The correlation matrix between break-even inflation rate movements and real interest rate movements across several countries shows puzzling features. Correlation is significantly positive for nearly all cross-border pairs whereas it is nil, positive or negative unsystematically within countries. By means of a correlation matrix decomposition, we give an explanation for this puzzle.Inflation-linked bonds

Gilbert Cette

Marielle de Jong

English

Research Papers in Economics

The rocky ride of break-even inflation rates 
Marielle de Jong Gilbert Cette
Sinopia Asset Management Banque de France and Université de la Méditerrannée
Abstract
The correlation matrix between break-even inflation rate movements and real interest rate
movements across several countries shows puzzling features. Correlation is significantly
positive for nearly all cross-border pairs whereas it is nil, positive or negative
unsystematically within countries. By means of a correlation matrix decomposition, we give
an explanation for this puzzle.
The authors wish to thank two anonymous referees of the Economics Bulletin for their useful remarks.This article reflects the
opinions of the authors and does not necessarily express the views of the institutions they work for.
Citation: de Jong, Marielle and Gilbert Cette, (2008) "The rocky ride of break-even inflation rates." Economics Bulletin, Vol. 5,
No. 30 pp. 1-8
Submitted: April 4, 2008.  Accepted: October 17, 2008.
URL: http://economicsbulletin.vanderbilt.edu/2008/volume5/EB-08E40007A.pdf  1 
1.  Introduction 
 
The break-even inflation rate (BEIR) is the spread between the nominal bond yield (NBY) 
and the real bond yield (RBY). According to the Fisher hypothesis, the BEIR conveys the 
inflation expectations of capital market participants. In practice, however, a series of studies 
surveyed by Christensen, Dion and Reid (2004) report that the BEIR is being distorted by 
certain market-related factors. Market liquidity is mentioned as one of them, for example by 
Shen and Corning (2001), Craig (2003) and Shen (2006), who observe a liquidity premium on 
inflation-linked bonds as opposed to nominal bonds. Others argue that there is a risk premium 
priced in the BEIR, which varies depending on the aversion to inflation uncertainty among the 
market participants (see for example Hördahl and Tristani, 2007, on euro area data, Emmons, 
2000, on US data, Evans, 1998, on US and UK data and Côté et al., 1996, on Canadian data). 
Ejsing, Garcia and Werner (2007) show, using euro area data, that the seasonality in consumer 
prices over the year is also adding to the distortion in the calculated BEIR. These sources of 
price distortion are all time-varying1. In this respect, it is often pointed out that information 
extracted from BEIR data should be used cautiously when assessing market players’ inflation 
expectations and is not fully reliable for evaluating central bank credibility. 
 
All studies conclude that market-related factors are de facto giving a rocky ride to break-even 
inflation rates. We show in this paper that it is symptomatic that the comovements of the 
BEIR in various countries with those of the RBY are being distorted as well. The correlation 
matrix between changes in BEIR and changes in real interest rates across several countries 
shows puzzling features. We analyse these features and provide an explanation for them. 
 
 
2.  The data 
 
Our  analysis  is  based  on  data  from  Barclays’  World  Government  Inflation-Linked  Index 
covering Inflation-Linked Gilts (ILG) in the United Kingdom, Treasury Inflation Protected 
Securities  (TIPS)  in  the  United  States,  Obligations  Assimilables  du  Trésor  indexées  sur 
l’Inflation  (OAT∈I)  in  the  euro  area,  Treasury  Indexed  Bonds  (TIB)  in  Australia,  Index-
Linked Treasury Bonds (ILTB) in Sweden and Real Return Bonds (RRB) in Canada. Japan, 
which entered the index in 2004, has been discarded due to its short data history. Minimum 
requirements on aggregate issuance and bond rating are set on index entrance so as to make 
direct comparison possible. We retrieve the nominal bond yields from the Barclays Capital 
database as well. We use the 10-year yields between July 2002 and June 2008 on a weekly 
data frequency. 
 
