FinanceandEconomicsDiscussionSeries
DivisionsofResearch&StatisticsandMonetaryAffairs
FederalReserveBoard,Washington,D.C.
TipsfromTIPS:theInformationalContentofTreasury
Inflation-ProtectedSecurityPrices
StefaniaD’Amico,DonH.Kim,andMinWei
2014-024
NOTE:Staffworkingpapersinthe FinanceandEconomics DiscussionSeries(FEDS)arepreliminary
materials circulatedtostimulatediscussionandcriticalcomment. . The e analysis andconclusions set forth
are those of the authors s anddo not t indicate concurrence by other members of the researchstaff or r the
BoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthan
acknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.
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Tips from TIPS: the Informational Content of Treasury
Inflation-Protected Security Prices
Stefania D’Amico, DonH. Kim,and MinWei
Firstdraft: April23,2006
Thisversion: February19,2016
1
D’Amico,sdamico@frbchi.org,EconomicResearchDepartment,FederalReserveBankofChicago,
Chicago,IL60622;Kim,don.h.kim@frb.gov,andWei,min.wei@frb.gov,DivisionofMonetaryAffairs,
FederalReserveBoardofGovernors,Washington,DC20551.Partoftheworkonthispaperwasdone
whileKimwasattheBankforInternationalSettlements.Wethankananonymousreferee,AndrewAng,
GeertBekaert,RuslanBikbov,ClaudioBorio,SeamusBrown,MikeChernov,JimClouse,GregDuffee,
CampbellHarvey,PeterH¨ordahl,MikeJoyce,ChiragMirani,AthanasiosOrphanides,FrankPacker,
GeorgePennacchi,JenniferRoush,BrianSack,JonathanWright,andseminarparticipantsatthe11th
InternationalConferenceonComputinginEconomicsandFinance(June2005),ECBWorkshopon
InflationRiskPremium(April2006),DallasFedConferenceonPriceMeasurementforMonetaryPolicy
(May2007),the2008AFAAnnualMeetings,andtheSanFranciscoFedforhelpfulcommentsor
discussions.Thisworkisbasedinlargepartondataconstructedbycurrentandpreviousmembersofthe
Monetary&FinancialMarketsAnalysisSectionintheMonetaryAffairsDivisionoftheFederalReserve
BoardofGovernors,towhomwearegrateful.Wealoneareresponsibleforanyerrors.Theopinions
expressedinthispaperdonotnecessarilyreflectthoseoftheFederalReserveBoardortheFederalReserve
SystemortheBankforInternationalSettlements.
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Abstract
TreasuryInflation-ProtectedSecurities(TIPS)arefrequentlythoughtofasrisk-freerealbonds.
Usingno-arbitragetermstructuremodels,weshowthatTIPSyieldsexceededrisk-freerealyields
byasmuchas100basispointswhenTIPSwerefirstissuedandupto300basispointsduringthe
recentfinancialcrisis.ThisspreadreflectspredominantlythepoorerliquidityofTIPSrelativeto
nominalTreasurysecurities.Otherfactors,includingtheindexationlagandtheembedded
deflationprotectioninTIPS,playamuchsmallerrole.Ignoringthisspreadalsosignificantly
distortstheinformationalcontentofTIPSbreakeveninflation,awidely-usedproxyforexpected
inflation.
Keywords:TIPS;Breakeven;No-arbitragetermstructuremodel;Liquidity;Expectedinflation;
Inflationriskpremium;Surveyforecasts;Indexationlag;Deflationfloor
JELclassification:G12,G01,E43,E44
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I. Introduction
TreasuryInflation-ProtectedSecurities(TIPS)arefixed-incomesecuritieswhosecouponsand
principalpaymentsareindexedtothenon-seasonally-adjustedconsumptionpriceindex(CPI)for
allurbanconsumers.
1
Sinceitsinceptionin1997,themarketforTIPShasgrownsubstantially
andnowcomprisesabout8.6%oftheentireTreasurydebtmarket.Morethanfifteenyearsof
TIPSdataprovidesarichsourceofinformationtoinvestors,policymakers,andresearchersalike.
TIPSyieldscanbeviewedasroughmeasuresofrisk-freerealinterestrates,animportant
determinantofthecostsforfinancingprivateinvestmentandpublicdebtandarguablyabetter
gaugeofthestanceofmonetarypolicythannominalinterestrates.Importantly,thespread
betweenyieldsonnominalTreasurysecuritiesandonTIPSofcomparablematurities—the
“breakeveninflationrate”(BEI)or“inflationcompensation”—isoftenusedasareal-timeproxy
formarketparticipants’inflationexpectations.
