T h e r e a l b o n d - n o m i n a l b o n d a r b i t r a g e : E v i d e n c e f r o m G 7 c o u n t r i e s

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1 T h e r e a l b o n d - n o m i n a l b o n d a r b i t r a g e : E v i d e n c e f r o m G 7 c o u n t r i e s Zorka Simon (ANR: ) 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.

2 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 Table II : Summary Statistics for the TIPS-Treasury Mispricing for the subsample of List of Figures 1. Figure 1 : Average TIPS-Treasury Mispricing Figure 2 : Average TIPS-Treasury Mispricing in basis points Figure 3 : Average TIPS-Treasury Mispricing during the financial crisis of Figure 4 : Average TIPS-Treasury Mispricing across different bond issues Figure 5 : Average TIPS-Treasury Mispricing in basis points across different bond issues Figure 6 : Correlation between the level of the mispricing series Figure 7 : Correlation between daily changes in the mispricing series 35 2

3 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 3

4 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 longterm 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 4

5 mispricing. In the second part of the analysis 1, 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. 5

6 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 shortterm 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, inflationindexed bond returns are negatively correlated to equity returns, which make indexed bonds safe assets and good hedge against equity risk (Campbell et al. 2009). 6

7 Consequently, many governments 2 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 ILBs 3. 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 underpriced 4 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 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. 7

8 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 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 offthe-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 8

9 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 inflation 5 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 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. 9

10 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 countries 6. 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, 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. 10

11 Treasury Inflation Protected Securities have first been issued by the U.S. Treasury in Similarly to nominal Treasury bonds to which they resemble in most respects, they are direct obligations of the Treasury. Though, the key difference between the two securities is that for indexed bonds the principal amount is adjusted on a daily basis to reflect the changes in the Consumer Price Index for All Urban Consumers, also known as CPI-U 7. Since the fixed coupon rate is applied to the variable principal of the bond, the resulting coupon payment also changes over time with a factor that depends on the corresponding period s reference CPI-U. Analogously, the final principal amount that is paid to the bondholder equals the maximum of the original principal amount or its inflation-adjusted counterpart making the investor protected against deflation. The US Treasury bond and TIPS markets are two of the largest and most liquid fixed-income markets in world, yet Fleckenstein, Lustig and Longstaff (2013) find a persistent and time-varying mispricing between the two bonds. Furthermore, this relationship seems to be unidirectional: nominal debt appears to be consistently overpriced relative to TIPS between 2004 and They show that even though this difference in prices gives rise to a text-book arbitrage that is not driven by a similar mispricing in the inflation swap markets, its execution might be risky for investors with funding constraints. They claim that the presence of mispricing is due to investors perceiving the safety or quality of the two securities differently, whereas its persistence is due to slow-moving capital. The latter finding implies that if the arbitrage opportunity arises due to slow-moving capital, it will be correlated with other such opportunities across different markets and predictable from changes in funding liquidity of market participants. 7 Details on how TIPS are adjusted for inflation are described on the U.S. Treasury s website. 11

12 The idea behind the TIPS-Treasury arbitrage is simple: an investor matches the maturities of a nominal bond issue and its synthetic counterpart. The latter is essentially an inflation swapped-indexed bond, whose cash flows are converted to fix payments exactly matching that of the corresponding nominal bond. For the analysis, to create the above-mentioned arbitrage strategy for all bonds in the sample 8, an investor should take the following asset positions. First, he needs to go long in a TIPS issue and short a nominal bond at the same time. Next, the investor executes a zero-coupon inflation swap with the same maturity and notional amount as the coupon payment of the TIPS issue and does so for each coupon payment as well as for the principal amount, that results in the execution of an entire swap portfolio. The rationale for swapping the bond is that the sum of the two cash flows, the variable coupon payment from the bond and the payoffs depending on the reference CPI-U rate of the inflation swap contracts, is a constant. The investor also needs to take a small long or short position in Treasury STRIPS due to the disparity in the nominal and TIPS coupon payments. The latter amount equals the difference of the swapped ILB cash flow, namely the payoff from the inflation swap contract applied to the maturity and notional of the TIPS coupon, and the Treasury bond coupon. Based on this logic the investor applies these steps to all coupon payments, which results in the successful conversion of the TIPS variable cash flow stream to the fixed one of the corresponding nominal bond. In the end, the investor ends up shorting the nominal bond, buying the TIPS issue and holding portfolios of zero-coupon inflation swap contracts and Treasury principal STRIPS. The latter three components exactly replicate the fixed periodic coupons and the principal of the nominal bond. Finally, to 8 For a visual demonstration of the arbitrage strategy, I refer to Table 1 in Fleckenstein et al (2013) that shows the various components and the corresponding cash flows of the strategy described below. Table 2 provides a specific example applied for a bond pair as executed on December 30,

