Tài liệu An Empirical Decomposition of Risk and Liquidity in Nominal and Inflation- Indexed Government Bonds pptx

Copyright © 2011 by Carolin E. Pflueger and Luis M. Viceira
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An Empirical Decomposition
of Risk and Liquidity in
Nominal and Inflation-
Indexed Government Bonds

Carolin E. Pflueger
Luis M. Viceira




Working Paper

11-094

An Em pirical Decom position of Risk and Liquidit y
in Nom inal and Inflation-Indexed G o v ernmen t
Bonds
Caro lin E. Pflueger and Luis M. V iceira
1
First draft: July 2010
This version: March 2011
1
Pflueger: Harvard Business School, Boston MA 02163. Email cpfl Viceira:

Harvard Business School, Boston MA 0216 3 and NBER. Email We are gra teful to
seminar participants at the HBS-Harvard Economics Finance Lunch, John Campbell, Graig Fantuzzi,
Josh G ottlieb, Robin Gr eenwood and J eremy Stein for helpful comments and suggestions. We are
also grateful to Martin Duffell and Anna Christie from the UK Debt Mana gement Office for their
help providing us with UK bond data. This ma te rial is based upon work supported by the Harvard
Business School Research Funding.
Abstract
This paper decomposes the excess return predictab ility in inflation-in de xed and nom-
inal govern ment bonds in to effects from liquidity, market segmentation, real interest
rate risk and inflation risk. We estimate a large and variable liquidity premiu m in US
Treasury Inflatio n P rotected Securities (TIPS) from the co-mo ve m ent of breakeven
inflation with liquidity proxies. The liquidity pre m ium is around 70 basis points in
normal times, but m u c h larger during the early years of TIPS issuance and during the
height of the financial crisis in 2008-2009. Th e liquidity prem ium exp lain s the high
excess returns on TIPS as compared to nominal Treasuries over the period 1999-2009.
Liquid ity-adju ste d breakeve n inflation appears stable, suggesting stable in flation ex-
pectations o v er our sample period. We find predictability in both inflation-in dexed
bond excess returns and in the spread between nominal and inflation-indexed bond
excess returns even after adjusting for liquidity, providing evidence for both tim e-
varying real i nterest rate risk premia and time-varying inflation risk premia. L iq-
uidit y appears uncorrelated with real interest rate and inflatio n risk premia. We
test w het he r bond re tu rn predictability is d u e to segmenta tion betwe en nominal and
inflation-indexed bond m arkets but find no evid e n ce in eith e r the U S o r in the UK.
1Introduction
TheyieldsonUSTreasuryInflation Protected Securities (TIPS) have declined dra-
matically since they were first issued in 1997. Over the 10 year period starting in
1999 the average annua lized excess log return on 10 year TIPS equalled a substantial
416%, almost a full percentage point higher than that on comparab le nomina l US
governm ent bonds. These differen tial returns are notable, because both nominal and
inflation-indexed bonds are fully backed b y the US government. Moreover, the real

cash flows on nomin al bonds are exposed to surprise inflation while TIPS coupons
and principal are inflation-indexed. This paper asks to what extent the returns on
nominal and inflation-indexed bonds in both the US and the UK can be attributed to
differential liquidity and market segment ation or to real inte r es t rate risk a n d inflation
risk.
There is strong em pirical evidence that the excess return on US nom inal go vern-
ment bond s o ver the return on Treasu ry bills exhibits predictable variation over time
(Cam pbell and Shiller 1991, Fama and Bliss 19 87, Cochran e a nd Piazzesi 2005 ). In
recen t wo rk, Pflueger and Vice ira (2011) provide stron g empirical evid enc e t hat the
excess return on inflation-indexed (or real) bonds and the return differential between
nominal and inflation-ind exe d bonds are also time varying both in the US and in the
UK.
Although gov ernmen t bonds in large and stable economies are generally considered
default-free, their real cash flow s are exposed to other risks. The prices of both
inflation-indexed and nominal go vernmen t bonds ch ange with the economy-wide real
in t erest rate. Consequently, bond risk premia will reflect investors’ perception o f real
in t erest rate risk, which may vary over time. The prices of n om inal governm ent bonds,
but not inflation-inde xe d government bonds, also vary w ith expected inflation, so that
inflation risk will impact th eir risk premia (Campbell and V iceira 2001). Cam pbell,
Sunderam, and Viceira (2010) pro v id e a model, in whic h inflation risk and real interest
rate risk vary over time and lead to p redictable variation in bond excess returns .
In addition to cash flow risk, institution al factors and trading frictions might
also impact bond p r ice s and bond risk p re mia. For any in ve st or the riskles s asset is
an inflatio n- in dexed bond whose cash flows m atch h is consumption p lan (Campbell
and Viceira 2001, Wac hter 2003), so that inflation - ind e xe d bonds should typically
be he ld by buy-and-ho ld inve stors . This sugge sts that even i n normal tim e s one
might expect a liquidity premiu m in the yield of inflation-inde xe d bonds . Wh ile US
1
nom inal Treasury bonds are amon g t he most liquid inves tme nts in the world, TI PS
empirically have a significant ly sm aller and less liquid m arket (Cam p bell, Sh iller,

and Viceira 2009, Gur ka y nak , Sack, and Wright 2010 , Fleming and Krishnan 2009,
Dudley, Roush, and Stein berg Ezer 2009).
If liquidity d iffere nce s are t im e- varying, liquid ity c an make re tu rn s r isk y and in-
duce an add ition al liquidity risk premium. For exam p le, if the liqu id ity of inflation-
indexed bonds deteriorates during periods when inves tors wo uld like to sell, risk
ave r se investors will demand a liquidity risk p r e m ium for hold ing these bonds (Am i-
hud, M end elson and Pedersen 2005, Ac harya and Pedersen 2 005). Our researc h aims
to understand ho w much of the observed variation in the expected excess return
on inflation-indexed bonds and of the expected return differential between inflat ion-
indexed and nominal bonds can be explained by liquidity premia, w hic h we argue
reflec t both the leve l and the r isk of liquidity.
We adop t an empirically flex ible approach to estimating the liquidity differenti al
between inflation-indexed bonds and nominal bonds. In our exercise w e explicitly
proxy for the liquidit y premium inherent in inflation-indexed US bonds using the
transaction vo lum e of T IPS , the financin g cost for buying TIPS, the 10-yea r nomin al
off-the-run spread and the Ginnie Mae (GNMA) spread. We then use these estimates
to adjust bond yields and returns for liquidity, and test for predictable variation in
liquidity-adju ste d nom in al and inflation-indexed bond excess returns. Our approac h
con tr a sts with the approach of D ’A m ico, Kim and Wei (2008), who model nom in al
and re al inte res t r a t es u s ing a tight ly param e te rize d a ffine term structure model and
then measur e the liquidity p re m ium as the difference between m odel-implied and
observed TIPS yields.
We estimate a statistically significa nt and econ omica lly important time-varyin g
liquidity componen t in breakeven inflationintheUS.Wefind that the yield on TIPS
is about 106 basis points larger o n aver age o ver our sample period than i t w ou ld
be if TIPS were as liquid as nominal Tr easu ry bonds of equivalent matu rity. This
high average reflects extraordinary even ts associated with very low liquidit y in this
mark et. We find a high liquidity discount in th e years following the introduction of
TIPS (about 120 bps), whic h w e attribute to learning and low trading v olume, and
during the fall of 2008 at the heigh t of the financial crisis (beyond 200 bps). We

