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Section B – TWO questions ONLY to be attemptedGNT Co is considering an investment in one o

Section B – TWO questions ONLY to be attempted

GNT Co is considering an investment in one of two corporate bonds. Both bonds have a par value of $1,000 and pay coupon interest on an annual basis. The market price of the first bond is $1,079？68. Its coupon rate is 6% and it is due to be redeemed at par in five years. The second bond is about to be issued with a coupon rate of 4% and will also be redeemable at par in five years. Both bonds are expected to have the same gross redemption yields (yields to maturity).

GNT Co considers duration of the bond to be a key factor when making decisions on which bond to invest.

Required:

(a) Estimate the Macaulay duration of the two bonds GNT Co is considering for investment. (9 marks)

(b) Discuss how useful duration is as a measure of the sensitivity of a bond price to changes in interest rates. (8 marks)

答案
(a)Inordertocalculatethedurationofthetwobonds,thepresentvalueoftheannualcashflowsandthepriceorvalueatwhichthebondsaretradingatneedtobedetermined.Todeterminethepresentvalueoftheannualcashflows,theyneedtobediscountedbythegrossredemptionyield(i).GrossRedemptionYield(b)Thesensitivityofbondpricestochangesininterestratesisdependentontheirredemptiondates.Bondswhichareduetoberedeemedatalaterdatearemoreprice-sensitivetointerestratechanges,andthereforeareriskier.Durationmeasurestheaveragetimeittakesforabondtopayitscouponsandprincipalandthereforemeasurestheredemptionperiodofabond.Itrecognisesthatbondswhichpayhighercouponseffectivelymature‘sooner’comparedtobondswhichpaylowercoupons,eveniftheredemptiondatesofthebondsarethesame.Thisisbecauseahigherproportionofthehighercouponbonds’incomeisreceivedsooner.Thereforethesebondsarelesssensitivetointerestratechangesandwillhavealowerduration.Duration,ontheotherhand,assumesthattherelationshipbetweenchangesininterestratesandtheresultantbondislinear.Thereforedurationwillpredictalowerpricethantheactualpriceandforlargechangesininterestratesthisdifferencecanbesignificant.Durationcanonlybeappliedtomeasuretheapproximatechangeinabondpriceduetointerestchanges,onlyifchangesininterestratesdonotleadtoachangeintheshapeoftheyieldcurve.Thisisbecauseitisanaveragemeasurebasedonthegrossredemptionyield(yieldtomaturity).However,iftheshapeoftheyieldcurvechanges,durationcannolongerbeusedtoassessthechangeinbondvalueduetointerestratechanges.(Note:Creditwillbegivenforalternativebenefits/limitationsofduration)
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