Arbitrage vs. Informed Short Selling

50 Pages·2017·0.3 MB·English

Arbitrage vs. Informed Short Selling:
Evidence from Convertible Bond Issuers*

John Hackney
University of South Carolina
[email protected]

Tyler R. Henry
Miami University, Ohio
[email protected]

Jennifer L. Koski
University of Washington
[email protected]

March 8, 2018

Abstract

Prior literature examines the effect of either informed or arbitrage short selling on equity
markets. We test the relative importance of informed and uninformed short selling around
convertible bond issues and earnings announcements for the same firms over the same time
period. Convertible arbitrage short selling is associated with temporary price pressure,
consistent with downward sloping demand curves. Earnings announcement short selling is
consistent with informed traders who anticipate future returns. Firm-specific characteristics
related to the cost of short selling similarly affect both informed and arbitrage short selling.
Deal-specific characteristics capturing hedging demand also strongly determine convertible
arbitrage short selling.

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*Henry acknowledges financial support from the Frank H. Jellinek, Jr. Endowed Assistant Professor Chair in Finance.
Koski thanks the Kirby L. Cramer Endowed Chair in Finance for financial support. We thank Philip Bond, Jonathan
Karpoff, Andreas Stathopoulos, Julie Wu, and seminar participants at the University of Washington for helpful
comments, and Jon Kalodimos for valuable research assistance.
1. Introduction

There is much discussion in the existing short selling literature about why a trader would short sell,
what a short sale would imply about the trader’s information set, and therefore how a short sale
should affect future returns. These relations have critical implications for asset pricing [e.g.,
Ringgenberg (2014)]. The effect of short selling on returns has its theoretical roots in the models of
Miller (1977) and Diamond and Verrecchia (1987), which lay the groundwork for short sellers as
informed traders. Empirically, most of this literature has explored the role of short sellers as
informed traders. A smaller subset of papers investigates the role of short sellers as uninformed
traders executing market-neutral arbitrage strategies.1 Due to the prevalence of work that takes the
former approach, the literature generally concludes that the dominant effect of short selling is to
precede negative future returns, implying that short selling contains value-relevant information.
However, most of these studies examine the differential motives for short selling in isolation. In this
paper, we consider them simultaneously in an effort to distinguish different shorting demand motives
and their consequences for price discovery.
We test the relative importance of informed and uninformed short selling in a setting that
facilitates direct comparison: new convertible bond issues and earnings announcements for the same
firms over the same period. We find that short selling on convertible bond issue dates is over twice
as large as short selling on earnings announcement dates, suggesting that arbitrage short selling may
be large in economic magnitude relative to informed short selling. Given this empirical observation,
we ask two fundamental research questions: Does the relation between short selling and stock

