The real bond-nominal bond arbitrage

35 Pages·2012·2.09 MB·English

by  Zorka Simon

The re al bond - nomi na l bond
arbi trage :
E v id e nc e from G7 c ountri e s

Zorka Simon
(ANR: 425293)

Supervised by J. J. A. G. Driessen

October 24, 2012

CentER Graduate School
Tilburg University

Abstract

This thesis shows that the price of a US Treasury bond and its replicating
portfolio consisting of a maturity-matched TIPS issue, inflation swap
contracts and stripped bonds can differ substantially. This gives rise to an
arbitrage opportunity as inflation linkers tend to be undervalued relative to
their nominal counterparts. This violation of the law of one price is not only
persistent and unidirectional, but it also displays significant time series
variation and is correlated with mispricing arising from other such
strategies. However its riskiness depends on other market frictions, such as
asset and market liquidity, funding availability or slow-moving capital in
financial markets. The above analysis is extended to other G7 countries.
Table of Contents
List of Tables 2
List of Figures 2
I. Introduction 3
II. Inflation linked bonds: issuance, profitability and riskiness 6
III. The indexed bond-nominal bond arbitrage 10
IV. What describes the existence and the magnitude of the arbitrage? 13
V. Data 17
VI. Size and drivers of the arbitrage 20
VII. Summary and concluding remarks 25
References 27

List of Tables
1. Table I : Summary Statistics for the TIPS-Treasury Mispricing 30
2. Table II : Summary Statistics for the TIPS-Treasury Mispricing for the
subsample of 2004 -2009 31

List of Figures
1. Figure 1 : Average TIPS-Treasury Mispricing 32
2. Figure 2 : Average TIPS-Treasury Mispricing in basis points 32
3. Figure 3 : Average TIPS-Treasury Mispricing during the financial
crisis of 2007-2009 33
4. Figure 4 : Average TIPS-Treasury Mispricing across different bond
issues 33
5. Figure 5 : Average TIPS-Treasury Mispricing in basis points across
different bond issues 34
6. Figure 6 : Correlation between the level of the mispricing series 34
7. Figure 7 : Correlation between daily changes in the mispricing series
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I. Introduction

Several governments of both developed and developing countries issue
nominal and indexed bonds. Despite both being guaranteed by the
government thus considered riskless, nominal and indexed bonds and their
clientele tend to differ in many aspects. Yet, a considerable stream of the
fixed-income literature focuses mostly on nominal sovereign debt,
predominantly on US Treasury securities.

However, during the past two decades inflation-indexed bonds, that
constitute the safest asset class for long-term investors, started to attract more
attention from both academics and practitioners. The growing demand for
inflation-linkers and the size of their markets require deeper understanding of
the mechanics of how these securities work and how institutional investors or
governments can benefit from buying and holding or issuing them.

Nevertheless, the relative pricing of nominal and real bonds in an
international context is a niche in the literature: existing work exclusively
concentrates on the US bond market (Campbell et al 2009, Fleckenstein et al
2013, and Haubrich et al 2012). This thesis aims to fill this gap by exploring
the aforementioned relationship in other developed economies, particularly
focusing on cross-country dissimilarities. Furthermore, my objective is not
solely to document the existence of the mispricing and its causes, but to
uncover its underlying nature that might carry important policy implications.

The main drivers of the mispricing are supply of bonds, market and asset
liquidity, slow-moving capital and credit risk, thus factors that tend to differ
substantially across countries. Investigating the latter differences helps to
reveal the fundamental characteristics of sovereign debt markets of European
and other G7 countries. Furthermore, understanding what drives the
mispricing across countries, how prices of government debt, thus interest
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rates and inflation expectation are formulated, is crucially important for
institutional investors – especially insurers and pension funds, the reason
being twofold. First, exploring the true real rate of an economy is essential for
risk management: to find the appropriate discount factor to evaluate
liabilities. Second, from a portfolio management perspective, it is necessary to
know what additional risks are introduced into a portfolio and what
corresponding hedges should take place to control for the risk stemming from
the inclusion of indexed bonds. Governments also have comparable interest
to unveil whether the abovementioned relative pricing is a result of a long-
term relationship or it is rather a short-lived phenomenon.

