Introduction to Experience Rating Casualty Actuari

IntroductiontoExperienceRatingCasualtyActuarialSocietyReinsurancePricingSeminarDaveClark,ActuaryandVPMunichReinsuranceAmerica,Inc.2IntroductiontoExperienceRatingAgenda:BasicExperienceRatingMethodologyDiagnostics:tellingthestoryCredibilityweightingwithexposurerateExamplesProblems&Challenges(timepermitting)3IntroductiontoExperienceRatingBasicExperienceRatingMethodologyStepsinExperienceRating:1.AssembleData2.AdjustSubjectPremiumtoFutureLevel3.TrendandLayerLosses4.ApplyLossDevelopment4IntroductiontoExperienceRatingBasicExperienceRatingMethodology(1)AssembleDataFirstRule:Apples-to-ApplescollectionofhistoricalsubjectpremiumandlossdataTrendedOnLevelSubjectPremiumTrendedUltimateLayerLossesExperienceRate=5IntroductiontoExperienceRatingBasicExperienceRatingMethodology(1)AssembleDataSecondRule:Getallthedetailonhistoricallosses1.Includeallhistoricallossesthatwouldtrendintothelayer(ruleofthumb:getalllosseshalfofyourattachmentpoint)2.SplitoutALAEforeachloss3.Includehistoricalpolicylimits(andSIRifapplicable)4.Confirmthatlossesareassembledbyoccurrence,notbyclaimant6IntroductiontoExperienceRatingBasicExperienceRatingMethodology(2)AdjustSubjectPremiumtoFutureLevelFiled[manual]ratechanges“Price-level”changesSchedule-Rating,companytiers,etcAlsoinclude“soft”changessuchasterms&conditions,changesinunderwritingstandards,etcExposureTrend(forinflation-sensitiveexposurebases)7IntroductiontoExperienceRatingBasicExperienceRatingMethodology(2)AdjustSubjectPremiumtoFutureLevelGoalistoadjusthistoricalpremiumtoalevel“asif”ithasbeenwrittenduringthefutureperiod.Thesplitbetween“rate”and“price”isnotalwaysobvious(e.g.,whereareLCMsorpackagefactorsincluded?):getafulldescriptionfromthecedingcompany.8IntroductiontoExperienceRatingBasicExperienceRatingMethodology(2)AdjustSubjectPremiumtoFutureLevelPrimaryLossRatios0%10%20%30%40%50%60%70%80%90%100%1996199719981999200020012002200320042005200620072008AccidentYearUltimateLossRatioTrendandOnlevel9IntroductiontoExperienceRatingBasicExperienceRatingMethodology(2)AdjustSubjectPremiumtoFutureLevelNotetoactuariescomingfromaprimaryrate-filingbackground:Inaratefiling,youtypicallyadjustpremiumtothecurrentratelevel.Inreinsurancepricing,youwanttoadjustpremiumtotheaverageratelevelinthefutureperiod.10IntroductiontoExperienceRatingBasicExperienceRatingMethodology(2)AdjustSubjectPremiumtoFutureLevelObviousobservation:Ifthecedingcompany’seffectiveratesdropby-10%fortheprospectiveperiod,butweassumethatratesare“flat,”thenourexperienceratingwillbeunderstatedby10%.RecommendedReading:TrentVaughn’sCommercialLinesPriceMonitoring;CASForumFall2004HandoutsfromChrisNyceandBrianHughesatthe2007CASRatemakingSeminar()11IntroductiontoExperienceRatingBasicExperienceRatingMethodology(2)AdjustSubjectPremiumtoFutureLevelChangeinNetWrittenPremium(DetrendedbyGDP)Industrywide,AllLines-6.00%-4.00%-2.00%0.00%2.00%4.00%6.00%8.00%10.00%12.00%1987198819891990199119921993199419951996199719981999200020012002200320042005200612IntroductiontoExperienceRatingBasicExperienceRatingMethodology(2)AdjustSubjectPremiumtoFutureLevelNonproportionalCasualtyReinsurance(ScheduleP)Industrywide0%20%40%60%80%100%120%140%160%180%1987198819891990199119921993199419951996199719981999200020012002200320042005200613IntroductiontoExperienceRatingBasicExperienceRatingMethodology(3)Trend&LayerLossesPurposeistobringthehistoricalvalueuptotheaveragelevelinthefutureperiodTypicallyweapplytrendandthencapthetrendedlossatthehistoricalpolicylimitHiddenassumption:Alllossestrendatthesamepercent(trenddoesnotvarybysizeofloss)14IntroductiontoExperienceRatingBasicExperienceRatingMethodology(3)TrendLosses:DependsonTreatyBasis:ExperiencePeriod(AY)RisksAttachingTreatyExperiencePeriod(AY)LossesOccurringTreaty15IntroductiontoExperienceRatingBasicExperienceRatingMethodology(3)TrendLosses–LeveragedEffect1,000,0001,200,000trend16IntroductiontoExperienceRatingBasicExperienceRatingMethodology(3)TrendLosses-ImpactonExcessLayerLayer:500,000excessof500,000UntrendedTrendedTrend%Total#ofClaims100100ParetoB125,000135,000ParetoQ1.551.55OverallSeverity227,273245,4558.0%LayerCounts8.39.19.9%LayerSeverity313,899315,6870.6%LayerLossCost2,590,5132,864,00810.6%Allnumbersareforillustrationonly,andnotforuseinpricing.17IntroductiontoExperienceRatingBasicExperienceRatingMethodology(4)DevelopLossestoUltimateFactorsdependonLayerofReinsurancebeingpricedWeapplyLDFstotrendedlayerlossessothatallyearsareonthesamebasis.DevelopmentisanaggregatelossconceptIncludesnewclaims(“trueIBNR”),developmentonknownclaims,reopeningofclosedclaims,etc18IntroductiontoExperienceRatingBasicExperienceRatingMethodology(4)DevelopLossestoUltimateCumulativeReportingPattern0.0%10.0%20.0%30.0%40.0%50.0%60.0%70.0%80.0%90.0%100.0%01224364860728496108120132144156168180192204216228240%ReportedasofEvaluationAgePrimary400xs1001Mxs1MAllnumbersareforillustrationonly,andnotforuseinpricing.19IntroductiontoExperienceRatingBasicExperienceRatingMethodology(4)DevelopLossestoUltimateProblem:Mostrecentperiodsareverygreenandmayhavezeroloss