1 While the finance literature generally refers to arbitrage as the activity of informed traders enforcing equilibrium
values, the short selling literature often refers to arbitrage short selling as a component of long-short strategies
implemented by traders without value-relevant fundamental information. It is in this sense that arbitrage short selling is
“uninformed.” Goldstein and Guembel (2008) and others point out that a third group, opportunistic short sellers, may
trade manipulatively to distort the informativeness of stock prices. Although our primary focus is on unformed versus
uninformed short selling, we present evidence on one type of manipulative short selling which may occur in our setting
in Section 3.2, below.
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returns depend on the motivation for short selling? And how do the determinants of uninformed
short selling compare to the determinants of informed short selling? We address these questions
using a sample of 331 convertible bond offerings made by 301 distinct firms between January 1,
2005, and August 6, 2007, corresponding to the availability of daily short selling data from the
Securities and Exchange Commission’s Regulation SHO (RegSHO). We also analyze 2,734 earnings
announcements for the same firms during this same event window.
Our first test explores the relation between short selling and stock returns. If demand curves
for shares are downward sloping and convertible arbitrage short selling is uninformed, higher levels
of short selling should be related to more negative issue day returns [Scholes (1972)]. These effects
would be temporary, so arbitrage short selling should be positively related to future returns as the
stock price recovers from price impact. In contrast, if informed short sellers anticipate changes in
firm fundamentals or future returns, higher levels of informed short selling should be associated with
more negative future returns. For many of our convertible bond offerings, the announcement occurs
on the issue date. Therefore, short sellers during this period may be trading on information in the
announcement as well as setting up arbitrage positions. We use the predictions for stock returns to
examine whether short selling around convertible bond issue dates is relatively more consistent with
arbitrage or informed trading. We also test these predictions for short selling around earnings
announcements. Our ex ante expectation is that short selling around earnings announcements is more
likely to be informed than short selling around convertible bond offerings.
Results show that convertible short selling is significantly negatively related to issue-day
stock returns and positively related to future returns, consistent with temporary price pressure and
subsequent price recovery from arbitrage short selling. In contrast, short selling on earnings
announcement dates is negatively related to future returns, consistent with informed short sellers
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who short more in anticipation of lower future returns. In addition to providing evidence on the
pricing effects of convertible arbitrage trading in the stock market, these results validate the claim in
prior literature that short selling around convertible bond issue dates is arbitrage rather than informed
trading. The pricing consequences of short selling in the stock market differ significantly depending
on whether the short selling is motivated by arbitrage or information. Not all short selling is the
same, and it is important to distinguish the different types.
We next examine the determinants of different types of short selling. Extensive prior
literature investigates the determinants of informed short selling or short selling in general [e.g.,
D’Avolio (2002)]. Relatively few papers focus on the determinants of arbitrage short selling. We use
our setting to examine the determinants of (convertible) arbitrage short selling and compare them to
informed short selling. Our main results show that many firm-specific characteristics, in particular
those that proxy for the cost of short selling (such as institutional ownership, share price, and firm
size), have similar effects on both informed and arbitrage short selling. Several convertible deal
characteristics are significantly related to convertible arbitrage short selling. Convertible arbitrage
short selling is primarily determined by particular deal characteristics related to hedging demand but
is unrelated to convertible bond underpricing itself. It is not the magnitude of the underpricing, per
se, that drives the amount of short selling. Rather, short selling serves to hedge out the directional
risk of the convertible arbitrage and is associated with the delta hedge. Hedging activity appears to
last about two days after the issue date before largely tapering off. Finally, explanatory power is
much higher for regressions explaining convertible short selling than it is for informed short selling.
Overall, results show firm characteristics that facilitate informed short selling also facilitate arbitrage
short selling; however, deal characteristics also play a significant role in the extent to which
arbitrage short sellers trade.
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Our results add to the literature providing evidence of downward sloping demand curves.
Prior research in this area has focused on positive, non-information motivated demand shocks such
as index additions [e.g., Shleifer (1986), Harris and Gurel (1986) and Petajisto (2009)]. Our setting is
relatively unique in that we have a quasi-exogenous shock to supply rather than demand [e.g.,
Ringgenberg (2014)]. We anticipate that, especially for the subsample of events for which the
convertible announcement strictly precedes the issue date, convertible arbitrage short selling on the
issue date should not be motivated by negative information. We show that convertible arbitrage short
selling on convertible bond issue dates is associated with negative temporary price pressure,
consistent with downward sloping demand curves.
Our paper also contributes to other areas of the literature. First, our paper adds to research
that examines the relation between short selling and stock returns. Our paper, however, focuses on
this relation for uninformed, arbitrage short selling, rather than the usual focus on informed short
selling, and we show that the effects are quite different. Short selling is more nuanced than
previously described in the literature. We also extend the literature that looks at the determinants of
short selling with a comparison between the determinants of informed versus uninformed short
selling. Our tests hold both the sample firms and the time period constant, minimizing concerns that
variations in sample selection or across time periods may affect inferences.
The remainder of the paper is organized as follows. Section 2 describes our sample. In
Section 3 we present results on the relation between short selling and returns. In Section 4, we
compare determinants of the two types of short selling. Section 5 concludes.