estimate a mu ch lower liqu id ity discount of about 70 bp s between 2004 and 2007 and
after the crisis in 2009.
The yie ld differen tial between nominal and inflation-indexed bonds is often used
2
as a gauge of long -term in flation ex pectations. Breakeven inflation, as this yield
differential is popularly know n am ong pra ctitio ners, migh t reflect not only inflation
expectations and possibly an inflation risk premium, but also a liquidity prem ium
due to differential liquidity of inflation-indexed bonds relativ e to nominal bonds.
We obtain a liquidity-adjusted measure of breakev en inflation whic h suggests that
breakeven inflation has been fairly stable between three and four percent du r ing our
sample period.
Our analysis also she ds light on the sourc es of the differential liquidity premium
in TIPS relativ e to nominal go vernm en t bonds.
2
Following Weill (2007) and others
one can in terp ret the TIPS transaction volu m e as a measure of illiquid ity due to
searc h frictions.
3
Our findings suggest that the impact of searc h frictions on inflation -
indexed bond prices might ha ve been exacerbated during the early period of inflat ion-
indexed bond issuance, when the amount of bonds outstanding wa s relatively lo w and
perhaps only a small number of sophisticated in vestors h ad a good understanding of
the mechanics a nd pricing of these n ew bonds. In fact, TIPS transaction volume was
very low relative to nominal Treasuries during this early period. As TIPS trading
v olu m e increased relative to US Trea sury trading volu m e between 1999 and 2004,
TIPS yields cam e down fr om their d ramat ically high leve ls of up to 4% to under 2%
While arguably search frictions and learning specific to the no v elty of TIPS driv e
part of the liquidity differential between no minal and i nflation-indexed bonds, “flight-
to-liquidity” episodes m ight also help exp lain th is differential. In a flight to liqu id ity
episode some market participants sudde nly prefer highly liquid securities, such as

on-the -r un nominal Treasury securities, rather than less liquid securitie s.
4
Longstaff
(2004) finds evidence for flight -to-liqu id ity episodes by looking at the s pre ad betwe en
govern m ent agency bonds and US Treasury bonds. Krishnamu rthy (200 2) documen ts
a similar liquidit y effect by comparing the most recently issued on-the-run nominal
Tr easury bond with an older off-the-run nominal Treasury bond, whose pa y offsare
almost identical.
2
There exists a wide literature on the rela tionship between liquidity and asset prices, see Amihud,
Mendelson and Pedersen (2005) for a surv ey.
3
See Duffie, Garleanu and Pedersen (2005, 2007) and Weill (2007) for models of over-the-counter
markets, in whic h traders need to search for counterparties and incur opportunit y or other costs
while doing so.
4
In the search m odel with partially segmented marke ts of Vayanos and Wang (2001) s hort-horizon
traders endogenously concentrate in one asset, making it more liquid. Vayanos (2004) pre sents a
model of financial intermediaries and exogenous transaction costs, where preference for liquidity is
time-varying and increasing with volatility.
3
We find that breakeven inflation m oves negatively with both the on-the-run versus
off-the-run spread in Treasury bonds and the GNM A-Treasury spread in our sample
period. This empirical finding indicates that while during a flight- to- liqu id ity episode
inv estors rush into nominal US Treasuries, they do not buy US TIPS to the same
degr ee . This is especially intere s ting give n that both t ypes of bonds are fully ba cked
by the same issuer, the US Treasury, which is generally considered the safest borro we r.
Controllin g for liquidity allows us to disentan gle the effects of liquidity, real in terest
rate risk and inflation r isk on expected returns an d to shed furth er light on the results
in Pflueger an d Viceira (2011), who find that inflation-indexed bond returns in both

the US and the UK exhibit predictable time-variation. We find that liquidity is a
large co ntrib u tor to return predictabilit y in inflation-indexed bonds, but that real rate
risk and infla tion risk are also statistically and economically significant contributors
to return predictability in both i n flation-indexed and nominal bonds. 17% of the
variance of TIPS realized exc ess returns can be expla ined b y a time-varying liquidity
premium, and 6% of the variance by a time-varyin g real inte r est rate risk premium.
We find that both inflation risk premia and real rate risk premia are presen t in nominal
bond returns and explain 3% an d 5% of the variance of their realiz ed e xce ss re tu rn s,
respectively.
We als o investigate the hy pothesis that the markets for nominal and inflat ion -
indexed deb t are segmented, lead ing to relat ive price fluctuations and returns pre-
dictabilit y. Recent researc h has emphasized the role of limited arbitrage and bond
in vestors habitat preferen c e s to exp lain predictab ility in nomina l bond returns. By
building on the preferred-habitat hypothesis of Modigliani and Sutch (1966) , Vayan os
and Vila (2009) show that investors’ preference for certain ty pes of bonds, com b ined
with risk aversion by bond mark et arbitrageurs, can result in bond return predictabil-
ity not directly attributab le to rea l inte rest rate risk or inflation risk, but to m arket
segmen ta tion . This segmen tation is the result of bond m arket arbitrageurs not fully
offsetting the positions of “habitat investors” in respon se to shocks in the bond mar -
k e t. Greenwood and Va yano s (20 08) and Ham ilton and Wu (2010) emp irically explore
market segm entation across different maturities in t he US Treasury nominal bond
mark et using the maturit y structure of outstanding go v ernment debt as a proxy for
supply shoc ks, and find that it predicts bond returns.
In the context of real versus nominal bonds, it seems plausible that the preference
of certain investors–such as pension funds with inflation- ind e xe d liabilities–for real
bonds, and the preference of others–such as pension funds with nominal liabilities–
4
for nominal bonds might lead to im perfect market integra tion between both markets
and this could generate return predictability.
Following Green wood and Vayanos (2008) we use the outstanding supply of real

