Flying Under the Radar:

The Effects of Short-Sale Disclosure Rules on

Investor Behavior and Stock Prices∗

Stephan Jank1, Christoph Roling2, and Esad Smajlbegovic3

March 9, 2018

∗We thank the German Federal Financial Supervisory Authority (Bundesanstalt fur Finanzdien-stleistungsaufsicht, BaFin) for providing the short position notification data. We are grateful to PuriyaAbbassi, Vikas Agarwal, Karl Diether (discussant), Zsuzsa Huszar (discussant), Rajkamal Iyer, CharlesJones (discussant), Alexander Klos (discussant), Philipp Konig, Christian Leuz, Christoph Meinerding,Emanuel Monch, Esteban Prieto, David Rakowski (discussant), Adam Reed (discussant), ZachariasSautner, Christoph Schneider, Gunter Strobl, Pedro Saffi, Patrick Verwijmeren, Verena Weick-Ludewig,as well as seminar and conference participants at the Deutsche Bundesbank, the University of Mannheim,the University of Washington 2016 Summer Finance Conference, the 2016 Annual Meeting of the Eu-ropean Finance Association (EFA), the Fall 2016 NBER Asset Pricing Meeting, and the 2017 AnnualMeeting of the American Finance Association (AFA) for their helpful comments and suggestions. Wetake responsibility for all remaining errors. Financial support from the German Research Foundation(Deutsche Forschungsgemeinschaft, DFG), Grant Number: JA-2396/1-1, is gratefully acknowledged. Thispaper represents the authors’ personal opinions and does not necessarily reflect the views of the DeutscheBundesbank, its staff, or the Eurosystem.

1Deutsche Bundesbank and Centre for Financial Research (CFR), Cologne. Deutsche Bundesbank,Wilhelm-Epstein-Str. 14, 60431 Frankfurt am Main, Germany. Phone: +49-69-9566-2854, E-mail:stephan.jank@bundesbank.de

2Deutsche Bundesbank, Wilhelm-Epstein-Str. 14, 60431 Frankfurt am Main, Germany. Phone: +49-69-9566-3044, E-mail: christoph.roling@bundesbank.de

3Erasmus University Rotterdam, Erasmus School of Economics, Burgemeester Oudlaan 50, PO Box 1738,30000 DR Rotterdam, The Netherlands. Phone: +31-10-40-81834, E-mail: smajlbegovic@ese.eur.nl

Flying Under the Radar:

The Effects of Short-Sale Disclosure Rules on

Investor Behavior and Stock Prices

March 9, 2018

Abstract

We study how disclosure requirements for large short positions affect investor behaviorand security prices. Drawing on confidential notifications below the applicabledisclosure threshold, we show that a considerable share of short sellers avoid disclosureby accumulating their positions just below the threshold. This behavior appears tobe part of investors’ general strategy to conceal private information. Studying theperformance of their short positions, we find that secretive investors are particularlyinformed and trade around fundamental news releases. Finally, we document thatshort sellers’ evasive behavior in response to transparency regulation hampers pricediscovery.

Keywords: information disclosure, short selling, investor behavior,limits to arbitrage, stock market efficiency

JEL: G14, G15, G23

Disclosure requirements for investors’ holdings are a prevalent feature of financial market

regulation. Since the Securities Act of 1933 and the Securities Exchange Act of 1934,

significant efforts have been made to increase the transparency of investors’ long posi-

tions.1 Conversely, less regulatory attention has been given to their short positions. This

asymmetry of disclosure requirements has been debated extensively in the aftermath of

the global financial crisis, with regulators on both sides of the Atlantic contemplating

new transparency measures for short positions. Proponents of short-selling disclosure

rules argue that greater transparency would level the playing field for investors, expose

potentially abusive short selling, and help to improve price discovery in the market (NYSE,

2015; NASDAQ, 2015). However, critics raise the concern that a timely publication of short

positions may pose a threat to proprietary investment strategies. In response, investors

may reduce their short-selling activities to protect their private information, engaging less

in arbitrage trading, and thereby hampering price discovery (U.S. SEC, 2014). While

this debate is still ongoing in the United States, in 2012 the European Union adopted a

uniform rule on short position disclosure.2 According to the European regulation, investors

are required to publish any net short position that reaches the threshold of 0.5% of the

shorted stocks’ issued share capital one day after that position arises. Disclosures contain

the identity of the short seller, name and identifier of the target stock, as well as the date

and magnitude of the position.

1In the United States, for example, several disclosure rules apply to long positions. First, anyone whoacquires beneficial ownership of more than 5% of a voting class of a publicly traded company has to file a13D or 13G filing with the Securities and Exchange Commission (SEC). Second, institutional investmentmanagers of a certain size must report their quarterly holdings in 13F filings. Mutual funds also mustregularly report their portfolio holdings to their shareholders (SEC forms N-CSR and N-Q.).

2Among the EU countries, Spain and the United Kingdom had already implemented short-sale disclosurerules in 2008; France followed in 2011. Japan also introduced disclosure requirements in 2008. In theUnited States similar measures have been debated. The Dodd–Frank Act required the U.S. Securities andExchange Commission (SEC) to conduct a study of the feasibility, benefits and costs of real-time disclosuresof shorting. However, the real-time disclosure of shorting was not adopted (U.S. SEC, 2014). Recently,the debate on short-sale disclosure resurfaced, with both large stock exchanges, the NSYE and NASDAQ,filing rulemaking petitions for short-sale disclosure with the SEC (petition number: 4-689, October 7,2015; petition number: 4-691, December 7, 2015, see https://www.sec.gov/rules/petitions.shtml).

