Arbitrage Trading: The Long and the Short of It

56 Pages·2016·0.91 MB·English

Arbitrage Trading: The Long and the Short of It

Yong Chen
Zhi Da
Dayong Huang

First draft: December 1, 2014
This version: August 30, 2016

Abstract

This paper examines the relationship between arbitrage force and stock returns, with net arbitrage
trading measured by the difference between abnormal hedge fund holdings and abnormal short
interest. In the cross section, net arbitrage trading strongly predicts stock returns. This
predictability is consistent with information advantage of arbitrageurs and copycat trading of
other institutional investors. More importantly, across a broad set of stock anomalies, abnormal
returns are realized only among anomaly stocks experiencing strong arbitrage trading, and such
stocks are associated with high arbitrage cost on average. Finally, aggregate arbitrage trading
predicts returns on mispriced stocks over time.

Keywords: Arbitrage trading, hedge fund holdings, short interest, stock anomalies, arbitrage cost

JEL Classification: G11, G23

* We are grateful to Charles Cao, Roger Edelen, Samuel Hanson, Johan Hombert (Paris conference
discussant), Byoung-Hyoun Hwang (AFA discussant), Hagen Kim, Weikai Li (CICF discussant),
Bing Liang, Jeffrey Pontiff, Marco Rossi, Kalle Rinne (Luxembourg conference discussant), Thomas
Ruf (EFA discussant), Clemens Sialm, Sorin Sorescu, Zheng Sun, Robert Stambaugh, Jianfeng Yu,
and seminar and conference participants at Texas A&M University, University of Hawaii, University
of Notre Dame, the 2015 European Finance Association Meeting in Vienna, the 4th Luxembourg
Asset Management Summit, 2015 Macquarie Global Quantitative Research Conference in Hong
Kong, the 2016 American Finance Association Annual Meeting in San Francisco, the 8th Annual
Hedge Fund Research Conference in Paris, and the 2016 China International Conference in Finance
for helpful comments. Chen acknowledges financial support from the Republic Bank Research
Fellowship at Texas A&M University. Da acknowledges financial support from the Zych Family
Fellowship at the Notre Dame Institute for Global Investing. We are responsible for all remaining
errors. Chen is at Mays Business School, Texas A&M University, College Station, TX 77843, Email:
[email protected]; Da is at Mendoza College of Business, University of Notre Dame, Notre
Dame, IN 46556, Email: [email protected]; Huang is at Bryan School of Business, University of North
Carolina at Greensboro, Greensboro, NC 27412, Email: [email protected].
1. Introduction
Arbitrageurs play a crucial role in modern finance. Textbooks describe arbitrageurs as
entities that, by simultaneously taking long and short positions in different assets, help eliminate
relative mispricing and enforce market efficiency. As a result, their trading pins down the expected
return on these assets, according to the Arbitrage Pricing Theory (APT) of Ross (1976). On the
other hand, investors’ behavioral biases and agency frictions may lead to persistent mispricing
when arbitrageurs face limits to arbitrage (e.g., De Long, Shleifer, Summers, and Waldman, 1990;
Shleifer and Vishny, 1997).1 Relative to theoretical development, however, our understanding
about arbitrage activity from empirical research is still rather limited.
One major challenge in studying arbitrage activity empirically has been the lack of data on
arbitrageurs.2 However, as hedge funds emerged as institutionalized arbitrageurs and the data of
their stock holdings became available in recent years, a series of papers has inferred the long side
of arbitrage trading by investigating hedge fund stock holdings (e.g., Brunnermeier and Nagel,
2004; Griffin and Xu, 2009; Cao, Chen, Goetzmann, and Liang, 2015). Meanwhile, since short
positions are involved in arbitrage trades, several studies track the short side of arbitrage trading
by examining short interest on stocks (e.g., Hanson and Sunderam, 2014; Hwang and Liu, 2014;
Wu and Zhang, 2014).
In this paper, we propose a measure of net arbitrage trading against a stock by combining
hedge fund holdings as the proxy for the long side with short interest as the proxy for the short
side. It is intuitive that combining the two sides helps obtain a complete view about arbitrage
trading that usually involves both long and short positions. The advantage of our measure,
however, is not simply adding up the effects from the two sides. Arbitrageurs may disagree on the
value of a stock, so that the same stock is bought by some arbitrageurs and sold short by others.