 
3.  An empirical puzzle 
 
 Table 1 displays the correlation matrix between the variation in the break-even rates and the 
variation  in  the  real  bond  yields  of  the  six  countries  under  study.  Standard  (Pearson) 
correlations are measured over the estimation period. Surprisingly, correlation (i) can be nil, 
positive  or  negative  unsystematically  within  a  country,  (ii)  whereas  it  is  almost  always 
significantly positive for the cross-border pairs. The nil observations within countries are in 
line with economic theory. As a real bond offers, by construction, protection against inflation 
                                                       
1 Using US data, Hunter and Simon (2005) show that because of the liquidity and risk premiums, real bond 
issuance may have actually increased rather than reduced the US Treasury’s borrowing costs to date.    2 
uncertainty,  we  would  expect  its  yield  movement  to be  uncorrelated  to  the  movement  in 
break-even  rates  that  capture  inflation  uncertainty.  But  how  should  the  positive  cross-
correlation be interpreted? For example, how can it be explained that someone who buys a 
TIPS is not exposed to inflation in the US but seems to be exposed to inflation in Canada? We 
note that this exposure represents mark-to-market risk, which is relevant for holders if they 
intend  to  sell  the  bond  before  its  maturity  date.  For  the  US  Treasury  it  is  important  to 
understand why the domestic BEIR is correlated to the Canadian real bond market. 
 
Table 1 
Correlation matrix between changes in break-even rates (BEIR) and changes in real 
interest rates (RBY) 
RBY    
Australia  Canada  Euro area  Great 
Britain 
Sweden  United 
States 
Australia  0.27***  0.19***  0.37***  0.33***  0.41***  0.34*** 
Canada  0.30***  -0.06  0.37***  0.33***  0.29***  0.45*** 
Euro area  0.20***  0.04  -0.18***  0.09  0.11**  0.13** 
Great Britain  0.20***  0.14**  0.31***  -0.07  0.28***  0.29*** 
Sweden  0.30***  0.19***  0.43***  0.39***  0.13**  0.37*** 
B
E
I
R
 
 
United States  0.19***  0.10*  0.10*  0.15***  0.13**  -0.03 
***: significant at the 1% level (critical value at 0.15);   **: significant at the 5% level (critical value at 0.11);   
*: significant at the 10% level (critical value at 0.09) using an asymptotic T-test with T=312. 
 
This empirical puzzle, which has not been identified in the literature to our knowledge, is not 
a random result. As can be observed in Table 1, it is the case for nearly all pairs of countries. 
In complementary tests displayed in the Appendix, we verify that this result is robust to the 
choice of test period and data frequency. How can these results be explained?  
 
 
4.  Decomposition 
 
We  decompose  the  correlation  matrix  into  two  components,  one  reflecting  the  overall 
comovement in all countries, and one reflecting the idiosyncratic movements. For this, we 
first decompose the individual variables.  
 
 
-  Variable decomposition 
 
We decompose the individual variables Y as follows: 
 
t , i t i t , i . Y ε + γ β =                                   (1) 
 
where i is the country index, t the time index, ∆Yi,t = Yi,t   Yi,t 1, γt is the common movement at 
time t and βi the sensitivity of variable Y in country i to the common movement. From this, we 
obtain  for  each  country  i  and  each  variable  Y  the  simple  variance  decomposition: 
Var(∆Yi,) = Var(βi .γ) + Var(εi,), where the first term represents the changes in comovements 
and the second term the idiosyncratic ones.  
   3 
We calculate the share of comovements and idiosyncratic movements in the variance of ∆Yi, 
( )
( ) i
i com
Y Y Var
Var S
i   = γ β . and  ( )
( ) i
i idi
Y Y Var
Var S
i   = ε summing to one. The result of this calculation 
is given in Table 2 for the three variables (NBY, RBY and BEIR) in the six countries. 
 
Table 2 
Share of the comovements in the variance of the variables - % 
NBY: Nominal bond yield; RBY: Real bond yield; BEIR: Break-even inflation rate 
  Australia  Canada  Euro area  Great Britain  Sweden  United States 
NBY  59  70  85  80  79  80 
RBY  39  41  77  69  63  77 
BEIR  44  55  24  29  50  39 
Note: the share of idiosyncratic movement is the complement to 100%. 
 