13 determine the mispricing, I first price the synthetic bond by calculating the yield to maturity of the replicating portfolio, then I also adjust the price of the nominal bond for the potential maturity mismatch between the two securities. Thus, if the resulting prices of the nominal bond and the replicating portfolio differ, an arbitrage opportunity arises. I will refer to this difference as the TIPS-Treasury mispricing. To evaluate the profitability of the arbitrage, transaction costs should also be taken into account. I apply a conservative cost estimate calculated 9 by Fleckenstein et al (2013) that is 69.1 cents per $100 notional. I will show that this transaction cost is orders of magnitude smaller than the profit achievable from the arbitrage, thus this market friction cannot solely account for the magnitude of the mispricing. The next section aims to unveil factors that are most likely to cause this violation of the law of one price. IV. What describes the existence and the magnitude of the arbitrage? Uncovering the existence of a persistent mispricing in such a highly developed market as the US is already intriguing, though it would be interesting to know whether the ILB-nominal bond arbitrage is exclusive to that market. I expect that this trading strategy would result in similar arbitrage opportunities in other G7 bond markets, where the perception and demand of ILBs might be determined in fundamentally different ways potentially due to institutional or other country-specific factors. Thereupon the first testable hypothesis is the following: H1: There are deviations from the law of one price between nominal bonds and their replicating portfolios in other G7 countries. This results in 9 Based on Fleming (2003), Fleming and Krishnan (2009), Daves and Ehrhardt (1993), Grinblatt and Longstaff (2000) and Jordan, Jorgensen and Kuipers (2000). 13

14 a potentially persistent mispricing and yield difference between nominal and indexed bonds. Fleckenstein et al (2013) investigate whether the TIPS-Treasury mispricing might be due to mispricing in the inflation swap market. To test this conjecture they apply a similar trading strategy to nominal and indexed corporate bonds. Although the same inflation swap prices are used, they find that the corporate mispricing values never exceed the magnitude that could be explained by liquidity or credit risks, or other frictions in the market. If inflation swap contracts are correctly priced in the US market, they are likely to be so in Continental European and in the UK markets, as they are likewise active as their US counterpart (Kerkhof 2005) 10. Other potential drivers of the mispricing are most likely supply of bonds, market and asset liquidity, slow-moving capital and lastly credit risk. Financial globalization and the fact that G7 countries have the biggest and the most developed financial markets in the world imply that the latter factors will carry equal importance in all markets. Hence it may be easier to execute the described arbitrage strategy if there is an increased supply of bonds. 11 An alternate conjecture is that the aforesaid markets have parallel or interlinked market frictions, such as transaction costs, market liquidity and slow-moving capital. Such commonalities suggest, that the mispricing could be driven by comparable forces, thus the arbitrages are likely to be correlated - potentially exhibiting variation over time. I also expect countries, which are economically closely interlinked 12, to cluster and demonstrate correlative patterns that are distinctive from others. 10 Thus the same hypothesis might be tested in Canada and Japan if corresponding data is available. 11 Based on Amihud and Mendelson (1991), Krishnamurthy (2002), Han et al (2007) and previous work on on-the-run or recently auctioned bonds. 12 A straightforward measure of economic interlinkedness is membership of an economic union, such as the EU or the North American Union, or alternatively monetary union and/or similar levels of inflation rate. 14