bonds relative to total go vernment debt as a proxy for supply shocks in the inflat ion -
indexed bond mark et. We cannot find an y evidence for bond supply effects either
in the U S or in t he UK. One potential inter pret atio n for this finding could be that
go ve rn m ents u nderstand investor dem and f or t he differen t types of securities and
adjust their issuance accordingly, effect ively a cting as an arbitrag e ur between the two
mark ets.
The structure of th is article is as follo w s. Section 2 estimates th e liquidity prem ium
in US TIPS vers us nom ina l bonds using our liquidity proxies. Section 3 tests the
market segm entation hy pothesis in the US and in the UK , and section 4 considers
time-varying real in terest rate risk and inflation r isk p remia. Finally, sectio n 5 offers
some concluding remarks.
2 E st ima t ing t he Li quidity Co mpon e nt o f Br ea keve n
Inflation
Our approach to m odelling liquid ity premia is empirical. We estimate the US TIPS
liquidity premiu m by regre ssing inflation com pensation on measures of liqu id ity, fol-
lowing authors such as Gurka y na k, Sac k , and Wright (2010 ). We use four liquidity
proxies: the no m in al o ff-the-run spread, the GNMA spread, relativ e TIPS transaction
v olume and the difference bet ween TIPS asset-sw ap-spreads and nominal US Trea-
sury asset-sw ap spr eads. Since w e have data for liquidit y proxies only for the US in
the most recent period, our analysis is restricted to the last 10 yea r s of US experience
and we cannot conduct a similar study for UK bonds.
We interpret relativ e TIPS transaction volume as a measure of TIPS-specific liq-
uidit y. O ne might think that when TIPS were first issued in 1997, the mark et needed
to learn about TIPS and the mark et for TIPS took some time to get established. This
should be refle ct ed in initially low trading v o lumes in TIP S and high yield s during
the early period. T he off-the-run spread and the GNMA spread are though t to cap-
ture flight-to-liquidity even ts in the US Treasury bond market (Krishnam urthy 2002).
Finally, the asset swa p spread variable captures extraordinary ev en ts during the fi-
5
nanc ial crisis. (See Campbell, Shiller, and Viceira (2009) for an ac co u nt of liquidity

ev ents dur ing the Fall of 2008.)
While the relative t r an saction volume of TIPS likely only cap tu res th e curren t ease
of trading TIPS and theref ore a liquidity premium , the off-the-run spread , the GNMA
spread and the asset-swap - spr ead are likely to represe nt both the level of liquidity
and liquidity risk. Our estim a te d liquid ity premium is therefore likely to rep res e nt a
comb in ation of current ease of trading TIPS ver s us nomin al US Trea su ries and the
risk that the liquidit y of TIPS might deterio rate.
2.1 Bond Notation and Definitions
We denote b y 
$

and 


the log (or continuously compounded) y ield with 
periods to maturity for nominal and inflation-indexed bonds, r espectively. We use
the superscript  to denote this quantity f or both US and UK inflation- in de x ed
bonds.
We define breakeven inflation as the difference bet ween nominal and inflation-
indexed bond yields:


= 
$

− 


(1)
Log excess returns on nominal and inflation-indexed zero-coupon -period bonds

held for one period before maturit y are given by

$
+1
= 
$

− ( − 1) 
$
−1+1
− 
$
1
 (2)


+1
= 


− ( − 1) 

−1+1
− 

1
 (3)
Therefore, the log excess one-period holding return on break eve n inflation is equal to



+1
= 
$
+1
− 

+1
 (4)
The yield spread is the difference between a long-term yield an d a short-term
yield:

$

= 
$

− 
$
1
 (5)



= 


− 

1
 (6)




= 

− 
1
 (7)
6
Inflation-indexed bonds are commonly quoted in terms of real yields, b ut since


+1
is an excess return over the real short rate it can be in terp reted as a real or
nominal excess return. In all regressions we approximate 
$
−1+1
and 

−1+1
with

$
+1
and 

+1
.
2.2 Estimation Strategy
At tim es wh en TIPS are relatively less liquid than nominal bond s we wo u ld ex pect

TIPS to trade at a d isc ou nt an d the TIPS yield to increase relative to nom ina l yields.
To account for this prem ium, we estimate the following regression for breakeven
inflation:


= 
1
+ 
2


+ 

 (8)
where 

is a vector con tain in g our four liquidit y pro xie s: the off-the-run spread,
the G NMA spread, the relativ e TIPS transactions volume a nd the difference between
TIPS and nominal asset swap spreads. Section 2.3.2 giv es a detailed description of
the data sources and construction of these variables.
In (8) we would ex pect variables that indicate less liquid ity in the TIPS marke t
to en ter negativ ely and variables that indicate higher liquidit y in the TIPS mark et
to enter positively. Th at is, the o ff-the-run spread, the GNMA spread and the asset
swap spread should enter negatively. On the other hand higher transaction volu me
in the TIPS market indicates that TIPS are easily traded an d therefore it should
enter positively. Since the off-th e -ru n spread and GNMA spread capture the liquidity
premium in differ ent bu t related secu ritie s we wou ld expect the magn itu d e of the
regression coefficients on these spreads to be less than one.
Theasset-swapspreadreflects the financing costs that a levered investor incurs
from holding TIPS instead of a similar maturity no minal bonds. If the m arginal

in vestor in TIPS is such a leve r ed inves t or, we would expect brea ke ven inflation to
fall approximately one for one with the asset sw ap spread.
Our liquidity variables are normaliz ed in such a way that they go to zero in
a world of perfect liqu idity. W h en liquidity is perfect t h e off-the-run spread, the
GNM A spread and the asset-swap spread should equal zero. The transaction volu me
is normaliz ed so that its maximu m is equal to zero. That is, we assume that the
liquidity prem ium a ttribu ta ble to low transac tion volume w as negligible during t he
7
period of 2004-2007.
We obt a in liquidity-adju st ed TIP S yields b y assumin g that the liquidity premium
estimated from the breakeve n regression (8) is en tirely attributable to time-varying
liquidity in TIPS rather than in n ominal bond s. The estimate d liquidity com ponent
in TIPS yields the n equ als
ˆ


= −ˆ
2


 (9)
where ˆ
2
is the vector of slope estim ates in (8). Thu s an increase in
ˆ


reflects a
reduction in the liquidity of TIPS relative to nominal Treasury bonds. Liquidity-
adjusted TIPS yields and breakeven inflationthenequal




= 


−
ˆ


 (10)



= 

+
ˆ


 (11)
Tha t is, the observ ed yield on TIPS is larger than t he liquidity-ad ju ste d yield d u rin g
times of lo w liquidit y and accordingly the observ ed break ev en inflation will be smaller
than the liquidity-ad ju ste d breake ven inflatio n. For simplicity we assume that the
liquidity premium on one -qu arte r real bonds is constant.
2.3 Data
2.3.1 Yield Data
We use data on constant-maturity inflation-indexed and nominal yields both in the
US and in the UK. Inflation-indexed bonds hav e been available in the UK since 1983
and in the US since 1997. Inflation-indexed bonds are bonds whose principal adjusts

