小编整理了“历年真题5：北美精算师（Course8IC）”，供考生参考，希望对大家有所帮助。
COURSE8I:Fall2004-1-GOONTONEXTPAGE
IndividualInsurance–Canada
MorningSession
**BEGINNINGOFEXAMINATION8**
INDIVIDUALINSURANCE–CANADA
MORNINGSESSION
1.(5points)ABCLifehasacareeragencydistributionsystem.ABC’smanagementis
reviewingtheirfinancingplanfornewagents.
(a)Describethedifferenttypesoffinancingplansfornewagentsandexplainthe
advantagesanddisadvantagesofeachaccordingtoLIMRA.
(b)Youaregiventhefollowinginformation:
YearAverage
AnnualizedFirst
YearPremium
Agent
Termination
Rate
SubsidyValidation
Schedule
Commission
1$60,00050%120%$20,000
2$80,00025%80%$25,000
3$100,00010%40%$30,000
4+$120,0000%0%$0
•Commissionsarepaidonannualizedfirstyearpremium.
•Agentterminationoccursattheendoftheyear.
•6%offirstyearpremiumispricedintoproductstocoveragentfinancing.
•Theinterestrateis0%.
(i)Calculatetheaveragefinancingcostforanewagentasapercentageof
firstyearpremiumforeachofthefirstthreeyears.Showallwork.
(ii)DeterminethenumberofyearsitwilltakeforABCtorecoverthe
financingcostson100newagents.Showallwork.
COURSE8I:Fall2004-2-GOONTONEXTPAGE
IndividualInsurance–Canada
MorningSession
2.(11points)XYZLifeisevaluatingablockofidenticalspeciallifecontingentannuities
issuedJanuary1,2004byABCLife.Youaregiven:
•Totalrequiredcapitalasapercentageofsolvencyreservesis5%.
•Assumedinvestmentinterestrateonrequiredcapitalis4%.
•Hurdlerateis15%.
•Eachannuitypaymentis$71,280.
•Paymentsaremadeattheendofeachyearduringtheannuitant’slifetime.
•Deathsoccurattheendoftheyearbeforetheannuitypayment.
•Notaxesormaintenanceexpenses.
ActualProjected
1/1/200412/31/200412/31/200512/31/2006
Policycount100755025
Solvencyreserves(‘000s)$9,864$5,011$1,697$0
Premium(‘000s)$10,000$0$0$0
Commission(‘000s)$400$0$0$0
Benefits(‘000s)$0$5,346$3,564$1,782
Investmentincomeon
solvencyreservesand
cashflows(‘000s)
$0$838$426$144
(a)(3points)WithrespecttoMinimumContinuingCapital&SurplusRequirements
forLifeInsurancecompaniesandeachofthefollowingrisks:
•Mortality
•Pricinginterestmargin
•Changeintheinterestrateenvironment.
(i)Describethenatureoftherisks.
(ii)CalculatetheminimumcapitalrequirementatDecember31,2004forthe
risks.Showallwork.
(b)(4points)CalculatetheembeddedvalueofthisblockatJanuary1,2004.Show
allwork.
COURSE8I:Fall2004-3-GOONTONEXTPAGE
IndividualInsurance–Canada
MorningSession
2.(Continued)
(c)(3points)Youaregiventhefollowingbinomialdistribution:
nqf(25)F(25)
1000.250.09180.5525
Calculatetheprobabilityofsolvencyearningsexceeding$250,000in2004.
Showallwork.
(d)(1point)OnJanuary1,2005,XYZLifebuystheremainingblockof75
contracts.
CalculatethemaximumamountofassetsABCtransferstoXYZassumingno
transactionexpenses.Showallwork.
COURSE8I:Fall2004-4-GOONTONEXTPAGE
IndividualInsurance–Canada
MorningSession
3.(12points)ABCLifeissellingadeferredvariableannuityproductthatprovidesfora
returnofpremiumdeathbenefit.ABCisconsideringalternativedeathbenefitdesigns.
(a)(3points)Listthesectorsincludedinanenvironmentalanalysisandevaluatethe
sectorsastheyrelatetovariableannuitydeathbenefits.
(b)(3points)Themarketingareawouldliketoaddanannualratchetdesign.