Despitethepotentialusefulnessoftheseassets,thispaperpresentsevidencethatitisessential
toaccountforthelowerliquidityofTIPSrelativetotheirnominalcounterpartswhenusingthem
tomeasurerealinterestratesandinflationexpectations.TIPSinvestorsappeartodemandextra
compensationsforholdingtheselessliquidsecurities,therebypushingupTIPSyieldsabovethe
realyieldsthatareconsistentwithnominalTreasuryyields,andpushingdownTIPSBEIbelow
itsfundamentallevels.TreatingtheTIPSBEIasacleanproxyforinflationexpectationcanbe
especiallyproblematic,sinceacombinationofeconomicallysignificantTIPSliquiditypremiums
andinflationriskpremiumscouldpotentiallydriveanotablewedgebetweentheTIPSBEIand
trueinflationexpectations.Indeed,weshowthattheearlyyearsoftheTIPSmarketandtherecent
financialcrisisprovidetwoprominentexampleswhenpoorliquiditysignificantlydistortedthe
informationcontentofTIPSprices.
Herewerefertoabroadconceptofilliquiditythatmayoriginatefromavarietyofmarket
imperfections,suchasthoseassociatedwiththeintroductionofanewfinancialinstrument(asin
1
SackandElsasser(2004)providesadetaileddescriptionoftheTIPSmarket.
1
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theearlyyearsofTIPS),variousformsoftradingcostsandfundingconstraints(asexperienced
acutelyduringtherecentfinancialcrisis),andthedemandimbalancesbetweennominal
TreasuriesandTIPS(asduringflight-to-safetyepisodes).Regardlessofthesourceofilliquidity,
weemphasizeitistheexpectedfutureliquidityofTIPSrelativetoacomparablenominal
Treasurysecurity,ratherthanmerelythecurrentortheabsolutelevelofliquidity,thatshould
determinetheliquiditypremiumembeddedinthecurrentTIPSyield.Recognizingthedifficulty
ofcapturingsuchawidevarietyofcurrentandexpectedfutureTIPSmarketconditionswithafew
observablemeasures,manyofwhichhadnotbeenavailableuntilrecently,wechooseinsteadto
modelTIPSliquidityasdrivenbyanunobservedTIPS-specificriskfactor.
Asabriefoutlineofthepaper,wefirstpresentmodel-freeevidencethatasignificantportion
ofthemovementinTIPSyieldsisnotspannedbynominalTreasuryyields.Wethenintroducea
no-arbitrageassetpricingframeworkthatjointlymodelsnominalTreasuryyields,TIPSyields,
andrealizedinflation,allowingforawedgebetweenTIPSyieldsandrisk-freerealyieldsadjusted
fortheindexationlag.ThiswedgeismodeledasafunctionoftheTIPS-specificriskfactor
mentionedabove,andisreferredtoasthe“TIPS-indexedbondspread”orthe“TIPSspread”for
short.HavingobtainedestimatesoftheTIPSspread,weexaminehowtheyarelinkedto
observablemeasuresoftherelativeilliquidityofTIPSversusnominalTreasurysecurities,while
controllingforothertechnicalfactorssuchasCPIseasonality,theembeddeddeflationfloorin
TIPS,flight-to-safetydemandfornominalTreasurysecurities,andFederalReservepurchasesof
TIPS.
Weobtainthreemainfindings:First,astandard3-factormodelthattreatsTIPSyieldsas
risk-free,indexationlag-adjustedrealyieldsgeneratesapoorfitofTIPSyieldsandBEI,aswell
asestimatesofinflationexpectationsandinflationriskpremiumswithcounterintuitiveproperties.
