Real Return Bonds, Inflation Expectations, and the Break-Even Inflation Rate Ian Christensen, Frédéric Dion, and Christopher Reid

Transcription

1 Bank of Canada Banque du Canada Working Paper / Documen de ravail Real Reurn Bonds, Inflaion Expecaions, and he Break-Even Inflaion Rae by Ian Chrisensen, Frédéric Dion, and Chrisopher Reid

2 ISSN Prined in Canada on recycled paper

3 Bank of Canada Working Paper November 2004 Real Reurn Bonds, Inflaion Expecaions, and he Break-Even Inflaion Rae by Ian Chrisensen, 1 Frédéric Dion, 2 and Chrisopher Reid 2 1 Moneary and Financial Analysis Deparmen 2 Financial Markes Deparmen Bank of Canada Oawa, Onario, Canada K1A 0G9 ichrisensen@bankofcanada.ca fdion@bankofcanada.ca chrisreid@bankofcanada.ca The views expressed in his paper are hose of he auhors. No responsibiliy for hem should be aribued o he Bank of Canada.

4 iii Conens Acknowledgemens iv Absrac/Résumé v 1. Inroducion Mehodology and Previous Findings Previous research Premiums Embedded in he BEIR Mismached cash flows Term-varying inflaion expecaions Inflaion risk Liquidiy risk Marke segmenaion RRBs: The Hisorical Experience Calculaing he BEIR How Imporan Are he Risk Premiums/Disorions? Mismached cash flows The erm srucure of inflaion expecaions Inflaion-risk premium Liquidiy-risk premium Marke segmenaion Inflaion Expecaions Forecasing Power Conclusions and Suggesions for Fuure Research References Appendix: Why Is he Inflaion-Expecaion Term Srucure Imporan?

5 iv Acknowledgemens The auhors are graeful o Allan Crawford, Oumar Dissou, Sco Hendry, Grahame Johnson, Marianne Johnson, Glen Keenleyside, Jack Selody, Carolyn Wilkins, Craig Wilson, and seminar paricipans a he Bank of Canada and he 2004 Norhern Finance Associaion meeings for helpful discussions and/or commens on an earlier draf. We also hank Brian Sack for sharing his code wih us.

6 v Absrac According o he Fisher hypohesis, he gap beween Canadian nominal and Real Reurn Bond yields (or break-even inflaion rae) should be a good measure of inflaion expecaions. The auhors find ha his measure was higher, on average, and more variable han survey measures of inflaion expecaions beween 1992 and They examine wheher risk premiums and disorions embedded in his ineres rae gap can accoun for hese facs. Their resuls indicae ha disorions were likely an imporan reason for he high level and variaion of his measure over much of he 1990s. There is lile evidence ha he disorions examined were as imporan beween 2000 and 2003, bu he high level of he break-even inflaion rae in 2004 may be evidence of heir reurn. Given he poenial disorions, and he difficuly in idenifying hem, he auhors conclude ha i is premaure o consider his measure a reliable gauge of moneary policy credibiliy. In addiion, i is no as useful as compeing ools for shor- and medium-erm inflaion forecasing. JEL classificaion: E31, E43 Bank classificaion: Ineres raes; Inflaion and prices; Marke srucure and pricing Résumé Selon l hypohèse de Fisher, l écar de rendemen enre les obligaions canadiennes à rendemen nominal e à rendemen réel (ou aux d inflaion neure) devrai êre un bon indicaeur des aenes d inflaion. Les aueurs consaen qu enre 1992 e 2003, ce écar a éé supérieur, en moyenne, aux mesures de l inflaion aendue éablies par enquêe, e plus variable égalemen. Ils cherchen à savoir si les primes de risque e les disorsions comprises dans l écar de rendemen y son pour quelque chose. D après leurs résulas, les disorsions expliquen probablemen en bonne parie le niveau élevé e les variaions de l écar de rendemen duran la majeure parie des années Rien ne pore à croire qu elles aien éé aussi imporanes enre 2000 e 2003, mais le niveau élevé du aux d inflaion neure en 2004 pourrai êre le signe de leur résurgence. Éan donné les disorsions possibles e la difficulé de les prendre en compe, les aueurs concluen qu il es prémauré de considérer cee mesure comme un baromère fiable de la crédibilié de la poliique monéaire. En oure, le aux d inflaion neure n es pas aussi uile que les aures ouils exisans pour la prévision de l inflaion à cour e à moyen erme. Classificaion JEL : E31, E43 Classificaion de la Banque : Taux d inérê; Inflaion e prix; Srucure de marché e fixaion des prix

7 1. Inroducion According o he Fisher hypohesis, he spread beween nominal and real ineres raes should provide a good measure of inflaion expecaions. Real ineres raes can be derived from he price of Real Reurn Bonds (RRBs) (inflaion-indexed bonds issued by he Governmen of Canada), because hey compensae he invesor for realized inflaion, guaraneeing he real value of coupon paymens and principal. Nominal ineres raes from convenional bonds compensae he invesor for he fuure inflaion rae expeced a he ime of sale. The spread beween nominal and real ineres raes is commonly referred o as he break-even inflaion rae (BEIR), because i is he inflaion rae ha equaes reurns across he wo ypes of bond. Since Canada issues only RRBs ha have a 30-year mauriy, he BEIR is consruced from yields on long-erm bonds and (in he absence of disorions) indicaes he expeced average inflaion rae over a 25- o 30-year horizon ha is priced ino he marke. To deermine wheher he BEIR is a good measure, we examine he hisorical experience for conformance wih our priors abou he behaviour of long-run inflaion expecaions. The broad rends do conform, bu he BEIR is volaile and a imes shows persisen movemens in he opposie direcion from oher measures of inflaion expecaions. This paper examines wheher hese movemens can be aribued o changes in risk premiums and oher disorions ha affec he BEIR, raher han changes in inflaion expecaions. I is useful for he conduc of moneary policy o have a good measure of inflaion expecaions. The worh of he BEIR in his capaciy depends on how i is o be used and over wha horizon. Based on he experience o he end of 2003, we argue ha he BEIR shows promise as a measure of agens views abou he long-run credibiliy of a cenral bank s commimen o keep inflaion near is arge. Noneheless, evens in 2004 sugges ha premiums and disorions may recur. Due o he difficuly in idenifying and quanifying hese disorions, one should no place much weigh on he BEIR as a measure of credibiliy a his ime. In addiion, he Canadian BEIR is a less reliable ool han compeing mehods used o obain shor-erm inflaion forecass. 1