automa tically with the e volution a consume r price in d e x, which i n the US is the
Consumer Price Index (CPI-U) and in the UK is the Retail Price Index (RPI). The
coupons are equal to the inflation-adjusted principal on the bond times a fixed c oupon
rate. Thu s the coupons on these bonds also adjust with inflation.
5
5
There are further details suc h as in inflation lags in principal updating and tax treatment of the
coupons tha t slightly complicate the pricing of these bonds. More details on TIPS can be found in
Viceira (2001), Roll (20 04) and Gu rkay nak, Sack, and Wright (2010). Campbell and Shiller (1996)
offer a discussion of the taxation of infla t ion-indexed bonds. Campbell, Shiller, and Viceira (2009)
provide an overview of t he history of inflation-indexed bonds in the US and the UK.
8
For t he US we u se an e x pan ded version of the Gurka ynak , S a ck, and Wright
(2007) and Gurkayn ak , Sac k , and Wright (2010, GSW henceforth) data set. GSW
have con structed a zero-coupon yield curv e sta rtin g in January 1961 for nom in al
bonds and for TIPS starting in January 1999 b y fitting a smoothe d yield curve. We
expand their data bac k to 1951 using the McCu lloc h, H ou ston , a nd Kw o n (1993)
data for US nominal zero coupon yields from Jan u a ry 1951 through December 1960.
The GS W data set contains constant maturity yie lds for m atu rities of 2 to 20 years.
Our empirical tests will focus on the 10-year nom inal and real yields, because this
maturity bracket has the longest an d most continuous history of TIPS outstanding.
We measure US inflation with the all-urban seasonally adjusted CPI, and the short-
term no m in al int ere st rate w ith th e 3 month T -bill rate from the Fama-Blis s riskle ss
in t erest rate file from CRSP. TIPS pa y outs are linked to the all-urban non seasonally
adjusted CPI and our results become slightly stronger when using the non seasonally
adjusted CPI instead.
For the UK we use zero-coupon yield curves from the Bank of England. Anderson
and Sleath ( 2001) desc ribe th e spline-base d techniqu e s used to estim ate the yield
curves. No min al yields are available starting in 1970 fo r 0.5 to 20 years to maturity.
Real yields are a vailable starting in 1985 for 2.5 to 25 yea r s to m atu rity. We focus

on the 20-y e ar nominal and real yields. We use the 20-year maturity in our tests
because 20-year nominal and real yields are a vailable from 1985, while for instan ce
10-y e ar real yields are available only since 1991.
6
Inflationismeasuredbythenon
seasonally adjusted Retail Price Index, which serv es as the measure of inflation for
inflation-indexed bond pa youts.
Since neith er th e US nor the U K go vern ments issue inflation-ind e xe d bills, w e need
to resort to an empirical procedure to build a h ypothetical short-term real in terest
rate. We follow the procedur e described in Pflueg er and Viceira (2011). Finally,
although our yield data sets are available at a monthly frequency, we sample our data
at a quarterly frequency in order to reduce the influence of high-frequency noise in
observ ed inflatio n and sh ort-te rm n ominal inter es t rate vo latility in our tests.
6
For some months the 20 year yields are not available and instead we use the longest matur ity
available. The maturity used fo r the 20 year yield series drops do wn to 16.5 years for a short period
in 1991.
9
2.3.2 Data on Liquidity Proxies
Our first pro xy for liquidity in the Treasury mark et is the spread between the on-
the-run and o ff-the-run 10 year nom inal Treasury yields. The Treasury regularly
issues new 10 year nominal notes, and the newest 10 year note is considered the m ost
liquidly traded security in the Treasur y bond m a r ke t. The most rec ent Treasury
note (or bond) is kno wn as the “on-the-run note” b y market participants. After the
Trea sury issues a new 10-year note, the prior n ote goes “off-the-run.”
The off-the-run bond t ypically trades at a discount over the on-the-run bond–i.e.,
it tra des at a higher yield–, despite th e fact that it offers almost iden t ical cash flows
with a v e ry similar remainin g time to maturity. Similarly, older bonds with longer
maturities at issuance tha t have almost the same cash flows and remain in g tim e
to maturity as the on-the-run bond also trade at a discount. Market participants

attribute this spread to lo wer liquidit y of the off-the-run bond relative to the on-the-
run bond. Treasury bonds are typically held by buy-and-hold investors, and older
bonds are more difficult to find and to trade than more recently issued bonds. We
obtain the 10 yea r off-the-run spread from the Federal Reserv e and from Bloomberg.
7
A second type of governmen t-bac k ed bond that is also less liquidly traded than
on-the-run Treasuries is GNM A bonds. The G ove rn ment N ation al M ortgage As soci-
ation (GNMA) guaran tees the timely payment of interest and principal on residential
mortga ge ba cked securities. A s such GN MA bonds do not contain any defau lt risk,
although they do contain prepa ym ent risk, because mortgage h old ers can prep ay with-
out penalt y. We use the spread between GNMA bond yields and on-the-run Treasury
yields as a pro xy for a market-wide desire to hold and trade only the most liquid
securities. Spreads bet ween agency bonds and Treasury bonds ha ve previously been
used as indicators of the liquidity premium in the TIP S and Treasury marke ts by
Gurkayn ak, Sack, an d Wright (2008) and by Longstaff (2004 ). We obtain a GNMA
spread adjusted for prepaym ent risk from Bloomberg.
8
Our third m easure of liquidity aims to capture liquidit y developments specificto
the TIPS market. There is evidence suggesting that the TIPS mark et might have
been subject to specific liquidity events. For example, the first issues of TIPS i n
7
The o n the run data is from Bloomberg (USGG10YR), and the off the run is from the Federal
Reserve publication H.15 “Interest Rates”.
8
Ticker GNSF060. This is the prepayment-option adjusted spread based on a 6% coupon 3 0 year
GNMA generic bond. It is adjusted for prepayment risk using t he Bloomberg prepayment model.
10
the late 1990’s carrie d unusu a lly high real yields. Campbell, Sh iller, and Viceira
(2009) and others have argued that perhaps TIPS w ere not well understood initially
and may therefore have traded at a discount. In their study of t he TIPS market

microstruc ture Fleming and K r ishn an (2009) conclu de that t rad ing activity is a good
mea sur e of cross-s e ctional TIPS liquidity. We follow Gurkayn ak , Sack , and Wr ight
(2010) in u sing the transaction vo lum e of TIPS relative to the transaction volume of
Treasuries as an indicator for time-varying TIPS liquidity.
We obtain Primar y Dea lers’ transaction v o lume s for TIPS and nominal Treasury
securities from the New York Federa l Reserve FR-2004 surv ey. We c onstruct our
measure of relative transaction v olume as log
¡