15 H2a: There is a significant, time-varying correlation between ILB-nominal bond arbitrages both within and across different markets. H2b: The correlation is stronger between countries, which are economically highly interrelated (e.g.: European countries or between Canada and the US). The next step is to scrutinize how the magnitude and the persistence of the mispricing are related to the above factors. The supply of the bonds is determined by both monetary policy and/or catering motives of governments that is likely to vary amongst countries. Analogously to supply, I expect investor demand and perception to differ across markets. If so, I would pay special attention to institutional investors who might play an important role in determining bond demand. In such economies the demand for inflationlinkers will drive asset prices closer to their fundamental values. I expect the latter effect to be stronger in countries where the pension and insurance industries are significant in size and/or hedge fund activity is high. Thus, I anticipate that due to demand pressure, the mispricing between nominal and real bonds and liquidity premia to be considerably lower than their US counterparts. H3a: The relative importance of factors that explain the size of the arbitrage differs across G7 countries. In countries where the demand for inflation linkers is higher, the mispricing will be smaller in magnitude. H3b: In countries, where institutional investors actively participate in the ILB market, the mispricing is less severe. Yet in an international comparison the dissimilarities between countries captured by factors, such as systemic risk, country credit risk or asset and market liquidity, are equally important. Market wide liquidity both relies upon the size and the relative development of a market segment. Also, asset 15

16 liquidity is determined by its demand: how investors perceive the safety or value the inflation protection offered by ILBs. On the other hand, systemic or country credit risks 13 induce risk premia that are incorporated in prices, moreover they might affect the two government bonds differently. Fleckenstein et al (2013) compare nominal and indexed debt to foreigncurrency-denominated and local-currency-denominated debt from a credit risk perspective. They claim that Euro-denominated CDS prices reflect that investors attach a positive probability to the U.S. Treasury defaulting on its debt. Therefore one can imagine such scenarios when the Treasury can pay back its nominal debt by increasing inflation, while it cannot honor its inflation-indexed debt. In sum, the relative pricing of the two debt securities might reflect this difference in sovereign risk premium incorporated in bond prices. H3c: In countries where the sovereign risk premium is greater, I also expect the mispricing to be more severe especially during the recent economic and euro crises. Moreover, this implied risk premium varies across countries, but also over time. Another interesting aspect of asset demand is that in Europe, where only few countries issue ILBs, other countries institutional investors might induce sizeable excess-demand pressure on an issuing country s government. H4: In Europe, the mispricing narrows due to demand of institutional investors from non-issuing countries, e.g.: euro denominated ILBs, especially where inflation is more correlated among the respective countries. Having both time series and panel dimensions in my data allows me to inspect the cross-sectional and time series changes of the bond market 13 See Ang and Longstaff (2011) on systemic sovereign risk in the US and Europe. 16

17 dynamics. I anticipate that the relative importance of the factors explaining the mispricing do change over time, depending on the economic conditions and on the business cycle. Moreover, the magnitude of the latter effects can also vary across countries. Finally, my aim is not just to document the existence of the mispricing and its drivers in the G7 countries, but to uncover its underlying nature that might carry important policy implications. The presence of such a mispricing suggests that either the bond or the inflation swaps markets are distorted to some extent consequently they might imply different real or breakeven inflation rates. The latter rates are the most important inputs for the risk management of institutional investors, thus their knowledge is crucial for prudential compliance and appropriate portfolio management. And lastly, I would like to shed light to whether the mispricing is a short-term, or more likely a long-lived phenomenon in developed financial markets. The latter finding conveys relevant information for government agencies and treasuries issuing both indexed and nominal debt securities, as well as to market participants who want to engage the aforementioned arbitrage strategy. H5: What is the real real interest rate? Which market appears to be more distorted in an international context: indexed bond or inflation swap markets? H6: Are prices of the nominal bond and its replicating portfolio cointegrated? Is the nature of the mispricing is essentially short or long term? V. Data The data consist of daily closing prices for US Treasury bonds and TIPS issues; STRIPS and zero-coupon inflation swap contracts for the period between July 21, 2004 and December 31, All data are obtained from Bloomberg and crosschecked with DataStream. TIPS and Treasury bonds 17

18 have maturities ranging from 2007 to The daily closing prices of both nominal and indexed bonds are adjusted for accrued interest based on standard market conventions. Implementing the arbitrage strategy requires the construction of inflation swap rate curves for each day in the sample. The inflation swap curves are based on available swap contracts, which are quoted in terms of constant rates on the contracts fixed leg. The traded maturities span 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 20, 25 and 30 years. To obtain swap rates for the intermediate maturities, e.g. for 16.5 years, I use simple linear interpolation. In later stages of the analysis cubic spline interpolation, liquidity correction of lessfrequently traded maturities or correction for inflation seasonality can also be incorporated into my approach. To construct the aforementioned arbitrage strategy, I first create maturitymatched nominal and indexed bond pairs. I define maturity mismatch as the difference in days between the maturity of a TIPS issue and that of the closest possibly maturing Treasury bond. For instance, to match the 10-year TIPS issue maturing at January 15, 2007, I select a 10-year nominal bond with the maturity of February 15, 2007 and the resulting mismatch is 31 days. In the sample I only include pairs of TIPS and Treasury bonds if the maturity mismatch is less than 61 days for maturities before 2025, and allow for larger mismatches afterwards. This leads to 38 indexed bond-nominal bond pairs, as can be seen in the left columns of Table I: there is one pair with an exact match, six mismatches of 15 days; 27 instances there is a mismatch of 31days, two mismatches of 61 days and two pairs with very long maturities, whose mismatches exceed 61 days. Thereupon the mismatches constitute only a small fraction of the bonds maturities. Also, as mentioned before, the mismatch is corrected in the price of nominal bond such that it has the exact 18

