Noise as Information for Illiquidity

• Author: JUN PAN,JIANG WANG,GRACE XING HU
• Published date: 01 December 2013
• Date: 01 December 2013
• DOI: http://doi.org/10.1111/jofi.12083

THE JOURNAL OF FINANCE •VOL. LXVIII, NO. 6 •DECEMBER 2013

Noise as Information for Illiquidity

GRACE XING HU, JUN PAN, and JIANG WANG∗

ABSTRACT

We propose a market-wide liquidity measure by exploiting the connection between

the amount of arbitrage capital in the market and observed “noise” in U.S. Treasury

bonds—the shortage of arbitrage capital allows yields to deviate more freely from

the curve, resulting in more noise in prices. Our noise measure captures episodes of

liquidity crises of different origins across the financial market, providing information

beyond existing liquidity proxies. Moreover, as a priced risk factor,it helps to explain

cross-sectional returns on hedge funds and currency carry trades, both known to be

sensitive to the general liquidity conditions of the market.

THE LEVEL OF LIQUIDITY in the aggregate financial market is closely connected to

the amount of arbitrage capital available. During normal times, institutional

investors such as investment banks and hedge funds have abundant capital,

which they can deploy to supply liquidity. Consequently, big price deviations

from fundamental values are largely eliminated by arbitrage forces, and assets

are traded at prices closer to their fundamental values. During market crises,

however, capital becomes scarce and/or willingness to deploy it diminishes,

and liquidity in the overall market dries up. The lack of sufficient arbitrage

capital limits arbitrage forces and assets can be traded at prices significantly

away from their fundamental values.1Thus, temporary price deviations, or

noise in prices, being a key symptom of shortage in arbitrage capital, contains

important information about the amount of liquidity in the aggregate market.

In this paper, we analyze the noise in the price of U.S. Treasuries and examine

its informativeness as a measure of overall market illiquidity.

∗Grace Xing Hu is from Faculty of Business and Economics, University of Hong Kong, and Jun

Pan and Jiang Wang are from MIT Sloan School of Management, CAFR, and NBER. Weare grate-

ful to Cam Harvey (the Editor), the Associate Editor, two anonymous reviewers, Darrell Duffie,

Mark Kritzman, Krishna Ramaswamy, Dimitri Vayanos, Adrien Verdelhan, and Haoxiang Zhu

for valuable discussions. We are also grateful for comments from seminar participants at Boston

University, Shanghai University of Finance and Economics, University of Maryland, University

of Michigan, University of Pennsylvania, University of Western Australia, Capula Investment

Management LLC, 2011 NBER Asset Pricing Program Spring Meeting, Moody’s 2011 Credit Risk

Conference, Morgan Stanley, and Q Group 2012 Spring Conference.

1An extensive literature focuses on how the amount of arbitrage capital in a specific market

affects the effectiveness of arbitrage forces, or ”limits of arbitrage,” and possible price deviations.

See, for example, Merton (1987), Leland and Rubinstein (1988), Shleifer and Vishny (1997), Gromb

and Vayanos (2002), Brunnermeier and Pedersen (2009), and Duffie (2010).

DOI: 10.1111/jofi.12083

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2342 The Journal of Finance R

Our basic premise is that the abundance of arbitrage capital during normal

times helps smooth out the Treasury yield curve and keep the average dis-

persion low. This is particularly true given the presence of many proprietary

trading desks at investment banks and fixed-income hedge funds that are ded-

icated to relative value trading with the intention to arbitrage across various

habitats on the yield curve.2During liquidity crises, however, the lack of arbi-

trage capital forces proprietary trading desks and hedge funds to limit or even

abandon their relative value trades, leaving the yields to move more freely in

their own habitats and resulting in more noise in the yield curve. We argue that

abnormal noise in Treasury prices is a symptom of a market in severe shortage

of arbitrage capital. More importantly, to the extent that capital is allocated

across markets for major marginal players in the market, this symptom applies

not only to the Treasury market, but also more broadly to the overall financial

market.

In addition to its close connection to arbitrage capital, the U.S. Treasury

market is ideal for our empirical investigation for several reasons. First, it is

a market of central importance and investors of many types come to the Trea-

sury market to trade, not just for investment but also funding needs (Trea-

suries are probably the most important collateral in short-term financing).