8 2. Mehodology and Previous Findings We consider he usefulness of he BEIR from wo perspecives: as a measure of moneary policy credibiliy and as an aid o inflaion forecasing. Moneary policy is credible when agens expec ha fuure inflaion will be near he inflaion arge. If he BEIR capures inflaion expecaions accuraely, is posiion relaive o he arge should be a good measure of credibiliy. Since he rue expeced inflaion rae is unobservable, we mus find indirec ways o assess he accuracy of he BEIR. In his paper, we assess wheher he BEIR s behaviour over is 12-year hisory fis wih wha we hink we know abou inflaion expecaions. Survey daa serve as he primary basis for comparison. We find ha he BEIR and survey measures of inflaion expecaions are someimes a odds over our sample; we herefore evaluae he abiliy of premiums and disorions in he BEIR o explain hese divergences. The BEIR may also be useful if i improves our abiliy o forecas inflaion. We assess he forecas performance of he BEIR relaive o survey measures of expecaions and oher simple models. Many of he sudies in he lieraure rely on he use of survey measures of inflaion expecaions as he benchmark for comparison, and we coninue his pracice. Noneheless, consensus survey measures have been criicized for a number of reasons. Survey respondens are weighed equally, regardless of heir convicions or abiliy o forecas inflaion well. They may also have lile incenive o reveal privae informaion. 1 In principle, marke-based measures do no have hese shorcomings. They are deermined by acions, which are more revealing han opinions. The convicions of marke players are weighed by heir dollar voes, which reflec he confidence and sake people have in heir predicions (Haubrich and Dombrosky 1992). Marke paricipans who have good informaion can profi a he expense of hose who are irraional or who have poor informaion. In addiion, marke-based measures are available a a much higher frequency han survey daa, and hey herefore should provide more curren informaion abou expecaions. 1. Professional forecasers may behave sraegically, providing forecass ha are close o consensus raher han reflecing heir rue forecas o avoid being he only one who was wrong. Conversely, hey may make conrarian forecass o arac more aenion o heir producs. 2

9 We use survey measures of inflaion expecaions as a benchmark for comparison because rue expecaions are unobservable and survey measures are he main alernaive source of informaion. They are no subjec o inflaion uncerainy, liquidiy risk, and he oher disorions ha are poenial sources of bias in he BEIR. Noneheless, differences beween survey measures and he BEIR may be due o biases in he survey measures, in addiion o hose in he BEIR. An exploraion of he size and naure of survey biases, however, is beyond he scope of his paper. 2.1 Previous research In counries ha issue inflaion-linked deb, he BEIR has ofen given a differen signal han surveys of inflaion expecaions. The U.S. BEIR is, on average, lower han long-run inflaion expecaions obained from surveys, and i is much more volaile. In addiion, changes in he BEIR do no coincide wih changes in survey measures. In conras o he Unied Saes, long-erm BEIRs in he Unied Kingdom are higher, on average, han consensus survey measures of inflaion expecaions over similar horizons (Scholes 2002). The lieraure ha seeks o explain hese findings invesigaes wheher he Fisher hypohesis he heoreical basis for he BEIR is sricly applicable in he real world, where ineres raes may conain premiums and disorions. Shen and Corning (2001) and Craig (2003) argue ha he U.S. findings are due o he presence of a liquidiy premium embedded in he BEIR. Shen and Corning furher argue ha variaion in his premium may be he cause of he BEIR s volailiy. Sack (2000) finds ha he mismached cash flows of he indexed and convenional Treasuries and erm-varying inflaion expecaions explain only a fracion of he variabiliy of he BEIR. Emmons (2000) poins ou ha U.S. nominal bonds of 10+ years o mauriy may possess a scarciy value, which may in par explain why he U.S. BEIR is lower han survey measures of inflaion expecaions. 2 In he Unied Kingdom, here is evidence ha he inflaion-risk premium is more imporan han in he Unied Saes, and ha i is possibly ime-varying (Evans 1998). 2. In addiion, he saus of he U.S. dollar as reserve currency may resul in a disproporionae demand for nominal Treasuries, which would have he effec of lowering he BEIR. 3

10 Côé e al. (1996) argue ha an inflaion-risk premium and facors relaed o he small size of he Canadian RRB marke make he level of he BEIR an unreliable indicaor of he level of inflaion expecaions. Noneheless, hey hold ou some hope ha changes in he BEIR over ime may be a good indicaor of movemens in long-erm inflaion expecaions. 3. Premiums Embedded in he BEIR If invesors are risk-neural and markes efficienly price a homogeneous real ineres rae across markes, he difference in yields beween a zero-coupon index-linked bond and a zero-coupon nominal bond of similar mauriy would express he marke s expeced average inflaion rae over he remaining period o mauriy. 3 In his perfec world, he Fisher hypohesis is valid and he nominal ineres rae is equal o he required real rae of reurn o he invesor plus compensaion for expeced inflaion: e e 1+ i Fisher hypohesis: ( 1+ i) = (1 + r)(1 + π ) π = 1. (1) 1+ r In he real world, however, he various assumpions ha underlie he Fisher hypohesis may no hold sricly. The BEIR may conain disorions ha mask he underlying informaion abou inflaion expecaions. Noneheless, even if he premiums and disorions were o shif he level of he BEIR away from rue inflaion expecaions, he BEIR migh sill be a useful indicaor if hese disorions were relaively sable over ime. If hey were, changes in he BEIR would indicae when changes in inflaion expecaions were occurring. We are herefore ineresed no only in he magniude of premiums and disorions, bu he exen o which hey may vary over ime. 3.1 Mismached cash flows The RRB and nominal bond ha are used o consruc he BEIR have approximaely he same mauriy. Boh bonds also pay a coupon, which complicaes he comparison of heir yields, because heir cash flows are mismached: he coupon paymens of he RRB rise 3. This is rue apar from he effec of Jensen s inequaliy, which means here is a negaive bias in he BEIR. 4

