《債券市場：分析與策略（第七版）》Ch25

Chapter25

Liability-DrivenStrategies

25-1Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHall25-2LearningObjectivesAfterreadingthischapter,youwillunderstandthetypesofliabilitiesthataninstitutionmayfacethetwoimportantdimensionsofaliability:theamountandtimingofthepaymentwhythesamefactorsthataffecttheriskoffinancialassetsalsoaffectliabilitiesthegoalsofasset/liabilitymanagementthedifferencebetweenaninstitution’saccountingsurplus,regulatorysurplus,andeconomicsurplushowassetsarehandledforaccountingpurposeshowtousethedurationofassetsandliabilitiestocalculatethesensitivityoftheeconomicsurplusofaninstitutionwheninterestrateschangewhataliability-drivenstrategyistherisksassociatedwithmismatchingportfolioassetsandliabilitieswhatimmunizingaportfolioisCopyright?2010PearsonEducation,Inc.PublishingasPrenticeHallLearningObjectives(continued)Afterreadingthischapter,youwillunderstandthebasicprinciplesofanimmunizationstrategyandtheroleofdurationinanimmunizationstrategytherisksassociatedwithimmunizingaportfoliowhatacontingentimmunizationstrategyisandthekeyfactorsinimplementingsuchastrategythetwoliability-drivenstrategieswhentherearemultipleliabilities:multiperiodliabilityimmunizationandcashflowmatchingtheadvantagesanddisadvantagesofamultipleliabilityimmunizationstrategyversusacashflowmatchingstrategyhowliabilityfundingstrategiescanbeextendedtocasesinwhichtheliabilitiesarenotknownwithcertaintywhatanactive/immunizationcombinationstrategyisliability-drivenstrategiesfordefinedbenefitpensionplans25-3Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallGeneralPrinciplesofAsset/LiabilityManagementClassificationofLiabilitiesAliability

isacashoutlaythatmustbemadeataspecifictimetosatisfythecontractualtermsofanissuedobligation.Aninstitutionalinvestorisconcernedwithboththeamountandtimingofliabilities,becauseitsassetsmustproducethecashtomeetanypaymentsithaspromisedtomakeinatimelyway.Infact,liabilitiesareclassifiedaccordingtothedegreeofcertaintyoftheiramountandtiming,asshowninExhibit25-1(seeOverhead25-5).Theclassificationassumesthattheholderoftheobligationwillnotcancelitpriortoanactualorprojectedpayoutdate.25-4Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit25-1ClassificationofLiabilitiesofInstitutionalInvestorsLiabilityTypeAmountofCashOutlayTimingofCashOutlayIKnownKnownIKnownUncertainIIIUncertainKnownIVUncertainUncertain25-5Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallGeneralPrinciplesofAsset/LiabilityManagement(continued)ClassificationofLiabilitiesThedescriptionsofcashoutlaysaseitherknownoruncertainareundoubtedlybroad.Whenwerefertoacashoutlayasbeinguncertain,wedonotmeanthatitcannotbepredicted.Therearesomeliabilitiesforwhich“l(fā)awoflargenumbers”makesiteasiertopredictthetimingand/oramountofcashoutlays.Thisworkistypicallydonebyactuaries,butevenactuarieshavedifficultypredictingnaturalcatastrophes,suchasfloodsandearthquakes.Justlikeassets,therearerisksassociatedwithliabilitiesandsomeoftheserisksareaffectedbythesamefactorsthataffectassetrisks.25-6Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallGeneralPrinciplesofAsset/LiabilityManagement(continued)TypeILiabilityAtypeIliabilityisoneforwhichboththeamountandtimingoftheliabilitiesareknownwithcertainty.TypeIliabilities,however,arenotlimitedtodepositoryinstitutions.Amajorproductsoldbylifeinsurancecompaniesisaguaranteedinvestmentcontract(GIC).TypeIILiabilityAtypeIIliabilityisoneforwhichtheamountofcashoutlayisknownbutthetimingofthecashoutlayisuncertain.ThemostobviousexampleofatypeIIliabilityisalifeinsurancepolicy.25-7Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallGeneralPrinciplesofAsset/LiabilityManagement(continued)TypeIIILiabilityAtypeIIIliabilityisoneforwhichthetimingofthecashoutlayisknownbuttheamountisuncertain.Atwo-yearfloating-rateCDinwhichtheinterestrateresetsquarterlybasedonamarketinterestrateisanexample.TypeIVLiabilityAtypeIVliabilityisoneinwhichthereisuncertaintyastoboththeamountandtimingofthecashoutlay.Probablythemostobviousexamplesareinsurancepoliciesissuedbypropertyandcasualtyinsurancecompanies.25-8Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallGeneralPrinciplesofAsset/LiabilityManagement(continued)LiquidityConcernsBecauseofuncertaintyaboutthetimingand/ortheamountofthecashoutlays,aninstitutionmustbepreparedtohavesufficientcashtosatisfyitsobligations.Alsokeepinmindthattheentitythatholdstheobligationagainsttheinstitutionmayhavetherighttochangethenatureoftheobligation,perhapsincurringapenalty.Inadditiontouncertaintyaboutthetimingandamountofthecashoutlaysandthepotentialforthedepositororpolicyholdertowithdrawcashearlyorborrowagainstapolicy,aninstitutionhastobeconcernedwithpossiblereductionincashinflows.Inthecaseofadepositoryinstitution,thismeanstheinabilitytoobtaindeposits.25-9Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallGeneralPrinciplesofAsset/LiabilityManagement(continued)SurplusManagementThetwogoalsofafinancialinstitutionaretoearnanadequatereturnonfundsinvested,andtomaintainacomfortablesurplusofassetsbeyondliabilities.Thetaskofmanagingfundsofafinancialinstitutiontoaccomplishthesegoalsisreferredtoasasset/liabilitymanagementorsurplusmanagement.Institutionsmaycalculatethreetypesofsurpluses:economic,accounting,andregulatory.Themethodofvaluingassetsandliabilitiesgreatlyaffectstheapparenthealthofafinancialinstitution.Unrealisticvaluation,althoughallowableunderaccountingproceduresandregulations,isnotsoundinvestmentpractice.25-10Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallGeneralPrinciplesofAsset/LiabilityManagement(continued)SurplusManagementTheeconomicsurplusofanyentityisthedifferencebetweenthemarketvalueofallitsassetsandthemarketvalueofitsliabilities;thatis,theeconomicsurpluscanbeexpressedas