As such, trading in the Treasury market contains information about liquid-

ity needs for the broader financial market. Second, the fundamental values

of Treasury bonds are characterized by a small number of interest rate fac-

tors, which can be easily captured empirically. This gives us a more reliable

benchmark to measure price deviations, which is important because we would

like to keep the information content as “pure” as possible. Other markets

such as the corporate bond market, the equity market, or the index options

market might also be informative, but their information is “contaminated” by

the presence of other risk factors. Third, the U.S. Treasury market is one of

the most active and liquid markets, one with the highest credit quality, and

thus is the number one safe haven during crisis. A shortage of liquidity in

this market therefore provides a strong signal about liquidity in the overall

market.

Using the CRSP Daily Treasury database, we construct our noise measure

by first backing out, day by day, a smooth zero-coupon yield curve. We then use

this yield curve to price all available bonds on that day. Associated with each

bond is the deviation of its market yield from the model yield. Aggregating

the deviations across all bonds by calculating the root mean squared error,

we obtain our noise measure. We use the term “noise” in the sense that, as

in the fixed income literature, deviations from a given pricing model are often

referred to as noise.3

2Vayanos and Vila (2009), for example, model the interaction between habitat investors and

risk-averse arbitrageurs and its impact on bond yields.

3Other authors have also considered the fitting or pricing errors of Treasury securities. For ex-

ample, Bennett, Garbade, and Kambhu (2000)andFleming(2000) use median difference between

market and model yields as a possible indicator of market inefficiency in the Treasury market.

Noise as Information for Illiquidity 2343

Whether this noise measure indeed captures the liquidity condition of the

overall market is largely an empirical matter. If it does, we expect it to

exhibit the following properties. First, it should serve as a good indicator dur-

ing liquidity crises in different parts of the market. Second, it should provide

new information about market liquidity beyond various existing liquidity mea-

sures. Third and importantly, given its systematic nature, as an additional

risk factor, it should help us understand returns on assets beyond the Trea-

sury market, especially those that are sensitive to the liquidity condition of the

overall market.

Our results show that the noise measure is rather informative about the

liquidity condition of the overall market. During normal times, the noise is

kept at an average level of around 3.61 basis points, which is comparable to

the average bid ask yield spread of 2 basis points. In other words, the arbitrage

capital on the yield curve is effective in keeping the deviations within a range

that is unattractive given the transaction cost. During crises, however, our

noise measure spikes up much more prominently than the bid ask spread,

implying a high degree of misalignment in bond yields that would have been

attractive for relative value arbitrage during normal times and are in fact

attractive given the contemporaneous transaction cost. Such crises include the

1987 crash, when the noise was over 13 basis points; the aftermath of the Long-

Term Capital Management (LTCM) crisis, when the noise peaked at 5.89 basis

points; the first trading day after the 9/11 terrorist attack, when the noise was

at 12.54; the days following the sale of Bear Stearns to JP Morgan, when the

noise peaked at 8.08 basis points; and the aftermath of the Lehman default,

when the noise was above 15 basis points for a sustained period of time. Given

the sample standard deviation of 2.17 basis points for the noise measure, these

are large deviations from the mean.

To further understand the uniqueness of the information captured by the

noise measure, we examine its relation to other known measures of liquidity.

One popular measure of liquidity for the Treasury market is the premium

enjoyed by on-the-run bonds. Since our noise measure is a daily aggregate of

cross-sectional pricing errors, the on-the-run premium is in fact a component of

our measure. We find a positive relation between the two, but our noise measure

is by far more informative about the overall liquidity condition in the market.

In particular, our noise measure spikes up much more prominently than the

on-the-run premium during crises. This is because our noise measure collects

information over the entire yield curve, while the on-the-run premium focuses

only on a couple of isolated points on the yield curve. As such, our noise measure

is much more sensitive to the commonality in pricing errors across the yield

curve. If such commonality heightens during crises, then it will be captured by

our noise measure, but not by a measure that focuses only on a couple of isolated

points on the yield curve. Indeed, this is how noise becomes information. Our

results also show that factors known to be related to systematic liquidity such

the Chicago Board Options Exchange (CBOE) VIX index and the Baa-Aaa yield

spreads have a significant relation with our noise measure. By contrast, term

structure variables such as the short- and long-term interest rates and interest