(22)-CFA固定收益证券

CFA固定收益证券Chapter3.5FlatPrice,AccruedInterests,andFullPrice第三章第五节：债券的报价，应计利息与全价BondPricingbetweenCouponDatesForthebondvaluationwehavelearnedinprevioussections,wehaveassumedthatthenextcouponpaymentispreciselyinonepaymentperiodfromnow,eitherayearforanannualcouponbondorsixmonthsforasemiannualcouponbond.Butnormally,investorswanttopricethebondall365daysoftheyear,notjustononeortwodateseachyearthatitmakescouponpayment.Nevertheless,wecanstillpricethebondbydiscountingallfuturecashflows,butjustmakecertainadjustmentsinthediscountfactor.ThebondpricecalculatedinthiswayiscalledInvoicePrice(FullPrice),whichispricethatbuyerpaysseller.9/12/2023Page1BondPricingbetweenCouponDatesTocalculatethebondpricebetweencouponsdates,weneedtodeterminetheFractionPeriod(w)betweensettlementdateandnextcouponpaymentdate.9/12/2023Page2C1C2CT-1C3………012………T-13TCT+PartwAccruedInterestIfabondistradedbetweentwocoupondates,thenthenextcouponpaymentencompassestwocomponentsasshownbelow:InterestearnedbythesellerInterestearnedbythebuyer

Theinterestearnedbytheselleristheinterestthathasaccruedbetweenthelastcoupondateandsettlementdate.Accruedmeanstheinterestisearnedbutnotdistributed.WecallitAccruedInterest(AI).9/12/2023Page3Day-CountConventionsTherearedifferentconventionsusedinbondmarketstocountdays.Thetwomostcommonday-countconventionsareactual/actualand30/360.Fortheactual/actualmethod,theactualnumberofdaysisused.Itismostcommonforgovernmentbonds.30/360methodassumesthateachmonthhas30daysandthatafullyearhas360days.Itoftenusedforcorporatebonds.9/12/2023Page4CalculationofAccruedInterestExample1:Considera6%semi-annualcouponbondwith$1000parvaluepaidlastcoupononMar1,2019andthenextcoupondatewouldbeSep1,2019.SupposethebondispurchasedonJuly17,2019,whatisitsaccruedinterestifactual/actualor30/360day-countconventionsareused,respectively?Solution:Ifactual/actualday-countconventionisused:

9/12/2023Page5DaysbetweenlastcoupondateandsettlementdateMar2toMar3130daysApr30daysMay31daysJune30daysJul1toJul1717days138daysDaysinthecouponperiodMar2toMar3030daysApr30daysMay31daysJune30daysJul31daysAug31daysSep11day184daysSincethesemi-annualcouponpaymentis1000*0.06/2=$30AccruedInterest=30*138/184=$22.5CalculationofAccruedInterestSolution(continue):If30/360day-countconventionisused:

9/12/2023Page6DaysbetweenlastcoupondateandsettlementdateMar2toMar3029daysApr30daysMay30daysJune30daysJul1toJul1717days136daysSincethesemi-annualcouponpaymentis1000*0.06/2=$30AccruedInterest=30*136/180=$22.67Daysinthecouponperiod180daysCalculationofFullPriceExample2:Aninvestorpurchasesa6%semi-annualcouponbondwith$1000parvalueonJuly17,2019.ThebondpaidlastcoupononMar1,2019andthenextcoupondatewouldbeSep1,2019.Ifthebond’sYTMis5%tillitsmaturityonSep1,2021,whatisitsfullprice?(useactual/actualday-countconvention)Solution:ThebondpriceonMar1,2019shouldbe$1023.23,asN=5,I/Y=2.5,PMT=30andFV=1000.ThefractionperiodbetweenJuly17andSep1,w=46/184=0.25SothebondpriceonJuly17,2019shouldbe1023.23*(1+0.025)1-0.25=$1042.369/12/2023Page7FlatPriceFlatPrice(CleanPrice)isthedifferencebetweenInvoicePriceandAccruedInterest.Moreimportant,itisthequotedpriceinbondmarkets,whichmeansbondpricesarequotednetofaccruedinterest.Therearetworeasonstouseflatpriceratherthanfullpricetoquoteabond:Ifthefullpriceweretobequotedbydealers,investorswouldseethepricerisedayafterdayeveniftheyield-to-maturitydidnotchange.Thatisbecausetheamountofaccruedinterestincreaseseachday.Then,afterthecouponpaymentismade,thequotedpricewoulddropdramatically.Usingtheflatpriceforquotationavoidsthatmisrepresentation.Theaccruedinterestpartofthefullpricedoesnotdependontheyield-to-maturity.Therefore,itistheflatpricethatisaffectedbyamarketdiscountratechange.9/12/2023Page8QuotesforTreasuryCouponSecuritiesTreasurycouponsecurities(notesandbonds)arequotedonapricebasisinpointswhereonepointequals1%ofpar(equivalenttosayquotedatthepercentageofthepar).Onepointcanbesplitintounitsof32nds,andthe32ndscanbefurthersplitbytheadditionofaplussignoranumbertoindicatethedecimalnumbers.Aplussignindicatesthathalfa32nds(ora64th)isaddedtotheprice,andanumberindicateshowmanyeighthof32nds(or256ths)areaddedtotheprice.9/12/2023Page991+19/32=91.5937591+19/32+1/64=91.609375109+6/32+6/256=109.2109375CalculationofFullPriceExample3:Thequotedpricefora$1000parvalueT-bondonJun10i