CHAPTER4BONDPRICEVOLATILITYCHAPTERSUMMARYTouseeffectivebondportfoliostrategies,itisnecessarytounderstandthepricevolatilityofbondsresultingfromchangesininterestrates.Thepurposeofthischapteristoexplainthepricevolatilitycharacteristicsofabondandtopresentseveralmeasurestoquantifypricevolatility.REVIEWOFTHEPRICE-YIELDRELATIONSHIPFOROPTION-FREEBONDSAnincrease(decrease)intherequiredyielddecreases(increases)thepresentvalueofitsexpectedcashflowsandthereforedecreases(increases)thebond’sprice.Thisrelationshipisnotlinear.Theshapeoftheprice-yieldrelationshipforanyoption-freebondisreferredtoasaconvexrelationship.PRICEVOLATILITYCHARACTERISTICSOFOPTION-FREEBONDSTherearefourpropertiesconcerningthepricevolatilityofanoption-freebond.(i)Althoughthepricesofalloption-freebondsmoveintheoppositedirectionfromthechangeinyieldrequired,thepercentagepricechangeisnotthesameforallbonds.(ii)Forverysmallchangesintheyieldrequired,thepercentagepricechangeforagivenbondisroughlythesame,whethertheyieldrequiredincreasesordecreases.(iii)Forlargechangesintherequiredyield,thepercentagepricechangeisnotthesameforanincreaseintherequiredyieldasitisforadecreaseintherequiredyield.(iv)Foragivenlargechangeinbasispoints,thepercentagepriceincreaseisgreaterthanthepercentagepricedecrease.Anexplanationforthesefourpropertiesofbondpricevolatilityliesintheconvexshapeoftheprice-yieldrelationship.CharacteristicsofaBondthatAffectitsPriceVolatilityTherearetwocharacteristicsofanoption-freebondthatdetermineitspricevolatility:couponandtermtomaturity.First,foragiventermtomaturityandinitialyield,thepricevolatilityofabondisgreater,thelowerthecouponrate.Thischaracteristiccanbeseenbycomparingthe9%,6%,andzero-couponbondswiththesamematurity.Second,foragivencouponrateandinitialyield,thelongerthetermtomaturity,thegreaterthepricevolatility.EffectsofYieldtoMaturityAbondtradingatahigheryieldtomaturitywillhavelowerpricevolatility.Animplicationofthisisthatforagivenchangeinyields,pricevolatilityisgreaterwhenyieldlevelsinthemarketCopyright©2010PearsonEducation,Inc.PublishingasPrenticeHall.60arelow,andpricevolatilityislowerwhenyieldlevelsarehigh.MEASURESOFBONDPRICEVOLATILITYMoneymanagers,arbitrageurs,andtradersneedtohaveawaytomeasureabond’spricevolatilitytoimplementhedgingandtradingstrategies.Threemeasuresthatarecommonlyemployedarepricevalueofabasispoint,yieldvalueofapricechange,andduration.PriceValueofaBasisPointThepricevalueofabasispoint,alsoreferredtoasthedollarvalueofan01,isthechangeinthepriceofthebondiftherequiredyieldchangesby1basispoint.Notethatthismeasureofpricevolatilityindicatesdollarpricevolatilityasopposedtopercentagepricevolatility(pricechangeasapercentoftheinitialprice).Typically,thepricevalueofabasispointisexpressedastheabsolutevalueofthechangeinprice.Pricevolatilityisthesameforanincreaseoradecreaseof1basispointinrequiredyield.Becausethismeasureofpricevolatilityisintermsofdollarpricechange,dividingthepricevalueofabasispointbytheinitialpricegivesthepercentagepricechangefora1-basis-pointchangeinyield.YieldValueofaPriceChangeAnothermeasureofthepricevolatilityofabondusedbyinvestorsisthechangeintheyieldforaspecifiedpricechange.Thisisestimatedbyfirstcalculatingthebond’syieldtomaturityifthebond’spriceisdecreasedby,say,Xdollars.ThenthedifferencebetweentheinitialyieldandthenewyieldistheyieldvalueofanXdollarpricechange.Thesmallerthisvalue,t...