19 same maturity date as the replicating portfolio. This is done before the TIPS- Treasury mispricing is calculated. During the matching procedure, I aim to choose the bond pairs with the longest commonly available price history. Having long enough series of the mispricing allows me to identify trends and changes in its nature. However, I also expect bonds with different remaining maturities to exhibit diverse magnitudes and ranges of mispricing. Therefore I split the bonds in my sample into three groups: bonds maturing before 2015 constitute short-term investment strategies, whereas bonds with maturities after 2020 are long-term strategies. The rest of the bonds with maturities between 2015 and 2019 are called middle-term strategies. As a result, I have three balanced groups of bonds, with 10 short-term, 10 middle-term and 11 long-term trading strategies. It is also worth noting, that for 30 out of the 38 matches, the coupon payments of the nominal bonds coincide: they appear on February 15 and August 15. To filter out the pattern arising due to the accrued interest of the bonds, I apply the following correction. Before calculating the mispricing as the difference of the price of the nominal bond and that of the replicating portfolio, I subtract the accrued interest from both the nominal bond price and the replicating portfolio. However, to compute the correction factor for the latter, I need to determine the accrued interest for a given day of a bond that has a coupon rate equal to that of the nominal bond, whereas its coupon and maturity dates are identical to those of the corresponding TIPS issue. The aforesaid correction eliminates any trend or seasonality-like pattern from the mispricing series that would arise due to the above described accrued interest effect. 19

20 VI. Size and drivers of the arbitrage Table I provides summary statistics for the mispricing of each of the 38 pairs of TIPS and Treasury bonds in the sample, for the period between July 21, 2004 and December 31, The first two columns show the maturity and coupon dates for the TIPS issue in each pair. The next two columns display the same features for the nominal Treasury bonds that are matched to the TIPS issues. The next column exhibits the maturity mismatch measured in days between the previous two bonds. The two central panels report summary statistics of the mispricing measured in both dollar values and in basis point difference in the yields of the nominal bond and that of its replicating portfolio. Table II has a similar structure, with the only difference being the sample period it spans from July 23, 2004 to November 19, 2009 as in Fleckenstein et al (2013). The extent of mispricing reported in Table I and Table II is astonishing, given that based on the conservative cost estimate provided by Fleckenstein et al (2013) all strategies on average seem to be profitable. Moreover, the size of the mispricing is orders of magnitude larger than the aforementioned transaction costs. In almost every case, the mispricing seems to be unidirectional as nominal bonds are almost all the time more expensive than their replicating portfolios. This effect is so strong that for more than half of the bond pairs the price of the replicating portfolio never exceeds that of the nominal bond during the entire sample period. The average sizes of the mispricing from both Tables I and II are equally stunning. For example, the average size of the mispricing between the TIPS and Treasury bond maturing in January 2025 and February 2025, respectively, is $4.37 on $100 notional, but reaches its maximum at $24.44 during the sample period. Similarly, for the same pair of bonds the average mispricing measured in basis points is , which peaks at during 20