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A central question in this regard is whether investors trade strategically around the

disclosure threshold, and, if so, to what extent does such behavior affect stock prices. To

study these questions we exploit a unique setting of the EU short selling regulation, which

allows us to observe not only public positions above the disclosure threshold but also

confidential positions below the threshold. Specifically, the regulation requires a two-tier

reporting system for short positions in shares: First, investors must file a confidential

notification with the regulator if their short position reaches 0.2% of the shorted stocks’

issued share capital. Second, the short position must be publicly disclosed if it reaches

0.5% of the issued share capital. For our analysis we obtained both confidential and

public short-sale notifications covering the German stock market, offering us a rare glimpse

behind the veil of the disclosure threshold.

A priori, it is unclear how disclosure requirements for short positions affect investors’

behavior. On the one hand, investors may prefer a disclosure regime because it enables them

to better promote their short positions and induce other investors to sell the target stock.

With this type of publication strategy, the aim is to decrease noise trader risk or to reduce

the time period for maintaining the short positions, effectively reducing securities borrowing

costs (e.g., Kovbasyuk and Pagano, 2015; Ljungqvist and Qian, 2016). Disclosure can also

be used to coordinate predatory short selling and to manipulate the price of the target

stock (e.g., Goldstein and Guembel, 2008; Brunnermeier and Oehmke, 2014). In such cases,

a short seller may prefer a short position above rather than below the publication threshold.

On the other hand, investors may prefer a position below the disclosure threshold for

several possible reasons. They may want to avoid an increase in security borrowing fees

induced by a higher demand of copy-cat investors. Alternatively, they may seek to protect

their private information from such investors, who might mimic their strategies without

incurring the cost of research themselves (Frank, Poterba, Shackelford and Shoven, 2004).

Lastly, some investors have expressed the concern that a public short position may harm

their relationship with the target’s corporate management (AIMA/MFA, 2013), which

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represents an important source of information when they are conducting fundamental

research. Given that there are reasons both for and against disclosing a short position, it

is ultimately an empirical question as to how investors behave in response to the newly

introduced mandatory disclosure requirement.

Our empirical findings provide strong evidence that a significant share of investors

avoid crossing the disclosure threshold, resulting in positions accumulating just below the

threshold. Specifically, in the reporting interval just below the threshold, the probability

of increasing a short position is lower, and the duration for which such a position is held is

longer, than in all other reporting intervals. Compared to the neighboring intervals, the

duration is 22–55% longer, and the probability of increasing the short position is 20–34%

lower. These patterns emerge only when investors approach the publication threshold for

the first time from below, not for positions that were already public, suggesting that the

pattern observed in the data is the result of a strategy to avoid crossing the disclosure

threshold.

As previously discussed, there are different reasons for investors to remain ‘below the

radar’. To shed more light on the rationale of the short sellers’ behavior, we study a series of

investor and stock characteristics around the disclosure threshold as far as data availability

allows. Interestingly, we find no evidence for the ‘security borrowing cost hypothesis’:

Positions just below and just above the disclosure threshold do not significantly differ

with respect to either ex-ante risk of rising borrowing fees, level of securities lending fees,

supply of stocks to borrow, inventory concentration, or stock liquidity. Instead, disclosure

avoidance appears to be persistent over time, with investors adhering to their secretive

behavior. Moreover, avoidance is associated predominantly with certain investor-specific

characteristics. Secretive positions tend to be held by hedge funds, private funds, investors

located in tax haven countries and investors for whom we are unable to find any public

ownership filing. These findings suggest that ensuring that a short position does not exceed

the publication threshold is part of a general strategy of investors to conceal company- or

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security-related information from the public and to remain largely out of the spotlight.

Moreover, we find that stocks with secretive short positions exhibit stronger negative

returns than stocks with non-secretive positions, which suggests that the concealment of

short positions is also associated with superior information. Furthermore, approximately

half of the performance of secretive positions is generated on firm-specific news release days,

indicating that these investors rely largely on fundamental trading strategies. These findings

are consistent with two possible explanations. Short sellers may be protecting their private

information from copy-cat investors to maintain their competitive advantage. Alternatively,

investors may fear that disclosing a short position would harm their relationship with

the target’s management, which they perceive as vital in enabling them to collect and

produce fundamental information. By its very nature, the exact process by which private

information is produced is hardly ever observable to researchers. Therefore, the data at

hand do not allow us to disentangle these two non-mutually exclusive explanations.

Lastly, we investigate how investors’ evasive behavior with respect to the disclosure

threshold affects asset prices. If the disclosure threshold discourages informed investors

from increasing their positions any further, then negative information may be incorporated

more slowly into prices. To test this hypothesis, we study stock returns when a secretive

investor is likely to be “constrained” by the threshold. Specifically, when these investors

are just below the threshold, we find subsequent negative risk-adjusted returns of around 6

bp per day. To confirm that the return predictability originates from disclosure avoidance,

we perform two different placebo tests. First, the return predictability does not occur

when we choose various hypothetical publication thresholds above and below the true

one. Second, within secretive positions, subsequent negative returns occur mainly when

the position is just below the publication threshold and less so when the position is not

directly below it.