economicsurplus=marketvalueofassets–presentvalueofliabilitiesIfinterestratesrise,boththeassetsandliabilitiesdecline,sotheeconomicsurpluscanincrease,decrease,ornotchange.Ifthedurationoftheassetsisgreaterthanthedurationoftheliabilities,theeconomicsurpluswillincreaseifinterestratesfall.Theneteffectonthesurplusdependsonthedurationorinterest-ratesensitivityoftheassetsandliabilities,soitisimperativethatportfoliomanagersbeabletomeasurethissensitivityforallassetsandliabilitiesaccurately.25-11Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallGeneralPrinciplesofAsset/LiabilityManagement(continued)SurplusManagementAccountingsurplusissurplusofassetsoverliabilitiesasreportedinfinancialstatementsbasedongenerallyacceptedaccountingprinciples(GAAP)accounting.Institutionalinvestorsmustprepareperiodicfinancialstatementsthatincludethereportingofassetsandliabilities.Withrespecttothefinancialreportingofassets,therearethreepossiblemethodsforreporting:amortizedcostorhistoricalcost,marketvalue,orthelowerofcostormarketvalue.FASB115specifieswhichofthesethreemethodsmustbefollowedforassets.Specifically,theaccountingtreatmentrequiredforasecuritydependsonhowthesecurityisclassified.25-12Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallGeneralPrinciplesofAsset/LiabilityManagement(continued)SurplusManagementTherearethreeclassificationsofinvestmentaccounts:heldtomaturity,availableforsale,andtrading.Theheld-to-maturityaccountincludesassetsthattheinstitutionplanstoholduntiltheymature.Anassetisclassifiedasintheavailable-for-saleaccountiftheinstitutiondoesnothavetheabilitytoholdtheassettomaturityorintendstosellit.Anassetthatisacquiredforthepurposeofearningashort-termtradingprofitfrommarketmovementsisclassifiedinthetradingaccount.Forallassetsintheavailable-for-saleandtradingaccounts,marketvalueaccountingisused.25-13Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallGeneralPrinciplesofAsset/LiabilityManagement(continued)SurplusManagementUnderFASB115,theaccountingtreatmentforanyunrealizedgainorlossdependsontheaccountinwhichtheassetisclassified.Specifically,anyunrealizedgainorlossisignoredforassetsintheheld-to-maturityaccount.Thus,forassetsinthisaccountthereisnoaffectonreportedearningsortheaccountingsurplus.Fortheothertwoaccounts,anyunrealizedgainorlossaffectstheaccountingsurplusasdescribedpreviously;however,thereisadifferenceastohowreportedearningsareaffected.Forassetsclassifiedintheavailable-for-saleaccount,unrealizedgainsorlossesarenotincludedinreportedearnings;incontrast,forassetsclassifiedinthetradingaccount,anygainsorlossesareincludedinreportedearnings.Exhibit25-2(seeOverhead25-15)summarizestheaccountingtreatmentofassetsassetforthbyFASB115.25-14Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit25-2SummaryofKeyProvisionsofFASB115AccountClassificationAccountingMethodforAssetsWillAffectSurplusWillAffectReportedEarningsHeldtomaturityHeldtomaturityNoNoHeldtomaturityHeldtomaturityYesNoHeldtomaturityHeldtomaturityYesYes25-15Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiabilityAnimmunizationstrategyreferstotheinvestmentoftheassetsinsuchawaythattheexistingbusinessisimmunetoageneralchangeintherateofinterest.SupposethatalifeinsurancecompanysellsaGICthatguaranteesaninterestrateof6.25%everysixmonths(12.5%onabond-equivalentyieldbasis)for5.5years(11six-monthperiods).Alsosupposethatthepaymentmadebythepolicyholderis$8,820,262.Then,thevaluethatthelifeinsurancecompanyhasguaranteedthepolicyholder5.5yearsfromnowis$8,820,2621(1.06252)11=$17,183,033Wheninvestingthe$8,820,262,thetargetaccumulatedvaluefortheportfoliomanagerofthelifeinsurancecompanyis$17,183,033after5.5years,whichisthesameasatargetyieldof12.5%onabond-equivalentbasis.25-16Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability(continued)Supposethattheportfoliomanagerbuys$8,820,262parvalueofabondsellingatparwitha12.5%yieldtomaturitythatmaturesin5.5years.Willtheportfoliomanagerbeassuredofrealizingthetargetyieldof12.5%or,equivalently,atargetaccumulatedvalueof$17,183,033?AsweexplainedinChapter3,theportfoliomanagerwillrealizea12.5%yieldonlyifthecouponinterestpaymentscanbereinvestedat6.25%everysixmonths.Thatis,theaccumulatedvaluewilldependonthereinvestmentrate.Todemonstratethis,wewillsupposethatimmediatelyafterinvestingthe$8,820,262inthe12.5%coupon5.5-yearmaturitybond,yieldsinthemarketchangeandstayatthenewlevelfortheremainderofthe5.5years.Exhibit25-3illustrateswhathappensattheendof5.5years.(SeetruncatedversionofExhibit25-3inOverhead25-18.)25-17Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit25-3AccumulatedValueandTotalReturnAfter5.5Years:5.5-Year12.5%BondSellingtoYield12.5%