We can interpret the pricing of nominal bonds as the most international and the pricing of 
break-even rates (through inflation swaps) as the least international. 
 
Table 3 gives the βi terms resulting from the estimation of relation (1), for each of the three 
variables and each of the six countries.  
 
Table 3 
β β β βi resulting from the estimation of relation (1) 
NBY: Nominal bond yield; RBY: Real bond yield ; BEIR: Break-even inflation rate 
  Australia  Canada  Euro area  Great Britain  Sweden  United States 
NBY  1.05  0.76  0.95  0.98  0.99  1.26 
RBY  0.77  0.55  1.19  0.12  0.85  1.47 
BEIR  1.26  1.19  0.59  0.69  1.15  1.05 
 
It is interesting to note that the US nominal bond market and real bond market are more 
reactive than average. 
 
 
-  Correlation matrix decomposition 
 
We denote the correlation matrix displayed in Table 1 as Γ and the corresponding covariance 
matrix as V. Per definition:  
 
2
1
2
1
* *
− −
Σ Σ = Γ RBY BEIR V    where 
( )
( )









 
⋅
 
= Σ
6
1
0
.
0
Y Var
Y Var
Y , Y=BEIR, RBY.                 (2) 
 
We decompose the covariance matrix and express it in correlation notation: 
[ ] 2
1 2
1
2
1
2
1
2
1
2
1
* * * *
* *
− −
− −
Σ


















Σ
Σ








Γ Γ
Γ Γ
Σ Σ Σ
= Σ 







Σ = Γ
RBY idi
RBY
com
RBY
idi idi com idi
idi com com com
idi
BEIR
com
BEIR BEIR
RBY idi idi com idi
idi com com com
BEIR V V
V V
       (3) 
   4 
where, for example, V
com 
com represents the 6x6 covariance matrix between the common BEIR 
variation and the common RBY variation.  
 
Introducing the definition of variance shares simplifies the equation to: 
 
[ ]
















Γ Γ
Γ Γ
= Γ idi
RBY
com
RBY
idi idi com idi
idi com com com
idi
BEIR
com
BEIR
S
S
S S * *                 (4) 
 
We  rewrite  the  correlation  matrix  as  a  weighted  sum  of  the  four  component  correlation 
matrices, the weights being the respective share of variance explained. Table 4 displays the 
empirical numbers. 
 
Table 4  
Decomposed  correlation  matrix  between  the  variation  in  break-even  rates  and  the 
variation in real interest rates 
 
=  


 


Γ Γ
Γ Γ
idi idi com idi
idi com com com
 
 
{ } { }
{ } { } 

























































−
− −
− −
−
− − − − −
− −




















− − − − − −
− − − − − −
− − − − − −




















− − −
− − −
− − −
− − −
− − −
− − −




















.33
.45
.57
.60
.43
.08
.48 .48 .48 .48 .48 .48
.48 .48 .48 .48 .48 .48
.48 .48 .48 .48 .48 .48
.48 .48 .48 48 .48 .48
.48 .48 .48 .48 .48 .48
.48 .48 .48 .48 .48 .48
12 . 18 . 02 . 21 . 12 .
02 . 14 . 16 . 05 . 04 .
16 . 18 . 21 . 09 . 01 .
15 . 12 . 07 . 10 . 16 .
25 . 10 . 04 . 02 . 05 .
05 . 19 . 00 . 00 . 04 .
26 26 26 26 26 26
10 10 10 10 10 10
02 02 02 02 02 02
19 19 19 19 . 19 19
10 10 10 10 10 10
12 12 12 12 12 12
00 02 03 02 19 11
00 02 03 02 19 11
00 02 03 02 19 11
00 02 03 02 . 19 11
00 02 03 02 19 11
00 02 03 02 19 11
.
. . . . . .
. . . . . .
. . . . . .
. . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . .
. . . . . .
. . . . . .
 
