaroutsideofWashington.Despitetheproximitytothecapitalofwhathademergedasthemosteconomicallypowerfulnationoftheworldjustafewyearsearlier,FischerJr.nonethelesshadabucolicupbringinginaclosefamily,withayoungersister,JaniceBlakeney,andbrother,LouisEngleman.Likemostofthegreatmindsinthisseries,youngFischerwasintellec-tuallyprecocious.Hewasabletoreadbytheageoffourandlovednewchallenges.Whenhisfatherdecidedtotryhishandatpublishing,the TheEarlyYears91familyhadtomovetoaBronxville,justnorthofManhattan,NewYorkCity,in1948,justastheten-year-oldFischerwasbeginningthesixthgradeayearearly.Despitethemove,youngFischercontinuedtothrive.HehadthegoodfortunetofindhimselfintheNewYorkpublicschoolsystem,thenoneofthebestinthecountry.HeexcelledthereanddiscoveredatypicalNewYorksensibilitythatstayedwithhimfortherestofhislife.Helearnedthetoolsofrhetoricandargument,oftakinganunpopularoranindefensiblepositionandenjoyingthedebateandemotionsthatensued,andthensittingback,watchingandthoroughlyentertained,oncethepotwasstirred.ThistendencybroughtoutinhimwouldbodewellinhisforayintotheroughandtumbleworldoftheUniversityofChicago,whichtookgreatprideindevouringyoungminds.Despitethebustleofthepost-SecondWorldWareraintheBronx,youngFischeractuallypreferredabookishexistence.Hehadafewclosefriends,allofwhomwerealsohighachievers.Becausehehadskippedagrade,hewastypicallysurroundedwithteenagersalittleolderthanhewas,atatimeinlifewhenoneyearmakesabigdifference.But,despitethishandicap,hisconfidence,intelligence,andheight(hewasalready6’2”at17yearsofagein1955,hissummerbeforecollege)combinedforaboyishcharmthatmanyfoundveryattractive.OnesuchfriendwasCynthia“Tinna”Carpenter,fromnearbyScarsdale,whomhehadmetonastudentexchangetripjustbeforeenteringHarvardinthefallof1955.ShewasonherwaytoSmithCollege,inNorthampton,Massachusetts,about100milestothewestofCambridge,Massachusetts.Unfortunately,Tinna’sfamilydidnotquiteembraceFischer’sbohemianwaysadecadebeforebeatnikyouthforgedanationalmovement.Nevertobeintimidatedintoconformingtothepreferencesofothers,FischeraskedTinnatomarryhimayearbeforegraduatingfromcollege.HewasattractedtotheidyllicimageofhischildhoodanddidnotfathomtheincongruencyofCambridgeonthecuspofthe1960s,thepressuresofcompletingcollegeasa20-year-oldhusband,and,almostimmediately,afather,andtheneedforhimtoestablishacareertrajectoryproportionaltohisconfidence,ambition,andtalents.Themarriagedidnotlast,butdidproduceason,TerryLinton.Incollege,Fischerwasthebright,able,andinquisitivestudentacaringfacultymemberwantedtolikebutfoundwanting.Hewaseasilydistractedorbored,andwouldworkonlyonthosetopicsandideashefoundinteresting,notthosethathisprofessorsdeemedimportant.Hewasacompletenon-conformistinaplacewherepeoplecompetedto 92TheRiseoftheQuantsout-conform.Andhejumpedfromfieldofstudytofieldofstudylikeabeefromflowertoflower.Asinhighschool,hefoundhimselfdrawntomathematicsandphysics,evenasheexploredeverypossiblediver-sionaryalternative.Upongraduation,hesuccumbedagaintophysicsatthegraduateschoolatHarvardasawaytoremaininCambridgeinadisciplineinwhichhefelthehadhisbestshotatadmission.Superlativescoresonhisgraduaterecordsexammadeitimpossibleforhisalmamatertodenyhimentry.Thescores,intheSputnikera,alsoearnedhimaprestigiousandlucrativescholarship.However,theleoparddidnotchangehisspots.Hefailedtoenrollintheusualphysicscurriculumandinsteadexploredphilosophy,mathematics,andthenewtheoryofcomputerscience.Toextendhisstayevenasheworeoutthepatienceofhisadvisors,hewonacom-petitionbysolvinganalmostintractableprobleminmathematics.Hethenbegantoimmersehimselfinthetechniquesofartificialintel-ligencewellbeforethiscomputingprocesswaslabeledassuchbytheeminentcomputerscientistJohnMcCarthy.Heprovedbrilliantatthattooandusedhisnovelcomputingskillsasaforayintojobsforyears.However,hecouldnolongercharmhissupervisor,whoputhimonanot-unreasonablytightacademicregimewhich,bothprobablyknew,hecouldnothelpbutfail.Hedidnotmeetthedeadlineshissupervisorimposedandhewasnotinvitedbacktoreturntohisprograminthefallof1962.BlackhadseentheinevitabilityofpartingofwayswithHarvardcomingforsometimeandhadpreparedhimselfbysecuringapositionattheRANDInstituteinSantaMonica,California,forthesummerof1961,andthenataCambridgeconsultingfirmwhenhewasforcedtoleaveHarvardin1962.Bythen,Tinnahadleftwithhischild,andhebegandating.HethrewhimselfintotheCambridgeenergiesthathehadmissedoutonyearsbeforewhenhewasprematurelypreparingforfatherhood.TheworkBlackfoundatfirstwasincomputing.Then,asnow,MIT,acoupleofmileseastdownCambridgeAvenuefromHarvardSquare,wasoneoftheworld’sleadingcentersforartificialintelligence.Thepatriarchoftheartificialintelligenceprogramthere,MarvinMinsky,discoveredhisworkandencouragedhimtoreturntoschool.Incoop-erationwithanewHarvardprofessor,hesuccessfullycompletedaPhDinappliedmathematicsbythesummerof1964.Finally,hisfatherwasconfidentthattheBlacknamesakewouldparlayhisPhDinthenewfieldofcomputerscienceintoasuccessfulcareer.Characteristically,Fischerthoughtotherwise,andreturnedto TheEarlyYears93theworldthathadtriedtodrumhimout.Hewantedtowritejournalarticlesandpapers.However,hewasprobablyill-preparedfortherigorsofteaching.Instead,hejoinedtheoperationsresearchdepartmentofarapidlyexpandingArthurD.LittleconsultingfirmtooverlapwithandthentakeoverthepositionofJackTreynor,wholeftbecausethefirmwouldnotmeethisrevisedsalaryexpectations.CrossedpathsatArthurD.Little,JackTreynor,andMITArthurD.Littleisoneoftheworld’spremierbusinessconsultingfirms.In2011,itadvertisedthatitwascelebratingits125thanniversary.Namedafteritsfounder,achemicalengineerwhosetouttoadviseontechnicalmatters,thisCambridge-basedfirmstartedbranchingoutintobusinesswiththedevelopmentoftheworld’sfirstsupplychaincontrolsystemin1951.Alwaysemployingleading-edgetechnologies,itslogisticsgroup,whichhadhiredBlack,wasanearlyadopterofcomputersinmanagementoperationsresearchandbegantoadviseonandprovidecomputer-basedmanagementcontrolsystemstoleadingcompaniesbeginninginthe1950sand1960s.Black’sPhDthesisonacomputerized“DeductiveQuestionAnsweringSystem”seemedtofitperfectlyintoArthurD.Little’sstrategicplan.Hewashiredtosupportthefirm’sconsultantswhoworkeddirectlywithclientstosolvetheiroperationsresearchproblems.SoonafterhisarrivalatArthurD.Little,BlackwasgroomedtoreplaceJackTreynor,theco-developeroftheCAPMmodeldiscussedearlier.TreynorhadworkedinthefinanceareaatthecompanyandhadleftBlackwithaninvestmentfundmanagementassignmentonbehalfofYaleUniversityandagrab-bagportfoliooffinanceintuitionclientstowhichhehadneverbeforebeenexposed.However,heattackedtheinvestmentfundmanagementwithhisusualingenuityandlearnedthenecessaryskillsoffinanceonthejob.Treynor’sfinanceknowledgecamefromacombinationofhistrainingatHaverfordCollegeasamathematicsmajorandfromhissubsequentMBAattheHarvardBusinessSchool.Asdiscussedearlier,hisinsightintotheCAPMmodelwasnotfromtheperspectiveofthepricethataninvestormaybewillingtopayforasecurityofgivenrisk,butratherfromthenecessaryreturnforacorporationtoundertakeaprojectwithagivenrisk.EversinceJohnBurrWilliams,theHarvardBusinessSchoolgraduateandchemicalengineer,exploredtheimportanceofthedis-countrateonthepresentvalueoffutureflowsofincome,discountedfutureflowsofincomehadbeenamainstayincalculationsinfinance. 94TheRiseoftheQuantsTreynor’sinnovationwastodeterminehowsuchanapproachmustbemodifiedinordertotakeriskintoaccount.Henotedthatitistheriskoftheproject,relativetotheriskofthefirm,thatwouldaffectthefirm’soverallriskiness.Hence,itisthecovarianceofrisk,ratherthanthesharedvariance,thatmustbefactoredintothefirm’sinternalvalua-tioncalculations.Ofcourse,WilliamSharpehadindependentlyarrivedatthesameconclusion,butfromtheexternalperspective.Treynorinitiallymadeacareeroutofmodelingvaluationsoffirms’assetsandprojects,initiallyinservicetoArthurD.Little.Thisman-agementconsultancystyleofanalysismadeastrongimpressiononBlack,who,forhislackoffinancetraining,didnotyethavethebroadperspectiveinfinancethatmoreformaltrainingwouldhaveprovided.Thiscursemaywellhavebeenablessing.TheassignmentwhichBlackandTreynorsharedsoughttodevelopvariouspossiblerankingschemesthatwouldhelpmanageYaleUniversity’sinvestmentfundsthatperformedstatisticallydifferentlyrelativetoeachother.BlackusedaningeniousportfoliorankingsystemthathehaddevelopedwithTreynor.Tohelpintheanalysisanddevelopmentofarankingsystem,heassembledWilliamSharpe,thenattheUniversityofWashingtonandanobviousadvocateoftheCAPMwayofviewingfunds,andtheyoungprofessorMichaelJensen,whobroughttothemixthenotionofthenewefficientmarkethypothesisapproachfromhishomeinstitution,theUniversityofChicago.Obviously,threegreatmindsbringingtobearthreedifferenttechniquesononeproblemwouldreleaseagreatdealofintellectualenergy.Attheendoftheircollaboration,theefficientmarkethypothesisprevailedandtheyagreedthatnostrategycouldconsistentlybeatthemarket,eventhoughtheirclientwishedtobetoldotherwise.Blackwroteuphisreasoningbybuildingoninsightsfromhiscol-laborationandfrompastfiles,notes,andpapersTreynorhadleftatArthurD.Little.WhileTreynorhadsincemovedtoMerrillLynch,hislegacyandinfluencenonethelessbecamethebasisofco-authoredpaperswithBlack.Indeed,Blackproducedaseriesofsuchcollaborationsandpresentedthematjointpractitionerandacademicianconferencesateveryopportunity.Hewasbeginningtoestablishareputationforhim-selfandhiscolleagueTreynorinthatvoidbetweentheoryandpractice.WhenTreynorgrewtiredofMerrillLynchandtookontheeditorshipoftheFinancialAnalystsJournal,therewasfinallyaforumthatcouldpublicizesuchpapersandfillthevoidbetweentheoryandpractice.Treynortookonthetaskofguidingpractitionersandanalystsclosertothescienceoffinance,whileatthesametimeinformingtheorists TheEarlyYears95abouttheartofinvesting.Withhisbullypulpit,healsofoundalifelongcollaboratorinBlack,theonlyothergreatmindinfinancewhohadnotbeenindoctrinatedintotheeconomicsparadigmthroughthecompletionofaneconomicsPhDorapositioninanacademicdepartment.Actually,Black’sTreynor-derivedCAPMviewoftheworld,withnon-systematicprojectriskbiasingoverallcorporaterisk,developedasacharacteristicallyuniqueFischerianwayoflookingatthefinancialandeconomicworld.MoretraditionaleconomistsorfinancialtheoristsmayhavelookedattheworldthroughaKeynesianlens,oraclassicallens,orperhapsanefficientmarkethypothesislensoraModernPortfolioTheorylens.Black’slenswasonehesharedwithonlyoneotherperson,andTreynorwasnotcirculatinginacademiccircles.Thismeantthathecameoffasbrilliantandcompletelyoriginaltosome,andperhapsasanunconventionalcrackpottoothers.However,withthehelpofTreynor’sjournal,alongwithhisfrequenttalksatmeetingsthatincludedacademicians,someofBlack’sargumentsbegantobepublished.Hewasslowlybuildingforhimselfareputation,butfromoutsidethetraditionalivorytower.HedidArthurD.Little’sworkduringtheday,but,inaparticularflourishofintellectualenergyin1969,hewasproducinguniqueideasinmacroeconomics,finance,andbusinesscycletheoryateveryotheravailablemoment.Blackhadsomebrilliantideas.However,heneededpolish,someacademicrigor,andacademiclegitimacyinordertobringhisuncon-ventionalideastothepureacademicmarket.Thistransitionwouldbedifficult,though.Whilealayreadermightimaginethattheivorytoweristheultimatelastbastionofliberalthought,innovation,progressivity,andthemarketplaceforideas,oftentheoppositeistrue.Academiciansinvestalltheirlearningintoschoolsofthought,andintheperpetua-tionofresearchagendasthatoftencamefromtheirPhDsupervisorsormentors,andthementorsbeforethem.Todiscardthestatusquois,tomanyacademicians,todiscardtheirentireinvestmentintheirhumancapitalandmanyofthetoolsintheirtoolbox.Unconventionality,ahallmarkofBlackeversincehewasachildinBronxville,wasnotalwaysappreciatedorencouraged.Everygreatcollaborationofferscomplementaryskillsthatresultinasynergyforwhichthewholeisgreaterthanthesumofitsparts.MyronScholeswouldhelpprovidesomeacademiclegitimacyandamoreconventionalandrobustinterpretationofBlack’sinsights. 14TheTimesThepricingofthemostelementaryofsecuritieshasbeenwellunderstoodsincethenineteenthcentury.Financialpractitionershadusedthesimplebondpricingformulatodeterminethepriceofabondwithaspecifiedcouponpaymentrateandtheredemption(orface)value.AnefficientbondpriceisequaltothevalueoftheperiodiccouponpaymentsCdiscountedbytheappropriaterisk-adjustedinterestrateandthepresentvalueofthereturnofthefacevalueFuponmaturityinTyears.Then,basedonthediscountednetpresentvaluemodel,thebondpriceisgivenby:PC/(1r)1C/(1r)2…C/(1r)TF/(1r)TTheprocessworkedwellforbondswithnodefaultrisk,andhenceworkedformostbondsissuedbystrongcompaniesforwhichbondownershadthefirstclaimonassetsinthecaseofliquidation.IttookmanymoredecadestodeveloptheCAPMthatallowedequitysharestobepricedbasedontheirobservedpatternofrisk.However,financialpractitionershaveforyearsincludedcombinationsofbonds,stocks,andoptionsorwarrantsintheirportfoliosaswaystooptimizereturnsandhedgerisk.Theyproducedtheseinstrumentsofoptionsandwar-rantsthatderivetheirvaluebasedontheunderlyingsecuritywithoutanypricingformulagroundedinsoundfinancialtheory.Nonetheless,thetwoscholarsLyndonMooreandSteveJuhrecentlystudiedthewarrantpricesforminingstockstradedontheJohannesburgStockExchangealmost100yearsagoandfoundthat,withoutthebenefitoftheBlack-Scholesequation,themispricingofwarrantsonlydeviatedfromtheBlack-Scholespredictionbyabout27percentbasedonhistoricalmeasuresofvolatilityatthattime.96 TheTimes97Interestingly,theseresearchersre-rantheanalysisfortradingofwarrantsonthesameexchangebetween2001and2003,whentheappli-cationofthemodernBlack-Scholesequationhadbecomeroutineandcommonplace,andtheystilldiscoveredcomparableexpostmispricing.1Clearly,intuitiveinvestorsunderstoodtheartofoptionspricingeveniftheydidnothaveitdowntoascience.InthebeginningInfact,theartofoptionshasbeenwithhumankindsinceancienthis-tory.TheGreeksusedoptionstosecurepricesforoliveoilatalaterharvest.AGreekmathematicianandphilosopherwasevenpurportedtohavepurchasedatlowcostintheoff-seasontheoptiontouseoilpressmachinerycapacityforthefallharvest.Hisstrategywastoexercisehisoptionswhentheolivepresseswereingreatdemandinthespring,oncethehigh-demandperiodarrived.Hecouldthenexercisehisoptionandrentoutthemachinesforahandsomeprofit.Aristotlereferenced:Thereis,forexample,thestorywhichistoldofThalesofMiletus.Itisastoryaboutaschemeformakingmoney,whichisfatheredonThalesowingtohisreputationforwisdom;butitinvolvesaprincipleofgeneralapplication.Hewasreproachedforhispovertywhichwassupposedtoshowtheusefulnessofphilosophy;butobservingfromhisknowledgeofmeteorology(sothestorygoes)thattherewaslikelytobeaheavycropofolives[nextsummer],andhavingasmallsumathiscommand,hepaiddownearnest-money,earlyintheyear,forthehireofalltheolive-pressesinMiletusandChios;andhemanaged,intheabsenceofanyhigheroffer,tosecurethematalowrate.Whentheseasoncame,andtherewasasuddenandsimultaneousdemandforanumberofpresses,heletoutthestockhehadcollectedatanyratehechosetofix;andmakingaconsider-ablefortunehesucceededinprovingthatitiseasyforphilosopherstobecomerichiftheysodesire,thoughitisnotthebusinesswhichtheyarereallyabout.2Thales’anecdoteisinteresting.Evenmillenniaago,therewasthesamelamentweheartodayovertheseparationofproductionfromthosethatwouldmakemoneythroughbettingontheproductionofothers.Theseearlyspeculationswerenotintheoptionscontractsoftoday.First,productionhadtobesecuritizedandfutureproductionwouldrequirecontingentclaims.Second,theremustbeaforumforthetrading 98TheRiseoftheQuantsofcontingentclaims.Theseinnovationsrequiredthedevelopmentoffinancialinstitutions,financialmarkets,andestablishedprinciplesoftrade.Theabilitytoreducetheuncertaintyoffutureeventsisthenatureofinsurance.Infact,bothinsuranceandthetradingofoptionsrequiredthesameprecursorsandarosethroughsimilarmarketsandinstitutions.ThegloballyorientedmarketsofLondon,Amsterdam,andAntwerpprovidedtheseprecursors.Eachoftheseregionsspecializedinthetradeofcertaingoods,andthetradersofthesegoodsbothtriedtoprofitandtocreatepredictabledeliveryofgoodstradedonlongsupplychainsbyengaginginoptionsandfutures.Forinstance,thegreattuliptradeofHollandcreatedwildspeculationandthedesirebytulipdealersofsecuringasteadyfuturesupplyatapricenegotiatedearlyon.Calloptionsusedbytulipbuyersensuredagoodpriceondelivery,andputscouldbeusedtoprovidesellerswithapredictablepricefortheirproductuponharvest.Whilethesemecha-nismsactedatfirstasawaytoensurepredictabilityforbuyersandsellersoftulips,itsoonbecameobvioustospeculatorsthatprofitscouldbehad.Asspeculatorswroteputsandcalls,itwouldnotbelongbeforegyrationsintulipmaniacausedmismatchesinoptionsanddeliveredpricesandquantitiesthatthosespeculatorsonthelosingendcouldnotcover.Suchbreakdownsinmarket-makingalsocreatedbreakdownsintrustinoptionsandinfinancialmarketsingeneral.Bythe1600sand1700s,largeglobaltradingcompanies,suchastheSouthSeasTradingCompany,werecontributingtoanoptionsfrenzyontheirsecurities.Tocurryfavorfrompoliticiansinexchangeforhelpfullegislation,companyrepresentativesofferedthepoliticianswarrantsortherighttobuycompany-issuedstockatalaterdatebutatapre-determinedprice.Theseoptions,whichrequirednoinvestmentfromthepoliticiansuntiltheychosetoexercisethem,presumablywhenthestockpricehadrisen,createdastrongincentivefortheking’sagentstopavethewayfortheSouthSeaTradingCompany’sprofitability.MerelytheknowledgethattheSouthSeasTradingCompanyhadcur-riedsuchfavordrovethestockpriceupdramaticallyasaself-fulfillingprophecy.Tofurtherfuelthefrenzy,thecompanyevenofferedtolendmoneytothosewhowishedtobuyitsstock.However,oncewordarrivedinLondonthatoneoftheSouthSeasTradingCompany’sinitiativeintheNewWorld,theMississippiScheme,hadfailedtomaterialize,ram-pantprofittakinginducedamasssell-offthatburstthespeculativebubbleandcausedmillionsofpoundsoflossesforallbuttheearliestpurchasersofthestock.Aftermakingahandsomeprofitfromearly TheTimes99purchasesofthestockandrollingtheprofitoverintolaterpurchasesandlosingeverything,SirIsaacNewtonwasquotedashavingquippedthathecouldnotcalculatethemadnessofpeople:“Icancalculatethemovementofthestars,butnotthemadnessofmen.”3TheburstingoftheSouthSeaTradingCompanybubbleandthelossofhugepotentialprofitsbylegislatorsastheirwarrantsbecameworth-lessinducedthoselegislatorsbribedwiththesewarrantstoputinplacewavesofregulationthatrestrictedoptionstrading.Regulationalsorequiredbrokerstomaintainashareasaprincipleintheunderwrit-ings.Infact,thecallforregulation,morecompletesecuritization,andmorescrupulousunderwritingandbrokeragewastheimpetusfortheformationoftheLondonStockExchange.Whilesuchregulationmaynothavecompletelyremovedthegamblingaspectofoptionstradingthatalmostentirelydisplacedthelegitimatehedgingrolethatoptionscouldprovide,itdidhelpincreatinganairofestablishmentonthepractice.Lessestablishedentitiesfounditmoredifficulttounderwriteandbrokeroptionstrades.EarlyoptionspricingWiththediscoveryofspeculationinoptionsbeyondthosethathadanyfundamentalinterestintheunderlyingsecurity,themotivationandthetoolsofoptionstradingwerethoseofthegambler.Theseeven-tuallybecamegamblesinwhichthetheoreticalsettlingofpurchasesanddeliveriesonspecifiedsettlementdays,calledtherescontre,werepermittedtoberolledovertothenextsettlementday.Thisinnovationpermittedalmostperpetualspeculation.Productionanddeliveryhadbecomedisconnectedfromoptionstrading,andonlytheforcesofarbi-tragetocapitalizeonspeculativeimbalancescoulddisciplineamarketinperpetualtradingofaderivateinstrument.However,bythelate1800s,itwasobservedthatsellers(writers)ofoptionsseemedtoconsistentlymakemoreprofitsthanbuyers.Theseunderwritersofoptionscontractsseemedtobeabletocreateoptionsthatsuccessfullycapitalizeonmarketpsychology,andperhapsalsoprofitfromthemanipulationsmadepossiblebylargemarketshareandpower.Thisrelativesophisticationcreatedevenfurtherrewardforgreaterstudyofthemechanismsofoptions.Soon,writerswereabletoprofitfromput-callimbalancesanddiscoveredtheycouldearnthesearbitrageprofitsuntiltherewasput-callparity.Notionsofput-callparitydatebackasfarasthe1600sand1700s,asdocumentedatthetimebydelaVega(1688)4anddePinto(1771).5 100TheRiseoftheQuantsPut-callparityforaEuropeanoptionthatcouldnotbesettledfortheunderlyingsecurityuntilsettlementdateTdeterminestheputpricefortherighttothesecurityofexercisepricexatsettlementisP0(x,t)atpresenttimet=0.Thisputpricemustequalthepriceoftherighttobuythesecurity,C0(x,t),plusthediscountedvalueoftheexerciseprice,lessthecurrentpriceoftheunderlyingsecurityS0:XP00[][]XT,,=+CXT−S01+rTAnotherwayofstatingthisrelationshipisthatthedifferencebetweentheputandcallpricetodayshouldequalthedifferencebetweenthepresentvalueoftheexercisepriceandthesecuritypricetoday.Ifthiswerenotthecase,itwouldbepossibletoearnanarbitrageprofit.Forinstance,iftheputpriceweretoolow,thenitwouldbepossibletowriteacallandcollectC,borrowX/(1r)T,andstillhaveenoughtobuyboththeputthatcancelsoutthecallonEuropeansettlementdateT,andthestock,witharisk-freearbitrageprofitleftover.AmericanoptionsOptionsintheUSAfollowedsimilarpaths,butdevelopedinaslightlydifferentway.TheAmericanversionofoptions,originallycalledprivileges,wereidiosyncraticcontractualarrangementsandlackedthestandardizationthatallowedthemtobetradedeasily.Eventually,inthewaveofregulationaftertheGreatCrashin1929andtheRooseveltregulatorywaveduringtheGreatDepression,optionswereenshrinedbytheInvestmentActof1934andregulatedbythenewlyestablishedSecuritiesandExchangeCommission.However,thereremainedlittleoptionsactivityuntiltheChicagoBoardOptionsExchange(CBOE)createdamuchbroaderandmoreliquidforumfortheirexchangethatwouldlowertransactionscostsandeasetrading.Infact,war-rants,orcompany-issuedoptions,originallyplayedarelativelylargerroleinfuturessecuritiestradingvis-à-visoptionsthantheydotoday.ThisexplainswhypioneeringworkbyscholarssuchasthegreatmindPaulSamuelsoninitiallystudiedwarrantsratherthanoptionsinthemid-1960s.AnewexchangeTheChicagoBoardofTrade(CBOT)istheworld’soldestfuturesexchange.Itwascreatedin1848tosatisfytheneedforfarmerstosecurebuyers TheTimes101ofthebountyoftheUSMidwestbreadbasketandformerchantsandprocessorstoensureasteadysupplyatapredictableprice.Thiscommod-ityexchangeformulatedstandardizedforwardcontracts,calledfuturescontracts,toreduceuncertaintiesandhencefacilitatecreditforbuyers.Inthiscapacity,theCBOTassistedinriskhedgingsothatboththefarmerandthefoodprocessorcouldbudgetbasedonpredictableprices.TheCBOTwasalsooneofthefirstfinancialmarketstofacilitatethetradeinoptionstopurchaseorsellAmericansecurities.However,theseAmericanoptionsdifferedfromtheirEuropeancounterpartsinthattheoptioncanbeexercisedatanytimeuptothesettlementdate.Inpractice,though,thispartoftheoptionisrarelyexercisedbecausepartofthepricepaidforanoptionistheopportunityforthederivativetoriseovertimeasthestockpricegrows.Tosellearlymeanstoleavethatportionofthepriceonthetable.Hence,inpractice,AmericanoptionsbehaveinthesamewayasEuropeanoptions.Bythelate1960s,themanagersoftheCBOTrecognizedthatthevolumeofcommoditiesexchangedbegantoshrinkasthecomplexionofUSagriculturemovedmoretowardlargefarmsalliedtolargecorpora-tions.Theseentitiescouldcontractwithouttheneedforanarm’s-lengthfacility.Hence,theVicePresidentforPlanningoftheBoard,JosephSullivan,proposedthattheCBOEshouldcreateanover-the-counteroptionsmarket.Healsorecognizedthatvalueforsuchoptions,asacontractingtool,wouldbeimprovedifthetermsofoptionsweredefinedwithasfewparametersasnecessary.Thisstandardizationwouldsimplifycontractingbutwouldalsomakepriceanalysiseasier.Inordertoreducetransactionscosts,Sullivanrecommendedthatmultipleputandcallintermediariesbereplacedwithmarketmakersthatmatchedbothsidesofthemarket,justasthespecialistsdoonfloor-tradedstockmarkets.Thesemarketmakerswouldthenprovideforgreaterefficiencybyprovidingbestprices.ThesevariousinnovationsproposedbySullivaneventuallyprovidedthebasisfortheCBOE.Withconsiderablefanfare,theexchangebegantradinginoptionsonahandfulofstocksonApril26,1973.Ayearlater,itsaveragedailyvolumehadincreasedbymorethan21times.Thenumberofstockslistedalsodoubled,asdidthenumberofmemberswhocouldparticipateintheexchange.Meanwhile,financialmarketderegulationfurtherpavedthewayforrapidgrowth,andbytheendof1974,lessthantwoyearsafteritstarted,theCBOEvolumehadincreasedbymorethan20,000percent.Whiletheexchangebeganbypermittingthebuyingandsellingoftherighttobuytheunderlyingsecurityatagivenstrikepriceupto 