(i)Comparetheriskassociatedwiththeannualratchetdesigntootherpossible
deathbenefitdesigns.Explainyouranswer.
(ii)Describetechniquestomanagetherisksassociatedwithalternativedeath
benefitdesigns.
(c)(6points)Youaregiven:
AccountValueonvaluationdate$980.00
SeparateAccountValueonthevaluationdate$980.00
Netassetcharges1%
Valuationrate7%
Assumedyear1dropinAccountValue-14%
Assumedrecoveryrate14%
SurrenderchargesNone
HighestAnniversaryAccountValue$1,000.00
AverageAccountValueyear1$1,009.40
AverageAccountValueyear2$1,069.96
AccountValueattime1$1,038.80
AccountValueattime2$1,101.13
Mortalityrateforyear10.017
Mortalityrateforyear20.019
Survivalratefromtime0toendofyear10.983
Survivalratefromtime0toendofyear20.964
Calculatethestatutoryreservefortheannualratchetdeathbenefitattime0,1and
2usingthemethodologyprescribedintheValuationofLivingandDeathBenefit
GuaranteesforVariableAnnuitiesnote.Showallwork.
COURSE8I:Fall2004-5-GOONTONEXTPAGE
IndividualInsurance–Canada
MorningSession
4.(5points)
(a)Describetheadvantagesanddisadvantagesof:
(i)YRTreinsurance,and
(ii)Coinsurance.
(b)Youaregiventhefollowinginformationforaleveltermlifeinsuranceproduct:
TotalFaceAmount$100,000,000
FirstYearPremium$1,000,000
PolicyFeeNone
PremiumTax2%
FirstYearCommission50%offirstyearpremium
OtherFirstYearExpenses$750,000
SolvencyReserveatIssue$50,000
Assume:
•Premiumandreinsurancepremiumarepaidannuallyatthebeginningof
theyear.
•Unearnedportionofaone-yearterminsurancebenefitequals50%ofthe
YRTreinsurancepremium.
•Nofederalincometaxorrequiredcapital.
•Cededpercentageequals90%.
•YRTreinsurancepremiumrateequals0.20perthousandoffaceamount.
•Coinsurancereinsuranceallowanceequals90%.
Calculatetheestimatedfirstyearstrainatissuefor:
(i)YRTreinsurance,and
(ii)Coinsurance.
Showallwork.
COURSE8I:Fall2004-6-GOONTONEXTPAGE
IndividualInsurance–Canada
MorningSession
ThisquestionpertainstotheCaseStudy
5.(6points)YouareSaturnLife’sproductmanagementactuaryforthetermlifeinsurance
portfolio.Yourresponsibilitiesinclude:
•Monitoringtermlifenew-businesssalesandin-forceexperience,
•Advisingproductdevelopment,investmentandmarketingdepartmentsof
currentdevelopments,and
•Reportingproductprofitabilityandcapitalrequirementstosenior
management.
(a)(1point)Identifyanddescribethetypesofinternalproductmanagementreports.
(b)(5points)ExplainhoweachwouldbeusedtomanageSaturn’stermlife
business.
COURSE8I:Fall2004-7-GOONTONEXTPAGE
IndividualInsurance–Canada
MorningSession
6.(12points)XYZLifeisdevelopingadual-lifestatusflexiblepremiumjointandlast
survivoruniversallifeinsuranceproduct(SurvivorUL).
(a)(3points)ForpricingtheSurvivorULproduct:
(i)Describeapproachestoreflectthedual-lifestatusincludingtheadvantages
ordisadvantagesofeachapproach.
(ii)Explainotherfactorstobeconsideredindevelopingamortality
assumptionuniquetoalastsurvivorproduct.
(b)(3points)XYZLife’scurrentsingle-lifeULproductshaveexperienced
withdrawalratesof7%inpolicyyear1,gradingto5%bypolicyyear5.
(i)DescribeconsiderationsinsettingpersistencyassumptionsforSurvivor
UL.
(ii)Proposechangestothelapserateassumptiontoreflectpersistencyina
volatileinterestrateenvironment.
(c)(6points)ThefollowingstepsoutlineaproceduretodetermineminimumUL
reservesfordurationt.
ReviseoraddinformationtomakeeachstepconsistentwiththeCanadianAsset
LiabilityMethod.
