债券定价和风险管理(证券投资学北大,杨云红).ppt

第八章债券定价和风险管理,CAPM,APT:treatsecuritiesatahighlevelofabstraction,assumingimplicitlythataprior,detailedanalysisofeachsecurityalreadyhadbeenperformed,andthatitsriskandreturnfeatureshadbeenassessed.Specificanalysesofparticularsecuritymarkets:valuationprinciples,determinantsofriskandreturn,portfoliostrategiescommonlyusedwithinandacrossthevariousmarkets,固定收益证券Promiseeitherafixedstreamofincomeorastreamofincomethatisdeterminedaccordingtoaspecifiedformula.Havetheadvantageofbeingrelativeeasytounderstandbecausethelevelofpaymentsisfixedinadvance.Riskconsiderationareminimalaslongastheissuerofthesecurityissufficientlycreditworthy.,BondanalysisBondattributesBondpricingAppropriateyieldtomaturityIntrinsicvalueTherelationshipbetweentheyieldandpriceBondriskmanagementWhenthematurityandthepaymenttimeisnotconsistentInterestriskReinvestmentriskTheapproachofriskmanagementDurationConvexity,1.Bondanalysis,债券是最基本的固定收益证券。债券的定价债券的特性,1.1CapitalizationofIncomeMethodofValue,Promisedyield-to-maturity如果，则定价过低(underpriced)。如果，则定价过高(overpriced)。的确定依赖于债券的特征以及现时的市场条件。,例子：一个债券，现价为900元，面值为1000元，三年到期，息率为6%。得到如果通过分析，得到问题：定价如何？如何确定？,Intrinsicvalue例子：两种程序所得结果的一致性，即价格与回报率之间的关系。,为了利用CapitalizationofIncomeMethodofValue，必须决定，的值。和容易确定的确定依赖于投资者对债券的特征的主观看法，以及现实的市场条件。从而债券分析中，最关键的部分是确定,1.2Bondattributes,在债券定价过程中，债券的六个重要的属性：lengthoftimeuntilmaturitycouponratecallprovisionstaxstatusmarketabilitylikelihoodofdefault,在任何时间，这些性质不同的债券的市场价格结构，以到期收益来描述。整个结构也称为收益结构(yieldstructure)。期限结构(differentmaturities)：不同到期日风险结构(differentdefaultrisk)：不同违约风险yieldspread：两种债券之间的收益差。被考虑债券和具有相同的到期日和息率的无违约风险债券定价是一个相对的概念,Couponrateandlengthoftimeuntilmaturity这两个性质决定了发行者承诺支付给持有者的现金流的时间和规模。由这两个属性可以决定债券的到期收益率，再与基准的收益率作比较。通常以国库券的到期收益作为基准。,例子：前面例子里的债券与下面的国库券比较：面值1000元，息率5%，价格910.61元。到期收益为8.5%，yieldspread为152个基点。,Callandputprovisionscallpricecallpremium当收益率剧烈下降后，债券的发行者回购已经发行的债券具有财务上的优势，因为发行者能够用收益更低的债券来代替。,例子：考虑10年期债券以面值（1000元）发行，息率为12%，上市5年以后，可以以回购价格1050元进行回购。5年后，类似的5年期的债券的收益为8%。为什么会回购10年的到期收益（实际回报）为10.96%。,Yieldtocall例子：面值为1000元，息率8%，30年到期的无回购协议的债券和面值为1000元，息率8%，30年到期，回购价格为1100元的债券,price1200100005%10%15%20%interestrate,Athighinterestrates,theriskofcallisnegligible,andthevaluesofthestraightandcallablebondsconverge.Atlowerrates,however,thevaluesofbondsbegintodiverge,withthedifferencereflectingthevalueofthefirmsoptiontoreclaimthecallablebondatthecallprice.两者之差反映了公司以1100元进行回购这样一个权利的价值。当有回购风险时，更加关注回购收益而不是到期收益回购收益的计算,例子：假设息率为8%，30年到期的债券价格为1150元，10年后以1100元回购回购收益为6.64%，到期收益为6.82%,Thehigherthecouponrateofacallablebond,thegreateristhelikelydivergencebetweenactualandpromisedyields.一般来说，息率超过5%的债券都会回购回购可能性越大，到期收益应该越高，即，息率越高，或者回购酬金越低，到期收益应该越高当别的性质相同时，息率越高或者回购酬金越低的可回购债券，其内在价值(intrinsicvalue)应该越低。,Putprovisionsputablebonds当利率上涨时，投资者采用该策略,Taxstatus因为税收的延迟性，低息债券比高息债券有更高的内在价值。,Marketability度量债券流动性的一个方式是Bid-Askspread交易活跃的债券比交易不活跃的债券具有更低的bid-askspread.