FRM工行总行培训材料4_Valuation_and_Risk_Models

謝承熹1BruceTuckman,FixedIncomeSecurities,2ndEdition(Hoboken,NJ:JohnWiley&Sons,2002)Chapter1–BondPrices,DiscountFactors,andArbitrage---------------------------------------------------------------------------------------------------------AIM1:Describeandcontrastindividualandmarketexpressionsofthetimevalueofmoney.---------------------------------------------------------------------------------------------------------DETERMININGTHECASHFLOWSCouponsareoftenstatedinannualtermsandmustbeadjustedforperiodicity.Oncethecashflowsaredetermined,thepresentvalue(PV)ofthecashflowscanbecomputed.FOUNDAMENTALSOFBONDVALUATIONThevalue(orprice)ofanyfinancialassets–suchasabond–canbedeterminedbysummingtheasset’sdiscountedcashflows.Therearethreestepsinthebondvaluationprocess:Estimatethecashflow.Forabond,therearetwotypesofcashflows:(1)theannualorsemiannualcouponpaymentsand(2)therecoveryofprincipalatmaturity,orwhenthebondisretired.Determinetheappropriatediscountrate.Theapproximatediscountrateiseitherthebond’syieldtomaturity(TYM)oraseriesofspotrates.CalculatethePVoftheestimatedcashflows.Inthistopic,theconcentrationisonbondsthatpaycouponssemiannuallyineven6-monthfromsettlement.PRICEQUOTATIONSBondsarequotedonapercentagebasisrelativetoaparvalue.Treasurynotesandbondsusea“32nds”convention.A“+”inthequoteindicatesahalftick.Corporateandmunicipalbondsarequotedineighths.謝承熹2DISCOUNTFACTORS---------------------------------------------------------------------------------------------------------AIM2:Definediscountfactoranduseadiscountfunctiontocomputepresentandfuturevalues.---------------------------------------------------------------------------------------------------------Thediscountfactorforaparticulartermgivesthevaluetoday,orthepresentvalueofoneunitofcurrencytobereceivedattheendofthatterm.謝承熹3DETERMININGVALUEUSINGDISCOUNTFUNCTIONS---------------------------------------------------------------------------------------------------------AIM3:Definethe“lawofoneprice”,supportitusinganarbitrageargument,anddescribehowitcanbeappliedtobondpricing.AIM6:Identifyarbitrageopportunitiesforfixedincomesecuritieswithcertaincashflows.---------------------------------------------------------------------------------------------------------Sinceinvestorsdonotcareabouttheoriginofacashflow,allelseequal,acashflowfromonebondisjustasgoodasacashflowfromanotherbond.Thisphenomenoniscommonlyreferredtoasthelawofoneprice.謝承熹4TREASURYCOUPONBONDSANDTREASURYSTRIPS---------------------------------------------------------------------------------------------------------AIM4:DiscussthecomponentsofaU.S.Treasurycouponbond,andcompareandcontrastthestructuretoTreasurySTRIPS,includingthedifferencebetweenP-STRIPSandC-STRIPS.---------------------------------------------------------------------------------------------------------Zero-couponbondsissuedbyTreasuryarecalledSTRIPS(separatetradingofregisteredinterestandprincipalsecurities)STRIPSarecreatedbyrequestwhenacouponbondispresentedtotheTreasury.Thebondis“stripped”intotwocomponents:principalandcoupon(P-STRIPSandC-STRIPS,respectively).謝承熹5TheTreasurycanalsoretireaSTRIPbygatheringthepartsuptoreconstitute,orremake,thecouponbond.C-STRIPScanbeputwithanybondtoreconstitute,butP-STRIPSareindentifiedwithspecificbonds.STRIPSareofinteresttoinvestorsbecause:Zerocouponbondscanbeeasilyusedtocreateanytypeofcashflowstreamandthusmatchassetcashflowswithliabilitycashflows.Zero-couponbondsaremoresensitivetointerestratechangesthanarecouponbonds.Thiscouldbeanissueforasset-liabilitymanagementorhedgingpurposes.STRIPSdohavesomedisadvantages,whichincludethefollowing:Theycanbeilliquid.Shorter-termC-STRIPStendtotraderich.Longer-termC-STRIPStendtotradecheap.P-STRIPStypicallytradeatfairvalue.LargeinstitutionscanpotentiallyprofitfromSTRIPmispricingsrelativetotheunderlyingbonds.謝承熹6CONSTRUCTINGAREPLICATINGPORTFOLIO---------------------------------------------------------------------------------------------------------AIM5:Deriveareplicatingportfoliousingmultiplefixed-incomesecuritiesinordertomatchthecashflowsofasinglegivenfixedincomesecurities.---------------------------------------------------------------------------------------------------------Supposea2-yearfixedincomesecurityexistswith$100facevalueanda10%couponrate.Thecouponsarepaidonasemiannualbasis,andthesecurity’sYTMisassumedtobe4.5%.Thepresentvalueofthisbond,Bond1,anditscashflowsarecalculatedasfollows:Todemonstratethecreationofareplicatingportfolio,assumethefollowingfourfixedincomesecuritiesexists.Tocreateareplicatingportfoliousingmultiplefixed-incomesecurities,wemustdeterminethefaceamountsofeachbondtopurchase,Fi,whichmatchBond1cashineachsemiannualperiod.Itiseasiesttostartfromtheend–withthebondthatmatchesBond1’stimehorizon.謝承熹7謝承熹8謝承熹9謝承熹10BruceTuckman,FixedIncomeSecurities,2ndEdition(Hoboken,NJ:JohnWiley&Sons,2002)Chapter2–BondPrices,SpotRates,andForwardRatesANNUALCOMPOUNDINGVS.SEMIANNUALCOMPOUNDING---------------------------------------------------------------------------------------------------