2025年CFA《固定收益》真题集

2025年CFA《固定收益》真题集考试时间：______分钟总分：______分姓名：______试卷内容1.Acorporatebondwithafacevalueof$1,000paysasemi-annualcouponof6%.Thebondmaturesin5years.Whatisthepriceofthebondiftheyieldtomaturityis5%?2.Explaintherelationshipbetweenabond'spriceanditsyieldtomaturity.Underwhatcircumstanceswillabondsellatapremium?3.Considertwobonds,BondAandBondB.Bothbondshaveafacevalueof$1,000andmaturein10years.BondApaysa4%annualcoupon,whileBondBpaysa6%annualcoupon.Theyieldtomaturityforbothbondsiscurrently5%.CalculatetheMacaulaydurationforBondA.IsBondB'sMacaulaydurationlongerorshorterthanBondA's?Brieflyexplainyourreasoning.4.Defineduration.Howdoesdurationmeasurethesensitivityofabond'spricetochangesininterestrates?Whyisdurationtypicallyexpressedinyears?5.Abondportfolioisworth$10millionandhasaneffectivedurationof7.5years.Theportfoliomanagerexpectsinterestratestoincreaseby1%.Usingthedurationapproximation,whatistheestimatedchangeintheportfolio'svalue?6.Explainthedifferencebetweeneffectivedurationandmodifiedduration.Whichmeasureisgenerallyconsideredmoreusefulforportfoliomanagement,andwhy?7.Abondhasayieldtomaturityof4%andadurationof8years.Ifthebond'syieldtomaturityincreasesto5%,whatistheapproximatepercentagechangeinthebond'sprice?Iftheyielddecreasesto3%,whatistheapproximatepercentagechangeinthebond'sprice?8.Defineconvexity.Howdoesconvexityaffecttheaccuracyofthedurationapproximationforbondpricechanges?Whyisconvexityimportantforbondportfoliomanagement?9.Aportfoliomanagerwantstoimmunizeabondportfolioagainstinterestraterisk.Whatarethekeyconditionsthatmustbemetfortheportfoliotobeperfectlyimmunized?Explaintheconceptof"immersion."10.Whatisthedifferencebetweenafloating-ratebondandafixed-ratebond?Whataretheadvantagesanddisadvantagesoffloating-ratebonds?11.Acompanyisconsideringissuingbondstofinanceanewproject.Thecompany'screditratingisBBB.Whattypeofriskdoesthebondholdersface?Whatfactorswouldinfluencethecreditspreadonthebondsissuedbythecompany?12.Definecreditdefaultswap(CDS).WhatistheprimarypurposeofaCDS?HowistheCDSpremiumtypicallydetermined?13.Explainthedifferencebetweenazero-couponbondandacouponbond.Whataretheadvantagesanddisadvantagesofzero-couponbonds?14.Abondhasayieldtomaturityof5%andacreditspreadof1%.Whatisthebond'stotalyield?Iftherisk-freerateis3%,whatisthebond'sexpectedreturn?15.Whatisabondladderstrategy?Howdoesabondladderhelpmanageinterestrateriskandreinvestmentrisk?16.Explainhowabondfuturescontractworks.Whatisthedifferencebetweenalongpositionandashortpositioninabondfuturescontract?17.Abondfuturescontracthasasettlementvalueof100.Theinitialmarginrequirementis5%.Whatisthemaximumpermissiblelossforatraderwhoentersintoashortpositioninthecontract?18.Explaintheconceptofdurationmatching.Howdoesdurationmatchinghelpreduceinterestrateriskforabondportfolio?19.Aportfolioconsistsoftwobonds:BondXwithadurationof5yearsandaweightof60%,andBondYwithadurationof10yearsandaweightof40%.Whatisthedurationoftheportfolio?20.Whatisthetermstructureofinterestrates?Whatarethemaintheoriesthatexplaintheshapeoftheyieldcurve?试卷答案1.Price=$947.06*解析思路：计算债券价格需要将所有未来现金流（半年度利息和到期面值）折现到当前。公式为：Price=Σ[C/(1+r/n)^(nt)]+F/(1+r/n)^(nt)，其中C是半年度coupon，r是年收益率(0.05)，n是每年复利次数(2)，t是年数(5)。代入计算得到价格约为947.06美元。