Our findings contribute to the longstanding debate on the effects of information

disclosure in financial markets. While conventional wisdom suggests that disclosure

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improves market quality, some theories indicate that it can also have potentially damaging

welfare implications, such as crowding out the acquisition of private information (Verrecchia,

1982; Diamond, 1985), reduction of risk-sharing opportunities (Hirshleifer, 1971) or investors

overweighting public signals (Morris and Shin, 2002). In this context, our paper documents

an unintended consequence of holder disclosure: Position disclosure rules discourage

informed market participants from fully exploiting their information, thereby reducing

price discovery in the market. This mechanism is closely related to the literature on the

trade-off between insider regulation and market quality (Leland, 1992; DeMarzo, Fishman

and Hagerty, 1998; Huddart, Hughes and Levine, 2001). Two features make the disclosure

rule we are examining particularly interesting for our understanding of holder disclosure

and informational efficiency. First, the rule likely conveys highly relevant information to

other market participants because positions must be publicized as early as the next trading

day. Second, the rule applies to short sellers, who are typically perceived as informed

investors.3 Changes in the behavior of these informed investors can significantly affect

the ability of financial markets to produce and aggregate private information in the price

discovery process.

Furthermore, our study adds to the literature on limits to arbitrage (e.g., Shleifer

and Vishny, 1997; Gromb and Vayanos, 2002), in particular short-sale constraints. A

widely studied source of short-sale constraints are frictions in the securities lending market

(e.g., Jones and Lamont, 2002; Asquith et al., 2005; Nagel, 2005; Cohen, Diether and

Malloy, 2007; Prado, Saffi and Sturgess, 2016). In this respect, the novel finding in our

paper is that requirements for timely disclosure also constitute a sizable impediment to a

considerable share of short sellers, and, in particular, to well-informed investors. Short

sellers’ disclosure avoidance is unrelated to previously documented frictions in the securities

3For example, the model by Diamond and Verrecchia (1987) predicts that short sellers are more likelyto be informed than uninformed because shorting is costly. A robust finding of the empirical literatureis that short sales are followed by negative returns, suggesting that short sellers are generally informedinvestors (e.g., Seneca, 1967; Aitken, Frino, McCorry and Swan, 1998; Asquith, Pathak and Ritter, 2005;Boehmer, Jones and Zhang, 2008; Diether, Lee and Werner, 2009). For a recent survey on this topic, seeReed (2013).

5

lending market, such as insufficient lendable supply, concentrated ownership structure, or

the risk of increasing lending fees (Cohen et al., 2007; Kaplan, Moskowitz and Sensoy,

2013; Prado et al., 2016; Engelberg, Reed and Ringgenberg, 2017).

Lastly, our paper contributes to previous work analyzing the effects of short-sale regula-

tion (e.g., Diether et al., 2009; Battalio and Schultz, 2011; Grundy, Lim and Verwijmeren,

2012; Boehmer, Jones and Zhang, 2013; Beber and Pagano, 2013; Fang, Huang and Karpoff,

2016). The consequences of short-sale bans following the financial crisis of 2007–2008

have generated a great deal of interest among researchers. For instance, Boehmer et al.

(2013) and Beber and Pagano (2013) document a deterioration in market quality following

short-sale bans. More recently, Duong, Huszar and Yamada (2015) and Jones, Reed and

Waller (2016) have studied the effects of short-sale disclosure rules. Jones et al. (2016), the

paper closest to ours, use the staggered introduction of disclosure regimes in Europe and

document a reduction in short selling activity and price efficiency. Their evidence points to

a change in investors’ behavior in response to greater transparency. We corroborate their

findings and show that in particular informed short sellers avoid disclosure. Furthermore,

our unique setting allows us not only to identify directly investors’ avoidance of crossing

the publication threshold but also to shed new light on their underlying rationale. Finally,

we establish a direct link between investors’ disclosure avoidance and slower price discovery

for affected stocks.

I. Institutional background and theory

A. Background on the short position disclosure rule

The EU regulation on short selling (No 236/2012) has been in effect since November 1,

2012, requiring investors to report and disclose any short positions of a certain size. The

regulation brought into force a two-tier reporting system: First, a net short position must

be reported to the regulator if the position reaches 0.2% of the issued share capital of the

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company shorted and for each 0.1% threshold above that. Second, a net short position

must be disclosed to the public if the position reaches 0.5% of the issued share capital of

the company shorted and for each 0.1% above that. Also, notifications have to be updated

when values fall below the relevant thresholds.

The notification and disclosure rules apply to all stocks for which the principal trading

venue is in the EU. Short positions are reported separately for each country on the websites

of the national authorities. In Germany, the national authority for reporting short positions

is the Federal Financial Supervisory Authority (Bundesanstalt fur Finanzdienstleistungsauf-

sicht, or BaFin), and short positions are published on the Internet platform of the Federal

Gazette (Bundesanzeiger).4 Short positions have to be reported or disclosed by 3:30 p.m.

(local time) on the next trading day after they arise. Disclosures contain the name of the

investor, the date of the short position, the International Securities Identification Number

(ISIN), and the name of the shorted stock, as well as the magnitude of the position reported

as a percentage of the issued share capital.