11 wih inflaion, whereas hose for he nominal bond are consan. Since he price of a bond is simply he sum of discouned cash flows, he wo bonds will have differen sensiiviies o he expeced pah of real ineres raes and real ineres rae risk. As we discuss below, his will make he BEIR lower, on average, han rue inflaion expecaions. In addiion, mismached cash flows will mean ha changes in he expeced pah of real ineres raes will cause he BEIR o flucuae. 3.2 Term-varying inflaion expecaions Anoher consequence of using coupon bonds o consruc he BEIR is ha i will be more sensiive o shor-erm inflaion expecaions han longer-erm expecaions. Implici in he consrucion of he BEIR is an assumpion ha inflaion expecaions are roughly consan over he various horizons up o he mauriy of he bonds. If boh componen bonds paid no coupon, his assumpion would be innocuous. Insead, he nominal yields of hese bonds are influenced by he expeced pah of inflaion, and no jus he expeced average inflaion over he period o mauriy. As a resul, when he erm srucure of inflaion expecaions he se of expecaions a increasing horizons is no fla, a bias is inroduced ino he BEIR, and his bias is mos sensiive o changes in inflaion expecaions a shor horizons. This effec could be imporan, since shor-erm inflaion expecaions are likely o be more variable han long-erm ones: inflaion shocks are more likely o offse in he long erm. Term-varying inflaion expecaions could emporarily change he level of he BEIR, hereby adding o is variabiliy even when he expeced average of inflaion over he long run is unchanged. 3.3 Inflaion risk Inflaion risk reflecs he probabiliy ha he acual inflaion rae will no mach he expeced inflaion rae. A person s inflaion expecaions are he mean of heir subjecive probabiliy disribuion for inflaion, and inflaion uncerainy is he variance around he mean. If inflaion is significanly higher over he erm of a nominal bond han was expeced a he ime of purchase, he realized real rae of reurn will be lower han he expeced real rae of reurn. Invesors in convenional bonds require compensaion for his risk, which resuls in higher nominal yields ceeris paribus. In conras o nominal 5

12 bonds, inflaion risk is reained by he issuer of RRBs no passed on o he invesor. For his reason, he BEIR conains a posiive inflaion-risk premium. The value of he proecion from unexpeced higher inflaion should depend on he degree of uncerainy abou fuure inflaion and he degree of risk aversion. 4 The size of he inflaion-risk premium will vary as inflaion uncerainy changes. Inflaion uncerainy is posiively correlaed wih he level of inflaion or inflaion expecaions, so he BEIR will end o rise o a greaer degree han he increase in inflaion expecaions. If he BEIR is o be used o indicae he credibiliy of he cenral bank, he exisence of he inflaion-risk premium is no a drawback, since uncerainy abou fuure inflaion developmens mus reflec invesors views abou he cenral bank s willingness and abiliy o ake acions o conrol fuure inflaion. A lower or less-variable inflaion-risk premium would signal increased credibiliy. 3.4 Liquidiy risk Liquidiy risk is he risk ha invesors will no be able o sell an asse wihou incurring large coss eiher from he price pressure hey creae or he lengh of ime i akes o sell heir asse. In Canada, he secondary marke for RRBs is much smaller han he marke for nominal bonds, so here may be an imporan liquidiy-risk premium differenial. To compensae, invesors may demand a higher expeced reurn for his produc, which would lead o a higher RRB yield and, ceeris paribus, a narrowing of he BEIR. This liquidiy premium should decline over ime as he RRB marke develops, bu his gradual decline should no be an imporan shor-run source of variaion in he BEIR. The amoun of liquidiy risk may vary over ime, in line wih he marke s percepion of overall risk. In imes of financial disress or rising economic uncerainy, invesors are willing o pay a premium (accep a lower reurn) for he safes, mos liquid asses. During hese imes, he RRB yields may rise and he nominal yields may fall, reducing he BEIR unil invesor behaviour reurns o normal. 4. Jensen s inequaliy implies ha, if invesors are risk-neural, he yield spread beween real and nominal bonds will undersae inflaion expecaions by an amoun ha increases wih he uncerainy ha surrounds inflaion. 6

13 3.5 Marke segmenaion Côé e al. (1996) and Mayer (1998) argue ha he BEIR may no reflec he marke s overall view on inflaion expecaions, bu raher reflec he view of hose wih he highes inflaion expecaions or inflaion-proecion needs. The argumen ha he RRB marke is segmened, having invesors wih very differen characerisics han average invesors, requires ha he supply of RRBs be relaively inelasic. If only a small amoun of inflaion-linked deb is supplied, i is likely o be owned by hose who have he highes inflaion expecaions or he bigges need for inflaion proecion. Inflaion-sensiive invesors may have higher forecass of inflaion or be more averse o inflaion risk, and herefore value he cerainy of RRBs more highly. If he RRB yield reflecs heir views and preferences, i will be lower, and he BEIR will be higher, han if he marke was no segmened. In Canada, some invesors are exemp from he axes applicable o RRBs, which is anoher source of segmenaion. The ax burden o RRB holders depends on inflaion oucomes, since boh income and capial gains axes are applied o he inflaion-uplifed coupon and principal componens. 5 Life insurance companies and pension funds ha are exemp from hese axes are willing o pay more for RRBs han he average invesor. In addiion, RRBs are aracive o hese firms because hey have real liabiliies and need o mach heir asses o inflaion. Marke segmenaion is no likely o lead o more variabiliy in he BEIR on is own. I may, however, magnify he shifs in he BEIR ha resul from changes in inflaion uncerainy. Changes in he degree of segmenaion of he RRB marke, perhaps as a resul of changes in he ax code, would likely lead o permanen changes in he level of he BEIR. 5. Given his ax reamen, he majoriy of RRBs are held by ax-exemp insiuions or in axexemp accouns, such as RRSPs. The ax implicaions are herefore a driving force behind he segmenaion of he marke. 7