2.Abond'spriceandyieldtomaturityhaveaninverserelationship.Abondsellsatapremiumwhenitscouponrateishigherthanitsyieldtomaturity.*解析思路：债券的理论价格由其未来现金流按照市场要求的回报率（YTM）折现而成。如果债券的票面利率（现金流）高于市场回报率，投资者愿意支付高于面值的价格来获取这份高息，即溢价发行。反之，如果票面利率低于市场回报率，则折价发行。3.MacaulayDurationofBondA=approx.4.57years.BondB'sMacaulaydurationisshorterthanBondA's.*解析思路：久期衡量债券现金流发生的时间加权平均值。对于期限相同但票面利率不同的债券，票面利率较高的债券（BondB）的现金流发生更早，其久期通常较短。计算精确值需要使用MacaulayDuration公式，涉及各期现金流的现值和加权平均。4.Durationmeasuresthepercentagechangeinabond'spricefora1%changeinyieldtomaturity.Itisexpressedinyearsbecauseitrepresentstheweightedaveragetimeuntilcashflowsarereceived.*解析思路：久期是一个重要的敏感性指标，它量化了当市场利率（YTM）发生微小变动时，债券价格预计会发生多大比例的变化。其单位是年，反映了将债券的未来现金流（利息和本金）按现值加权平均后所得到的时间点，这个时间点大致代表了利率变动对价格影响的时间中心。5.Estimatedchangeinportfoliovalue=-7.5%*1%=-7.5%.*解析思路：使用久期近似公式计算价格变动百分比：%ΔP≈-D*Δy，其中D是有效久期(7.5)，Δy是收益率变动(1%)。代入计算得到价格预计下降7.5%。6.ModifieddurationiscalculatedasMacaulayduration/(1+y/t)，whereyistheyieldtomaturityandtisthetimetomaturity.Modifieddurationprovidesamoredirectmeasureofthepercentagepricechangefora1%yieldchange.Itisgenerallymoreusefulforportfoliomanagementbecauseitisindependentofthebond'syieldtomaturityanddirectlyrelatestothebond'syieldsensitivity.*解析思路：修正久期是Macaulay久期除以（1+YTM/时间），它消除了到期时间的影响，更准确地衡量了1%YTM变动引起的债券价格百分比变动。因此，它在风险管理中比有效久期更常用，因为它不依赖于债券的当前收益率，直接反映了价格对利率变动的敏感度。7.ApproximatepriceincreaseifYTMdecreasesto3%=-8*(-2%)=+16%.ApproximatepriceincreaseifYTMincreasesto5%=-8*1%=-8%.*解析思路：使用修正久期（这里用有效久期近似代替，假设修正久期接近有效久期8年）和1%的YTM变动进行计算：%ΔP≈-D*Δy。当YTM从4%降至3%时，久期D=8，Δy=-1%，价格上升约16%。当YTM从4%升至5%时，久期D=8，Δy=1%，价格下降约8%。8.Convexitymeasuresthecurvatureoftherelationshipbetweenabond'spriceanditsyieldtomaturity.Itprovidesabetterestimateofthepricechangewhentherearelargeryieldchanges.Convexityisimportantbecauseithelpstocorrectthelinearapproximationerrorfromduration,especiallyforlargeryieldshifts,leadingtomoreaccuratepricepredictions.*解析思路：凸性衡量债券价格-收益率关系曲线的弯曲程度。与仅考虑线性（久期）效应不同，凸性考虑了收益率变动时久期本身也在变化的非线性影响。当收益率发生较大变动时，凸性效应变得显著，使用凸性可以更精确地预测价格变动，弥补仅用久期近似的误差。9.Thekeyconditionsforperfectimmunizationare:(1)Thedurationofthebondportfoliomustequalthedurationoftheassetsbeingimmunized(orthedurationoftheliabilitiesifimmunizingagainstfundingneeds).(2)Allcashflowsmustbeperfectlymatchedintiming.Perfectimmunizationensuresthattheportfolio'svaluewillnotchange(innominalterms)aslongasinterestratesmoveparallel.Immersionreferstothechangeinthevalueoftheimmunizedportfolioduetointerestratechangesotherthanthosepredicted,oftencausedbyimperfectdurationmatchingorchangesintheshapeoftheyieldcurve.*解析思路：免疫策略的目标是使债券组合的久期与需要融资的资产（或负债）的久期相匹配，以消除利率变动对组合名义价值的影响。这需要精确匹配现金流的时间和规模。如果条件完全满足，组合价值对平行利率变动免疫。但现实中可能存在误差，这种误差被称为“浸没”。10.Afixed-ratebondpaysacouponratethatremainsconstantthroughoutthebond'slife.Afloating-ratebondhasacouponratethatadjustsperiodicallybasedonabenchmarkinterestrate(e.g.,LIBOR,SOFR).Advantagesoffloating-ratebondsincludeprotectionagainstrisinginterestrates(whichcanreducethebond'sprice),makingthemlesssensitivetointerestraterisk.Disadvantagesincludereinvestmentrisk(theuncertaintyofreceivingthefloatingcouponatafavorablerate)andpaymentuncertainty(couponscanbehigherorlowerthanfixed-ratebonds).*解析思路：固定利率债券的票面利率在债券期内不变。浮动利率债券的票面利率则根据某个基准利率定期调整。浮动利率债券的主要优势是能够对冲利率上升的风险，因为其收益率随市场利率变动。主要劣势是存在再投资风险（浮动利息的再投资回报不确定）以及现金流的不确定性（浮动利息可能高于或低于固定利率）。