[ ]




























































=
78 . 0
71 .
84 .
87 .
67 .
0 75 .
63 . 0
71 .
54 .
49 .
74 .
0 66 .
idi
BEIR
com
BEIR S S  
[ ]




























































=
.48 0
.60
.56
.48
.77
0 .78
.88 0
.80
.83
.88
.64
0 .63
idi
RBY
com
RBY S S    5 
 
The  decomposition  is  helpful  in  solving  the  correlation  puzzle.  Two  sets  of  correlation 
numbers are particularly significant, i.e. all coordinates in the top left matrix of Γ and the 
coordinates on the diagonal in the bottom right matrix, indicated in bold. Since the weights in 
the variance share matrices are fairly homogeneous we can ignore them. The same applies for 
the numbers in the two cross matrices of Γ as they are relatively small and unsystematic. 
Thus,  the  two  sets  in  bold  determine  to  a  large  extent  the  total  correlation.  To  take  an 
example, let us look at the numbers in braces that define the correlation between the BEIR 
and RBY in the United States. The near-zero total correlation between these two interest rates 
is the net result of a strongly positive correlation between the global comovements of the two 
and  a  strongly  negative  correlation  between  the  idiosyncratic  movements  specific  to  the 
United States. The decomposition reveals that there is significant correlation on a world scale 
between  break-even  and  real  interest  rates,  yet  that  within  countries  this  is  offset  by  the 
idiosyncratic negative correlation. 
 
The negative idiosyncratic correlation is a direct consequence of the time-varying distortions 
discussed in the literature and reiterated in the introduction. As soon as the RBY moves due to 
a market-related event, which is typically not mirrored by the NBY, the BEIR moves exactly 
in the opposite direction. 
 
The positive correlation between BEIR and RBY on a world scale is an interesting market 
phenomenon. Market practitioners recognise this phenomenon indirectly when they cite the 
“beta effect” (see, for example, Pond, 2008). It is very often observed that the RBY moves in 
the  same  direction  as  the  NBY  but  with  a  smaller  magnitude.  From  a  macroeconomic 
standpoint, the two interest rates could move together with the same magnitude after a shock 
that has no significant impact on inflation expectations (for example, at the first order, a 
technological shock). Or the nominal interest rate could move alone after a ‘pure’ inflation 
shock. The fact that most of the time we observe the net result of the two scenarios means that 
the two types of shock very often coincide or that somehow shocks combine the two types of 
effect.  
 
 
5.  Concluding remarks 
 
We have provided an interpretation of an empirically observed puzzle. Someone who buys a 
TIPS is factually unexposed to the US inflation risk, since the common positive correlation 
between RBY and BEIR is offset by the idiosyncratic negative correlation. But the common 
correlation vis-à-vis Canada is not offset. This solves the puzzle, however, it does not answer 
all the questions concerning the pricing of real bonds. 
 
 
References 
 
Christensen, I., F. Dion and C. Reid (2004) “Real Return Bonds, Inflation Expectations and 
the Break Even Inflation Rate”, Bank of Canada working paper 2004-43. 
 
Côté, A., J. Jacob, J. Nelmes and M. Whittingham (1996) “Inflation Expectations and Real 
Return Bonds”, Bank of Canada Review, Summer, 41-53. 
   6 
Craig,  B.  (2003)  “Why  are TIIS Yields so  High? The case of the Missing  Inflation-Risk 
Premium”, Federal Reserve Bank of Cleveland Economic Commentary. 
 
Ejsing, J., J. A. Garcia and T. Werner (2007) “The Term Structure of Euro Area Break Even 
Inflation Rates”, European Central Bank, Working Paper Series, n° 830, November.  
 
Emmons,  W.  (2000)  “The  Information  Content  of  Treasury  Inflation-Indexed  Securities”, 
Federal Reserve Bank of St Louis Review, November/December. 
 
Evans, M. (1998) “Real Rates, Expected  Inflation and  Inflation Risk Premia”, Journal of 
Finance, 187-218. 
 
Hördahl, P., and O. Tristani (2007) “Inflation risk premia in the term structure of interest 
rates”, BIS Working Papers, n° 228, May. 
 