21 the crisis. I note that the average size of the mispricing seems to vary across different issues both measured in dollars or basis-point difference. For instance, the average mispricing for many TIPS-Treasury pairs with maturities of 2015 can go up to $3.56, while the latter quantity for bonds with maturities of 2028 is $6.99. Analogously, the largest mispricing is in excess of $12 and $17 for the respective bond maturities. I also calculate the equally weighted average of the mispricing over all bond pairs and the corresponding standard deviation. The result is $3.67 and $2.31, respectively, whereas the same in basis points are and The latter values are derived from the full sample, but comparable numbers can be calculated from the subsample in Table 2: the overall average of the dollar value mispricing is $4.67 with a standard deviation of $2.75, while it is and 9.21 in basis points, respectively. To illustrate the average size of the TIPS-Treasury mispricing, I compute the above average of the mispricing for each date during the sample period, where the average is taken over all available TIPS-Treasury bond pairs at a given date. Figure 1 depicts the average dollar mispricing for the above pairs, whilst Figure 2 plots the corresponding average basis points mispricing. The existence of the above relative pricing relation is evident throughout the entire sample period, not just during the extraordinary market conditions of the recent financial crisis. Figure 3 specifically focuses on the period of In particular, it is visible that the mispricing skyrocketed shortly after the Lehman bankruptcy and reached its peak at $12.86 in the Fall of During the crisis period the overall average mispricing was $4.92 with a standard deviation of $2.13. Note that although the level of the average mispricing has more than tripled, interestingly the latter standard deviation is smaller than the corresponding value of the full sample. The three figures confirm my supposition that there is significant time series fluctuation in the TIPS-Treasury bond mispricing. Moreover, having a 21

22 relatively long sample allows me not only to scrutinize the variation in magnitude but also the changes in the level of the mispricing. Based on eyeballing the three figures, I conjecture that the mispricing had a steady level prior to the crisis, to which it started to revert afterward. However, to conclude that there is an equilibrium level of mispricing, that is to say that the mispricing is long-term in nature requires formal testing for trends, cointegration or regime-switch in the mispricing series. Although the latter idea would suggest interesting asset pricing and policy implications, testing for it is beyond the scope of this thesis. On the other hand, it is in line with Hypothesis 6, thus this is definitely one of the directions to extend the analysis. Since this thesis partially replicates the analysis of Fleckenstein et al (2013) it is natural to contrast their results 14 to mine. Their sample period spans the period from July 23, 2004 to Nov 19, They claim that the mispricing for TIPS-Treasury pairs with maturities of 2015 is in excess of $10, whilst the same amount is $23 for issues maturing in As another example, the average size of the mispricing between the same TIPS and Treasury bond pair as previously mentioned, maturing in January 2025 and February 2025 respectively, is $4.27 on $100 notional, but can go up to $23.06 during the sample period. The overall average mispricing across the 29 pairs in their sample is $2.92, which reaches its zenith in the Fall of 2008 at $9.60. These numbers are fairly similar to those reported in the previous paragraphs. Moreover, their figure plotting the time variation of the mispricing is also very similar to Figures 1 and 3, despite being weighted by the notional amount of the respective TIPS issues. However, the differences are stemming from three major sources: the bond matching, the construction 14 Note that they define basis point mispricing differently than I do, thus the latter numbers are not strictly comparable between the two studies. However, given my definition, both the direction, the magnitude and the time variation in the basis point yield differences seem to be in line with prior expectations 22

23 of the arbitrage strategy and the sample. First of all, the maturity-matched bonds pairs differ between the two studies: the arbitrage strategy based on different bonds can differ due to dissimilar coupons payments and bond prices, yet maturity mismatch is not a problem as corrections described in Sections III and V are applied. The second source of variation stems from the construction of arbitrage strategy. To get non-traded swap prices, I apply linear interpolation, whereas Fleckenstein et al (2013) use cubic spline interpolation and correction for seasonality in inflation. Additionally, when I construct the arbitrage I match all cash flows to that of the nominal bond, yet when calculating the mispricing the maturity of the replicating portfolio, thus the TIPS issue is taken into account. Specifically, I calculate the yield to maturity and then the price of the nominal bond that has the same maturity as the TIPS and take the price difference of the latter Treasury bond and the replicating portfolio. Fleckenstein et al (2013) also constructs the trading strategy relative to the nominal bond, yet they adjust the price of the replicating portfolio to have equal maturity to the nominal bond. There is clearly a deviation between the extrapolated prices concerning the two dates as corresponding asset prices are likely to differ. The third, most trivial difference arises due to the breadth and the length of the sample: my sample is longer and also consists of more bonds pairs. An innovation relative to Fleckenstein et al (2013) is that I study how the TIPS-Treasury mispricing varies across different bonds issues Figures 4 and 5 plot this difference between the groups based on their remaining maturities. Therefore I compare short, middle and long-term strategies, as described in the Section V. From Figure 4 it is clearly visible, that the longer the remaining maturity of the respective bond group, the larger the average and the range in variation of the dollar mispricing are. Consequently, the average dollar mispricing of short-term strategies is $1.95 with a standard deviation of $1.01, whereas for middle-term strategies it is $3.59 and $1.83, respectively. Lastly, for the group of bonds with maturities later than 2025 the 23

