Capital Allocation - Casualty Actuarial Society C

1CapitalConsumptionDonMangoAmericanRe-Insurance2003CAReSeminar2GoalsforToday1.Getyoutoadmitthisisavalidalternativeframework(albeitorthogonal)tocapitalallocation/release/IRR2.Demonstratehowitcanbepracticallyimplementedasameansofpricingreinsurance3.Demonstrateconnectionstoleadingedgethinkinginfinancialscience3ProblemStatementsCapitalallocationisadefactoparadigmarequirementornecessityThereforeweforce-fitourbusinessintoamanufacturing-basedcapitalinvestmentframework4ProblemStatementsButinsurancecapitalusageisfundamentallydifferentthanitisformanufacturing,beinginfactthemirror-imageintimeForthesedecisionevaluationprocesses,capitalallocationissufficientbutnotnecessary5ProblemStatementsEvenworse,theresultinginsuranceIRRframeworkisnowcompletelyfictional(“imputed”),sincenocapitalisactuallytransferredorreturnedHowever,insurancecapitalisactuallyconsumedwhenresultsareworsethanplanned6Actually…ThisIScapitalallocationforinsurance,donerightButIneedednewterminologytoshakeloosetheoldthoughtprocesses7TwoBetsBet#1Youpayme$10nowImightpayyou$50laterBet#2Ipayyou$10nowYoumighthavetopayme$50later8PayoffDiagramsBet#1-20-100102030405060NowLaterBet#2-60-50-40-30-20-1001020NowLater9Bet#1SpendthenMaybeReceiveYouspendnow,hopetoreceivelaterYouspendNOW,voluntarilyWiththeoddsIgiveyou,youcancomputeanexpectedvalueanddecideifyouwanttomakethebet10Bet#2ReceivethenMaybeSpendYoureceivenow,hopeyoudon’thavetospendlaterYouMAYspendLATER,involuntarilyWiththeoddsIgiveyou,youcancomputeanexpectedvalueanddecideifyouwanttomakethebet11Capital?Bet#1=$10Youspend$10capitalNOWnomatterwhatThecapitalinvestmentiscurrentandcertain–i.e.,notcontingentAllocated=spentNaturalcapacityconstraint=yourbudget12Capital?Bet#2=$???Ishouldbesureyouhave$40availableLATER,butyoudon’tspendanythingNOWIfBet#2hits,youspend$40capitalLATERCapitalexpenditure(=allocation)iscontingentandinthefutureCapacityconstraints=???Perception13TwoBets?Bet#1=themanufacturinginvestmentdecisionSpendthenreceiveBet#2=theinsuranceinvestmentdecisionReceivethenspend14AllocationvsConsumptionTwodifferentbutequallyvalidframeworksforTreatingcapitalEvaluatinginsurancebusinesssegmentsDevelopingindicatedpricesforreinsuranceNearlyorthogonal15AllocationvsConsumptionFourquestions:1.Whatdoyoudowiththetotalcapital?2.Howdoyouevaluatebusinesssegments?3.Whatdoesitmeantobeinaportfolio?4.Howisrelativeriskcontributionreflected?16AllocationvsConsumptionQuestion1:Whathappenstothetotalcapital?AllocationConsumptionDividedupamongthesegments.Eitherbyexplicitallocation,orassignmentofthemarginalchangeinthetotalcapitalrequirementfromaddingthesegmenttotheremainingportfolioLeftintactEachsegmenthastherightto“call”uponthetotalcapitaltopayitsoperatingdeficitsorshortfalls17AllocationvsConsumptionQuestion2:Howarethesegmentsevaluated?AllocationConsumptionGivetheallocationstoeachsegmentEvaluateeachsegment’sreturnontheirallocatedcapitalMustcleartheirhurdlerateGiveeachsegment“accessrights”totheentirecapitalEvaluateeachsegment’spotentialcalls(bothlikelihoodandmagnitude)onthetotalcapitalMustpayforthelikelihoodandmagnitudeoftheirpotentialcalls18AllocationvsConsumptionQuestion3:Whatdoesbeinginaportfoliomean?AllocationConsumptionBeingstandalonewithlesscapitalButstillhavingaccesstoallthecapitalifnecessary,althoughitisunclearhowthisisreflectedBeingstandalonewithpotentialaccesstoallthecapitalButallothersegmentshavesimilaraccessrightsThedifferencebetweenhavingyourownkiddiepoolandjoiningaswimclubThisisTHECRITICALSLIDE!19AllocationvsConsumptionQuestion4:Howisrelativeriskcontributionreflected?AllocationConsumptionUseasingleriskmeasuretodeterminerequiredcapitalSelectadependencestructurefortheaggregationofsegmentdistributionsintoaportfolioaggregatedistributionThemarginalimpactofaddingasegmenttotheremainingportfolioisthatsegment’sriskcontributionUsescenario-leveldetailgeneratedbystochasticmodelingUseexplicitrisk-returnevaluationviautilityfunctionSegment’sriskcontributionisdeterminedatthescenariolevel,thenaggregatedoverallscenarios20DetailsoftheFrameworkScenarioanalysisDefault-freediscountingScenario-levelcapitalconsumptionEvaluationofcapitalconsumptionusinga“quasi~utility”approach21Default-FreeDiscountingConditionalonitsoccurrence,agivenscenario’soutcomeiscertaindiscountatthedefault-freerateRisk-adjusteddiscountingistooclumsyOverloadedoperatorTrysplittingoutdefaultprobabilityfrompriceofriskinriskydebtspreadsReflectuncertaintybetweenscenarios,notwithinWhatisuncertaintywithinascenarioanyway?Doyoubelievethescenarioispossibleornot?22ScenarioCapitalConsumptionExperiencefundFromFiniteReinsuranceFundintowhichgoesallrevenue,fromwhichcomesallpaymentsBakesininvestmentincomeWhenitdropsbelowzero,andfurtherpaymentsneedtobemade,gotta“calltheparents”forsomecapitalThatcapitalisspentCONSUMED23ExperienceFundLong-TailedLOBExample1ExperienceFundforLong-tailedContract120%LossRatioScenarioProbability10.0%InvestmentRate8.0%LossRatio116.2%UltimateLoss120,000123456789TimeBeginningFundBalan