交易活跃的债券比交易不活跃的债券具有更低的到期收益和更高的内在价值。,Likelihoodofdefaultinvestmentgradespeculativegrade对公司债券而言，好的级别一般与下列条件有关：低的财务杠杆大的和稳定的利润大的公司规模大的现金流从属债务少,级别评估公司以发行公司的财务比的水平和未来趋势为基础，通过建立模型对公司债券级别进行评估：Coverageratios-ratioofcompanyearningstofixedcostsLeverageratio-debttoequityratioLiquidityratios-currentassetstocurrentliabilityratioProfitabilityratios-returnonassetsorequityCashflow-to-debtratio-totalcashflowtooutstandingdebt,债券有违约风险，计算期望到期收益率(expectedyield-to-maturity)只要有违约或者推迟支付的可能，期望收益就会小于承诺收益(promisedyield)一般来说，违约的风险越大，违约时损失的数量越大，在收益上的差别越大。,Promisedyieldtomaturityandexpectedyieldtomaturity.例子：在1993年8月，WangLaboratories,Inc.即将破产，它的到期日为2009年的债券发行时以面值的35%折价发行，使得Promisedyieldtomaturity超过26%。投资者并不真正期望获得26%的回报率，他们预期不可能得到所有承诺支付，以期望现金流为基础的收益远远小于以承诺现金流为基础的收益。,例子：某公司20年前发行的债券还有10年到期，息率为9%，现在公司有财务困难，投资者预期利息将不受影响，但在到期日，公司将破产，投资者只能得到面值的70%，债券现在的价格为750元。具体情况见下表,承诺到期收益为13.7%.期望到期收益为11.6%,Defaultpremium:thedifferencebetweenthepromisedyieldonacorporatebondandtheexpectedyield.,违约的概率越大，违约酬金越高。一个关于违约酬金大小的模型：如果每期违约的概率为，违约时支付的数量为前一年市价的，则当债券公平定价时承诺的到期收益为承诺到期收益和期望到期收益之间的差为债券的违约酬金。,例子：,Oneparticularmannerinwhichyieldspreadsseemtoveryovertimeisrelatedtothebusinesscycle.Yieldspreadstendtobewiderwhentheeconomyisinarecession.Apparently,investorsperceiveahigherprobabilityofbankruptcywhentheeconomyisfaltering,evenholdingbondratingsconstant.Theyrequireacommensuratelyhigherdefaultpremium.,Riskpremium对风险债券而言，它的期望到期收益和具有同样到期日、息率的无风险债券到期收益之间的差称为风险酬金。每种具有违约风险的债券都有违约酬金。但风险酬金是另一种酬金。例子：考虑一组公司，都有破产的可能性，但破产的原因各不相同，由这些公司的债券组成的证券组合的实际回报率近似等于其期望回报率，系统风险为0。每种债券的风险酬金为0，但违约酬金显然大于0。,一种债券，它的持有期收益率可能和别的债券以及股票的收益率相关。最重要的，在某种程度上，它的持有期收益率可能和风险分散化的市场证券组合的收益率相关。这部分风险称为债券的系统风险，使得债券具有风险酬金，以它的期望收益率与无违约风险利率的差表示。,例子：DefaultpremiumyieldspreadRiskpremium,Default-freeyield-to-Maturity,12%promisedyield-to-maturity,9%expectedyield-to-maturity,8%yield-to-maturityonadefault-freebondofsimilarandcouponrate,0%,债券的违约性越大，它对市场潜在的敏感度越大。实证结果表明，债券的级别越低，平均回报率越高，标准差越大。实证结果表明，与股票市场比较，级别越低的债券，对股票市场的波动敏感性越大。,预测违约的财务比(financialratio),对一个公司而言，当下面情况发生时，违约的概率变大：theexistingcashbalanceissmallertheexpectednetcashflowissmallerthenetcashflowismorevariable单变量方法多变量方法,单变量方法,theratioofnetcashflow（incomebeforedepreciation,depletion,andamortizationcharges)tototaldebt,多变量方法,Z-score=(currentassets-currentliabilities)/totalassets=retainedearnings/totalassets=earningsbeforeinterestandtaxes/totalassets=marketvalueofequity/bookvalueoftotaldebt=sales/totalassets,Z-score小于1.8公司作为违约对象，并且Z-score越小，违约的可能性越大。,1.3.Yieldspread的确定,评估yieldspread的四种测度：Theextenttowhichthefirmsnetincomehadvariedovertheprecedingnineyears(measuredbythecoefficientofvariationofearnings-thatis,theratioofstandarddeviationofearningstoaverageearnings)Thelengthoftimethatthefirmhadoperatedwithoutforcinganyofitscreditorstotakealoss.Theratioofthemarketvalueofthefirmsequitytotheparvalueofitsdebt.Themarketvalueofthefirmsoutstandingdebt.,Yieldspread=1.987+0.307(earningsvariability)-0.253(timewithoutdefault)-0.537(equity/debtratio)-0.275(marketvalueofdebt)Thisformoftherelationshipaccountedforroughly75%ofthevariationinthebondsyieldspread,1.4.