102TheRiseoftheQuantsapre-determinedsettlementday,anation’sfascinationwithoptionsinducedtheCBOEtoalsooffertheoptiontosellsecuritiesatapre-determinedpriceuptoapre-determineddate.Theseputcontracts,whichareboughtandsoldinlotsof100,sawevenfurtherdramaticgrowthandreachedanannualvolumeofalmost40millioncontractsbytheendofthedecadeand60millionbytheendofthecentury.Despitethedramaticinterest,therewasnoanalyticmethodtodeter-minethevalueofanoptionatthemarket’sinception.However,thegroundworkhadbeenlaiddecadesbefore,butremainedinrelativeobscurity.Bachelier’sbigideaTherehavebeentimeswhenthefinancedisciplinehasbeenheldback,sometimesfordecadesorcenturies,forreasonsastrivialaslanguagebarriers.ThefamedStPetersburgParadoxframedandresolvedbytheBernoullicousinsin1738mayhaveadvancedthenotionofdiminishingmarginalutilityacenturyandahalfearlierhaditnotbeenwritteninLatin.Similarly,ÉmileBorelandJohnvonNeumannwouldhavebeenabletoadvancetheirnotionsoftheminimaxsolu-tioningametheoryhadanobscurePolishmathematiciannamedHugoSteinhausspecifiedhisconceptofdominantstrategiesinEnglishinsteadofPolish.Steinhaus’paperin1925remainedinrelativeobscu-rityuntilOskarMorgensterninquiredaboutitin1952,andSteinhaushaditpublishedinEnglishin1960.6Thisoversightonlydelayedtheliteraturebyahandfulofyears.AndLeonardJimmieSavage,thefatherofpersonalprobabilities,wouldhavebeenabletoadvancethesub-jectiveschoolofthoughtonprobabilitiesandnotionalstockmarketpricesagenerationorsoearlieriftheworkofBrunodeFinettihadbeenpublishedinEnglish,oriftheEnglishmanFrankP.Ramseyhadlivedalongerlifeandhadnotbeensofaraheadofhistimeinthe1920sinCambridge,England.However,ofmoreimportanceisthedelayinourunderstandingofoptionsbyalmostthree-quartersofacenturybecausethebrilliantPhDcandidateLouisBachelierpublishedhisSorbonnePhDinFrenchanddidnotfollowuphisgraduateworkinawaythatwouldpopularizehisfeatintheEnglishliterature.LouisJean-BaptisteAlphonseBachelierwasborninLeHavre,FranceonMarch11,1870totheVice-ConsulofVenezuelatoLeHavre.Hisfatherwasawinemerchantbutwasalsoanamateurscientist.Hismotherwasthedaughterofawell-knownbanker.Whenhisparents TheTimes103diedbeforehehadcompletedhighschool,Bachelierwasforcedtostruggletocompletehighschoolwhileheprovidedforhisyoungersis-terandinfantbrotherandmanagedthefamilybusiness.WhileotherswentofftocollegeinParis,hewasschooledinlifeandinfinancialmarketsuntilhewasfinallyabletoentertheSorbonneinParisin1892attheageof22.Bachelierwasanon-traditionalstudent,withmoredistractionsthanusualandwithless-than-idealgrades.However,hewasfortunatetocomeunderthesupervisionofJulesHenriPoincaré(1854–1912),ahighlyrespectedmathematicianandphysicist,famousforhisPoincaréconjecture,atheoremonthree-dimensionalspheresthattookalmostacenturytoprove.Bachelier’sgraduationthesiswassurprisinglyadvanced,especiallyhisinsightsintotheGaussiantheoryoferrors,whichearnedwordsofpraisefromPoincaré:[Bachelier’streatmentis]veryoriginal,andallthemoreinterestinginthatFourier’sreasoningcanbeextendedwithafewchangestothetheoryoferrors...ItisregrettablethatM.Bachelierdidnotdevelopthispartofhisthesisfurther.7Poincaréseemedtovoicesomefrustrationwithhisuntraditionalstudent.HefeltBachelier’sthesiswasunconventionalandskirtedsometopicsofgreatsignificance.Withthefaintpraiseofhishighlyplacedsupervisor,Bachelierdidnotearnthehighestthesisgradeoftrèshonorableandthusdidnotcarrytheweighthemighthavewishedforashetriedtofindanacademicappointment.ThereasonforPoincaré’sfaintsupportmayhavebeenthesubjectmatter.BachelierchosetodevotehismathematicalphysicsskillstoanunderstandingofthestockmarketandtheoptionspriceslistedontheParisStockExchange.EversinceIsaacNewton’sdamningoffinancialmarkets,seriousscientistsandmathematiciansviewedthestockmarketasfollyatbestandgamblingatworst.Nonetheless,Bachelier’slifeexpe-riencesendowedhimwithafascinationforthefinancialmarketandhewouldnotbepersuadedtostudyelsewhereovermereissuesofacademicsnobbery.Hisdoctoraldissertation,entitled“Théoriedelaspeculation,”wassuccessfullydefendedonMarch19,1900andwasacceptedtobepublishedinoneofFrance’stopjournals,theAnnalesScientifiquesdel’ÉcoleNormaleSupérieure.Forthenextfewyears,Bacheliercontinuedtostudythetheoryoftherandomwalkandofdiffusionprocesses,whichwenowknowisso 104TheRiseoftheQuantsessentialinourunderstandingofstockprices.However,ittookuntil1909forhimtosecuretherankofFreeProfessorattheSorbonne.FollowingthepublicationofhishighlysuccessfulbookLeJeu,laChance,etleHasard(Games,Chance,andRisk)in1914,hewasofferedapermanentprofessor-shipattheSorbonne.However,hisdraftingintotheensuingWorldWarintervenedand,uponhisreturn,hebouncedfromschooltoschooluntilheagainsecuredapermanentprofessorshipin1927attheUniversityofBesançonattheageof57.Heremainedthereuntilheretired.Despiteapatternofmisinterpretationormisunderstandingofhiswork,Bachelierremainedsurprisinglyproductiveandprescient.Inhislatercareer,hepublishedfivebooksandmorethanadozensignificantacademicpapersinprestigiousjournalsinsciencesandpuremathematics.Infact,hisworkbecamemorepublishedandcirculatedafterhisdeath,includingaseriesofcompletedpapersthathadnotbeenpublishedbeforehedied.However,heisrenownedinfinancetheoryfortwoinnovationsstemmingfromhis1900SorbonnePhDthesis.Inthenextvolumeofthisseries,wewilldescribehislifeandhisderivationoftherandomwalkmorefully.Fornow,though,wewilldiscusshisremarkablederivationofthefirstoptionspricingformula.MuchtothecreditofPaulSamuelson,whopopularizedBachelier’swork,wenowhaveabetterappreciationoftheroleBachelierplayedindefiningtheoptionspricingmodelandanticipatingthetheoryofefficientcapitalmarkets.WhileoptionsmarketshadbeeninexistenceformorethantwocenturiesbeforetheBacheliertreatment,theyhadinvariablybeenviewedashighlyspeculativeandonthevergeofgambling.AsBachelierwaspreparinghisthesisonoptionspricing,theParisStockExchangewasexpandingitslistingstoincludefuturesandoptionscontracts.Bachelieraimedtoprovidethetheorybehindtheserathercomplexinstrumentsthatmustbetreatednotonlybasedontheirpricesbutalsoontheirexpirationdate,theexerciseprice,andtherighttoeitherbuy(calls)orsell(puts)atthatprice.Bacheliermodeledoptionspricingbynotinghowincrementstothestockpricewouldaffectthepriceoftheoptionderivedfromit.Heassumedthatthestockexperiencedidenticallyandindependentlydistributedrandommovements,whichallowedhimtousethecentrallimittheoremtodescribetheprobabilitydistributionofthesemove-mentsbythenormaldistribution.Healsoallowedadriftofzeromeanofthesecuritypriceandassumedthatthevarianceofthepricedriftisproportionaltothelengthoftimeoftherandomwalk.Incombination,hehaddescribedwhatwenowcallaWeinerprocess. TheTimes105WhileBachelierwasthefirsttoapplyBrownianmotiontofinance,themethodologyisnowcommonplace.Theterm“Brownianmotion”originatedin1828fromtheobservationsofthebotanistRobertBrown,whodiscoveredthatpollensuspendedinwaterseemedtoexperienceunusualandrandomjumpswhenobservedunderamicroscope.TherenownedMITmathematicianNorbertWeinerdescribedthemath-ematicsofBrownianmotioninhis1918PhDthesis.Bachelierhadalreadydiscoveredthis,though.HisstatementthatstockpricescouldbemodeledasarandomwalkaccordingtoaWeinerprocesswasamenabletoempiricalverification.AlfredCowles,whowouldfoundtheCowlesCommission,andHerbertJonesexploredandsubsequentlyvindicatedthisnotionthatthereisnomemoryeffectinthepriceofstocksina1937papertogether.8Whilethenotionoftherandomwalkhassincebeenreplacedwiththelessrestrictiveconceptofamartingaleprocess,muchoffinancepricingtheorystillretainstherandomwalkbecauseofitssimplefirstandsecondmomentcharacterizationofpricemovements.TherandomwalkofabsolutepricesBachelierconstructedatheoryofabsoluteratherthanrelativepricemovements.Nowwerecognizeitassomeofthemostanalyticallyandtheoreticallycomplexworkinstochasticcalculusinfinanceuntilthelate1950sor1960s.ItisalsoasmathematicallysophisticatedasanyworkineconomicsuptotheworkofFrankPlumptonRamseyinthelate1920sandallothersforanothertwodecades.Inanunu-sualgestureamongeconomists,butnotasunusualamongfinancialtheorists,Bachelierprovidedthetheoryandalsoconductedhisownempiricaltestsofhistheory.Itistrulyamazingthathediscoveredthathistheoryfittedtheobserveddataverywell,especiallygiventhatthosetradingontheParisStockExchangedidsowithoutthebenefitofhistheory.SubsequentscholarsworkingonthepriceofoptionshavesincerefinedsomeofBachelier’sassumptions,withoutanynecessarymodi-ficationofhisintuition.Forinstance,wenowusethelogarithmofpricessothatitisthepercentagechangeofpricesthatfollowsthenormaldistribution.ThismodificationavoidstheunfortunateresultofnegativepricesthatBachelier’sanalysiscouldafford.Wealsonowallowforapositivedriftofpricestoresolvetheissuethatstockpriceswouldappealtoaninvestorwithapositiverateoftimepreference.However,noneofthesereasonableextensionsreducestheamazingintuitionofBachelier’smodel. 106TheRiseoftheQuantsThenextpricingmodelWhilethesimplebondpricingformuladatedbacktotheworkofthegreatmindIrvingFischerataroundtheturnofthetwentiethcentury,andHarryMarkowitzandJamesTobinhaddemonstratedhowaport-folioofsecuritiescouldbepricedbythemid-twentiethcentury,andWilliamSharpehadappliedthesetechniquestoindividualsecuritiesby1964,thedefinitiveworkonthepricingofderivativeshadeludedfinancialtheoristsandpractitionersalikeuntilFischerBlackandMyronScholesteamedupinthelate1960s.Obviously,theartofoptionspricingisinaneducatedguessabouthowasharepricewillevolveinanuncertainenvironmentuptothesettlementdate.Theanalystmustthendeterminewhichriskpre-miumtoattachonthisevolutionofthefuturestockpricesothatthepresentvalueoftheoptioncanbedeterminedtoday.Thisintellectualprocesshasmuchincommonwiththedeterminationofinvestmentprojectswithinagivenfirm.Assuch,theissueofoptionspricingcanbeapproachedfromeitherthemarketorthecorporatefinanceperspective,justastheCAPMhadbeenderivedforsecuritiespricingfromboththemarketpricingandcorporatefinanceperspectives.Fromeitherperspective,researcherslookedattheoptionspricingproblemasinvolvingtimeandthediscountrate,theriskpremiumandtheaver-siontoriskofinvestors,ashadpreviousresearchersinsimilarpricingexercises.Theseoptionsinstrumentsthatderivetheirvaluebasedonthecontingentrealizationofthevalueofanunderlyingsecurityhadlongbeenthesubjectofvarioustheoriesofcontingentclaimsvaluation.Infact,Bachelier’sextensioninhis1900treatmentofsecuritiespricesderivedaformulaforthepricingofoptionscallsandputs.9HederivedthepriceC(S,T)ofaEuropeancallasafunctionoftheunderlyingstockpriceandthetimeTtomaturityofthecall,forvariousstrikepricesKandinstantaneousstandarddeviations.Heshowedthat,undertheassumptionthatnon-dividend-payingstocksforwhichreturnsarenormallydistributedandazerorisk-freeinterestrate,thepriceofaEuropeancallwasgivenby:C(S,T)(SK)N((SK)/(T1/2))T1/2n((SK)/T1/2),wheren(x)istheprobabilitydensityfunctionexp(x2/2)/(2)1/2forthestandardizednormaldistributionandN(z)istheintegralofn(x)overthedomainfromtoz,i.e.,thecumulativenormaldensityfunction. TheTimes107However,theBachelierderivationofanoptionpricedidnotincludeatermfortherateoftimediscounting.Also,becausethenormaldistri-butionaffordsnegativeprices,itassumesthatstockpricescouldalsobenegative.Topreventtheproblematicnegativevaluesresult,log-normaldistributionsarenowused.Morethan60yearslater,atheoristnamedCaseSprenkleextendedtheBachelierresultbyallowingagentstoberisk-averseagents.10Underhisformulation,thecallpriceisgivenby:C(S,T)eTSN(d)(1A)KN(d),12whered(ln(S/K)T(2/2))/(T1/2),ddT1/2,istherateof121growthofthestockprice,andthedegreeofriskaversionisgivenbyA.Asatheoreticalconstruct,thisformulaoffersaclosedformsolutiontotheoptionspricingproblem.However,becausethedegreeofriskaversionisanunobservablevariable,itcouldnotbeusedtoprovideestimatesofthevalueofastockoption.ThreeyearsafterSprenklepublishedhiswork,A.JamesBonnessaddedtherateoftimediscountingtotheproblemandmodifiedSprenkle’sresultonlyslightly:C(S,T)SN(d)KeTN(d).12Independentlyoftheseanalyses,PaulSamuelsonpublishedin1965someresultsrelatingtohisexplorationofwarrantpricing.HisderivationrepresentedahybridbetweenbothSprenklesandBonness.Hefoundthat:C(S,T)Se()TN(d)KeTN(d)12basedontheaveragerateofgrowthofthecall’svalue.However,thissolutionrequireseitherthattheobservedgrowthinthecall’svalueiseffi-cientandobservableor,alternately,thatitexpressedanimplicitequationbetweenthevalueofacallanditsgrowthrate,andhencedidnotoffertheclosedformsolutionthatwouldallowthepricingofoptions.UnabletoprovideacompleteclosedformsolutionthatagreatmindlikeSamuelsonwouldsearchforandexpect,helefthispartiallycom-pletedworkunfinisheduntiltheyounggraduatestudentRobertMertonbegantoworkwithhiminthelate1960s.MertonexpressedinterestintheoptionspricingproblemandSamuelsonsharedwithhimsomedusted-offworkthathehaddone. 108TheRiseoftheQuantsTogether,SamuelsonandMertonjointlydevelopedthekeystrategythatwouldeventuallyallowFischerBlackandMyronScholestounlocktheproblem.Theysurmisedthatifaninvestorconstructedanoptimalhedgingportfoliothatcontainedjustthecorrectweightingofanoptioncallandtheunderlyingstock,thenthestrategyshouldyieldthemarketdiscountrate.Hence,thediscountrate,stockprice,optimalweighting,andcallpricecouldberelatedinawaythatwouldpermitapossiblesolution. 15TheBlack-ScholesOptionsPricingTheoryTherehasperhapsbeennoothertimeinthehistoryofeconomicsandfinancewhenanewfinancialtheorywasmoretimelyandinfluential.PaulSamuelsonandothershadbeenworkingontheoptionsandwar-rantsissueinthe1960s,butthetopicseemedtohavelittlepressingneed.However,bytheendofthe1960s,ashrinkingbusinessinfuturestradingfortheCBOTmotivatedtheformationofanewmarketforoptionstradingasavehicleforitssurvival.Yet,onlyifsuchoptionscontractswerestandardizedandifamodelcouldbedevelopedforthepricingofoptionsastherehadbeenadecadeearlierforsecuritiescouldtheoptionsmarketbesuccessfulandthederivativebecomeanefficientandeffectiveinstrumentforhedgingrisk.TheCBOTcouldtakecareofthefirstprecedent.TheteamofFischerBlackandMyronScholeswouldtakecareofthesecond.TheyoungboywonderMyronScholeshadarrivedattheSloanSchoolatMITin1968,withhisfreshlymintedPhDfromtheUnivesityofChicagoinhand.Hewasstrongmathematically,buthewasalsobrilliantwithcomputing,whichmadehimasinvaluablefortheMITfacultyashehadbeenfortheChicagofaculty.HehadteamedupwithMertonMilleratChicagoandhadalsoworkedwithMiller’sfamouscol-laborator,thegreatmindFrancoModigliani,whohad,veryearlyon,championedlarge-scalecomputermodelingofthemacroeconomy.WhenScholesleftChicago,hiscolleagueMichaelJensensuggestedthathelookupFischerBlackinCambridgeatArthurD.Little.JensenhadbeenimpressedwithBlack’sfreshideasinfinance,unencumberedbyformaltraininginfinance,whenthetwoofthemhadworkedwithWilliamSharpeonapplicationsoftheCAPMmodeltoperformanalysesonbehalfoftheYaleUniversityendowmentfund.Almostimmediately109 110TheRiseoftheQuantsuponarrivinginCambridge,ScholesfollowedJensen’sadviceandscheduledalunchmeetingwithBlack.Atthatmeeting,BlackandScholesimmediatelysharedtheirexperi-encesandoptimismfortheroleofcomputersinthefutureoffinancialanalysis.Clearly,theywerekindredspiritsonthisnewplayingfield.Theyalsocomplementedeachother–BlackforthebigpictureandScholesforthedetails,BlackwhowaxedphilosophicalandScholestheconsummateacademicentrepreneur.Theyalmostimmediatelybegantodiscussunansweredquestionsintheoryandpractice,andtheyalsostartedtoexplorehowtheycouldworktogetheronvariouslucrativeconsultingprojects.BlackhadmovedintotheArthurD.LittleanalyticdivisiontofillinforCAPMco-developerJackTreynorwhenArthurD.Littlerefusedtomeethissalaryincreasedemands.In1969,Blackmadeasimilardemandforasalaryincrease,withthesameunfortunateresult.Salarydemandsarebestmadeascrediblethreats,andwhenthedemandsarenotmet,credibilityrequiresthedemandertofollowthrough.BlacklefttostarthisownfinancialconsultancyinBoston,andScholesjoinedhimasanassociate.ScholeswasanacademicattheSloanSchoolinthemorningsthroughmidday,andjoinedBlackinconsultingprojectsacrosstheCharlesRiverinBostonintheafternoon.OneofthefirstcontractswasthedevelopmentofanotherCAPMmethodology,thistimeforWellsFargoratherthanfortheYaleprojectBlackhadworkedonwithJensenandSharpewhileatArthurD.Little.BlackreassembledateamthatagainincludedJensen,butthisnexttimearoundincludedScholesratherthanSharpe.Asaconsequenceoftheircollaboration,theyproducedapaperthatdemonstratedthattheCAPMmodelseemedtobeunabletoexplainthehigherthanpredictedreturnsonlowbetastock,justasScholeshadobservedinhisPhDwork.Thethreeconcludedthat,iftheycouldfigureoutwhy,theycouldcapitalizeonwhattheylabeledthisalphaeffect.Indeed,theydevelopedanumberofpossiblescenariosbywhichWellsFargocoulduseportfoliosofsecuritiessegmentedbyreturnsandbyconstructingportfoliosthatarebothlongandshortinstocksinordertobeatthemarket.Thislatterlong-shortstrategyseemedtoproducethebestreturnsinthepost-Warperiod,anditmotivatedBlackandScholestodevelopatheoreticalmodeltoexplainwhy.Intheensuingmodeling,BlackandScholesneglectedtaxationandtransactionscosts,andassumedaninvestorhasperfectaccesstobor-rowingattherisk-freeinterestrate.Onestrategytheyproposedandanalyzedwaswhattheycalledthezero-betaportfolio.Theirideawasto TheBlack-ScholesOptionsPricingTheory111holdlowbetastockslongthattheypredictedwouldperformbetterthanthemarket.Theshortsellingofhighbetastocksshouldthenallowthepurchaseofthelowbetastocks,withsomeprofitleftoverandwithverylittleor,ideally,zerorisk.Thishigherrisk-freereturncouldthenbeusedtobuyandsellalongaMarkowitzsecuritylinewithahigherrisk-freereturnintercept.Aninvestorcouldthenearnasuperiorrisk-returntrade-offforanylevelofdesiredriskthroughleveragepurchasesofthemarketportfolio.TheirclientsatWellsFargothoughttheFischer-Scholesintuitionwaslikefinancialalchemythatsomehowdeniedthebytheninvogueandwidelyacceptedefficientmarkethypothesis.Thefirm’srejectionoftheirinsightselicitedthesamereactionfromBlackasanysuchrejectionhadhadonhimsinceadolescence–itmadehimbelievehishypothesiswithevengreaterfervor.Undaunted,Blackbegantothinkmoreabouttheoptimalinvest-mentportfoliothatcouldbeatthemarket.Hesawoptionsasonewaytoadjustinvestmentriskexposureatagiventime.ThisisincontrasttotheSamuelsonapproach,whichsawoptionsasadiscountingprob-lemtosettlementbasedonanindividualinvestor’srisktolerance.Theformerisamarket-basedapproach,whilethelatteristheeconomist’srepresentativeagentapproach.Blackstartedwiththeassumptionthatanoptionpriceissimplyafunctionoftheunderlyingstockpriceandtheamountoftimeremain-inguntilsettlement.RewritinginmodernstandardnotationthewarrantdenotationthatSamuelsonhadusedin1965,wecanexpressBlack’srelationshipasC(S,t).Then,wecandeterminetheeffectonthetimepathofthewarrantpriceforaninfinitesimalchangeinthestockpriceasC(S,t)(C(S,t)/t)dt.Next,hediscoveredthattheeffectoftimeonthevalueofthewarrant(C(S,t)/t)/tcanbedeterminedbynotingthatthetimeeffectmustinvokeboththerisk-freerateofreturnovertimeandthereturnoftheriskyassetovertimefromtheCAPMmodel.Fromthis,Blackhadframedthefollowingimplicitpartialdifferentialequation,butwithoutthepersonalmathematicaltoolstosolveit:δδ2C(S,t)t2=rCrSC(S,t)SvS−δδ−222δδC(S,t)S2wherev2isthevarianceoftheunderlyingstockandristherisk-freediscountrate.HislogicisasimpleanalogyoftheCAPMmodeltothepricingofanoption. 112TheRiseoftheQuantsNotethatthereisoneseeminglycounter-intuitiveaspectofthisrelationship.TheCAPMmodelincludesthefirstmoment,ortheexpectedreturn,ofthestock,aswellasthesecondmoment,orvariance,asseenabove.Intuitively,Black’sformulationdidnotincludetheexpectedreturnofthestockintheimplicitrelationshipthatdefinesitsoptionprice.ToBlack,thiswascurious.Andthesecond-orderpartialdifferentialequationforthevalueofawarrantcallC(x,t)wasdaunting.Awhilelater,atoneoftheirafternoonworksessions,Scholescommentedontheworkofoneofhisgraduatestudentsinoptionspricing.BlackshowedScholeshisequation,writtenonasinglesheetofpaperinoneofthemanilafoldersthatrepresentedBlack’slifelongthoughtorganizationsystem.JustasBlackandScholeswereastrongteambecausetheylookedatthingsdifferently,Scholesdidnotseetheequationasapricedeterminationmechanism,butratherastheendstageofspeculativearbitrage.Usingthesamereasoninghehaddevelopedinhisstrategytosellshorthighbetastockstofundthepurchaseoflowbetastocks,heaskediftheseoptionscouldbeusedtoprovidethereturnbypurchasingthecalloptiontobuythestock,whileaninvestorsimultaneouslysoldthestockshort.Hence,thecallisthecoverfortheshort.Hethenaskedwhatcombinationoftheoptionandthesecurityonewouldhavetolongandshorttosetrisktozero.Moreover,wouldthisoptimalweightingyieldapositiveprofit,basedonBlack’spricingformula?Scholesconcludedthatthisalmostrisk-freecombinationshould,accordingtotheCAPM,offertherisk-freereturn.Then,Scholesasked,whatmustbetheoptimalrelativeweighting?HeconcludedthattheoptimalweightingmustbeonelongoptionforeachC(x,t)/xshortsofthestock.Withabitmoremanipulation,hismotivationfortheunderlyingdifferentialequationarrivedatthesameconclusionasBlack,butfromadifferentperspective.Twodif-ferentformulationsthatnonethelessyieldedthesamesolutiongavebothBlackandScholesconfidencethattheymightbeontosomethingfundamental.Tosolvethedifferentialequation,thetwotookanotherlookatCaseSprenkle’sYalePhDresult,discussedearlier.However,theyhadalreadyconcludedthatthestock’sexpectedreturnshouldnotfeatureintheequation,sotheyrecastSprenkle’ssolutioninthespecialcaseinwhichtheriskoftheoptionisexactlyoffsetbytheriskoftheshortedstock,whichwaswhattheoptimalhedgeweightingwasdesignedtodo.Assuch,theysettheexpectedreturnofthestocktotherisk-freerateof TheBlack-ScholesOptionsPricingTheory113return,andlikewisethediscountratetotherisk-freerate.Fromthis,theycalculatedthevalueofanoptionthatwouldresultiftheunderlyingstockwererisk-free.TheresultingsolutionalsosatisfiedBlack’sdifferen-tialequation,sotheirhunchturnedouttobethebackdoorsolutiontotheequation.TheywereleftwiththeBlack-Scholesequation:−−rtt()∗C(S,t)=−SN(d)Ke12N(d)whereKisthestrikeprice,d(ln(S/C)(t*t)(rv2/2))/(r(t*t)1/2),1ddv(t*t)1/2,t*istheexpirationdate,andtheoptimalhedge21C/SissimplyN(d1).AsinSpreckle’ssolutionand,forthatmatter,Bachelier’sderivation70yearsearlier,N(d)isthenormalizedcumulativeprobabilitydistributionfunction.AlternativederivationsoftheBlack-ScholesformulaBlackandScholeshadmadeafewimplicitassumptionsintheiranalysis.First,theyassumedthatthenumberofsharesoutstandingdoesnotchangebeforethesettlementdate.Ifso,thiswoulddilutethepriceofthestockandaffecttheoptionprice.Similarly,theyassumedthatnodividendsarepaidandthatthestockevolutionfollowsalog-normalrandomwalkwithaconstantdriftandvolatility.Finally,individualscanborrowandlendwithoutrestrictionattherisk-freerateofreturn.Thelog-normaldriftofreturnsimpliesthatthestockpricex(t)followsthefollowingprocessasafunctionofitsdriftrateandstandarddeviation:dS(t)=μS(t)dt+σS(t)dB(t)whereµisthedriftrateandisthestandarddeviationoftheBrownianmotiondefinedbyB(t).ThevelocityofthemovementofthestockdS(t)canthenbeintegratedtogiveitspathovertimeas:S(t)S(0)exp((µσ2/2)t)SB(t)Fromthispathofthestockmovementwhenstockreturnsdriftbasedonalog-normaldistribution,thetechniqueofItô’slemmacouldthenbeappliedtoderivehowthepriceC(S,t)ofthestockoptionchangesasthestockpriceS(t)evolves. 114TheRiseoftheQuantsToseethis,wecanconstructtheportfolioScholesproposed,withC/Sunitsofthestockshortperunitofthecalloptionlong,thatis,continuouslyadjustedovertimeasthestockpricechanges.Inthisdynamiccontextwithoffsetseliminatingrisk,theportfoliomustprovidetherisk-freerateofreturn.Ifnot,therewouldbeanarbitrageopportunity.Economistsdenytherecanbesucha“freelunch.”TheItôdrift-diffusionprocessItô’slemmastatesthatforanItôdrift-diffusionprocess:dS(t)=μS(t)dt+σS(t)dB(t)WecanusethislemmaforastockthatdriftsasabovetodeterminethevalueofaEuropeancalloptionforastockthatdoesnotpayadivi-dend.Intuitively,wecanpresumethatthepriceCofanoptionatanymomentoftimeshouldevolvewithtimet,thecurrentstockpriceS,theexercisepriceK,timetoexpirationt,therisk-freeinterestrater,theexpectedreturnonthestockµ,anditsstandarddeviation,i.e.:CC(S,K,t,r,µ,σ).Then,Itô’slemmastates:dC/dz[(C/t)(C/S)µS(1/2)(2C/S2)σ2S2]dt(C/S)σS.Then,usingthestrategyScholessuggested,ifonecallofvaluewisoffsetbyw/xshares,thevalueVofthisportfolioisequalto:V(C/S)SCThisvaluechangesaccordingto:dVC/SdSdCThen,fromItô’slemma,thechangeinthevalueoftheportfoliodVovertheintervaldtis:dV(C/S)(µSdtSdz)[(C/S)µS(C/t)(1/2)(2C/S2)σ2S2]dt(C/S)σCdz. TheBlack-ScholesOptionsPricingTheory115Noticethattheterm(C/S)Cdzenterstheequationbothpositivelyandnegatively,asdothetermsinvolvingthereturnµ.Whenthesearecanceled,theBrowniandrifttermisoffsetandweareleftwith:dV[(C/t)(1/2)(2C/S2)σ2C2]dt.Becausetheexpectedreturnisoffset,theportfoliomustriseattherisk-freeinterestrate:dVrVdtr[(C/S)SC]dtwhichrequires:(C/t)(1/2)(2C/S2)σ2S2r(C/S)SrCor:(C/t)(C/S)rS(1/2)(2C/C2)σ2S2rCwhichistheimplicitBlack-Scholesdifferentialequationforacalloptionvalue,subjecttotheterminalboundaryequationthatthevalueoftheoptionatthesettlementtimeisequaltomax(xK,0).Thesamereasoningcanpriceaputinsteadofacall,withtheboundaryconditionreplacedwithpmax(Kx,0)uponsettlement.InterpretationofthesolutionLetusrecapandinterprettheBlack-Scholessolution:C(S,t)SN(d)Ker(t*t)N(d),12ThissolutionforthecallpriceofaEuropeanoptioncanbebrokendownintotwoparts.Thefirstpart,SN(d1),canbeinterpretedastheexpectedvalueoftheoptionfromtheunderlyingstock,i.e.,theproductofthestockpriceSandtherateofchangeinthecallpricearisingfromachangeinthestockprice.ThesecondpartistheproductoftheexercisepriceK,thepresentvaluediscountingfactor(toexercisedatet*),andtheprobabilitythatthecallwillbeexercisedattheexerciseprice.Thecallpriceisthedifferencebetweenthetwo. 