2025年CFA《固定收益》真題集考試時間：______分鐘總分：______分姓名：______試卷內(nèi)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?試卷答案1.Price=$947.06*解析思路：計算債券價格需要將所有未來現(xiàn)金流（半年度利息和到期面值）折現(xiàn)到當前。公式為：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是每年復(fù)利次數(shù)(2)，t是年數(shù)(5)。代入計算得到價格約為947.06美元。2.Abond'spriceandyieldtomaturityhaveaninverserelationship.Abondsellsatapremiumwhenitscouponrateishigherthanitsyieldtomaturity.*解析思路：債券的理論價格由其未來現(xiàn)金流按照市場要求的回報率（YTM）折現(xiàn)而成。如果債券的票面利率（現(xiàn)金流）高于市場回報率，投資者愿意支付高于面值的價格來獲取這份高息，即溢價發(fā)行。反之，如果票面利率低于市場回報率，則折價發(fā)行。3.MacaulayDurationofBondA=approx.4.57years.BondB'sMacaulaydurationisshorterthanBondA's.*解析思路：久期衡量債券現(xiàn)金流發(fā)生的時間加權(quán)平均值。對于期限相同但票面利率不同的債券，票面利率較高的債券（BondB）的現(xiàn)金流發(fā)生更早，其久期通常較短。計算精確值需要使用MacaulayDuration公式，涉及各期現(xiàn)金流的現(xiàn)值和加權(quán)平均。4.Durationmeasuresthepercentagechangeinabond'spricefora1%changeinyieldtomaturity.Itisexpressedinyearsbecauseitrepresentstheweightedaveragetimeuntilcashflowsarereceived.*解析思路：久期是一個重要的敏感性指標，它量化了當市場利率（YTM）發(fā)生微小變動時，債券價格預(yù)計會發(fā)生多大比例的變化。其單位是年，反映了將債券的未來現(xiàn)金流（利息和本金）按現(xiàn)值加權(quán)平均后所得到的時間點，這個時間點大致代表了利率變動對價格影響的時間中心。5.Estimatedchangeinportfoliovalue=-7.5%*1%=-7.5%.*解析思路：使用久期近似公式計算價格變動百分比：%ΔP≈-D*Δy，其中D是有效久期(7.5)，Δy是收益率變動(1%)。代入計算得到價格預(yù)計下降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/時間），它消除了到期時間的影響，更準確地衡量了1%YTM變動引起的債券價格百分比變動。因此，它在風(fēng)險管理中比有效久期更常用，因為它不依賴于債券的當前收益率，直接反映了價格對利率變動的敏感度。7.ApproximatepriceincreaseifYTMdecreasesto3%=-8*(-2%)=+16%.ApproximatepriceincreaseifYTMincreasesto5%=-8*1%=-8%.*解析思路：使用修正久期（這里用有效久期近似代替，假設(shè)修正久期接近有效久期8年）和1%的YTM變動進行計算：%ΔP≈-D*Δy。當YTM從4%降至3%時，久期D=8，Δy=-1%，價格上升約16%。當YTM從4%升至5%時，久期D=8，Δy=1%，價格下降約8%。8.Convexitymeasuresthecurvatureoftherelationshipbetweenabond'spriceanditsyieldtomaturity.Itprovidesabetterestimateofthepricechangewhentherearelargeryieldchanges.Convexityisimportantbecauseithelpstocorrectthelinearapproximationerrorfromduration,especiallyforlargeryieldshifts,leadingtomoreaccuratepricepredictions.*解析思路：凸性衡量債券價格-收益率關(guān)系曲線的彎曲程度。與僅考慮線性（久期）效應(yīng)不同，凸性考慮了收益率變動時久期本身也在變化的非線性影響。當收益率發(fā)生較大變動時，凸性效應(yīng)變得顯著，使用凸性可以更精確地預(yù)測價格變動，彌補僅用久期近似的誤差。9.Thekeyconditionsforperfectimmunizationare:(1)Thedurationofthebondportfoliomustequalthedurationoftheassetsbeingimmunized(orthedurationoftheliabilitiesifimmunizingagainstfundingneeds).(2)Allcashflowsmustbeperfectlymatchedintiming.Perfectimmunizationensuresthattheportfolio'svaluewillnotchange(innominalterms)aslongasinterestratesmoveparallel.Immersionreferstothechangeinthevalueoftheimmunizedportfolioduetointerestratechangesotherthanthosepredicted,oftencausedbyimperfectdurationmatchingorchangesintheshapeoftheyieldcurve.*解析思路：免疫策略的目標是使債券組合的久期與需要融資的資產(chǎn)（或負債）的久期相匹配，以消除利率變動對組合名義價值的影響。這需要精確匹配現(xiàn)金流的時間和規(guī)模。如果條件完全滿足，組合價值對平行利率變動免疫。但現(xiàn)實中可能存在誤差，這種誤差被稱為“浸沒”。10.Afixed-ratebondpaysacouponratethatremainsconstantthroughoutthebond'slife.Afloating-ratebondhasacouponratethatadjustsperiodicallybasedonabenchmarkinterestrate(e.g.,LIBOR,SOFR).Advantagesoffloating-ratebondsincludeprotectionagainstrisinginterestrates(whichcanreducethebond'sprice),makingthemlesssensitivetointerestraterisk.Disadvantagesincludereinvestmentrisk(theuncertaintyofreceivingthefloatingcouponatafavorablerate)andpaymentuncertainty(couponscanbehigherorlowerthanfixed-ratebonds).*解析思路：固定利率債券的票面利率在債券期內(nèi)不變。浮動利率債券的票面利率則根據(jù)某個基準利率定期調(diào)整。