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  • AnEmpiricalInvestigationoftheEffectofGrowthonLossReserveErrors

    MichaelM.Barth1andDavidL.Eckles2

    Abstract:ThisstudyanalyzestherelationshipbetweentheexcessgrowthriskfactorintheNationalAssociationofInsuranceCommissioners(NAIC)riskbasedcapitalformulaandsubsequentreservedevelopmenterror.The inclusionof theexcessivegrowth risk charge for reserveswas predicated on the assumption that excessivegrowthcreatesreserveerrorbias.WemeasuretheimpactondifferentlinesofbusinessandfindnorelationshipbetweensubsequentreserveerrorsandtheexcessivegrowthriskfactorincludedintheNAICriskbasedcapitalformula.Wedofindarelationship,however,betweenreserveestimationerrorandanalternativemeasureofgrowthrisk,basedonclaimcountsreportedinSchedulePPart5.[Keywords:riskbasedcapital,growth risk, insurance regulation, insurance reserve errors.] JEL Classification:G22, G28

    INTRODUCTION

    hepurposeofthisresearchistotesttheimpactofaggregatepremiumgrowthonlossreserveestimationerrors.Wetesttwoalternatemea

    suresofgrowthwhilecontrollingforotherfactorsassociatedwithreserveerrorbias,includingtaxes,incomesmoothing,andproductvariations.Wespecifically test thegrowth risk charge for reservedevelopment that isincludedintheNationalAssociationofInsuranceCommissioners(NAIC)RiskBasedCapital(RBC)formulaagainstanalternativebylinegrowthmeasure,claimcounts.TheNAICRBCgrowthriskfactoriscomputedonaggregatepremiumsandappliedtoaggregatereserves,butinsurerscan

    1Associate Professor, The Citadel.Office: (843) 9530835, Email:mike.barth@citadel.edu,SchoolofBusinessAdministration,171MoultrieStreet,Charleston,SC294092AssociateProfessor,UniversityofGeorgia.Office:(706)5423578,Email:deckles@uga.edu,296BrooksHall,UniversityofGeorgia,Athens,GA30602

    T

    96JournalofInsuranceIssues,2015,38(1):96123.Copyright2015bytheWesternRiskandInsuranceAssociation.Allrightsreserved.

  • EFFECTOFGROWTHONLOSSRESERVEERRORS 97

    haveexcessgrowthinsomelinesandshrinkageinothers.Wetestwhethertheaggregategrowthriskfactorispredictiveofbylinereserveerrorbias.Wealsotestwhetherbylinemeasuresofgrowtharepredictiveofbylinereserveerrorbias.

    TheimpactofthegrowthriskchargeintheNAICformulaistypicallyminorfortheindustryasawhole,buttheimpactonindividualinsurerscanbematerial.This isparticularly importantwhenoneconsiders thatpremiumgrowthattributabletopricestrengtheningmayactuallybebeneficial.However,thereislittleempiricalresearchintothespecificeffectsofgrowth.Asanexample,during litigationwith theCalifornia InsuranceDepartment,theStateCompensationInsuranceFund(SCIF),Californiascompetitivestateworkerscompensationinsurancefund,madetheargumentthattheexcessivegrowthitexperiencedduringahardmarketinthelate1990sandearly2000sresultedinamorefinanciallysoundposition.However,SCIFactuallytriggeredregulatoryactionunderCaliforniasRBCstatutebecauseitsgrowthratetriggeredexcessivegrowthratechargesforbothitswrittenpremiumsanditsreservesundertheNAICsRBCformula.DisruptionsintheCaliforniaworkerscompensationmarkethadincreasedSCIFsshareof theCaliforniaworkerscompensationmarket toover50percent,thoughthosesamemarketdisruptionsallowedSCIFtoraiseitspremiumssimultaneously.SCIFarguedthattheincreaseinpolicycountswascoupledwithsignificantpriceincreases,andthereforetheexcessivepremiumgrowthwasactuallymaking the facility sounder,despite theresultsoftheRBCformula.