116TheRiseoftheQuantsThesolutionassumedalog-normaldistributionofreturnsandthattherisk-freeinterestrateisknownandconstantovertheperiodofanal-ysis.ItalsoassumedefficientmarketsforaEuropeanoptiononastockthatpaysnodividendsbeforetheexpiration.TheEuropeanoptioncanonlybeexercisedatexpiration,asopposedtoAmericanoptions,whichcanbecalledatanytimeuptoexpiration.However,suchearlycallsofanAmerican-styleoptiondonottypicallyoccurbecauseonethensacrificestheoptionvalueofnotexercisingthecallovertheremainingperiod.ZerotransactioncostsandmarketefficiencyarealsorequiredbecausethemodelassumesthatthestockfollowsacontinuousItôprocess.Suchaprocessissimplythecontinuous-timeversionofthediscreteMarkovprocessinwhichobservationsatatimetdependonlyontheobservationintheprecedingperiod.ItappearsthatallpathsandprescriptionsledtothesameBlack-Scholesoptionspricingtheoryfor-mula.Confidentinthismulti-perspectivevalidation,BlackandScholestooktheirequationontheacademicroadandalsosoughtoutpathsforpracticalapplicationfortheirmutualprofit. 16ApplicationsTherehasperhapsbeennoapplicationinthedecisionsciencesforwhichtherewassuchadireneedforatheoreticalsolutiontoanimpor-tantpracticalproblemaswiththeoptionspricingproblemonthecuspoftheformationofanewandpotentiallylargeandlucrativefinancialmarket.Norhastherebeenanapplicationonwhichtensoftrillionsofdollarsofactivityperyearwoulddepend.AlmostimmediatelyuponthereleaseoftheBlack-Scholesequation,itstwoprincipalauthorswereenlistedinaninstitutionofpotentialsizeandimportancebeyondtheirwildestdreams.TheChicagoBoardOptionsExchangeWhileitwouldtakeacoupleofyearsforthepaperbyFischerBlackandMyronScholestobepublished,championsofpractitionerssawwhatacademicianscouldnot.Theequationprovidedthebestmethodologyyetforanalyststopriceoptions.SomeonWallStreetbegantoclamorforanopportunitytohedgeriskorperhapstoallowforhighlylever-agedhedgesforspeculatorswhoarelessrisk-averse.Meanwhile,BlackandScholescontinuedastheyhadstarted.Scholestaughtandsuper-visedgraduatestudentsattheSloanSchoolandBlackcontinuedtoscoutoutconsultingopportunitiesandworkwithScholesinmeetinghisclient’sneeds.Indeed,Blackwroteinapaperentitled“ACentralMarketinOptionsforSecurities:OpportunitiesandUnrealisticHopes”that“Optionsareanexcitingwaytogamble,andtheChicagoBoardOptionsExchangewantstoactasthegamblinghouseandtakeitscut.There’snothingwrongwiththat;butifwearetopermitthisformofgambling,itseemslogicaltotaxitheavily,asthegovernmenttaxesbettingathorse117 118TheRiseoftheQuantsraces.”1Meanwhile,Black,Scholes,andtheirMITcolleagueRobertMertonhadmanagedtolosesomemoneyonwarrantsinvesting,buttheirlivesotherwiseremainedmuchthesame.Theacademiccommunityremainednonplussedabouttheirinnova-tionbecausetheycontinuedtobeskepticaloftheconclusionthattheoptionformuladidnotincorporatethemeanreturnoftheunderly-ingstock,asopposedtothespecificationoftheCAPMthatexplicitlyrequiredameasureofmeanreturn.EvenBlackandScholesfoundthisresultodd,atleastuntiltheircolleagueMertonexplainedthatthereturnisincludedimplicitlyinthepriceofthestock,whichispartoftheirequation.DisseminatingandmarketinganewfinancialtoolHowever,practitionersfoundtheequationliberatingandwerewillingtoputacademicreservationsasideinpragmaticreturnfortheoverwhelm-ingusefulnessofapricingequationthatisrelativelysimpletocalculate.Inaddition,theassumptionsoftheequationseemedreasonableandwerealreadybroadlyacceptedinotherapplicationsinfinance,statistics,economics,andthedecisionsciences.Finally,theequationcouldactasabrightlightinapreviouslyunilluminatednewfrontier.Inthisrespect,itprovidedafocalpointfromwhichspeculationcoulddeviate.ThechampionsoftheCBOEknewintuitivelyjusthowvaluabletheBlack-Scholesoptionspricingequationcouldbe.Uptothatpoint,thefinanceliteraturewasnascentandqualitative,wellbeforedevelopmentsfromeconomictheoryhadbecomemainstreamandwellbeforethequantitativewavehadsweptoverWallStreetandtheliterature.BlackandScholeshadaimedfortheeconomictheoryliteratureasaresultoftheperceivedlackofrigorwithinfinance,butmetwiththesameresist-anceingettingtheirworkpublishedashadWilliamSharpeandhisCAPMmodelalmostadecadeearlier.However,oncetheirarticlewasacceptedforpublicationintheprestigiousJournalofPoliticalEconomyforits1973volume,2Black’sstarwasinitsascendancy,especiallyattheUniversityofChicago,wheretheJournalofPoliticalEconomywaspublished.WordhadalreadygotoutaboutthepaperandcaughttheearoftheUniversityofChicago’sinfluentialfinanceprofessorJamesH.Lorie(1922–2005)andtheCBOE’schampionandfirstViceChairman,EdmundO’Connor.LoriewasrenownedatthetimeforhiscreationoftheCenterforResearchinStockPrices(CRSP)database,stillthemostcommonlyemployedfinancedatabaseforfinancialacademicstoday.Hehadalso Applications119comeacrossBlackwhenBlackandAssociateswasadvocatingforWellsFargotocreatevariousindexfunds.Atthesametime,O’ConnorhadrisentoleadershipattheCBOTandhadconvincedskepticsontheBoardthatthetimewasripefortheworld’sfirstoptionsexchange.O’ConnorwasconvincingandhelpedbringtheCBOEtofruitionin1973,withinmonthsofBlackandScholes’publication.WilliamBrodsky,ChairmanoftheCBOE,reportedthat:“AlthoughtheideacamefromEdandacoupleofothersattheBoardofTrade,theywereconstantlyfightingattheBoardofTradeaboutwhetheritshouldevenhappenandwhetheritshouldcontinuetobefunded.TheywerefightingtheSecuritiesandExchangeCommissionontheotherhand,whichwasn’tparticularlythrilleditwashappeningeither.”3However,O’ConnorandLoriesawthevision,andLorieinparticularunderstoodthatitwouldbeamajorcoupintimingiftheUniversityofChicagocouldattractBlackfromCambridgejustastheCBOEwasabouttoopentotheinvestingpublic.Blackcouldnotresisttheofferofacademiclegitimacy,especiallyattheUniversityofChicagoin1971,evenifitwereonlyforavisit-ingprofessorship.Togetherwithhiswife,Mimi,andyoungfamily,hearrivedinChicagojustastheCBOEwaspreparingtoopen.AndoncehewasinthehotbedofefficientmarkettheoryattheUniversityofChicagoandthehotbedofoptionstradingattheCBOE,hebegantobedrawnintothenewoptionsmystique,andintheworkofthenewInternationalMonetaryMarket(IMM)thatopenedupayearafterhearrivedandayearbeforetheCBOEbegan.BlackthrivedintheacademicenvironmentofChicago.NeverabletosuffertheorthodoxyofacademicsinCambridgeforlong,hefoundhimselfthrustintogreatdebatesatChicago,aschoolthattookprideincastingofforthodoxywithrelish.Blackcertainlywasunorthodox,iffornootherreasonthanthefactthathislackofformaltrainingmeantthathehadneverbeenindoctrinatedwithpettheoriesineconomicsandfinance.Blackhadauniquewayoflookingatproblemsbasedonwhathehadknownandlearned,andthatmostothersmoresteepedinformaltrain-ingandindoctrinationcouldnotsee.Hisanglewasodd,butthismadehisvantagepointunique.Hesawproblemsininstitutionaltermsandinequilibriumtermsthatwereunconventionalbutweresufficientlyuniquetogivehiscolleaguesflashesofhisbrilliance.Black’spenchantforunconventionalthoughtandprovocationactuallyfitsurprisinglywellintotheChicagocommunity.Likethewilynewkidatschool,hegainedareputationalmostimmediatelyforhiswillingnesstotakeonthegreatmindandChicagoinstitutionMilton 120TheRiseoftheQuantsFriedmanatseminarsonmonetarytheory.Remarkably,giventhatFriedmanhadawell-deservedreputationasaruthlessandconvincingdebater,Blackheldhisown,evenifhebroughtwhatheknew,fromCambridge’sKeynesianrootsandModigliani’sinfluences,intotheepicenterofanti-Keynesiantheory.Itmusthavebeenaremarkablespectacletowatchthetwotitansarguetheirperspectives.DespiteorperhapsbecauseofhisnotoriousdebateswithFriedman,whowasbythentheChicagoSchoolpatriarch,Blackthrivedandmanagedtoextendhisstay.BlackalsoencouragedScholestojoinhim,whichScholesdidin1973.However,hisshiftfromthethree-piecesuitsoffinancialconsultingtotheelbow-patchedlifeofauniversityprofessordidnotsitaswellwithBlack’swife,Mimi.Frustratedandpregnant,shemovedbacktoCambridgewithouthim.Ayearlater,heandScholesbothreturnedtoCambridgewithaninvitationofpermanentpositionsforbothofthemattheSloanSchoolatMIT.However,beforetheyleft,thesetwofoundersofmodernoptionspricingtheoryhelpedopentheCBOEandofferedacademiclegitimacytoaninstitutionthatevenBlackhadlikenedtoagamblinghouse.AlternativeapproachesOnceBlackandScholes’paperwaspublishedintheprestigiousJournalofPoliticalEconomy,andwiththeopeningoftheCBOE,optionspricingtheoryhadarrivedasthemostsophisticatedandpotentiallymostvaluabletoolforfinancialmarketanalysts.Astheoristsstruggledtounderstandandinterprettheirresult,andasMertonsoonpublishedhiscomplementarywork,arenewedinter-estdevelopedinBachelier’sworkfrom70yearsearlier,andevenEinstein’stheoryofBrownianmotion.Withinafewyears,Brownianmotion,Markovprocesses,martingales,andstochasticcalculushadbeguntobeintegratedintothefinancediscipline.Thequantitativeschooloffinancehadtakenroot.Atthattime,thosemostschooledinstochasticcalculusweretrainedinphysicsandappliedmathematics.Withtheadventofthestatisti-calapproachtophysicsthatarosefromtheoriesofthermodynamicsandquantummechanicsintheearlytwentiethcentury,physicistshadbecomeaccustomedtothepathofprocessesbuffetedbyrandomshocks.Theanalogytothepathofstocksoroptionswasobvious,atleasttothosewiththestochastictoolstoseepatternsindatawhereothershadonlyseenrandomness. Applications121Soon,variousalternativederivationsofandmotivationsfortheBlack-Scholesequationwereproduced.Forinstance,HarrisonandKrebs(1979)4introducedintofinancethetheoryofmartingales,combinedwitharbitrage,thatcouldbeusedtoderiveBlackandScholes’results.Indoingso,theyadvancedtheuseofmathematicsinfinancestillfurther.OthersdrewanalogiesbetweenmodelsofdiffusionofheatflowtosolvetheBlack-Scholesdifferentialequation.Meanwhile,stillothersusedthesamehedgingandarbitrageargumentthatScholeshadusedtomodelthepricingofotherformsofderivatives,frombondstofor-eignexchange.Infact,theequationwasshowntobeusefulformanyvaluationproblemsofderivativesinwhichreturnscanreasonablybeexpectedtofollowalog-normalrandomdistribution.ItdidnottakelongfortheBlack-Scholesanalysistogiverisetoanentirelynewfinancialterminology.IthadactuallybegunwithSharpe’sbetaandJensen’salpha,butthe“Greeks”multipliedinthisoptionspricingRenaissance.TheGreeksBlackandScholes’workintroducedtothefinanceliteraturethenow-standardizedGreeklettersµ,,,,andformeasuresofthemean,areturninexcessofthatpredictedbytheCAPM,therelativerewardandrisk,theoptimalweightingofalongoptionandshortstock,andthevariancerespectively.Thesemeasuresrequiretheassumptionsofnormalorlog-normaldistributionsofreturns,whichhavesubsequentlybeenmodifiedtoaddmorerealism.Forinstance,theliteraturenowmodifiestheBlack-Scholesresultsbyallowingforacoefficientthatmeasurestheskewnessofobserveddistributionsofreturnsthatdepartfromthesymmetricnormalandlog-normaldistributions.Otherdistortionsofdistributions,intheirexcessivelylongorfattails,orhighpeaks,canberepresentedbymeasuresofkurtosis.Thesecoefficientscanmodifyandimprovetheformulaethatwererapidlyadoptedtomodelderivativespricing.Excelandfinancialcalculatorspreadsheetsnowroutinelysolveforthesemodifieddistributionsandtheireffectsonderivativesprices.Thesecalculatorscannoweasilyindicatetotheanalysttheprobabilitythataknownpatternofpricesorreturnscanexceedcertainupperorlowerlimits.However,alltoolsdependonwhatisknownbecauseithasbeenobserved,notonwhatisnotyetknownbecauseithasyettooccur. 122TheRiseoftheQuantsEstimatesofpastvolatility,forinstance,maynotberepresentativeoffuturevolatility.Wecanobservethemovementofoptionspricesbasedoncurrentmarketconditionstoderiveanimpliedvolatility,andanalystscanatleastcomparecurrentvolatilitytrendsagainsthistoricalpatterns.WhiletheBlack-Scholesequationdemonstratedthatmeasuresofvolatilityaffectoptionsprices,theexpectedrateofreturnµoftheunderlyingsecuritydoesnot.Thismeansthatanalystscandifferintheirvaluationofastock,butnotintheirvaluationofitsassociatedoption.Infact,MonteCarlosimulationsofoptionspricesastheunder-lyingstockpriceisallowedtoevolveshowthattheoptionpriceremainsremarkablystablefordifferentratesofdriftoftheunderlyingstock.ThistendencyofoptionstomeasuremarketvolatilityratherthanmarketstrengthhasbeenenshrinedthroughtheVolatilityIndex(VIX)talliedbytheCBOE.Thisimpliedvolatilityiscalculatedbysolvingforthevolatilitythatjustifiedtheprevailingoptionsprice,basedontheunderlyingsecurityprice.ThemeasureisderivedfromBlack-Scholescalculationsasagaugeofthevolatilityperceivedbythemarket.Thisvol-atilityisimplicitlyincorporatedbythemarketintothepricesofoptionscontracts.Itcanbeeitherdownsideorupside,andisameasureofthedemandforhedgesandwhatthisdemandtellsthemarketabouttheperceptionsofinvestors.Ifanalystsexpecthighupsidevolatility,theybecomeunwillingtosellcallswithhigherexercisepricesunlesstheyareofferedahighpremium.ThisisbecauseanAmericancallismorelikelytobeexercisedifthereisahigherprobabilitythattheunderlyingstockwillrisedramatically.Asimilarconcernforthesaleofputsatstrikepricesbelowthestockpriceexistsifthereisanexpectationofdownsidevolatility.Theseout-of-the-moneycallandputprices,whicharegreaterthanthosepredictedbyBlack-Scholespriceestimatesbasedonpastvola-tility,thenactasameasureofchangingvolatilitypatterns.ExtensionsTheBlack-Scholesmodelmustbemodifiedtoovercometwoofitssim-plifyingassumptions.First,ittreatsEuropeanoptionsthatcannotbeexercisedbeforeexpiration,unliketheirAmericancounterpart.Second,itdoesnotproperlypriceoptionsthatpaydividendsbeforeexpiration.However,boththeseweaknessescanbeovercomesomewhatthroughslightmodificationsoftheformula.Forinstance,onesuchextension,thebinomialmodel,breaksthepricingofoptionsdownintoanumberofstepsfromthecurrentdateto Applications123theexpirationdate.Inessence,thepricepathbecomesachainofestimatesbasedonexpectedvolatilityandtheremainingtimetoexpiration.Thevariouspossiblepathscanbelikenedtothebranchesofatree.Certainly,weknowthat,atexpiration,thestockpriceanditscorre-spondingoptionpricemustconcur.Fromtheendpoint,wecanthenworkbacktothebeginningtoseewhichbranchisaccurate,evenasbranchessproutedtotakeintoaccountvariousdividendscenarios.ThefinancialtheoristsJohnCox,StephenRoss,andMarkRubinsteinoriginatedsuchamodelthathasnowbeenincorporatedintostand-ardfinancialcalculatorsthatrequireasinputstheusualexpirationdate,strikeprice,andvolatility,butalsoassumptionsonthetimingandsizeofdividends.5Infact,theCox,Ross,andRubinsteinmodelisidenticaltotheBlack-Scholesmodelwhendividendsarenotpaidandifthereareaninfinitenumberofbranchpointsinthelimitbetweenagiventimetandt*,theexpirationdate.However,suchfinenessindiscretecalculationsisacomputerpower-intensiveandcumbersomewaytoapproximateacontinuousmodelsolutionliketheBlack-Scholesapproach.In1977RichardRoll6offeredananalyticsolutiontothedividendproblemthatRobertGeske7subsequentlycorrectedtwoyearslaterandRobertWhalley8furtherrefinedtwoyearsafterthat.ThistechniqueoffersmoreaccuratepricingofAmericanoptions,albeitwithamuchhigherneedforcomputationalpower.Likewise,modernalgorithmsandcomputersaremuchbetterabletoperformthesecalculationsaccurately.Allthesemethodsrequiretheanalysttodetermineanunbiasedmeasureforthedelta,whichistheoptimalratiobetweentheoptionandstockforahedgethatreducesrisktothetheoreticallowerbound.ThisdeltaisincorporateddirectlyintothefirsthalfoftheBlack-Scholessolution:N(d)N(ln(S/C)(t*t)(rv2/2))/(r(t*t)1/2)1Thisexpressioniscalledthedeltabecauseitalsocalculatesthesensitiv-ityoftheoptionpricetoasmallchangeinthepriceoftheunderlyingstock.Calloptionsfaroutofthemoneywillhaveadeltathatisnearlyzero,whilecalloptionsinthemoneywithastrikepriceveryneartothestockpricewillhaveadeltaclosetoone.Adeltaof0.5meansthattheoptionpricemoveshalfasmuchasdoesthepriceoftheunderly-ingstock.Ofcourse,becauseputpricesriseasthestockpricefalls,putdeltasarenegative. 124TheRiseoftheQuantsNoticethattheexpressionforthedeltadependsonthetimeremaininguntiltheexpirationdate.AnotherGreek,thegamma,measurestherateofresponsivenessofthestockpriceovertime.OtherGreeksincludethevega,thesensitivityoftheoptionpricetoaonepercentagepointchangeinmeasuredvolatility,thethetaτ,whichgivestheeffectofaone-dayreductioninthetimeuntilexpirationontheoptionprice,andtherho,whichgivestheeffectontheoptionpriceforaonepercentagepointchangeintherisk-freerateofreturn.Thesemeasuresofferfinancialanalystsalanguagetocompareanddescribeoptionpricedynamics.Ofcourse,theyalldependonacceptanceoftheunderlyingBlack-Scholesmodel.SubsequenttothepublicationoftheBlack-Scholesmodel,butbeforethemanyvariantsthatfollowed,StephenA.Rosspublishedin1976anentirelydifferentapproachtopricingcalledarbitragepricingtheory(APT).Hismodelwillbediscussedingreaterdetailwithinthecontextoftheefficientmarkethypothesisinthenextvolumeofthisseries.JustasFischerBlackusedthelogicofWilliamSharpe’sCAPMtoformulatehisoptionspricingtheoryformula,RossextendedtheintuitionofRobertMerton’sintertemporaloptionspricingtheorytodevelopAPT.ItisMerton’sdynamicextensionoftheBlack-Scholesequationthatwillbecoveredinthenextpart,followingourdocumentationofthelegacyofBlackandScholesandtheirfamousequation. 17TheNobelPrize,Life,andLegacyEachintheirownway,FischerBlackandMyronScholesredefinedfinancetheoryandapplicationinawaythatisperhapsmoresubstantialthananyonebeforeorsince.Manyothers,suchasIrvingFischerandhisintertemporalmodelofconsumptionandsavings,madecontribu-tionsthatinformedanddefinedtheliterature.Some,likeJohnMaynardKeynesandhisconceptofliquiditypreference,motivatedotherstofurtherfleshouthisidea.EvenFrancoModiglianiandhisLifeCycleModel,andHarryMarkowitzwithhisModernPortfolioTheory,creatednewwaystolookatoldproblemsthatmayhavebeenrevolutionarybutyetwereunabletotranscendtheirimmediateapplication.Ontheotherhand,Black’sdifferentialequationandScholes’moti-vationandintuitionproducedasolutionthatwasunderstandable,elegant,andlentitselftoimmediateapplicationinthemarketforderivativesthatisnowvaluedatapproximately$15trillion.1TheBlack-Scholesequation(andrelativelyminormodificationsofit)isthebasis,ifnotmathematicallythencertainlyintuitively,ofnearlyallderivativespricing.And,withoutsuchatool,therecouldbenomarketthatwouldbeabletodeliverontheneedforefficiencyandaccuracythatsuchinvestmentsrequire.AstheCBOEexpandeddramaticallyoverthe1980sand1990s,BlackhadleftChicagotoreturntoCambridgeandreunitewithhiswifeMimiandhischildren,whohadreturnedtoCambridgeearlier,withorwithouthim.TheSloanSchoolofManagementatMITrepatriatedbothBlackandScholestoCambridge,andallowedthesetwogreatmindstocontinuetheircollaborations.However,whileScholeswasalwaysanacademic,withafewtoesinconsultancywork,Blackwasalwaysaconsultantandpractitioner,withafoot,andsometimesanarm,inacademia.UponhisreturntoCambridge,125 126TheRiseoftheQuantshecontinuedwritingregularpositionpapers,manyofwhichwouldgounpublished.Hedidsofortheloveoftheintensityofthepursuitofknowledge.However,afteralmostadozenyearsatMIT,heagainreturnedtotheinvestmentsideoffinancejustafewyearsafterhiscolleagueScholesdepartedMITforStanfordUniversity.In1984heacceptedaposi-tionatGoldmanSachs,theworld’spremierinvestmentbank.Twoyearslater,hehadbecomeapartnerthereandsoonbecamethedirectoroftheirQuantitativeStrategiesGroup.There,hecontinuedtoworkinoptionsand,increasingly,inimprovingfinance’sunderstandingofinterestrates.Blacksawthedescriptionandpredictionofinterestratestobeamulti-facetedandchallengingproblem.Whilehehaddemonstratedthatanoptionspricedependsontheunderlyingstockpricemeanandvolatility,andtherisk-freeinterestrate,theoverallmarketforinterestratesismuchmoremulti-dimensional.Theinterestrateyieldcurve,whichgraphsratesagainstmaturities,dependsonmanymarketsandinstruments,eachofwhichissubjecttostochasticprocesses.HisinterestandcollaborationwithEmanuelDermanandBillToyresultedinamodelofinterestratesthatwasfirstusedprofitablybyGoldmanSachsthroughthe1980s,buteventuallyenteredthepublicdomainwhentheypublishedtheirworkintheFinancialAnalystsJournalin1990.2Theirmodelprovidedreasonableestimatesforboththepricesandvolatilitiesoftreasurybonds,andisstillusedtoday.BlackwasunusualamongtheWallStreetquantswithwhomherubbedshoulders.The1980sand1990swasaperiodofbrashnessandexcess.Blackhadshakenthereactionaryrootsthatcharacterizedhisteenageandearlyadultyears.Asaseasonedanalystandfinancialstrategist,heexudedasenseofsoft-spokenconfidence,consistentwithatheoryoflifethatcontentismeasuredbywordsandnotbyflam-boyance.Hewasalsounusualinthebreadthofhisinterests.Hewasalwaysseekinglinksandrecognizedthatfinancialmarketsalsodependonmacroeconomicpolicy,insuranceinnovations,taxpolicy,thebusi-nesscycle,andeventhetheoryoforganizations.Heretainedthebroadinterestsofaparticularlyeclecticacademic,buthealsohadtheconfi-dencetorecognizethelimitationsofhisowntheories.3HeworriedthattheBlack-Scholesformulawouldbemisappliedifpeopledidnotrecog-nizethat,intherealworld,astockpricecouldjumpmuchmorethananticipatedbytheMarkovprocess,andthatreal-worldvolatilitycouldbewideratthetailsthanpredictedbythelog-normaldistribution.Infact,heencouragedotherstomodifyandimproveuponhisownmodel,anddidnotexhibitthedefensivenessthatlessermindsoftenexhibitwhentheirworkiscriticized. TheNobelPrize,Life,andLegacy127Bythe1990s,Blackhadhithisstride.Unfortunately,inthefirsthalfof1994,hereceivedaprognosisofthroatcancer.Doctorsrecommendedsurgeryandbelievedtheyhadexcisedthecancer.However,itreturnedinaninoperableform,andBlackdiedonAugust30,1995.Hewas56yearsold.Hewassurvivedbyhisdaughters,Ashley,Melissa,Paige,andnotedauthorAlethea,hisson,TerryLinton,hisstepdaughterKristenandstepsonKevin,andhiswife,CatherineTawesBlack.Black’sgreatestrecognitioninhislifewashisappointmenttotheprestigiouspresidencyoftheAmericanFinanceAssociationin1985.HeismemorializedthroughtheannualFischerBlackPrizeofferedbytheAmericanFinanceAssociation.ThePrizewascreatedin2002tohonorindividualswhosebodyofworkbestexemplifiestheFischerBlackprincipleofpursuingresearchamenabletopracticalapplication.ItistheonlyprizesponsoredbytheAmericanFinanceAssociationandnamedafteranindividualcontributortothetheoryoffinance.HeisalsomemorializedthroughtheFischerBlackVisitingProfessor-shipofFinancialEconomicsatMIT.Mostsignificantly,though,washowhewasfondlyrememberedbyhiscolleagues.AsJonCorzine,hisformerGoldmanSachscolleagueandformerGovernorofNewJerseyandSenatoroftheUSA,andmostrecentlyastheCEOwhentheinvest-mentbankMFGlobalfailedspectacularly,remembered:“FischerBlackwassimplythebest.Giantswithoutarrogancearerare.”4MyronScholesWhileFischerBlackwasamanoffew,carefullychosenwords,andhadasoft-spokennature,henonethelessstoodtall,bothphysicallyandintellectually,especiallyonthepractitionersideoffinance.However,whileitwashewhogeneratedthedifferentialequationwhichMyronScholeswouldhelpsolve,Scholes’contributiontotheequation,andespeciallyitsintuition,shouldnotbeunderestimated.ScholesremainedimmersedinresearchandteachingatMITuntilStanfordUniversitysuccessfullyattractedhimtoCaliforniain1981.Hehadplannedtoonlyvisit,butheremainedthereuntilheretiredfromteachingin1996.WhileatStanford,hecontinuedwithhisinterestsintaxpolicy,corporatefinance,andinvestmentbanking.Sincehisretirement,hehasheldthepositionofFrankE.BuckProfessorofFinanceEmeritusatStanford.WhileatStanfordhisresearchinterestsconcentratedontheeconomicsofinvestmentbankingandtaxplanningincorporatefinance. 