StepProcedure
1Theamountofpolicyliabilitiesforascenarioequalstheamountof
supportingassetswhichtheactuarydeemsasareasonableallocation.In
forecastingthecashflow,theactuaryshouldtakeaccountallpolicyholder
expectations,andmakeprovisionforanyadversedeviationsthatthe
insurermayexperience.
2Thepolicyliabilitiesinrespectofarelevantpolicycompriseallofthat
policy’scashflowafterthedateofissueofarelevantpolicy.Policy
liabilitiesconsistofclaimliabilitiesincludingallbenefitandexpensecash
flows.
3Ifapplicableregulationrequirespolicyliabilitiestobevaluedwithout
takingaccountofthetimevalueofmoney,thentheactuaryshouldreport
avalueforthepolicyliabilitiesinaccordancewithacceptedactuarial
practice,andreportthisamountwithreservationonaccountofthe
regulation.
4Theactuary’sbestestimateofmortalityshouldincludetheeffectofany
anti-selection.Thelowmarginforadversedeviationisanadditionof
3.75tothemortalityrateper1000.Thehighmarginforadversedeviation
isanadditionof10tothemortalityrateper1000.
5Themarginsforadversedeviationforwithdrawalsareanadditionof
between5%and25%ofthebestestimatewithdrawalrates.
COURSE8I:Fall2004-8-STOP
IndividualInsurance–Canada
MorningSession
7.(5points)YourcompanyisdesigningaproductfortheLotteryCommission.Winners
haveachoicebetweenalumpsumpaymentandanequivalent25-yearperiodcertain
annuity.
(a)Describekeyconsiderationsindevelopingpricingassumptionsfortheannuity.
(b)Youareconsideringthefollowingproductdesignfeaturesfortheannuity:
•Surrenderprovision
•Medicalbailoutprovision
•Variablepayoutbasedoninvestmentresults
Describeadvantagesanddisadvantagesofincludingthesefeaturesintheproduct
design.
8.(4points)
(a)(3points)Describetheindicatorsbeingusedaspreferredriskcriteriaforlife
insuranceaccordingtotheReportoftheSocietyofActuariesTaskForceon
PreferredUnderwriting.
(b)(1point)Acompanywithasinglenon-smokerclasswouldliketointroducea
preferredclass.
Youaregiven:
•Maleage55aggregatemortalityis6.00perthousand.
•30%ofthenon-smokerclassisexpectedtoqualifyforthenewpreferred
class.
•A15%reductioninmortalityisexpectedforthenewpreferrednonsmoker
class.
Calculatetheexpectedmortalityrateforboththepreferrednon-smokerandthe
residualnon-smokerclasses.Showallwork.
**ENDOFEXAMINATION**
MORNINGSESSION
COURSE8I:Fall2004-9-GOONTONEXTPAGE
IndividualInsurance–Canada
AfternoonSession
**BEGINNINGOFEXAMINATION8**
INDIVIDUALINSURANCE–CANADA
AFTERNOONSESSION
BeginningWithQuestion9
9.(6points)ABCLifeoffersadisabilitypremiumwaiverbenefitridersoldwithlife
insuranceproducts.
(a)(5points)Explaintheassumptionsrequiredtocalculatetheexperiencepremiums
forthisrider.
(b)(1point)Youaregiventhefollowinginformationforanindividualinsured
age55:
•Levelannualpremiumwaivedis$100.
•Disabilityoccursatthemiddleofthepolicyyearwhentheinsuredisage55.
•Waiverbenefitsendatage60.
•Thereisa6-monthwaitingperiod,withcoverageretroactivetothedateof
disability.
•Premiumandbenefitpaymentsarepayablecontinuouslythroughoutthe
policyyear.
[1]1
x+k+2+s+211
22
i
xksD⎡⎣++⎤⎦++
11
22
i
xksD⎡⎣++⎤⎦++
[1]1
552+297.80100.16
[1]1
552+1293.1995.47
[1]1
552+2288.7290.94
[1]1
552+3284.3886.53
[1]1
552+4280.1882.27
[1]1
552+5276.0978.12
Calculatethepresentvalueofthenetbenefitattheendofthewaitingperiod.
Showallwork.