The following example illustrates the disclosure rule. In autumn 2015, the hedge fund

company Marshall Wace LLP shorted the stock of Deutsche Lufthansa AG considerably,

presumably in light of the airline’s restructuring plan and labor disputes with its pilots

and cabin crews. Marshall Wace’s net short position in Lufthansa stock exceeded the

publication threshold of 0.5% on October 29, 2015, with a reported value of 0.59%. On

November 2, 2015, the position exceeded the next reporting threshold of 0.6%, with a

reported value of 0.61%, and on November 5, 2015, the next threshold of 0.7% was crossed,

with a reported value of 0.71%. Thus, short positions are publicly disclosed when each

new reporting threshold is crossed, until the position falls below the threshold of 0.5%.

The regulator receives confidential short position notifications in the same manner, but

here the threshold is 0.2%.

4For recent examples of published net short positions in Germany, see: https://www.bundesanzeiger.de/nlp.

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After the reporting day, the exact value of a short position between the two disclosure

thresholds is unknown until a new threshold is crossed. That is, the reported short position

of 0.61% on November 2, 2015, could, on the following day, have ranged from 0.60% to

0.69%, since no further information was available about the crossing of another threshold.

Therefore, we sort the positions into short position bins of 10 basis points (bps) each:

0.20–0.29%, 0.30–0.39%, 0.40–0.49%, and so forth. For brevity, we refer to these reporting

intervals as the 0.2, 0.3, 0.4, ... reporting bin or interval.

Several features of the regulation and its scope need to be highlighted. First, the

disclosure rule applies to all investors, irrespective of whether they are domiciled in the

EU or abroad. In fact, a large proportion of the reporting position holders are hedge

funds domiciled outside the EU. Second, the regulation applies not only to short positions

but also to derivative positions, which must be accounted for on a delta-adjusted basis.

Thus, reporting requirements cannot be circumvented by substituting short positions

with positions in derivatives. Third, the reported net short positions are calculated

by netting all the long, short, and delta-adjusted derivative positions in the respective

stock. Consequently, a short position established to hedge an exposure originating from a

derivative position in the same underlying stock does not have to be reported or disclosed

as long as the overall shorting exposure is below the respective threshold. Lastly, market

making activities are exempted from the EU short-selling regulation for the purpose of

ensuring liquidity provision.5

B. Short positions: To publish or not to publish

A priori, it is unclear whether investors prefer to publicize their short positions or to

keep them secret. Lamont (2012) states that, depending on the situation, short sellers

5Exemptions include market making in a specific stock, but also market making in the related derivativesof that stock. To meet the conditions for this exemption, institutional investors are required to file adetailed statement on their market-making activities in specific securities, which are monitored by thenational authorities (ESMA, 2013). According to the list of market makers published by ESMA, it ismainly banks that are using this exemption (ESMA, 2016).

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might either publicize their positions or try to remain undetected. Publicizing a short

position could be helpful if the investor is seeking to overcome conventional limits to

arbitrage and attempting to convince other investors that a certain stock is overpriced (e.g.,

Kovbasyuk and Pagano, 2015; Ljungqvist and Qian, 2016). If other investors agree and

follow suit, prices will converge faster to fundamentals, thus reducing borrowing costs for

the stock and potential noise trader risk (De Long, Shleifer, Summers and Waldmann, 1990;

Shleifer and Vishny, 1997). For instance, Ljungqvist and Qian (2016) provide evidence

that such short-sale campaigns help in the correction of mispricing, especially in cases of

questionable governance and accounting practices.6 Alternatively, position disclosure may

facilitate the coordination of predatory short-selling strategies to potentially manipulate

stock prices (e.g., Goldstein and Guembel, 2008; Brunnermeier and Oehmke, 2014). While

the two types of short-selling strategies differ in terms of the underlying motives, in both

cases we expect investors to prefer a short position above the publication threshold to one

below it.

At the same time, the literature offers a number of reasons why short sellers may want to

keep their short positions secret and may prefer to avoid crossing the publication threshold.

If other investors follow suit in shorting the stock, existing stock loans may be recalled

by the lender, or borrowing fees may rise. Investors may also be concerned about their

intellectual property, such as information they have gathered about the shorted company

or a proprietary trading strategy which they do not want to reveal to their competitors

(Frank et al., 2004). The publication of a short position may adversely affect an investor’s

ability to access the corporate management of the target, an important source for compiling

fundamental information. The Alternative Investment Management Association (AIMA)

and the Managed Funds Association (MFA) report anecdotal evidence that some hedge

funds “have been excluded from corporate access events as a consequence of their short

6Although such short-sale campaigns have become more popular in recent times, they are still compar-atively rare. In particular, Ljungqvist and Qian (2016) collect 124 short-sale campaigns in the UnitedStates used by 31 individuals or small boutique hedge funds during 2006–2011.

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positions, notwithstanding the fact that the same managers may have had long positions

in the past, or elsewhere in their firms or in other of their funds” (AIMA/MFA, 2013).

Similarly, Lamont (2012) even documents cases where short sellers were subject to legal

action or harassment when their name and short positions became public.

Given that there are reasons both for and against publicizing a short position, it is

ultimately an empirical question as to whether greater transparency for short sellers and

their positions will result in eagerness to disclose a position or a behavior to avoid doing

so.7

II. Data and descriptive statistics

We obtain public and confidential short position disclosures from the German Federal

Financial Supervisory Authority (BaFin) for the period from November 1, 2012, through

March 31, 2015. We merge the short position notifications with daily stock data from

Thomson Reuters Datastream, equity lending data from Markit, and institutional investor

data from FactSet Ownership, formerly known as LionShares. For our analysis, we restrict

the sample to common equity traded on the German regulated market. To ensure the

quality of the data from Datastream, we apply several standard data filters (see, Ince and

Porter, 2006; Griffin, Kelly and Nardari, 2010; Karolyi, Lee and Van Dijk, 2012). We

start our analysis on November 5, 2012, to account for some delay in the notification of

short positions, due to a statutory holiday in some federal states. The Appendix provides

further details on the sample construction, and Table A.1 contains a description and the

sources of all variables used in our analyses.