浮動利率債券的主要優(yōu)勢是能夠?qū)_利率上升的風(fēng)險，因為其收益率隨市場利率變動。主要劣勢是存在再投資風(fēng)險（浮動利息的再投資回報不確定）以及現(xiàn)金流的不確定性（浮動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：信用風(fēng)險是指債券發(fā)行人（公司）無法按時足額償還本金或利息的風(fēng)險。對于信用評級為BBB的公司債券，投資者面臨的信用風(fēng)險相對較高。信用利差（CDS溢價或債券收益率與無風(fēng)險收益率之差）反映了這種風(fēng)險的大小，受公司信用質(zhì)量、宏觀經(jīng)濟環(huán)境、行業(yè)前景、債券期限以及市場流動性的影響。12.Acreditdefaultswap(CDS)isafinancialderivativecontractthatprovidesprotectionagainstthedefaultofaspecifiedunderlyingbondorloan.TheprimarypurposeistotransferthecreditriskoftheunderlyingreferenceentitytotheCDSbuyer.TheCDSpremium(spread)istypicallydeterminedbythecreditqualityofthereferenceentityandthemarket'sassessmentofitsdefaultprobability.*解析思路：信用違約互換是一種衍生品合約，買方支付保費給賣方，以獲得在合約標定的參照實體（如發(fā)行人）發(fā)生信用事件（如違約）時獲得補償?shù)臋?quán)利。其主要目的是轉(zhuǎn)嫁信用風(fēng)險。CDS的保費（利差）通?；趨⒄諏嶓w的信用狀況和市場上對其違約可能性的評估。13.Azero-couponbonddoesnotpayperiodiccouponpayments;itissoldatadiscounttoitsfacevalueandpaysthefullfacevalueatmaturity.Acouponbondpaysperiodicinterestpayments(coupons)throughoutitslifeinadditiontothefacevalueatmaturity.Advantagesofzero-couponbondsincludetaxdeferral(inmanyjurisdictions)andpotentiallyhigherreturnsforinvestorswillingtowaituntilmaturity.Disadvantagesincludehigherpricevolatilityduetothelackofcouponpaymentstooffsetinterestraterisk,andlowercashflowcertainty.*解析思路：零息債券在整個持有期內(nèi)不支付利息，以低于面值的價格發(fā)行，到期時按面值償付。附息債券則定期支付利息，到期時償還本金。零息債券的優(yōu)勢在于稅收處理（如美國可遞延資本利得稅）和潛在的高回報率，劣勢在于缺乏利息現(xiàn)金流來對沖利率風(fēng)險，導(dǎo)致價格波動性更大。14.Totalyield=5%+1%=6%.Expectedreturndependsontheprobabilityofdefaultandrecovery,butthequotedtotalyieldrepresentstheblendedreturnincorporatingboththerisk-freerateandthecreditriskpremium.*解析思路：債券的總收益率是無風(fēng)險利率與信用利差之和。在本題中，總收益率為5%+1%=6%。預(yù)期回報率則取決于違約的可能性、回收率等信用風(fēng)險因素，但總收益率本身已經(jīng)包含了信用風(fēng)險溢價。如果假設(shè)沒有違約，預(yù)期回報率就接近總收益率。15.Abondladderstrategyinvolvespurchasingaportfolioofbondswithstaggeredmaturities(e.g.,onebondmaturingeachyearforthenextfiveyears).Thisstrategyhelpsmanageinterestrateriskbyspreadingoutmaturitydatesandcapturingvaryingyieldsovertime.Italsohelpsmanagereinvestmentriskbecauseasbondsmature,theprincipalcanbereinvestedatprevailingmarketrates,ratherthanrelyingonasinglelargelump-sumreinvestment.Itprovidesaregularstreamofprincipalrepayments.*解析思路：債券階梯策略是指購買一系列到期日相互錯開的債券（例如，未來五年內(nèi)每年都有一筆到期）。這種策略通過分散到期日來管理利率風(fēng)險（避免集中受利率變動影響）并捕捉不同時期的收益率。它還通過分期收回本金來管理再投資風(fēng)險（避免一次性大額再投資的壓力）。核心是分散化。16.Abondfuturescontractisastandardizedlegalagreementtobuyorsellaspecifiedbond(orabasketofbonds)atapredeterminedpriceonaspecificfuturedate(expirationdate).Alongpositionmeansthetraderagreestobuythebond(s)atthefuturedateatthecontractprice;ashortpositionmeansthetraderagreestosellthebond(s)atthefuturedateatthecontractprice.Futurescontractsaremarkedtomarketdaily,meaninggainsandlossesaresettleddaily.*解析思路：債券期貨合約是一種標準化的協(xié)議，規(guī)定買賣雙方在未來特定日期以約定價格交割特定債券。做多（long）是指同意未來按合約價格買入債券，做空（short）是指同意未來按合約價格賣出債券。與現(xiàn)貨不同，期貨合約通常每日結(jié)算盈虧。17.Maximumpermissibleloss=SettlementValue*InitialMarginRequirement=100*5%=$5.*解析思路：初始保證金是交易者必須存入保證金賬戶的資金，用于覆蓋可能發(fā)生的潛在損失。最大允許損失等于合約結(jié)算價值乘以初始保證金比例。在此例中，最大損失為100*5%=5美元。18.Durationmatchinginvolvesadjustingthedurationofabondportfoliotomatchthedurationoftheassetsitisintendedtohedgeagainst(e.g.,liabilitiesoraspecificinvestmenthorizon).Bydoingso,itaimstoneutralizetheinterestratesensitivityoftheportfolio,reducingtheimpactofparallelshiftsininterestr