Incomparison,thetwo4-factormodelsthatallowforaTIPSspreadgeneratenotablysmaller
TIPSpricingerrors,morereasonableestimatesofinflationriskpremiums,andestimatedinflation
expectationsthatarebetteralignedwithsurveyinflationforecasts.Second,theestimatedvalues
oftheTIPSspreadwerelarge(1%)whenTIPSwerefirstissued,declinedsteadilythereafter
2
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throughlate2003,andremainedatrelativelylowlevelsuntiltherecentfinancialcrisis,consistent
withthenotionthatTIPSmarketliquidityconditionshadbeenimprovingovertime.Those
estimatesjumpedtocloseto3%inJuly2008duringtheTIPSsell-off,buthadlargelyreturnedto
theirpre-crisislevelsbythebeginningof2010,apatternsimilartowhathasbeendocumentedfor
manyotherilliquidand/orriskyassetprices.Finally,regressionanalysisshowsthataround85%
ofthevariationsinourestimatesoftheTIPSspreadscanbeexplainedbyobservablemeasuresof
theliquidityconditionsintheTIPSmarket.Otherfactors,includingCPIseasonalityandTIPS
deflationfloors,playaminorrole.
TheapproachoutlinedabovediffersfromthatoftheothertwostudiesofTIPSliquiditiesin
theliterature,Shen(2006)andPfluegerandViceira(2013),whobasedtheirresultsonregression
analysisofeitherTIPSBEIitselforthedifferencebetweenTIPSBEIandsurvey-basedmeasures
ofinflationexpectations.Theusageofapricingmodelallowsustobringinadditional
informationfromthecrosssectionofnominalyieldsandTIPSBEIandfromrealizedinflation.In
addition,unlikeChen,Liu,andCheng(2010),whostudyTIPSinamultivariateCIRframework,
allmodelsinthispaperarefromtheGaussianessentially-affineno-arbitragetermstructurefamily
thatallowsaflexiblecorrelationstructurebetweenthefactorsandthemarketpricesofrisk.Such
flexibilitiesareimportantforcapturingthedynamicsofbondriskpremiums,asshownbyDuffee
(2002)andothers,andforourpurposeofaccuratelydecomposingTIPSBEIintoexpected
inflation,theinflationriskpremium,andtheTIPSspread.
Tothebestofourknowledge,thisisthefirstpaperexaminingTIPSliquidityinano-arbitrage
frameworkandisthereforerelatedtothefast-growingliteratureonthelinkbetweenliquidityand
assetreturns.
2
Previousstudieshavedocumentedthatassetswithsimilarpayoffscancarry
significantlydifferentpricesduetotheirvaryingdegreesofliquidity.
3
Weaddtotheevidenceby
2
VayanosandWang(2013)andAmihud,MendelsonandPedersen(2013)providerecentsurveysofthis
literature.
3
See,forexample,AmihudandMendelson(1986)andBrennan,Chordia,andSubrahmanyam(1998),and
BrennanandSubrahmanyam(1996)forequities,AmihudandMendelson(1991)andLongstaff(2004)fornominal
Treasurysecurities,Longstaff,Mithal,andNeis(2005),Chen,Lesmond,andWei(2007),Bao,Pan,andWang
3
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showingthatthisisalsothecaseforTIPSandnominalTreasurysecurities.Ourpaperisalso
relatedtostudiesofindexedbondpricing,mostofwhichareconductedusingdatafromcountries
withlongerhistoriesofsuchbonds.
4
StudiesusingTIPSandotherU.S.inflation-linkedassets
arefairlyrecentandrelativelyfew,
5
andmostofthoseusingTIPSyieldstakethemattheirface
value.Incontrast,thispapershowsthatthereisapersistentliquiditypremiumcomponentin
TIPSyieldsthat,whenignored,willsignificantlybiastheresults.Finally,thispaperisalso
relatedtothevastliteraturestudyingthebehaviorofrealinterestrates,inflationexpectations,and
inflationriskpremiumswithorwithoutincorporatinginformationfromindexedbonds.
6
As
discussedinSectionVII,ourestimatesofinflationexpectationsandinflationriskpremiumsare
consistentwiththoseobtainedinotherstudiesusingsampleperiodssimilartoours.
Theremainderofthispaperisorganizedasfollows.InSectionII,weprovideevidencethat
portionsofTIPSyieldsandBEIarenotspannedbynominalinterestratesandarelikelylinkedto
therelativeilliquidityofTIPS.SectionIIIspellsoutthedetailsofourno-arbitragetermstructure
models,includingthespecificationoftheTIPS-specificfactorandthetreatmentoftheindexation
lag.SectionIVdescribesthedataandourestimationmethodology,andSectionVpresentsthe
mainempiricalresults.SectionVIexaminesthepropertiesoftheestimatedTIPSspreads,
(2011),andDick-Nielsen,Feldh¨utter,andLando(2012)forcorporatebonds,Bongaerts,DeJong,andDriessen
(2011)forcreditdefaultswaps,andMancini,Ranaldo,andWrampelmeyer(forthcoming)fortheforeignexchange
market.