To address these issues, I investigate the following questions: Is there a
systematic mispricing between nominal and real bonds? And if so, can the
latter be exploited by a persistent and profitable arbitrage strategy? Which
market forces drive the arbitrage? Are there cross-county differences in the
relative importance of those factors? If there is such a differential pricing of
government bonds, then why do governments engage in issuing both real
and nominal bonds? Is there a particular catering effect? And lastly, how
large is the error in real rates estimated from nominal and real bonds that
affects insurers’ and pension funds’ asset and liability management?

To reveal the cross-country differences in the relative pricing of
government bonds, I run a two-step analysis. In the first part, I construct
arbitrage strategies based on matching the maturities of nominal bonds to
that of their synthetic counterparts. The synthetic bond is a portfolio of
indexed bonds, inflation swap contracts and stripped bonds that exactly
replicates the cash flows of the nominal bond. The difference between the
prices of the two ‘nominal’ cash flows represents the ILB-nominal bond
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mispricing. In the second part of the analysis1, I explore the drivers of the
cross-country differences in the mispricing by incorporating systemic, market
and funding liquidity as well as country-specific credit risks, joint with
supply and demand factors.

My findings are to a large extent similar to Fleckenstein et al (2013): I find
a persistent and time-varying arbitrage opportunity in the US bond markets.
This main result is summarized in Figure 1 that depicts the evolution of the
average mispricing over the sample period, where the average is taken over
all available TIPS-Treasury bond pairs at a given date. Positive mispricing
implies that the latter relationship is in almost all cases unidirectional:
nominal bonds tend to be overpriced relative to their indexed counterparts.
The size of the mispricing differs across different issues and over time,
potentially reflecting the perceived quality of the corresponding bonds, asset
and market liquidity differentials and/or crisis periods. I also find difference
in the magnitude of the mispricing depending on the remaining maturity of
the corresponding issues. Moreover, Figure 1 reveals that the mispricing
became more severe during the recent financial crisis but started to converge
to its pre-crisis level afterwards. Yet, despite the descriptive nature of my
current analyses, the latter observation points to the liquidity, whereas the
relatively high correlation between the mispricing series is in line with the
slow-moving capital explanations. But providing causal interpretations of the
described phenomena requires further analyses, which is beyond the scope of
this thesis.

The remainder of the thesis is organized as follows. In Section II, I provide
a literature review of indexed bonds, their most notable features and their

1 This thesis is part of a larger project which aims to document and discover the relative
pricing of nominal and indexed bonds in G7 countries. Thus, for the moment I focus on
introducing the mechanics of the arbitrage strategy, documenting the mispricing in the US
bond markets and listing the testable hypotheses concerning the potential drivers of this
relationship.
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pricing relative to nominal bonds. Section III gives a broader view on the aim
of this thesis and describes the arbitrage strategy to be implemented. Section
IV presents the various hypotheses. Section V describes the data, whereas
Section VI is to present the results. Section VII summarizes my findings and
presents concluding remarks.
II. Inflation linked bonds: issuance, profitability and riskiness

The riskless asset for long-term investors is an inflation-indexed consol.
Such a security is available in many countries in the form of long maturity
inflation-indexed bonds, henceforth ILBs. These bonds are safe in the long run
as they have payments that are fixed in real terms: both the par and the
coupons are adjusted to the issuing country’s consumer price index.