24 latter average is $6.95 with a standard deviation of $2.80. The peak values of the average mispricing across groups follow a similar pattern: it is $7.34, $13.18 and $21.39 for the respective categories. Note that the pattern of the basis point differences from Figure 5 is exactly the reverse: differences in yields seem to be less dispersed and smaller in magnitude for long-term strategies than for their shorter term counterparts. And indeed the average basis point mispricing and the corresponding standard deviation values confirm this: they are with for shortterm, with for middle-term and and 9.36 for long-run strategies, respectively. Supposedly, the latter pattern in the short-run strategies is driven by the first four bond pairs, where both the dollar and basis point mispricing series often switch signs that is from time to time TIPS are relatively more expensive than nominal bonds. As in Fleckenstein et al (2013), these pairs involve TIPS with coupon rates comparable to their nominal counterparts, thus negative mispricing or positive yields could reflect temporary investor preference for short-term high-coupon TIPS issues. Finally, I also inspect the correlation between both levels and changes in the mispricing series arising from different bond pairs. The overall average correlation across the 31 series is 0.73 in levels and 0.68 measured in changes in mispricing. For visual illustration, Figure 6 plots the correlation in levels, while Figure 7 depicts correlation in changes of mispricing across bonds in the three-dimensional space. The horizontal axes comprise the serial number of the 31 bonds, whereas the vertical axis measures their correlation with brighter values corresponding to higher positive values. Note that the 45 degree line corresponds to the diagonal of the correlation matrix. The two figures show that most bonds are highly and positively correlated in the sample according to both measures, though the values of correlation in levels being slightly higher. The positive correlation is in line with the slow-moving capital explanation of Fleckenstein et al (2013): they claim that the explanation 24

25 implies the persistent nature of the arbitrage, in addition to arbitrages in different markets and over time being correlated with each other. This conjecture seems to be also verified by the high positive correlation in changes of mispricing, which suggests that the mispricing of the bond pairs under scrutiny tend to change together thus they will potentially be driven by similar factors. To uncover what factors drive the mispricing is beyond the scope of the current analysis, though Section IV offers some propositions to be tested in the future. However, there are also instances of negative correlation though these are exclusive to the third and fourth pairs in Table I. Moreover, the latter two pairs have the lowest average correlation with the rest of the bonds: 0.01 and 0.23 in levels, and 0.18 and 0.60 in changes. As noted before, the mispricing series stemming from the bonds with maturities January 15, 2009 and November 15, 2008 and the January 15, 2010 and February 15, 2010 often switch signs and therefore seem to behave differently than other pairs in the sample. A possible theoretical explanation for the negative correlation could be the preferred habitat hypothesis, nonetheless, this supposition requires further inspection and potentially formal testing. VII. Summary and concluding remarks 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. 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. 25

26 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. Nevertheless, my overall objective is not solely to document the existence of the mispricing and its causes, but to uncover its underlying nature. Specifically, by discovering what drives the mispricing across countries, how prices of government debt, thus interest rates and inflation expectation are formulated, institutional investors, government agencies and treasuries, as well as other market participants engaging in the arbitrage strategy, gain important knowledge of how sovereign bond markets function. 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 developed economies; namely in the G7 countries. All the steps taken 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. 26