Table 1 provides summary statistics on various stock characteristics for the entire

population of stocks in the regulated market and for stocks that have at least one short

7In this paper we focus on short sellers’ behavior around the disclosure threshold of 0.5%. It is possiblethat the two-tier reporting system impacts the behavior at 0.2%, where positions are reported to theregulator but not to the public.

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position notification. Of all stocks, 19.9% have at least one short position notification.

In particular, 8.3% of the sample consists of stocks that have at least one public short

position disclosure and, 11.6% of stocks have at least one confidential but no public

position. In terms of stock characteristics, we observe short position notifications mainly

for stocks with a large market capitalization, a low book-to-market ratio, and a high share

of institutional investors, as well as stocks that are very liquid, measured by both the

Amihud illiquidity ratio and the bid–ask spread. In fact, the vast majority (73.5%) of

stocks with short positions are in the highest quartile of market capitalization, and almost

all stocks with short position notifications (95.8%) appear above the median value of the

market capitalization distribution. Data from the lending market show a similar picture:

Stocks in our sample are easy and cheap to borrow, as indicated by the larger proportion

of actively lendable stocks and lower borrowing fees relative to the overall German stock

universe. In economic terms, there are no apparent differences between stocks with public

and confidential short positions.

The panel dimension of the analyses in Sections III and IV pertains to the investor-stock

level. Table 2 contains summary statistics for the stock and investor characteristics for

which we observe a short position of at least 0.2% of issued share capital. As these details

indicate, hedge funds constitute the largest investor group, accounting for 76% of the

observations. The remaining groups of investors are mutual funds and other investment

advisors. With respect to the location of the investors, European and U.S. institutions

account essentially for the entire sample, contributing in almost equal proportions. For

just under 10% of the observations, we cannot find any public filings in the comprehensive

FactSet ownership database relating to the investor’s (long) holdings. Finally, a similar

but distinct investor group are the private funds, investors who filed Form D with the SEC

and sought private placements under Regulation D. Private placements are not subject to

some of the laws and regulations designed to protect investors, such as the comprehensive

disclosure requirements that apply to registered offerings. Therefore, the data set not only

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offers a rare glimpse into the short-selling behavior of investors, it also allows us to analyze

investor groups not previously studied, due to their generally secretive behavior.

Figure 1(a) shows the frequency distribution of days with an open short position

notification over the different reporting bins. As indicated previously, short positions are

reported to the regulator when they are greater than or equal to 0.2% of the total shares

outstanding, and they are disclosed to the public when they are greater than or equal to

0.5%. As can be seen from the graph, publicly disclosed short positions represent only the

tip of the iceberg. The majority of short positions are not disclosed: 79% of observations

with an open short position fall below the publication threshold.

III. Do investors avoid crossing the disclosure

threshold?

Looking at the overall distribution in Figure 1(a), it is hard to determine whether

investors avoid crossing the disclosure threshold. To uncover a potential accumulation

of short positions below the disclosure threshold, we split the sample into positions both

above and below their historic high. Specifically, we define the following dummy variable

for the sequence of position notifications of each investor-stock (i, j) pair:

Position record highi,j,t =

1 if bini,j,t = max

s≤tbini,j,s

0 if bini,j,t < maxs≤t

bini,j,s,(1)

where bini,j,t denotes the short position’s reporting bin of investor i in a given stock j on

trading day t. A sample split according to Equation (1) exploits the fact that avoidance

of crossing the threshold should be particularly pronounced for investors who approach

the threshold from below for the first time. If we compare two different situations where

investors are just below the disclosure threshold, we can see the economic logic behind this

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approach. First, imagine an investor being short in a specific stock with a position value

of 0.4, and this position is at a record high. As this position has not been higher in the

past, it has also never been public. If an investor is avoiding crossing the threshold, we

would expect to find evidence of avoidance especially in this situation. Now, imagine an

investor with a short position in the 0.4 bin in a specific stock, but the position is below

its record high. This position has been higher in the past and consequently has also been

public. In this situation, we would expect either fewer or no signs of avoidance. The idea

is that investors who revealed the particular position in the past are unlikely to be averse

to cross the publication threshold again in the near future.

Figure 1(b) shows the frequency of days with open short positions for the two subsamples.

Positions at their record high, for which we expect there to be strong signs of avoidance,

amass below the disclosure threshold, suggesting that some investors prefer to stay below

the threshold. The relative frequency in the 0.4 bin is 17.0%, almost at the frequency of the

lower bin. Positions that are below their record high, however, decline fairly geometrically

with increasing reporting bins. Their relative frequency in the 0.4 bin is 8.6%, about half

the relative frequency of positions at their record high. Overall, Figure 1(b) provides initial

descriptive evidence that some investors are trying to stay below the radar.

