1、(1)TFVr123(1)(1)(1)(1)TCCCFVCrrrr25550505010001.061.061.061.06$210.62$747.26$957.88PV 12310102525252510001.031.031.031.031.03$213.26$744.09$957.35PV 1Yearr1 = 0f1 r1 = 0f1 r2 = 0r2 represented by 1 year rate1f2 at t=0.CARPYTMYTMCGenericlowqualitybondAGenerichighqualitybondMCYTMnAAAnB0321$14311.1268$
2、1000100(1.10)100(1.10)10011001431CCBCCallDateValueARRPARRCallDateValue071037101$1431(1.08)1.0938$1000(1.1268) (1.08)1.0938HDHDBHDHDHDValueARRPARRARR9.38%10%HDARRYTMCallNCRPYTMYTMRPgreater in higher interest rate periodsRRP YTMPB0AAYTM*ACPAA NonCallable BondAA Callable Bondr ()INT on INT PtB2.51.5.53
3、.53.5.564611/3.53.5100(1.10)100(1.10)100(1.10)1395.971000 100:1048.81(1.10)10010001000(1.10)(1.10)1395.971.101000BBBttHDValuePwhere PPARR2.51.5.53.53.5.564611/3.53.5100(1.12)100(1.12)100(1.12)1319917.77 100:961.70(1.12)1001000917.77(1.12)(1.12)13191.08231000BBBttHDValuePwhere PPARR2.51.5.53.53.5.564
4、611/3.53.5100(1.08)100(1.08)100(1.08)1482.821092.46 100:1147.44(1.08)10010001092.46(1.08)(1.08)1484.821.11951000BBBttHDValuePwhere PPARR3.58% 11.95%10% 10.00%12% 8.23%R ARR3.58% 9.845%10% 10.00%12% 10.16%R ARR.52.51.53.53.5.51/3.53.54041200(1.12)200(1.12)200 1.1218481000200:1134(1.12)18481.101613172
5、001000:1317(1.10)(1.10)BBBttHDValuePwhere PARRWhere P3.58% 10%10% 10%12% 10%R ARR10()MtBtPV CFDtPpiiDwDDtPV CFPtBtM()01tCFCFPV CFPt WeightPDttttBB( .)()( )().1101908181800844960084496290743480076815015363039067618006983202094964109074448507688573075428968303520000%BBPPDYTMYTM010%()1(1)BMtBtPPV CFDtY
6、TMYTMP ModifiedDurationMacaulay sDuration:1(3.5)3.18(1.10)ExampleModifiedDuration 21001(/ )1(1)(1)%MMBBCM FC yyyyPyP DurationfornperiodsAnnualizedDurationn2202104.5120100(4.5/.045)1.045(1.045)(1.045)%13100136.52BPyAnnualizedDuration %()% ()BBPModifiedDurationYTMPModifiedDurationYTM% 6.5(.0910.09).00
7、65BP % 6.5(.11.09).13BP YTM0BP0y0BPYTM1y2yKLoss0y1y2yKGain0120yyyy0210/(1)()1(1)BMtBttSlope Pt tPV CFConvexityyPy2ConvexityfornlengthAnnualizedConvexityn32120212(1)(/ )1(1)(1)(1)MMMBCCMM MFC yyyyyyConvexityP3202212222(4.5)12(4.5)(20)(20)(21)100(4.5/.045)1.045(1.045)(.045) (1.045)(1.045)225.43100225.
8、4356.362ConvexityAnnualizedConvexity%/ %BPy21%()2BPModifiedDurationyConvexityy 21% 6.5(.02)56.36(.02).11872BP 29%11% :1% 6.5(.02)56.36(.02).11872ByfromtoP 29%7% :1% 6.5( .02)56.36( .02).14132ByfromtoP 01112012(1)(1)(1)(1)(1)MMBttttttBMMCFPCFyyPCFyCFyCFy 23(1)12( 1)(1)( 2)(1)()(1)BMMdPCFyCFyM CFydy 2
9、3(1)12( 1)(1)( 2)(1)()(1)BMMdPCFyCFyM CFydy 12121212121(1)(1)(2)(1)()(1)(1)1(1)(2)()(1)(1)(1)(1)1(1)()(2)()()()(1)BMMBMMBMdPCFyCFyM CFydyyCFCFCFdPMdyyyyydPPV CFPV CFM PV CFdyy 12000()()()1/1(1)(2)()(1)BMBBBPV CFPV CFPV CFdPdP PMdyPdyyPPP 10()/1(1)MtBtPV CFdP PModifiedDurationtdyyP 23(1)12( 1)(1)( 2)(1)()(1)BMMdPCFyCFyM CFydy 234(2)122022101220002(1)6(1)(1)(1)exp:(1)(1)()/11(1)(1)BMMBMMtBBttttBBBtd PCFyCFyM MCFydyDividethroughbyP andressasasummationt tCFt tPV CFdPd PyConvexitydyPdyPPy