 
$

¢
,where


denotes the av erage weekly transactions v olume over the past 3 mon ths and 
$

the corresponding figur e for nomin al bonds. We normalize the relative transaction
volume so th at its maximal value is equal to zero. For 
$
we use the transaction
v olu m e of gove rn m ent coupon securities with at least 6 (before 2001) or 7 (from 2001)
y e ars to matur ity.
We c hoose the transaction vo lume series for coupon bonds with a long time to
maturity because we are aiming at capturing the differential liquidity of TIPS with
respect to 10 y ear nomina l bonds. Includin g all matur ities or even T-bills would also

reflec t liquidity of short-term instruments versus long-term instruments. We then
smooth the m easure of relative transaction v o lum e ove r the past three months because
we think of it as c ap tu rin g secular learning effects. This smoothing also helps avoid
in troducing more volatility into TIPS yields in th e process of adju sting for liquidity.
It wou ld not seem accurate to have liquidity-a djus ted TIPS yields that w ere more
volatile than raw TIPS yields. Ou r comput ations are comp licated b y the fact that
in 2001 the Federal Reserv e c h anged the maturity cuto ffs for which the transaction
v olu m es a re reported. T h is m ean s that before 6/28 /200 1 we use the transaction
volume of Treasuries with 6 or mo re year s to matu rity while starting 6/28/20 01 we
use the transaction volume of Treasuries with 7 or m ore y ears to m atu rity. The series
after the break is scaled so that the gro w th in 
$
from 6/21/200 1 to 6/28/2001
is equal to the gro wth in transaction volume of all government coupon securities.
Finally, we wan t to c ap ture the co st th at le vered investors would incur when
holding TIPS. Such investors looking for TIPS exposure can either borrow by putting
the TIPS on re po or they might consid er en te ring into an as set swa p , which r equires
no initial capital. An asse t swa p is a derivativ e c ontract betwe e n two p a r ties where
onepartypaysthecashflows on a p articular g overnment bond (e .g. TIPS or nomin al)
11
and receiv es  plus a spread, which can be positive or negativ e. The payer of
the bond cash flo ws can hedge itself by holding the bond and financing the position
in the short term debt m arket. Therefore the a sset swap spread ()reflects the
current and expected financing costs of holding the long bond position. The initial
net value of an asset swa p spread is set to zero. For a lev ered inve stor a widening of
the spread can be cons idered equivalent to an increas e in the cost of financing a long
position in the bond.
Accordin gly, our fourth measure of liquidity is the difference between the asset
swap spread (ASW) for TIPS and the asset sw ap spread for nominal Treasuries,




= 


−
$

. This is a measure of the relativ e cost of financing a
long position in the TIPS mark et v ersus in the nom inal Treasury market. A widening
of th is relative spread indicates that the cost o f financing a long position in th e TIPS
market has increased relative to the cost of financing a long position in the nominal
Treasury market.
We only ha v e data on 


from July 2007 until April 2009, and set it to
its July 2007 value of 40 bps w hen the asset swap spread series is not a vailable. The
data source for the Asset Swap Spreads is Barclays Capital. For the 10 y ear TIPS
Asset Swap Spread w e use the July 2017 Asset Swap and for the 10 year nominal
Asset Swap w e use the generic 10 Year On-the-Run P ar Asset Swap Spread.
Figure 1 shows our four liquidity variable s. Th e dissimilar time -ser ies patte rn s of
the variables suggest that each o ne represen ts a different as pect of m arke t liquidit y,
although the spread v ariables all jump during the financ ial crisis of 2008 -2009. T he
on-the-run off-the-run spread exhibits high frequency variation. The GNMA spread,
on the other hand, moves relativ ely slowly. One reason for the difference in the t wo
spreads could be that they h ave a differen t investor base. The GNMA spread pattern
of a lo wer spread between 2002 and 2007 agrees with anecdotes of long-term investors
who wer e particu larly willing to invest into less liquid sec u rities in order gain yield
during that period. The relativ e transaction vo lume rises linearly through 2004 an d

then to stabilize. This is consiste nt with the i d ea that it took t ime for TIPS to
become we ll-established relativ e to familiar nominal Treasu ries. It also suggests that
the liquidity premium due to the no velty of TIPS should have been modest in the
period since 2004.
Finally the asset swap spread variable 


varies within a relativ ely narrow
range of 35 b asis point to 41 basis points from July 2007 through August 2008, and it
rises sharply during the financial crisis, reaching 130 bps in December 2008. That is,
12
before the crisis financin g a long position in TIPS was about 4 0 basis more expensive
than financing a long position in nominal Treasury bonds, but this cost differential
rose to more than 120 basis points after th e Lehm an bankruptcy in Sep tember 2008.
Camp bell, Shiller, and Viceira (2009) argue that t he bank ru p tcy of Lehman Broth -
ers in Septem ber of 2008 had a s ignifican t effect on liquidity in the TIPS market,
because Lehman Bro thers had been ve ry active in the TIPS marke t. The unwinding
of its large TIPS in vent ory in the w eeks follo win g its ban krup tcy, comb in ed with a
sudden increase in the cost of financing long positions in TIPS appears to have in-
duced an unexpected do wnwa rd price pressure in the TIPS mark et. This led to a
liquidity- induced sharp tighten in g of breakeven inflation associated with a widening
of the TIPS a sset-swap-spread.
2.4 Estimation Resu lts
Tab le 1 reports OL S estimates of (8). Column 1 estima tes only the impact of the off-
the-runspreadonbreakeveninflation. Column 2 adds the GNMA spread, and column
3 adds TIPS transactions volume. C olumns 1 through 3 always include 


,
but with a slope set to its theoretical value of −1. Column 4 presen ts estim ates with

freely estimated coefficients for all four liquidity prox ies During the financial crisis
securities markets were sev erely disrupted and the buyers and sellers of asset sw a ps
may n ot have acted as the mar gin al buye r s and s ellers of TIPS . Estimating 
2
freely
accou nts for the possibility that th e asset swa p s p r ead only repre se nt s a fraction of
the financing cost for the margina l holder of TIPS. Column 5 estimates (8) for the
pre-crisis time-period 1999 -20 06, including the off-the-run spread, the GNMA spread
and transaction volu me but n ot the asset-swap sprea d.
Table 1 shows coefficients whose sig ns are consistent with e xpectatio ns and gen-
erally s tatis tically s ign ificant. Breakeven i nfla tion is decreasing in t h e o ff-the-r un
spread and in the GNM A spread, and increasing in the transaction volume of T IPS
relative to nom inal Tre as u ries . Intere stingly, our liquidity me asu res expla in a very
large fraction of the variabilit y of breakeven inflation, from 45% in column 1 to 67%
in column 4. T h e 
2
incre ases with ev ery additional liquidity con trol introduced,
indicating tha t each of the controls helps explain the liquidity premium on TIPS .
Thes e results are not sen sitive to the inclusion of the financ ial crisis in the sample
period. The 
2
of the regression in column 5 is still 47% when the sample period
ends in June 2007. Moreo ver, the signs an d ma gn itudes of the regression coefficients
13
do not depend on the inclusion of the financial crisis.
Column 4 in Tab le 1 shows that th e freely estimated coefficient on the asset swap
spread differential is at −159 somew h at large r in absolute value th an −1.Thestan-
dard error on the regression coefficient indicates that it is precisely estimated. The
large size of this parameter estimate suggests that the asset swap spread differen tial
might represen t only a fraction of the financing cost for the marginal holder of TIPS,

