MEASURING LIMITS OF ARBITRAGE IN FIXED‐INCOME MARKETS

• Published date: 01 September 2019
• Author: Guillaume Nolin,Jean‐Sébastien Fontaine
• Date: 01 September 2019
• DOI: http://doi.org/10.1111/jfir.12187

The Journal of Financial Research Vol. XLII, No. 3 Pages 525–552 Fall 2019

DOI: 10.1111/jfir.12187

MEASURING LIMITS OF ARBITRAGE IN FIXED‐INCOME MARKETS

Jean‐Sébastien Fontaine and Guillaume Nolin

Bank of Canada

Abstract

An emerging literature relies on an index of limits of arbitrage in fixed‐income

markets. We analyze the benefits of an index that is model‐free, robust, and intuitive.

This new index strengthens the evidence that limits of arbitrage proxy for risks

priced in the cross‐section of returns. Trading simulations show that the new index

improves identification of limits of arbitrage because it bypasses a noisy estimation

step. Relative value indices in the United States, United Kingdom, Japan, Germany,

Italy, France, Switzerland, and Canada exhibit strong commonality and high

correlations with local volatility and funding conditions. The indices are updated

regularly and available publicly.

JEL Classification: G12

I. Introduction

Bonds from the same issuer and with the same cash flows should have the same prices.

This is the law of one price. Yet, deviations from the law of one price are pervasive in

fixed‐income markets. Panels A and B of Figure I show the yields to maturity for every

outstanding bond issued by the U.S. Treasury for two days: one in 2008 when

deviations were large and one in 2014 when deviations were small.

Deviations like those in Figure I are common, persistent, and significant, even

after accounting for transaction costs (Amihud and Mendelson 1991). In an important

study, Hu, Pan, and Wang (2013) show that a broad measure of these deviations—the

noise index—reveals information about the quantity of capital available for arbitrage

deviations.

1

One key insight in Hu, Pan, and Wang is that a measure of limits of

arbitrage can reveal a risk premium in the cross‐section of asset returns, across a range

of market conditions, and beyond fixed‐income markets.

Estimates of the noise index now play an important role in an emerging literature

studying the impact of limits of arbitrage. Significant examples include Malkhozov et al.

(2016) in international markets, Musto, Nini, and Schwarz (2018) in the case of investor

We thank Sébastien Bétermier, Bruce Chen, Jens Christensen, Darrell Duffie, Bruno Feunou, Meredith

Fraser‐Ohman, Étienne Giroux‐Léveillé, Toni Gravelle, Sermin Gungor, Madhu Kalimipalli, Natasha Khan,

Gitanjali Kumar, Stéphane Lavoie, James Pinnington, Francisco Rivadeneyra, Adrien Verdhelan, Harri Vikstedt,

Jun Yang, Jing Yang, and Bo Young Chang for comments suggestions. We also thank James Pinnington for

invaluable research assistance.

1

The effectiveness of arbitrage capital can be limited by funding frictions and market segmentation (for

reviews, see, e.g., Duffie 1996; Vayanos and Weill 2008; Vayanos and Vila 2009; Fontaine and Garcia 2015).

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© 2019 The Southern Finance Association and the Southwestern Finance Association

clienteles, D’Amico and Pancost (2017) in repo markets, and Goldberg and Nozawa

(2018) in identifying liquidity and demand shocks. A noise index is also used in broader

contexts to discuss the impact of limits of arbitrage or capital scarcity on market conditions

(e.g., Bisias et al. 2012; Adrian et al. 2015; Dudley 2016).

The construction of a noise index involves two steps. The first step is to choose

and estimate a smooth yield curve. Figure I shows one estimate of the yield curve.

2

The

second step is to calculate the noise index by aggregating the differences between the yield

of each bond and the curve estimated in the first step (i.e., the root mean square of these

fitting errors). This is an intuitive approach that can be explained easily. Yet, the first step

introduces measurement errors because it is prone to estimation and specification risk.

Measurement errors introduce a well‐known attenuation bias that lowers ordinary least

squares (OLS) estimates and reduces the power of tests. This weakens the evidence of

limits of arbitrage and underestimates their impact. These measurement errors have the

potential to be large, as implementation of the first step can appear arbitrary. Judgment is

needed to choose a curve‐fitting method and to include or exclude bonds for estimation.

3

In this article, we propose a different construction of the limits‐to‐arbitrage index

that is model‐free and intuitive.

4

To be clear, our goal is to provide a robust measure that

researchers can use to broaden and strengthen the evidence in Hu, Pan, and Wang (2013).

Panel A. November 24, 2008 Panel B. November 24, 2014

Figure I. Dispersion of US Treasury Yields to Maturity. Yields to maturity for U.S. Treasury securities from

the Center for Research in Security Prices (CRSP) database plotted against each security’s duration.

Gürkaynak, Sack, and Wright (2007) (GSW) parametric par curve is plotted for comparison. [Color

figure can be viewed at wileyonlinelibrary.com]

2

Figure I shows the yield curve introduced by Gürkaynak, Sack, and Wright (2007) based on Svensson

(1994), which is available at the Federal Reserve Board website.

3

For a review, see Bliss (1996) or Bolder and Gusba (2002). For instance, Hu, Pan, and Wang (2013)

exclude bonds with maturities less than 1 year or more than 10 years, whereas Gürkaynak, Sack, and Wright

(2007) exclude bonds with less than three months to maturity as well as recently issued bonds (on‐the‐run

bonds).

4

This contrasts with Fontaine and Garcia (2012) and D’Amico and Pancost (2017), who use dynamic no‐

arbitrage models to identify deviations from no arbitrage.

526 The Journal of Financial Research