2. Sample and Data

2.1 Sample of Convertible Bond Events

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We search the Securities Data Corporation (SDC) Global New Issues database for all convertible
debt offerings by public, U.S. issuers. Our sample period is January 1, 2005, through August 6,
2007, which corresponds to the availability of short selling data through the RegSHO pilot program
(see Section 2.3 for more details on RegSHO). We exclude deals with total principal less than $10
million and require RegSHO data in order to be included in our sample. We also require data for our
other control variables (see Section 2.4). The sample consists of 331 offerings, including public,
private, and 144A convertible deals made by 301 distinct firms.
We verify the issue date and identify the announcement date for each deal using news
searches on Factiva. We use the Mergent Fixed Income Securities Database (Mergent FISD)
accessed through Wharton Research Data Services (WRDS) to obtain most of our convertible deal
characteristics, supplemented with data from SDC. We manually verify deal terms (and fill in any
missing observations) from the Securities and Exchange Commission (SEC) filings on Edgar.
Unlike seasoned equity offerings in which a pre-offer market value of the security is
observable, there is no pre-offer price for newly-issued convertible bonds. Therefore, in order to
estimate the issue discount (underpricing), we must have an estimate of the theoretical price of the
convertibles. Following the literature [e.g., Chan and Chen (2007), Loncarski, ter Horst, and Veld
(2009), and De Jong, Dutordoir, and Verwijmeren (2011)], we use the Tsiveriotis and Fernandes
(1998) model to estimate the theoretical value of the convertible bond, and calculate convertible
bond issue discounts as
Theoretical Value - Offer Price
Issue Discount = (1)
Theoretical Value
For most of the convertible bonds, the offer price is $100 and the theoretical value according to the
Tsiveriotis and Fernandes (1998) model is greater than $100. Therefore, larger positive values of the
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issue discount correspond to more underpriced convertible bonds, at least relative to this theoretical
model.
In Panel A of Table 1, we report summary deal statistics for the sample of convertible bond
offerings. The average principal amount is about $350 million and average maturity is 14.2 years.
The majority (213) of the deals are Rule 144A offerings [see Huang and Ramirez (2010) for more
about the 144A market]. In general, private offerings are smaller, with higher coupons and shorter
times to maturity. The average convertible bond offering in our sample is underpriced by 8.2
percent, with higher underpricing for private placements and lower underpricing for public and 144A
deals.
In Panel B of Table 1, we report the number of deals as a function of the length of time
between the announcement day (AD) and the issue day (ID). Many of our deals occur on the day
they are announced. Therefore, it is challenging to disentangle issue day from announcement effects,
and we are careful about this distinction in our tests and interpretations.

2.2 Sample of Earnings Announcements

In order to compare arbitrage and informed short selling in the same firms at the same time, we
analyze earnings announcements for the 301 firms with convertible bond offerings over our sample
period. We acquire earnings announcement dates using the I/B/E/S Summary History database from
Thomson Reuters, accessed through WRDS. We are able to obtain earnings announcements for 285
of the distinct 301 firms in our sample, with a total of 2,734 quarterly earnings announcements
during our sample period.
We expect that informed short selling around earnings announcements may be related to the
information content of the announcement. We estimate the information in an earnings announcement
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several different ways. Following Christophe, Ferri, and Angel (2004, p. 1856), we use returns
measured over Days [0,1] relative to the announcement day as our proxy for the earnings surprise.
We also calculate cumulative abnormal returns over Days [0,1] relative to the CRSP value-weighted
index, CAR[0,1]; because short sellers may not react symmetrically to positive and negative
abnormal returns in an announcement, we sort CARs into subsets based on the magnitude of the
announcement return and use indicator variables to represent the subsets [see Christophe, Ferri, and
Hsieh (2010)]. Finally, similar to Boehmer and Wu (2013), we compute earnings surprises as the
difference between actual earnings and analyst consensus forecasts (measured using the I/B/E/S
average forecast as of the quarter prior to our event window), scaled by the stock price two days
before the announcement. We sort firms into deciles based on the scaled decile rankings of these
earnings surprises.2