particularly during the finan cia l crisis. It also suggests the relevance of liquidity fac -
tors i n explaining the sharp fall in breakeven during the financial c risis, since the
sw ap spread differen tial beha ves almost like a dummy variable that spik es up dur-
ing the financial crisis. However, due to the significan t macroeconomic and financial
marketseventsitispossiblethatinflation expectation s fell at the same time that
liquidity in the TIPS market became sc arc e . Non eth e less, the difference between the
liquidity c omponent estimate d i n columns 3 and 4 a p pears small as ind icate d by the
v e ry similar 
2
. We will work with th e freely estimated ve rsion from column 4 fo r its
flex ibility.
Figure 2 shows our estimated liquidity prem ium. We find an a verage spread due
to liquidity of arou nd 106 bps. Although this ave rage is high, one mus t take into
accountthatitreflects periods of very low liquidity in this market. Figure 2 s h ows a
high liquid ity premiu m in the early 2000’s (about 120 bps), but a much lower liquidit y
premium between 2004 and 2007 (70 b ps) . The prem ium shoots up again bey o nd 200
bps during the crisis, and finally comes dow n to 70 bps after the crisis. The time
series of our liquid ity premiu m is co ns iste nt with the findin gs in D’Amico, Kim an d
Wei (2008) but the level of our liquid ity pr em ium is highe r. They find a large liquidity
premium during the early years of TIPS of around 100 bps and then a m uch lower
liquidity prem ium d ur ing the period 2004-2007.
Flec ken stein, Longstaff and Lustig (2010) present a measure of ave rage TIPS
mispricing by comparing breakeven inflation to synthetic zero-coupon inflation swaps.
Their series of ave rage TIPS-Treasury mispricing resembles our series of differen tial
financing costs 


both in term s o f level and tim e series variation. We allow
for additional variables that help us ide ntify so urces of illiquidity operating at d i fferent
frequencies. We find that the se variables drive strong time variation in the liquidity

premiu m, and also result in an ev e n highe r average liquidity prem iu m than pr e vious ly
estimated.
Figures 3 and 4 sho w liquidit y -adjusted b reake ve n in flation and TIPS yields, re-
spectiv e ly. Figure 3 shows t h a t liquidity-a dj us t e d breakeven inflation m oves bet ween
14
3% an d 3.5% for mu ch of the sample period. Mor eover our liquid ity adjustment at-
tributes most of the drop in breakeven inflation during the fa ll of 2008 to liquidity.
Figure 4 shows that if TIPS had remain ed as liquid as nom in al Treas ur ies their yields
wo uld have dropped dramatically in the fall of 2008. T h is has important implica-
tions fo r th e interpretation o f the dramatic reduction in breakeven inflation observed
during the financial crisis as an indicator of massiv e expected deflation among bond
market participants. We discu ss this poin t in detail in section 4.
3 Te sting Fo r M arket Seg m e nt ation Effects
Before using liq uid ity- ad just ed yields a nd retu rns to exp lore the relevance of real in-
terest rate risk and inflation risk in explaining the estimated predictable variation
in bond excess returns, we conside r first if in stitutional factors can explain this vari-
ability. In particular , in this section we ex plore wheth er the relative supply of nomi-
nal and inflation-inde xe d Treasury bonds is co rrela ted w ith their relative yie ld–i.e.,
breakeven inflation–and whether it forecasts excess bond returns.
The preferred-habitat h ypothesis of Modigliani and Sutch (1966) states that the
preference of certain types of in vestors for specific bond maturities might result in
supply im balances and price pressure in the bond market. In recent work Va yanos
and Vila (2009 ) formalize th is hypothesis in a theory where risk ave rse a rbitra geurs
do not fully offset the price imbalances generated b y the presence of preferred-habitat
in vestors in th e bond market. Greenwood and Va yanos (2008) and Hamilton and Wu
(2010) find statistically significan t correlation betw een the relative supply of nominal
Treasury bonds at different m atu ritie s and the behavior o f nom ina l interest rates .
Arguab ly the inflation -ind exed bond marke t is a natural candidate to look for seg-
mentation effects in th e bond market. Just as investors might differ in their preference
for bond m atu ritie s, the y might also differ in their preference for holding inflation-

indexed or nominal bonds. For example, some inv estors, such as traditional defined-
benefit pension funds in the US with a mature liability structure, have liabilities
which are mostly nomin al, while o the r inves tors , such as less matu re defined- benefit
pension funds or individuals investing for retirement, face liabilities which are mostly
indexed.
Follo wing Greenwood and Vayanos (2008) w e try to control for the po ten tial seg-
15
men tation bet ween both markets a nd supply effects using the outstanding supply of
real bonds relative to total government debt as a con trol variable. If supply is sub-
ject to exogenous shoc ks while client e le demand is s tab le over time we wou ld expect
increases in the relative supply of inflation-indexed bonds to be correlated with con-
temporary decreases in breakeve n inflation , as the price of inflation-indexed bonds
falls in response to excess supply. Subsequently w e would expect to see positive
returns on inflation-indexed bonds as their prices r ebound.
Alternatively, it could be the case that bond demand ch an ges over time, and
the governmen t tries to accommodate ch anges in demand. This would be consis-
ten t with a debt management policy th at tries to tak e advan tag e of in terest r ate
differen tials across both mark ets. In this case w e w ould expect the relativ e supply
of inflation-indexed bonds to be unrelated to subsequent returns, and possibly to be
ev en positive ly correlated w ith con temporaneous breake ven inflation .
We measure the relative supply of inflation-indexed bonds in the US as the nom-
inal amount of TIPS outstanding relative to U S government TIPS, notes and bonds
outstanding .
9
The face value of TIPS outstanding available in the data is the original
face va lue at issuance times the inflation incurred since then and there fore it increases
with inflation. The numbers inc lude both privately held Treasury securities and Fed-
eral Reserv e and intragovernmental holdings. This is similar to the supply measure
used by Greenwood and Va ya n os (2008).
We also look at bond supply effects in the U K bond mark et. The relative supply

variable for the UK is compute d similarly, as the total amount of inflation-linke d gilts
relativ e to the total amount of c o nventional gilts outstan ding. Convent ional gilts
exclude floating-rate and double-dated gilts but include undated gilts. The face value
of index-linked gilts does not inclu d e inflation-uplift and is reported as the original
nominal issuance va lue.
10
Our results are not sensitive to including or excluding the
inflation uplift.
Let 


denote the face value of inflation-indexed bonds outstanding and 

the combined face value of nom inal and inflation-indexed bonds outstanding at time
 for either the US or the UK. We define 

as 




.Wealsoconsider
9
The economic report of the president reports US Treasury securities by kind of obliga-
tion and reports T-bills, Treasury notes, Treasury bonds and TIPS separately. The data can
be found in Table 85 for the reports until 2000 and in Table 87 in subsequent reports at
h ttp://www.gpoaccess.gov/eop/download.html.
10
We are deeply grateful to the UK Debt Management Office for providing us with the UK data.
16

