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1、Chapter5:OptimalPortfoliowithFixed-IncomeAssetsThetermstructureofinterestratesChapter5OptimalPortfolioswithFixed-IncomeAssetsMaintopicsThetermstructureofinterestratesMeasuringinterestrateriskAsset/Liabilitymanagement–Portfoliodedication–PortfolioimmunizationcYongga
2、nZhao,SchoolofBusinessAdministration,DalhousieUniversity91Chapter5:OptimalPortfoliowithFixed-IncomeAssetsThetermstructureofinterestrates5.1Thetermstructureofinterestrates5.1.1YieldcurveLetPbethepriceofabondwithtimetomaturityT,thequantityysuchthatC1CT 1CT+FP=+++1+y(
3、1+y)T 1(1+y)Tiscalledtheyieldtomaturity,whereC1;;CTarethecoupons,Fisthefacevalue,andTismeasuredinyears.Theyieldtomaturityofabondisstronglytiedtogeneralconditionsinthefixed-incomesecuritiesmarket.Allyieldstendtomovetogether,butwithdif-ferentmagnitudes.Thevariationiny
4、ieldsacrossbondsisexplainedinpartbythebondqualities.Anotherfactoristhetimetomaturityofabond.Longtermbondsusuallyhavealargeryieldthanshorttermbonds.cYongganZhao,SchoolofBusinessAdministration,DalhousieUniversity92Chapter5:OptimalPortfoliowithFixed-IncomeAssetsThetermst
5、ructureofinterestratesThetreasuryyieldcurvedisplaystheyieldofaTreasurysecurityasafunc-tionofthecorrespondingtimetomaturity(Figure1).InvestorscanplaceaFigure1:Treasuryyieldcurvecorporatebondonthematurity-yieldspacetoseeageneralindicationofhowitispricedrelativetotreasur
6、ies.Ifitisfarfromthecurve,thereisprobablycYongganZhao,SchoolofBusinessAdministration,DalhousieUniversity93Chapter5:OptimalPortfoliowithFixed-IncomeAssetsThetermstructureofinterestratesareason,relatedtoaspecialfeaturesuchasacallprovisionornewsaffectingthequalityofthebo
7、nd.5.2ThetermstructureUnlikeyieldcurve,termstructurefocusesonpureinterestsarisingfromin-vestments.Supposeyouinitiallyinvest$M0andreceived$Mtattimet.Howdowemeasuretheinvestmentreturn?SpotratesSpotratesarethebasicinterestratesdefiningthetermstructure.Thespotratestisthera
8、teofinterest,expressedinyearlyterm,suchthat1=tM=M(1+s)t)s=Mt 1t0ttM0wheretismeasuredinyears-yearlycompounding.Undertheconv