An Empirical Decomposition of Risk and 

Liquidity in Nominal and Inf‡lationIndexed Government Bonds

Carolin Pflueger, Harvard Business School

Luis Viceira, Harvard Business School

November 8, 2011
Bond Risk

• Unlike single stocks, government bonds are exposed to 

multiple sources of systematic risk.

• Government bonds (Treasury Bonds in the U.S.) of stable 

large economies are not subject to credit risk (at least not 

until recently).

• But nominal bonds are subject to real interest risk (or 

reinvestment risk) and inflation risk.

• Inflation-indexed bonds (TIPS in the US) are subject to real 

interest rate risk
Nominal Bond Pricing

• Evidence that U.S. nominal bond excess returns are predictable 

(Campbell and Shiller 1991, Fama and Bliss 1987, Cochrane and 

Piazzesi 2005).

– Strong rejection of the expectations hypothesis in nominal interest 

rates.

• Hypotheses:

– Time-varying risk premium resulting from a time-varying aggregate 

market price of risk, a time-varying quantity of bond risk or a combo 

(Campbell, Sunderam, and Viceira, 2011).

– Supply/market segmentation effects resulting from habitat 

preferences and limits to arbitrage (Modigliani and Sutch 1966, 

Vayanos and Vila 2009, Greenwood and Vayanos 2008, Hamilton 

and Wu 2010)
Real Bond Risk Premium

• Time-varying risk premium: Which one? Inflation risk? Real 

interest rate risk?

• Recent evidence that U.S. and UK inflation-indexed bonds 

are also predictable (Pflueger and Viceira 2011).

– It suggests a time-varying real interest risk premium.

• But how about inflation risk?

• And liquidity?

– Liquidity differential between inflation-indexed and nominal 

bond markets.
Breakeven Inflation

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n t n t n t , , ,

b y y  
Breakeven Inflation

• Breakeven in‡flation re‡flects expected in‡flation, in‡flation risk 

premium and a liquidity premium:

• We can’t tell what drives time variation in breakeven 

inflation and the return differential between TIPS and 

Treasuries without an identification strategy. TIPS

n t n t

TIPS

yn,t y , L

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n t n t n t n t n t n t b y y L       
This Paper

• Can liquidity explain differences in yields and returns?

– D’’Amico, Kim, and Wei (2009), Campbell, Shiller, and Viceira 

(2009), Gurkaynak, Sack, and Wright (2010),

• Empirical examination of the liquidity differential between the 

Treasury and TIPS markets.

– Use empirical proxies to identify the liquidity discount in TIPS 

relative to Treasuries, and its variation over time.

– Show that it has a TIPS market-specific component, and an 

aggregate component.

– Evidence of existence of a systematic liquidity risk premium

• This paper is about liquidity in the TIPS market, not about 

liquidity and mispricing in the inflation swap market 

– Fleckenstein, Longstaff and Lustig (2010)
This Paper

• Time-varying real interest rate risk premia and/or time-varying 

in‡flation risk premia?

– Christensen, Lopez, and Rudebusch (2010), Campbell, Sunderam, 

and Viceira (2011), D’’Amico, Kim, and Wei (2009), Haubrich, 

Pennachi and Ritchken (2010), Piazzesi and Schneider (2006)

• Use liquidity-adjusted yields and returns on TIPS to disentangle 

inflation and real interest rate risk premia in inflation-indexed 

bonds and nominal bonds. 

– Interpret return predictability of inflation-indexed bonds as resulting 

from time-varying real interest rate risk and liquidity risk premia.

– Interpret return predictability of nominal bonds as resulting from 

time-varying real interest rate risk and inflation risk premia.
This Paper

• Can investors’ habitat preferences explain differences in yields 

and returns?

– Greenwood and Vayanos (2008), Hamilton and Wu (2010)

• Examine evidence of habitat preference driven predictability in 

inflation indexed bond market.

– No evidence of supply/segmentation effects in the TIPS market or 

the UK ILB market.
Data

• Zero-coupon US yields from Gurkaynak, Sack, and Wright 

(2007) and Gurkaynak, Sack, and Wright (2010).