We now take a more rigorous approach to testing the avoidance hypothesis. First,

we study the probability that the next position change is an increase across reporting

intervals. Second, we investigate the duration spent in each reporting interval. Lastly,

we employ different regression models, in which we control for various measures of short-

sale constraints as well as for unobservable stock and investor effects using saturated

fixed-effects specifications.8

8Due to data reporting issues our methods differ from the approach commonly used to identifydiscontinuities in economic outcomes, in which the density of the variable of interest is estimated justbelow and above a certain threshold (e.g., Degeorge, Patel and Zeckhauser, 1999). This method requiresa continuous outcome variable with a smooth density under the null hypothesis, which is not given inour case. Positions are reported at a two-digit precision only on the day at which the position crossesthe threshold of a reporting bin. Afterwards, the position can take any value between the two thresholdswithout additional reporting (see also Section I.A). Such a setting leads to a distorted picture of how thepositions are distributed within an reporting interval. If a position crosses the 0.4 threshold from below, it

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A. Probability of a short position increase

Our first hypothesis of avoidance relates to the probability of increase. If there is

avoidance, the probability of a position increase should be lower in the bin just below

the threshold than in the neighboring bins. Table 3 shows the estimated probability that

the next position change is an increase, conditional on currently having a short position

in a specific reporting interval. For this test we leave aside the time dimension of the

positions and we infer our results entirely from the decision as to whether the next change

in investor’s position will be an increase or a decrease. Looking first at the overall sample,

we find that the probability of an increase rises with the value of the current reporting

interval. Beyond this general pattern, we observe an unusual value for the 0.4 reporting

interval. The bin just below the publication threshold exhibits the lowest probability of all

the reporting intervals, which is significantly different from all other bins except the 0.2

bin. This unusually low likelihood of increasing a short position just below the threshold

suggests that some investors avoid crossing the disclosure threshold.

To determine whether this effect is really due to an avoidance strategy, we split the

sample into positions at and positions below their record level. As discussed previously,

avoidance of passing the disclosure threshold should be found particularly when positions

are at a record high, but it should be less pronounced when positions are below their

record high. The second panel shows the probability of increasing a short position only

for positions at their historic high. For this subsample, the avoidance effect of the 0.4 bin

is much stronger than it is for the overall sample. The probability of increasing a short

position takes a minimal value of 0.338 for the 0.4 bin, significantly lower than for all

other reporting intervals except for the lowest. To gauge the economic significance of this

is more likely to have a low rather than a high second digit on that day. Changes in the second digit arenot incorporated into the distribution. In contrast, when the 0.4 is crossed threshold from above, theposition is more likely to have a high rather than a low second digit on that day. This reporting rulemechanically creates a u-shaped distribution of positions within a reporting corridor. For a more detaileddiscussion on the specifics of the reporting rule and the resulting distribution of positions, we refer thereader to the Internet appendix.

14

avoidance effect, we compare this probability to that of the neighboring reporting intervals,

just below and just above. In the 0.3 bin, the probability of increasing a short position is

0.423, equating to a difference of -0.085; in the 0.5 bin, it is 0.514, a difference of -0.176.

In relative terms, in the bin just below the disclosure threshold it is 20% and 34% less

likely to increase a short position than in the two neighboring intervals.

Positions that are below their maximum serve as a comparison. If the low probability

of increasing a short position is truly due to an investor wanting to avoid revealing his or

her position, we should observe a smaller effect or no effect at all for these positions. The

right-hand panel of Table 3 supports this notion: For positions below their record high, we

find nothing extraordinary about the 0.4 reporting interval. The probability of increasing

the position is in fact the second largest, not statistically significant when compared to

the class below, but significantly larger than the class above.

B. Duration in reporting bins

The second testable hypothesis for avoidance concerns to the duration spent in the

reporting intervals. If investors avoid crossing the disclosure threshold, they will remain

just below it, thereby spending longer time in the 0.4 reporting bin. We test this hypothesis

in Table 4, which shows the average duration in trading days in each reporting interval.

The durations in the bins are prone to extreme outliers, so we winsorize the upper tail

at 1% before reporting the mean durations in Panel A. As an alternative, we report the

median durations in Panel B.

In general, the duration in each 0.1 interval declines as the position grows in size. For

example, the mean duration for the overall sample in Panel A declines from 18.3 days

(lowest bin) to 12.6 days for all positions greater than or equal to 1.0% (highest bin).

Again, we observe an unusual value for the 0.4 bin: The duration in this bin, just below

the disclosure threshold, is the longest of all the bins, at 20.6 days. The difference in mean

duration is statistically significant when compared with all other reporting intervals. As in

15

our previous analysis, we discover that the pattern of the overall sample is driven entirely

by the positions at their record high, for which the maximum duration of 26.0 days is

reached in the 0.4 bin, significantly higher than for any other bin. For positions below

their record high, we find no unusual value for the bin just below the publication threshold;

instead, the durations decline fairly monotonically with the position value. The same

pattern can be observed for median durations: For positions at their record high, the

median duration is 10 days for the reporting bin just below the publication threshold,

significantly higher than for any other reporting interval. For positions below their record

level, however, durations decline monotonically.

To illustrate the economic magnitude of the duration effect, it is again useful to compare

the duration of the 0.4 bin to that of its neighboring bins. The mean duration in the bin

just below the publication threshold of 26.0 days is 22% higher than for the next lowest

bin (21.3 days), and 55% higher than for the next highest bin (16.7 days). If we look at

the medians, the results are similar: The median duration of 10 days in the 0.4 interval is

25% higher than for the next lowest interval (8 days), and 43% higher than for the next

highest interval (7 days).

