Portfolio Management Under Stress Portfolio Management Under Stress offers a novel way to apply the well-established Bayesian-net methodology to the important problemofassetallocationunderconditionsofmarketdistressor, moregenerally,whenaninvestorbelievesthataparticularscenario (suchasthebreak-upoftheEuro)mayoccur.Employingacoher- entandthoroughapproach,itprovidespracticalguidanceonhow best to choose an optimal and stable asset allocation in the pres- enceofuser-specifiedscenariosor‘stressconditions’.Theauthors placecausalexplanations,ratherthanassociation-basedmeasures such as correlations, at the core of their argument, and insights from the theory of choice under ambiguity aversion are invoked toobtainstableallocationsresults.Step-by-stepdesignguidelines are included to allow readers to grasp the full implementation of theapproach,andcasestudiesprovideclarification.Thisinsightful bookisakeyresourceforpractitionersandresearchacademicsin thepost-financial-crisisworld. riccardo rebonato is Global Head of Rates and FX Ana- lytics atPIMCO, and a visitinglecturer inMathematical Finance atOxfordUniversity(OCIAM).Hehaspreviouslyheldpositions asHeadofRiskManagementandHeadofDerivativesTradingat severalmajorinternationalfinancialinstitutions.DrRebonatohas been on the Board of ISDA (2002–2011), and still serves on the BoardofGARP(2001topresent).Heistheauthorofseveralbooks on finance and an editor for several journals (International Jour- nal of Theoretical and Applied Finance, Journal of Risk, Applied MathematicalFinance,JournalofRiskforFinancialInstitutions). alexander denev isaseniorteamleaderintheRiskModels department at the Royal Bank of Scotland. He is specialized in CreditRisk,Regulations,AssetAllocationandStressTesting,and has previously worked in management roles at European Invest- mentBank,Socie´te´ Ge´ne´raleandNationalBankofGreece. ‘Standard portfolio theory has been shown by recent events to have two major short- comings: it does not deal well with extreme events and it is often based on mechanical statistical procedures rather than modelling of fundamental causal mechanisms. In this book, Rebonato and Denev put forward an interesting approach for dealing with both of these problems. Their method is flexible enough to accommodate individual views of underlying causal mechanisms, but disciplined enough to ensure that decisions do not ignore the data. Anyone with a serious interest in making good portfolio decisions or measuringriskwillbenefitfromreadingthisbook.’ IanCooper,ProfessorofFinance,LondonBusinessSchool ‘This book is self-contained in that it covers a lot of familiar but diverse material from a fresh perspective. Its purpose is to take an ambitious new approach to combining this material into a coherent whole. The result is a new methodology for practical portfolio managementbasedonBayesiannets,whichsatisfactorilytakesintosimultaneousaccount bothnormalandextrememarketconditions.Whilereadersmaythemselvesbeunderstress inabsorbingthedetailsofthenewapproach,seriousfundmanagersandfinanceacademics willignoreitattheirperil.’ M.A.H.Dempster,EmeritusProfessor,DepartmentofMathematics, UniversityofCambridge;CambridgeSystemsAssociatesLimited ‘RebonatoandDenevhavedemolishedthestatusquowiththeirradicalextensionofbest- practice portfolio management. The key is to integrate realistic “extreme” scenarios into risk assessment, and they show how to use Bayesian networks to characterize precisely thosescenarios.Thebookisrigorousyetcompletelypractical,andreadingitisapleasure, withthe“Rebonatotouch”evidentthroughout.’ FrancisX.Diebold,PaulF.andWarrenS.MillerProfessorof Economics,ProfessorofFinanceandStatistics,andCo-Director,Wharton FinancialInstitutionsCenter,UniversityofPennsylvania ‘Here is a book that combines the soundest of theoretical foundations with the clearest practical mindset. This is a rare achievement, delivered by two renowned masters of the craft,truepractitionerswithanacademicmind.Bayesiannetsprovideaflexibleframework totackledecisionmakingunderuncertaintyinapost-crisisworld.Modelingobservations according to causation links, as opposed to mere association, introduces a structure that allows the user to understand risk, as opposed to just measuring it. The ability to define scenarios,incorporatesubjectiveviews,modelexceptionalevents,etc.,inarigorousmanner isextremelysatisfactory.Iparticularlylikedtheuseofconcentrationconstraints,because history shows that high concentration with low risk can be more devastating than low concentration with high risk. I expect fellow readers to enjoy this work immensely, and monetizeontheknowledgeitcontains.’ MarcosLopezdePrado,ResearchFellow,HarvardUniversity; HeadofQuantitativeTrading,HessEnergyTradingCompany ‘InarecentbookofmyownIbemoanrampant“confusion”amongacademicsaswellas practitionersofmodernfinancialtheoryandpractice.Iamdelightedtosaythattheauthors ofPortfolioManagementUnderStressarenot confused.Itisheart-warmingtofindsuch clarityofthoughtamongthosewithpositionsofgreatinfluenceandresponsibility.’ HarryM.Markowitz,NobelLaureate,Economics1990 ‘RebonatoandDenevhaveploughedforallofusthevastfieldofapplicationsofBayesian netstoquantitativeriskandportfoliomanagement,leavingabsolutelynostoneunturned.’ AttilioMeucci,ChiefRiskOfficerandDirectorof PortfolioConstructionatKeposCapitalLP Portfolio Management Under Stress A Bayesian-Net Approach to Coherent Asset Allocation Riccardo Rebonato and Alexander Denev UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom CambridgeUniversityPressisapartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781107048119 ©RiccardoRebonatoandAlexanderDenev2013 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2013 PrintedintheUnitedKingdombyCPIGroupLtd,CroydonCR04YY AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationdata Rebonato,Riccardo. Portfoliomanagementunderstress:aBayesian-netapproachtocoherentasset allocation/RiccardoRebonatoandAlexanderDenev. pages cm Includesbibliographicalreferencesandindex. ISBN978-1-107-04811-9(hardback) 1.Portfoliomanagement–Mathematicalmodels. 2.Investments–Mathematical models. 3.Financialrisk–Mathematicalmodels. I.Denev,Alexander. II.Title. HG4529.5.R43 2013 332.601(cid:2)519542–dc23 2013037705 ISBN978-1-107-04811-9Hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication, anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. Tomyfather,mywifeandmyson. [rr] Tomymother andbrother.WhatIamtoday,Iowetothem. [ad] Contents Listoffigures pagexviii Listoftables xxiii Acknowledgements xxvi PartI Ourapproachinitscontext 1 1 Howthisbookcameabout 5 1.1 Anoutlineofourapproach 6 1.2 Portfoliomanagementasaprocess 9 1.3 Planofthebook 10 2 Correlationandcausation 13 2.1 Statisticalversuscausalexplanations 13 2.2 Aconcreteexample 19 2.3 Implicationsforhedginganddiversification 22 3 Definitionsandnotation 23 3.1 Definitionsusedforanalysisofreturns 23 3.2 Definitionsandnotationformarketriskfactors 25 PartII Dealingwithextremeevents 27 4 Predictabilityandcausality 31 4.1 Thepurposeofthischapter 31 4.2 Isthistimedifferent? 32 4.3 Structuralbreaksandnon-linearities 34 4.4 Thebridgewithourapproach 37 5 Econophysics 40 5.1 Econophysics,tailsandexceptionalevents 40 ix