27 References Acharya, V. and Pedersen, L. H. (2005): Asset Pricing with Liquidity Rosk, Journal of Financial Economics, Vol. 77, pp Amihud, Y. and Mendelson, H. (1986): Asset pricing and the bid-ask spread, Journal of Financial Economics, Vol. 17, pp Amihud, Y. and Mendelson, H. (1991): Liquidity, Maturity, and the Yields on U.S. Treasury Securities, Journal of Finance, Vol. 46, pp Amihud,Y., Mendelson, H. and Pedersen, L. H. (2005): Liquidity and Asset Pricing, Foundations and Trends in Finance, Vol.1, pp Ang, A. and Longstaff, F. A. (2011): Systemic Sovereign Default Risk: Lessons from the U.S. and Europe, Working paper, UCLA Bodie, Z. (2009): TIPS for Holland: Inflation-Linked Bonds, Transparency and the Public Interest, Netspar NEA Research Papers No. 22 Brunnermeier, M. and Pedersen, L. H. (2009): Market Liquidity and Funding Liquidity, Review of Financial Studies, Vol. 22, pp Campbell, J. Y, Shiller, R. J. and Viceira, L. M. (2009): Understanding Inflation-Linked Bond Markets, in David Romer and Justin Wolfers, ed.: Brookings Papers on Economic Activity, Spring 2009 (Brookings Institution Press), pp Christensen, J. H. and Gillan, J. M. (2011): Has the Treasury Benefited from Issuing TIPS?, FRBSF Economic Letter Daves, P. R. and Ehrhardt, M. C. (1993): Liquidity, Reconstitution, and Value of U.S: Treasury Strips, Journal of Finance, Vol. 48, pp Duarte, J., Longstaff, F. A. and Yu, F. (2006): Risk and Return in Fixed- Income Arbitrage: Nickels in Front of a Steamroller?, Review of Financial Studies, Vol. 20, pp Duffie, D (2010): Asset price Dynamics with Slow-Moving Capital, Journal of Finance, Vol. 65, pp Duffie, D. and Kan, R. (1996): A Yield-Factor Model of Interest Rates, Mathematical Finance, Vol. 6, pp

28 Fleckenstein, M., Longstaff F. A. and Lustig, H. (2013): Why does the Treasury Issue TIPS? The TIPS-Treasury Bond Puzzle, forthcoming in Journal of Finance Fleming, M. J. (2003): Measuring Treasury Market Liquidity, Federal Reserve Bank of New York Economic Policy Review (Spetember), pp Fleming, M. J. and Krishnan, N. (2009): The Microstructure of the TIPS Market, Working paper, Federal Reserve Bank of New York Gârleanu, N. and Pedersen, L. H. (2011): Margin-based Asset Pricing and Deviations form the Law of One Price, Review of Financial Studies, Vol. 24, pp Grinblatt, M. anf Longstaff, F. A. (2000): Financial Innovation and the Role of Derivative Securities: An Empirical Analysis of the U.S. Treasury s STRIPS Program, Journal of Finance, Vol. 55, pp Gürkaynak, R. S., Sack, B. and Wright, J. H. (2010): The TIPS Yield Curve and Inflation Compensation, American Economic Journal: Macroeconomics, Vol. 2:1, pp Han, B., Longstaff, F. A. and Merrill, C. (2007): The U:S: Treasury Buyback Auctions: The Cost of Retiring Illiquid Bonds, Journal of Finance, Vol. 62, pp Haubrich, J., Pennacchi, G. and Ritchken, P. (2012): Inflation Expectations, Real Rates, and Risk Premia: Evidence from Inflation Swaps, Review of Financial Studies, Vol. 25, pp Hunter, D. M. and Simon, D, P. (2005): Are TIPS the real deal?: A conditional assessment of their role in a nominal portfolio, Journal of Banking and Finance, Vol. 29, pp Jordan, B., Jorgensen, R. and Kuipers, D. (2000): The Relative Pricing of U.S. Treasury STRIPS, Journal of Financial Economics, Vol. 56, pp Kerkhof, J. (2005): Inflation Derivatives Explained, Fixed Income Quantitative Research, Lehman Brothers (July), pp Krishnamurthy, A. (2002): The Bond/Old Bond Spread, Journal of Financial Economics, Vol. 66, pp

29 Krishnamurhty, A. and Vissing-Jorgensen, A. (2010): The Aggregate Demand for Treasury Debt, Working paper, Northwestern University Liu, J. and Longstaff, F. A. (2004): Losing Money on Arbitrages: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities, Review of Financial Studies, Vol. 17, pp Longstaff, F. A. (2004): The Flight to Liquidity Premium in U.S. Treasury Bond Prices, The Journal of Business, Vol. 77, pp Mitchell, M, Peresen, L. H. and Pulvino, T. (2007): Slow Moving Capital, American Economic Review, Papers and Proceedings, Vol. 97, pp Pflueger, C. E. and Viceira, L. M. (2011a): An Empirical Decomposition of Risk and Liquidity in Nominal and Inflation-Indexed Government Bonds, NBER Working Paper No available at Pflueger, C. E. and Viceira, L. M. (2011b): Inflation-Indexed Bonds and the Expectations Hypothesis, Annual Review of Financial Economics, Vol.3, pp Schleifer, A. and Vishny, R. W. (1997): The Limits of Arbitrage, Journal of Finance, Vol. 52, pp

