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1、Chapter1BondFundamentalsRiskmanagementstartswiththepricingofassets.Thesimplestassetstostudyarereg-ular,fixed-couponbonds.Becausetheircashflowsarepredetermined,wecantrans-latetheirstreamofcashflowsintoapresentvaluebydiscountingatafixedyield.Thusthevaluationofbondsinvolvesunde
2、rstandingcompoundedinterest,discounting,andtherelationshipbetweenpresentvaluesandinterestrates.Riskmanagementgoesonestepfurtherthanpricing,however.Itexaminespo-tentialchangesinthepriceofanassetastheinterestratechanges.Inthischapter,weassumethatthereisasingleinterestrate,
3、oryield,thatisusedtopricethebond.Thiswillbeourfundamentalriskfactor.Thischapterdescribestherelationshipbe-tweenbondpricesandyieldandpresentsindispensabletoolsforthemanagementoffixed-incomeportfolios.Thischapterstartsourcoverageofquantitativeanalysisbydiscussingbondfun-dam
4、entals.Section1.1reviewstheconceptsofdiscounting,presentvalues,andfuturevalues.Section1.2thenplungesintotheprice-yieldrelationship.ItshowshowtheTaylorexpansionrulecanbeusedtorelatemovementsinbondpricestothoseinyields.TheTaylorexpansionrule,however,coversmuchmorethanbonds
5、.Itisabuildingblockofriskmeasurementmethodsbasedonlocalvaluation,asweshallseelater.Section1.3thenpresentsaneconomicinterpretationofdurationandconvexity.Thereadershouldbeforewarnedthatthischapter,likemanyothersinthishand-book,israthercompact.Thischapterprovidesaquickrevie
6、wofbondfundamentalswithparticularattentiontoriskmeasurementapplications.Bytheendofthischap-ter,however,thereadershouldbeabletoansweradvancedFRMquestionsonbondmathematics.34PARTI:QUANTITATIVEANALYSIS1.1Discounting,PresentValue,andFutureValueAninvestorconsidersazero-coupon
7、bondthatpays$100in10years.SaythattheinvestmentisguaranteedbytheU.S.governmentandhasnodefaultrisk.Becausethepaymentoccursatafuturedate,thecurrentvalueoftheinvestmentissurelylessthananup-frontpaymentof$100.Tovaluethepayment,weneedadiscountingfactor.Thisisalsotheinterestrat
8、e,ormoresimplytheyield.DefineCtasthecashflowattimetandthediscountingfac-torasy.WedefineTasthenumberofperio