14 4. RRBs: The Hisorical Experience The Governmen of Canada firs issued RRBs in December Formal inflaion arges, which specified he rae of inflaion o be achieved over a 2-year horizon, were adoped in Canada in February of 1991, and subsequenly lowered o he curren arge of 2.0 per cen. Figure 1 shows he RRB yield, he yield from a 30-year nominal Governmen of Canada bond, and he BEIR calculaed from hese wo yields. Figure 1: Nominal and RRB Yield and BEIR BEIR Nominal yield RRB yield % Dae Table 1 shows he sample means and measures of he variabiliy of he nominal and real yields and he BEIR. The drop in he mean and variabiliy of he BEIR in he laer half of he sample coincides wih a drop in he mean and variabiliy of he nominal yield, which is wha we would expec if inflaion expecaions or inflaion uncerainy were falling over he sample. The real yield also dropped, on average, in he laer half of he sample, bu is variabiliy was relaively unchanged. This is consisen wih a fall in he liquidiy premium. Table 1: Full and Subsample Saisics, Nominal and Real Yields and BEIR Mean Sandard deviaion Nominal RRB BEIR Figure 2 shows ha he BEIR was above he inflaion arge (he midpoin of he arge band is shown in he figure) in he early o mid-1990s, below i from lae 1997 o lae 1999, and very close o arge since ha ime. Longworh (2002) and ohers sae ha he 8

15 falling level of he BEIR beween 1992 and 1997 is consisen wih moneary policy becoming more credible Figure 2: Four Measures of Inflaion Expecaions BEIR 6 o 10 yrs survey 4 o 14 yrs survey 2-yrs-ahead survey Also shown in Figure 2 are hree measures of inflaion expecaions from surveys of professional forecasers: he median expeced average rae of inflaion 4 o 14 years ahead, from an annual survey conduced by Wason Wya; he mean expeced average rae of inflaion 6 o 10 years % Dae ahead, from a semi-annual survey by Consensus Economics; and 2-years-ahead inflaion expecaions, from he Conference Board s quarerly Survey of Forecasers. 6 The BEIR is higher han he oher measures of inflaion expecaions for he firs half of he sample a imes by more han 150 basis poins. I regisers boh he highes reading (4.9 per cen in March 1992) of he four measures and he lowes reading (abou 1.0 per cen in lae 1998). I also falls much more slowly han he survey measures. From 2000 o 2003, however, i was very close o 2.0 per cen, he middle of he Bank of Canada s arge range for inflaion, along wih he oher measures of inflaion expecaions. Over his recen period, any permanen disorions o he level of he BEIR were eiher small or offseing, on average. Even if all of hese series were perfec measures of inflaion expecaions, we would no expec heir levels o be idenical over his sample, because hey capure expecaions over differen horizons. For example, if a recen shock o inflaion is expeced o be shorlived, we migh expec near-erm inflaion expecaions o rise wih lile impac on longer-erm expecaions. The measures of inflaion expecaions are, in fac, quie 6. Two-years-ahead inflaion is he expeced rae of inflaion for he following calendar year, raher han over he nex 12 monhs. The oher survey measures are defined similarly. 9

16 differen. The mean level of he BEIR over he 1992 o 2002 sample is 2.8 per cen, above ha of he 4- o 14-year expecaions (2.5 per cen), he 6- o 10-year expecaions (2.1 per cen), and he 2-years-ahead expecaions (2.0 per cen). The longer he horizon over which he expecaion applies, he higher is average over he pas 11 years. This is consisen wih slowly increasing moneary policy credibiliy, because expecaions over longer horizons fall more slowly. I is puzzling, however, ha he long-erm measures are so differen from each oher. For example, i seems unlikely ha here is enough addiional informaion abou inflaion developmens 10 o 30 years in he fuure o jusify a difference of 0.8 percenage poins beween he BEIR and he 6- o 10-year survey measure. Such a wide difference may reflec uncerainy regarding he moneary policy regime over he longes horizons, or he influence of premiums embedded in he BEIR. The BEIR is he mos variable measure, showing an average annual absolue change of 0.56 percenage poins, a leas double ha of he survey measures a any horizon. This is sill rue if we consider only he laer half of he sample. The firs differences in hose measures show very lile correlaion, which suggess ha changes in one (or boh) of hese measures reflec some phenomenon oher han changing inflaion expecaions. 7 On he basis of similar evidence, Shen and Corning (2001) argue ha he U.S. BEIR may be oo volaile o be a reliable proxy of inflaion expecaions. The higher peaks and lower roughs of he BEIR are mainly linked o wo episodes: , when he BEIR increased rapidly as oher measures sabilized or fell, and , when he BEIR dropped sharply while oher measures fell moderaely or flaened. 5. Calculaing he BEIR The curren value of a bond is he sum of is discouned fuure cash flows and principal (equaion (2)). Using marke daa on bond prices (B ), he coupon rae on he bond (c), and seing he value of principal o $100, we can solve for he yield o mauriy (ym) using his relaionship. The ym is he average annual reurn over he remaining life of he bond: 7. Alernaively, longer-horizon expecaions may behave differenly. 10

17 B N = n= 1 c n ( 1+ i ) ( + i ) N ym, ym,. (2) In he case of a nominal bond, we obain a nominal ym. In he case of he RRB, we use he marke price and he real coupon rae o obain a real ym. In he absence of disorions, he spread beween he yield on a nominal 30-year Governmen of Canada bond and a 30-year RRB provides a measure of he expeced average annual rae of inflaion over he 30-year horizon. To undersand he shor-run impac of a large increase in he CPI on he RRB price, we need o consider how he RRB coupon paymens are calculaed. In his secion, we follow he exposiion of Sack and Elsasser (2004) closely. RRBs guaranee heir holder a real reurn, proecing hem from lower reurns caused by inflaion. To do so, he coupon paymen and he principal repaid a mauriy are adjused o include compensaion for inflaion ha has occurred since he issuance of he bond: RRB ( P + n P ) n ( 1+ i ) ( P N P ) ( + i ) N c (3) N + = + n= 1 n, 1 N, An RRB issued a ime, wih a real coupon rae c, a mauriy of N years, and a par value of $100 has a coupon paymen of c 100 ( P + n P ) 100 ( P ) a mauriy. The index raio ( P ) P + N e ( ) n 1+ π n,, where periods. n, and reurns a principal paymen of P + is rewrien in equaion (4) as e π n, is he expeced average annual rae of inflaion over he nex n i n, is he n-period zero-coupon ineres rae a ime (i.e., he reurn on a bond ha pays no coupon and maures in period n). The se of zero-coupon yield curve: i n, for all n periods gives he RRB N c 100 = n= 1 e ( 1+ π n, ) n ( 1+ i ) n, n e ( 1+ π N, ) ( 1+ i ) N N, N. (4) 11

18 Define he n-period zero-coupon real ineres rae by he following: ( 1 r ) n, Equaion (4) hen becomes he following: ( 1+ in, ) e ( 1+ π ) + =. (5) n, RRB N = n= 1 c n ( 1+ r ) ( + r ) N n, N,, (6) which is essenially he equaion for valuing a nominal bond (equaion (2)), excep ha coupon paymens are discouned by real ineres raes, raher han nominal ones. Therefore, we can derive he real ym using only he fixed coupon rae and marke informaion abou he bond price. If fuure inflaion is known, he reurns from an invesmen making a real paymen in n periods and one making a nominal paymen mus equae, which implies ha ( + r) ( 1+ i) N N 1 = e ( ). (7) 1+ π The yield spread beween a nominal and an indexed zero-coupon bond should be equal o he expeced average rae of inflaion over he life of he bond when premiums are no presen. When bonds also pay a coupon, however, his relaionship becomes more complicaed. The pah of inflaion affecs he size of he coupon paymens of he RRB and, as a resul, differen expeced pahs for inflaion may cause he bond price o change even when he average annual inflaion rae over he life of he bond is kep consan. Under he assumpion ha inflaion is expeced o be sable a he level p over ime, we can replace he zero-coupon ineres raes in equaion (7) wih he ym from he RRB and nominal coupon bonds: ym ym ( ) ( 1+ i ) r = e ( 1+ π ) ym ( 1+ i ) ( 1+ r ) e 1 π = 1. (8) + ym 12

19 This equaion can be approximaed by i ym - r ym = p e ; however, he geomeric difference (equaion (8)) is usually used. The BEIR is supposed o capure he expeced average annual inflaion rae over he remaining life of he bond. 6. How Imporan Are he Risk Premiums/Disorions? If he BEIR is a biased measure of inflaion expecaions, i would be of greaer use o policy-makers or invesors if his bias could be esimaed or removed. Alernaively, if he facors creaing he bias are sable over ime, hen changes in he yield spread would reflec movemens in long-run inflaion expecaions. Figure 3 shows he difference beween he BEIR and he wo measures of long-erm inflaion expecaions as a proxy for he risk premiums in aggregae. 8 If survey expecaions are he relevan benchmark, he differences should also capure any premium conained in he BEIR, and no jus he inflaion-risk premium. Basis Poins Figure 3: Difference Beween BEIR and Surveyed Expecaions The proxies for he aggregae of he risk premiums are posiive before 1997 and negaive beween 1997 and Beween 1999 and 2003, hey are somewha smaller and ake differen signs, which suggess ha he risk premiums were close o zero, on average, over his period. These proxies sugges ha he impac of hese premiums and disorions can be sizeable and differen premiums mus be acive a differen imes. For example, he large and posiive differenial beween he BEIR and surveys before 1997 migh be an inflaion-risk premium, bu even if his premium wen o zero i could no explain he o 14 yr 6 o 10 yr Dae 8. Using he BEIR adjused for he effec of he mismached cash flows (described in secion 6.1) does no change his picure significanly. 13

20 negaive premium in he subsequen wo years. In secions 6.1 o 6.5, we will use economic daa and informaion available from financial markes o assess he likelihood ha he differenial beween he BEIR and he surveys was due o risk premiums and disorions. One imporan cavea is ha he individual disorions in he BEIR measure may no be independen of inflaion expecaions or each oher. For example, inflaion uncerainy will rise wih inflaion expecaions. Also, higher inflaion uncerainy may cause a larger change in he BEIR han i would if marke paricipans had he same aversion as he average person o inflaion risk. The imporance of ineracions beween he disorions and inflaion expecaions is a subjec for fuure research. These ineracions will complicae any aemp o esimae he impac of hese disorions economerically. We examine hese disorions independenly as a firs sep. 6.1 Mismached cash flows Exracing inflaion expecaions by comparing he RRB ym o ha of a nominal bond of he same mauriy may lead o a biased measure. Even hough boh asses have he same mauriy, here are differences beween he paerns of heir coupon paymens (i.e., he duraion and he convexiy of each bond may differ grealy, exposing each bond o differen discoun facors). These differences will influence he yield spread beween he securiies for reasons unrelaed o expeced fuure inflaion, and will inroduce a bias when measuring inflaion expecaions. This bias will no be consan hrough ime, because he size of he impac on he BEIR is a funcion of (i) he coupon and mauriy of he real and nominal bonds, and (ii) he erm srucure of ineres raes. 9 Typically, paymens on an RRB are more back-loaded han hose of a sandard nominal coupon bond. Expressed in real erms, he paymens of he RRB are fixed, while hose of he nominal securiy decline over is mauriy as inflaion erodes heir real value. Since 9. In pracice, he 30-year nominal bonds and RRB do no have he same mauriy. Since he beginning of he RRB program, mismaches of up o six years have been observed. This will direcly influence he impac of mismached cash flows. 14