COURSE8I:Fall2004-10-GOONTONEXTPAGE
IndividualInsurance–Canada
AfternoonSession
10.(12points)Youaregiventhefollowingfeaturesforaproposedsingle-premiumequityindexed
annuityproduct:
IndexS&P500
IndexPeriod3years
IndexGrowthMethodPoint-to-Point
RatchetAnnual
ParticipationRate90%
Margin0.5%
Cap15%
Theparticipationrate,marginandcapfeaturesareappliedintheorder
listedabove.
TheproductprovidesaGuaranteedMinimumAccountValueof90%
ofthesinglepremium,accumulatedat3%annualinterestrate.
Youarealsogiventhefollowinginformation:
•Thenetearnedrateis5.5%.
•Themarketingareaestimatesitwillsell$100millioninsinglepremiuminthe
firstyear.
•Theannuityproductwillbemarketedprimarilythroughindependent
stockbrokers.
•Variableexpensesare4%ofthesinglepremium.
•Fixedexpensesare$1millionineachofthenext3years.
•Toimprovepolicyholderpersistency,themarketingareahasproposedaseries
ofdiscretionary“customerappreciationcampaigns”thatenhancethe
product’saccountvalues.Therevisedpresentvalueofindex-basedinterest
budgettosupportthesecampaignsisestimatedtoincreasefrom6%to9%.
COURSE8I:Fall2004-11-GOONTONEXTPAGE
IndividualInsurance–Canada
AfternoonSession
10.Continued
(a)(2points)YouaregiventhefollowingvaluesoftheS&P500index:
TimeS&P500
01000
11050
21250
31175
CalculatetheIndexAccountValueasapercentageofthesinglepremiumatthe
endoftheIndexPeriod.Showallwork.
(b)(5points)A100%increaseinthepresentvalueofindex-basedinterestbudget
generatesa150%increaseinthedemandfortheproduct,measuredindollarsof
singlepremiumsold.
(i)Describefactorsthataffectthepriceelasticityofdemand.
(ii)Determinethechangeinthepresentvalueofprofitsindollarsfrom
offeringtheproposedcampaignsandrecommendwhethertoproceed.
Showallwork.
(c)(5points)
(i)Explaintheconceptofpolicyholderreasonableexpectationswithrespect
toCanadianvaluationstandardsofpractice.
(ii)Assesstheimplicationstheproposedcustomerappreciationcampaigns
mayhaveonthevaluationofpolicyliabilitieswithrespecttopolicyholder
reasonableexpectations.
COURSE8I:Fall2004-12-GOONTONEXTPAGE
IndividualInsurance–Canada
AfternoonSession
11.(9points)Afinancialreviewofthetermportfoliorevealsalowerlevelofprofitability
fromthe5-yearleveltermproductthanoriginallyprojected.Youhavebeenaskedto
re-pricethe5-yearleveltermproductforyourbrokerageanddirectresponsedistribution
channels.
(a)Comparetheeffecteachofthesedistributionchannelshasonthefollowing
assumptions.
(i)Mortality
(ii)Lapse
(iii)Interest
(iv)Expense
(b)Describeelementsofcompensationusedforbrokeragedistribution.
(c)Thetermportfoliohasexperiencedlowerpolicypersistencythanexpected.
(i)Describethefactorsthataffectpersistency.
(ii)Recommendstepstoimprovepersistencyfortheproduct.
COURSE8I:Fall2004-13-GOONTONEXTPAGE
IndividualInsurance–Canada
AfternoonSession
12.(6points)XYZLifehasbeenexperiencingpoorsalesandalowerthanexpectedreturn
onequity(ROE)ontheirFixedPremiumIndividualUniversalLife(UL)product.The
followingtablesummarizestheassetsinXYZ’sportfolio:
AssetAmount
Cash$10,000
AAARatedBonds$0
AARatedBonds$0
ARatedBonds$1,000,000
BBRatedBonds$5,000,000
CommonStock$10,000,000
RealEstate$1,000,000
CommercialMortgages$5,000,000
ImpairedInvestments$0
Assume:
•CurrentMCCSRratiois150%.
•XYZLifeguaranteesa4%creditedrate.
•Overthepastfouryears,themarkethasshownasignificantreductiontoboth
shortandlongterminterestrates.