1 See Gromb and Vayanos (2012) for a survey of theoretical development in the literature on limits of arbitrage.
2 The type of arbitrageurs we are interested in is those, as described in the APT, who take long and short positions in
well-diversified portfolios with similar risk exposures but different expected returns. It is different from pure arbitrage
in which assets in long and short positions have identical cash flows.
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Moreover, a correctly priced stock may be purchased by some arbitrageurs while sold short by
others for hedging purposes.3 Therefore, as long as the correlation between the two sides is not –1
(which is confirmed in our empirical analysis), our measure based on the net position, i.e., the
difference between the two sides, differs from the summation of the effects from the two sides and
represents a more accurate proxy for arbitrage trading. Based on this measure, we attempt to better
understand the informational content of arbitrage activity, the possible channels of arbitrage profit,
and the interaction between arbitrage trading and stock anomalies.
For the empirical analysis, we combine hedge fund holdings and short interest at the stock
level over the period 1990–2012. To capture quarterly variations in arbitrage activity relative to
the trend, we define abnormal hedge fund holdings (AHF) and abnormal short interest (ASR) as
their values in a quarter minus their moving averages in the past four quarters. Then, we measure
net arbitrage trading by the difference between AHF and ASR, denoted by AHFSR, which captures
trade imbalance of arbitrageurs. For example, an AHFSR of 1% on a stock means that arbitrageurs,
as a group, have purchased an additional 1% of the stock (as the percentage of total number of
shares outstanding) during the quarter relative to their past average.
Our analysis provides five sets of main results. First, we show that net arbitrage trading
(AHFSR) significantly predicts future stock returns. Stocks in the highest AHFSR quintile
outperform those in the lowest quintile by 0.68% per month (t-value = 7.93) in the next quarter.
The return spread declines over time to 0.42% per month (t-value = 4.90) in the second quarter,
further down to 0.18% per month (t-value = 1.90) in the third quarter, and then becomes
insignificant in the subsequent quarters within two years. Further, the return predictability of net
arbitrage trading in the first two quarters remains significant on a risk-adjusted basis. Meanwhile,
the absence of subsequent return reversal suggests that the return spread associated with AHFSR