the change in supply ∆

, whic h we compute as the relativ e c hange in 


minus the relative chan ge in 

so th at ∆

=
¡



− 

−1
¢


−1
−
(

− 
−1
) 
−1
. Figure 5A plots the relative supply of TIPS, 





,and10
year breakeven inflation in the US, while Figure 5B plots the relative supply of UK
inflation-linked gilts and 20 ye ar bre akeven inflationintheUK.
Figure 5A illustrates a rapid inc rea se in the relativ e amount of TIPS outstandin g.
Starting from less than 2% in 1997 TIPS increased to rep resen t o ver 14% of the US
notes, bonds and TIPS portfolio in 2008. Subsequen tly to the financial crisis the US
go ve rn m ent issued substant ial amounts of nominal notes and bonds, leading to a drop
intherelativeTIPSsharein2009.Atthesametimethelevelofbreakeveninflation
remaine d relatively steady over this 11 year period with a large drop in the fall of
2008, as discussed e arlier.
Figure 5B illustrates the histo ry of the relative sh are of UK inflation-linked gilts
outstanding. The relativ e share of link ers has increased over the period from about
8% in 1985 to o ver 17 % in 2008. At the same time 20 year UK breakeven inflation
has fallen in the period 1985-200 9, reach ing a lo w of 2.1% in 1998. The increase in
inflation-link e d bonds outstanding accelerated noticeab ly after 2004. Greenwood and
Vayanos (2009) analyze this episode in ligh t of the UK P ensions Act of 200 4, wh ich
pro vided pension funds with a strong incentiv e to buy long-maturit y and inflation-
linked gov ernm ent bonds and subsequently led the governm ent to increase issuance
of long-maturity and inflatio n- lin ke d bonds.
Table 2 s hows regr e ss ions of bre a keven inflation on to the relative supply and the
change in supply of inflation-indexed bonds. Panel A sho ws results for US bonds.
Neither the relative supply nor ∆

appear to be related to breakeven infla-
tion. C olum n 4 in the panel shows a regression of breakeven inflation o nto 

,

∆

and our liquidit y proxies. T he magnitude and statistical significance of the
coefficie nts o n thes e proxies is ver y similar to the results tha t obta in witho u t co n -
trolling for the supply of TIPS, sho wn in Table 1, w h ile the supply variab le s remain
statistically not significant.
P anel B in Table 2 shows regressions of UK break ev en inflation onto the relative
supply and the change in supply of inflation link ers. Due t o data constraints we
are not able to control for liquidit y. To control for possible spurious correlation
bet ween breakeven inflation and bond supply, w e run these regressions with and
without including a time trend. The results are very similar to the US results, even
though the maturities of the bonds and the sample periods are differen t: The supply
17
variable is significant but it switc hes sign as we include a time trend in the regression,
while the c hange in supply does not enter significantly. The time trend is statistically
significant and increases the 
2
fro m 26% (colum n 1) to 65% (column 3).
Figure 5B helps understand this sign change. Since the m id-1980’s the supply of
inflation linkers in the UK has risen, while breakeven inflation has been generally
declining. Th is secular decline in breakeven in flation likely reflects for the most
part c h anges in m on etary policy and declines in both realized and expected inflation
(Campbell, Shiller, an d Viceira 2009), rather than c hanges in bond supp ly. This
explains wh y a simple regression of UK breakeven regression on the supply of inflation
linkers gives a negative slope. Introducing a time trend take s care of this common
in verse tren d , and switc he s the sign of the slope on the supply variable to positive.
This positive partial correlation suggests that at the margin periods of low breakeven
inflation are associated with relative ly more issuance of nominal bonds b y the UK
go vernm ent. One could interpret these results as the government reacting to increased
demand for inflation-linked bonds by issuin g m ore in flation-indexed bonds. T his

interpretation is co nsisten t with the episode described in G reenwood and Va y anos
(2009).
If market s are segme nte d we would expect increases in the relative supp ly of
inflation-indexed bonds to predict excess returns on inflation-indexed bonds. Table
3 explores whether our bond supply variables and liquidit y variables predict bond
excess returns. Pa nel A shows results for the US. Our left-hand-side variables are
the nominal, inflation-index ed a nd breakeven retu r ns as definedin(2),(3)and(4).
Pflueger and Viceira (2011) show that nominal, TIPS and breakeven term spreads
are significant predictors of the corresponding excess returns. We therefore control
for these spreads in our regressions.
P anel A in Table 3 shows that the TIPS and breakeven term spreads still enter
significantly and predict TIPS excess returns and breakeven excess returns, respec-
tiv ely, after controlling for liquidit y and supply e ffects. The liquidity premiu m ent ers
significantly and in particular helps predict the breakev en return. By contrast, the
supply variables a re n ot statistically sign ificant.
11
Ove rall, we find little evidence of
supply effects explaining either the spread bet ween n ominal and re al interest rates in
the US or bond risk premia, but we do fin d evide n ce that liqu idity helps predict the
11
Arguably ∆

is more appropriate than 

for use in excess return regressions, since


exhibits a time trend. Ho wever, our results do not change if we consider 

and

∆

in isolation instead of simultaneously.
18
excess return on nominal bonds over TIPS.
P anel B in Table 3 sho w s similar return-predictabilit y regressions for the UK,
using 

and ∆

as ad dition al explanatory variables. Both variables are
generally not statistically significant . Hence it seems that the mark ets for nominal
and in flation-indexed bonds are not subj ect to exogenous differen tial supply shoc ks.
On e wo uld expect this result if th e g ov ernment accommodate s dem and pre ss ures from
investors for nominal or inflation-indexed bonds.
In summary, there is very little evidence of bond supply effects in either the UK or
US bond marke ts. Moreover, the return predictability results in P flueger and V iceira
(2011) gene rally ap pear to hold up to the inclusion of liquidity and supply variables.
The inflation -ind ex ed bond spread still predicts inflation-indexed bond excess returns
and the bre ake ven spread predict s breakev en exce ss retu rns . Pane l A in Table 2
show s that liquidity is a ls o a very strong pred ictor of bre akeve n e xc es s returns. We
therefore proceed to decompose breakeven inflation int o a liquidity componen t and
a liquidit y-adjusted breakeven inflation and exam in e th e pred ictability of these two
components separately.
4 Time-Variation of Real In terest Rate and Infla-
tion Risk Pr emia
4.1 Predictive regressions with liquidity -adjusted yields and
returns
Pflueger and Viceira ( 2011) find that the real term spread predicts excess r eturns on
inflation-indexed bonds and the breakev en inflation spread predicts break even returns

in the US and the UK, similarly to th e return predictability in US nominal gove rn ment
bonds document e d in Cam p bell and S h iller (1991) an d Fama and B liss (19 87). They
also sho w that the eviden ce on pr e d icta b ility in nom in al bond excess returns holds
for the most recen t historical period.
Inflation- in de x ed bond retu r n predictability could be the result o f eith e r a time-
varying real intere st rate risk premiu m, a time-varying liquidity pre m ium, or a c om-
bination of both–since supply effects do not seem to matter. Break even and nominal
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bond excess retu rn p r e d icta bility could be the res ult of a time-varyin g inflation-risk
premium, but this finding may again p art ly be d ue to tim e -varyin g liquidity. We can
use our estimates of liquid ity effects on inflation-indexed bond p rices and returns to
disen tan gle these effects.
We start by running return predictability regressio ns , similar t o those in Pfluege r
and Viceira (2011), replacing the TIPS yield b y the liquidity-adju sted TIPS yield
(10) and bre akeve n by liquidity-ad ju ste d breakeven (11). Evid en c e of p red ic tab ility
in liquidity-adjusted TIPS excess returns and breakeven returns w ould suggest that a
time-varying real interest rate risk premium and a time-vary ing inflation risk p remium
help explain the estimated predictable va riation in inflation-indexed and nominal
bond excess returns, conditional on our measure o f liquidity.
We also examin e whether there is evidence of a time-varying liquidity risk pre-
mium , by looking at the p red ic tab ility of th e liquidity return . We define the liquidity
return as