    Overtheyears,anumberofstudieshavecitedexcessivegrowthasoneoftheleadingcausesoffinancialimpairment(e.g.,AmericanAcademyofActuaries2010,A.M.Best,2010a,2006,2001;GovernmentAccountabilityOffice,1989).Excessivegrowthcancauseaninsurertobookalargeamountof unprofitable business, resulting in an immediate effect on surplus.However,excessivegrowthcanalsomakeitmoredifficulttoestimatetheultimateobligationsandcanleadtounderestimatedlossreserves.Therefore,theeffectofexcessivegrowthonaninsurersreservingerrorsisanimportantquestion,andeveniftheeffectisonaveragebenign.Thatis,ifthelossreserveestimatesbecomemorevariable,thenfinancialimpairmentriskisincreased.

    TheNAICincludespremiumgrowthratiosinbothofitsprimaryearlywarning systemsthe InsuranceRegulatory Information System (IRIS)andtheFinancialAnalysisandSolvencyTrackingsystem(FAST).Additionally,boththeNAICRBCformulaandtheA.M.BestCompanysBestCapitalAdequacyRatio(BCAR)includespecificcapitalchargesforexcessivegrowth.UnliketheNAICsRBCformula,BestsBCARformulausesexposuredatatomeasuregrowthrisk:

  • 98 BARTHANDECKLES

    GrowthCharge:Thereservegrowthchargereflects theadditionalriskthattypicallycomesfromgrowthandisbasedonthegrowthinacompanysexposures.Thegrowthchargeappliedtothelossreserveaggregate requiredcapital reflects the substantial riskacompanyfacesintheclaimsandreservingareasduringatimeofsignificantgrowth(A.M.Best,2010b,p.12).

    Theinclusionofthegrowthchargeisbased,inpart,onpastresearchshowingthatinsolventinsurersoftenexperiencehighperiodsofgrowthjustprior to insolvency.However, other studies have shown that highperiodsofgrowtharecommoninfinanciallysolventinsurersaswell.Barth(2002)reportsthatonequarterofallinsurersfailedIRISRatio5ChangeinNetWrittenPremiums,duringtheperiod19921996.3Historicalinsolvencyratesforinsurershoveraroundonepercent,however,whichismuchlower than the twentyfivepercentof insurers thatroutinely trigger theabnormalgrowthmeasureseachyear.

    The Impact of Growth on Reserve Estimation Errors

    Premiumgrowthcanbetheresultofaninfluxofnewcustomers,butcanalsoarisefrompriceincreasesontheexistingcustomerbase.Eithertypeofgrowth canaffect reserveerrors.Pricechangesalter themixofcustomersandmayresultinestimationerrorsbecausethepastincurredlossdevelopmenthistorymaynotaccuratelypredictthefutureincurredlossdevelopment.Aninfluxofnewcustomerswouldproducethesametypeofestimationerrors,buttheinfluxmayalsobetheresultofunderpricing.Theunderpricingmaybedeliberateor inadvertent.Deliberateunderpricing, also known as cash flowunderwriting,may result in adeliberateunderstatementofreservestoavoidregulatoryscrutiny.Inadvertentunderpricingmayleadtoreserveerrorsbecausethebusinessturnsout to have higher expected loss costs than anticipated in the pricingstructure.

    Currentregulatorysolvencymodelsdonotdistinguishbetweenthesetwodistinctsourcesofrisk(pricerelatedandexposurerelated).A.M.Best,ontheotherhand,usesexposuredatatocalculateexcessivegrowthinitsBestsCapitalAdequacyRatio(BCAR)model.PolicycountsfromtheA.M.BestSupplementalRatingQuestionnaireorotherexposurecountinformationfromtheinsurerisusedtocalculateoneyearandthreeyeargrowthrates, and growth in excess of the industry average generates capital

    3Althoughnotspecifically included in thisresearch, theauthorscalculationsshow thatasignificantnumberofinsurerscontinuetotriggerIRISRatio5,aswellastheexcessgrowthratechargeintheNAICsRBCformula.

