以下是历年SOA真题之北美精算师——May2005Course6（1），烦请各位珍惜美好的学习时光，且背且珍惜哦。
　　Course6:Spring2005-1-GOONTONEXTPAGE
　　MorningSession
　　COURSE6
　　MORNINGSESSION
　　SECTIONA–WRITTENANSWER
 
　　Course6:Spring2005-2-GOONTONEXTPAGE
　　MorningSession
　　**BEGINNINGOFEXAMINATION**
　　MORNINGSESSION
　　1.(5points)Yourcompanyis*uatingactiveandquasi-passiveinvestmentstrategiesfor
　　bondportfoliomanagement.
　　(a)Defineeachquasi-passiveindexationapproach.
　　(b)Describetheadvantagesanddisadvantagesofeachquasi-passiveindexation
　　approach.
　　(c)Explainthereasonsyourcompanywouldconsideranactiveinvestmentstrategy.
　　(d)Describethesectorandsecuritystrategiesthatanactiveinvestmentmanager
　　wouldusetoselectindividualbonds.
　　2.(7points)Yourcompanyisofferinga15-yearterm-certainimmediateannuitywith
　　paymentslinkedtotheCPI.Policyholderscanwithdrawfundsondemandatmarket
　　values.
　　Theuniverseofavailableinvestmentsconsistsofthefollowing:
　　?Short-termT-bills
　　?Realreturnpublicbonds
　　?Corporatebonds
　　?Realestate
　　(a)Outlinetheadvantagesanddisadvantagesofeachinvestmentforbackingthis
　　annuity.
　　(b)Recommendaninvestmentstrategyusingtheinvestmentsavailable.
　　(c)Describethemajorcomponentsofanaccumulatedcashflowscenario-based
　　model.
　　(d)Outlinethemajorcomponentsoftheinvestmentpolicystatementforthisproduct.
 
　　Course6:Spring2005-3-GOONTONEXTPAGE
　　MorningSession
　　3.(5points)Youaregiventhefollowinginformation:
　　BondTermEffectiveDurationEffectiveConvexity
　　A53.1-41.7
　　B54.523.4
　　C54.221.3
　　D52.764.5
　　TheoptionandpricecharacteristicsofBondsA,B,CandDareasfollows:
　　?onebondisoption-freewithacurrentpriceabovepar
　　?onebondisoption-freewithacurrentpricebelowpar
　　?onebondiscallable,pricedatpar
　　?onebondisputable,pricedatpar
　　(a)DeterminetheoptionandpricecharacteristicscorrespondingtoeachofBondsA,
　　B,CandD.Explainyouranswer.
　　(b)Assessthelimitationsofdurationasaninterestrateriskmeasure.
　　(c)Defineconvexity.Compareeffectiveconvexityandmodifiedconvexity.
　　(d)CalculatetheapproximatepercentagepricechangeforBondsAandBassuminga
　　decreaseinyieldof0.50%.
　　Showallwork.
 
　　Course6:Spring2005-4-GOONTONEXTPAGE
　　MorningSession
　　4.(10points)Youaregiventhefollowingwithrespecttotreasurysecuritiesasoftoday,
　　May13,2005:
　　SecurityYearstoMaturity
　　AnnualCouponRate
　　PaidSemi-annuallyYield-to-maturity
　　A0.50%3.0%
　　B1.00%3.2%
　　C1.56%3.5%
　　D2.05%3.6%
　　(a)Calculatethespotrateforeachmaturitydate.
　　(b)Explainhowarbitrageprofitscouldbemadefromcouponstripping.
　　(c)Calculatetheone-yearforwardrate,oneyearfromtoday.
　　(d)Withrespecttothepureexpectationstheory
　　(i)Describethetheory
　　(ii)Describetheinterpretationsofthetheorythathavebeenputforthby
　　economists
　　(iii)Explaintheshortcomingsofthetheory
　　(e)Withrespecttoothertheoriesoftermstructureofinterestrates:
　　(i)Brieflydescribeeachtheory
　　(ii)Usingeachtheory,comparetheone-yearspotonMay13,2006,withthe
　　one-yearforwardratecalculatedin(c)
　　Showallwork.
 
　　Course6:Spring2005-5-GOONTONEXTPAGE
　　MorningSession
　　5.(5points)YouaregiventhefollowinginformationwithrespecttoStockXYZ:
　　?price:50
　　?variance:4%
　　?dividendrate:0%
　　Therisk-freeratecompoundedcontinuouslyis6%.
　　YouarealsogiventhefollowingselectedvaluesfromtheStandardNormalCumulative
　　DistributionFunction:
　　ZN(Z)ZN(Z)ZN(Z)
　　.010.5040.110.5438.210.5832
　　.020.5080.120.5478.220.5871
　　.030.5120.130.5517.230.5910
　　.040.5160.140.5557.240.5948
　　.050.5199.150.5596.250.5987
　　.060.5239.160.5636.260.6026
　　.070.5279.170.5675.270.6064
　　.080.5319.180.5714.280.6103
　　.090.5359.190.5753.290.6141
　　.100.5398.200.5793.300.6179
　　(a)Listtheassumptionsrequiredforput-callparity.
　　(b)UsetheBlack-Scholesformulatocalculatethepriceofaone-yearEuropeancall
　　optiononStockXYZwithastrikepriceof52.
　　(c)Calculatethepriceofaone-yearEuropeanputoptiononStockXYZwithastrike
　　priceof52.
　　Showallwork.
 
　　Course6:Spring2005-6-GOONTONEXTPAGE
　　MorningSession
　　6.(6points)Youaregiventhefollowingwithrespecttoaportfolioofbonds:
　　Bond
　　Annual
　　CouponPar
　　Market
　　Value
　　Option
　　Features
　　Yearsto
　　Maturity
　　A4.50%100100none2
　　B6.00%100
　　callableinone
　　yearat1012
　　Youaregiventhefollowingwithrespecttoabinomiallattice:
　　?rL:4%
　　?σ:15%
　　?timeintervalbetweennodes:1year
　　(a)Calculatetheone-yearspotrate.
　　(b)Calculatethetwo-yearspotrate.
　　(c)Calculatetheone-yearimpliedforwardrate.
　　(d)Calculateth*ueoftheoptioninBondB.
　　Showallwork.
　　高顿网校之精品语录珍藏：梦想无论怎样模糊，总潜伏在我们心底，使我们的心境永远得不到宁静，直到这些梦想成为事实。——林语堂