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1、MANAGINGINTERESTRATERISK:DURATIONGAPANDMARKETVALUEOFEQUITYChapter9BankManagement,5thedition.TimothyW.KochandS.ScottMacDonaldCopyright©2003bySouth-Western,adivisionofThomsonLearningDurationGAP…focusonmanagingNIIorthemarketvalueofequity,recognizingthetimingofcashflows.Interestrateriskismea
2、suredbycomparingtheweightedaveragedurationofassetswiththeweightedaveragedurationofliabilities.IfAssetduration>LiabilitydurationinterestratesMarketvalueofequitywillfall.Durationversusmaturity1.)1000loan,principal+interestpaidin20years.2.)1000loan,900principalin1year,100principalin20y
3、ears.1000+int
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6、01020900+int100+int
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10、011020Whatisthematurityofeach?20yearsWhatisthe"effective"maturity?2.)=[(900/100)x1]+[(100/1000)x20]=2.9yrs12Duration,however,usesaweightedaverageofthepresentvalues.SolveforPrice
11、:P-Durationx[y/(1+y)]xPPrice(value)changesLongermaturity/durationlargerchangesinpriceforagivenchangeini-rates.Largercouponsmallerchangeinpriceforagivenchangeini-rates.Duration…approximatemeasureofthepriceelasticityofdemandIngeneralnotation,Macaulay’sduration(D):Examples1000face,10%coup
12、on,3year,12%YTMMeasuringdurationIfYTM=5%1000face,10%coupon,3year,5%YTMIfYTM=20%1000face,10%coupon,3year,20%YTMIfYTM=12%andCoupon=01000face,0%coupon,3year,12%YTM1000
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16、0123DurationandmodifieddurationDurationallowsmarketparticipantstoestimatetherelativepricevolatil
17、ityofdifferentsecurities:Usingmodifiedduration:modifiedduration=Macaulay’sduration/(1+y)Wehaveanestimateofpricevolatility:%changeinprice=modifieddurationxDyEffectiveDuration…usedtoestimateasecuritiespricesensitivitywhenthesecuritycontainsembeddedoptions.EffectivedurationisWherePi-=price
18、ifratesfall,Pi+=priceifratesrise;P0=initial(current)price;i+initialmarketrateplustheincreaseinrate;i-=initialmarketrateminusthedecreaseinrate.Effectivedurationcomparesasecurity’sestimatedpriceinafallingandrisingrateenvironment.Effectivedurationexample:Considera3