  • EFFECTOFGROWTHONLOSSRESERVEERRORS 99

    charges.Ifexposurecountsarenotavailable,thengrowthinunaffiliatedgrosspremiumsisused(A.M.Best,2014).

    Notably, theBCAR calculation isbasedongrowth in excess of anindustryaverage,whiletheNAICsmodelisbasedongrowthinexcessofafixed10percent.

    Settingasideforamoment itseffectonreserving,pricegrowthcanactually enhance financial solvency and reduce an insurers insolvencyrisk.Theoretically,ifaninsurerdoubleditspricesacrosstheboardwhilemaintaining the same set of loss exposures, or even increasing its lossexposures,thehigherratespaidbyboththenewcustomersandtheexistingcustomerswould increase the insurers financialhealth.Surpluswouldincreasebecausetheinsurercollectsmorepremiumdollarstopayforthesamesetofclaims.

    If an insurerwere to double the number of loss exposureswhilemaintaining the sameprices, theeffecton the insurers financialhealthwoulddependonthedegreetowhichthebusinesswasfairlypriced.Ifthebusinesswereunderpriced,addingtwicethenumberofexposureswoulddrain surplus twice as fast.However, therewould be a salutary effectregardlessofthepricingbecauseoftheeffectonpredictabilityofultimateclaimscosts.Thelawoflargenumberssuggeststhatdoublingthenumberofexposureswouldreducethestatisticalvarianceoftheestimatedvalueoftheportfolioofclaims,evenifitwereunderpriced.

    Incompetitive insurancemarkets,an insurer shouldnotbeable todoublepriceswhileatthesametimemaintainingthesamesetofcustomers.4Changesinpricewouldcausesomeoftheexistingexposurestomovetootherinsurancecarrierswhilealsoaffectingtheinfluxofnewexposures.Dependingonthepriceelasticityoftheproduct,increasesinpricescouldleadtoreductionsinoverallpremiums,justasreductionsinpricecouldleadtoincreasesinoverallpremiumvolume.Theinsurersfinancialriskchangesbecausethemakeupofthebookofbusinesschanges,which inturnmakes it harder to forecast the future loss experience. Since thepremiumsforagivenblockofpoliciesmustbeestablishedinthepresentatanadequateleveltopayallfuturelossesassociatedwiththatblockofpolicies, anything thatmakes that forecasting processmore difficultincreasestheinsurersfinancialimpairmentrisk.

    Additionally, changes in themakeupof the insurersbasicbookofbusinessmakes itmore difficult to forecast the insurers ultimate lossexperience,whichwouldtendtoincreasethevariabilityofreserveestimationerrors.Additionally,theagingphenomenon(wherenewbusiness

    4CaliforniasStateCompensation InsuranceFund isoneof the exceptions to thisgeneralrule.

  • 100 BARTHANDECKLES

    hasatendency towardspoorerprofitability thanagedbusiness),wouldtend toexacerbate thevariabilityofreserveestimates.5Therefore,whilepriceincreases,bythemselves,mayactuallyreduceaninsurersinsolvencyrisk, the changes to the insurersbookofbusiness resulting frompriceincreasesmaymakeithardertoestimatereservesaccuratelysincethesepricechangesaffectthecustomermixinthebookofbusiness.Similarly,anincreaseinthenumberoflossexposuresinthebookofbusinessmayormaynotdirectlyalterhistoricallossreservedevelopmentpatterns,butmaysimplycausemoreinstability.

    Inaddition togreater instability in forecastingerrors, insurersmayalsodeliberatelymanipulatelossreserveestimatesforavarietyofotherreasons,suchastogarnertaxbenefits,

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