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ACTSC 445 (24)
Lecture

unit5 measuring interest rate risk

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Department
Actuarial Science
Course
ACTSC 445
Professor
Jiahua Chen
Semester
Fall

Description
ACTSC445AssetLiabilityManagementDepartmentofStatisticsandActuarialScienceUniversityofWaterlooUnit5MeasuringInterestRateRiskReferencesrecommendedreadingsChap9ofFabozzietalAsmentionedbeforetheholderofaxedincomesecurityorportfolioisexposedtointerestrateriskThatisifinterestratesincreasethepriceofthesecuritywilldropwhichmayresultintoalossfortheinvestorifhesheneedstosellthesecuritybeforematurityItisimportantforinvestorstoassessthesensitivityofxedincomesecuritiestochangesininterestratesinaprecisequantitativewaysothattheinterestrateriskcanbebetterunderstoodInthisunitwellseedierentwaystodothat1Thefullvaluationapproach2Pricevalueofabasispoint3DurationandconvexitywellspendmostofourtimeonthatapproachWewillalsodiscussalternativedenitionsofdurationthatcanbeusedinmorecomplexsettingsBeforewegooverthesedierentapproachesitisimportanttomentionthatinwhatfollowsmostofthetimewewilllookatinterestrateschangesasbeingobservedonytmsAlsounlessotherwisestatedweassumebondspaysemiannualcouponsAsanexampleweshowinTable1howthepriceofdierentbondsvarywhentheytmgoesfrom4todierentvaluesrangingbetween2and6AllratesbelowareassumedtobeannualcompoundedsemiannuallyFigure1givesagraphicaldepictionofthenumbersgiveninTable1Table1Bondpricesasafunctionofyieldytm44year412year84year812year210765121241229616373310374110021187115008351018510487116661437939100371009511505138993991000410009114691379441001001146513783401999699911146113771419963990611425136674598199540112681321859641910611076126836929883061070211694Equivalentlywecancomputetheinstantaneouspercentagechangeofthebondspriceforthedierentchangesintheytm1Figure1BondpricesasafunctionofyieldTable2Bondspricepercentagechangeasafunctionofyieldytm44year412year84year812year27652124724187933741002354889351854871754323903709503508539900400900300840100400900300841037094035084451814601724105359894340798670216946661516SeveralcommentsaboutthesensitivityofthebondspricetochangesininterestratescanbeobservedfromTables1and2ForsmallchangesintheytmthepercentagepricechangeforagivenbondisroughlythesamewhethertheytmgoesupordownForlargechangesintheytmthepercentagepricechangeisusuallylargerinabsolutevalueforadecreaseintheytmiewhenthepricegoesupthanforanincreaseintheytmiewhenthepricegoesdownThatisthepercentagepricechangeisasymmetricThedegreeofsensitivityofthebondspriceisaectedbydierentpropertiesofthebondmaturitythelongermaturitiesseemtohaveagreatersensitivity2
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