债券定价,给定合理的利率，给债券公平定价何为合理利率？合理的利率（或者折现率）是由市场唯一确定的，包括：实利率通货膨胀率yieldspread一级市场：以面值发行息率近似为市场收益率,二级市场：债券价格受市场的影响，市场利率波动是固定收入证券市场的主要风险根源。Theinverserelationshipbetweenpriceandyieldisacentralfeatureoffixed-incomesecurities.Interestratefluctuationsrepresentthemainsourceofriskinthefixed-incomemarket,andonekeyfactorthatdeterminesthatsensitivityisthematurityofthebond.Ageneralruleinevaluatingbondpriceriskisthat,keepingallotherfactorsthesame,thelongerthematurityofthebond,thegreaterthesensitivityofpricetofluctuationsintheinterestrate.Thisiswhyshort-termTreasurysecuritiessuchasT-billsareconsideredtobethesafest.Theyarefreenotonlyofdefaultrisk,butalsolargelyfreeofpriceriskattributabletointerestratevolatility.,当息率等于市场利率时，价格等于面值Inthesecircumstances,theinvestorreceivesfaircompensationforthetimevalueofmoneyintheformoftherecurringinterestpayments.Nofurthercapitalgainisnecessarytoprovidefaircompensation.,当息率小于市场利率时，价格小于面值Thecouponpaymentsalonewillnotprovideinvestorsashighareturnastheycouldearnelsewhereinthemarket.Toreceiveafairreturnonsuchaninvestment,investorsalsoneedtoearnpriceappreciationontheirbonds.Thebondwouldhavetosellbelowparvaluetoprovidea“built-in”capitalgainontheinvestment.,例子：面值1000元，息率7%，公平利率8%，三年到期现在公平价格=70（）+1000（）=974.23一年后公平价格为=70（）+1000（）=982.17过去的一年的回报率为70+7.94/973.23=8%,Whenbondpricesaresetaccordingtothepresentvalueformula,anydiscountfromparvalueprovidesananticipatedcapitalgainthatwillaugmentabelow-marketcouponratejustsufficientlytoprovideafairtotalrateofreturn.,Ifthecouponrateexceedsthemarketinterestrate,theinterestincomebyitselfisgreaterthanavailableelsewhereinthemarket.Thepriceisgreaterthantheparvalue,theresultingcapitallossesoffsetthelargecouponpaymentssothattheinvestorreceiveonlyafairrateofreturn.,Eachbondoffersinvestorsthefairtotalrateofreturn.Althoughthecapitalgainversusincomecomponentsdiffer,thepriceofeachbondissettoprovidecompetitiverates,asweshouldexpectinwell-functioningcapitalmarkets.,Securityreturnsallshouldbecomparableonanafter-taxrisk-adjustedbasis.Iftheyarenot,investorswilltrytoselllow-returnsecurities,therebyderivingdownthepricesuntilthetotalreturnatthenowlowerpriceiscompetitivewithothersecurities.Pricesshouldcontinuetoadjustuntilallsecuritiesarefairlypricedinthatexpectedreturnsareappropriate(givennecessaryriskandtaxadjustments),2.Fixed-incomeportfoliomanagement,这里所谓的风险管理，是针对债券的利率风险控制，而债券本身的风险（例如，违约风险）不在讨论范围之内。,2.1利率风险,Asinterestratesriseandfall,bondholdersexperiencecapitallossesandgains.Thesegainsorlossesmakefixed-incomeinvestmentsrisky,evenifthecouponandprincipalpaymentsareguaranteed,asinthecaseofTreasuryobligations.Whydobondpricesrespondtointerestratefluctuations?Inacompetitivemarketallsecuritiesmustofferinvestorsfairexpectedratesofreturn.,Thesensitivityofbondpricestochangesinmarketinterestratesisobviouslyofgreatconcerntoinvestors.,债券定价定理：说明市场收益变化和价格变动之间的关系（定性描述）。