128TheRiseoftheQuantsThroughouttheirprofessionallives,BlackandScholesbothsharedthequalitythatneitherwouldshyawayfromexpressingtheiropinions.And,justasBlackremainedconcernedabouttheinappropriateuseofderivativesmarketsortheapplicationoftheBlack-Scholesformula,Scholesisfrequentlyaskedtocommentonexcessesandmalaiseinmodernfinancialmarkets.Blackhadpassedawaybeforesomeoftheseexcessesinfinancialmarketshadcometopass.However,Scholesremainedactivethroughsomeofthemostturbulenttimesinfinancialmarkets,andindeedmayevenhavecontributedpersonallytosomeofthatturbulence.ScholesbeganconsultingwithSalomonBrothers,Inc.,in1990,andlaterjoinedanumberofhiscolleaguestoco-foundLongTermCapitalManagement.In2005heandsomepartnerswereimplicatedinataxavoidanceschemevaluedat$106million.ThePrizeTheSverigesRiksbankPrizeinEconomicSciencesinMemoryofAlfredNobelistypicallyawardedtoeconomictheoristsormathe-maticaltheoristswhoapplytheirworktoeconomicdecision-making.ThePrizesareoftenawardedtocontributionstounderstandingthatcanimprovethehumanconditionoradvanceoureconomicunder-standingdramatically.IfthesewerethestrictcriteriaforthePrize,therewouldbefewawardsforinnovationsthatcontributeprimarilytoourunderstandingoffinance.However,ifthecriteriarelatetoinnovationsthataffectmillionsofpeopleandtrillionsofdollarsmostprofoundly,thentheBlack-Scholesequationismostdeservingoftheprize.In1997theRoyalSwedishAcademyofSciencesawardedtheEconomicsPrizetoMyronScholesforhisworkincollaborationwithFischerBlack,andtoRobertC.Merton,whoiscoveredinthenextpartofthisbook,forhisrelatedcontributions.TheCommitteeofferedthePrizefor“anewmethodtodeterminethevalueofderivatives…[Theyhave]developedapioneeringformulaforthevaluationofstockoptions.Theirmethodologyhaspavedthewayforeconomicvaluationsinmanyareas.Ithasalsogeneratednewtypesoffinancialinstrumentsandfacilitatedmoreefficientriskmanagementinsociety.”5ThereislittledoubtthatBlackwouldhavesharedthatstagewithScholesandMertonhadhelivedjustacoupleofyearslonger. TheNobelPrize,Life,andLegacy129Thepost-NobelperiodOfcourse,theothersideofthedouble-edgedswordofthebroadrecognitionofsharedfatherhoodoftheprimaryformulainderivativesmarketsflasheswhenderivativesmarketscaptureournationalattention.In1973,onthecuspofthepublicationoftheBlack-ScholesformulaandthecreationoftheCBOE,noonecouldhavereasonablyimaginedthatderivativesmarketscouldcometoaffectusallinincrediblyprofoundways,bothpositivelyandnegatively.Derivativesmarketsaremoreesotericthantheunderlyingsecuritiesfromwhichtheyderivetheirvalue.Theseareinstrumentsthatallowustheoptiontobuyastockatafuturedate,oracontracttodeliveroracceptacommodityatsomefuturedate.Theycouldbethecreditdefaultswapsthatarebets,accordingtosome,orinsurancehedges,accordingtoothers,thatotherinstrumentswilldefault.Ineverycase,thederivativecanservesomeusefulpurposeasahedgeorinsuranceforthosewhomustholdormarkettheunderlyingsecurity.However,justaswecansellshortastockwedonotownandhavenotborrowed(anakedshort),derivativestradersmaynothavetoowntheunder-lyingsecurity,andmostlikelywillhavelittleornointerestintheunderlyingsecurity.Inotherwords,alargeshareoftradesinderiva-tivesmarketsarepurespeculation.Thisspeculationcanevenbehighlylevered.Ithasbeensaidthatthevalueofallderivativescontractsisamultipleoftheaggregatesizeofalltheworld’seconomies.Ultimately,veryfewoftheseoptionsorswapswillactuallybeexercised,andbuyersmustonlyfrontatinypercentageofthecostofsuchcontracts.Assuch,thisvalueismuchmorethantheactualinvestment,whichwasintherangeof$15trillionatthecuspoftheglobalcreditcrisisin2007–2008andtheGreatRecessionthatbecamemostobviousby2008–2009.Thesehighlyleveragedspeculationsgenerategreatprofitswhenthingsgowell.However,highlyleveragedderivativestradingalsoimpliesthatanunexpectedsystemicshockofonlyafewpercentagepointscanwipeoutone’sinvestmentandforcemargincallsthatrequirespeculatorstocoverevengreaterlosses.Itwastheinabilityofafewlargeinsurancecompanies,mostnotablyAmericanInternationalGroup(AIG),Citibank,theBankofAmerica,WellsFargo,andafewothers,tocoveradeclinethatwasgreaterthanexpectedthatplungedtheworldintotheworstrecessionsincetheGreatDepression.Whensuchadisplacementoccursonsuchagrandscale,thereareliterallyriotsinthestreetsanddemonstrationsonWallStreet.Insuch 130TheRiseoftheQuantstimes,financestranscendintoculture.Peoplewanttounderstandhowinstitutionssocomplex,intricate,andexudingsuchsophisticationandconfidencecanbecomesovulnerable,andwhyoureconomicleadersusethepublicpursetobailoutthesebastionsofprivateenterprise.InonesuchexplorationinthepublicinterestinMarch2009,MyronScholeswasinvitedtoaforumatNewYorkUniversitythatwasmoder-atedbyPaulVolcker,thelastdirectoroftheFederalReservetoleadanationthroughadeeprecession.6Inhistalk,Scholesagreedthatthecreditdefaultswapmarkethadbecomecompletelydecoupledfromitsoriginalpurposeintherun-uptotheglobalfinancialmeltdownof2008–2009.Herecommendedmuchmoreextensiveregulatoryintervention,withawindingdownofallcontractsatmid-marketprices,andwithareconstructionofthemar-ketbasedonclearerrules,greatertransparency,andshorter-durationcontracts.Duringtheforum,VolckertookacoupleofopportunitiestolaysomeresponsibilityforthepredicamentinthelapofScholeshimself.However,Scholesdidnottakethebaitandinsteadlamentedthehighdegreeofleveragethatregulatorsallowderivativestradersand,presum-ably,hedgefunds.Inafinancialworldinwhichatradercancontrol$40offinancialassetsbyputtinguponly$1ofhisorherownassets,theprofitsmaybelarge,butsoistherisk.Ineffect,thisextremeleverageallowsinvestorstomovedangerouslyuptherisk/rewardline.Inaneraofinvestmentbankstoobigtobeallowedtofail,ifamarketsuddenlyseizesandpreventsinvestorsfromunwinding,theymayfindthem-selvesowinghundredsofbillionsofdollars,asAIGhaddiscovered.Insuchacase,inwhichcompanieskeeptheirprofitsingoodtimesbutmustbebailedouttopreventevengreaterfinancialcatastropheinbadtimes,thefinancialsystemcreatesthemoralhazardproblemofprivatizedgainsandsocializedlosses.Scholesagreedthattherealityinwhichfinancefounditselfby2007wasproblematic.Scholesproposedthatthefinancialsystemshouldbedeleveraged.However,heacknowledgedthedifficultyofsuchaproposal.Ifinvestorsmustestablishasaferbalancebetweenassetscontrolledandthecapitalinvested,thenalargeportionoftheirsecuritiesassetswouldhavetobesold.However,suchdeleveragingwoulddrivedownsecuritiespricesandhencerequireevenmoresalestorebalanceasinvestors’equityislost.Itisanaspectofhumannaturethatweoftenlookforsimpleorevensimplisticsolutionstocomplexissues,especiallywhentheseissuescatchourcollectiveattentionandrisetothelevelofsocietyortearatourculturalfabric.Theglobalfinancialmeltdowncreatedanewand TheNobelPrize,Life,andLegacy131troublingrealityinwhichafinanceindustrythatgeneratedoneoutofeverythreedollarsofprofitintheUSAin2007plungedusallintofinan-cialperiljustayearlater.Globalcitizenswantedtounderstand,repair,andensuretherewouldbenorepeat,anditwouldbecomfortingtobeabletotracethemeltdownbacktooneortwoeventsorindividuals.Suchasimplificationgivesusthecomfortofanall-too-easysolution.Scholes,asthesurvivingnamesakeoftheequationthatinspiredderiva-tivestrading,wasforcedtotakeunfairresponsibilityforamarketnotofhismaking.Inhisdefense,anyinvestorinterestedinhedgingriskneedstoolstomeasureandbalancerisk.Todootherwisewouldbeimprudent.TheBlack-Scholesformulaisoneofthebestandmostintuitivetoolsforfinancialriskmanagementtodate.Theinventorsofausefultoolcannotbeheldresponsiblefortheuseofthattoolinwaysthatbecomedangerousfortheiroverconfidenceratherthanforthetoolitself.Sincehisretirement,Scholeshasbeenactiveasaspeakerandconsult-ant,andisthechairmanofahedgefundlocatedinCalifornia,calledPlatinumGroveAssetManagement.HeisalsotheChairmanoftheBoardofEconomicAdvisorsofStamosPartners.Scholeshaswonnumerousawardsandrecognitionsthroughouthislifetime,inadditiontotheNobelPrize.Hewonthe2011CMEGroupFredArdittiInnovationAward,wasappointedtotheAmericanAcademyofArtsandSciencesin2010,wasawardedmembershiptotheAmericanEconomicAssociation,andwasappointedasaFellowtotheAmericanFinanceAssociationin2000.HewasalsoaseniorfellowtotheHooverInstitutionandwasamemberoftheNationalBureauofEconomicResearch.Scholes’currentwife,JanBlausteinScholes,isalsoadirectorofinvestmentfundsandhasactedasgeneralcounselforvariouscompa-nies.SheisagraduateofthelawschoolattheUniversityofCaliforniaatBerkeley,andoftheUniversityofMichigan.TheylivetogetherinPasadena,California.Scholeshastwodaughters,AnneandSara.OnestorylefttobetoldThereremainsonesignificantstorylefttobetoldinMyronScholes’life.BeforethesagaofLongTermCapitalManagementcanbetold,wemustfirstdescribethelife,times,andtheoriesofonefinalgreatmindinpricingtheory. Thispageintentionallyleftblank PartIVRobertMertonOurlastgreatmindinpricingtheoryisappropriateforanumberofreasons.First,hesharesanAmericanpioneerpedigreethatiscommonamongthegreatquantmindsinthisvolume.Second,heworkedcloselywithFischerBlackandMyronScholestobringtheirideatofruition,andthentooktheirideasstillfurther.Third,hewaspartoftheintellectualhubthathadshiftedfromChicagotowardCambridge,Massachusetts,butoftenwiththesamecastofcharacters.HesharedtheNobelPrizein1997withScholesfortheworkthatBlackandScholesinitiatedandhecompleted,individuallyandtogether.Inaddition,hejoinedScholesintheill-fatedLongTermCapitalManagementfiasco.WeconcludewiththegreatmindofRobertMerton. Thispageintentionallyleftblank 18TheEarlyYearsWhiletheBlack-Scholesformulaforoptionspricingremainsthecontributionmostassociatedwiththatpairofgreatminds,theresultsweremotivatedbehindthescenesbyanothermostintellectuallygener-ouscollaborator.AndwhileFischerBlackcamefromalonglineagethatdatedrightbacktothefirstEuropeansettlersintheUSA,andMyronScholeswasthegrandsonofanentrepreneurialsetofimmigrantsfromPolishRussia,RobertCarhartMertonembodiedbothsuchlineages.RobertCarhartMertonInsomesenses,RobertMertonbridgedtheapproachesoftheEuropeanSchool,withitselegantandsophisticatedmodeling,andthenewquantitativeAmericanSchool,whichsoughtequationsthatweresim-pleandlentthemselveseasilytopracticalapplication.HisEuropeansensibilitiesaresharedasacommonheritagewiththemajorityofearlygreatmindsinfinancewhocamefromanareacontainedwithintheAustro-HungarianEmpireandthewesternRussianEmpirejustbeforeandafterthestartofthetwentiethcentury.Merton’sgrand-father,AaronSchkolnickoff,andAaron’swife,IdaRasovskaya,cametotheUSAfromRussiain1904withtheirtwo-year-olddaughterEmma.Upontheirarrival,AaronchangedhisnametoHarrie,orHarry,Skolnik.Thefamilysettledat414WilderSt.inPhiladelphia,Pennsylvania,whereHarry,originallytrainedasatailor,foundemploymentasamerchant.MeyerR.SkolnikwasbornonAmerica’s134thbirthday,July4,1910.Thefamilylivedabovetheirsmallshopthatsoldmilk,cream,andcheese,untilafiredestroyedthehome,andwithitthefamily’sliveli-hoodandbelongings.Asimmigrantsaccustomedtorebuildingtheirlives,135 136TheRiseoftheQuantsHarrySchkolnick(1882–?)BorninRussia,immigratedtoPennsylvaniaRobertKingMerton(1910–2003)IdaSchkolnick(1882–?)BorninRussia,immigratedtoPennsylvaniaRobertCarhartSpouse:ThomasCarhartMerton(1944–)JuneRose(1650–1696)BorninEngland,immigratedChildren:toNewJerseyWilliamH.CarhartPaulJ.MertonSamanthaJ.Merton(1872–?)RobertF.MertonMaryLord(1668–1718)BorninConnecticutSuzanneCarhart(1911–1992)RebecaCarhart(1880–?)Figure18.1TheMertonfamilytreeHarrysoonfoundemploymentasacarpenter.LikemanyEasternEuropeanJewishimmigrantfamilies,theSkolniksvaluededucationandsoughttoprovidetheircarpenter.LikemanyEasternEuropeanJewishimmigrantfamilies,theSkolniksvaluededucationandsoughttoprovidetheirsonMeyerwiththebesteducationalenrichmentthatAndrewCarnegie-endowedPhiladelphiacouldmusterinthoseleanyearsforthefamily.Indeed,attheageof84,inalecturetotheAmericanCouncilofLearnedSocieties,theintellectuallycurioussonofHarrySkolnikrelatedthat:“MyfellowsociologistswillhavenoticedhowthatseeminglydeprivedSouthPhiladelphiaslumwasprovidingayoungsterwitheverysortofcapital–socialcapital,culturalcapital,humancapital,andaboveall,whatwemaycallpubliccapital–thatis,witheverysortofcapitalexceptthepersonallyfinancial.’’1WhileMeyerbecamewellknown,wedonotnowknowhimbyhisAmericanizedbirthname.AsayoungteenagerinSouthPhiladelphia,heearnedpocketmoneybyperformingmagictricks.HequicklydecidedthattheGreatMeyerSchkolnick,orSkolnik,forthatmatter,didnothavetheringofaRobertHoudin,theinspirationforHarryHoudini.Hediscussed TheEarlyYears137withhismotherthepossibilityofchanginghisname.Hewantedsomethingthatsoundedmagical,perhapswithaMerlinconnotation,andalso,hopefully,somethingthatevokedawhiteAnglo-SaxonProtestantimagethatwouldbodewellforhisscholarshipapplicationstocollege.HesettledonthenameRobertKingMerton.AndhegainedentrywithascholarshiptoTempleUniversity.Thenamestuck.WhileTempleisnowconsideredanestablishedtop-tieruniversity,inthosedaysitwasstillafledglingnewschoolcateringtotheworking-classyouthofPhiladelphia.There,RobertKingMertoncameunderthetutelageofGeorgeE.Simpson,whoemployedRobertinhissociologyresearch.ProfessorSimpsonbroughthimtoprofessionalmeetingsandintroducedhimtosociologyprofessorsfromsomeofthecountry’smosteliteuniver-sities.OneoftheseintroductionswastoPitirmSorokin,whohadearlierfoundedHarvard’ssociologydepartment.RobertsubsequentlyappliedtoattendHarvard,despitetheadvicethatsuchanIvyLeagueschoolwasbeyondthereachofaJewishchildofimmigrantparents.Harvardacceptedhim,nodoubtasaresultoftheinterventionofSorokin,whopromptlyhiredRobertashisnewresearchassistantandcollaborator.RobertKingMertoncompletedhisPhDinsociologyatHarvardandbecamerenownedinandbeyondsociologycirclesforhisbril-liantinsightsandmethodologies.HespentmostofhisprofessionalcareerinNewYorkCityatColumbiaUniversity.HewastheformerPresidentoftheAmericanSociologicalAssociationand,in1994,wasawardedaNationalMedalofSciencebyPresidentBillClinton,thefirstsociologisttobegrantedthisaward.Healsocoinedsuchtermsas“self-fulfillingprophecy,”“rolemodel”and“focusgroups,”whicharestillusedtoday.Andinhisepicbutundertitledessay,“ANoteonScienceandDemocracy,”hequotedIsaacNewtonashavingsaid“IfIhaveseenfarther,itisbystandingontheshouldersofgiants.”Hemayhaveanticipatedtheworkofhissonandofafinancedisciplinegrap-plingwithuncertaintythroughthelastbookofhislife,TheTravelsandAdventuresofSerendipity.RobertKingMerton,thefirst-generationsonofJewishimmigrants,marriedSuzanneCarhartin1934.WhilehisparentsarrivedintheUSAonlyafewyearsbeforehewasborn,Suzanne’sancestorsweresomeofthefirstfamiliestoarriveinNorthAmericafromEnglandinthe1600s.Hernamesake,ThomasCarhart,wasbornin1650inAntony,Cornwall,England,andsettledinNewYork.Theirfirstson,RobertCarhartMerton,wasbornonJuly31,1944inNewYorkCityandsharedthenamesofthosefromthefirstandthelastbigwaveofEuropeanimmigrants.Thecouplealsohadtwodaughters,StephanieandVanessa. 138TheRiseoftheQuantsTheyoungerRobertwasraisedinoneofthemostintellectuallystimulatingenvironmentsimaginable,atthefamilyhomeinHastings-on-Hudson,asmallvillageof8,000peoplejustoutsideNewYorkCity.ThecommunitywasmiddleincomeandbluecollarinWestchesterCounty.Itwasdominatedbyalargewire-makingcompany,nowownedbytheAnacondaCopperCompany.Ithadanexcellenteducationsys-tem.Eachofthethreeschools,HillsideElementary,FarragutMiddleSchool,andHastingsHighSchool,has,atonetimeoranother,beendeclaredaprestigiousNationalBlueRibbonSchool.Classsizeswerealsosmall,withagraduatingclassforyoungRobertthatnumberedlessthan100.Yet,whilehewasmostaccomplished,hewasunabletoreachthetopofhisclass.Therewereothersinhisclasswhowerealsofromfamiliesofdistinction,includingthesonsofNobelPrizeinPhysicswinnersJamesRainwaterandJackSteinberger.AlsointhetownwasMaxTheiler,the1951NobelPrizewinnerinPhysiologyorMedicineforhisvaccineagainstyellowfever.Subsequently,WilliamVickreyandEdmundPhelps,twootherHastings-on-HudsonresidentsandColumbiaprofessors,wonNobelPrizesinEconomics.Infact,theremaynotbeacommunityanywherethathassuchahighpercapitaassociationwiththeNobelPrize.IfyoungRobertcouldnotbethetopstudentinhisclass,hecouldatleastdevotehistimetootherpursuits.Heplayedhighschoolfootballandhecompetedintrack-and-fieldevents.HeplayedneighborhoodbaseballandcompetedinLittleLeaguebaseball.Inhispre-teenyears,hedevelopedapassionforcarsandbegancountingdowntothedaywhenhecouldearnhisdriver’slicense,startingfrom1,800days.Hecouldquotespecificationsaboutcarsandengines,andhebuiltsouped-uphot-rodcarsthatcompetedlegallyindragracesinupstateNewYork,orperhapsillegallyinthestreetsofHastings-on-Hudson,despitethedifficultyofremaininganonymousinsuchasmalltown.HisdreamwastobecomeanengineerforFordMotorCompanyandheevensecuredsummerjobsatFordwhileatcollege.Helaterrelatedthatthiswastheonlyjoboutsideofacademiaheeverhad,exceptforastintworkingatthelocalcemetery.Robert’sfamilylifewasahappyandfulfillingone.Hisamateurmagi-cian/professionalsociologistfathertaughthimmagic,poker,baseball,andthestockmarket.RobertSr.wasarolemodelforyoungRobert,evenifheappliednoacademicpressure.RobertsSr.andJr.remainedcloseinadulthood,eveniftheywentthroughtheusualfather–sontribulationsduringtheteenageyears. TheEarlyYears139RobertJr.’sinterestinfinancealsocameearly.Inanincrediblyunusualgesturefromachild,orfromanyone,hewouldoffertobalancehismother’scheckbook.Heplayedwithmade-upbankslikeotherchildrenplayedCowboysandIndians.Atayoungage,healreadysharedacharacteristicwithMyronScholesinhisteenageyears.Bothhadafasci-nationwiththestockmarketandwithinvesting.YoungRobertMertonboughthisfirststockattheageof11,unsurprisingly,sharesofGeneralMotors,givenhisteenagegearheadtendencies.Whileatcollege,helikedtohangaroundbrokeragehousesandlistentotherhythmofthebanteramongbrokersandtraders.Meanwhile,hismotherprovidedacaringandgentlematernaltouch.Sheoncecounseledhimwithamessageherememberedintohisadultlife:“Firstshowthemthatyoucandoittheirway,sothatyouearntherighttodoityourway.”2CollegeatColumbiaWhenMertonwasadmittedtoColumbiaUniversityandenrolledinaprogramofappliedmathematicswithintheengineeringschool,hewasimmersedintothetypesofmathematicsthatsolvereal-worldengineeringproblems.However,hepreferredthemoreesoterictoolsofmathematicsusedinengineeringphysicsratherthantheformulaictoolsofcalculususedinsuchfieldsaselectricalengineering.Hehadapenchantforpartialdifferentialequations,whichwouldcomeinhandyinsolvingthetypesofproblemshewouldidentifyinfinance,wherefewpeoplehadsolvedapartialdifferentialequation.Healsodabbledineconomics,sociology,andtherequiredEnglishliterature,althoughthelatterbroughtdownhisgradepointaverage.BeforeandduringhistimeatColumbia,MertonbegantodateayoungtelevisionstarintheNewYorksoapoperaindustry.ShewasalsoaregulardancerontheteenagemainstaymusicprogramAmericanBandstandwithDickClark,andshedidmodelingassignments.HemetJuneRoseayearbeforeattendingColumbiaandmarriedherwithinaweekofgraduatingfromColumbia.Theyremainedtogetherfor30yearsandraisedtwoboys,RobertandPaul,andagirl,Samantha.Theyseparatedin1996.Followinghisscienceandmathematicsimmersionattheaward-winningHastings-on-HudsonHighSchoolandhisattendanceatColumbiaUniversity,wherehisfatherwasteaching,MertonearnedaBachelorofSciencedegreeinengineeringmathematicsin1966.HefollowedhisBachelor’sdegreeayearlaterwithaMasterofAppliedScienceatCaltech,theCaliforniaInstituteofTechnology,inPasadena,California. 140TheRiseoftheQuantsCaltechandbeyondThroughout,Mertonmaintainedhisfascinationwithfinanceandthestockmarket.Asearlyas1963,attheageof19,hegambledthatacor-poratemergerwouldgothroughandcalculatedtheoptimalratetobuyonestockandselltheotherinordertoprofitfromthemerger.Hisriskarbitragestrategywassuccessful,andhisearlysuccessesinducedhimsoonafterhisarrivalatgraduateschoolattheCaliforniaInstituteofTechnologyintheWestCoastuniversitytownofPasadenatohangoutintheearlymorningatbrokeragehousesinanticipationofthemarketopeninginNewYork.Histrades,firstinbuyingstocks,theninbuyingandshorting(sellingstocksborrowedbythetrader)stocks,andthenintheincreasinglysophisticatedinstrumentsofwarrants(stockoptionsissuedbythecorporationsthemselves),options,andbonds,taughthimaboutthemarketandhelpedputhimselfthroughschool.Mertonalsoengagedinthesomewhatriskypracticeofinvestingonmargin.ThisstrategyallowstheinvestortomovefurtheroutontheMarkowitzefficientsecuritiesmarketlinetoapointofhigherrewardbutalsomagnifiedrisk.Infact,hediscoveredthattheinvestmentbankunderwritinghisinvestmentmarginingpermittedhimtofinanceupto85percentofconvertiblebondpurchases,whichresultedinalever-agerateofalmost7:1.Thismagnifiedrewardandriskwasmuchhigherthanthe2:1leveragelegallypermittedinstockpurchases.Throughthisexercise,helearnedthatsubtlereal-worldlessonsaresometimesmissedbytheoreticalanalystsconfinedtothewallsoftheirivorytoweroffices.Mertonwaschallenged,inthemostbeneficialandprofoundway,byadecisiontoembarkonaPhDinappliedmathematicsatCaltech.WhileheendedupleavinginsteadwithaMaster’sdegreeafterayear,hestockeduphismathematicaltoolboxsignificantlyinhisbrieftimeinthatveryrichmathematicalenvironment.HisCaltechexperiencethrusthimintothemiddleofleading-edgeresearchasavehicleforthemathe-maticshewasstudying.WhilehealsorealizedatCaltechthathewouldprefertoapplyhistoolstofinanceandeconomicsratherthanrocketryandparticlephysics,henonethelessappreciatedtheexperienceandhisfreshlyacquiredmathematicalskills.Hisswitchfromappliedmathematicstoeconomicsandfinancewasasaconsequenceofthewaveofincreasinglysophisticatedeconomicunderstandingthatwasbeingco-optedbythegovernmentinthe1960s.WiththeelectionofPresidentJohnFitzgeraldKennedy,economists,mostlyfromHarvard,werebeingbroughtintoengineerthenationaleconomy.Thepromisewasthatgoodeconomicpolicycouldfreethe TheEarlyYears141countryfromthedebilitatingeffectsofinflationandunemployment,andcouldthusproduceasmuchvalueforhumansasdidtheIndustrialRevolution,thetransportationrevolution,andtheelectronicsrevolu-tion.LikeothersinCambridge,Massachusetts,hebelievedthetoolsofappliedmathematicscouldbeappliedtotheeconomytocreatehappinessandwealthforall.Andhisintuitivegraspofthewayfinan-cialmarketsworkreinforcedhisoptimismandsenseofdestiny.MertondecidedthatCambridgewastheplacetobe.Assuch,heappliedforadmissiontotheotherpremiertechnologyschoolinthecountry,thisonewithaneconomicsdepartmentandasmallgroupoffinanceprofessors.HewasonhiswaytoMITinthefallof1967,withhisCaltechMaster’sinappliedmathematicsinhandandlikelywithabettergraspofmathematicsthanmanyinMIT’seconomicsandfinancePhDprograms,facultyandstudentsalike.Threeyearslater,hecompletedhisPhDatMIT.WhileatMIT,MertonhadthegoodfortunetoworkunderthementorshipofPaulAnthonySamuelson,thefirstAmericantoearnaNobelPrizejustafewyearslater,andasubjectofthenextvolumeinthisseries.WhileitisexceptionallyunusualforaresearchinstitutionofMIT’scalibertoofferaprofessorshipimmediatelytooneofitsgraduates,MertonwasaskedupongraduationtojointhefacultyoftheSloanSchoolofManagementthere,wherehewouldremainuntilhemovedacrosstowntoHarvardin1988.TheMITSchoolAmongphysicistsandtheoreticaleconomists,MITisanexaltedinstitution.TheUniversityofChicagohasalsocreatedalargenumberofNobellaureates,primarilythroughitsearlyassociationwiththeCowlesCommission,itsemphasisonmicroeconomicanalysesofmarkets,anditsadvocacyforneweconometricandstatisticaltools.However,MITisrenownedforpureeconomicandfinancialtheorythatisabstractandelegant,innovativeandwithauniqueMITflavor.MertonspentalmosttwodecadesatMIT,inthewakeoftherevolutionthatbroughtthetheo-reticaltoolsoftheCAPMandtheBlack-Scholesoptionspricingformulaintopractice.Fromthelate1960stothemid-1980s,thebusinessandtheeconomicsschoolatMIThousedMyronScholesandFischerBlack,StewartMyers,JohnCox,Chi-fuHuang,StanleyFischerandPaulSamuelson,fourofwhomwouldwintheNobelPrizeinEconomics.TheMITeraforMertonwashighlyproductive.HeproducedbothalargequantityandahighaveragequalityofpaperswithintheMIT 142TheRiseoftheQuantstraditionofelegantandsimplecontinuous-timestochasticmodelsthatoftenemployedtherepresentativeagentapproach.Thesemodelsdifferentiatedthemselvesfromthelesssophisticateddiscrete-timemodelsinvogueelsewhere.Suchacontinuous-timeapproachdependedcruciallyonsolutionstodifferentialequations,whilethediscrete-timeanalogtookafarlesselegantapproachusingalgebra,somecalculus,andseeminglymyriadspecialcases.Whilemoremathematicallydifficult,thecontinuous-timeapproachoftheMITSchoolwasmuchmoreelegantandpowerful.Becauseofitseleganceandgenerality,thecontinuous-timeapproachcould,inturn,takeonmoredifficultproblemsandteaseoutmoregen-eralandgeneralizableresults.VerysoonafterhisarrivalatMIT,Mertondiscoveredhowhemanagedtogetintooneofthepremiereconomicsprogramsintheworld,despitehisdearthofeconomicstraining.MITwaswellonitswaytoforgingareputationasaschoolofthoughtinfinanceandeconomics,firstatthehandsofthegreatmindFrancoModiglianiandthenundertheleadershipofthegreatmindPaulSamuelson.In1967HaroldFreeman,along-timememberoftheeconomicsdepartmentbuthailingfromamathematicalstatisticsbackground,sawvalueintheunconventionalmethodologicaltoolwhichMertonhadmasteredandincludedinhischock-fullmathematicstoolbox.Freemanlobbiedonhisbehalfandimmediatelycounseledhimuponhisarrivalinthefallof1967.FreemanfearedthatifMertontookayearsimplytoolinguponeconomics,hewouldquitoutofsheerboredom.Instead,heencouragedMertontosubscribetothestimulationofSamuelson’smathematicaleconomicsclass,aseminarthatotherlesserstudentsfeared.WhileinSamuelson’sclass,Merton,asafirst-yearstudentwithalmostnotraininginformaleconomics,gottoknowsecond-yearstudentsStanleyFischerandMichaelRothschild,whowouldalsoeventuallywinaNobelPrizeinEconomics.Moreover,heimpressedhisfirstMITprofessorSamuelson.UnderSamuelson’stutelagethatfirstyear,hewroteacoursepaperonoptimalgrowththatwouldsubsequentlybepublished.HewassoonhiredasSamuelson’sresearchassistantbeforetheendofhisfirstyearatMIT.HeabsorbedfromSamuelsonaneconomicintuitionfromhisNobelPrize-calibermentor.Togethertheysharedaninterestinthemoreesotericfinancialmarketderivativeinstrumentsofconvertiblebondsandoptions.Finally,Merton’savoca-tioncouldalsobehisvocation.SamuelsonandMertonbegantocollaborateasequalsontheextensionofapaperonwarrantpricingthatSamuelsonhadproduced