Investmenthorizon(years):5.5;Couponrate:0.125;Maturity(years):5.5;Yieldtomaturity:0.125;Price:100;Parvaluepurchased:$8,820,262;Purchaseprice:$8,820,262;Targetaccumulatedvalue:$17,183,033After5.5yearsNewYieldaCouponInterestInterestonInterestPriceofBondbAccumulatedValueTotalReturn0.160$6,063,930$3,112,167$8,820,262$17,996,3600.13400.1556,063,9302,990,7168,820,26217,874,9080.13260.1456,063,9302,753,1778,820,26217,637,3690.13000.1406,063,9302,647,0378,820,26217,521,2300.1288….….….….….….0.0656,063,9301,088,0038,820,26215,972,1950.11090.0606,063,930996,5778,820,26215,880,7690.10980.0556,063,930906,5118,820,26215,790,7030.10870.0506,063,930817,7858,820,26215,701,9770.1077aImmediatechangeinyield.bMaturityvalue.25-18Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability(continued)Supposethatinsteadofinvestinginabondmaturingin5.5yearstheportfoliomanagerinvestsina15-yearbondwithacouponrateof12.5%thatissellingatpartoyield12.5%.Exhibit25-4presentstheaccumulatedvalueandtotalreturnifthemarketyieldchangesimmediatelyafterthebondispurchasedandremainsatthenewyieldlevel.(SeetruncatedversionofExhibit25-4inOverhead25-20.)Thefourthcolumnofthetableisthemarketpriceofa12.5%coupon9.5-yearbond(because5.5yearshavepassed),assumingthemarketyieldsshowninthefirstcolumn.Ifthemarketyieldincreases,theportfoliowillfailtoachievethetargetaccumulatedvalue;theoppositewillbetrueifthemarketyielddecreases:Theaccumulatedvalue(totalreturn)willexceedthetargetaccumulatedvalue(targetyield).25-19Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit25-4AccumulatedValueandTotalReturnAfter5.5Years:15-Year12.5%BondSellingtoYield12.5%