11.Theriskthatthecompanywilldefaultonitsbondobligations.Factorsinfluencingthecreditspreadincludethecompany'screditworthiness(measuredbyratingagencies),theoverallhealthoftheeconomy,industryconditions,thebond'smaturity,andmarketliquidity.*解析思路：信用风险是指债券发行人（公司）无法按时足额偿还本金或利息的风险。对于信用评级为BBB的公司债券，投资者面临的信用风险相对较高。信用利差（CDS溢价或债券收益率与无风险收益率之差）反映了这种风险的大小，受公司信用质量、宏观经济环境、行业前景、债券期限以及市场流动性的影响。12.Acreditdefaultswap(CDS)isafinancialderivativecontractthatprovidesprotectionagainstthedefaultofaspecifiedunderlyingbondorloan.TheprimarypurposeistotransferthecreditriskoftheunderlyingreferenceentitytotheCDSbuyer.TheCDSpremium(spread)istypicallydeterminedbythecreditqualityofthereferenceentityandthemarket'sassessmentofitsdefaultprobability.*解析思路：信用违约互换是一种衍生品合约，买方支付保费给卖方，以获得在合约标定的参照实体（如发行人）发生信用事件（如违约）时获得补偿的权利。其主要目的是转嫁信用风险。CDS的保费（利差）通常基于参照实体的信用状况和市场上对其违约可能性的评估。13.Azero-couponbonddoesnotpayperiodiccouponpayments;itissoldatadiscounttoitsfacevalueandpaysthefullfacevalueatmaturity.Acouponbondpaysperiodicinterestpayments(coupons)throughoutitslifeinadditiontothefacevalueatmaturity.Advantagesofzero-couponbondsincludetaxdeferral(inmanyjurisdictions)andpotentiallyhigherreturnsforinvestorswillingtowaituntilmaturity.Disadvantagesincludehigherpricevolatilityduetothelackofcouponpaymentstooffsetinterestraterisk,andlowercashflowcertainty.*解析思路：零息债券在整个持有期内不支付利息，以低于面值的价格发行，到期时按面值偿付。附息债券则定期支付利息，到期时偿还本金。零息债券的优势在于税收处理（如美国可递延资本利得税）和潜在的高回报率，劣势在于缺乏利息现金流来对冲利率风险，导致价格波动性更大。14.Totalyield=5%+1%=6%.Expectedreturndependsontheprobabilityofdefaultandrecovery,butthequotedtotalyieldrepresentstheblendedreturnincorporatingboththerisk-freerateandthecreditriskpremium.*解析思路：债券的总收益率是无风险利率与信用利差之和。在本题中，总收益率为5%+1%=6%。预期回报率则取决于违约的可能性、回收率等信用风险因素，但总收益率本身已经包含了信用风险溢价。如果假设没有违约，预期回报率就接近总收益率。15.Abondladderstrategyinvolvespurchasingaportfolioofbondswithstaggeredmaturities(e.g.,onebondmaturingeachyearforthenextfiveyears).Thisstrategyhelpsmanageinterestrateriskbyspreadingoutmaturitydatesandcapturingvaryingyieldsovertime.Italsohelpsmanagereinvestmentriskbecauseasbondsmature,theprincipalcanbereinvestedatprevailingmarketrates,ratherthanrelyingonasinglelargelump-sumreinvestment.Itprovidesaregularstreamofprincipalrepayments.*解析思路：债券阶梯策略是指购买一系列到期日相互错开的债券（例如，未来五年内每年都有一笔到期）。这种策略通过分散到期日来管理利率风险（避免集中受利率变动影响）并捕捉不同时期的收益率。它还通过分期收回本金来管理再投资风险（避免一次性大额再投资的压力）。核心是分散化。16.Abondfuturescontractisastandardizedlegalagreementtobuyorsellaspecifiedbond(orabasketofbonds)atapredeterminedpriceonaspecificfuturedate(expirationdate).Alongpositionmeansthetraderagreestobuythebond(s)atthefuturedateatthecontractprice;ashortpositionmeansthetraderagreestosellthebond(s)atthefuturedateatthecontractprice.Futurescontractsaremarkedtomarketdaily,meaninggainsandlossesaresettleddaily.*解析思路：债券期货合约是一种标准化的协议，规定买卖双方在未来特定日期以约定价格交割特定债券。做多（long）是指同意未来按合约价格买入债券，做空（short）是指同意未来按合约价格卖出债券。与现货不同，期货合约通常每日结算盈亏。17.Maximumpermissibleloss=SettlementValue*InitialMarginRequirement=100*5%=$5.*解析思路：初始保证金是交易者必须存入保证金账户的资金，用于覆盖可能发生的潜在损失。最大允许损失等于合约结算价值乘以初始保证金比例。在此例中，最大损失为100*5%=5美元。18.Durationmatchinginvolvesadjustingthedurationofabondportfoliotomatchthedurationoftheassetsitisintendedtohedgeagainst(e.g.,liabilitiesoraspecificinvestmenthorizon).Bydoingso,itaimstoneutralizetheinterestratesensitivityoftheportfolio,reducingtheimpactofparallelshiftsininterestr