Copyright © 2011 by Carolin E. Pflueger and Luis M. Viceira Working papers are in draft form. This working paper is distributed for purposes of comment and discussion only. It may not be reproduced without permission of the copyright holder. Copies of working papers are available from the author. 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 cpflueger@hbs.edu. Viceira: Harvard Business School, Boston MA 0216 3 and NBER. Email lviceira@hbs.edu. 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 [...]... returns, and possibly to be even positively correlated with contemporaneous breakeven in ation We measure the relative supply of in ation -indexed bonds in the US as the nominal amount of TIPS outstanding relative to US government TIPS, notes and bonds outstanding.9 The face value of TIPS outstanding available in the data is the original face value at issuance times the in ation incurred since then and therefore... predictor of future in ation and other macroeconomic variables Third, different classes of investors have different degrees of exposure to time-varying liquidity, real interest rate risk and in ation risk It would be interesting to understand the implications for portfolio management and pension investing and how these implications vary by investment horizon and the investor’s share of real and nominal liabilities... pricing of these bonds More details on TIPS can be found in Viceira (2001), Roll (2004) and Gurkaynak, Sack, and Wright (2010) Campbell and Shiller (1996) offer a discussion of the taxation of in ation -indexed bonds Campbell, Shiller, and Viceira (2009) provide an overview of the history of in ation -indexed bonds in the US and the UK 8 For the US we use an expanded version of the Gurkaynak, Sack, and Wright... our analysis of supply effects in the in ationindexed market suggests to further explore strategic behavior by the government in accommodating shifts in the demand for nominal and real bonds 25 6 References Acharya, Viral V., and Lasse Heje Pedersen, 2005, "Asset Pricing with Liquidity Risk" , Journal of Finance, 77:375—410 Anderson, Nicola and John Sleath, 2001, "New estimates of the UK real and nominal. .. relative supply of in ationindexed debt The relative supply of indexed debt does not enter significantly into predictive regressions of nominal and in ation -indexed bond returns, again offering no support for a market-segmentation hypothesis If anything, our results are consistent with the government trying to accommodate shifts in the demand for nominal bonds, relative to in ation -indexed bonds We find... liquidity- adjusted breakeven in ation For simplicity we assume that the liquidity premium on one-quarter real bonds is constant 2.3 2.3.1 Data Yield Data We use data on constant-maturity in ation -indexed and nominal yields both in the US and in the UK In ation -indexed bonds have been available in the UK since 1983 and in the US since 1997 In ation -indexed bonds are bonds whose principal adjusts automatically... amount of conventional gilts outstanding Conventional gilts exclude floating-rate and double-dated gilts but include undated gilts The face value of index-linked gilts does not include in ation-uplift and is reported as the original nominal issuance value.10 Our results are not sensitive to including or excluding the in ation uplift  Let    denote the face value of in ation -indexed bonds outstanding... in ationlinked government bonds and subsequently led the government to increase issuance of long-maturity and in ation-linked bonds Table 2 shows regressions of breakeven in ation onto the relative supply and the change in supply of in ation -indexed bonds Panel A shows results for US bonds Neither the relative supply nor ∆ appear to be related to breakeven in ation Column 4 in the panel shows... real interest rate risk premium in US bonds, and a smaller in ation risk premium over this period Our estimates for UK bonds suggest a much larger in ation risk premium for UK bonds for the period 1985-2009, and in particular during the financial crisis of 2008 and 2009 We estimate the liquidity premium on TIPS yields relative to nominal Treasury bond yields using a variety of indicators of liquidity in. .. rate risk premium and the risk premium on breakeven in ation reflects the in ation risk premium, our estimates imply that an average real rate risk premium of 1.66% p.a., and an average in ation risk premium of 1.81% per annum in UK bonds Both components of bond risk premia are highly economically significant In particular, we estimate a much larger in ation risk premium for UK bonds than for US bonds In . constant-maturity in ation -indexed and nominal yields both in the US and in the UK. In ation -indexed bonds hav e been available in the UK since 1983 and in. excess return on in ation -indexed bonds and of the expected return differential between in at ion- indexed and nominal bonds can be explained by liquidity premia,