Investmenthorizon(years):5.5;Couponrate:0.125;Maturity(years):15;Yieldtomaturity:0.125;Price:100;Parvaluepurchased:$8,820,262;Purchaseprice:$8,820,262;Targetaccumulatedvalue:$17,183,033After5.5yearsNewYield

aCouponInterestInterestonInterestPriceofBondAccumulatedValueTotalReturn0.160$6,063,930$3,112,167$7,337,902$16,513,9990.11730.1556,063,9302,990,7167,526,48816,581,1340.11810.1456,063,9302,753,1777,925,48116,742,5880.12000.1406,063,9302,637,0378,136,54216,837,5090.1211….….….….….….0.0656,063,9301,088,00312,527,91419,679,8470.15140.0606,063,930996,57712,926,30119,986,8080.15440.0556,063,930906,51113,341,61720,312,0580.15760.0506,063,930817,78513,774,67720,656,3920.1609aImmediatechangeinyield.25-20Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability(continued)Exhibit25-5summarizesthechangeininterestoninterestandthechangeinpriceresultingfromachangeinthemarketyield.(SeetruncatedversionofExhibit25-5inOverhead25-22.)Forexample,ifthemarketyieldrisesinstantaneouslyby200basispoints,from12.5%to14.5%,interestoninterestwillbe$454,336greater;however,themarketpriceofthebondwilldecreaseby$894,781.Theneteffectisthattheaccumulatedvaluewillbe$440,445lessthanthetargetaccumulatedvalue.Thereversewillbetrueifthemarketyielddecreases.Thechangeinthepriceofthebondwillmorethanoffsetthedeclineintheinterestoninterest,resultinginanaccumulatedvaluethatexceedsthetargetaccumulatedvalue.25-21Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit25-5ChangeinInterestonInterestandPriceDuetoInterestRateChangeAfter5.5Years:15-Year12.5%BondSellingtoYield12.5%

NewYieldChangeinInterestonInterestChangeinPriceTotalChangeinAccumulatedValue0.160$746,911–$676,024$70,8870.155635,377–583,31452,0630.145417,235–394,11223,1230.140310,580–297,57913,0010.135205,504–199,7305,7740.130101,985–100,5441,4410.1250000.120–100,473101,9251,452….….….….0.060–1,195,9211,441,399245,4780.055–1,278,6321,563,494284,8620.050–1,360,1121,687,328327,21625-22Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability(continued)Exhibit25-6showstheaccumulatedvalueandtotalreturnoverthe5.5-yearinvestmenthorizon.(SeetruncatedversionofExhibit25-6inOverhead25-24.)Thesecondcolumnshowstheaccumulatedvalueaftersixmonths.Thethirdcolumnshowsthevaluethatisaccumulatedafter5.5yearsbyreinvestingthevalueaccumulatedaftersixmonthsattheyieldshowninthefirstcolumn.Byinvestinginthissix-monthbond,theportfoliomanagerincursnointerest-raterisk,althoughthereisreinvestmentrisk.Thetargetaccumulatedvaluewillbeachievedonlyifthemarketyieldremainsat12.5%orrises.Onceagain,theportfoliomanagerisnotassuredofachievingthetargetaccumulatedvalue.25-23Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit25-6AccumulatedValueandTotalReturn:Six-Month,12.5%BondSellingtoYield12.5%