TheEarlyYears143in1965.Weshouldrecallthatawarrantisanoptiontobuyastockatafuturedateandpriceissuedbythepubliclytradedcompanyitself.Thepricingofsuchaninstrumentisaproblemofinternalcorporatefinance,infurtheranceofcorporateobjectives,ratherthananinstrumentforsecondarymarkets.JustasWilliamSharpehaddeterminedthecapitalassetpricingequationfromanexternalper-spectiveasCambridgeresearchersJohnLintnerandJackTreynorwereindependentlygoingthroughthesameexercisefromtheinternalcor-poratefinanceperspective,SamuelsonandMertonwerelookingattheequivalentofoptionsfromthecorporatefinanceperspective.Earlyinhissecondyear,inthefallof1969,onthecuspoftheawardingofthefirstNobelPrizeinEconomics,MertonwasgivingaseminarontheirjointworktotheprestigiousHarvard/MITJointSeminarinMathematicalEconomics.WithnumerousfutureNobelPrizewinnersintheaudience,youngMertonaspresenteramongthisillustriousgroupwastheequivalenttosendingoutarookieastheleadhitterinbaseball’sWorldSeries.Needlesstosay,thepresentationofthepaperwassuccessfulandMertonwaslearningeconomicsfromthemasters,notnecessarilyintheclassroom,butinsteadinthelaboratoryofideas,verymuchliketheprincipleespousedbyCaltech.FromhiscollaborationwithSamuelson,Mertonwasindoctrinatedintherepresentativeagentexpectedutilityregimethathassincebecomethestandard-bearingmodeloffinance.Hebegantoexplorehowtoextendthetraditionalstaticapproachoffinanceandeconomicstoatime-variantdynamicversionofintertemporaloptimization.Thisextensionwouldtakeadvantageofhisskillandinterestindynamicmodels,thecalculusofvariations,andpartialdifferentialequations.Hedidnotknowthattheproblemwasbeingactivelypursuedbysomeverybrightpeopleandhaddeterredmanymore.Nonetheless,theexpedienceofnecessityforcedhimtolearnthetoolsofstochasticcalculusthatwouldallowhimtosolvetheproblemathand.Hesuc-ceededincreatingacontinuous-timedynamicportfoliotheorythatwasmuchmoreelegantandgeneralthanthediscreteversionsthatotherswereproducing.Amonthafterpresentingthepaperco-authoredwithSamuelsontothefacultyseminar,hepresentedhisownpapertotheHarvard/MITgraduatestudentseminar.ThispaperwaspublishedthefollowingsummerastheotherbookendtoapaperthatSamuelsonhadwrittenonthelifecycleofportfoliorisktolerance.Infact,Mertonlateradmittedthathisstrategywastolearnthemathematicsheneededratherthantheeconomicshisprofessorstaught,muchlikeAlbertEinsteinhaddoneasagraduatephysics 144TheRiseoftheQuantsstudent.Heagreedthatthiswasnotthebeststrategytosecuresuperiorgrades.However,theproofisinthepudding.HeproducedfiveessaysforhisPhDthesis,threeofwhichwerepublishedbyrefereedfinanceandeconomicsjournalsevenbeforehisdissertationteamcouldwitnesshisPhDdefense.AfourthpaperwaspresentedattheSecondWorldCongressoftheEconometricSocietyinthesummerhegraduatedandalsoappearedinprintwithinayear.InthatlastyearofhisgraduatestudiesatMIT,MertonalsoimmersedhimselfintheassetpricingtheoryforwhichhewouldbecomemostrecognizedandwhichcomplementedtheworkofBlackandScholes.Uponhisgraduation,FrancoModiglianisuccessfullyattractedMertonacrosscampustothefinancedepartmentoftheSloanSchoolofBusiness.SamuelsonhadnominatedMertontothepositionofJuniorFellowatHarvard,whichcarriedagenerousstipendbutwithnoexpectationotherthantopursueresearchoftheawardee’schoice.Modiglianipre-vailedtoconvinceMertontotakeapositionattheSloanSchoolinthefinancedepartment,despitethesmalltechnicalitythatMertonhadnevertakenafinancecourse.ModiglianithoughtveryhighlyofMertonandlikedhowMerton’sdynamicoptimaldecisionmodelsupportedhisLifeCycleModel,forwhichhewontheNobelPrize,alongwithhisworkwithMertonMilleroncorporatefinance.Clearly,ModiglianiwantedtokeepMertonaround.Modiglianiwaswellknownforsuchgenerousmentorshipofyoungandbrilliantscholars,buthetookapar-ticularinterestinthesuccessofMerton.Afewyearslater,ModiglianihadevenaskedhimtospeaktotheAmericanEconomicsAssociationfortheluncheonhonoringModigliani’s1985NobelPrizeinEconomics.MertonfoundhimselfwithanMITPhDinhandandaninterviewforhisfirstacademicpositionattheesteemedSloanSchoolofBusiness.MyronScholeshadalsobythensettledintoteachingandresearchasayoungfacultymemberattheSloanSchool,followingthecompletionofhisChicagoPhD.Almostimmediately,ScholeswasassignedtotherecruitingcommitteechargedwiththeresponsibilitytofillavacantfacultylineforwhichMertonhadapplied.Thesetwosharedtheirinterestinappliedmathematicsandphysics,andtheapplicationofcomputerstoaidintheirresearch.TheybecameclosecolleaguesandfriendssoonafterMertonwashired.Atthattime,theSloanSchoolfinancedepartmentwassmall.ItincludedthepatriarchModiglianiandanotherseniorprofessor,DanielHolland.Therestwereyoungprofessors.InadditiontoMertonandScholes,StewartMyersandGerryPogueroundedoutthefaculty.Itwasthesefourwhowouldconstitutethecenterofmassofthedepartment TheEarlyYears145andwouldforgethemathematicallysophisticated,dynamic-timemodelingapproachforwhichMITremainsrenowned.Andbecausetheseniorfacultymembersweresobusyandtheirtimewassomuchindemand,thejuniorfacultymemberstaughtthevastmajorityofthecourses,andorganizedandpresentedattheHarvard/MITjointseminars.ThisintenseenvironmentturnedouttobemostproductiveforMertonastheenergyoftheyoungdepartmentseemedtocreateevenmoreenergy,capacity,andinnovation.MertonandScholesweresoonjoinedbyDavidMullins,EricRosenfeld,andLawrenceHilibrand.ThisgroupoffiveSloanfacultymemberswouldlaterreuniteandjoinsomeMITalumnitofoundLongTermCapitalManagement.Meanwhile,ScholeshadbeenspendingpartofhistimeconsultingintheCambridgeareaandhadenlistedMertontodothesame.Oneoftheprojectsthatbroughtthemtogetherdealtwithoptionspricing.Mertonbelievedthathisresearchwouldbenefitfromtherealitytestoffinancialpractice,justasheusedtheclassroomasalaboratoryforhisideas.Inthisearlypartofhiscareer,hewaslikeanacademicbeethatabsorbedideasfrommanydifferentavenuesandinturnpollinatedvariousforumswithconceptsemerginginhisheadandathispen.Whilehedidnotknowityet,hehadcreatedtheinsightsthatwouldsoonwinhimaNobelPrizeataveryyoungage,justasMarkowitz,Sharpe,andScholeshaddiscoveredNobelPrize-qualityinsightsveryearlyintheirstudiesandcareers.Suchearlysuccessismostunusualforwinnersofaprizethatistypicallyawardedforalifetimeofachievements. 19TheTimesMostsuccessfulscholarsareaproductoftheirtimes.Manyacademiciansstruggleoveracareertokeepupwiththeacademictimes.Itisthehall-markofgreatmindsthattheydefinethetimes.Inthisrespect,RobertMerton’sworkearlyinhisstudiesandcareerwasnoexception.Butifhewasaproductofhistimes,itcannotbesaidthathewasnecessarilyaproductbothofspaceandtime.Hedefinedanewspaceofresearchinfinance,onethathadmoreincommonwithrocketscienceandmathematicsthanwithfinancialoreconomictheory.Whilehedidnotdevelopanewfieldofmathematics,themathematicshefreshlyappliedtofinancewasnovel.Anditwasrevolutionary.IncollaborationwithFischerBlackandMyronScholes,hefirmlyplacedfinanceonarigorousandquantitativefoundation.However,thetoolshebroughtover,andtheintuitionhedevelopedtomotivatehisbestwork,initiatedarevolutioninfinance.Thestudyofpersonalfinanceisuniqueamongalldecisionsciences,andperhapsallofscience,exceptrocketscience.Infact,financehasmoreincommonwithrocketsciencethanperhapsanyotherdisciplineforonereason.Bothdisciplinesarethestudyoftrajectoriesinanenvi-ronmentinwhichthesubjectisbuffetedbyforcesthatarepartiallypredictablebutalsopartiallystochastic.Therocketscientistmustcalculatetherocket’strajectoryasitmovesthroughanatmosphereofvaryingdensityandrisingordeclininggravity,astheweightofthevehiclechangeswithfuelburnovertime.Theequationsthatgovernthetrajectoryareknowntothephysicistasequationsofmotion,inwhichlocationordistanceismeasuredagainsttime.Financetheoristsdothesame.Theirsisthestudyofthesecuritypriceastheunderlyingvalueisbuffetedbymacroeconomicforcesandthedynamicsofthefirmovertime.Theequationsofmotionhave146 TheTimes147theanalogyoftherateofchangeofthestockpricefrommomenttomoment.Whileallsecuritiesarebuffetedbythesamesystematicforces,somesecuritiesaremoresensitivetoshocksandtoforcesuniquetothatindustry,oreventothatsecurity.Certainly,asthewaveofphysicistswhofoundtheirwaytothestudyoffinancecanattest,thetoolsofrocketsciencecanbeadaptedtofinance.Evenso,arocketscientistcan-notexpectthesamepredictableanalyticsolutionsascanbedeterminedwithinthecontextofthemovementofbodies.Wemightimaginethateconomicsisthenaturalspringboardtofinance.Certainly,modernfinanceflowedoutofworkbyeconomists,fromIrvingFishertoJohnMaynardKeynes,MiltonFriedman,JacobMarschak,andKennethArrow.However,alltheseeconomistswhohelpedforgethefoundationofmodernfinancebeganineithermathematicsorphysics,ashasLouisBachelier.Indeed,Mertontoohadfollowedthissametradition.Perhapsintribute,PaulSamuelsononcelabeledhimtheNewtonofmodernfinance.Afterphysicsandappliedmathematics,economicsisthenextbestpreparationforthestudyoffinance.Intuitionabouthowmarketsfunctionandinsightsintomodelsofdecision-makingareimportantinbothfinanceandeconomics,butnotsoimportantorasrigorouslytreatedinotherdisciplines.However,unlikerocketscience,econom-icsoftentreatsproblemsinwhatiscalledthesteadystate,orinwhichthesystemunderreviewnolongerconvergesorisbuffetedovertime.Asaconsequence,thetoolsofmatrixalgebraorsettheorymaybeemployed,asmightthecalculusthatcomparesonequantityvariabletoanother.Rarelyisdealingwiththespeedofadjustmentnecessaryorputintopractice;rather,itisthestableequilibriumthatischaracterized.TheriseofthequantsSuchasteady-statecharacterizationisfineforlong-termanalysesineconomictheory.However,itisill-suitedtotheshort-termandfast-pacedworldoffinance.Whilephysicistscannotescapethedescriptionofmovementandfinancialtheoristsalmostuniversallytrytomodelthechangeinpricesovertime,economistsrarelydoso.Physics,analyticalmathematics,andeconomicsallrequiretherigorsharedbyfinancialtheorists.Itisphysicsandfinancethatalsorequirethetoolsofdynamicanalysis.Thosewiththeskillsandaptitudeofphysicistsfoundquicksuccessinfinance.Studentsoffinancearedrawneitherfromaninterestinbusiness,andhencethroughbusinessschoolsasundergraduates,or 148TheRiseoftheQuantsfromscienceandengineering,andseekanacademicshiftingraduateschool.Theirrespectivebackgroundscouldnotbemoredifferent.Thegroupthatarrivesinfinancefromaninterestinbusinessoftentriestoavoidmathematicsandsuffersonlyenoughformalmathematicstocopewiththeequationsoffinance.Thosethatcomefromthemathe-maticallyintensivesciencesfindthemselvesinthesciencesoftenfortheirloveofmathematics.Infact,asMertondemonstrated,agreataptitudeinmathematicsorphysicscanbodewellforthepotentialfinancetheoristwhocangarnerthefinanceintuitionnecessarytomotivateandinterprettheequations.Giventhistechnicalaspectofequationsofmotioninfinance,itshouldcomeasnosurprisethattheinstitutionmostassociatedwiththestudyofphysicsandengineeringintheUSAshouldlikewisebeahotbedfordynamicmodelsinthedecisionsciences.ThissharedvocationofMITwasdemonstratedacrossitseconomicsfaculty.Forinstance,RobertSolowwentontowinaNobelPrizeforhisworkingrowththeory,whichmodelshoweconomicsystemsgrowandevolveovertime.AndthefirstAmericaneconomisttowintheNobelPrizewasSamuelson,whowasuniversallyrenownedasthepersonwhobroughtmathematicalrigortothedecisionsciences.MITdevelopedacertainflavorofscholarswithstrongandsophisticatedmathematicalskills.ThenewlyformedandstillsmallfinancedepartmentattheSloanSchoolinthe1960sandearly1970swasnoexception.Theessentialtoolinequationsofmotionisaparticulartypeofdiffer-entialequationinwhichtherateofchangeofavariableisdeterminedovertime.Thesetime-dependentdifferentialequationshadbeenthepurviewofmathematicianssincetheseventeenthcenturyandtheworkofimmortalslikeNewton,Leibniz,andtheEulerandBernoullifamiliesofmathematicians.Einsteinusedthesetoolsin1905inhisdevelopmentofthespecialtheoryofrelativity,ashadBachelierjustfiveyearsbeforeEinstein’smagnificentyear,inhisprecociousmodelingofsecuritiesprices.ThemathematicianFrankPlumptonRamsey,whoalsodabbledineconomicsinthe1920s,usedtime-dependentdifferentialequations,ashadSolowinhisNobelPrize-winningtheoriesofeconomicgrowth.However,beyondthesenotableexceptionsineconomics,theo-ristsfoundwaystoavoidspecializedstudyindifferentialequations,oftenbyframingtheirproblemsastwoperioddifferenceequationsratherthanthemorechallengingcontinuous-timedifferentialequations.EvenBlack,whohadformulatedthemostcomplexdifferentialequationtobeseenandeventuallysolvedinfinanceatthatpoint,wasunabletoinitiallysolvehisnow-famousequation.Hadhebeen TheTimes149morefamiliarwiththesolutionsemployedinphysics,hemighthaverecognizeditsformasanalogoustoatypeofprobleminheatdiffusion,asBachelierhadrealized70yearsearlier.However,onceScholespuzzledwithhimoverasolutionandcomparedtheirworktoworkperformedinanobscureYalePhDthesisafewyearsearlier,theyfinallyteasedoutthesolution.Theirsolutionwouldformthebasisforanentiremovementinthepracticeoffinance–theriseofthequants.TheyhadsomehelponthesidelinesfromRobertMerton,though,asweshalldescribebelow.Aswenotedearlier,BlackandScholesexperiencedagreatdealoftroublegettingtheirpaperpublishedatfirst.Theysurmised,likelyquiteaccurately,thattheywouldhavemoresuccessintryingtohavetheirpaperpublishedinoneofthemoremathematicallysophisticatedeconomicsjournalsthaninafinancejournalthatwasstillmostlydescriptiveratherthanquantitativeandanalyticatthattime.However,theclubofmathematicallysophisticatedeconomistswasasmallandeliteone,anditacceptedfewnewmembers.Blackwasanunknown,andhisreturnaddresswasasmallconsultingfirm,notapowerhouseuniversitydepartment.Thecombinationofthesestrikesagainstthem,withasubjectmatterthatwassomewhatunusualforeconomists,anddelaysinpublication,or,forthatmatter,failuretopublishatall,shouldnothavebeensurprising.Afterall,theproblemhadevenstumpedtheeminentmathematicaleconomistSamuelsonjusthalf-a-dozenyearsearlier.Itseemedunlikelythattworelativeunknowns,fromoutsideofeconomics,coulddowhatSamuelsoncouldnot.Ontheotherhand,Merton,theprodigyofbothSamuelsonandFrancoModigliani,certainlyhadthetoolsofmathematics,andespe-ciallycontinuous-timedifferentialequations,tomakesenseofBlack’sequation.Infact,Mertonhadalreadybeenforgingareputationforhisdynamicmodelingskillsandshowedgreatabilityingettingacademicpaperspublished,evenwellbeforethecompletionofhisPhD.AnewdynamicapproachtofinanceMertonhadbeeninterestedindynamicmodelingalmostfromthedayhearrivedatMIT.FromhisearlypairingwithhismentorSamuelson,whohadbeenworkingonhiswarrantpricingprobleminthetraditionalstaticframeworkofeconomicsasearlyas1965,itquicklyoccurredtoMertonthattheremightbemanyavenuesforproductiveresearchbytakingthesestaticmodels,aspracticedbySamuelsononpricingandbyModiglianionthelifecycleofconsumption,andextendingthemintoacontinuous-timedynamiccontext.Atthattime,therewere 150TheRiseoftheQuantsotherspursuingthesamepotentiallyfruitfulresearchagenda,buttheyoungMerton,agraduatestudentinexperiencedineconomics,wasnotfamiliarwiththiswork.Fortunatelyforhim,ignoranceturnedouttobebliss.Inhiscourseworkinappliedmathematics,Mertonhadbeenwelltrainedincontinuous-timemodeling.However,stochasticdynamicprogramming,and,inparticular,Itô’slemma,hadnotbeenpartofhiscurriculum.Hewasresourcefulandhediscoveredonhisownthetoolsnecessarytosolveproblemsinstochasticdynamicoptimization.Infact,Mertonbeganpresentinghisleading-edgeworkattheHarvard-MITgraduatestudentseminarandatfacultyseminarswellbeforehisPhDwascomplete.HeevenhadhisworkonthedynamicextensionoftheLifeCycleModelandtheportfoliochoiceproblempublishedbeforeheearnedhisdoctoratedegreeatMIT.Infact,whilehewassurroundedwithsomeofthebesteconomistsintheworld,fourofwhom(Samuelson,Modigliani,Solow,andPeterDiamond)wouldgoontowintheNobelPrize,hewaslearningmorefromhisownresearchthanfromthecoursesthatconstitutedhisPhDcurriculum.Mertonwasalreadyestablishingtheresearchagendathatwouldconstitutehisfirstdecadeofscholarlywork.Theyearsleadinguptohisthesisdefensein1970,andthedozenyearsthatimmediatelyfollowedit,constitutedthemostresearchproductiveperiodinhislifeintermsoforiginality,sophistication,andacademicsignificance.InhisNobelspeech,heplacedhisworkasrestingsomewherebetweenthesimple,elegant,andinsightfultwoperiodmodelsthathadbeenthehallmarkofMITandCambridgeresearchontheEastCoastforalmosttwodecadesandthemoreabstractgeneralequilibriummodels,producedontheothercoast,thatwerethehallmarkofBerkeleyattheUniversityofCalifornia.Merton’sinnovation,andhisresearchsignature,isthepowerfultoolofcontinuous-timemodeling.Asopposedtoallthespecialcasesandindeterminatesolutionsthatdiscrete-timemodelsprovideonceeventwoorthreetimeintervalsareconnected,thecontinuous-timemodelsoftenprovidedsurprisinglysimpleandanalyticsolutions,despitethemoresophisticatedtoolsnecessarytosolvethem.Becauseofthesimplicityofthesolutionsandtherelativelysmallnumbersofvariableshechosetoinclude,hismodelswerealsomoreamenabletoeconometricverification.Merton’sresearchagendaintheperiodleadinguptohisinfluentialcontributiontotheBlack-Scholesequationproducedtenpapersinfiveyears.Theyincluded“AnIntertemporalCapitalAssetPricingModel” TheTimes151inoneofthetopeconomicsjournals,1acommententitled“TheRelationshipbetweenPutandCallOptionPrices:Comment”intheJournalofFinance,2andanotherfinancetheorypaperintheJournalofFinancialandQuantitativeAnalysisentitled“AnAnalyticalDerivationoftheEfficientPortfolioFrontier.”3Healsopublished“TheoryofRationalOptionPricing”intheBellJournalofEconomicsandManagementScience4and“OptimumConsumptionandPortfolioRulesinaContinuous-TimeModel”inthehighlytheoreticalJournalofEconomicTheory.InatributetoSamuelson,hissupervisorandmentor,healsowroteanappendixentitled“Continuous-TimeSpeculativeProcesses”forSamuelson’sbookMathematicsofSpeculativePrice,andjointlypublishedwithSamuelson“ACompleteModelofWarrantPricingthatMaximizesUtility”in1969.5Meanwhile,Mertonwasalsousinghisdynamicmodelingskillstoequaleffectintheareasofeconomicsunrelatedtofinance.Hepublished“AGoldenGolden-RuleforWelfare-MaximizationinanEconomywithaVaryingPopulationGrowthRate”6and“LifetimePortfolioSelectionunderUncertainty:TheContinuous-TimeCase”in1969.7Afewyearsearlier,hehadalready,asagraduatestudent,publishedthemorewhimsical“A‘Motionless’MotionofSwift’sFlyingIsland”intheJournaloftheHistoryofIdeas.8Hehad,injustafewshortyears,producedtenhigh-qualitypapersintopjournalsinfinanceandeconomics,includinghisBellJournalpaperthatenabledhimtoearnhisNobelPrize.WiththeexceptionofapaperwithSamuelson,theywereallsole-authored,andmostwereofgreatoriginality.Hisprofoundproductivitysoearlyinhiscareer,andevenbeforehisgraduation,wasalmostunprecedented,butisnotuncommonamongthesmallcircleofgreatminds. 20TheTheoryFischerBlackderivedthedifferentialequation.MyronScholesprovidedaninterpretationandassistedinitssolution.However,itwasRobertMertonwhosparkedtherevolutionthattransformedfinance.WeshouldrecallthatBlackmotivatedhisoriginaldifferentialequationfromtheperspectiveoftheCAPMmethodology.Scholeshadlessenedthemodel’sdependenceontheCAPMbylookingatthespecialzerobetacasewhich,hearguedinhisChicagoSchool-motivatedintuition,shouldresultinarisk-freereturnifthereisperfectarbitrage.Fromthere,theywereabletoderivethesamesolutionasthealternateCAPMapproachhaddetermined.Atthetime,financialtheorists,especiallyMerton,wereincreasinglyskepticalofthestaticandbackward-lookingcharacteristicsoftheCAPM,andwereseekingtocreatedynamicextensionsofit.MertonwasconvincedthattheBlack-Scholesformula,whichwasaspecialcaseofSpreckle’sderivation,mustbeafurtherspecialcaseofamoregeneralanddynamicCAPM.BlackhadalreadyrealizedthatitmightbesafertointerprettheformulaasScholeshaddonewhilewearinghisChicagoarbitrageandefficientmarketlenses.TheintuitionMeanwhile,MertonmanagedtoovercomehisskepticismofanyapproachbasedonthestaticCAPMmodel.1Hereasonedthat,evenifhelookedfromthedynamicCAPMperspectiveataportfoliothatisreadjustedateachperiodintime,hecouldmimictheoptionreturnsspecifiedbytheBlack-Scholesformulabycombiningpositionsontheunderlyingstockwithborrowingattherisk-freeinterestrate.Hethen152 TheTheory153realizedthedualityofhisidea.Ifhecoulddescribesuchaprocesswithknownpricesofthesecurityandwithknowledgeoftherisk-freeinterestrate,theequivalentoptionpricecouldbecalculatedfromthepriceoftheportfoliothatincludedtheoption.Todoso,Mertonaccuratelyinterpretedacalloptionassimplyaleveragedholdingofw/xunitsofthestock,fundedbyborrowingequaltothecostofthestocklesstheproceedsfromsellingthecalloptions,i.e.:Borrowing=δδ−xwxw.Fromthisinterpretationandwithsomemanipulation,MertoncametothesamedifferentialequationashadBlackusinganothermotivationandScholesusingyetanother.HeconcludedthatBlackandScholesmustbecorrectafterall,basedonwhatisnowcalleda“noarbitrageopportunity”strategy.Thestrengthofhisinterpretation,though,isthatitdoesnotrelyatallonpricingmodelsfortheunderlyingsecurity.Itissimplyanaturalimplicationofnoarbitrageopportunities.WhiletheBlack-Scholesapproachwasstatic,inthatitgivestheoptionpriceatafixedpointintime,Merton’sintuitionandcomparativeadvantagewasinlookingatdynamicsystemsasprocesses.Inhistreatment,interestratescanchange,andtheequationalsoper-mitteddividends,asapercentageofthestockprice.But,whileMerton’sderivationisthemostelegantandgeneralofthethreeapproaches,andwhilehewasencouragedtopublishhisresultsimmediately,hedeclinedtodosountilBlackandScholeshadsuccessfullypublishedtheirderivation.AssumptionsforMerton’sderivationMerton’sintuitiontookaleafoutofthebookoftheChicagoSchool.Intheabsenceoftransactioncosts,thecorrectcombinationofanytwoofthefollowinginstrumentsshouldbeabletopredictthethirdifarbitrageexists:therisk-freerateofreturn,astockprice,anoptionwrittenonthestockprice.Inthiscase,hisdynamic(continuous)tradingstrategyusingjustthestockandtherisk-freerateofreturnshouldpricetheoptionaspredictedbytheBlack-Scholesequationintheabsenceofarbitrageopportunities.MertondemonstratedtheaccuracyofBlack-Scholesthroughtheapplicationoftechniqueshehadalreadydevelopedinhisworkin 154TheRiseoftheQuantscontinuous-timeportfolioselection.Tobeginwith,hemadeanumberofassumptionsthatarenowstandardinfinancetheory:1.Frictionless,continuouslytradedperfectmarketswithouttaxesandwithfreeaccesstoborrowingandlendingatacommonrisk-freeinterestrate.2.ThepriceoftheunderlyingassetxfollowsaWeinerprocesswithameanrateofreturnandstandarddeviation,adjustedforthedividendrateD1:dx[xD1(x,t)]dtxdZ3.Therisk-freeinterestrateisderivedfromabondmarketthatfollowsasimilarWeinerprocess.Fornow,considerthisratetobeconstant,i.e.,itsmeanandvariancearezero.4.Allinvestorsobserveandassumethesamevarianceeveniftheymaydifferontheexpectedreturnoftheunderlyingstock.TheyalsobelievethatthesecurityfollowstheWeinerprocess.5.Theoptionpriceiscontinuouslytwicedifferentiableintheunder-lyingassetprice,therisk-freeinterestrate,andtime.(Mertonlaterdemonstratedthatthisisaresultratherthananassumption.)2Basedontheseassumptions,inthespecialcasewhereD0(i.e.,therearenodividendspayments),thesolutiontothedifferentialequationisasgivenbyBlackandScholes.Mertonwasabletorelaxtheassumptionsusinganinterestingficti-tioustool.Whilehisproofiscomplicated,itispossibletononethelessgetaflavorofhistechnique.Mertonassumedthatthereisatypeofcontractthatyieldsapayoutf(x(t),t)fortheoptionatatimetiftheoptionvalueexceedsanupperfunctionalbound,orapayoutg(x(t),t)ifatatimettheoptionpricedropsbelowalowerfunctionalbound.Atterminaltimet,theoptionearnsapriceh(x(t),t).Inotherwords,thefictitiousinstrumentbindstheoptionvaluetoanupperandlowerenvelopeshouldtheoptionvalueexceedtheenvelopebounds.Mertonthensetupthecostofrunningsuchaconstructedfictitiousportfolio.IttooisofavaluethatfollowsaWeinerprocessbecauseallassetsthemanagerusestofundhisorherportfoliowouldfollowaWeinerprocess.Then,thedifferencebetweentheproportionaldriftofthesumofassetsSusedtofundthisportfolioandtheportfoliopayoutVwillalsofollowaWeinerprocess:dSS−=dVV()μ−αdt+θdB, TheTheory155whereµisthemeanreturnonthefundingportfolio,isthemeanreturnonthepayoutportfolio,andtheBrownianmotiontermattheendisacombinationofthestandarddeviationonthefundingportfolioandtheunderlyingstockmultipliedbytheBrownianmotionoftheunderlyingasset.Mertonthenestablishedthatthetrackingerroronsuchafundingportfoliomadeupofmarketsecuritiesisuncorrelatedwiththetrackingerrorontheunderlyingsecurity.Thisisaconsequenceofthechoiceofafundingportfoliothatminimizesitscorrelationwiththetrackingerrorssothatonecouldnotcapitalizeonpredictabledifferences.Tocompletehisargument,Mertonthendeterminedthepatternofpricesthisfundingportfoliomustfollowtocontainthepaymentspromisedthatreplicatetheoption.Heshowedthattheprocessofprop-erlybalancingthefundingportfolioandmakingtherequiredpay-offsfordividendsandforconversions,shouldthevalueoftheoptionfalloutofthepromisedenvelope,isarelativelystraightforwardcalculation.Hecompletedhisproofbyshowingthatthisfeasiblefundingportfoliowillexactlyreplicatethepay-offsateachpointintimeoftheoption,or,forthatmatter,asimilarderivative.Ofcourse,Mertonalreadyhadtheluxuryofknowingthattherewasasolutiontothedifferentialequation,aspostulatedbyBlackandScholes.However,theBlack-Scholessolutionrequiredthattheunderlyingstockexhibitednojumpsanddidnotpaydividends.TheportfolioderivedbyMerton,though,solvedthediscontinuityproblembypayingoffthederivativesownershoulditjumpoutsideoftheenvelope.Thesedeviationsoneitherendwillbeunbiased,andhencehaveameancostofzero.Thederivedportfoliothatreplicatestheoptionfollowsthepriceoftheoptionarbitrarilycloselyandhasthetwice-continuouslydifferentiablepropertynecessaryforthesolutiontoexist.Throughhisclevermathematicalconstruct,MertonwasabletorelaxsomeofthestrongestassumptionsthatoffendedthosemostcriticaloftheBlack-Scholesformula.Consequently,hewasabletoincreasethegeneralityoftheBlack-Scholesformula.Hedemonstratedthatdividendsandearlycallscouldalsobeaccommodatedbyhisenvelopingportfolio.Hemanagedtoshowthatthisenvelopingportfoliowassmoothandhencethediffer-entialequationfortheenvelopingportfoliocouldbesolved.Infact,thisenvelopingportfolioofanoptionforanunderlyingstockthatmayexhibitjumpsanddividendsnonethelessfollowsthesamedifferentialequationdefinedbyBlack.MertondemonstratedthattheBlack-Scholesformulaisaccurate,eveniftheoptionmayneedtobecontinuouslyrebalancedateachpointintimetoaccommodatejumpsorex-dividendrepricing. 