– Focus on 10-year maturity

– 1999-2010

• Zero-coupon UK yields from the Bank of England 

(Anderson and Sleath 2001)

– Focus on 20-year maturity

– 1985-2009

• Empirical proxies for market-specific and market-wide 

liquidity in US market
Data

• Empirically proxy for short-term real interest rate as in 

Pflueger and Viceira (2011):

– US: Fama-Bliss 3 month riskfree rate from Center for Research in 

Security Prices.

– UK: 3-month short rate from Datastream

– US inflation measured by all-urban seasonally adjusted consumer 

price index.

– UK inflation measured by Retail Price Index (RPI).
Fitted US Short-Term Real Rate 
Table I

Summary Statistics

US data is monthly 1999.7-2010.12 and UK data is monthly 1985.4-2009.12.
Estimating the Liquidity Component

• Regress breakeven onto liquidity proxies Xt:

• Estimate liquidity premium as fitted values:

– Liquidity variables are normalized to equal zero when liquidity is 

perfect.

• Adjust yields and breakeven for liquidity:

– Breakeven should be lower when TIPS are less liquid

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TIPS adj TIPS

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Estimating the Liquidity Component

• Need to distinguish between

– Liquidity discount/premium

– Liquidity risk premium
Liquidity Proxies

• Market-wide desire to hold only most liquid Treasuries:

– Off-the-run spread (Krishnamurthy 2002)

– Based on same off-the-run issue as GSW

– [GNMA spread (Longstaff 2004)]

– Source: Bloomberg, Federal Reserve

• Learning and search costs in the TIPS market:

– Transaction volume of TIPS relative to nominal Treasuries 

(Gurkaynak, Sack and Wright 2010, Fleming and Krishnan 2009, 

Duffie, Garleanu and Pedersen 2005, 2007, Weill 2007)

– Source: Primary Dealers’ transaction volumes from Federal 

Reserve.
Liquidity Proxies

• Transaction costs

– Bid-ask spread for the 10-year TIPS market (scaled by 10).

– Source: Bloomberg (via George Pennachi).

• Cost to levered investors of holding TIPS.

– Asset-Swap-Spread (ASW), 10 year maturity.

– If ASW investor is marginal the slope of breakeven onto the ASW 

should equal -1 (Campbell, Shiller, and Viceira 2009)

– Spread between synthetic (or inflation swap) breakeven and cash 

breakeven, 10 year maturity (Viceira 2011).

– Source: Barclays Live, and Bloomberg
ASW market and IS market

• The inflation swap market and the ASW market are 

flipsides of the same coin:

– Jeremie Banet (BNP Paribas): “It is key that the inflation 

derivatives market has actually two completely different 

complements: one, which is the inflation swap; and the flipside, 

which is the asset swaps.” (Risk Magazine, November 2009)
TBond-TIPS-Inflation Swap Arbitrage

• Empirically, lS bei > cash bei consistently.

• If lS bei > cash bei:

– Short T-Bond, long TIPS, enter IS receiving IS bei (and paying 

inflation)

Payoff Payoff

Zero investment T-Bond –

TIPS portfolio

yt – st – πt→T cash bei – πt→T

Short IS f – πt→T IS bei – πt→T

Note: bei = breakeven inflation
ASW market and IS market

• If you are a levered investor (bank, hedge fund), taking advantage of 

the arbitrage implies:

– Entering a long TIPS position through an asset swap, paying LIBOR + 

TIPS ASW spread, and receiving TIPS payoffs.

– Entering a short T-Bond position through an asset swap, paying T-Bond 

payoffs and receiving LIBOR + TB ASW spread.

• Cost = TIPS ASW spread - TB ASW spread 

– Normally, both spreads are negative

– And | TIPS ASW spread | < | TB ASW spread |

– Arbitrage is costly

• Abnormal times (Fall 2008 and Winter 2009): TIPS ASW spread >> 0.
Implementation

• In practice, (IS bei – cash bei) appears to have moved in sync with 

asset swap spread differential:

IS bei – cash bei (July 2017 bond pair)

TIPS ASW spread

Source: Campbell, J.Y., Robert J. Shiller, and L.M. Viceira, "Understanding Inflation-Indexed Bond Markets," with, Brookings Papers on Economic Activity 79-120, Spring 2009. 