假设每年支付一次利息，以到期收益为研究对象：,1.如果债券的市场价格上升，则收益下降；反过来，如果债券价格下降，则收益上升。,2.如果债券的收益在到期日之前不变，则它的折价或者酬金的规模将随着到期日的接近而下降。,Today,MaturityDate,ParValue,Priceofapremiumbond,Priceofadiscountbond,premium,discount,3.如果债券的收益在到期日之前不变，则它的折价或者酬金的规模变化速度随着到期日的靠近加快。4.当债券的收益上升和下降相同的数量时，收益上升导致价格下降的规模，小于收益下降导致价格上升的规模。,5.债券的息率越高，由收益变化导致的价格变化的百分比越小。,例子,BondC:couponrate=7%,yield=7%,P=1000BondD:couponrate=9%,yield=7%,P=1082whenyieldchangetobe8%bondC:price1000960.03,3.993%bondD:price10821039.933.889%,6.长期债券的价格对利率变化的敏感度大于短期债券的敏感度。即，长期债券有更大的利率风险。7.债券发行时的初始到期收益越低，则它对收益变化的敏感度越大。债券价格对市场利率变化的敏感度受三个关键因素的影响：到期日，息率，到期收益,2.2Duration,Thepropositionsconfirmthatmaturityisamajordeterminantofinterestraterisk.However,thealsoshowthatmaturityaloneisnotsufficienttomeasureinterestratesensitivity.,例子：息率8%的债券,Becauseweknowthatlongtermbondsaremoresensitivetointerestratemovementsthanareshorttermbonds,insomesenseazerocouponbondrepresentsalonger-termbondthananequal-time-maturitycouponbond.Thisistheinsightabouteffectivematurity.,比较20年到期的零息债券和带息债券(8%couponrate)。The20-year8%bondmakesmanycouponpayments,mostofwhichcomeyearsbeforethebondsmaturitydate.Eachofthesepaymentsmaybeconsideredtohaveitsown“maturitydate”,andtheeffectivematurityofthebondisthereforesomesortofaverageofthematuritiesofallthecashflowspaidoutbythebond.Thezero-couponbond,bycontrast,makesonlyonepaymentatmaturity.Itstimetomaturityisawelldefinedconcept.,Todealwiththeambiguityofthematurityofabondmakingmanypayments,weneedameasureoftheaveragematurityofthebondspromisedcashflowstoserveasausefulsummarystatisticoftheeffectivematurityofthebond.Wewouldlikealsotousethemeasureasaguidetothesensitivityofabondtointerestratechanges.,Duration,这里表示在时间接受的现金流的现值，利用债券的到期收益作为折现率得到。表示债券现在的市场价格。表示债券剩下的距到期日的时间。,8%,Bond,Time,years,Payment,PVofCF,(10%),Weight,C1X,C4,.5,40,38.095,.0395,.0197,1,40,36.281,.0376,.0376,1.5,2.0,40,1040,sum,34.553,855.611,964.540,.0358,.,8871,1.000,.0537,1.7742,1.8852,DurationCalculation:ExampleusingTable16.3,Duration,当到期收益保持不变时，证券组合duration是单个债券duration的加权和,Duration在固定收益投资组合管理中的作用测量证券组合有效平均到期日的统计量度量证券组合对利率的敏感度（定量刻画）anessentialtoolinimmunizingportfoliosfrominterestraterisk,Duration和股票价格变化之间的关系,这里表示债券价格的变化是债券的初始价格是到期收益的变化是初始的到期收益,例子,Bond:couponrate8%,yieldtomaturity8%,parvalue1000,price1000,duration10whenyieldtomaturity8%9%,Whatdeterminesduration?,DurationMaturity,Zerocouponbond,15%couponYTM=6%,3%couponYTM=15%,15%couponYTM=15%,Ruleforduration零息债券的duration等于其到期日到期日保持不变，息率越低，duration越高息率不变，到期日越大，duration一般越大。对等价或者溢价发行的债券，上述关系总是成立别的因素不变，到期收益越低，带息债券的duration越高。,永久性现金流的duration为到期日与duration的差别当到期日越来越大时，duration接近于相应永久性现金流的duration注意支付时间单位与利率之间的一致性,2.3Convexity,Asameasureofinterestratesensitivity,durationclearlyisakeytoolinfixedincomeportfoliomanagement.Thedurationrulefortheimpactofinterestratesonbondpricesisonlyanapproximation.,Yield,Price,Duration,PricingErrorfromconvexity,DurationandConvexity,Thedurationruleisagoodapproximationforsmallchangesinbondyield,butitislessaccurateforlargerchanges.Thedurationapproximationalwaysunderstatesthevalueofthebond,itunderestimatestheincreaseinbondpricewhentheyieldfalls,anditoverestimatesthedeclineinpricewhentheyieldrises.Thecurvatureofthepriceyieldcurveiscalledtheconvexityofthebond.,Asapracticalrule,wecanviewbondswithhigherconvexityasexhibitinghighercurvatureinthepriceyieldrelationship.Convexityallowsustoimprovethedurationapproximationforbondpricechanges.,CorrectionforConvexity,CorrectionforConvexity:,Ex.A30-yearmaturity,an8%coupon,andsellsataninitialyieldtomaturityof8%.Thebondsellsatparvalue,$1000.Themodifieddurationis11.26years.Ifthebondsyieldincreasefrom8%to10%,thebondpricewillfallto$811.46,adeclineof18.85%.ThedurationrulewouldpredictTheduration-with-convexityruley,Whydoinvestorslikeconvexity?,BondA,BondB,BondAhasgreaterpriceincreasesandsmallerpricedecreaseswheninterestratesfluctuatebylargeramounts.,2.4Passivebondmanagement,Passivemethods假设债券市场时半强有效的。证券选择(securityselection)和决定交易时间(markettiming)都是无用的，不会带来超平均的收益。Activemethods假设债券市场不是非常有效的。通过准确预测利率来辨别误定价的债券或者制定交易时间，从而能够获得超额收益。,Passivemethods,消极债券管理认为债券的价格是公平的，只能控制固定收入证券组合的风险主要策略：指标化策略:复制给定债券指标的行为Immunization策略：shieldtheoverallfinancialstatusoftheinstitutionfromexposuretointerestratefluctuations.,两者认为市场价是公平的两者的区别债券-指标证券组合和债券市场指标具有相同的风险-收益回报Immunization建立了零风险的证券组合，利率的波动对公司的价值没有影响。,Bond-indexfundsCreateaportfoliothatmirrorsthecompositionofanindexthatmeasuresthebroadmarket.债券市场指标LehmanBrothers,MerrillLynch,SalomonBrothersNumberofissuesmaturityofincludedbondsexcludedissuesweightingreinvestmentDailyavailability,构造反映债券市场指标的证券组合问题：债券种类过多，难以一一购买交易少，很难以公平市价买到指标中包含的所有债券指标不断更换到期日少于1年的债券不断调整，利息收入重投资方法：精确复制债券指标不可行，采用cellular方法把债券市场分成几类指标中债券在各类中占的比例按这一比例构造债券组合,Intheseway,thecharacteristicsoftheportfoliointermsofmaturity,couponrate,creditrisk,industrialrepresentation,andsoon,willmatchthecharacteristicsoftheindex,andtheperformanceoftheportfoliolikewiseshouldmatchtheindex.,Immunization,两种不同的看待利率风险的方式银行，使得资产净现值不受利率波动的影响养老金，使得资产将来的值不受风险的影响Whatiscommontothebankandthepensionfundisinterestraterisk.Thenetworthofthefirmortheabilitytomeetfutureobligationsfluctuateswithinterestrates.通过适当调整证券组合的到期日结构，规避利率风险Immunizationtechniquesrefertostrategiesusedbysuchinvestorstoshedtheiroverallfinancialstatusfromexposuretointerestratefluctuations.,Networthimmunization,例子：承诺在两年后支付1000000元，有两种债券可供选择：债券1年2年3年yiel2107010%,例子：保险公司以价格10000元发行一种guaranteedinvestmentcontract(GIC)，5年到期，保证利率为8%。假设公司选择息率8%，6年到期、价格为10000元的带息债券为债务提供基金。价格风险重投资风险,Terminalvalueofabondportfolioafter5years(allproceedsreinvested)A.ratesremainat8%,Terminalvalueofabondportfolioafter5years(allproceeds