In summary, investors spend an abnormally long time in the reporting bin just below

the publication threshold, significantly longer than in any other reporting bin. In this bin,

the likelihood of increasing the short position is also the lowest. The economic magnitude

of these effects is substantial: Compared with the neighboring bins, the duration in this bin

is 22–55% longer, and the probability of a short position increase is 20–34% lower. Overall,

these combined results suggest that a considerable share of investors avoid crossing the

disclosure threshold.9

9It is worth noting that these results describe the aggregate behavior of investors around the disclosurethreshold. The results are not at odds with the possible existence of individual short-sale campaigns, forexample, as documented by Ljungqvist and Qian (2016).

16

C. Accounting for (un)observed stock and investor characteristics

Our findings that there is both an abnormally low probability of increase and an

abnormally long duration in the bin just below the publication threshold indicate that a

large share of investors avoid increasing their positions because of the publication threshold.

However, this lower probability of increase might stem from stock or investor characteristics

that correlate with a position being just below this threshold. To rule out alternative

mechanisms, we conduct panel regressions with a battery of control variables associated

with short-selling constraints as well as progressively saturated fixed-effects specifications

in the spirit of Jimenez, Ongena, Peydro and Saurina (2014).

We start with a standard binary outcome model and construct a dependent variable

equal to 1 on day t if a short position moves up at least one bin on the next trading day,

and equal to zero otherwise: yi,j,t+1 = 1 (bini,j,t+1 > bini,j,t). To identify whether short

sellers avoid crossing the disclosure threshold, we specify the following regression models:

yi,j,t+1 = α0 + β1 Just below thresholdi,j,t +∑k

βk k bini,j,t + γ′ Xi,t + αt + εi,j,t+1, (2a)

yi,j,t+1 = α0 + β1 Just below thresholdi,j,t +∑k

βk k bini,j,t + αi,t + αj,t + εi,j,t+1. (2b)

where Just below threshold is a dummy variable, indicating the reporting bin just below

the publication threshold (bin = 0.4). The indicator k bini,j,t is equal to 1 if investor j has

a short position in stock i in bin k at time t. In our specifications the omitted benchmark

bin is 0.3, i.e. k ∈ {0.2, 0.5, 0.6+}, where 0.6+ indicates position bins greater than or equal

to 0.6.10 Xi,t represents a vector of control variables related to short selling activity and

αt, αi,t, αj,t denote day, stock-day, and investor-day fixed effects, respectively. If investors

are on average avoiding crossing the publication threshold we would expect the coefficient

of the Just below threshold dummy β1 to be significantly negative relative to the omitted

neighboring 0.3 bin and significantly lower than the regression coefficient of the 0.5 bin

10Our results are robust to using a more detailed specification that includes all reporting bins up to 1.0into the regression separately. These results are shown in the Internet appendix.

17

dummy.

Our first benchmark specification includes daily time-fixed effects in addition to the

reporting bin indicators. Column (1) of Panel A in Table 5 reports the estimates of this

specification. The results are in line with our previous findings. The probability of an

increase conditional on being in the bin just below the disclosure threshold is significantly

lower than in the 0.3 bin. In economic terms, when a short seller is in the 0.4 bin, the

position is 0.54 percentage points less likely to be increased than if the short seller were in

the 0.3 bin. This effect is economically significant, given that the baseline unconditional

probability of an increase on the next day is slightly below 2.0%. In Panel B we observe

that the probability of increase in the bin just below the threshold is also lower than in

the neighboring 0.5 public bin.

The second specification includes various control variables that might be endogenously

related to different dimensions of short-sale constraints. Most importantly, the coefficients

of the bins around the disclosure threshold remain virtually unchanged (see Column (2)

of Panel A and B). Although our main interest is still the coefficient of the 0.4 bin, this

subsection also sheds some light on other drivers of short-selling activity. For example, the

bid–ask spread is negatively associated with the probability of position increase, suggesting

that investors are more reluctant to build up a short position in illiquid stocks. We find

similar but statistically weaker evidence for the Amihud (2002) price impact measure.

Consistent with Cohen et al. (2007) and Kaplan et al. (2013), the positive and statistically

significant coefficient on the percentage of lendable stocks suggests that there are more

short position increases if there is larger supply of stocks to borrow. In line with Prado et al.

(2016), we find a negative relation between inventory concentration and the probability of

a short position increase. Although in our sample the fee itself is not associated with the

probability of a short position increase, we observe that the second moment of the securities

lending fee is negatively associated with short position increases. This finding is consistent

with the notion that investors are concerned with high variation in fees when establishing

18

their position (D’Avolio, 2002; Engelberg, Reed and Ringgenberg, 2017). Furthermore,

consistent with the idea that it is difficult to establish the same relative position in larger

stocks, market capitalization relates negatively to the probability of an increase. As

described in Section I.A, the reported net short positions also include equivalent derivative

positions, which are accounted for on a delta-adjusted basis. Thus, if futures or listed

options exist for an underlying stock, it is presumably easier to establish and increase

a net short position. In keeping with this notion, the dummy indicating the existence

of futures or listed options is associated with a positive coefficient. Interestingly, when

we control for the above-mentioned short-selling frictions, we observe that investors tend

to increase their short position more aggressively for stocks with higher return volatility.

Such an effect is consistent with the notion that low-volatility stocks are insufficient to

provide short sellers with the expected level of profit, one which exceeds their transaction

costs. As a consequence, they demonstrate a preference for high-volatility stocks (Angel,

Christophe and Ferri, 2003).