156TheRiseoftheQuantsWemightimaginethattherecouldbegreatprofitstobehadifBlack,Scholes,andMertonkepttheirequationsecretandstartedtheirowninvest-mentfirm.Together,allthreegreatmindsbegantoemploytheirderivationtomakemoneyonexistingwarrantsbytradingwarrantsthatseemedtobegrosslymispricedbasedontheirformula.Ifanoptionwereconsist-entlypricedtoohighbutstillofferedthedesiredpatternofriskoffset,theycouldsellcallsinsteadofbuyingthem,buytheunderlyingwarrantinsteadofsellingit,andmakeaconsistentprofitovertherisk-freerate.Conversely,anoptionpricedtoolowwouldallowafullhedgethroughpurchasesofoptionscontractsfundedbyshortsalesoftheunderlyingstock.Thisstrategywouldearntherisk-freereturnandthecompletehedgeatalowerprice,andhencewouldearnahigherreturn.Ifthesethreeinvestor-scholarsusedtheirtechniqueaggressivelyenough,theirarbitragewouldforcewarrantstothecorrectarbitrageprice.Theconsistentlossesfromthoseontheotherendofthetransactionswouldreducethevalueofoptionsandhencereducethepricethathedgerswouldbewillingtopaytopurchasecalls,orraisethepricetheywoulddemandtosellcalls.Infact,iftheoptionsmarketisconsistentlymispricedsothatitisnotpossibletoearnarisk-returntrade-offconsistentwiththesecuritiesmarketline,thentraderswouldwithdrawfromthemarketandcausethesamearbitrageconvergencethatBlack,Scholes,andMertonassumedintheirtheory.However,knowledgeoftheirformulawouldspeeduptheprocess.Thethreedecidedtoemploytheiradvantagetoprofit.Andalllostmoney.ThiswasintheerabeforetheCBOTopeneditsnewoptionsexchange.ThethreehadnoticedthatacompanynamedNationalGeneralhadwarrantsofunusuallylowcost.Theyinvestedsomeoftheirjuniorprofessors’salaryonthesewarrantsandlostmoneybecausetheyfailedtorealizethatthewarrantswerepricedbasedoninsiderknowl-edgeofimminentcorporatetakeovers,informationthatneithertheoptionsformulanortheyoungprofessorshadincorporated.Theotherpotentialflawinthearbitrageargumentisthatconvergencetorationalityonlyworksifmarketparticipantsarealsorational,totheextentthattheholderofasecuritytruststhatitspricetrulyreflecteditslong-termprofitability.LeonardJimmieSavageandhispredecessorBrunodeFinettispenttheirentireacademiclivestryingtodemon-stratethatprobabilityandsecuritiespricesexistonlyinthe(sometimesirrational)mindsofinvestors,justasbeautyisnotobjective,butratherisintheeyeofthebeholder.Itisthissubjectoftheefficientmarketthatwillbecoveredinthefourthvolumeofthisseries. 21ApplicationsAtraditionhadbeenstartedbyLouisBachelierin1900buthadbeenlostfromfinanceuntilRobertMertonresurrecteditintheearly1970s.Mertonrecognizedtheimportanceofeconomicanalysesovertimewhenuncertaintyexists.HealsorecognizedtherelevanceofthetoolsofstochasticcalculusdevelopedforthespaceracearisingasaresultoftheColdWar.However,hisreintroductionofcontinuous-timestochasticcalculustofinanceandeconomics,afterthe70-yearperiodofdormancy,awakenedbotheconomicsandfinance,andhasresultedinaproductiveoutpouringofresultsthathaverewrittenandgeneralizedmuchofwhatwethoughtwepreviouslyunderstood.Thereinventionoffinance,infitsandspurts,throughJohnBurrWilliamsandJacobMarschak,FrancoModiglianiandKennethArrow,HarryMarkowitzandWilliamSharpe,andthenfromFischerBlackandMyronScholes,eachrepresentedadeparturefromthetraditionsoffinance.Despitetheworkoftheseinnovators,thestudyofinvestmentsbeforethe1960scouldrarelybedescribedasfinancetheory,butratherrepresentedcasestudies,empiricalstudies,orloosequalitativerulesofthumbbasedonanecdotalandinformedobservation.Thetheoriesthatweredevelopedwerenotoftenamenabletoempiricaltestingastheyweretoovagueintheirconclusions.Anempiricaltestcouldnotsuc-cessfullyrulethemout,or,forthatmatter,ruleoutothercompetingtheories.Lackofrigoralsomeantlittleopportunityforscientificverifi-cation.Hence,financepre-Merton,Black,Scholes,andSharpewasmoreofanartandlessascience,evenifthedisciplineexhibitedsomeoftheaccoutrementsofthetraditionalsciences.ThisrevolutionreallyadvancedawhileafterBlackandScholesbecausetheBlack-Scholesdifferentialequationwasinitiallyregardedasanabstractresultthatbeggedforanexplanationandofferedasolutiontoaminor157 158TheRiseoftheQuantsproblemthatdidnotyetcommandamajorsolution.Blackwasinitiallyinterestedinasmallproblem,butwasdrivenbythecuriosityofapuremathematician.HeandScholesdidnotbeginwithapressingneedtounderstandacollectionofdata,andcertainlydidnotappreciatetheimpor-tanceoftheirworkatfirst.Likewise,neitherthejournalwheretheysoughttopublishtheirfindingsnorthereadersoftheliteratureappreciatedtheimplicationsoftheresultrightaway.Ofcourse,evenwhiletheCBOE,theexchangetheywouldsodramaticallyinfluence,hadbeendiscussedforyears,thefortunatecoincidenceofitsfoundingandthepublicationoftheBlack-Scholesequationwasjustthat–acoincidence,ifahappyone.However,oncethefirst-ordertime-dependentpartialdifferentialequa-tioncatwasoutofthebag,therecouldbenogoingback.Theproblemwassocentralandthenewtoolssocompact,efficient,andprofoundthatfinancehadtotaketheleap,asintellectuallyuncomfortableasitmayhavebeen.Andtheapplicationsofcontinuous-timecalculusmeantthatnearlyallinvestmentproblemswereripetoberecast.FinancecouldhavebeenredefinedafewyearsearlierwiththecreationoftheCAPM.However,discussioninthefinanceliteratureoftheCAPMcenteredaroundthereasonabilityofitsassumptionsratherthantheutilityofitsconclusions.TheCAPMwasalsoanorderofmagnitudelesssophisticatedandlessgeneralthantheoptionspricingmodel.TheconclusionsoftheCAPMdidnottransformthepricingofsecurities;rather,givenitsassumptions,itaddedtoourvocabularywithoutdefininganewlanguage.Inaddition,theCAPMoccurredinaneraoflowvolatilityandsteadygrowth,withfundamentalsanalysisandarbitrageofferedenoughtimetorespond,andwithstillenoughrudimentarycomputingpowertokeepaheadoftheanalysis.However,bythe1970s,societywaschanging,marketswereglobalizing,theBrettonWoodsfixed-exchangerateregimewasabandoned,andmacroeconomicshocks,fromoilpricesonthesupplysidetomonetarypolicyandinflationonthedemandside,werebuffetingfinancialmar-ketsbytheendofthedecade.Stockmarketsshiftedintoanewregimeofvolatility.WhiletheCAPMandfundamentalsanalysiscouldprovideunbiasedestimatesofstockprices,therewasasuddenandpressingneedtomanageriskandvolatility.TheBlack-ScholesformulafilledthisvoidandtheCBOEofferedthemarkettodoso.Thisneedtomanageriskwasnolongerconfinedtopractitionersofhighfinance.Withthebabyboomgenerationenteringitsyearsofmaximumwealthcreation,withthemovementawayfromdefinedbenefitspensionstoself-managedretirementaccounts,andwiththedevelopmentofover-the-counterstockmarkets,thenumberofmarket Applications159participantsgrewdramatically,andcontinuestogrowtoday,evenifhouseholdsparticipatedreluctantly.Derivativesmarketshelpedincreasinglysophisticatedinvestorsandfundmanagerstomanageriskefficientlyandwithlowertransactioncosts.Optionsweremuchlessexpensivethantheunderlyingsecuritiesfromwhichtheyderivedtheirvalue.Consequently,anoptimalportfoliocouldbeestablishedwithouttheneedtoholdlargenumbersofdiversesecurities.AndpractitionersbecamesurprisinglyadeptatusingthenewfinancialtoolsofoptionsandtheanalytictoolssuchastheBlack-Scholesequation.Atthesametime,investmenthousesandsophisticatedcorporationscouldnotaffordtoneglectthesenewtoolsiftheywishedtoremaincompetitive.SincethepublicationoftheBlack-ScholesequationandthecreationoftheCBOE,thenumberofavailablestockshaverisenproportionally.However,thenumberofinstrumentsthatderivetheirvaluefromunderlyingsecuritieshaverisengeometrically.ManyofthemarelistedontheCBOE.MostofthemcanbepricedaccordingtotheBlack-Scholesformula,perhapswithsomemodification.Andallofthemhaveallowedmoderatelysophisticatedinvestorstoreduceriskwithoutengaginginthehighcontractingcoststhatwereoncethesoledomainofinsuranceinstruments,theformerwaytohedgerisk.Infact,thenewspapersarenowrepletewithpagesofderivativesthatmostwouldhaveonceconsideredexoticinstruments.Black,Scholes,andMertondemocratizedtheuseofexoticfinancialderivativesbydevelopingthepricingformulathatdisciplinesthemarketandensuresthatarbitragewillforcepricestowardtheirproperrewardcommensuratewithrisk.Therearemultipleoptionsforeachmajorstock,commodity,bond,orcurrency.Andtheyhaveevenbeenincorporatedintothecom-pensationplansofexecutivesandbluecollarworkersalikewhobelievethattheircollectiveeffortcanenhancethevalueofthecompanyandhencegreatlyenhancethevalueoftheoptionsthatoftenconstitutepartoftheircompensationpackages.NovelapplicationsWhenweinsureahomeoralifeforaspecifiedterm,wepayapremiumandcansecurethecontracted(exercise)priceiftheinsuredeventoccursonorbeforetheexpirydate.Ifthisisaputoption,wepayapremiumfortherighttoreceivetheexercisepriceatanytime,uptoexpiration,inthecaseofanAmericanput.Theseproblemsarefunctionallyequivalent,sotheBlack-Scholesequationcanbeusedtomeasure 160TheRiseoftheQuantstheappropriatecostofanyinsureditemforwhichaninvestorseeksprotectionfromitsfluctuationinvalue.Acommonlytradedtypeofderivativescontractinsuresagainstdefaultofpromisestopay.Forinstance,wemaywishtoinsureagainstthedefaultofaportfolioofsubprimemortgageswithaninsuredvalueof$50,000,000.Thesellerofacreditdefaultswapwrittenfor$40,000,000onthis$50,000,000receivestheequivalentofaputpriceasapremiumandisobligedtopaythepurchaseroftheswapthedifference,or$10,000,000,iftheportfoliovaluefallstolessthan$40,000,000.Theinsuranceroleforsuchcreditdefaultswapsisobvious.Theinves-torcanpurchaseapolicythatlimitsthedownsiderisk.However,thesecreditdefaultswapscanalsobepurchasedbyaninvestorwhodoesnotowntheunderlyingportfolios.Suchapurchaseisaspeculationonanother’smisfortune,butalsoprovidesanopportunityforliquidityandmoreefficientvaluationsthroughaverybroadinsurancemarket,withlowtransactioncostsandrelativelysimplecontracting.Thisapproachcanbeusedinmanysimilarcircumstances.Wecanwriteanoptionwhichensuresthatanindividualwillreceiveamini-mumpriceperbushelonacrop,aminimumpriceofapatentthatispending,oraminimumpriceforanoffshoreoilpermitright.Mutualfundshavebeendesignedthatcontainanoptioncomponentwhichtradesoffsomeofthereturninexchangeforanoptionprotec-tionincasetheportfoliovaluedropsbelowathresholdlevel.Indeed,in1976,MertonandScholesteameduptocreatetheworld’sfirstsuchinstrumentintheUSA,theMoneyMarket/OptionsFund.Optionscanalsobeusedtoprotectagainstadecliningyieldonafixedincomesecurity.Alternatively,aninvestorcanbooksomeprofitsimmediatelyinthesecuritybysellingacallonabond.Ifthebondpricerisesaboveacertainlevel,thesellerofthecallmustsacrificetheunderlyingbondandinturnsacrificethegainabovetheexerciseprice,butisabletobooksomeprofitwithcertainty.Assumingthatthesefixed-incomeoptionsareproperlypricedinanefficientmarket,wecanevencalculatetheimpliedvolatilitybysolvingtheBlack-Scholesequationforthevolatilitynecessarytogeneratetheprevailingprice.ThistechniqueallowstheFederalReservetomeasurepointvolatilityinbondmarkets,oranalyststoobtainameasurefortheperceivedlevelofvolatilityinasecuritiesmarket.PlayingwithfinancialfireWhileoptionscanbeusedasalegitimatewaytoshareandhedgerisk,theirhighlyleveragednaturecanalsobedangerous.Inabullmarket, Applications161putsoutofthemoney,ortherighttosellanunderlyingsecurityatbelowprevailingprices,mayberelativelyinexpensive.Ifalargenumberofsuchputsaresoldunderaprevailingsenseofoptimismthatthemar-ketwillcontinuetorise,thenadeepdownturnmayresultinverylargelossesandpotentialdefaults.Suchlossesoncreditdefaultswapsin2009eventhreatenedoneoftheworld’slargestinsurancecompanies,AIG.Topreventthebankruptcyofoneofthelargestcompaniesinthecountry,theUSgovernmentsupplied$182.5billionincredittothecompanyinwhatconstituted,atthetime,thelargestcorporatebailoutinhistory.1Ofcourse,thedangerofprivatizedprofitsbutsocializedlossesininsurableactivitiesisthemoralhazardproblem.TheBlack-Scholesequationassumesthattherandomwalkoflog-normalvaluesfollowsalog-normaldistribution.Thisisasymmetricdistribution,andassumesthatupsideanddownsideriskareequallylikelyconsequencesofexternalforces.Whentheinsuredentitycanaffecttheriskprofileandhenceincreaseitsprobabilityofcrossingtheexercisethreshold,theBlack-Scholesestimateofefficientoptionspricingisbiased.Inessence,theinsuredcanpurchasetheoptiontoocheaply,or,inthecaseofmoralhazard,exhibitinsufficientprudencebecauseoftheprotectionofinsurance.GiventheextremeleverageandthedependenceontheBlack-Scholesequationforpricing,optionsmarketsareparticularlysusceptibletomarketmanipulationandtheresultingdistortionsoftheassumptionofalog-normaldistributionofreturnsthatareassumedtobeindependentovertime.Thefinanceworldhaswitnessedonenotoriousexampleoftheeffectsofmarketmanipulationinoptionsmarkets.Enron,thelargeenergycompanythatwentbankruptonDecember2,2001,hadanextensiveenergyoptionsbusiness.ThecompanypurchasedrightsandoptionsonmuchofthesupplyofelectricityontheWestCoastoftheUSA,inadditiontonaturalgasrightsandoptionsthroughouttheWesternStatesandtheMidwest.Italsodirectlyoperatedlargepowerplantswithinitsgrid.Duringhigh-demandperiods,thecompanywasaccusedoftakingsomelargegeneratingfacilitiesofflineduringperiodsofveryhighdemandforelectricity.Thisdecisionwasdesignedtocreateashortagethatcouldpushthegoingpriceofelectricityfromabout$60permegawatt-hourtoalmost$1,000permegawatt-hour.Enroncouldthenexerciseoptionstopurchaseenergycapacityforapre-determinedpricethatwashigherthanregularrates,butmuchlowerthanthespotratesduringtheshortages.Inturn,itcouldpocketthedifference,whichcouldamounttomanymultiplesofthegoingrateforevenmoreenergythanittookoffline,asenergyresellersacrossmanystatesscrambledtosecurepowerandavoidblackouts. 162TheRiseoftheQuantsTheseabusesdemonstratetheproblemwiththemisuseoftoolsthatcanprovidesomuchgoodbutcanbeusedinunintendedways.Acleverresearchercanproduceamethodologythatcanmeetmanyobjectives,includingenhancedmarketefficiency,improvedrisksharing,andevencarveoutprivateprofits.Ofcourse,eachsuccessfulinnovationmanagestodogoodasitsdevelopersdowell.However,acomplexworldcanworkinwaysthatareunanticipatedbytheinnovators.Indeed,amodelbroughtfromtheacademicwhiteboardtotherealworldcanfunctionverywell,justashopedandintended,untilsomeonespotsacleverwaytomanipulateandsubvertitsbestintentionsforpersonalprofit.Attimestheseunintendedconsequencescanprovideprofitsforafew,butdramaticlossesformanyunsuspectingparticipants.Whenbrilliancemeetsacomplexworld,anideacanbetoocleverbyhalf.WhiletheBlack-Scholes-Mertonmodelofoptionspricinghaswith-stoodthetestoftime,itsapplicationhasnotbeenimmunetocriticism,evenifthetoolitselfcanplaynomorethanasupportingroleinvariousderivativesabuses.Forinstance,thedot.comhigh-technologycompanybubblethatoverinflatedstocksinthe1990sandcausedaspectacularbustontheNASDAQexchangewasatlastpartlyduetothediscoverythatthesecompanieswerehidingtheircompensationliabilities,intheformofunexercisedwarrants,intheirbooks.Awarrantwillonlybeexerciseduponexpiry,unlessapermanentslideinthestockpriceisanticipated.Thedelaydefersanytaxliabilityforwhichtheownerwillbeobligeduponexercisingthewarrant.Likewise,corporationscandelaytheirexpensingandcantemporarilyinflatetheirprofitsandshareprices.Mertonwasavocalcriticofthislackoftransparencyandhasinjectedhimselfintothepublicdebateagainstcriticswhomightconfuseahelpfulmethodologywiththebadactorwhomightabuseanysuchtool.However,thenextbigideaScholesandMertoncameupwith,thistimeforproprietaryprofit,wasmuchmoreproblematic. 22TheNobelPrize,Life,andLegacyRobertMertonmaybestbeknownasthenamethatwasomittedfromthemostimportantnamesakeequationinfinanceandeconomics.Fewwhoknowhim,includinghismorefamouscolleagueandcollaboratorMyronScholes,underestimatehiscontribution.IntheearlydaysoftheBlackandScholescollaboration,MertonandScholesandtheirconsultingcolleagueFischerBlackweregoodfriends.However,MertondidnotknowatfirstaboutBlackandScholes’worktogether.Infact,his1970workingpaper,givenattheJulyWellsFargoCapitalMarketConference,offeredhisfirstbrushwiththe“Black-Scholes”equation.InhisNobelPrizelecture,herelatedhowheoversleptandmissedthethemorningsessionandtheworkshopatwhichBlackandScholespresentedtheirpaper.Mertonwentonthecementthelabel“Black-Scholes”inanappendixhewrotetoa1972paperpublishedbyPaulSamuelson.1Whileeachhadbeenworkingonthesametimelyproblemoverthe1960s,theirpathsdidnotcrossimmediately.However,whenMertondiscoveredin1970thatBlackandScholeswereworkingonthesameproblemasheandSamuelsonhadbeenstudying,andthatBlackandScholeshadsolvedtheequation,hegraciouslysteppedasideanddidnotpublishhismoregeneralresultsuntilBlackandScholeshadpublishedtheirs.In1973,boththeBlack-ScholespaperandthentheMertonpapercameoutinrapidsuccession.Yearslater,Blackremarked:“AkeypartoftheoptionpaperIwrotewithMyronScholeswasthearbitrageargumentforderivingthefor-mula.Bobgaveusthatargument.ItshouldprobablybecalledtheBlack-Merton-Scholespaper.”2Infact,Black,Merton,andScholeswereandremainedgoodfriends.WhenBlack’swifeMimireturnedtoBostonfromChicago,itwasMertonwhousedtheopportunitytoattract163 164TheRiseoftheQuantsbothBlackandScholestoreturntotheSloanSchool.Theyweregreatcolleagues,withtheirpastandfuturesinextricablytied.MertonandScholesremainedclosestofthetroikaasBlackincreasinglybecameengrossedinthepracticesideoffinance.Forinstance,in1974thepairstartedcollaboratingonthedesignofthedownside-protectedmutualfundthattheywouldmanagetohavelistedafteracoupleofyearsofdesigninginanticipationofanySecuritiesandExchangeCommission(SEC)concernsthatitmightbetoospeculative.TheSECactuallyconcurredthattheoptionhedgeaugmentedsafety,andapprovedtheMoneyMarket/OptionsInvestmentFundtobegininFebruaryof1976.Whilethisearly“floor”investmentproductwasinnovativeandaheadofitstime,MertonandScholes’investmentcompanydidnothavesufficientpromotionandmarketingresourcesanddidnotmeetwiththesamesuccessassomeimitatorsthatcroppedupshortlythere-after.Theirappetiteforhighfinanceandhighstakeswaswhetted,though,andtheywouldonedayreturntotheworldofinvestmentonamuchgranderscale.Meanwhile,MertonandScholesbothcontinuedaresearchagendathatcombinedtheory,empiricalstudy,andpractice.WhileScholesresidedatChicago,hiscomputingexpertisecontributedtohisappoint-mentastheDirectoroftheprestigiousCenterforResearchinSecurityPricesdatabaseatChicago.Scholeshadintimateaccesstotheworld’sbeststockpricedatabaseandcouldthustesttheefficiencyofrealmarketsasbenchmarkedagainstthepredictionsofhistheories.MertonandScholescollaboratedonsomeofthesestudies,especiallyfollowingScholes’returntotheSloanSchool.BothMertonandScholesalsosupervisedgraduatestudentsandcon-sultedwithmutualfundandinvestmenthousesparttime.Onmanyoccasions,theyhadthechancetoworkwithJohnMeriwether,theinfluentialandsuccessfulinvestmentdirectorofSalomonBrothers,asignificantemployerofMITfinancegraduates.Theinvestmenthouse’sproprietaryalgorithmsforthetradingoffixed-incomesecuritiesemployedBlack-Scholes-Mertonmodelsthathadbeenmodifiedandextendedin-housetoearnarbitrageprofitsforSalomonBrothers.Fortenyears,from1978to1987,Mertoncontinuedtoexploreissuesofriskbearingandsharing,butincreasinglyfromaninstitutionalper-spective.Duringthisperiod,heservedasthePresidentoftheAmericanFinanceAssociation,andexploredmeasuresofmarketefficiency.HeevendelvedintomacroeconomicissueswithfellowMITSloanSchooleconomistStanleyFischer. TheNobelPrize,Life,andLegacy165Intheinterim,ScholesmovedtoStanfordUniversityin1981.MertonandScholeswerereunited,though,whentheywerebothinvitedtojoinalong-termadvisingconsultancywithSalomonBrothers.Bothimmersedthemselvesinglobalinvestmentbankingatthehighestlevel,justasUSinvestmentbankingwasmakinganewandpermanentglobalthrust.WhileScholesfoundhimselfincreasinglydrawnintoinvestmentbanking,Mertonappreciatedhisexperiencebutreturnedtoacademiaafterafewyearsandembarkedonhisfirstsabbaticalleave.Hespenttheyearof1987–1988catchinguponpastunfinishedresearchandembarkingonnewavenuesforresearchinformedbyhisinvestmentbankingexperi-ence.Eversincethen,hisresearchagendahasbeenmoreinstitutionalandmoreengagedinadesiretounderstandthegreaterfinancialsystemthanthemicrofinancedetailsofindividualsecuritypricing.Immediatelyfollowinghissabbatical,theHarvardBusinessSchoolfinallyattractedMertontojointhemandpromptlyofferedhim“theDean’sChair,”theprestigiousGeorgeFischerBakeprofessorship,resignedbythethenDeanJohnMcArthursothatMertoncouldtakeit.The1997NobelexperienceTheNobelCommitteerecognizedthegreatsignificanceoftheBlack-Scholes-MertonformulawhenitannouncedonOctober14,1997thatithadawardedbothScholesandMertontheNobelPrizeinEconomicsfortheirdevelopmentof“apioneeringformulaforthevaluationofstockoptions.Theirmethodologyhaspavedthewayforeconomicvaluationsinmanyareas.Ithasalsogeneratednewtypesoffinancialinstru-mentsandfacilitatedmoreefficientriskmanagementinsociety.”3TheCommitteeacknowledgedinitsannouncementtheabsenceofFischerBlackbecauseofhisearlydeath.TheNobelPrizeisannouncedinthemorningatStockholm,Swedentime.Atanytime,thereareperhapsadozenortwodozeneconomistswhobelievetheymaybecandidatesfortheaward.Foreachpotentialawardee,thereisaloosecoalitionofsupporterswhonominateandcampaignonbehalfofhimorher.Itwouldbedifficultforagreatmindtobeobliviousoftheseefforts.However,theNobelCommittee’sdelibe-rationsanddecisionareawell-keptsecret.WhenMertonreceivedthefatefultelephonecallthatinformedhimthathewouldsharetheprizewithScholes,hewasabouttoleavehisMassachusettshomeforanearlymorningshuttleflighttoNewYorkCity.Thephonerangjustbefore6amonthatOctobermorningin1997.Merton,inahurry,nonethelessdecidedtopickitup.TheCommittee 166TheRiseoftheQuantsrepresentativeofferedthathehadsome“interestingnewsforyou.”Mertonprofessedbothhissurpriseandhisjoyattherecognition.4BythenithadbeennineyearssinceMertonhadmovedupMassachusettsAvenueandacrosstherivertojointheHarvardBusinessSchool.TheSchoolimmediatelyplannedanimpromptureception.OneofthefirstthingsMertondidwastocallhisfatherandnamesake,theprominentsociologistRobertK.Merton.MertonJr.cancelledhistriptoNewYork,andthe87-year-oldMertonSr.immediatelymadehiswaytoLaGuardiaAirporttocatchthefirstshuttletobewithhissonatthereceptionandnewsconference.Acoupleofmonthslater,theveryclosefatherandsonpairtraveledtogethertoStockholmtoaccepttheaward.AttheNobelPrizeceremonyinStockholm,MertonandScholesmusthaveseemedanunlikelypair.Mertonhadthequietandconfi-dentreserveofanacademicchildofanesteemedacademic.Hewassurroundedbyeducationandtheeducatedasachild,andgrewupinahigh-achievingenclaveofNewYorkCity.Inhisphotographs,hehasaslightandcharacteristicsmile.Ontheotherhand,ScholeswasraisedinaminingtownbyamotherthatwasfromaRussian/Polishimmigrantfamilyofentrepreneurs.Hehadalwayshadagreaterpenchantforentrepreneurism,recognitionofopportunity,andperhapssomebrashness.Inhisphotographs,heinva-riablyhasatoothygrin.Hewasextrovertedandshowedhisemotions,allthewhilewithmannersandgrace.AswitnesstoScholes’youthfulexuberance,RichardRoll,theequallyeminentfinancialtheorist,likestotellthestoryofScholes’confidenceandexuberance:“I’djustboughtanewmotorcycle,[Myron]wantedtogetonittoseehowitfelttodrive.Isaid,‘Waitaminute,that’sabigenginethere,’andbeforeIknewithehadlaidrubber,hitacurbandlandedinmyneighbor’syardinamangledheap.’’5The1998ignobleexperienceAfewyearsbeforetheirsharedNobelPrize,bothMertonandScholesreunitedonceagainoveranewinvestmenthouseopportunity.In1993JohnMeriwether,theSalomonBrothersinvestmentguruwhohadlefthisemployeracoupleofyearsearlier,gottogetherwithtwoinves-torcolleagues,EricRosenfeldandJamesMcEntee,andformulatedaschemeforanewtypeofinvestmenthouse.TheyaskedMertontojointhem.Soon,anumberofSalomonBrotherstraders,analysts,advisors,anddirectorshadalsobeenenlisted,includingScholes.MertonandScholeswerereunitedforafourthtimeintheircareers.Thecompany TheNobelPrize,Life,andLegacy167representedawho’swhoofacademic/practicecrossovers,withsevenoftheelevenfoundersofthenewenterprise,LongTermCapitalManagement,havingbeenenlistedfromeitherMITortheHarvardBusinessSchool.Eachwasbroughtinforaparticularstrengthhecouldbringtotheenterprise.Thefledglingcompanyhadtoassemblecomputertechnolo-gies,establishtelecommunicationsnetworks,implementnewtheoriesandmodels,andputintopracticefinancialstrategies,writecontracts,attractclientsandestablishcontacts,arrangeforcounterpartiesthatwouldbewillingtoexchangetradesworthbillionsofdollarsbasedonatelephonecall,and,notleast,designanorganizationalandmanage-mentstructurethatcouldkeepalltheseelementsworkinginharmony,allthewhilewithacollectionoftheprimadonnasofhighfinance.Ittookayeartoorganizethiseffort,but,byFebruary1994,theirarrangementsweremade,officeswereestablishedinthefinancialcapi-talsofGreenwich,Connecticut,justaquickdrivefromWallStreet,andLondon,abilliondollarshadbeenraised,andthetradingcomputerswereturnedon.Threeyearslater,athirdoffice,inTokyo,hadbeenadded,andthecompanyhadgrownto180employees.Theirswasanewtypeofinvestmenthouse.Atonetime,tradingstrategiesweredesignedbyhardenedandexperiencedpractitionersinsmoke-filledroomsthroughacombinationof75percentintuitionandcourage,and25percenttheory.Infact,thetheoriesofivorytowerscholarswereonlyslowlyabsorbedbytheindustry.Academiciansandpractitionerseachhadtheirownjournals,andeachfoundtheother’suninterestingorunhelpful.Ifpractitionerswantedtoincorporateanemergingtheoryintotheirinvestmentstrategies,theywouldhireascholarasaconsultanttohelpdesignacomputerprogram,andtheywouldthenmodifythealgorithmovertimetomakeitproprietary.Whilethehallmarkofscholarship–andthereputationsitengenders–isentirelybasedonthesharingofideas,investmenthousesaresecretive.Thisneworganizationwasofaverydifferentbreed.Yes,secrecyoftheirtechniqueswouldbeessentialiftheyweretomaintaintheirmarketadvantage.Buteverybodyunderstoodthatthiscompanywasthemosttheoreticallysophisticatedinvestmenthouseevercreated.Thatwastheircallingcard,andinvestorsclamoredtohaveLongTermCapitalManagementinvesttheirwealth.Thesefinancialtheoristsunderstoodonething.Theirmodelstypi-callyassumethattherearezerotransactioncosts.Wemightconsidera180-personfirmtobeexpensivetooperate,buttheinitialfundingofthefirmrepresentedmorethan$5millioninvestedperemployee. 