4SeeWoodward(1990),BarrandCampbell(1997),Evans(1998),Remolona,Wickens,andGong(1998),Risa
(2001),andJoyce,Lildholdt,andSorensen(2010)fortheUK,Kandel,Ofer,andSarig(1996)forIsreal,andH¨ordahl
andTristani(2012)fortheEuroarea.
5
ThispaperandacontemporaneousstudybyChenetal.(2010)arethefirsttwotostudyTIPSinano-arbitrage
framework.MorerecentpapersanalyzingTIPSorinflationswapsincludeChernovandMueller(2012),Adrianand
Wu(2008),Haubrich,Pennacchi,andRitchken(2012),Christensen,Lopez,andRudebusch(2010),Pfluegerand
Viceira(2013),Fleckenstein,Longstaff,andLustig(2014b),ChristensenandGillan(2012),FlemingandKrishnan
(2012),GrishchenkoandHuang(2013),Abrahams,Adrian,Crump,andMoench(2013).
6
Forstudiesnotusingindexedbonds,see,amongothers,Pennacchi(1991),Foresi,Penati,andPennacchi
(1997),andBrennan,Wang,andXia(2004),BuraschiandJiltsov(2005),andAng,Bekaert,andWei(2008).
4
showingthattheyaccountforasignificantportionofthetimeseriesvariationsinTIPSBEIand
aremostlydrivenbytheperspectiveandrelativeliquiditycharacteristicsofTIPSversusnominal
Treasurysecurities.SectionVIIcomparesourestimatesofexpectedinflationandinflationrisk
premiumstothosefromotherstudies.Finally,SectionVIIIconcludes.
II. A TIPS-Specific Factor: Simple Analysis
InthissectionwepresentevidencethatthereisacomponentofTIPSyieldsthatisnot
reflectedinnominalTreasuryyieldsandislikelyrelatedtotherelativeilliquidityofTIPS.This
servesasthemotivationforintroducingaTIPS-specificfactorwhenwemodelnominalandTIPS
yieldsjointly.
SimpleRegressionAnalysis
Asastartingpoint,weregressthe10-yearTIPSBEI,definedasthespreadbetweenthe
10-yearnominalyieldandthe10-yearTIPSyield,on3-month,2-yearand10-yearnominal
yields.
7
Standardfinancetheorysuggeststhatnominalyieldsofanymaturity,y
N
t;
,canbe
decomposedintotherealyield,y
R
t;
,inflationexpectation,I
t;
,andtheinflationriskpremium,
}
t;
:
(1)
y
N
t;
=y
R
t;
+I
t;
+}
t;
:
IfTIPSyieldsaccuratelycapturetheunderlyingrealyields,theTIPSBEIisthesumofexpected
inflationandtheinflationriskpremium,bothpartsofthenominalyields.AregressionofTIPS
BEIontonominalyieldcurvefactorscanthenbeexpectedtogenerateahighR
2
.Ontheother
hand,variationsinTIPSyieldsthatareorthogonaltothoseinrealyieldscouldleadtoalowR
2
.
Weestimatetheregressionbothinlevelsandinweeklydifferencesforthreesamplesperiods:
7
WethankGregDuffeeforthissuggestion.Resultsusingthreedifferentnominalyieldsorusingthefirst
principalcomponentsofnominalyieldsaresimilar.SeeSectionAfordatadetails.
5
thefullsampleofJanuary6,1999toMarch27,2013,thepre-crisisperiodfromJanuary6,1999
toJuly25,2007,andthepost-crisisperiodfromAugust1,2008toMarch27,2013.Asshownin
PanelAofTable1,theR
2
fromthefull-sampleregressionismerely6%inlevelsand39%in
weeklydifferences,wellbelowtheR
2
inexcessof95%typicallyfoundwhenregressingone
nominalyieldontoothernominalyields.Inthepre-crisissample,theR
2
ishigherforboth
specifications,30%inlevelsand59%indifferences,indicatingthattheverylowR
2
ismostlydue
tothepost-crisisperiod,duringwhichtheadjustedR
2
declinesto5%inlevelsand26%in
differences,respectively.Thisevidencesuggeststhatalargeportionofvariationsinthe10-year
BEIcannotbeexplainedbyfactorsdrivingthenominalyields,andevenmoresowhenthemost
recentfinancialcrisisisincludedintheanalysis.
