博迪投资学Chapter16-PPT

INVESTMENTS|BODIE,KANE,MARCUSCopyright©2011byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCHAPTER16ManagingBondPortfoliosINVESTMENTS|BODIE,KANE,MARCUS16-21.Bondpricesandyieldsareinverselyrelated.2.Anincreaseinabond’syieldtomaturityresultsinasmallerpricechangethanadecreaseofequalmagnitude.3.Long-termbondstendtobemorepricesensitivethanshort-termbonds.BondPricingRelationshipsINVESTMENTS|BODIE,KANE,MARCUS16-34.Asmaturityincreases,pricesensitivityincreasesatadecreasingrate.5.Interestrateriskisinverselyrelatedtothebond’scouponrate.6.Pricesensitivityisinverselyrelatedtotheyieldtomaturityatwhichthebondisselling.BondPricingRelationshipsINVESTMENTS|BODIE,KANE,MARCUS16-4Figure16.1ChangeinBondPriceasaFunctionofChangeinYieldtoMaturityINVESTMENTS|BODIE,KANE,MARCUS16-5Table16.1Pricesof8%CouponBond(CouponsPaidSemiannually)INVESTMENTS|BODIE,KANE,MARCUS16-6Table16.2PricesofZero-CouponBond(SemiannuallyCompounding)INVESTMENTS|BODIE,KANE,MARCUS16-7•Ameasureoftheeffectivematurityofabond•Theweightedaverageofthetimesuntileachpaymentisreceived,withtheweightsproportionaltothepresentvalueofthepayment•Durationisshorterthanmaturityforallbondsexceptzerocouponbonds.•Durationisequaltomaturityforzerocouponbonds.DurationINVESTMENTS|BODIE,KANE,MARCUS16-8Price)1(yCFwttttwtDTt1Duration:CalculationCFt=cashflowattimetINVESTMENTS|BODIE,KANE,MARCUS16-9PricechangeisproportionaltodurationandnottomaturityD*=modifieddurationDuration/PriceRelationship(1)1PyDxPy*PDyP债券价格和久期成比例，而不是到期INVESTMENTS|BODIE,KANE,MARCUS16-10Example16.1Duration•Twobondshavedurationof1.8852years.Oneisa2-year,8%couponbondwithYTM=10%.Theotherbondisazerocouponbondwithmaturityof1.8852years.•Durationofbothbondsis1.8852x2=3.7704semiannualperiods.•ModifiedD=3.7704/（1+0.05）=3.591periodsINVESTMENTS|BODIE,KANE,MARCUS16-11Example16.1Duration•Supposethesemiannualinterestrateincreasesby0.01%.Bondpricesfallby:•=-3.591x0.01%=-0.03591%•BondswithequalDhavethesameinterestratesensitivity.yDPP*INVESTMENTS|BODIE,KANE,MARCUS16-12Example16.1DurationCouponBond•Thecouponbond,whichinitiallysellsat$964.540,fallsto$964.1942whenitsyieldincreasesto5.01%•percentagedeclineof0.0359%.Zero•Thezero-couponbondinitiallysellsfor$1,000/1.053.7704=$831.9704.•Atthehigheryield,itsellsfor$1,000/1.053.7704=$831.6717.Thispricealsofallsby0.0359%.INVESTMENTS|BODIE,KANE,MARCUS16-13RulesforDurationRule1Thedurationofazero-couponbondequalsitstimetomaturityRule2Holdingmaturityconstant,abond’sdurationishigherwhenthecouponrateislowerRule3Holdingthecouponrateconstant,abond’sdurationgenerallyincreaseswithitstimetomaturity零息债券久期=到期当到期不变的时候，久期和couponrate成负相关当couponrate不变的时候，久期和到期成正相关INVESTMENTS|BODIE,KANE,MARCUS16-14RulesforDurationRule4Holdingotherfactorsconstant,thedurationofacouponbondishigherwhenthebond’syieldtomaturityislowerRules5Thedurationofalevelperpetuityisequalto:(1+y)/y到期收益率越低，久期越长INVESTMENTS|BODIE,KANE,MARCUS16-15Figure16.2BondDurationversusBondMaturityINVESTMENTS|BODIE,KANE,MARCUS16-16Table16.3BondDurations(YieldtoMaturity=8%APR;SemiannualCoupons)INVESTMENTS|BODIE,KANE,MARCUS16-17Convexity•Therelationshipbetweenbondpricesandyieldsisnotlinear.•Durationruleisagoodapproximationforonlysmallchangesinbondyields.•Bondswithgreaterconvexityhavemorecurvatureintheprice-yieldrelationship.INVESTMENTS|BODIE,KANE,MARCUS16-18Figure16.3BondPriceConvexity:30-YearMaturity,8%Coupon;InitialYTM=8%INVESTMENTS|BODIE,KANE,MARCUS16-19ConvexityntttttyCFyPConvexity122)()1()1(1CorrectionforConvexity:21[()]2PDyConvexityyPINVESTMENTS|BODIE,KANE,MARCUS16-20Figure16.4ConvexityofTwoBondsINVESTMENTS|BODIE,KANE,MARCUS16-21WhydoInvestorsLikeConvexity?•Bondswithgreatercurvaturegainmoreinpricewhenyieldsfallthantheylosewhenyieldsrise.•Themorevolatileinterestrates,themoreattractivethisasymmetry.•Bondswithgreaterconvexitytendtohavehigherpricesand/orloweryields,allelseequal.INVESTMENTS|BODIE,KANE,MARCUS16-22CallableBonds•Asratesfall,thereisaceilingonthebond’smarketprice,whichcannotriseabovethecallprice.•Negativeconvexity当利率下行的时候，凸性为负值•Useeffectiveduration：无法计算t/EffectiveDuration=PPr可赎回债券INVESTMENTS|BODIE,KANE,MARCUS16-23Figure16.5Price–YieldCurveforaCallableBondINVESTMENTS|BODIE,KANE,MARCUS16-24Mortgage-BackedSecurities•Thenumberofoutstandingcallablecorporatebondshasdeclined,buttheMBSmarkethasgrownrapidly.•MBSarebasedonaportfolioofcallableamortizingloans.–Homeownershavetherighttorepaytheirloansatanytime.–MBShavenegativeconvexity.有抵押品的债券（资产债券化）INVESTMENTS|BODIE,KANE,MARCUS16-25Mortgage-BackedSecurities•Oftensellformorethantheirprincipalbalance.•Homeownersdonotrefinanceassoonasratesdrop,soimplicitcallpriceisnotafirmceilingonMBSvalue.•Tranches–theunderlyingmortgagepoolisdividedintoasetofderivativesecuritiesINVESTMENTS|BODIE,KANE,MARCUS16-26Figure16.6Price-YieldCurveforaMortgage-BackedSecurityINVESTMENTS|BODIE,KANE,MARCUS16-27Figure16.7CashFlowstoWholeMortgagePool;CashFlowstoThreeTranches优先级次优级垃圾级次贷危机就是这样产生的INVESTMENTS|BODIE,KANE,MARCUS16-28•Twopassivebondportfoliostrategies:1.Indexing2.Immunization•Bot