•Longtermyieldsongovernmentbondsarenowlessthan5%andareexpected
toremainlevel.
(a)(5points)XYZLifeisreviewingthesurpluspositionrelativetotheMCCSR
guidelinesforCanadianlifeinsurancecompanies.
(i)DefineeachoftheriskcomponentsthatareapplicabletoXYZLife’sUL
productaccordingtotheMCCSRguidelines.
(ii)Proposechangestotheassetportfolioandproductdesigntoreducethe
requiredsurplusofXYZLife.
(iii)ExplainhowyourproposedchangesimpacttheROEofXYZLife.
(b)(1point)Describetheimpactthedeclineininterestrateshashadonthe
prescribedinterestratescenariosusedbytheAppointedActuaryinsettingthe
interestrateassumption.
COURSE8I:Fall2004-14-GOONTONEXTPAGE
IndividualInsurance–Canada
AfternoonSession
Questions13and14pertaintotheCaseStudy.
13.(8points)ThevaluationactuaryatSaturnLifeisconcernedaboutthemortality
experienceofthetermportfolio.
(a)AssesstheeffectofSaturn’sconversion,re-underwritingandterminationoptions
ontherenewalARTmortalityassumption.
(b)YouaregiventhefollowingadditionalinformationforSaturn’s5-yearlevelterm
plan:
•Mortalityis90%ofthe1975-80UltimateTableintheabsenceofselective
lapsation
•qx+5,t−5equals80%ofqx,t
•Durationfivelapserateis20%
•75%ofdurationfivelapsesareassumedtobeselective
Calculatethedurationfivemortalityrateforafemaleage40usingthe
conservationofdeathsprinciple.Showallwork.
(c)Saturn’scurrenttermvaluationmortalityassumptionisasfollows:
•Bestestimateequals95%ofexpectedmortality
•Therearenoadjustmentsforanti-selectionatrenewal
•Marginforadversedeviationequals3.75/ex
Assesstheappropriatenessoftheseassumptionsandrecommendanychanges.
COURSE8I:Fall2004-15-GOONTONEXTPAGE
IndividualInsurance–Canada
AfternoonSession
Questions13and14pertaintotheCaseStudy.
14.(6points)YouhavebeenhiredbyMercuryLifetoevaluatetheirprimarymarkets.
(a)(1point)Describethecriteriainvolvedinevaluatingpotentialtargetmarkets.
(b)(5points)EvaluatethesuitabilityofeachofMercuryLife’sprimarymarketsas
targetmarkets.
15.(5points)XYZLifeplanstoentertheterminsurancemarket.
(a)Describethefiveelementsthatshouldbeincludedinthecomprehensivebusiness
analysis,aspresentedintheLOMAtext,todecidewhethertoentertheterm
insurancemarket.
(b)ExplainwhyXYZLifewouldusereinsurancetomanagethefinancialpositionof
itstermportfolio.
COURSE8I:Fall2004-16-STOP
IndividualInsurance–Canada
AfternoonSession
16.(8points)Youaregiventhefollowingannuitypayments:
PaymentDatePaymentatPaymentDate
January1,2006$50,000
July1,2006$60,000
January1,2007$55,000
July1,2007$70,000
January1,2008$60,000
July1,2008$80,000
(a)DescribetheModifiedDurationmethodofdurationmatchingincludingany
problemsassociatedwithit.
(b)CalculatetheModifiedDurationoftheannuitypaymentsasofJuly1,2005,
basedonaninterestrateof4%.Showallwork.
(c)DescribetheExactMatchingmethodofdurationmatchingincludingany
problemsassociatedwithit.
(d)Non-callablebondshavebeenpurchasedtoexactlymatchtheannuitypayments
asofJuly1,2005usingtheExactMatchingMethod.
Informationaboutthebondsisshowninthefollowingtable:
YearstoMaturityAnnualCouponRate
1.54.0%
2.04.5%
2.55.0%
3.05.5%
Bondshaveaparvalueof$100.
Couponsarepaidsemi-annually.
Determinethenumberofbondswithamaturityof2yearsthatwerepurchased.
Showallwork.
(e)DescribetheHorizonMatchingmethodanditsappropriatenessfortheannuity
payments.
**ENDOFEXAMINATION**
AFTERNOONSESSION
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