Investmenthorizon(years):5.5;Couponrate:0.125;Maturity(years):0.5;Yieldtomaturity:0.125;Price:100;Parvaluepurchased:$8,820,262;Purchaseprice:$8,820,262;Targetaccumulatedvalue:$17,183,033After5.5yearsNewYieldaAfterSixMonthsAccumulatedValueTotalReturn0.160$6,063,930$3,112,167$8,820,2620.1556,063,9302,990,7168,820,2620.1456,063,9302,753,1778,820,2620.1406,063,9302,647,0378,820,262….….….….0.0656,063,9301,088,0038,820,2620.0606,063,930996,5778,820,2620.0556,063,930906,5118,820,2620.0506,063,930817,7858,820,262aImmediatechangeinyield.25-24Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability

(continued)Consider,aneight-year10.125%couponbondsellingat88.20262toyield12.5%.Supposethat$10,000,000ofparvalueofthisbondispurchasedfor$8,820,262.Exhibit25-7providesthesameinformationforthisbondasExhibits25-3and25-4didforthepreviousbonds.(SeetruncatedversionofExhibit25-7inOverhead25-26.)Lookingatthelasttwocolumns,weseethattheaccumulatedvalueandthetotalreturnareneverlessthanthetargetaccumulatedvalueandthetargetyield.Thus,thetargetaccumulatedvalueisassuredregardlessofwhathappenstothemarketyield.Exhibit25-8showswhy.(SeetruncatedversionofExhibit25-8inOverhead25-27.)Whenthemarketyieldrises,thechangeintheinterestoninterestmorethanoffsetsthedeclineinprice.Whenthemarketyielddeclines,theincreaseinpriceexceedsthedeclineininterestoninterest.25-25Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit25-7AccumulatedValueandTotalReturn:Eight-Year10.125%BondSellingtoYield12.5%

Investmenthorizon(years):5.5;Couponrate:0.10125;Maturity(years):8;Yieldtomaturity:0.125;Price:88.20262;Parvaluepurchased:$10,000,000;Purchaseprice:$8,820,262;Targetaccumulatedvalue:$17,183,033After5.5yearsNewYield

aCouponInterestInterestonInterestPriceofBondAccumulatedValueTotalReturn0.160$5,568,750$2,858,028$8,827,141$17,253,9190.12580.1555,568,7502,746,4948,919,85217,235,0960.12560.1455,568,7502,528,3529,109,05417,206,1560.12530.1405,568,7502,421,6979,205,58717,196,0340.1251….….….….….….0.0655,568,750999,15610,824,18017,392,0860.12730.0605,568,750915,19710,944,56517,428,5120.12770.0555,568,750832,48611,066,66017,467,8960.12820.0505,568,750751,00511,190,49417,510,2490.1268aImmediatechangeinyield.25-26Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit25-8ChangeinInterestonInterestandPriceDuetoInterestRateChangeAfter5.5Years:Eight-Year10.125%BondSellingtoYield12.5%

NewYieldChangeinInterestonInterestChangeinPriceTotalChangeinAccumulatedValue0.160$746,911–$676,024$70,8870.155635,377–583,31452,0630.145417,235–394,11223,1230.140310,580–297,57913,0010.135205,504–199,7305,7740.130101,985–100,5441,4410.1250000.120–100,473101,9251,452….….….….0.060–1,195,9211,441,399245,4780.055–1,278,6321,563,494284,8620.050–1,360,1121,687,328327,21625-27Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability

(continued)Let’slookatthecharacteristicofthisbondthatseemstoassurethatthetargetaccumulatedvaluewillberealizedregardlessofhowthemarketyieldchanges.ThedurationforeachofthefourbondswehaveconsideredisshowninExhibit25-9(seeOverhead25-29).Becausethebondsinourillustrationareallassumedtobeoption-freebonds,modifiedduration(insteadofeffectiveduration)isused.However,whenportfoliosincludesecuritieswithembeddedoptions,theneffectivedurationisused.Formostinstitutionalportfolios,thiswilltypicallybeeffectiveduration.25-28Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallExhibit25-9ModifiedDurationsofSelectedBondsBondModifiedDuration5.5-year12.5%coupon,sellingatpar3.9015-year12.5%coupon,sellingatpar6.706-month12.5%coupon,sellingatpar0.488-year10.125%coupon,sellingfor88.202625.1825-29Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability

(continued)Theequalityofthedurationoftheassetandthedurationoftheliabilityisthekeytoimmunization.Generalizingthisobservationtobondportfoliosfromindividualbonds,thekeyis:Toimmunizeaportfolio’stargetaccumulatedvalue(targetyield),aportfoliomanagermustconstructabondportfoliosuchthatthedurationoftheportfolioisequaltothedurationoftheliabilitythepresentvalueofthecashflowfromtheportfolioequalstothepresentvalueofthefutureliability.25-30Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability(continued)RebalancinganImmunizedPortfolioTheprinciplesunderlyingimmunizationneednotjustassumeaone-timeinstantaneouschangeinthemarketyield.Eveninthefaceofchangingmarketyields,aportfoliocanbeimmunizedifitisrebalancedperiodicallysothatitsdurationisequaltothedurationoftheliability’sremainingtime.Ontheonehand,themorefrequentrebalancingincreasestransactionscosts,therebyreducingthelikelihoodofachievingthetargetyield.Ontheotherhand,lessfrequentrebalancingwillresultinthedurationwanderingfromthetargetduration,whichwillalsoreducethelikelihoodofachievingthetargetyield.25-31Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability

(continued)ImmunizationRiskThesufficientconditionfortheimmunizationofasingleliabilityisthatthedurationoftheportfoliobeequaltothedurationoftheliability.However,aportfoliowillbeimmunizedagainstinterest-ratechangesonlyiftheyieldcurveisflatandanychangesintheyieldcurveareparallelchanges(i.e.,interestratesmoveeitherupordownbythesamenumberofbasispointsforallmaturities).Immunizationriskistheriskofreinvestment.Theportfoliothathastheleastreinvestmentriskwillhavetheleastimmunizationrisk.Whenthereisahighdispersionofcashflowsaroundtheliabilityduedate,theportfolioisexposedtohighreinvestmentrisk.Whenthecashflowsareconcentratedaroundtheliabilityduedate,asinthecaseofthebulletportfolio,theportfolioissubjecttolowreinvestmentrisk.25-32Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability

(continued)ImmunizationRiskResearchershavedevelopedameasureofimmunizationrisk,whichdemonstratesthatiftheyieldcurveshiftsinanyarbitraryway,therelativechangeintheportfoliovaluewilldependontheproductoftwoterms.Thefirsttermdependssolelyonthecharacteristicsoftheinvestmentportfolio.Thesecondtermisafunctionofinterest-ratemovementonly.Thesecondtermcharacterizesthenatureofthechangeintheshapeoftheyieldcurve.Becausethatchangewillbeimpossibletopredictapriori,itisnotpossibletocontrolforit.Thefirstterm,however,canbecontrolledforwhenconstructingtheimmunizedportfolio,becauseitdependssolelyonthecompositionoftheportfolio.25-33Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability

(continued)ImmunizationRiskThisfirstterm,then,isameasureofriskforimmunizedportfoliosandisequaltowhereCFt=cashflowoftheportfolioattimeperiodt,H

=length(inyears)oftheinvestmenthorizonorliabilityduedate,y

=portfolioyield,andn

=timetoreceiptofthelastcashflow.Theobjectiveinconstructinganimmunizedportfolioistomatchtheportfolio’sdurationtotheliability’sdurationandselecttheportfoliothatminimizestheimmunizationrisk.Theimmunizationriskmeasurecanbeusedtoconstructapproximateconfidenceintervalsforthetargetyieldandthetargetaccumulatedvalue.25-34Copyright?2010PearsonEducation,Inc.PublishingasPrenticeHallImmunizationofaPortfoliotoSatisfyaSingleLiability

(continued)Zero-CouponBondsandImmunizationAnalternativeapproachtoimmunizingaportfolioagainstchangesinthemarketyieldistoinvestinzero-couponbondswithamaturityequaltotheinvestmenthorizon.Thisisconsistentwiththebasicprincipleofimmunization,becausethedurationofazero-couponbondisequaltotheliability’sduration.However,inpractice,theyieldonzero-couponbondsistypicallylowerthantheyieldoncouponbondsmakingthisstrategymorecostly.CreditRiskandtheT