Correlation = 97.3%
Table I

Summary Statistics

US data is monthly 1999.7-2010.12 and UK data is monthly 1985.4-2009.12.

x 10
Figure 1. US Liquidity Proxies
Table II

Breakeven onto Liquidity Proxies US

Estimating the Liquidity Premium

n t t t , 1 2 b a a X   




Table II

Breakeven onto Liquidity Proxies US

Estimating the Liquidity Premium
Figure 2. TIPS Liquidity Premium

Learning

Normal

Crisis

Normal
Figure 3. Liquidity-Adjusted Breakeven Inflation
Figure 4. Liquidity-Adjusted TIPS
Time-Varying Risk Premia

• Nominal bond excess returns are predictable from nominal term 

spreads (Campbell and Shiller 1991):

– time-varying inflation risk premia or

– time-varying real rate risk premia

• Return-predictability of liquidity-adjusted TIPS returns would indicate a 

time-varying real interest rate risk premium.

• Liquidity-Adjusted Breakeven Returns = Nominal excess returns -

Liquidity-adjusted TIPS excess returns.

– Breakeven return predictability would indicate a time-varying 

inflation risk premium.

• Liquidity returns = component of TIPS returns due to changes in 

liquidity.
Table V

Liquidity-Adjusted Return Predictability US
Table VI

Moments of Realized and Fitted Bond Returns
Table A.IX

Sub-Period Betas
Table A.XI

Four Factor Regressions
Economic Significance of Liquidity Returns

• Estimated average liquidity return 1.36% p.a. (average 

TIPS excess returns 4.16% p.a)

• Liquidity returns highly systematic (Beta=0.53).

• Liquidity risk explains most of the systematic exposure of 

breakeven inflation.
Figure 6A. Estimated US Bond Risk Premia
Figure 6B. Estimated UK Bond Risk Premia
The Market Segmentation Hypothesis

• Preferred-Habitat hypothesis argues that the preference of 

certain types of investors for specific bond-maturities can 

result in price pressure (Modigliani and Sutch, 1966, 

Vayanos and Vila, 2009, Greenwood and Vayanos, 2008, 

Hamilton and Wu 2010)

• Just as investors differ in preferences for different 

maturities they might differ between inflation-indexed and 

nominal bonds. 

• Market segmentation between nominal and real bond 

markets could be a source of return predictability. 
The Market Segmentation Hypothesis

• Following Greenwood and Vayanos (2008) use the outstanding supply 

of real bonds relative to total government debt in the US and in the UK 

to proxy for supply shocks.

• If supply experiences exogenous shocks and demand is stable, shocks 

to the relative supply of inflation-indexed bonds should move

– negatively with breakeven inflation

– negatively with future breakeven returns

• In a different scenario the government could accommodate changes in 

demand. In that case expect no relationship of returns with quantities. 
Figure 5A. US Relative Supply and 10 Year Breakeven In‡flation
Figure 5A. UK Relative Supply and 20 Year Breakeven
Table III

Breakeven Inflation onto Relative Supply
Table IV

Excess Bond Returns onto Relative Supply of Inflation-Indexed Bonds
Table IV

Excess Bond Returns onto Relative Supply of Inflation-Indexed Bonds
Interpretation of Supply Regressions

• EH results are robust to controlling for bond supply 

variables.

• Bond return predictability does not appear to be driven by 

temporary price pressures.

• No relationship between relative supply and breakeven or 

returns in the US. 

• Some evidence of bond supply effects in UK.
Conclusions

• Large and time-varying liquidity premium in TIPS between 

50 bps and 200 bps.

• Liquidity-adjusted breakeven in‡flation has been stable over 

time.

• Is the liquidity premium a discount on TIPS or a 

convenience yield on nominal Treasuries?

– Very different implications for Treasury issuance policy in 

light of benefits of TIPS to long-term savers.
Conclusions

• Empirical evidence for three sources of excess return 

predictability:

– Real interest rate risk in inflation-indexed bonds and nominal 

bonds

– Liquidity risk in inflation-indexed bonds

– Inflation-risk in nominal bonds

• No evidence for market segmentation as a source of return 

predictability in inflation-indexed bonds.
Further Research

• Important to understand macroeconomic foundations of 

changing nominal-real covariance. 

– We are exploring new Keynesian macroeconomic models with 

changing volatilities of shocks to productivity, aggregate demand, 

and monetary policy.

• Adjust breakeven for liquidity and inflation risk risk premia

to obtain a predictor of expected inflation. 

• Implications of liquidity, real interest rate risk and inflation 

risk for portfolio management and pension-investing.