168TheRiseoftheQuantsLongTermCapitalManagementusedthefacilitiesofothers,suchasBearStearnsandMerrillLynch,andthecompanywasregisteredintheCaymanIslandstoreduceregulatoryoverheadandminimizetaxcon-sequences.Sothattheycouldavoidtheregulationimposedonmutualfunds,LongTermCapitalManagementwasorganizedasahedgefund,undertheInvestmentCompanyActof1940,whichimposeslittleoversightbutallowstheadmissionofonlyverywell-heeledmillion-aireswhounderstoodtherisksofahighlyleveragedstrategyandcouldaffordtolosesomemoneyonoccasion.Theorganizationwasalsobrandnew,soitdidnotsufferfromorganizationalcreepashadotheroldercompaniesinthebusiness.LongTermCapitalManagementwasdesignedtooperatelean,whichwasgoingtobeanessentialelementforitsstrategy–tobeabletotradequicklyandatverylowcost,sothatitcouldmakearbitrageprofitsbasedonperceivedpricediscrepanciesmeasuredincentsratherthannickelsordimes.Thecompany’sinitialideawassimple.ItscomputersscannedthepricesofbondswrittenbyEuropeancountries,Japan,andtheUSAthatweretradedaroundtheworld,acrossmanydifferenttimezonesthatseparatethesefinancialmarkets.Theadvantageoftradinginbondsisthatthereisnotalargesubjectiveelementtotheirpricing.Thetermsofthebondcontractarestandardizedandunderstood,theirrisksaredocumented,butaremostlyofextremelylowdefaultrisk,andtheirpriceisalmostcompletelydeterminedbasedontheirpostedinterestrate,ortheircouponrate,andupontraders’expectationsofsuchthingsascomparableinterestrates,inflationrates,andexchangerates.Ifthesefactorsareallcommonlysharedandpriced,thedifferencesinpricesshouldsimplyrepresentdifferencesinexchangeratesbetweenlistingcountries,whichiswellunderstoodandveryactivelytradedtoensureconsistency,andslightdelaysinpricerevisionsbecauseonemarketmaytradeasecuritywithmuchhighervolumethananother.Theprinciplesrealizedthatthelevelofliquidityforbrandnew,auctioned30-yearbondswasveryhigh,butthatthisliquiditydropsoffdramaticallypost-issue.However,boththenewandtheveryslightlyagedbondwouldbothbeagedwithinashorttimeandwouldstillhaveaverysimilarandlonghorizon.Thesedifferencesinliquiditymaybeslightlymorepronouncedevenbetweentwotradingcenterslocatedindifferenttimezonesandthousandsofmilesapart.LongTermCapitalManagementdevelopedastrategytocapitalizeonthesedifferences.Itcouldevendosowithalmostnoinvestedcapital,bybuyingthethinlytradedslightlyagedbondsandatthesametimeshortsellingthenewissuebondstoraisethefunds.Thisway,itcouldaffordtotradevery TheNobelPrize,Life,andLegacy169largevolumesofeach,andmakeperhapsonlypenniesperbond,butovermillionsofbondcontracts.Thesestrategieswerewildlysuccessfulatfirst.BecauseLongTermCapitalManagementhadtofrontlittlemoneyonthesecoveredtrans-actions,itsequitygrewtoalmost$5billionwithinfouryearsandithadborrowedtopurchasecontractsworthalmost$130billion.Thisleverageratioofequitytodebtofmorethan25:1washighinitsday,butwouldnotbeunusualforhedgefundsjusttenyearslater,whereleverageratiosbetween30:1and40:1becamethenorm.Atoneinstance,theactualnotionalvalueofthederivativesthatthecompanyownedwereabout$1.25trilliondollars,orofasizeequivalenttoaboutone-sixthoftheentireUSeconomyatthattime.However,justlikeanyarbitrageopportunity,priceseventuallycon-verge.Whentherewaspriceconvergencefortheselongest-termbonds,andothersbegantotakenoticeandtoimitateLongTermCapitalManagement’ssuccess,thecompanyhadtohuntforothermispricingopportunitiesandliquiditydifferentials.Theseincreasinglyaggressivetradesmaynolongerhavebeenoftheformofpriceconvergencearbi-tragetrades,andsometimeswouldnotdifferfromthestrategiesthatwereemployedbylesstheoreticallymotivatedtradinghouses.Theybegantradingtraditionaloptionsandplacedthemselvesinthepositionofactingastheinsureroffundsoperatedbyothertradinghousesthroughtheiroptionsstrategies.Ofcourse,asAIGalsodiscoveredmuchlater,everyinsuranceschemecanbeprofitablesolongastherearenoclaims.IfpricesroseasLongTermCapitalManagementpredicted,thepremiumsitcollectedweresimplypureprofit.LongTermCapitalManagement’sstrategywasveryprofitablesolongasthemarketcontinuedonatrajectorythathadbeenmaintainedeversincethecompany’sinception.However,inJuly1997,afinancialcontagionbeganinEastAsiaandspreadaroundtheworld.ItbeganwhenThailanddecidedtoendthefixedexchangerateregimethathadpeggedthevalueofitscurrency,thebaht,totheUSdollar.Onceitmovedtoafloatingexchangerateregime,thebahtdepreciatedsignificantly,anditspublicdebt,muchofwhichwasdenominatedinUSdollars,ballooneddramatically.TheThaigovernmentwasunabletomeetitsongoingdebtobligationsanditwastechnicallyindefault.Asaconsequenceofthedefault,therewasanimmediateflightoutofthebahtandthecurrenciesofotherneighboringnations.ThiscapitalflightfurtherexacerbatedtheplungeofthebahtandcausedcurrenciesinSingapore,Indonesia,Japan,SouthKorea,andthePhilippinestodeclineaswell. 170TheRiseoftheQuantsThesecurrencyflightsmadeimportedgoodsfromSouth-EastandSouthAsiannationsmoreexpensive,andhencereducedthevolumeofcommoditiestheycouldafford.Thecontagioninfectedcommoditymarkets,thestockmarketsofthesenations,andthepricesoflargemultinationalcompaniesthatdealtincommodities.Thefirstdramaticglobalfinancialdecline,exacerbatedbytheherdmentalityastradersranforthedoors,causeddramaticdeclinesinexchangerates,problematicinflation,andrecessionsinanumberofSouth-EastAsiancountries.Thereductionincommoditiespricesalsohadadramaticeffectoncommodityexportingcountries.Thepriceofoildroppedby$11asaresultofrecession-ledreduceddemandoverthenextyearandahalf.ThedropinoilpriceslikewiseprecipitatedafinancialcrisisinRussiain1998.IntheaftermathofRussia’sconversiontocapitalism,thenationtookonsignificantdebt,andexhausteditscapacitytoborrow,topayforthenecessaryinfrastructurerequiredtobecomeamajoroil-exportingnation.ThedropinoilpricessqueezedprofitstothepointthatRussiawasalsopushedintotechnicalbonddefault.ThisbreakdownoftheRussianfinancialsystemcausedLongTermCapitalManagementtolose$4.6billioninfourshortmonths.ThemovementawayfromRussianbondscausedadramaticflightofcapitalintoUSbonds.LongTermCapitalManagementhadbeenengaginginbondarbitrageusingmodelsthatdidnotanticipatethesuddenshiftinprices.ItlostbillionsnotonlyduetoitsUSbondexposurebutalsothroughthenecessityofliquidatingothermajorpositionsthathadnotyetturnedprofitable.Ittoowasforcedintobankruptcy.Itsequityin1998hadrisentoalmost$5billion,butittooklossesbothfromtheAsiancontagionandfromtheRussiandefault.Itsequitywasexhausted.TheFederalReserveBankofNewYork,astheFederalDistrictBankresponsiblefortheoversightofWallStreet,anditsChairmanAllanGreenspanorganizedabailoutofalmost$4billiontosaveLongTermCapitalManagementoutofconcernthatitsfailurewouldalsobringdowntheotherinvestmenthouseswithwhichtheysubscribedascounterparties.TheNewYorkFedassembledleadersofallthemajorinvestmenthousesinitsconferenceroomonSeptember23,1998toconstructaplanforthebailoutofthehighest-flyinginvestmenthouseoftheday.ThetalkresultedinanofferbyAIG,GoldmanSachs,andBerkshireHathawaytobuyoutthepartnersofLongTermCapitalManagementfor$250millionandinjectanadditional$3.75millionintothefund,whichtheyproposedwouldbeabsorbedintotheGoldmanSachstradingdepartment. TheNobelPrize,Life,andLegacy171ThegroupgaveJohnMeriwetherandLongTermCapitalManagementanhourtodecidewhethertheywouldaccepttheoffertheNewYorkFedthoughttheycouldnotrefuse.Thecompany’sprincipalslettheofferlapsebecausetheyfeltthefirmwasworthatleast$4.7billion.Instead,theNewYorkFedorganizeda$3.625billionbailoutnotsomuchtosavethecompanybuttoavoidthecollapseofothercompaniesrelatedtothefund.Intheend,aconsortiumofbanksabsorbedthefund.TheLongTermCapitalManagementpartnerswereoffered10percentofthereorgan-izedcompany.ThisforcedmarriageofferedtheLongTermCapitalManagementprincipalsabetterdealthanAIG,GoldmanSachs,andBerkshireHathawayhadpreviouslyoffered,butitstillfailedtocoverpartners’debtandpersonalinvestmentandreinvestmentstotalingalmost$2billion.Followingthereorganizationandforcedbuyout,theformerpartnerswereimplicatedin2005inchargesoftaxavoidance.InthecaseofLongTermCapitalHoldingsv.UnitedStates,thepartnersstoodaccusedofusingacontroversialtaxsheltertoskirttaxesonprofitsfromcompanyinvestments.InanefforttohelpitsclientssheltersomeofthehugeprofitsLongTermCapitalManagementwasearningontheirbehalf,thecompanybegantooffercertaintaxschemesthatwoulddivertproceedstowardthepurchaseofverylargesuminfrastructureprojectspursuedbyforeignstateandlocalgovernments.AquirkintheUStaxcodewasarguedtoallowtheinvestortoavoidthetaxontheinitialprofit,andthentax-sheltertheleasebackincomepaidbythelocalgovernmentsovertimefortheseinfrastructureprojects.Thislegallyquestionableshelterwasactuallypursuedbyanumberofotherinvestmenthousescateringtoverywell-heeledindividuals.LongTermCapitalManagementhadadoptedthispracticebasedontheadviceofJanBlaustein,thecompany’sgeneralcounselatthetime,andScholes’girlfriendandfuturewife.Thisshelterresultedina$100milliontaxavoidancesuitthatlandedtheprin-cipalsinthewitnessstandinagovernmentprosecution.Eachanexpertinfinance,andScholesanauthorofabookonfinanceandtaxlaw,whichhebeganasaresearchagendaoncehearrivedatStanford,thedefend-antswerequizzedabouttheirknowledgeoftheavoidancescheme.Theyalldeniedthattheyreallyunderstoodtheintricaciesoftheparticularstrategy.However,Scholeswaschallengedbytheprosecutingattorney,whopointedtoScholes’bookandthechaptersthereinthatreferredtotheprinciplesofsteptransactionsandtheneedtodemonstrateeconomicsubstance,bothofwhichtheUSInternalRevenueServiceclaimedwereviolatedbyLongTermCapitalManagement’sscheme.Thecompanylost 172TheRiseoftheQuantsthesuit.Thecourtruledthat$106millioninaccountinglossesdidnotmeettheeconomicsubstancetest,andthepartnerswereobligedtopay$40millionfortheillegaltaxsavingstheyhadbookedearlier.DuringtheunwindingofLongTermCapitalManagement,theNewYorkFedwasinvolvedinitsfirsthugefinancialcompanybailoutofafinancialcompanydeemedtoobigtofail.Itwouldnotbeitslast.Atthetime,asintheaftermathofevenlargerbailoutsin2008and2009,someexpressedgraveconcernthattobailoutfirmsdeemedtoobigtofailencouragedsimilarlypositionedfirmstotakeinordinaterisks.Suddenly,theinsuranceconceptofmoralhazardhadenteredthefinancelexicon.Intheaftermath,executivesofrelatedcompanieswereforcedtoresignbytheirboards.GoldmanSachsCEOJonCorzinewasoustedinaboard-leveleffortorganizedbyfutureTreasurySecretaryHenryPaulson.CorzinewentintopoliticsandrepresentedNewJerseyintheUSSenate,thenledthelargeinvestmentbankMFGlobaltoitsdramaticdemiseasitillegallycomingleditscustomer’sfundswithitsproprietaryinvestmentfundandlosthundredsofmillionsofdollars.TheNewYorkFedGovernorDavidW.MullinssufferedhisownreversaloffortuneattheFed.WhileFischerBlackhaddiedafewyearsearlier,theBlack-Merton-Scholesformulaandrelatedtheorieswerelambastedinthepressfortheirfailuretotakeintoaccountbroadsystemicfailures.MerrillLynchadmittedtoitsshareholdersthatthefinancialandriskman-agementmodelsitused“mayprovideagreatersenseofsecuritythanwarranted;therefore,relianceonthesemodelsshouldbelimited.”6Thelessonwaslearned.AnequationliketheBlack-Scholesoptionspricingformulashouldinformmarkets,notdefinethem.LaterlivesAnumberoftheLongTermCapitalManagementprincipalswentontodirectormanageotherhedgefunds,includingScholes,Blaustein,andMeriwether.ScholesretiredfromStanford,butMertonreturnedtotheHarvardBusinessSchool.After23yearsatHarvard,andafterwitnessinghisdaughterSamanthagraduatewithaneconomicsdegreefromtherein1992,hereturnedtotheSloanSchoolatMITin2011.Mertoncontinuestowriteandresearch.Hismostsignificantbookishis1990Continuous-TimeFinance,anareaofstudyinwhichhewasapioneer.Hehasproducedanumberofbookssince.InadditiontohisNobelPrizein1997andhisserviceasPresidentoftheAmericanFinanceAssociationin1986,Mertonhashadanumber TheNobelPrize,Life,andLegacy173ofawardsconferreduponhim.Hereceivedthe1983LeoMelamedPrizefromtheUniversityofChicagoandthe1989DistinguishedScholarAwardfromtheEasternFinanceAssociation.HetwicereceivedthefirstprizefromtheInstituteofQuantitativeResearchinFinance’sRogerMurrayAwardanda1993InternationalINA-AcademiaNazionaledeiLinceiPrizefromItaly’sNationalAcademyofLincei.HealsoearnedtheFinancialEngineeroftheYearAwardfromtheInternationalAssociationofFinancialEngineersandtheFORCEAwardforFinancialInnovationfromDukeUniversity.HewasinductedintotheDerivativesHallofFamebyDerivativesStrategyin1998.MertonalsoearnedtheMichaelI.PupinMedalforServicetotheNationfromColumbaUniversityin1998,theDistinguishedAlumniAwardfromtheCaliforniaInstituteofTechnology,andtheMathematicalFinanceDayLifetimeAchievementAwardfromBostonUniversityin1999.In2002,RiskmagazineappointedhimtotheRiskHallofFameandgavehimalifetimeachievementawardinthefollow-ingyear.Inthesameyear,hereceivedtheNicholasMolodovskyAwardfromtheCFAInstitute.In2005MITestablishedtheRobertC.MertonProfessorshipinFinan-cialEconomicsinhishonor,andtheFinancialEducationAssociationgavehimtheDistinguishedFinanceEducatorAwardin2008.In2009,hereceivedtheRobertA.MuhAwardintheHumanities,Arts,andSocialSciencesatMITandtheTjallingC.KoopmansAssetAwardfromTiburgUniversity.Alsointhatyear,hewasmadealifememberoftheSigmaXIScientificResearchSociety,andhishighschoolinHastings-on-HudsonhonoredhimwithitsAwardofExcellence.Finally,in2010heearnedtheLECGAwardforOutstandingContributionstoFinancialEconomicsandtheprestigiousKolmogorovMedalfromtheUniversityofLondon.MertonwaselectedtotheNationalAcademyofSciencesin1993andisaFellowoftheAmericanAcademyofArtsandSciencesandoftheAmericanFinanceAssociationandtheEconometricSociety.HeisaSeniorFellowoftheInternationalAssociationofFinancialEngineersandaDistinguishedFellowoftheQGroup.HereceivedanhonoraryDoctorofLaws(LLD)fromtheUniversityofChicagoin1991,aProfesseurHonorisCausadegreefromHautesEtudesCommercialesinFrancein1995,aDoctorHonorisCausadegreefromtheUniversityofLausannein1996,and,in1997,aDoctorHonorisCausadegreefromParisDauphineUniversity.HealsoreceivedaDoctorofManagementScience(HonorisCausa)degreefromNationalSunYat-SenUniversityin1998,aDoctorofScience(HonorisCausa)degreefromtheAthens 174TheRiseoftheQuantsUniversityofEconomicsandBusinessin2003,aDoctorHonorisCausadegreefromtheUniversidadNacionalMayordeSanMarcosofLima,Peru,aDoctorofPhilosophyHonorisCausadegreefromtheUniversidadNacionalFedericoVillarreal,Lima,in2004,andaDoctorofScience,HonorisCausadegreefromClaremontGraduateUniversityinCaliforniain2008.MertonremainsamemberoftheNationalBureauofEconomicResearchandoftheInternationalBoardofScientificAdvisersoftheTinbergenInstitute.Heservesonanumberofadvisoryandeditorialboards,includingtheJournalofFixedIncome,theJournalofBankingandFinance,andtheJournalofFinancialEducation.Hesitsontheadvi-soryboardsoftheEuropeanFinanceReview,theInternationalJournalofTheoreticalandAppliedFinance,MathematicalFinance,andtheReviewofDerivativesResearch.DespitehisexhilaratingandultimatelyhistoricallypainfulexperiencewithLongTermCapitalManagement,heremainstheconsummatescholarandacademic.ItwouldnotbeunwarrantedtoregardMerton,alongwithhispredecessorLouisBachelier,asafatherofcontinuoustimefinance. PartVWhatWeHaveLearnedThisbookisthethirdinaseriesofdiscussionsaboutthegreatmindsinthehistoryandtheoryoffinance.Whiletheseriesaddressesthecontributionsofsignificantindividualstoourunderstandingoffinan-cialdecisionsandmarkets,eachvolumecoversdifferentaspectsofthedevelopmentofthetheoryofpersonalfinance.Thisfirstvolumebeganbydescribinghowindividualsmakedecisionsovertime,andwhythesedecisionschangeasweageandourcircumstanceschange.Thesecondvolumedescribedthecharacterizationandexistenceofequilibrium.Thisthirdvolumeshowshowfinancegarnereditsunderstandingofsecuritiesandderivativespricing.Weconcludebysummarizingtheinnovationsofthepricinganalyststhatgaverisetothequants. Thispageintentionallyleftblank 23CombinedContributionsJamesTobin’s1958refinementofHarryMarkowitz’s1952paperonModernPortfolioTheoryusheredinanerainwhicheconomicsandfinancediverged.Whilethesescholarsinspiredthefinancerevolutionofthe1960s,theircontributionsremainedelegant,intuitive,esoteric,butprimarilyacademic.Whileeleganceremainedthegoalofecono-mists,financetheoristssoughtpragmatism,andpracticalconclusionswereparamount.Fortunatelyforthestudyandpracticeoffinance,otherstooktheirinspirationtocreateanewAmericanschooloffinancewithaneyetowardquantifiablemethodsandapplication.Thisnewquantitativeschooloffinancehasnotdisappointed.ThetheoriesofWilliamSharpe,FischerBlack,MyronScholes,andRobertMertondefinedmarketsandmotivatedtrillionsofdollarsoffinancialactivityeachyear.Now,marketsactasiftheyaremotivatedbythefirstandsecondmomentsofmarketreturns.Theprocessbywhichthesegreatmindsrevolutionizedfinancecanbelikenedtoaballrollingacrossabeach.JacobMarschakputtheballinmotionbymotivatinghowapriceprocessthatcanbedescribedbyitsfirstmoment,ormean,andsecondmoment,orvariance.MarkowitzcarriedtheballbycreatingModernPortfolioTheory.However,untilSharpepickeduptheballfromMarkowitz,amodelofindividualsecuritiespriceseludedmodernfinance.Actually,Sharpe,whoismostassociatedwiththeresultingCAPM,didnotdeveloptheconceptalone.Atthesametime,threeotherscholars,JanMossin,JohnLintner,andthepractitionerJackTreynor,wereworkinginisolationandwithdivergentapproachesforthesameproblemofassetpricing.Treynorwasarguablythefirsttodrawtheconclusionstheyallwouldeventuallydiscover,butwasthelasttopublishhisfindings.Hewould,though,carrytheballtoCambridge.177 178TheRiseoftheQuantsItwasserendipitousforthedisciplineoffinancethatTreynorwasworkingatArthurD.Little,amultinationalconsultancypracticeinCambridge,Massachusetts,andmentionedhisworktohisyoungnewcolleague,FischerBlack.TreynorpassedtheballtoBlack,whofoundanaturalplaymateinmathematicalfinanceinMyronScholes,whowasteachingatMITacrosstheCharlesRiveratthetime.ItistherethatScholes,Black,andMertoncameinclosecontact.Inturn,eachofthesetheoristswouldaddtheirmomentumandspintothepricingtheoryball.Sincetheirinnovations,thefinancialballcontinuestoroll.However,muchofwhatpractitionersuseandfinancehasfurtherrefinedtakesitscuefromtheworkofthesegreatmindswhosepathscriss-crossedoveragenerationthattransformedthedisciplinesoffinanceandfinan-cialmarketsworldwide.Thiswasthelegacyofaneraonecouldonlydescribeastheriseofthequants. 24ConclusionsThe1960ssawtheemergenceoffinanceasadisciplineofitsown,outoftheshadowofeconomics.Itmanagedthistransitionbyproducingmodelsthatwerebothrigorousandpractical,andarrivedatjusttherighttimetoprovidethetoolsfornewandburgeoningfinancialmarkets.Italsoheraldedinaneraofquantifiablemethodologies,alwayswithaneyetowardpracticalapplication.Thebackroomsofinvestmentbankswouldsoonbestaffednotbyseasonedcigar-smokingprofessionalswhoknewfinanceasanartform,butratherbyyoungphysicists,mathematicians,andprodigieswhograspedthesignificanceofcomplicateddifferentialequationsandcouldtranslatetheircascadeofGreeklettersintofinancialprofits.Thistransitiontothenewquantschoolwasmadepossibleonlybecauseoftheworkofafewlarger-than-lifeindividualswithvariedbackgroundsbutepitomizinganewpracticalitythatwasbredsome-wherebetweentheUniversityofChicagoandMIT.First,thedevelopmentofthemeanandvariancecharacterizationofreturns,thentheuseofWilliamSharpe’sCAPMtodeterminetherisk-adjustedvalueofindividualsecurities,andthen,finally,theBlack-Scholesequationforthepricingofderivatives,inboththestaticform,andinthemoredynamiccontextdevelopedbyRobertMerton,injustacoupleofdecadesendowedpersonalfinancewiththetoolsnecessarytocreateascienceoutofanartform.Withtheconfidence,orsometimesperhapswiththefalseconfidence,ofthescientificmethod,financedevelopedrapidly.Soon,financebecameatopindustry,andevencons-titutedoneoutofeverythreedollarsofprofitintheUSAby2006.Theeraoffinancialtheory,anditsintegrationintofinancialmarkets,hadarrived.Andtheacademicworldtooknotice.NobelPrizesarenowgrantedtofinancialtheorydiscoveriesalmostasoftenastotherest179 180TheRiseoftheQuantsofthestudyofeconomics.Thisallbeganwiththe1981NobelPrizeawardedtothegreatmindJamesTobinforhisseparationtheoremandotherinnovationsinfinancetheory,andwiththe1989NobelPrizetoWilliamSharpe,MertonMiller,andFrancoModiglianifortheirinsightsintotheworkingsofhighfinanceandfinancialmarkets.ThiscontinuedwithaNobelPrizetoMyronScholesandRobertMertonafewyearsafterthepassingoftheBlack-ScholesequationoriginatorFischerBlack.Infact,thelegitimacyoffinancearisingfromthetoolsoftheCAPMandtheoptionspricingtheory,amongotherinnovations,sooncreatedatrackofadvancedstudyinfinancealmostcompletelydisjointedfromitsparentdisciplineofeconomics.Now,financialtheoristsaretaughtinbusinessschools,whilePhDsineconomicsarestilltaughtprimarilyinschoolsfortheliberalartsandsocialsciences.AndwhileaPhDcreatesanalmostunitarytracktoacademiaforeconomists,thosewithPhDsinfinancemoreoftenfindtheirwaytoWallStreetratherthantheivorytower.Thereisperhapsnobetterexampleinthedecisionsciencesoftheevolutionofideasthataresorevolutionary.Certainly,Newton’sequationsofmotionandLeibniz’sdevelopmentofcalculus,andtheNobelLaureateEinstein’sTheoryofRelativityin1905anditsEmc2prophecyhadcomparabletransformationalpotencyonsocietyandoureconomy.SotoowasthediscoveryofpenicillinattributedtotheNobelLaureateAlexanderFlemingin1928.Theseinnovationsrevolutionizedpurescience,engineering,orhumanityitself.However,beforetheriseofthequants,financeoreconomicshadknownnosuchprofoundinsightthattrulytransformedmarkets.Nootherdiscoveryorinnova-tionhasdirectlygeneratedthesortofprofitsandeconomicactivitythattheseinnovationsinfinancecreated.Nordidanyoftheseotherinnovationsgiverisetoentirelynewacademicdisciplines.Theabilitytotransformmarkets,createaplethoraofnew,timely,andusefulresearch,andthecreationofalmostunfathomablewealtharethelegaciesofthishandfulofscholarswhoforgedthenewAmericanschooloffinance.Inthecreationofquantitativefinance,someofthesegreatmindswerecutbyadouble-edgedsword.Notonlycanthesenewtheoriescreategreatwealth,buttheconfidencetheyengenderinanuncer-tainfinancialworldhasalsohelpedtocreategreathardship,financialdestruction,andevenaglobalfinancialmeltdown.Itisinterestingtoobservethateventhesegreatmindswerenotevenpersonallyimmunetofinancialhardshipwhenmarketsgoterriblywronginwaysthatcan-notbeanticipatedbyequationsriddledwithGreeklettersandbasedonbackward-lookingmeasuresofrisk.Financehasnot,andcannot,create Conclusions181acrystalballtoforeseethefuture.Theworldisuncertainbecauseweneverknowhowmarkets,economies,resources,orinstitutionswillbeabusedorusedinwaysthatcouldnothavebeenbroadlyanticipated.ThefailureofLongTermCapitalManagementin1999andthecreditcrisisof2008broughtaboutbyafreezing-upofthederivativesmarketincreditdefaultswapsandcollateralizeddebtobligationsdemonstratesthat,whileriskcanbehedged,itcanneverbereducedtozero. Notes1Introduction1.JohnMaynardKeynes,“TheGeneralTheoryofEmployment,”QuarterlyJournalofEconomics,51(1937),209–23,atp.214.3TheEarlyYears1.www.newschool.edu/nssr/het/profiles/neisser.htm,dateaccessedJanuary23,2012.2.A.Cowles,“CanStockMarketForecastersForecast?”Econometrica,1(1933),309–24.5TheTheory1.FrankKnight,Risk,UncertaintyandProfit.Boston:HoughtonMifflin,1921.2.J.MarschakandH.Makower,“MoneyandtheTheoryofAssets,”Econometrica,6(1938),311–25.3.Keynes,“TheGeneralTheoryofEmployment,”pp.213–14.4.FrankPlumptonRamsey,“TruthandProbability,”inR.B.Braithwaite(ed.),FoundationsofMathematicsandOtherLogicalEssays.London:Routledge&KeganPaul,1931.5.J.R.Hicks,“ASuggestionforSimplifyingtheTheoryofMoney,”Economica,2(1935),1–19.6.JacobMarschak,“MoneyandtheTheoryofAssets,”Econometrica,6(1938),311–25.7.Ibid.,p.320.8.Ibid.9.JacobMarschak,“RationalBehavior,UncertainProspects,andMeasurableUtility,”Econometrica,18(2)(1950),111–41.10.Ibid.,p.120.11.JacobMarschak,“ProbabilityintheSocialSciences,”CowlesCommissionPaper,82(1954),referringtoalecturegivenonDecember6,1950.12.Ibid.,p.179.13.KennethArrowandFrankHahn,GeneralCompetitiveAnalysis.SanFrancisco:Holden-Day,1971,pp.361and369.6Applications1.KennethArrow,“TheTheoryofRiskAversion,”inAspectsoftheTheoryofRiskBearing.Helsinki:YrjoJahnssoninSaatio,1965.ReprintedinEssaysintheTheoryofRiskBearing.Chicago:Markham,1971,pp.90–109.182 Notes1832.J.W.Pratt,“RiskAversionintheSmallandintheLarge,”Econometrica,32(1/2)(1964),122–36.3.S.A.Ross,“SomeStrongerMeasuresofRiskAversionintheSmallandintheLargewithApplications,”Econometrica,49(3)(1981),621–39.4.JohnBurrWilliams,TheTheoryofInvestmentValue.Cambridge,MA:HarvardUniversityPress,1938.5.HenryLowenfeld,Investment,anExactScience.London:FinancialReviewofReviews,1909,p.49.6.ColinRead,ThePortfolioTheorists,GreatMindsinFinanceseries.Basingstoke:PalgraveMacmillan.7LifeandLegacy1.RoyRadner,“EquilibriumofSpotandFuturesMarketsunderUncertainty,”CenterforResearchinManagementScienceTechnicalReportno.24,UniversityofCalifornia,Berkeley,1967.2.RoyRadner,“CompetitiveEquilibriumUnderUncertainty,”Econometrica,36(1968),31–58.3.JacobMarschakandRoyRadner,EconomicTheoryofTeams.NewHaven,CT:YaleUniversityPress,1972.8TheEarlyYears1.www.rand.org/about/history.html,dateaccessedJanuary23,2012.2.http://en.wikipedia.org/wiki/George_Dantzig,dateaccessedJanuary23,2012.3.Ibid.4.HarryMarkowitz,“PortfolioSelection,”JournalofFinance,7(1)(1952),77–91.5.http://en.wikipedia.org/wiki/Jack_L._Treynor,dateaccessedJanuary23,2012.6.WilliamSharpe,“HowtoRateManagementofInvestmentFunds,”HarvardBusinessReview,43(1965),63–75.7.WilliamSharpeandKayMazuy,“CanMutualFundsOutguesstheMarket?”HarvardBusinessReview,44(1966),131–6.9TheTimes1.http://en.wikipedia.org/wiki/IBM_System/360,dateaccessedJanuary23,2012.10TheTheory1.WilliamF.Sharpe,“ASimplifiedModelforPortfolioAnalysis,”ManagementScience,9(2)(1963),277–93.2.F.ModiglianiandM.Miller,“TheCostofCapital,CorporationFinanceandtheTheoryofInvestment,”AmericanEconomicReview,48(3)(1958),261–97. 