Real bonds provide a safe long-term investment vehicle for lifecycle
saving of households and for institutional investors to match their assets and
liabilities on the long run. Nonetheless, the role of indexed bonds in short-
term portfolios is debatable. Hunter and Simon (2005) argue that although
TIPS have high volatility-adjusted returns relative to nominal bonds, in a
static mean-variance setting they do not provide significant diversification
benefits for investors holding already diversified portfolios. This lack of gains
is primarily due to the high correlation between TIPS and their nominal
counterparts. On the other hand, Pflueger and Viceira (2011a) claim that ILBs
can also be in interest of short-term investors, as inflation linkers carry
liquidity, market segmentation, real interest rate and inflation risk premia
that generate high excess returns over nominal bills. Moreover, inflation-
indexed bond returns are negatively correlated to equity returns, which make
indexed bonds safe assets and good hedge against equity risk (Campbell et al.
2009).

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Consequently, many governments2 recognizing the potential advantages
issue inflation-linked securities to prove their inflation-fighting credibility
and cater investors’ demand. Furthermore by issuing securities that are
denominated in real terms, they make a clear distinction between nominal
and real rates of return. The real rate of ILBs also provides a trustable
indicator to policymakers about inflation expectations, based on the
difference between real and nominal yields. Moreover, linking part of the
government’s debt to inflation reduces the temptation of creating inflation to
make debt cheaper by imposing an implicit tax on nominal bonds (Bodie
2009; Fleckenstein et al. 2013).

However, despite the above benefits, Fleckenstein et al. (2013) show that
governments lose a valuable fiscal hedging option by issuing ILBs3. This is
because by issuing indexed debt, the Treasury no longer has the option to
benefit from increasing inflation to make its nominal debt worth less. They
also claim that in the US, Treasury Inflation Protected Securities, henceforth
TIPS are systematically underpriced4 relative to nominal Treasury bonds. The
relative mispricing of TIPS and US Treasury bonds gives rise to a persistent
and time-varying arbitrage strategy that consists of creating a replicating
portfolio that exactly matches the cash flows of a nominal bond by taking
positions in TIPS, inflation swap contracts and stripped bonds. They also
investigate the potential causes of the arbitrage and conclude that the
mispricing and changes in its size are driven by the difference in investors’
perception of the quality of the two debt securities, slow-moving capital, as
well as other liquidity factors, such as issuance of new bonds or liquidity
breakdowns in financial markets. They discover that this arbitrage is
correlated with other fixed-income arbitrages based on Duffie (2010),

2 For specific features of inflation-linked bonds and their markets in both developed and
developing countries see Figure 181-182 in Bodie (2009).
3 See also Christensen et al (2011) on whether the Treasury benefited from issuing TIPS.
4 The underpricing is more severe during flight to quality and flight to liquidity episodes and
can cause large welfare losses for taxpayers.
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Krishnamurthy (2002) and Longstaff (2004). They also show that the TIPS-
Treasury mispricing is predictable from past mispricing and equity returns;
and is not stemming from mispricing in the inflation swap markets.

Other studies examining relative prices and liquidity differentials of
nominal and real bonds primarily focus on financial crises. Hunter and Simon
(2005) analyze flight to quality and liquidity episodes due to the Asian crisis
and the Russian government default in 1998. In addition, Campbell et al.
(2009) focus on the role of the Lehman bankruptcy in the 2008 crisis. They
claim that due to the market turmoil TIPS yields became highly volatile and
disconnected from nominal yields. These extraordinary events often result in
major portfolio reallocations, which suppress inflation-linked bond prices and
amplify the effects of market and liquidity shocks. By examining on and off-
the-run Treasury bonds, Longstaff (2004) shows that bond prices also contain
flight to liquidity premium. Moreover Krishnamurthy and Vissing-Jorgensen
(2010) identify a convenience yield between Treasury bonds and similar non-
Treasury securities.