30 Table I Summary Statistics for the TIPS-Treasury Mispricing. This table reports summary statistics for the TIPS- Treasury mispricing for the 38 pairs of TIPS and T-bonds shown in the left panel. The mispricing is the price or yield difference of a nominal T-bond and a portfolio that exactly replicates its cash flows. The latter portfolio consists of a maturity-matched TIPS issue, inflation swap contracts and STRIPS issues. The left central panel reports mispricing measured in dollars on $100 notional, whereas the right central panel exhibits the latter relationship as basis point yield difference of the two assets. Both mispricing measures defined as the difference of the corresponding values of the nominal bond and its replicating portfolio. The sample period is from July 21, 2004 to Dec 31,

31 Table II Summary Statistics for the TIPS-Treasury Mispricing for the subsample of This table reports summary statistics for the TIPS-Treasury mispricing for the 38 pairs of TIPS and T-bonds shown in the left panel. The mispricing is the price or yield difference of a nominal T-bond and a portfolio that exactly replicates its cash flows. The latter portfolio consists of a maturity-matched TIPS issue, inflation swap contracts and STRIPS issues. The left central panel reports mispricing measured in dollars on $100 notional, whereas the right central panel exhibits the latter relationship as basis point yield difference of the two assets. Both mispricing measures defined as the difference of the corresponding values of the nominal bond and its replicating portfolio. The sample period corresponds to that of Fleckenstein et al (2013) and span from July 23, 2004 to Nov 19,

32 14 Dollar mispricing per $100 notional Mispricing 2 0 Figure 1. Average TIPS-Treasury Mispricing. This figure plots the time series of the arithmetic average TIPS-Treasury Mispricing, measured in dollars per $100 notional, across the 31 pairs for which data are available throughout the sample Mispricing in basis points Mispricing in basis points Figure 2. Average TIPS-Treasury Mispricing in basis points. This figure plots the time series of the arithmetic average TIPS-Treasury Mispricing, measured in basis point difference between the yields of the nominal bond and that of its replicating portfolio, across the 31 pairs for which data are available throughout the sample. 32

33 Date 2/16/07 4/6/07 5/25/07 7/13/07 8/31/07 10/19/07 12/7/07 1/25/08 3/14/08 5/2/08 6/20/08 8/8/08 9/26/08 11/14/08 1/2/09 2/20/09 4/10/09 5/29/09 7/17/09 9/4/09 10/23/09 12/11/ Dollar mispricing per $100 notional 4 2 Mispricing 0 Figure 3. Average TIPS-Treasury Mispricing during the financial crisis of This figure plots the arithmetic average TIPS-Treasury Mispricing, measured in dollars per $100 notional, across the 22 pairs available in this subsample. The mispricing is the highest during the crisis, although both preceding and succeeding levels are significant. 25 Dollar mispricing per $100 notional Mispricing Short-term Mid Long -term Figure 4. Average TIPS-Treasury Mispricing across different bond issues. This figure plots the time series of the arithmetic average TIPS-Treasury Mispricing, across bonds groups based on their remaining maturities compared to the overall average denoted as Mispricing. The magnitude and the dispersion of the mispricing seem to differ substantially across the groups formed from short, middle and long-term bonds. 33

34 Mispricing in basis points Mispricing in basis points Short-term Mid Long -term Figure 5. Average TIPS-Treasury Mispricing in basis points across different bond issues. This figure plots the time series of the arithmetic average of yield differences between nominal bonds and their replicating portfolios measured in basis points and across bonds grouped based on their remaining maturity compared to the overall average denoted as Mispricing in basis points. The magnitude and the dispersion of the mispricing seem to differ substantially across the groups formed from short, middle and long-term bonds. Figure 6. Correlation between the level of the mispricing series. This figure plots the correlation between levels of all available mispricing series in the sample. The horizontal axes represent the 31 available bond pairs from Table I, whereas the vertical axis measures 34

35 correlation according to the scale on the right: brighter colors correspond to higher positive correlation. Figure 7. Correlation between daily changes in the mispricing series. This figure plots the correlation between changes in the available mispricing series in the sample, based on first differences of the mispricing. The horizontal axes represent the 31 available bond pairs from Table I, whereas the vertical axis measures correlation according to the scale on the right: brighter colors correspond to higher positive correlation. 35