184Notes11Applications1.G.Chamberlain,“ACharacterizationoftheDistributionsthatImplyMean-VarianceUtilityFunctions,”JournalofEconomicTheory,29(1983),185–201.2.KentD.Daniel,DavidHirshleifer,andAvanidharSubrahmanyam,“Overconfidence,Arbitrage,andEquilibriumAssetPricing,”JournalofFinance,56(3)(2001),921–65.3.MarkRubinstein,“TheValuationofUncertainIncomeStreamsandthePricingofOptions,”BellJournalofEconomics,7(1976),407–25.4.DouglasT.Breeden,“AnIntertemporalAssetPricingModelwithStochasticConsumptionandInvestmentOpportunities,”JournalofFinancialEconomics,7(1979),265–96.5.RichardRoll,“ACritiqueoftheAssetPricingTheory’sTestsPartI:OnPastandPotentialTestabilityoftheTheory,”JournalofFinancialEconomics,4(2)(1977),129–76.6.FischerBlack,MichaelC.Jensen,andMyronScholes,“TheCapitalAssetPricingModel:SomeEmpiricalTests,”inMichaelC.Jensen(ed.),StudiesintheTheoryofCapitalMarkets.NewYork:Praeger,1972,pp.79–121.7.JamesTobin,“LiquidityPreference,SeparationandAssetPricing,”ZeitschriftfürBetriebswirtschaft,3(1983),53–7.12LifeandLegacy1.JonathanBurton,“RevisitingtheCapitalAssetPricingModel,”DowJonesAssetManager(1998),pp.20–8.2.WilliamF.Sharpe,“CapitalAssetPrices–ATheoryofMarketEquilibriumUnderConditionsofRisk,”JournalofFinance,XIX(3)(1964),425–42.13TheEarlyYears1.www.nytimes.com/1998/11/14/business/when-theory-met-reality-special-report-teachings-two-nobelists-also-proved-their.html?pagewanted=all&src=pm,dateaccessedJanuary23,2012.2.Ibid.14TheTimes1.LyndonMooreandSteveJuh,“DerivativePricing60YearsBeforeBlack-Scholes:EvidencefromtheJohannesburgStockExchange,”JournalofFinance,61(6)(2006),3069–98.2.Aristotle,Politics,BookI,Chapter11,Sections5–10.3.JohnO’Farrell,AnUtterlyImpartialHistoryofBritain–Or2000YearsofUpperClassIdiotsinCharge.London:Doubleday,2007.4.J.delaVega(1688),ConfusiondeConfusiones;reprintedinM.Fridson(ed.),ExtraordinaryPopularDelusionsandtheMadnessofCrowds;andConfusiondeConfusiones(NewYork:Wiley,1996). Notes1855.IsaacdePinto(1771),AnEssayonCirculationofCurrencyandCreditinFourPartsandaLetterontheJealousyofCommerce,translatedwithannotationsbyS.Baggs(1774),London;reprintedbyGreggInternationalPublishers(1969).6.RobertJ.Leonard,“CreatingaContextforGameTheory,”HistoryofPoliticalEconomy,24(Supplement)(1992),29–76,atp.39.7.http://en.wikipedia.org/wiki/Louis_Bachelier,dateaccessedJanuary23,2012.8.AlfredCowlesandH.Jones,“SomeAPosterioriProbabilitiesinStockMarketAction,”Econometrica,5(3)(1937),280–94.9.LouisBachelier,“Theoriedelaspeculation,”Annalesscientifiquesdel’EcoleNormaleSuperieure,3rdseries,17(1900),21–86.10.C.M.Sprenkle,“WarrantPricesasIndicationsofExpectationsandPreferences,”YaleEconomicEssays,1(22)(1961),178–231.16Applications1.PerryMehrling,FischerBlackandtheRevolutionaryIdeaofFinance.Hoboken,NJ:Wiley,2005,p.138.2.FischerBlackandMyronScholes,“ThePricingofOptionsandCorporateLiabilities,”JournalofPoliticalEconomy,81(3)(1973),637–54.3.http://articles.chicagotribune.com/2011-01-19/business/ct-biz-0119-confidential-oconnor-20110119_1_cboe-edmund-o-connor-trading,dateaccessedJanuary23,2012.4.J.M.HarrisonandD.M.Krebs,“MartingalesandArbitrageinMulti-periodSecuritiesMarkets,”JournalforEconomicTheory,20(3)(1979),381–408.5.JohnC.Cox,StephenA.Ross,andMarkRubinstein,“OptionPricing:ASimplifiedApproach,”JournalofFinancialEconomics,7(1979),229–63.6.RichardRoll,“AnAnalyticalFormulaforUnprotectedAmericanCallOptionsonStockswithKnownDividends,”JournalofFinancialEconomics,5(1977),251–8.7.RobertGeske,“TheValuationofCompoundOptions,”JournalofFinancialEconomics(1979),63–81.8.RobertE.Whaley,“OntheValuationofAmericanCallOptionsonStockswithKnownDividends,”JournalofFinancialEconomics,9(1)(1981),207–11.17TheNobelPrize,Life,andLegacy1.www.thedailybeast.com/newsweek/2008/10/17/600-000-000-000-000.html,dateaccessedJanuary23,2012.2.F.Black,E.Derman,andW.Toy,“AOne-FactorModelofInterestRatesanditsApplicationtoTreasuryBondOptions,”FinancialAnalystsJournal(1990),24–32.3.F.Black,“HowtoUsetheHolesinBlack-Scholes,”JournalofAppliedCorporateFinance,1(4)(1989),67–73.4.Mehrling,FischerBlackandtheRevolutionaryIdeaofFinance,p.288.5.www.nobelprize.org/nobel_prizes/economics/laureates/1997/press.html,dateaccessedJanuary23,2012.6.JustinFox,“MyronScholes,IntellectualGodfatheroftheCreditDefaultSwap,SaysBlow‘emAllUp,”TimeMagazine,March6,2009:http://curiouscapitalist. 186Notesblogs.time.com/2009/03/06/myron-scholes-intellectual-godfather-of-the-credit-default-swap-says-blow-em-all-up/,dateaccessedJanuary23,2012.18TheEarlyYears1.www.nytimes.com/2003/02/24/nyregion/robert-k-merton-versatile-sociologist-and-father-of-the-focus-group-dies-at-92.html?pagewanted=3,dateaccessedJanuary23,2012.2.www.nobelprize.org/nobel_prizes/economics/laureates/1997/merton-autobio.html,dateaccessedJanuary23,2012.19TheTimes1.RobertC.Merton,“AnIntertemporalCapitalAssetPricingModel,”Econometrica,41(5)(1973),867–87.2.RobertC.Merton,“TheRelationshipbetweenPutandCallOptionPrices:Comment,”JournalofFinance,28(1)(1973),183–4.3.RobertC.Merton,“AnAnalyticalDerivationoftheEfficientPortfolioFrontier,”JournalofFinancialandQuantitativeAnalysis,10(1972),1851–72.4.RobertC.Merton,“TheoryofRationalOptionPricing,”BellJournalofEconomicsandManagementScience,4(1)(1973),141–83.5.PaulA.SamuelsonandRobertC.Merton,“ACompleteModelofWarrantPricingthatMaximizesUtility,”IndustrialManagementReview,10(1969),17–46.6.RobertC.Merton,“AGoldenGolden-RuleforWelfare-MaximizationinanEconomywithaVaryingPopulationGrowthRate,”WesternEconomicJournal,4(1969),307–18.7.RobertC.Merton,“LifetimePortfolioSelectionunderUncertainty:TheContinuous-TimeCase,”ReviewofEconomicsandStatistics,51(1969),247–57.8.RobertC.Merton,“A‘Motionless’MotionofSwift’sFlyingIsland,”JournaloftheHistoryofIdeas,27(1966),275–7.20TheTheory1.RobertC.Merton,“TheoryofRationalOptionPricing,”BellJournalofEconomicsandManagementScience,4(1)(1973),141–83.2.RobertC.Merton,“OnthePricingofContingentClaimsandtheModigliani-MillerTheorem,”JournalofFinancialEconomics,5(3)(1977),241–9.21Applications1.http://en.wikipedia.org/wiki/American_International_Group,dateaccessedJanuary23,2012. Notes18722TheNobelPrize,Life,andLegacy1.PaulSamuelson,“MathematicsofSpeculativePrice,”inR.H.DayandS.M.Robinson(eds),MathematicalTopicsinEconomicTheoryandComputation,Philadelphia,PA:SocietyforIndustrialandAppliedMathematics,1972.ReprintedinSIAMReview,15(1)(1973),1–42.2.PeterL.Bernstein,CapitalIdeas:TheImprobableOriginsofModernWallStreet.NewYork:FreePress,1992,p.223.3.www.nobelprize.org/nobel_prizes/economics/laureates/1997/press.html,dateaccessedJanuary23,2012.4.www.alumni.hbs.edu/bulletin/1997/december/theory.html,dateaccessedJanuary23,2012.5.GretchenMorgensonandMichaelM.Weinstein,“WhenTheoryMetReality:ASpecialReport;TeachingsofTwoEconomistsAlsoProvedTheirUndoing,”NewYorkTimes,November14,1998.6.DennisOverbye,“TheyTriedtoOutsmartWallStreet,”NewYorkTimes,March29,2009. GlossaryAlpha–theexcessreturnonasecurityoroverwhatispredictedbytheCAPM.Americanoptions–anoptiontopurchase(acall)orsell(aput)anunderlyingsecurityataspecifiedexercisepriceon(or,inthecaseofAmericanoptions,before)aspecifiedsettlementdate.Arrow-Prattmeasureofriskaversion–ameasureoftherelativedegreeofriskaversionasmeasuredbytherateofratioofanindividual’ssecondandfirstderivativesofutility.Beta–ameasureofthesystematicriskofarelativetothemarket.Binomialmodel–anoptionspricingmethodologythatbreaksthedynamicpathofthederivativesintoaseriesofstepsatvariouspointsintimebetweenthevaluationdateandtheexpirationdate.Black-Scholesmodel–amodelthatcandeterminethepriceofaEuropeancalloptionbasedontheassumptionthattheunderlyingsecurityfollowsageome-tricBrownianmotionwithconstantdriftandvolatility.Bond–afinancialinstrumentthatprovidesperiodic(typicallysemi-annual)interestpaymentsandthereturnofthepaid-incapitaluponmaturityinexchangeforafixedprice.Brownianmotion–thesimplestoftheclassofcontinuous-timestochasticprocessesthatdescribestherandommotionofaparticleorasecuritythatisbuffetedbyforcesthatarenormallydistributedinstrength.Calculusofvariations–amathematicaltechniquethatcandeterminetheoptimalpathofavariable,likesavingsorconsumption,overtime.Call–anoptiontopurchaseaspecifiedsecurityataspecifiedfuturetimeandprice.Capitalallocationline–alinedrawnonthegraphofallpossiblecombinationsofriskyandrisk-freeassetsthatshowsthebestrisk–rewardhorizon.CapitalAssetPricingModel(CAPM)–amethodologythatshowstherelationshipbetweenriskandexpectedreturnforafinancialsecurity.Cardinaltheory–atheoryineconomicsandfinancethatrequiresthemeasure-mentoftheobjectivefunctionratherthanthemereorderingofalternativeoutcomes.ChicagoBoardOptionsExchange(CBOE)–anexchangefoundedin1973totradeoptionsonsecurities.Itistheworld’slargestoptionsexchange.ChicagoBoardofTrade(CBOT)–acommodityexchangeestablishedin1848thatpermittedthetradingoffinancialandcommoditycontracts.ChicagoSchool–aphilosophyofeconomicandfinancialthoughtbasedonthepremisethatunfetteredmarketsarethemostefficient.Classicalmodel–amicroeconomic-basedapproachtoeconomicdecision-makingthatassumesthatallactorsarerationalandmaximizetheirself-interest,andisdrivenbytheprinciplethatpricesadjusttoensuresupplyisequaltodemand.Collateralizeddebtobligations–investment-gradesecuritiesbackedbyapackageofloans,mortgages,bonds,orotherdebtobligations.188 Glossary189ConsumptionCAPM–anextensionoftheCAPMthatincludesfutureconsumptionpreferences.Corporatefinance–thestudyoffinancialdecisionsmadebycorporationstomaximizeshareholdervalue.Correlation–thestatisticalrelationshipbetweentwovariables,typicallymeasuredbydemonstratingthatthemovementofonevariableisassociatedwithmovementoftheother.Covariance–ameasureofthedegreetowhichreturnsontworiskyassetsarecorrelatedintheirmovement.CowlesCommission–aresearchinstitutefoundedbyAlfredCowlestostimulatenewtheoriesinthedecisionsciencesthatcanhelpexplainfinancialmarkets.Couponratec–theperiodicpaymenttotheownerofabond.Creditdefaultswaps–securitiesthatallowtheexchangeofriskbytheunderwritingofinstrumentspronetodefaultrisk.Delta–theoptimalratiobetweentheoptionandstockforahedgethatreducesrisktothetheoreticalfloor.Derivative–inmathematics,theinstantaneousrateofchangeofonevariableasafunctionofthechangeofanother;infinance,afinancialinstrumentthatderivesitsvaluefromanotherunderlyingassetorinstrument.Differentialequation–anequationthatspecifiestherelationshipbetweentheratesofchangeofacollectionofvariables.Discountrate–therateatwhichhumanswillreducethevalueoffutureincomeinthedeterminationofitspresentvalue.Thistermisalsousedtosignifytheinterestratesetbyanation’scentralbank.Diversification–atechniquethatusesthecombinationofassetstoreducetheriskoftheportfoliowithoutloweringitsreturn.Dynamic–theanalysisofaprocessasitchangesovertime.Econometrics–thesetoftoolsusedtodemonstratepredictablestatisticalcorrela-tionsbetweenfinancialandeconomicvariables.Efficientmarkethypothesis–atheorybasedonthepremisethatonecannotsystematicallybeatthemarketbecausemarketpricesalreadyproperlyincor-porateallavailableinformation.Ellipticaldistributionofreturns–apatternofreturnsthatissymmetricinthatthereturncoulddeviateupwardordownwardwithequalprobability.Thenormaldistributionisamemberofthefamilyofallellipticaldistributions.Equilibrium–astateinwhicharelationshipconvergesuponaconstantbalance.Europeanoptions–optionsthatcanonlybeexercisedattheexercisedate.Existence–thepremiseusedinatheoryofequilibriumthatanequilibriumwillactuallyoccur.Expectations–thesetofbeliefsoverthefuturevalueofaneconomicorfinancialvariable.FacevalueF–thenominalvalueofabondthatisreturnedtothebondholderuponmaturity.Firstmoment–themeanofavariablethatcanbedescribedbyaknownprob-abilitydistributionfunction.Fullinformation–thedesirablequalitythatallknowableinformationaboutthevalueofasecurityisrevealed.Fundamentalsanalysis–estimationofthepriceofasecuritybasedontheunder-lyingpatternoffutureprofitabilityoftheenterprise. 190GlossaryGamma–therateofchangeoftheoptimalcombinationofanoptionandtheunderlyingsecurityovertime.Infinitetimehorizon–aneconomicplanninghorizonthathasnoend.Forinstance,aninfinitelylivedindividualorsocietywouldmakedecisionswithdueconsiderationtoaninfinitefuture.Interestrate–therateofperiodicpayments,asashareoftheprincipalamountborrowed,tocompensateforhumans’inherentpreferenceforthepresentoverthefuture.Intertemporal–areferencetodecisionsmadeacrosstime.IntertemporalCAPM–anextensionoftheCAPMbeyondthesimpleconside-rationofvariancestoalsoincludeadditionalconsumptionandinvestmentopportunitiesovertime.Keynesianmodel–amodeldevelopedbyJohnMaynardKeynesthatdemon-stratessavingsmaynotnecessarilybebalancedwithnewinvestmentandthegrossdomesticproductmaydifferfromthatwhichwouldresultinfullemployment.Kurtosis–astatisticalmeasureofthedistributionofobservationsabouttheexpectedmeanasadeviationfromthatpredictedbythenormaldistribution.Lifecycle–thecharacterizationofaprocessfromitsbirthtodeath.LifeCycleModel–amodelofhouseholdconsumptionbehaviorfromthebegin-ningofitsearningcapacitytotheendofthehousehold.Markovprocess–astochasticprocesswiththememorylessnesspropertyforwhichthepresentstate,futurestate,andpastobservationsareindependent.Markowitzbullet–theupperboundaryoftheefficientfrontierofvariousport-folioswhengraphedaccordingtoriskandreturn.Martingale–amodelofaprocessforwhichpasteventscannotpredictfutureoutcomes.Mean–amathematicaltechniquethatcanbecalculatedbasedonanumberofalternativeweightingstoproduceanaverageforasetofnumbers.MITSchool–anapproachtoeconomicandfinancialstudiesthatfavorsdynamic(time-variant)modelingandsimple,elegant,butpredictivelypowerfultheories.ModernPortfolioTheory–thesetoftechniquesdevelopedinthe1950sbyHarryMarkowitztodesignoptimalportfoliosandthemostefficientrisk–rewardtrade-off.MonteCarlosimulations–analgorithmthatrepeatssimulationsofapostulatedfinancialrelationshipwithrandomelements.TheMonteCarlosimulationoftenrevealspatternsthatcannotbegleanedbyanalyticmethods.Mortgage-backedsecurities–afinancialinstrumentthatderivesitsassetvalueonacollectionofunderlyingmortgages;inotherwords,afinancialsecuritythatisbackedbyacollectionoffinancialsecurities.Nakedshort–sellingofsecuritiesforwhichonedoesnotownthetitleorarighttosell.Normaldistributionofreturns–adistributionthatfollowsaprescribedandsymmetricpatternthatoccursfrequentlyinnaturalprocesses.Optimalcontroltheory–anextensionofthecalculusofvariationsthatisapowerfultoolinthemodelingofdynamicprocesses.Options–thecontractualrighttopurchaseasecurityatafuturedateunderspecifiedterms. Glossary191Optionspricingtheory–atheoryusedtodeterminetherationalpriceofanoptionorderivative.Ordinaltheory–atheorythathasasanobjectivefunctionandorderingthatcanrankthepreferenceofvariousoutcomesbutnotthedegreeofthepreference.Ordinaryleastsquares–amethodtosolvefortherelationshipbetweenadepen-dentvariableasaweightedsumofindependentvariables.Thistechniqueminimizesthesquareddifferencebetweenthedependentvariableandthepredictedamountfromanestimateofaweightedcombinationoftheinde-pendentvariables.Beforetherecentadventofsignificantcomputingpower,thisreadilycalculabletechniquewasusedtoestimaterelationshipsbetweendependentandindependentvariables.Perfectmarket–amarketthatischaracterizedbyaverylargenumberofbuyersandsellers,eachwithnomarketpower,andfullinformationandaccesstocredit.Personalfinance–thestudyofhouseholdandpersonalsavingsdecisionsasamethodtoenhancelifetimeconsumption.Price-earningsratio–theratioofasecurity’spricetoitsearningsasameasureofitspaybackperiod.Put–therighttosellasecurityataspecifieddateandprice.Quadraticutilityfunction–autilityfunctionthatriseswithwealth,income,orconsumptionthatcanbedescribedbyaquadraticequation.Onewithsuchaquadraticutilityfunctionwillonlybesensitivetothemeanandvarianceparametersofasecurity.Randomwalk–theexpectationthatasecurityreturnattimetisequaltoitslastperiodvalueplusastochastic(random)componentthatisindependentandidenticallydistributedwithzeromeanandvariance2.Rational–decision-makingbasedonfullandobjectiveanalysis.Regression–atechniqueusedtofitadependentvariableasaweightedsumofindependentvariables.Representativeagent–theuseofasinglerepresentativeentitytodeterminetherationaldecisionofafinancialoreconomicprocess.Return–theexpectedsurplusofferedtoenticeindividualstoholdafinancialinstrument.Rho–theeffectontheoptionpriceforasinglepercentagepointchangeintherisk-freerateofreturn.Risk–infinance,thedegreeofuncertaintyassociatedwithexchangingaknownsumforalargerfuturebutlesscertainsum.Risk-averse–apropertythatstatesanagentwouldpreferlessrisktomoreforanequalreturn.Risk-freeasset–anassetthatyieldsacertainreturnoverallpossiblestatesRisk-freerateofreturn–thereturnofferedbyanassetthatdoesnotvaryoverfuturestates.Risk–rewardtrade-off–anindividual’sdeterminationoftherequiredrewardtocompensateforadditionalrisk.Secondmoment–aweightedmeasureofthedeviationofarandomvariablefromitsmean,orfirstmoment.Securitiesmarketline–agraphthatcomparesthesystematicmarketriskforthemarketasawholecomparedtoitsreturn.Security–afinancialcontractthatestablishestherightsofownershipofanasset. 192GlossaryStPetersburgParadox–ascenariowhichpresentsasimpledecisionrulethatonlyregardstheexpectedvalueoftheoutcomebutwhichnorationalpersonwouldbewillingtotake.Static–theconsiderationofmathematical,physical,oreconomicrelationshipsthatdonotchangeovertime.Stochasticcalculus–theextensionofthetoolsofcalculustoprocessesthatarestochastic.Stochasticprocess–arandomprocessinwhichthereisindeterminacythatcannotbefullyknownandinsteadisdescribedbyaprobabilitydistribution.Systematicrisk–theunavoidableriskthatinherentlyaffectstheentiremarket.Taylor’sseries–theexpressionoftherangeofafunctionarisingfromdeviationsofitsdomainasrepresentedbyaninfiniteseriesofthefunction’sderivativesandthedeviationsofitsdomain.Thetaτ–theeffectofaone-dayreductioninthetimetoexpiryontheoptionprice.Transactionscosts–thesunkorupfrontcostofparticipatinginatransactionbeyondthecostofexchangeofthetransacteditemsthemselves.Thesecouldincludecontractingorparticipationfees.Uncertainty–thedegreetowhichthevalueoffuturevariablescannotbefullyknowntoday.Unsystematicrisk–theinherentsecurity-orindustry-specificriskthatcanbereducedthroughoptimaldiversification.Variance–aspecificmeasureofthedeviationofasetofdatapointsaroundthemeanvalueinwhichthedeviationsfromthemeanaresquared.Itiscalculatedastheexpectedsquareddeviationsofavariablefromitsmean.Vega–thesensitivityoftheoptionpricetoasinglepercentagepointchangeinmeasuredvolatility.Volatility–ameasureofthedegreeofuncertaintyandunexplainedmovementsofavariableovertime.Warrant–aderivativethatisofferedbyafirmasarighttopurchasetheunderlyingsecurityataspecificpricewithinacertaintimeframe.Wealthline–alocusofpointsthatconnectvariouslevelsofconsumptionofgoodsovertimeforagivenandknownlevelofincomeorwealth.Weinerprocess–acontinuous-timerandomwalkwithrandomjumpsateachpointintime. IndexAlpha,67,73,110,121Couponratec,168Americanoptions,100,101,116,123Covariance,23,32,34,58,59,60,62,Arrow,Kenneth,2365,66,74,93Arrow-Prattmeasureofriskaversion,29CowlesCommission,13,14,15,18,19,23,24,25,36,55,61,69,105,141Beta,66,67,69,72,73,110,111,112,Creditdefaultswaps,5,129,130,160,121,152161,181,185Binomialmodel,122Black-Scholesequation,96,97,113,Debreu,Gerard,23117,121,122,124,125,128,150,Delta,123,124153,158,159,160,161,163,179,Derivative,5,25,26,27,29,30,81,180101,106,109,121,125,128,Bond,5,33,59,96,106,121,126,129,130,131,142,155,159,140,142,154,159,160,168,169,160,162,169,173,174,175,170,185179,181,184Brownianmotion,32,105,113,120,Differentialequation,111,112,113,155115,121,125,127,139,142,143,148,149,152,153,154,155,157,Calculusofvariations,143158,179Call,98,99,100,101,104,106,107,Discountrate,53,58,93,106,108,108,112,114,115,116,122,123,111,113136,151,153,160,165,166,167,Diversification,23,32,59,66,67,76185,186Dynamic,5,14,67,68,71,114,124,Capitalallocationline,63,64,67143,144,145,146,147,148,149,CapitalAssetPricingModel(CAPM),150,151,152,153,1794,41,48,49,51–3,57,60,61,65–81,87,88,89,93,94,96,106,Econometric,14,19,36,39,61,78,109–12,118,121,124,141,150,79,141,144,150,173152,158,177,179,180Efficientmarkethypothesis,13,32,ChicagoBoardOptionsExchange70,72,73,94,95,111,124(CBOE),100,101,102,117,118,Ellipticaldistributionofreturn,69119,120,122,125,129,158,159Equilibrium,2,13,14,17,18,23,24,ChicagoBoardofTrade(CBOT),100,36,38,56,57,61,74,77,89,119,101,109,119,156147,150,175,183,184ChicagoSchool,86,120,152,153Europeanoption,100,101,115,116,Classicalmodel,17122Collateralizeddebtobligation,181Consumption,23FacevalueF,96ConsumptionCAPM,72Firstmoment,23,26,70,112,177Corporatefinance,32,76,81,106,Irving,1127,143,144Friedman,Milton,1Correlation,23,34,36,59,62,67,Fullinformation,14,7173,155Fundamentalsanalysis,33,58,158193 194IndexGamma,124Perfectmarket,71,154Personalfinance,76,146,175,179Hicks,John,21,22Price/earningsratio,58Homogenity,65Put,100,122,123Infinitetimehorizon,25Quadraticutilityfunction,26,70Interestrate,1,58,59,96,106,110,114,115,116,126,152,153,154,Ramsey,FrankPlumpton,1,24168,185Randomwalk,13,32,103,104,105,IntertemporalCAPM,71113,161Intertemporalchoice,1,69,71,75,Rational,21,23,37,38,58,66,70,124,125,143,150,184,186151,156Regression,67,70,75Keynes,JohnMaynard,1Representativeagent,65,73,74,111,Kurtosis,121142,143Return,2,4,22,23,25,26,27,28,53,Lifecycle,1,76,125,143,144,149,58,59,60,61,62,63,64,65,66–7,15068,70,79,88,92,93,104,111,112,LifeCycleModel,1,125,144,150113,114,115,118,121,122Rho,124Markovprocess,116,120,126Riskaversion,29,31,61,107,117Markowitz,Harry,23,63Risk-freeasset,2,59,62,63,65,70,73Markowitzbullet,63Risk-freerateofreturn,66,67,111,Marschak,Jacob,22,23,24112,113,114,124,153Martingale,105,120,121,185Risk–rewardtrade-off,46,87Mean,4,20,22,23,25,26,27,28,29,31,32,33,34,35,36,41,43,Savage,LeonardJimmie,2348,58,59,60,63,66,69,70,72,Secondmoment,4,23,26,27,28,34,104,118,121,126,154,155,177,43,59,69,70,105,112,177179,184Securitiesmarketline,2,140,156MITSchool,141,142Security,32–33,35,43–4,57–8,ModernPortfolioTheory,2,3,66–7,964,19,23,24,34,41,43,44,StPetersburgParadox,20,10246,48,56,57,61,64,68,Static,1,5,13,68,71,143,149,152,69,72,73,74,76,89,95,153,179125,177Steinhaus,Hugo,102Modigliani,Franco,1Stochasticcalculus,105,120,143,157MonteCarlosimulation,122Stochasticprocess,126Mortgage-backedsecurities,5Subjectiveprobability,24Systematicrisk,2,67,70Nakedshort,129Normaldistributionofreturn,Taylor’sseries,25,27,28116,161Theta,124Transactionscost,66,71,75,100,Optionspricingtheory,5,32,68,71,101,11072,77,109,111,113,115,116,120,124,180Uncertainties,2,20,36,53,101Ordinaltheory,22Uncertainty,1,2,4,15,16,19,20,Ordinaryleastsquares,7021,22,23,24,25,27,29,35,36, Index19537,38,43,47,61,68,69,79,98,Vega,99,124,184137,151,157Volatility,30,32,33,59,96,113,122,Unsystematicrisk,2,67123,124,126,158,160VonNeumann,John,22,23Variance,4,22,23,24,25,26,27,28,29,31,32,33,34,35,36,41,Warrant,96,97,98,99,100,43,48,57,58,59,60,61,62,63,107,109,111,112,118,140,64,65,66,67,69,70,72,93,142,143,149,151,156,162,104,111,112,121,154,177,185,186179,184Weinerprocess,104,105,154