Hunter, D. and D. Simon (2005) “Are TIPS the ‘real’ deal? A conditional assessment of their 
role in a nominal portfolio”, Journal of Banking and Finance, 29 (2005), 347-368.  
 
Pond,  M.  (2008)  “Effective  duration  of  linkers  and  beta”,  in  Barclays  Capital  Research: 
“Global Inflation-Linked Products”, February. 
 
Shen,  P.,  and  J.  Corning  (2001)  “Can  TIPS  Help  Identify  Long-Term  Inflation 
Expectations?”, Economic Review of the Federal Reserve Bank of Kansas City. 
 
Shen, P. (2006) “Liquidity Risk Premia and Breakeven Inflation Rates”, Economic Review, 
Federal Reserve Bank of Kansas City, Second Quarter, 29-53.   
 
   7 
Appendix 
 
Correlation  matrix  between  variation  in  the  break-even  inflation  rates  (BEIR)  and 
variation in real bond yields (RBY) 
 
Based on monthly data from 2002 to 2007 
RBY    
Australia  Canada  Euro area  Great 
Britain 
Sweden  United 
States 
Australia  0.24**  0.24**  0.51***  0.43***  0.33***  0.49*** 
Canada  0.40***  -0.18  0.32***  0.44***  0.25**  0.34*** 
Euro area  0.33***  0.01  0.01  0.26**  0.20*  0.18 
Great Britain  0.31***  0.10  0.25**  0.01  0.27**  0.20* 
Sweden  0.30**  0.18  0.34***  0.24**  -0.34***  0.20* 
B
E
I
R
 
 
United States  0.17  0.04  0.14  0.15  0.30**  0.15 
***: significant at the 1% level (critical value at 0.30);   **: significant at the 5% level (critical value at 0.23);   
*: significant at the 10% level (critical value at 0.19) using an asymptotic T-test with T=72. 
 
Based on weekly data from 1999 to 2004 
RBY    
Australia  Canada  Euro area  Great 
Britain 
Sweden  United 
States 
Australia  0.24***  0.29***  0.36***  0.34***  0.14**  0.36*** 
Canada  0.31***  0.04  0.32***  0.34***  0.12**  0.41*** 
Euro area  0.18***  0.14**  -0.03  0.22***  0.08  0.23*** 
Great Britain  0.13**  0.12**  0.31***  -0.05  0.12**  0.30*** 
Sweden  0.22***  0.19***  0.27***  0.27***  -0.34***  0.27*** 
B
E
I
R
 
 
United States  0.25***  0.18***  0.17***  0.24***  0.09  0.15*** 
***: significant at the 1% level (critical value at 0.15);   **: significant at the 5% level (critical value at 0.11);   
*: significant at the 10% level (critical value at 0.09) using an asymptotic T-test with T=312 

Are TIPS the ‘real’ deal? A conditional assessment of their role in a nominal portfolio”,

Can TIPS Help Identify Long-Term Inflation Expectations?”, Economic Review of the Federal Reserve Bank of Kansas City.

Effective duration of linkers and beta”,

Inflation Expectations and Real Return Bonds”,

Inflation risk premia in the term structure of interest rates”,

Liquidity Risk Premia and Breakeven Inflation Rates”, Economic Review, Federal Reserve Bank of Kansas City,

Real Rates, Expected Inflation and Inflation Risk Premia”,

Real Return Bonds, Inflation Expectations and the Break Even Inflation Rate”, Bank of Canada working

The Information Content of Treasury Inflation-Indexed Securities”, Federal Reserve Bank of St Louis Review,

The Term Structure of Euro Area Break Even Inflation Rates”, European Central Bank, Working Paper Series,

Why are TIIS Yields so High? The case of the Missing Inflation-Risk Premium”, Federal Reserve Bank of Cleveland Economic Commentary.

The rocky ride of break-even inflation rates

http://www.accessecon.com/pubs/EB/2008/Volume5/EB-08E40007A.pdf

The rocky ride of break-even inflation rates

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics