(29)-CFA固定收益证券

CFA固定收益证券Chapter3.12YieldSpread第三章第十二节：利差YieldSpreadandBenchmarkSpreadAyieldspreadisthedifferencebetweentheyieldsoftwodifferentbonds.Yieldspreadsaretypicallyquotedinbasispoints.Ayieldspreadrelativetoabenchmarkbondisknownasabenchmarkspread.Thebenchmarkbondmusthaveasamematurityasthenon-benchmarkbondwhencalculatingbenchmarkspread.Normally,on-the-rungovernmentbondsareusedasthebenchmarkbondsforfixedcouponbonds.SowealsocallthebenchmarkspreadastheG-spread.Forexample,ifa5-yearcorporatebondhasayieldof6.25%anditsbenchmark,the5-yearTreasurynote,hasayieldof3.50%,thecorporatebondhasabenchmarkspreadof625-350=275basispoints.Althoughthebenchmarkspreadonlyreflectsissuer-specificrisk,itmaystillbeaffectedbycertainchangesofmacroeconomicfactors.Forexample,inthefinancialcrisisperiod,thebenchmarkspreadsgenerallywiden.9/13/2023Page1YieldSpreadsOverTheBenchmarkYieldCurvesWhenwewanttopriceabondusingasinglediscountrate,

we

normallyfindtheaverageG-spreadofothersimilarbondsovertheTreasuryyieldcurveatagivenmaturity.Whenwewanttopriceabondusingspotrates,weneedtocalculateaconstantspreadcoversarangeofmaturitiesovertheTreasuryspotratecurve.Thisspreadiscalledzero-volatilityspread,orZ-spread.9/13/2023Page2G-SpreadandZ-SpreadExample1:A6%annualcouponcorporatebondwithtwoyearsremainingtomaturityistradingatapriceof100.125.Thetwo-year,4%annualpaymentgovernmentbenchmarkbondistradingatapriceof100.750.Theone-yearandtwo-yeargovernmentspotratesare2.10%and3.635%,respectively.CalculatetheG-spreadandZ-spreadofthecorporatebond.Solution:TheYTMofthecorporatebondiscalculatedasN=2,PV=-100.125,PMT=6,FV=100,getI/Y=5.932;TheYTMofthegovernmentbondiscalculatedasN=2,PV=-100.75,PMT=4,FV=100,getI/Y=3.605.Therefore,G-spread=5.932%-3.605%=233basispoints.9/13/2023Page3G-SpreadandZ-SpreadSolution(continue):TocalculatetheZ-spread,wehavethefollowingformula:ButwearenotabletousefinancialcalculatortogetavalueforZ,wehavetoadoptthetrial-and-errormethod.Finally,wewillfindthat,whenZ=0.0234,thepresentvalueofdiscountedcashflowsequalstothebond’smarketprice.Therefore,Z-spreadis234basispoints.9/13/2023Page4Option-AdjustedSpreadAnoption-adjustedspreadisusedforbondswithembeddedoptions.Looselyspeaking,theoption-adjustedspreadtakestheoptionyieldcomponentoutoftheZ-spreadmeasure.OAS=Z-spread–OptionValueIfacallablebondhasaZ-spreadof180basispoints,andthevalueofthecalloptionis60basispoints,theOASforthiscallablebondis180-60=120basispoints。IfaputablebondhasaZ-spreadof