3 For example, a correctly priced value stock with poor recent returns may be bought by a value trader and
simultaneously shorted by a momentum trader to hedge their respective long-short strategies. Similarly, a stock may
be sold short to hedge against a convertible bond purchase. In such cases, simultaneous increases in both long and
short sides do not necessarily indicate disagreement (i.e., differences of opinion) among arbitrageurs about the value
of the stock as described in Miller (1977). Our measure, however, captures net arbitrage force imposed on the stock.
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is less likely to reflect temporary price pressure caused by arbitrage trading, but more likely to
capture corrections to mispricing. As expected, the return predictability of net arbitrage trading is
much stronger than that of either the long or the short side alone.
The return predictability of net arbitrage trading holds in a battery of robustness checks,
including Fama-MacBeth cross-sectional regressions controlling for other return predictors,
alternative asset pricing models for risk adjustment, different sample screenings, two different
subperiods, and double sorting on AHF and ASR. More importantly, the predictability cannot be
generated by combining total institutional holdings and short interest. Thus, our results are not
driven by the interaction between short interest and institutional ownership previously studied in
the literature (e.g., Asquith, Pathak, and Ritter, 2005; Nagel, 2005). The finding also confirms that
hedge fund ownership reveals the long side of arbitrage trading much better than total institutional
ownership.
Second, we document two channels through which arbitrage profit is realized: one is
related to information advantage, and the other related to “copycat trading.” In particular, we find
that a significant fraction of arbitrage profit takes place around earnings announcements in the next
two quarters when fundamental information is released to the public, suggesting an information
channel. In addition, other institutional investors such as mutual funds subsequently trade in the
same direction as arbitrageurs, further facilitating price convergence. Interestingly, other
institutional investors trade in the opposite direction to arbitrageurs in the contemporaneous
quarter and only start to follow arbitrageurs with a lag of at least one quarter, consistent with a
pattern of copycat trading.
Third, we examine the relationship between arbitrage trading and stock anomalies. Our
analysis covers 10 well-known anomalies, including book-to-market ratio, gross profitability,
operating profit, return momentum, market capitalization, asset growth, investment growth, net
stock issues, accrual, and net operating assets. We find striking evidence that anomalous returns
are completely driven by anomaly stocks traded by arbitrageurs. Specifically, we define an
anomaly stock to be traded by arbitrageurs if it is in the long portfolio and recently bought by
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arbitrageurs (i.e., its AHFSR belongs to the top 30%) or it is in the short portfolio and recently
sold short by arbitrageurs (i.e., its AHFSR belongs to the bottom 30%). On average, this subset of
anomaly stocks exhibits significant return spreads (between the long and the short leg) of 0.88%
(t-value = 7.10), 0.61% (t-value = 4.88), 0.34% (t-value = 2.68), and 0.27% (t-value = 2.18) per
month during the first, second, third, and fourth quarters, respectively. In sharp contrast, the rest
of anomaly stocks do not earn any significant return spread over the same quarters.
Fourth, we show that anomaly stocks traded by arbitrageurs are, on average, harder to
arbitrage, with higher idiosyncratic volatility, smaller stock price, and less liquidity. This finding
is consistent with the notion that arbitrageurs bear arbitrage cost in their trading activities and
receive compensation through arbitrage profit. Meanwhile, among anomaly stocks not traded by
arbitrageurs, we find that those associated with higher arbitrage cost tend to earn smaller but more
persistent returns.
Finally, using a time-series regression, we show that arbitrage trading can predict future
returns on mispriced stocks. That is, for mispriced stocks, when the overall arbitrage trading is
greater in one quarter, stock returns tend to be larger in the next quarter. This result suggests that
arbitrageurs are informative about mispricing and their trading helps correct stock mispricing.
Our paper contributes to a growing literature that examines arbitrage activity by hedge fund
holdings and short interest.4 Using data on hedge fund holdings, Brunnermeier and Nagel (2004)
and Griffin, Harris, Shu and Topaloglu (2011) show that, during the tech bubble period, hedge
funds rode with the bubble and destabilized the market. Further, Griffin and Xu (2009) find weak
predictive power of changes in hedge fund ownership for future stock returns, while Agarwal,
Jiang, Tang, and Yang (2013) document strong return predictability of hedge fund “confidential
holdings.” Recently, Cao, Chen, Goetzmann, and Liang (2015) find that, compared with other
institutional investors, hedge funds tend to hold and purchase undervalued stocks, and undervalued

4 There exist other proxies for arbitrage trading in the literature. For example, Lou and Polk (2015) infer arbitrage
activity from the comovement of stock returns.
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stocks with larger hedge fund ownership and trades realize higher returns. Sias, Turtle, and Zykaj
(2016) show that shocks to hedge fund demand can predict stock returns.
Focusing on the short side, several papers document that stocks with higher short interest
realize lower returns (e.g., Asquith and Meulbroek, 1995; Desai et al., 2002; Boehmer, Jones, and
Zhang, 2008).5 Using institutional ownership to proxy for stock loan supply, Asquith, Pathak, and
Ritter (2005) find that, for small stocks with high short interest, low institutional ownership is
associated with negative returns, confirming the effect of short constraints on stock prices. Nagel
(2005) finds that short sale constraints help explain cross-sectional stock return anomalies. Further,
Boehmer, Huszar, and Jordan (2010) document a puzzling relation that stocks with low short
interest subsequently experience large, positive abnormal returns. Recently, Drechsler and
Drechsler (2016) find that short-rebate fee is informative about overpricing and arbitrage trades.
To the best of our knowledge, our paper is the first to combine information on both long
and short sides to study arbitrage trading. Our measure of net arbitrage trading provides substantial
value over examining either hedge fund holdings or short interest alone and produces a more
complete view about the impact of arbitrage activity. Indeed, the measure of net arbitrage trading
better predicts future stock returns. It also facilitates our investigation of the source of arbitrage
profit. Most importantly, when using the measure to study well-known anomalies, we find strong
evidence supporting the notion that arbitrage trading is informative about mispricing. Therefore,
our analysis sheds new light on how arbitrageurs operate in security markets and how their trading
affects security prices.
In one concurrent study, Jiao, Massa, and Zhang (2015) find that opposite changes in hedge
fund holdings and short interest, measured by dummy variables, are informative about future stock
returns. In their study, hedge funds are identified based on SEC Form ADV that became mandatory