21 paymens ha arrive laer in ime are usually more heavily discouned, he RRB price will be lower, and herefore he BEIR will be narrower. In a sudy of Treasury inflaion-indexed securiies (TIIS) in he Unied Saes, Sack (2000) compares wo measures of inflaion expecaions: he sandard BEIR (i.e., yield difference, as shown in equaion (8)) and a measure ha akes he slope of he yield curve and mismached cash flows ino accoun. He finds ha adjusing for mismached cash flows has only a modes impac on he BEIR. Those resuls, however, need no apply o he Canadian conex, because in he Unied Saes inflaion expecaions are derived from 10-year bonds. In Canada, only RRBs ha have a mauriy of 30 years have been issued, which allows for greaer mismached cash flows. Insead of comparing he ym of he RRB wih ha of a nominal bond, we exrac inflaion expecaions by comparing he ym of he RRB wih ha of a synheic nominal bond (creaed from a zero-coupon yield curve) ha has exacly he same sream of cash flows as he RRB. Saed differenly, by discouning he cash flows wih a zero-coupon curve, we solve ieraively for he consan inflaion expecaion ha is consisen wih he observed price. 10 Our mehodology relies heavily on he qualiy of he zero-coupon yield curve. We use he Merrill Lynch exponenial-spline mehodology o exrac he yield curve (Brenner e al. 2001), as calculaed by Bolder, Johnson, and Mezler (forhcoming). In a recen sudy, Bolder and Gusba (2002) find his mehodology o be he mos accurae. 10. The RRB price daa we use do no ake ino accoun all informaion regarding known pas inflaion. To ge a daily or weekly RRB price, a CPI index raio (he raio of he curren price level o he price level a he bond s issue dae) of he same frequency is required. By convenion, he CPI index raio used o calculae he RRB price a he firs of he monh is he CPI from he hird preceding monh divided by he CPI a issuance. In subsequen rading days, he index raio is calculaed using linear inerpolaion from he hird preceding monh o he second preceding monh o he CPI for he nex monh (which is already available). We adjus our measure o ake his ino accoun by using he laes CPI daa when hey become available. 15

22 6.0 Figure 4: The BEIR Adjused for Mismached Cash Flows Adjused BEIR BEIR Figure 5: Impac of Cash Flow Mismach on he BEIR (BEIR - adjused BEIR ) % 3.0 % Dae Dae Figure 4 shows a weekly measure of he BEIR adjused for mismached cash flows (hereafer, he adjused BEIR) versus he BEIR. Boh measures are reasonably close hroughou he period. From ime o ime, however, imporan differences occur. Figure 5 shows he difference beween he wo measures, which capure he bias inroduced by mismached cash flows. The average bias over he enire sample (January 1992 o May 2003) was 20 basis poins (bps) (Table 2). In oher words, inflaion expecaions compued from he sandard measure would undersae inflaion expecaions by 20 basis poins, on average. Over a more recen period (January 1999 o May 2003), he average bias was 8 basis poins. Table 2: Inflaion-Expecaion Differences Level and Variaion Average Sandard Min Max Sample bias (bps) deviaion difference difference Jan 92 o May 03 Jan 99 o May 03 1s percenile 99h percenile Level Firs difference Level Firs difference

23 Figure 5 also shows ha he difference beween boh measures is volaile and nonsaionary. From January 1992 o May 2003, he sandard deviaion was 14 basis poins and he minimum and maximum differences were -59 and 12 basis poins, respecively. The maximum posiive and negaive weekly variaions were 12 and -31 basis poins (26 basis poins and -14 basis poins over he more recen period). This analysis suggess ha changes in he BEIR may be due o he mismached cash flows and no o changes in inflaion expecaions. These resuls differ srongly from hose obained by Sack (2000), who finds ha he impac of mismached cash flows for he U.S. BEIR is small, ypically under 5 basis poins, and much less volaile. Our resuls imply ha Sack s conclusions do no apply o BEIRs ha are calculaed using bonds of longer mauriies The impac of mismached cash flows and he shape of he yield curve The differen cash-flow srucures of he RRB and nominal bond resul in he bonds having differen duraions and differen ym if he yield curve is no fla. The cash flows of an RRB are more back-loaded, leading o a higher modified duraion. 11 We define modified duraion as he exposure of a bond o real ineres rae variaion (modified duraion = dp/dr). 12 Figure 6 plos he modified duraions (measured in years) of he wo bonds used o measure inflaion expecaions. Throughou he period, he nominal bond duraion has increased and he duraion difference has narrowed, mainly due o falling nominal raes. Figure 7 shows ha he bias (he difference beween he BEIR and he adjused BEIR) is parly explained by duraion variaions. Paricularly, large shifs in duraion due o he issuance of new benchmark bonds have had an imporan impac on he BEIR. For example, in November 2001, a new RRB was inroduced o he marke, which increased he benchmark s duraion by 1.9 years. This shif in duraion led o a decline of 26 basis poins in he measure of he bias. Therefore, he level and variaion of he BEIR no only reflec inflaion expecaions, bu also he differen exposures of each bond o ineres rae risk. 11. We use duraion as a proxy for he cash-flow srucure. 12. See Rudolph-Shabinsky and Trainer (1999) for more deails on he duraion of inflaionindexed securiies. 17

24 The bias is also a funcion of he erm srucure. The BEIR is especially sensiive o he yields a he long end of he curves (he 20- o 30-year mauriy range), given he long 19 Figure 6: Modified Duraions Mod. duraion - Nominal bond Mod. duraion - RRB Figure 7: Duraion Difference and Impac of Cash Flow Mismach BEIR - Adjused BEIR Duraion difference Years 14 % Dae Dae mauriy of he componen bonds. In Ocober 1996, he yield curve was paricularly seep, which caused he BEIR o undersae inflaion expecaions by 31 basis poins. In March 2000, i was relaively fla and invered (i.e., 30-years ym, significanly lower han he 20-years ym), and inflaion expecaions were oversaed by 10 basis poins. This analysis suggess ha he BEIR is relaively sensiive o he erm srucure, and ha accouning for i will improve he measure of inflaion expecaions from RRBs. 6.2 The erm srucure of inflaion expecaions Sack (2000) finds ha he BEIR in he U.S. showed a surprising degree of responsiveness o he conemporaneous rae of CPI inflaion beween he beginning of 1997 and he end of This may have also been rue in Canada, since he Canadian BEIR racks Canadian CPI inflaion much closer han surveyed expecaions in his period 18