To understand the basic characteristics of ILB returns, Campbell et al.
(2009) distinguish three major factors that determine real bond yields: current
and expected future short-term real interest rates, differences between
expected returns on short and long-term real bonds caused by risk and
liquidity premiums, and lastly premia due to market segmentation of the
bond markets. According to the expectations hypothesis, the latter two factors
should be constant, whereas only the first component could be time-varying.
Pflueger and Viceira (2011b) provide empirical evidence that the expectations
hypothesis does not hold for either real or nominal bonds in the UK and in
the US. In another paper (Pflueger and Viceira 2011a), they find time-varying
and predictable risk premia in both real and nominal bonds - they decompose
excess return predictability into liquidity, real interest rate and inflation risks.
Using transaction volume of TIPS, financing cost for buying TIPS, 10 year
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nominal off-the-run spread and Ginnie Mae (GNMA) spreads, as proxies for
asset and market liquidity, facilitates disentangling liquidity differentials and
real cash flow risk.

On the other hand, Campbell et al. (2009) deepen the risk-based
explanation of the risk premia in real bonds based on asset pricing models of
risk and return. In a consumption-based framework with Epstein-Zin
preferences, they conclude that TIPS are risky if real interest rate covaries
positively with expected consumption growth. The model also suggests that
ILBs should have a constant and low or even negative risk premium, which
makes them safe assets. Their second, more reduced-form approach is based
on a stochastic discount factor model that allows for relating the risk premia
of ILBs to the covariance of these bonds with equity returns. The main
advantage of this paradigm is that it generates time-varying bond risk
premia. However, the risk-based explanation has the drawback that the
implied correlation between ILB and stock returns is rather small and moves
in a transitory fashion. Hence, it should not have a large effect on TIPS yields
unless investors were expecting more persistent variation and were surprised
by temporary changes in risk.

Nevertheless, discovering the real bond-nominal bond arbitrage is not
solely related to the expanding strand of the literature on ILBs. Pricing
inflation linkers is in line with the vast fixed-income literature, containing
yield curve and inflation5 related papers among many others. Likewise, a
number of recent studies focus on potential explanations for the existence of
persistent mispricing in financial markets. Among the competing theories,
one can find slow-moving capital (Mitchell et al. 2007 and Duffie 2010),
liquidity effects related to funding availability (Brunnermeier and Pedersen
2009), limits of arbitrage (Schleifer and Vishny 1997) or margin and other

5 From Duffie and Kan (1996) to Gürkaynak et al. (2010) and many others.
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collateral-related market frictions that might permit deviations from the law
of one price (Liu and Longstaff 2004 or Gârleanu and Pedersen 2011).
Additionally, Duarte et al. (2006) describe the most common fixed-income
arbitrage strategies such as the swap spread, yield curve or the capital
structure arbitrages.

Besides contributing to the growing literature of ILB pricing and arbitrage
returns, this study also discloses the effects of liquidity risk on asset prices
similarly to those that have shown how asset prices are influenced by market
liquidity (Amihud and Mendelson 1986, Longstaff 2004 and Amihud et al.
2006), or market liquidity risk (Acharya and Pedersen, 2005). Lastly,
exploring the forces that drive bond prices contributes to the emerging
literature on government finance, provide important policy implications and
facilitate the investors’ understanding of the sovereign bond market
dynamics.
III. The indexed bond-nominal bond arbitrage

This master thesis is a part of a larger project that aims to extend the
analysis of Fleckenstein et al. (2013) to an international setting by looking at
the relative pricing of indexed and nominal sovereign debt in other
developed economies; namely in the G7 countries6. All the steps, which
follow, are going to be executed for each country in my sample. Doing so will
enable me to uncover and understand the mechanics of different sovereign
bond markets as well as to shed light to their commonalities and fundamental
dissimilarities. Though, for the moment I direct my attention to the US
Treasury bond and Treasury Inflation Protected Securities markets, and to the
relative pricing of the latter government obligations, particularly focusing on
the period between July 21, 2004 and Dec 31, 2011.

6 G7 or G-7 is an international finance group formed by the finance ministers of Canada, the
United States, Japan, Germany, France, Italy and the United Kingdom.
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