5 There are theoretical arguments about why short sales or short sale constraints should be related to stock returns.
Miller (1977) argues that, in the presence of heterogeneous beliefs, binding short sale constraints prevent stock prices
from fully reflecting negative opinions of pessimistic traders, leading to overpricing and low subsequent returns.
Diamond and Verrecchia (1987) show that given their high costs (e.g., no access to proceeds), short sales are more
likely to be informative.
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filings for hedge fund companies only in 2011, and stock holdings of many hedge funds in early
years are likely to be missing by this approach. As a result, their study spans a short sample period
since 2000. In another concurrent paper, Nezafat, Shen, Wang, and Wu (2015) show similar
findings to those in Jiao, Massa, and Zhang (2015) based on the same hedge fund identification
method. In contrast, our sample represents a more comprehensive coverage of hedge funds, which
allows us to construct a continuous measure of arbitrage trading that is more informative than
dummy variables. More importantly, our paper focuses on the impact of arbitrage force on stock
anomalies, which is not studied in either of the two papers. Using our measure of net arbitrage
trading, we document several novel results about how arbitrage force affects anomaly returns and
stock mispricing.
The rest of the paper is organized as follows. Section 2 describes our data and sample.
Section 3 examines our net arbitrage trading measure (AHFSR) as a stock return predictor. Section
4 uses AHFSR to study the relationship between arbitrage activity and stock return anomalies.
Finally, Section 5 concludes.

2. Data and Sample Construction
2.1. Hedge Fund Holdings
For the long side, we employ the data on hedge fund stock holdings in Cao, Chen,
Goetzmann, and Liang (2015). The data are constructed by manually matching the Thomson
Reuters 13F institutional holdings data with a comprehensive list of hedge fund company names
and online sources. The list of hedge fund company names is compiled from six hedge fund
databases, namely TASS, HFR, CISDM, Bloomberg, Barclay Hedge, and Morningstar. Hedge
funds were historically exempt from registering with the SEC. However, hedge fund management
companies with more than $100 million in assets under management are required to file quarterly
disclosures of their holdings of registered equity securities. Common stock positions greater than
10,000 shares or $200,000 in market value are subject to disclosure.
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As 13F holdings data do not indicate which institutions are hedge fund companies, we
identify hedge fund companies through the following three steps. First, 13F institutions (excluding
banks, insurance companies, and mutual funds) are matched with the list of company names from
the six hedge fund databases. Second, among the matched institutions, we assess whether they are
indeed hedge fund management companies. Those unregistered with SEC are included in the
sample as hedge fund companies (Brunnermeier and Nagel, 2004). Meanwhile, more than half of
the matched companies have registered with the SEC and filed Form ADV. Historically, some
hedge fund companies registered with the SEC voluntarily. Registration is necessary for having
non-hedge fund businesses such as advising mutual funds. Hence, for such From ADV filing
companies, we follow Brunnermeier and Nagel (2004) and Griffin and Xu (2009) to assess whether
hedge fund management is their primary business based on the following two criteria: over 50%
of its clients are either high-net-worth individuals or invested in “other pooled investment vehicle
(e.g., hedge funds),” and the adviser receives compensation through performance-based fees.
Third, to address the concern that some hedge fund companies may not report to any database
because of its voluntary nature, we manually check the company website and other online sources
for each of the unmatched 13F institutions to decide whether it is a hedge fund company. The final
sample covers 1,517 hedge fund management companies.
The way hedge fund companies are identified in our sample is advantageous to an
alternative approach of matching 13F filings with Form ADV adopted by Jiao, Massa, and Zhang
(2015). Filing Form ADV became mandatory for hedge fund companies in July 2011, and hedge
fund companies that had closed their business before then cannot be identified based on Form
ADV.6 Thus, stock holdings of many hedge fund companies in early years may be missing by the
approach. Since Jiao, Massa, and Zhang (2015) use dummy variables of changes in hedge fund