PrincipalComponentsAnalysis
Wenextturntoaprincipalcomponentanalysis(PCA)ofthecrosssectionofnominaland
TIPSyieldsoverthefullsample.Itiswellknownthatthreefactorsexplainmostofthemovement
innominalyields.ThisisconfirmedbyPanelBofTable1: Over97%ofvariationsintheweekly
changesofnominalyieldscanbeexplainedbythefirstthreeprincipalcomponents.However,
onceweaddTIPSyields,atleastfourfactorsareneededtoexplainthesameportionofthetotal
variance.PanelCofTable1reportsthecorrelationsbetweenthefirstfourPCAfactorsextracted
fromnominalyieldsaloneandthosefromacombinationofnominalandTIPSyields.Thefirst,
second,andfourthfactorsconstructedfromallyieldslargelyretaintheirinterpretationsasthe
level,slopeandcurvatureofthenominalyieldcurve,asattestedbytheirhighcorrelationswith
thefirstthreenominalfactors,respectively.However,thethirdPCAfactorextractedfrom
nominalandTIPSyieldscombinedisnothighlycorrelatedwithanyofthenominalPCAfactors.
OnePotentialExplanation: TIPSLiquidityPremium
OneinterpretationoftheTIPS-specificfactoridentifiedaboveisthatitmayreflectthelackof
liquidityinTIPSrelativetonominalTreasurysecurities.TIPSwereintroducedfairlyrecentlyand
remainmuchlessliquidthantheirnominalcounterparts,againstwhichtheTIPSBEIis
6
computed.
8
InvestorsarethereforelikelytodemandextracompensationforholdingTIPS,
especiallyintheirearlyyearsandduringtherecentfinancialcrisiswhenoverallliquidity
deteriorated,therebypushingdownTIPSpricesandupTIPSyields.Indeed,TIPSoutstanding,
shownintheGraphAofFigure1,didnotbegintorisesubstantiallyuntil2004,aroundwhich
timebothTIPStransactionvolumesandTIPSmutualfunds,shownintheGraphsBandC,also
experiencedsignificantgrowth.
9
Transactionvolumesdeclinednotablyattheendof2008and
remainedlowthrough2011,butroseagaininrecentyears.Inviewofthishistory,itisplausible
thatTIPSyieldscontainasignificantliquiditypremiumintheirearlyyearsandagainduringthe
financialcrisis.
[InsertFigure1abouthere.]
ApositiveliquiditypremiuminTIPSyieldscanalsohelpresolveanapparentinconsistency
betweenlong-termsurveyinflationforecastsandthe10-yearTIPSBEI,plottedinFigure2.
10
ThetrueBEIcanbeexpectedtobehigherthansurveyinflationexpectationsiftheinflationrisk
premiumisonaveragepositive,andtheycanbeconsideredagoodmeasureoftrueexpected
inflationifsuchpremiumisrelativelysmallandconstantovertime.
However,Figure2showsthatthisisnotthecase:theTIPSBEIliedbelowsurveyinflation
forecastsalmosttheentiretimebefore2004.
11
Inaddition,TIPSyieldssurgedwhilenominal
TreasuryyieldsplummetedshortlyafterLehmanfailed,causing10-yearTIPSBEItocollapseby
8
SackandElsasser(2004)discussesliquidityconditionsintheTIPSmarketintheearlyyears.
9
DataonTIPSmutualfundisfromtheInvestmentCompanyInstitute(http://www.ici.org).
10
Weusethe10-yearinflationforecastsfromtheSurveyofProfessionalForecasters(SPF)orthelong-term
inflationforecastfromtheMichiganSurveyofConsumers.Mehra(2002)showsthattheseforecastsareunbiased,
efficient,andhavepredictivecontentforfutureinflation.Ang,Bekaert,andWei(2007)andChun(2012)showthat
SPF,BlueChip,andothersurveysforecastinflationbetterthanmanytypesofmodelsestimatedwithyieldsonly.
Finally,ChernovandMueller(2012)showthatallabove-mentionedsurveyforecastsareconsistentwithinflation
expectationsembeddedinyields.
11
Othermeasuresofinflationexpectationbasedontime-seriesmodelsalsotendtobeabovetheTIPSBEIinearly
years.SimilarpointsaremadebyShenandCorning(2001)andShen(2006).
7
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