25 (Figure 8). 13 There is also evidence ha he Canadian BEIR has Figure 8: The BEIR and Conemporaneous Inflaion BEIR Year-over-year CPI inflaion % Dae explanaory power for 1-year-ahead inflaion expecaions in he pos-1997 sample (IMF 2004). In his secion, we consider he exen o which curren CPI can affec he BEIR even when longererm inflaion expecaions are unchanged. This can occur because he curren CPI helps form shorerm inflaion expecaions. Recall ha, because of he coupon srucure of he componen bonds, he BEIR will be more sensiive o shor-erm inflaion expecaions han o longer-erm expecaions. In oher words, because of he coupon srucure, he nominal ym of an RRB will be a funcion of he inflaion pah. An expeced emporary increase in inflaion omorrow raises he expeced coupon paymens over he enire life of he bond, whereas an equal increase in inflaion expecaions one year before mauriy increases only he final wo coupon paymens. In each case, he impac on he acual average rae of inflaion over he period o mauriy is idenical, bu invesors are willing o pay more nominal dollars for RRBs in he firs case. Similarly, he nominal ym of nominal bonds is a funcion of he overall zero-coupon curve (see he appendix for he derivaion). Therefore, when he erm srucure of inflaion expecaions is no consan, a bias is inroduced ino he BEIR, and his bias is bigges when shor-erm inflaion changes. To measure he sensiiviy of he BEIR o he inflaion-expecaions erm srucure, we solve equaion (4) using a fla real-yield curve (and a consisen nominal curve compued using he Fisher relaionship) and a variey of inflaion pahs consisen wih differing 13. Figure 8 shows CPI inflaion excluding he impac of changes in indirec axes. 19

26 shor-erm and long-erm inflaion expecaions. 14,15 This gives he ne presen value of he RRB in each case. Nex, we pu ha price, along wih he fixed coupon rae, ino equaion (6), o ge he real ym consisen wih our hypoheical profiles of beliefs abou fuure inflaion. We hen calculae he spread beween he real ym and a ym for a nominal bond o obain our measure of inflaion expecaions. The sensiiviy analysis repored in Table 3 shows he BEIR ha would be obained under differen levels of shor-erm inflaion expecaions ha las for varying lenghs of ime before reurning o he inflaion arge. For example, if inflaion is expeced o be 3.0 per cen for he nex six monhs and 2.0 per cen for he remainder of he 30 years o mauriy, we should observe a BEIR of 2.03 per cen. Bu if we assume ha inflaion is going o be 5 per cen for six monhs, hen a consisen BEIR would be 2.08 per cen. In general, he difference is less beween he BEIR and long-erm inflaion forward raes (2.0 per cen in his example) when he credibiliy of he argeing regime is high, since shocks o inflaion become less persisen. This may be one reason for he reduced volailiy of he BEIR shown in Table 1. Table 3: The BEIR under Differen Inflaion Term Srucures Inerim period of high expeced inflaion before reurning o he arge (2%) BEIR (lef) and average inflaion (righ) 3% expeced inflaion for inerim period 4% expeced inflaion for inerim period 5% expeced inflaion for inerim period 10% expeced inflaion for inerim period 6 monhs 2.03% 2.02% 2.05% 2.03% 2.08% 2.05% 2.21% 2.13% 1 year 2.05% 2.03% 2.11% 2.07% 2.16% 2.10% 2.42% 2.26% 2 years 2.10% 2.07% 2.21% 2.13% 2.31% 2.20% 2.83% 2.51% 5 years 2.25% 2.17% 2.50% 2.33% 2.76% 2.49% 4.05% 3.29% 7 years 2.34% 2.23% 2.69% 2.46% 3.03% 2.69% 4.83% 3.81% 10 years 2.47% 2.33% 2.94% 2.66% 3.42% 2.99% 5.94% 4.60% 15 years 2.65% 2.50% 3.30% 3.00% 3.97% 3.49% 7.52% 5.92% 30 years 3.00% 3.00% 4.00% 4.00% 5.00% 5.00% 10.00% 10.00% Table 3 also provides he average inflaion rae for he 30-year horizon, assuming ha he pah of inflaion is exacly as was expeced. The BEIR will oversae average inflaion 14. We do no need a new yield curve for each inflaion pah, since we are rying o find pahs ha are consisen wih observed nominal ineres raes. 15. The compued BEIRs in Tables 3 and 4 assume a 30-year mauriy wih a 5.75 per cen semi-annual coupon rae nominal bond and a 30-year mauriy wih a 4.00 per cen semiannual coupon RRB. These coupon raes are similar o recen benchmarks. 20

27 expecaions when shor-erm expecaions are higher han hose for he longer erm (i.e., he erm srucure of inflaion expecaions is downward sloping). For example, if inflaion is expeced o be 5 per cen for he nex 10 years and 2 per cen for he subsequen 20 years, he BEIR would be 3.42 per cen, even hough acual average inflaion expecaions over 30 years are 2.99 per cen. Table 4 shows he impac (in basis poins) on he BEIR of a 1 per cen increase in inflaion expecaions for a six-monh period wih differen saring daes. A 1 per cen shock o inflaion ha lass six monhs will increase he average acual inflaion by 1.7 basis poins, regardless of when i happens. If expeced inflaion over he firs six monhs rises by 1.0 per cen, however, he BEIR will increase by 2.8 basis poins. If, insead, he inflaion rae expeced over he las six monhs before mauriy rises by 1.0 per cen, he BEIR will change by only 0.8 basis poins. To assess he possible impac, we need o invesigae he exen o which inflaion expecaions wih differen horizons can diverge. The experience of counries wih indexlinked bonds of differen mauriies suggess ha expecaions over differen horizons do diverge. Figure 2 shows ha survey measures for differen horizons also differ. Typical divergences, however, are insufficien o creae a significan bias in he measure of average inflaion expecaions. We esimae ha he ypical bias will no be bigger han 3 o 4 basis poins. Noneheless, his effec adds volailiy o he measure of inflaion expecaions, because i increases he sensiiviy of he BEIR o shor-erm inflaion expecaions. Furhermore, he bias will mos likely be a is maximum (approximaely 10 basis poins) a criical imes, perhaps following a large relaive price shock, when moneary auhoriies will be looking for evidence ha he bias is feeding ino inflaion expecaions. Table 4: Impac of Forward Inflaion- Expecaions Shock BEIR (lef) and average inflaion (righ) 6 monhs 1% inflaion shock (bps) bps 0 o 6 monhs o 12 monhs monhs o 2 years o 5 years o 7 years o 10 years o 15 years o 30 years

