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JWDD035-FM JWDD035-Vince February12,2007 7:3 CharCount=0 The Handbook of Portfolio Mathematics Formulas for Optimal Allocation & Leverage RALPH VINCE iii JWDD035-FM JWDD035-Vince February12,2007 7:3 CharCount=0 vi JWDD035-FM JWDD035-Vince February12,2007 7:3 CharCount=0 The Handbook of Portfolio Mathematics i JWDD035-FM JWDD035-Vince February12,2007 7:3 CharCount=0 Founded in 1807, John Wiley & Sons is the oldest independent publish- ingcompanyintheUnitedStates.WithofficesinNorthAmerica,Europe, Australia,andAsia,Wileyisgloballycommittedtodevelopingandmarketing printandelectronicproductsandservicesforourcustomers’professional andpersonalknowledgeandunderstanding. TheWileyTradingseriesfeaturesbooksbytraderswhohavesurvived the market’s ever-changing temperament and have prospered—some by reinventing systems, others by getting back to basics. Whether a novice trader,professionalorsomewhereinbetween,thesebookswillprovidethe adviceandstrategiesneededtoprospertodayandwellintothefuture. Foralistofavailabletitles,visitourWebsiteatwww.WileyFinance.com. ii JWDD035-FM JWDD035-Vince February12,2007 7:3 CharCount=0 The Handbook of Portfolio Mathematics Formulas for Optimal Allocation & Leverage RALPH VINCE iii FFOORR SSAALLEE && EEXXCCHHAANNGGEE wwwwww..ttrraaddiinngg--ssooffttwwaarree--ccoolllleeccttiioonn..ccoomm MMiirrrroorrss:: wwwwww..ffoorreexx--wwaarreezz..ccoomm wwwwww..ttrraaddeerrss--ssooffttwwaarree..ccoomm wwwwww..ttrraaddiinngg--ssooffttwwaarree--ddoowwnnllooaadd..ccoomm JJooiinn MMyy MMaaiilliinngg LLiisstt JWDD035-FM JWDD035-Vince February12,2007 7:3 CharCount=0 Copyright(cid:2)C 2007byRalphVince.Allrightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada. Chapters1–10containrevisedmaterialfromthreeoftheauthor’spreviousbooks,Portfolio ManagementFormulas:MathematicalTradingMethodsfortheFutures,Options,and StockMarkets(1990),TheMathematicsofMoneyManagement:RiskAnalysisTechniques forTraders(1992),andTheNewMoneyManagement:AFrameworkforAssetAllocation (1995),allpublishedbyJohnWiley&Sons,Inc. 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LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheir besteffortsinpreparingthisbook,theymakenorepresentationsorwarrantieswithrespect totheaccuracyorcompletenessofthecontentsofthisbookandspecificallydisclaimany impliedwarrantiesofmerchantabilityorfitnessforaparticularpurpose.Nowarrantymaybe createdorextendedbysalesrepresentativesorwrittensalesmaterials.Theadviceand strategiescontainedhereinmaynotbesuitableforyoursituation.Youshouldconsultwitha professionalwhereappropriate.Neitherthepublishernorauthorshallbeliableforanyloss ofprofitoranyothercommercialdamages,includingbutnotlimitedtospecial,incidental, consequential,orotherdamages. Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,please contactourCustomerCareDepartmentwithintheUnitedStatesat(800)762-2974,outside theUnitedStatesat(317)572-3993orfax(317)572-4002. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappears inprintmaynotbeavailableinelectronicformat.FormoreinformationaboutWiley products,visitourwebsiteatwww.wiley.com LibraryofCongressCataloging-in-PublicationData: Vince,Ralph,1958– Thehandbookofportfoliomathematics:formulasforoptimalallocation&leverage/ RalphVince: p. cm. ISBN-13:978-0-471-75768-9(cloth) ISBN-10:0-471-75768-3(cloth) 1.Portfoliomanagement–Mathematicalmodels. 2.Investments–Mathematicalmodels. I.Title. HG4529.5.V5552007 332.601(cid:3)51–dc22 2006052577 PrintedintheUnitedStatesofAmerica 10 9 8 7 6 5 4 3 2 1 iv JWDD035-FM JWDD035-Vince February12,2007 7:3 CharCount=0 “Youmustnotbeextendingyourempirewhileyouareatwarorrun intounnecessarydangers.Iammoreafraidofourownmistakes thanourenemies’designs.” —Pericles,inaspeechtotheAtheniansduringthePeloponnesian War,asrepresentedbyThucydides v JWDD035-FM JWDD035-Vince February12,2007 7:3 CharCount=0 vi JWDD035-FM JWDD035-Vince February12,2007 7:3 CharCount=0 Contents Preface xiii Introduction xvii PART I Theory 1 CHAPTER 1 The Random Process and Gambling Theory 3 IndependentversusDependentTrialsProcesses 5 MathematicalExpectation 6 ExactSequences,PossibleOutcomes,andthe NormalDistribution 8 PossibleOutcomesandStandardDeviations 11 TheHouseAdvantage 15 MathematicalExpectationLessthanZeroSpellsDisaster 18 Baccarat 19 Numbers 20 Pari-MutuelBetting 21 WinningandLosingStreaksintheRandomProcess 24 DeterminingDependency 25 TheRunsTest,ZScores,andConfidenceLimits 27 TheLinearCorrelationCoefficient 32 CHAPTER 2 Probability Distributions 43 TheBasicsofProbabilityDistributions 43 DescriptiveMeasuresofDistributions 45 MomentsofaDistribution 47 TheNormalDistribution 52 vii