+1
= − ( − 1) 
−1+1
+ 

 (12)

We can think of 

+1
as the return on TIP S retu rn du e to time-varying liquid ity.
Our estima tes for the liquidity premium 

are based on the full-period regression
allow ing for a flexib le regression coefficien t on the asset-swa p spread, reported in Table
1, column 4. We also include 

as an additional control in our predictive regressions.
Ta ble 4 shows the estimate s of t h e liquidity-adjusted predictive regressions. Since
we do not adjust the nominal yields for liquid ity, the nominal expectation s hypothes is
regression is omitted from the table. Ov erall, Table 4 provid es support for the hy -
pothesis that real and nominal bond yields re flect time-varying real in t erest rate and
inflation risk premia. Conditional on our estim a tes of liquidity - ad justed yields and
returns, the real yie ld spread positi vely forecasts inflation-indexed bond returns, and
the brea keven inflation spread forecasts break even returns–or the return on nom i-
nal bonds in excess of the return on inflation-indexed bonds. The coefficien t on the
liquidity- ad ju ste d real term spread in the re al bond p red ic tive regression is large an d
significant, and the coefficient on the liquidity-adjusted breakev en inflation spread
is also large and significant when the real term spread is added in as an additional
con trol.
Remarkably, Table 4 sho ws that the liquidity variable does not predict real bond
excess returns or break even excess returns. Hence, it appears that the current level
of the liquidity pre m iu m is not related to fundame ntal cash -flo w risk as r epresent ed
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by the real interest rate r isk premium or the inflation risk prem iu m.
The last column of Table 4 reports a regress ion o f the liqu id ity return 


+1
onto
the liquidity- ad ju sted real term pr emium, the liquidity-a dju st ed breake ve n inflation
spread, and 

. Table 4 shows that the liqu id ity return is p redictable from the
liquidity premium with a large and hig hly significant regression coefficient. Th us this
table suggests the presence of a time-varying and predictable liquidit y premium in
TIPS.
The results shown in Table 4 strongly suggest that the rejection of the real and
nominal expectations hypotheses in Pflueger an d Viceira (2011) is not solely driven by
liquidity fac tors. Instead our resu lts offer support for the hy pothesis of a time-varying
real interest rate risk premium and a tim e-varying inflation risk premium. Table 4 als o
offers support for the hypothesis of the existence of a time-varying liquidit y premium
in TIPS.
4.2 Historical Fitted Risk Pr emia
We next lo ok at the fitted bond risk premia and their components in order to better
understand the economic significance of bond return predictability. Specifically, w e
no w compare the means and variances of predicted excess log returns on real a nd
nominal bonds, and discuss the historical behavior of fitted risk premia and their
components extracted from our return pred ictab ility regressions. Thus ou r risk pr e-
mium calculations are based on log returns with no varia nce adjustmen ts for Jensen’s
inequality.
Table 5 shows the means and standard deviations of risk premia. We obtain the
nominal risk premium, the risk premium on TIPS and the risk premium on breakeven
as in Pflu eger and V iceira (2011). They specify the n ominal risk premium at any point
in time as the expected excess log return on nom inal bonds predicted by the nominal
term spread. They similarly obtain TIPS and breakeven risk p rem ia as fitted values
of expected excess log return regressions. We obtain the inflation risk p re mium ,
the real r ate risk premium and the liquidity prem iu m as the fitted values from our

liquidity- ad ju sted return pr ed ictab ility regressions shown in Table 4. The real rate
risk premium is given b y the expected liquidity-adjusted excess log return on TIPS
fittedincolumn1. Theinflation risk premium is given b y the fitted values for the
expected liquidity -adjusted log return differential between TIPS and nominal bonds
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as reported in column 3. Finally, we obtain ou r liquidity return premiu m as the
expected liquidit y return in colum n 4.
Due to data constraints we w ere not able to compute a liquidity-adjustmen t for
the UK. Howeve r, arguably liquidity-adjustm ent s in the UK bond market are likely to
be less significan t than in th e US bond m arke t. UK inflation-linked bonds have been
issued for a significantly longer period and therefore it appears plaus ib le that initial
learning should affect only a small portion of their time series. Moreove r, neither
UK nominal nor inflation-indexed bonds are likely to enjo y the same extraordinary
liquidity benefits as US nom inal Treasury bonds so arguab ly the liquidity pre mium
between inflation - ind e xe d a nd nominal UK bonds shou ld be less significant .
P anel A in Table 5 sho ws the annualized fitted US risk premia. The average excess
log return is 3.26% per annum (p.a.) for n ominal Treasury bonds and 4.16% p.a. for
TIPS over our sample period. The averag e log return on b reakeven, or the difference
bet ween nominal log excess returns and TIPS log excess ret urn s, is negative at -91
bps p.a. before adju stin g for liquid ity.
The estim ated aver age liquidity r etu rn prem iu m o n TIPS is large at 1.38% p.a
This pre m iu m is the averag e retu rn d u e to liquidity over the period and equ als the
aver age liquid ity prem iu m in yields plus a te rm adj ustin g for the change in liqu id ity
o ver our s am p le period. At the same time our estimates imp ly that a significant frac-
tion of the total bond prem ium is attributable t o the real interest rate risk p rem ium,
which at 2.86% p.a. on a ve r age is large even after adjustin g for liquidity.
Our estimates attribute the negativ e risk premium on breakeven o ver our sample
period to liquidity effec ts in TIPS . Afte r ad ju stin g for liquidity, we obta in an inflation
risk premium of 75 bps p.a., whic h is positive but smaller than the real interest rate
risk premium.

Another way to understand the economic significance of the estimated risk premia
is by calculating their variabilities and comparing them to the variability of re aliz ed
returns. From the second column of P an e l A in Ta ble 5 w e see that the liquidit y
prem iu m is th e most v o latile bond risk p re mium component. Its annu al v olat ility is
3.15%, comp ared to 1.90% for the real rate risk premium and 1.38% for t he inflation
risk p r em ium. The estimated inflation and real rate risk premia explain 3% and 5%
of the sample variab ility of realiz ed nomin al bond returns , respectively. Liquidit y
appears to be an important driv er of time-variation in TIPS returns. It explains 17%
of the variance of realiz ed TIPS return s, while the real rate risk pre mium explains
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