28 The simulaneous decline in he BEIR and conemporaneous CPI inflaion in he period is probably no due o bias from erm-varying inflaion expecaions. An alernaive argumen is ha his period was characerized by a large shif in he liquidiy premium ha happened a he same ime as he drop in inflaion. Large subsequen flucuaions in inflaion were no mached by large movemens in he BEIR. We explore his hypohesis in secion Inflaion-risk premium Lile empirical work has been done on he exisence of an inflaion-uncerainy premium in nominal yields and is imporance for he level of changes in he BEIR. The exising work ofen uses he difference beween varians of he BEIR and survey measures of expeced inflaion as a proxy for he inflaion-uncerainy premium, despie he possibiliy ha i includes oher disorions. Evans (1998) finds a posiive and significan correlaion beween he level of his U.K. BEIR and his proxy, providing evidence for a ime-varying inflaion-uncerainy premium. 16 In a sudy of index-linked bonds in Israel, Kandel, Ofer, and Sarig (1996) regress his proxy on anoher measure of inflaion uncerainy lags of he monhly dispersion of relaive prices in a consumer price index and find a posiive and significan relaionship. 17 The relaionship is no significan in a low-inflaion subsample. Boh Evans (1998) and Kandel, Ofer, and Sarig (1996) consider BEIRs ha have much shorer horizons han he ones in our work. Côé e al. (1996) use similar reasoning in heir analysis of he Canadian BEIR, arguing ha is rise in 1994, when oher survey measures of long-run inflaion expecaions were fla or declining, suggess ha he inflaion-risk premium was rising. Campbell and Shiller (1996) use a capialasse-pricing model o esimae he inflaion-risk premium in he Unied Saes and find i o be beween 50 and 100 basis poins. 16. Evans argues ha his is no due o forecas errors in he survey measure, because he obains similar resuls when he lef-hand-side variable is he difference beween he ineres rae measure and realized inflaion. 17. Kandel, Ofer, and Sarig jusify his proxy wih he following example: in a given monh, invesors do no ransac in all goods included in he CPI baske, so hey are likely o ge a less-accurae picure of inflaion when relaive price variabiliy is high. For his reason, if he mos recen CPI release shows a large degree of relaive price dispersion, invesors will be more uncerain abou heir curren views on inflaion. 22

29 Figure 9 shows wo measures of long-run inflaion uncerainy. The firs is a measure of he disagreemen among he forecasers who responded o he Wason Wya survey, calculaed as he difference beween he upper and lower quariles of Figure 9: BEIR/Survey Difference and Inflaion Uncerainy Wason Wya survey minus BEIR GARCH measure of uncerainy Survey disagreemen repored inflaion expecaions. 18 The second is a measure of inflaion uncerainy over a 5-year forecas horizon derived from a generalized auoregressive condiional heeroscedasiciy (GARCH) model developed by Crawford and Kasumovich (1996). 19 % Dae Boh measures of inflaion uncerainy fail o indicae a rise in inflaion uncerainy in 1994, or an imporan decline in Crawford and Kasumovich s measure of inflaion uncerainy fell dramaically during he 1980s, bu has been relaively sable since If inflaion uncerainy has changed lile, i canno be driving he movemen of he BEIR. Survey disagreemen fell beween 1991 and I also flucuaed o a greaer degree han he GARCH measure, bu no during he 1994 or 1997 periods, when he BEIR was moving in he opposie direcion from he survey measures. In addiion, alhough he iming varies, more forward-looking Markov regime-swiching models of inflaion uncerainy show a similar rend over he 1980s and 1990s (e.g., Demers 2003). Based on his evidence, he deviaions of he BEIR from survey measures of inflaion expecaions do no appear o resul from changing inflaion uncerainy. 18. Giordani and Söderlind (2003) argue ha disagreemen on poin forecass from survey respondens has a high correlaion wih movemens in more heoreically appealing measures of uncerainy. 19. Similar analyses were underaken using long-erm swapion implied volailiies as a proxy for long-erm inflaion uncerainies in he subsample We were no able o idenify any relaionship. 23

30 The measures of inflaion uncerainy are conrary o he explanaion given by Côé e al. (1996) for he evens in They argue ha his rise in he BEIR was relaed o concerns abou he abiliy of governmens o deal wih heir rising deb in he conex of increasing world ineres raes. In his environmen, invesors saw an increased risk ha governmen would resor o higher inflaion o ease he coss of servicing governmen deb. This view would have been paricularly relevan o invesors in governmen bond markes, bu perhaps i had lile impac on he expecaions or uncerainy of hose ouside he bond markes. Côé e al. also noe ha similar movemens in he nominal real ineres rae spread in his period were observed in oher counries wih index-linked bonds. 6.4 Liquidiy-risk premium Invesors may demand a higher yield on RRBs o compensae for he risk ha hey will no be able o sell hem quickly or will have o sell a unfavourable prices. If his liquidiy-risk premium is presen, i should fall over ime as more RRBs are issued and raded. Even hen, however, his premium may rise during episodes when invesors experience a heighened need for asses ha are highly liquid. A dramaic deerioraion in liquidiy, if here was one, migh explain he declining differenial beween he BEIR and survey measures of inflaion expecaions over he mid-1990s. In fac, here has been an improvemen in liquidiy since he beginning of he RRB program. The sock of RRBs ousanding increased from $4.1 billion a he end of 1994 o $17.3 billion a he end of 2003, rising from 9 per cen o 26 per cen of federal governmen markeable deb wih a mauriy of 10 years or greaer. The greaer supply of deb should have improved liquidiy, ceeris paribus. The secondary marke for RRBs is sill much smaller han he marke for nominal bonds in Canada. The average monhly RRB rading volume in 2003 was $1.6 billion, only slighly above he earlier peak of $1.5 billion in 1997, despie he increase in he ousanding sock of RRBs. Secondary marke RRB urnover, he raio of he volume raded o he sock ousanding, is less han one-fifh ha of nominal bonds wih a 24