高顿项目
北美精算师考试SOA：真题系列Course8V（Part 4）
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2014-07-25
以下则是北美精算师考试SOA：真题系列Course8V（Part 4），烦请重视小编的辛勤劳作，我们很认真在制作。
15.(4points)Aone-stepbinomialtreeisusedtomodeltheimpactofanimportant
15.(4points)Aone-stepbinomialtreeisusedtomodeltheimpactofanimportant
announcementonthestockpriceofCompanyXYZ.Thereisa50%chancethatthe
announcementwillbepositiveforthecompany.TheCompanydoesnotpaydividends.
Currentstockprice=$20
Stockpriceaftergoodnews=$30
Stockpriceafterbadnews=$15
Timeperiod=3months
Risk-freerate(continuouscompounding)=5%
(a)Calculatethepriceofa3-monthcalloptionontheCompanystockwithstrike
priceequalto$22.
(b)Thecallwriterdecidestodynamicallydelta-gammahedgetheoptionbasedona
standardlognormalmodel.Evaluatetheeffectivenessofthisapproachinthis
context.
COURSE8:Fall2005-7-GOTONEXTPAGE
Investment
AfternoonSession
16.(8points)YouareconsultingtoaP&Ccompanyregardingthefairvalueoftheir
insuranceliabilities.Youareexaminingasingleone-yearpolicywithanuncertainclaim
paymentpayableattheendoftheyear.Youranalysisdeterminesthefollowing:
?Theexpectedclaimpaymentis$2,000.
?Theexpectedannualreturnoftheassetportfoliobackingtheliabilityis7%.
?Theone-yearrisk-freerateis5%.
?Thecompany’staxrateis35%.
?Theratioofequitytoliabilitiesforsimilarproductsinthemarketplaceis20%.
?Thereturnonequityforsimilarproductsinthemarketplaceis15%.
(a)Calculatethefairvalueoftheliabilityatthebeginningofthepolicyyearusing
thecost-of-capitalapproach.
(b)CalculatetheMarketValueMarginthatwillproducethesamefairvaluewhen
discountingattherisk-freerate.
(c)Identifytheassumptionsunderlyingperfectmarketsthatmaynotholdinthereal
worldwithrespecttoinsurancerisks.
(d)ListtworeasonswhyU.S.Treasurysecuritiesmaynotbeappropriateastheriskfree
rateforfairvaluation.
COURSE8:Fall2005-8-GOTONEXTPAGE
Investment
AfternoonSession
17.(7points)YouhavebeenaskedtoapplytheExcessSpreadapproachtoevaluatethe
staticcreditedrateresetstrategyandthedynamicresetstrategy.
(a)DefineExcessSpreadandRequiredSpreadonAssets(RSA).
(b)ListtherisksassociatedwithanSPDApolicy.
(c)ListthestepswhenmeasuringinterestrateriskwiththeExcessSpreadapproach.
(d)CalculatetheExcessSpreadsofthefollowingtwostrategies:
?Thestaticcreditedrateresetstrategy:
RSA=80bp
Spreadonassetsis150bp,creditriskis5bp,andexpenseis15bp.
?Thedynamicresetstrategy:
RSA=70bp
Spreadonassetsis160bp,creditriskis10bp,andexpenseis20bp.
(e)AppraisetheuseofeachofthetwostrategiesforsettingtheSPDAcreditedrates.
COURSE8:Fall2005-9-GOTONEXTPAGE
Investment
AfternoonSession
18.(4points)Youareperforminganactuarialvaluationofadefinedbenefitpensionplan.
Yourresultsareshowingtheplantobeunder-funded,withafundingratioof70%.The
plansponsorwishestofindanassetportfoliousingthesurplusfrontierapproachthatwill
correcttheproblem.
Youaregiventhefollowing:
?Liabilitybeta=0.8
?Risk-freerate=4.0%
?Marketportfolioexcessreturnoverrisk-freerate=8%
?Alpha=0
(a)ExplaintheMinimumSurplusVariancePortfolio.
(b)Computetheminimumassetbetarequiredtogiveapositivesurplusreturn.
(c)Assesstheappropriatenessofthisstrategy.
COURSE8:Fall2005-10-GOTONEXTPAGE
Investment
AfternoonSession
19.(7points)Youworkforapubliclytradedcompanywithadefined-benefitpensionplan.
YourCFOreadrecentlythatshiftingpensionassetsfromstocksto100%bondsreduces
risk,andcreatesataxarbitrage,resultingingainstoshareholders.Youaregiventhe
following:
Currentpensionassets=$10,000,000
Currentpensionliabilities=$10,000,000
Currentpensionassetallocation:60%stocks,40%bonds
Corporatetaxrate=35%
Personaltaxrateonstocks=18%
Personaltaxrateonbonds=28%
Estimatedstockreturn=11%
Estimatedbondreturn=7%
(a)ComparetheTepperarbitrageandtheBlackarbitrage.
(b)Computethetheoreticalshareholdergainusingbothmethods.
(c)OutlinethechallengesandargumentsyourCFOmayfaceinmovingto100%
bonds.
COURSE8:Fall2005-11-STOP
Investment
AfternoonSession
20.(3points)AstheCFOofyourlifeinsurancecompany,youhavebeenaskedtoprovidea
singlemeasureofriskassociatedwithaportfolioofwholelifeinsuranceproducts.
Thecurrentvalueoftheportfoliois$61,125,856.Mostofthevalueoftheportfoliocan
beexplainedbyasetofmonthlyobservableindependentvariables.
The95%confidencelevelofVaRfortheportfoliovalueoveratwo-yeartimehorizonis
$30,170,914.
Critiquethisapproachasameasureofportfoliorisk.
**ENDOFEXAMINATION**
AFTERNOONSESSION
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