2.3 Short Selling Data
We use short selling data made available through RegSHO. We collect transactions-level short
selling data from all Self-Regulatory Organizations (SROs) for the period January 1, 2005 through
August 6, 2007.3 We aggregate the transactions-level data by date and firm, leaving us with a dataset
of daily short-sale volume for each firm. We follow de Jong, Dutordoir, and Verwijmeren (2011)
and scale short selling by shares outstanding. Our primary short selling variable is short selling
divided by shares outstanding, so short selling on day t is defined as
SS SSVOL[t]
[t]             (2) 
SO SHROUT[t]

2 Summary statistics for the earnings surprise measures are reported in Panel B of Table 2.
3 In June of 2004, the SEC’s RegSHO mandated that all SROs make transactions-level short sale data publicly available
beginning in January 2005. The SROs included the New York Stock Exchange (NYSE), NASDAQ, Amex, NASD ADF,
National Stock Exchange, Boston Stock Exchange, Chicago Stock Exchange, Philadelphia Stock Exchange, and
Archipelago Exchange (ArcaEX). We collect these data from all SROs for the duration of the RegSHO period.
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where SSVOL[t] is the daily short selling volume on day t, and SHROUT[t] is the number of shares
outstanding on day t.
In Figure 1, Panel A, we graph average short selling (scaled by shares outstanding) and
returns by day relative to Day 0, the convertible bond issue day. There is a significant jump in short
selling on Day 0, from an average of about 0.5% of shares outstanding on earlier and later days to
over 2.2% on the issue date. Short selling is also high on Day +1, but we find very little evidence of
increased short selling before the issue day. Stock returns are very negative (-2.0%) on the issue day.
In Panel B of Figure 1, we present the average price level by day relative to the convertible bond
issue day. Consistent with returns, price levels fall on the issue day and partially recover, suggesting
a combination of arbitrage and informed trading.
Figure 2, Panel A reports average daily short selling and returns relative to the earnings
announcement Day 0 for the full sample. Short selling increases noticeably, to about 1.1% of shares
outstanding on the earnings announcement day. However, this increase is only about half as large in
magnitude as the increase in short selling on Day 0 for convertible bond offerings from Figure 1.
These results suggest that arbitrage short sellers are large in magnitude relative to informed short
sellers, and may have a more significant impact on pricing. Results in Panel B for the subset of firms
with negative earnings surprises (measured by announcements with CAR(0,1) < 0) are similar for
short selling. By construction, returns are highly negative around these events. There is very little
evidence of abnormal short selling before earnings announcement dates.

2.4 Control Variables
We obtain data for the firm-specific control variables used in our analysis from several databases,
accessed through WRDS. In the Appendix, we provide more detailed definitions of all of our control
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variables. We obtain prices, returns, volume and exchange listing data from the Center for Research
in Securities Prices (CRSP). Dividend information comes from Compustat. Institutional ownership
data are from Thomson Reuters Institutional (13f) Holdings database. We obtain data on convertible
arbitrage hedge fund flows and returns from TASS, and data on options availability from
OptionMetrics.
All firm-specific control variables are calculated monthly where possible, otherwise quarterly
or annually (depending on the reporting frequency of the data, see the Appendix for details). We
obtain values for these variables for the 301 distinct firms in our sample from Dec. 2004 (the month
before our first events) through August 2007.4 Therefore, we have monthly values for each firm for
each variable. For convertible bonds, we define the event window as [AD-5, ID +5], where AD is
the announcement date and ID is the issue date. For earnings announcements, the event window is
[AD-5, AD+5], where AD is the earnings announcement date. Regressions use control variables
measured as of the last reporting period prior to the start of the event window. In Table 2, Panel A,
we report summary statistics for these control variables for our sample of convertible bond offerings.
Firm size averages $4.45 billion, and 43% of firms in our sample are listed on the NYSE. Short
selling in the prior month (Benchmark Short Selling) averages over 700,000 shares per day,
compared to average daily volume of 2.3 million shares. Panel B of Table 2 reports summary
statistics for control variables for the earnings announcement sample. Not surprisingly, given these
are the same firms over the same time period by construction, summary statistics are similar.

3. Results: Short Selling and Returns
3.1 Short Selling and Stock Returns

4 For variables reported less frequently, we obtain data starting as of the last reporting period of 2004.
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