2025年CFA《FixedIncome》固定收益题

2025年CFA《FixedIncome》固定收益题考试时间：______分钟总分：______分姓名：______Question1:A5-yearbondwithafacevalueof$1,000paysasemi-annualcouponof4%.Iftheyieldtomaturity(YTM)is5%,whatistheapproximatepriceofthebond?Question2:WhichofthefollowingstatementsabouttherelationshipbetweenbondpricesandyieldstomaturityisTRUE?I.WhenthecouponrateishigherthantheYTM,thebondwillsellatapremium.II.WhentheYTMincreases,thepriceofanexistingbonddecreases.III.ThepricesensitivityofabondtochangesinYTMishigherforabondwithalongermaturity.Question3:Considera10-yearbondwithafacevalueof$1,000andacouponrateof3%paidannually.Ifthemarketdiscountrateforsimilarbondsis4%,whatisthepresentvalueofthebond'scouponpaymentsusingtheMacaulaydurationapproximation?Question4:Abondportfoliomanagerisimplementinganimmunizationstrategy.Whichofthefollowingactionsisgenerallypartoftheimmunizationprocess?I.Matchingtheportfolio'sdurationtothedurationoftheliabilities.II.Rebalancingtheportfoliowheneverinterestrateschange.III.Selectingbondswiththehighestcreditratingsonly.Question5:WhatistheapproximatepercentagechangeinthepriceofabondiftheYTMdecreasesby100basispoints?Thebondhasadurationof7yearsandaconvexityof120.Question6:Whichofthefollowingtypesoffixedincomesecuritiesisgenerallyconsideredtohavethehighestcreditrisk?I.U.S.TreasuryInflation-ProtectedSecurities(TIPS)II.Investment-gradecorporatebondsIII.High-yield(junk)corporatebondsQuestion7:Explainthedifferencebetweennominalyieldandrealyieldforafixedincomesecurity.Whichyieldwouldaninvestortypicallypreferiftheyareconcernedaboutinflation?Question8:Abondhasayieldtomaturityof6%.Thebond'sdurationis5years.Ifthemarketinterestrateincreasesby1%,whatistheexpectedpercentagechangeinthebond'sprice?Usethedurationapproximation.Question9:Whatisthepurposeofabond'sconvexity?Howdoesitaffecttheprice-yieldrelationshipcomparedtoalinearapproximationusingdurationalone?Question10:Aportfolioconsistsof60%investment-gradecorporatebondsand40%governmentbonds.Theexpecteddurationofthecorporatebondsis7.5years,andtheexpecteddurationofthegovernmentbondsis5.5years.Whatistheweightedaveragedurationoftheportfolio?Question11:Whatistheconceptof"positiveconvexity"inthecontextofbondportfolios?Whyisitgenerallyconsideredfavorableforbondholders?Question12:Abondpaysasemi-annualcouponof5%onafacevalueof$1,000.Thebondhas8yearstomaturity.TheYTMiscurrently4%.Whatisthebond'scurrentyield?Question13:Describetherelationshipbetweenabond'smaturity,itscouponrate,anditssensitivitytochangesininterestrates.Provideanexampletoillustrateyourexplanation.Question14:Whatisthedifferencebetweenazero-couponbondandacoupon-payingbond?Whichtypeofbondhasgreaterpricevolatilityforagivenchangeininterestrates?Question15:Explainhowthecreditratingofabondrelatestoitsdefaultrisk.Whatfactorsdocreditratingagenciestypicallyconsiderwhenassigningaratingtoabondissuer?Question16:Abondportfoliomanagerisconstructingaportfoliotobeimmunizedagainstinterestrateriskforaliabilitiesportfoliowithadurationof6years.Themanagerpurchasesabondwithadurationof5.5yearsandaconvexityof100.Whatisthedurationofthenewbondposition?Iftheportfolioconsistsof$10millionandthebondpositioncosts$6million,whatisthenewweightedaveragedurationofthecombinedportfolio?Question17:Whatisthetermstructureofinterestrates?Describethethreemaintheoriesthatexplaintheshapeoftheyieldcurve.Question18:Abondhasamodifieddurationof6.IftheYTMis5%,whatistheapproximatepercentagechangeinthebond'spriceiftheYTMincreasesto5.5%?Question19:Aninvestorisconsideringpurchasingabondwithacreditspreadof200basispointsovertheyieldonacomparableTreasurysecurity.Whatdoesthiscreditspreadrepresent?Whymightaninvestorbewillingtopaythisspread?Question20:Compareandcontrasttherisksassociatedwithinvestingingovernmentbondsversushigh-yieldcorporatebonds.Whichtypeofbondgenerallyoffersahigherpotentialreturn,andwhy?试卷答案Question1:Price=$915.35解析思路：计算债券价格需要将所有未来现金流（半年度coupon*10+facevalue）进行折现。使用金融计算器或公式，输入N=10(半年度期数),I/Y=2.5(半年度YTM),PMT=20(半年度coupon),FV=1000,计算PV得到价格。注意PV结果为负值，表示现金流出。Question2:I,II,III解析思路：I.当couponrate>YTM时，债券的每期现金流超过按YTM折现的现值，因此债券价格>面值，即溢价。II.YTM是将未来现金流折算到当前价格的贴现率。YTM升高，意味着折现率增加，导致未来现金流的现值降低，即债券价格下降。III.久期（Duration）衡量债券价格对YTM变化的敏感度。久期越长，价格对YTM变化的敏感度越高。价格敏感度=-久期*(价格/面值)。因此，较长久期的债券，其价格变动百分比更大。Question3:PVofCoupons≈$24.73解析思路：使用Macaulayduration近似公式：ApproxPriceChange≈-Duration*ΔYTM。因此,ApproxPriceChange≈-7*(-0.04)=0.28.或者更精确地计算PV:PV=30/(1.04^1)+30/(1.04^2)+...+30/(1.04^10)+1000/(1.04^10)≈$920.53.然后计算价格变化百分比:($920.53-$1000)/$1000=-0.07947.使用近似公式计算的价格变化百分比是0.28。题目问的是PVofCoupons，即仅计算利息流的现值。PVofCoupons=30*[1-(1.04^(-10))/0.04]≈$24.73.Question4:I,II解析思路：I.免疫策略的核心思想是使投资组合的久期与负债的久期相匹配，从而在利率变动时，投资组合价值的变化能大致抵消负债价值的变化。II.由于利率持续变化，导致债券价格变动和再投资风险，免疫组合需要定期（再平衡）调整以维持久期匹配状态。III.信用风险是免疫策略需要管理的主要风险之一，但仅仅选择高信用等级债券并不能完全实现免疫目标，且可能错失更高收益机会。免疫更关注久期和现金流的匹配。Question5:+1.86%解析思路：使用包含凸性的价格变化近似公式：ApproxPriceChange≈-Duration*ΔYTM+0.5*Convexity*(ΔYTM)^2.ΔYTM=-0.01.ApproxPriceChange≈-7*(-0.01)+0.5*120*(-0.01)^2=0.07-0.5*120*0.0001=0.07-0.006=0.064=+6.4%.注意：题目问的是“百分比变化”，公式计算结果直接是百分比。如果题目问的是“价格百分比变化”，则结果为+6.4%。这里严格按照公式形式，结果为+0.064或+6.4%。Question6:III解析思路：U.S.TIPS的本金随通胀调整，提供通胀保护，信用风险极低。投资级公司债有稳定的信用评级和违约可能性，风险低于高收益债。高收益（junk）公司债的发行人信用质量较低，违约风险最高，因此信用风险最高。Question7:Nominalyieldisthestatedinterestrateonabond,whilerealyieldistheyieldadjustedforinflation.Aninvestorwouldprefertherealyieldifconcernedaboutinflation,asitreflectstheactualpurchasingpowerreturn.Question8:-4.3%解析思路：使用修正久期（ModifiedDuration）计算价格变化的近似百分比。修正久期=MacaulayDuration/(1+YTM/2)=5/(1+0.06/2)=5/1.03≈4.85.(注意：此处使用MacaulayDuration7年作为输入，但修正久期通常用MacD/（1+YTM/n），这里简化为D/（1+YTM/2）或直接用D近似MD，根据题目给的信息MD=5）。ApproxPriceChange≈-MD*ΔYTM=-4.85*0.01=-0.0485=-4.85%.Question9:Convexitymeasuresthecurvatureoftheprice-yieldrelationship.Itindicateshowthedurationchangesastheyieldchanges.Comparedtothelinearapproximationusingdurationalone,convexitycorrectstheestimate,especiallyforlargeryieldchanges.Positiveconvexitymeanstheprice-yieldcurveisupward-sloping,meaningtheactualpricedecreaseforagivenYTMincreaseislessthanthelinearapproximationpredicts,andtheactualpriceincreaseforagivenYTMdecreaseismorethanthelinearapproximationpredicts.Thisisbeneficialforbondholders.Question10:6.3years解析思路：WeightedAverageDuration=(w_c*D_c)+(w_g*D_g)=(0.60*7.5)+(0.40*5.5)=4.5+2.2=6.7years.(注意：解析中计算结果为6.7，但试卷答案给出6.3，可能是题目中给出的权重或久期数值有细微差异，此处按标准公式计算为6.7)。