6 Under the Dodd-Frank Act, major hedge fund management companies that were previously exempt from registering
with the SEC as investment advisers under the Investment Advisers Act of 1940 are required to do so since July 2011.
Before the Dodd-Frank Act, the SEC once issued a rule in December 2004 requiring hedge fund companies that
managed more than $25 million with over 14 investors and a lockup period of less than 2 years to register as investment
advisers by February 2006. As a response, while many hedge fund companies registered and filed From ADV, many
others avoided registration by controlling investor size and length of lockup period. The ruling was overturned in June
2006.
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positions over a short period since 2000, the missing information on hedge fund holdings likely
will not severely bias their results. In this paper, however, we examine arbitrage force captured by
a continuous measure and over a long period 1990–2012, and more importantly, we focus on the
interaction between arbitrage trading and stock anomalies. For our purpose, therefore, it is
important to have a comprehensive coverage of hedge funds.
For each stock in our sample, we compute its quarterly hedge fund holdings (HF) as the
number of shares held by all hedge fund companies at the end of the quarter divided by the total
number of shares outstanding. If the stock is not held by any hedge fund company, its HF is set to
zero. We define abnormal hedge fund holdings (AHF) as the current quarter HF minus the average
HF in the past four quarters. Though AHF is correlated with change in hedge fund ownership from
the one quarter to the next, it better captures quarterly variations in arbitrage activity relative to
the trend.

2.2 Short Interest
For the short side, short interest data are obtained from the Compustat Short Interest file
from 1990 to 2012, which reports monthly short interest for stocks listed on the NYSE, AMEX,
and NASDAQ. Because the Compustat Short Interest file only started coverage on NASDAQ
stocks from 2003, we follow the literature to supplement our sample with short interest data on
NASDAQ prior to 2003 obtained from the exchange. The data have been used in several previous
studies to examine the impact of short interest on stock prices (e.g., Asquith, Pathak, and Ritter,
2005; Hanson and Sunderam, 2014; Hwang and Liu, 2014).
For each stock in our sample, we compute its quarterly short interest (SR) as the number
of shares sold short at the end of the quarter divided by the total number of shares outstanding. If
the stock is not covered by our short interest files, its SR is set to zero. Similar to AHF, we define
abnormal short interest (ASR) as SR in the current quarter minus the average SR in the past four
quarters.
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2.3 Stock Anomalies
In our examination of the relationship between arbitrage activity and stock return
anomalies, we consider 10 well-known anomalies largely following Fama and French (2008) and
Stambaugh, Yu, and Yuan (2012).
The first anomaly is book-to-market ratio. Rosenberg, Reid, and Lanstein (1985) and Fama
and French (1993) document that stocks with high book-to-market ratio on average have high
future returns, even after adjusting for market risk based on the CAPM (Sharpe, 1964). The second
anomaly is operating profit. Fama and French (2015) show that firms’ operating profits are
positively related to their future stock returns. The third anomaly is gross profitability. Novy-Marx
(2013) shows that firms with higher gross profit have higher future returns. The fourth anomaly is
return momentum of Jegadeesh and Titman (1993). In our setting, at the end of each quarter, we
compute stock returns in the past 12 months by skipping the immediate month prior to the end of
the quarter, divide the stocks into winners and losers, and then hold them in the next quarter. The
fifth anomaly is market capitalization. Banz (1981) and Fama and French (1993) document a
negative relationship between firm size and expected stock return even after adjusting for market
risk. The sixth anomaly is asset growth. Cooper, Gulen, and Schill (2008), Fama and French
(2015), and Hou, Xue, and Zhang (2015) show that firms with higher growth rates of asset have
lower future returns. The seventh anomaly is investment growth. Xing (2008) shows a negative
relationship between firm investment and expected stock return. The eighth anomaly is net stock
issues. Ritter (1991), Loughran and Ritter (1995), and Fama and French (2008) find that larger net
stock issues are associated with lower future returns in the cross section. The ninth anomaly is
accrual. Sloan (1996) and Fama and French (2008) find a negative association of accrual with
future stock returns. The tenth anomaly is net operating assets. Hirshleifer, Hou, Teoh, and Zhang
(2004) show that firms with larger operating assets tend to have lower expected returns.
For each of the anomalies, we construct quintile portfolios at the end of each quarter. We
then compute monthly long-minus-short portfolio return spreads for the next quarter. Details of
the anomaly constructions are provided in the Appendix.
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