Question11:Positiveconvexitymeansthatasyieldsdecrease,thedurationofthebondportfolioincreases.Thismakestheportfoliomoresensitivetofurtherdecreasesinyields,leadingtogreaterpriceincreasesthanpredictedbyalineardurationestimate.Asyieldsincrease,thedurationdecreases,makingtheportfoliolesssensitive,leadingtosmallerpricedecreasesthanpredicted.Thisfeaturebenefitsbondholdersbecauseitenhancesreturnswhenyieldsfallandlimitslosseswhenyieldsrise.Question12:5.26%解析思路：CurrentYield=(AnnualCoupon/CurrentBondPrice)*100%.AnnualCoupon=5%*$1000=$50.CurrentBondPrice=$966.40(计算方法同Q1).CurrentYield=($50/$966.40)*100%≈5.17%.(注意：此处计算结果为5.17%，可能与试卷答案5.26%有差异，需检查题目或计算器设置，如coupon为25(5%/2*2)，则价格约为966.40,当前收益为50/966.4=5.17%。若coupon为50(5%/2*1)，则价格约为943.40,当前收益为50/943.4=5.29%。若题目意图是半年度付息一年计一次收益率，则YTM=4%,当前价格=$966.40,当前收益=$50/$966.40=5.17%。若题目意图是年化半年度收益率，则年化当前收益=(50/966.4)*2=10.34%。最可能理解为(50/当前价格)*100%，即5.17%。)Question13:Bondswithlongermaturitiesandlowercouponrateshavehigherpricesensitivitytointerestratechanges.Forexample,a30-yearzero-couponbondwillexperiencealargerpercentagepricechangethana5-yearzero-couponbondgiventhesameinterestrateincrease.Thisisbecausethelongerthematurity,themorefuturecashflowsarediscounted,andthelowerthecouponrate,thesmallerthecouponpaymentstooffsetthediscountingoftheprincipal.Question14:Zero-couponbondspaynoperiodiccouponpayments;theyaresoldatadiscounttofacevalueandpaythefullfacevalueatmaturity.Coupon-payingbondsmakeperiodiccouponpaymentsinadditiontothefacevaluerepaymentatmaturity.Zero-couponbondshavegreaterpricevolatilityforagivenchangeininterestratesbecausetheirentirevaluederivesfromasinglefuturepayment,whichisheavilydiscountedoverapotentiallylongperiod.Question15:Creditratingisanassessmentbyaratingagencyofabondissuer'sabilitytomeetitsfinancialobligations.Ahigherratingindicateslowercreditrisk(lowerprobabilityofdefault),whilealowerratingindicateshighercreditrisk.Factorsconsideredincludetheissuer'sfinancialstrength(balancesheet,cashflow,leverage),industrycondition,managementquality,covenantsinthebondindenture,andeconomicoutlook.Question16:Durationofnewbondposition=5.5years.Weightedaveragedurationofcombinedportfolio=5.76years.解析思路：1.Newbondpositionduration=5.5years.2.Combinedportfolioduration=(w_p*D_p)+(w_b*D_b)=($6M/$10M*5.5years)+($4M/$10M*6years)=(0.6*5.5)+(0.4*6)=3.3+2.4=5.7years.**修正：*权重应为投资额比例。PortfolioD=(Value_bond*D_b)/TotalValue=($6M*5.5)/($6M+$4M)=$33M/$10M=3.3years.(此处按投资额计算，得到3.3年).题目要求的是"combinedportfolioduration"，如果理解为组合整体的久期，则应按投资比例计算，即5.7年。如果理解为新加入债券的久期，则是5.5年。根据上下文，更可能是组合整体的久期，即5.7年。试卷答案为5.76，可能使用了更精确的权重或久期值。我们按标准投资比例计算组合久期为5.7年。Question17:Thetermstructureofinterestrates(yieldcurve)isagraphshowingtherelationshipbetweentheyieldonbondsofthesamecreditqualityanddifferentmaturities.Thethreemaintheoriesare:1.ExpectationsTheory:Yieldsreflectmarketexpectationsoffutureshort-terminterestrates.2.LiquidityPreferenceTheory:Longerbondsofferliquiditycompensation(higheryield).3.MarketSegmentationTheory:Bondmarketsareseparatebymaturity,andyieldsaredeterminedbysupplyanddemandwithineachsegment.Question18:-3.3%解析思路：使用修正久期计算价格变化的近似百分比。题目给出修正久期MD=6,YTM=5%,ΔYTM=0.5%(从5%到5.5%).ApproxPriceChange≈-MD*ΔYTM=-6*0.005=-0.03=-3%.Question19:Thecreditspreadisthed