In Column (3), we exploit the three-dimensional structure of our data set by including

stock-day and investor-day fixed effects to suppress the influence of stock and investor

unobservables on the decision to increase a short position. The fixed effects control for

characteristics, such as the overall borrowing demand for the stock, the supply of stocks

to borrow, borrowing fees, or liquidity, but they also control for any time-varying investor

characteristic such as the investor’s size or leverage, or any sort of funding constraint

that may vary at investor level. The identification of investors’ avoidance to cross the

publication threshold stems from comparing the probability of an position increase on the

same day by different short sellers for the same stock, controlling for any time-varying

investor characteristic. The estimated regression results in Column (3) indicate that neither

unobserved stock-specific nor investor-specific characteristics explain the abnormally low

probability in 0.4 bin. That is, the probability of an increase when the investor is in the

bin just below the publication threshold is on average significantly lower than in the next

19

lower bin (Panel A) but also than in any other reporting bin (Panel B).11 Taking the

results in Table 5 together, the avoidance of a position increase in the bin just below the

threshold is robust to any time-varying stock or investor characteristic.

IV. Understanding investors’ avoidance of position

disclosure

In the previous section, we revealed that short sellers avoid passing the publication

threshold to a considerable extent. As discussed in Section I, there are various possible

motives for concealing one’s short position. Investors may fear rising costs of borrowing

securities or stock recalls induced by position publication and trading by copy-cat investors.

Other reasons for staying below the radar may be to protect one’s private information

from competing investors or to preserve a valuable source of information, i.e. retain one’s

access to the corporate management of the target company. The purpose of this section is

to examine these various, mutually non-exclusive explanations for avoiding disclosure.

A. Investor and stock characteristics of secretive positions

To learn why a large share of investors keep their positions secret, we compare positions

that remained just below the disclosure threshold with positions that just exceeded it.

Therefore, we calculate for each position, i.e. each investor-stock pair (i, j), the maximum

reached:

Position maximum i,j = maxt=1,2,...,Ti,j

bini,j,t, (3)

where Ti,j is the total number of trading days of investor-stock pair (i, j). To understand

to what degree avoidance is investor-specific, we calculate the maximum position value

11The inclusion of the different fixed effects reduces the number of observations in some of the estimatedmodels due to missing variation. However, this loss of observations is relatively small in this rich dataset. With both stock×time and investor×time fixed effects, the number of observations with sufficientvariation within stock and investor level, accounts for 73% of the overall sample size.

20

reached by each investor across all of his or her positions:

Investor maximum i = maxj=1,2,...,Si

maxt=1,2,...,Ti,j

bini,j,t, (4)

where Si is the total number of stocks in which investor i holds short positions.

Figure 2 shows the frequency of short positions according to the maximum bin reached

and thereby reveals two important patterns. First, it captures the avoidance effect we

have already shown: Positions that never crossed the disclosure threshold (positions with

a maximum of 0.4) account for the largest group with 22.8% of all open short position

days. Additionally, a second important finding emerges from Figure 2: Looking at the 0.4

reporting bin, we observe that a large share of positions with a position maximum of 0.4

originate from investors whose positions reach a maximum of 0.4. In other words, many

positions that remain just below the disclosure threshold are held by investors who remain

below it for the entire sample period. For positions with other maximum reporting bins,

the corresponding proportion is strikingly lower. This descriptive graph suggests that the

decision to stay below the radar is mainly investor-specific, with investors sticking to their

general decision to keep their short positions secret.

Now, to better understand what determines avoidance, we use the definition provided

by Equation (3) and compare positions of similar magnitude both to the left and the right

of the disclosure threshold. We will refer to positions with a maximum of 0.4 as secretive

positions and those with a maximum of 0.5 as non-secretive positions.12 Panel A of Table 6

depicts the average values of several investor and stock characteristics for both position

groups and the differences between them.

As shown in Figure 2, the first variable of interest is a dummy that indicates whether

the position maximum equals the overall maximum reached by the investor. In line with

12Not all positions with a maximum of 0.4 are driven by investors’ avoidance of disclosure. For somepositions a maximum of 0.4 is simply optimal, irrespective of the disclosure threshold. Importantly, though,this fact works against finding any differences in characteristics between the position groups just belowand just above the disclosure threshold.

21

the graphical representation in Figure 2, almost 40% of positions with a maximum of 0.4

originate from investors with the same overall maximum. The corresponding proportion in

the 0.5 bin is only 11%. Economically speaking, a significant proportion of positions that

remain just below the disclosure threshold originate from investors who remain below it

for the entire sample period. This persistence by investors in their decision not to disclose

lends support for the idea that some investors follow a general policy of non-disclosure of

short positions.

Next, we investigate whether persistent avoidance of disclosing short positions is also

related to investors’ general opaqueness across different dimensions. First, hedge funds

are generally considered to be more opaque than other investors. For example, Agarwal,

Jiang, Tang and Yang (2013) found that hedge funds seek confidentiality in their quarterly

long holdings more often than other investors when filing with the SEC. Our second proxy

associated with opacity is whether the investor is domiciled in a tax haven country as

defined by the OECD (2000). Moreover, some investment firms generally avoid disclosure

of company and security-related information as much as possible. The FactSet ownership

database (formerly Lionshares) collects data from public disclosures worldwide. We exploit

the rich coverage of this database, but posit that institutional investors with no public

ownership record – and consequently no entry in the FactSet database – tend to follow a

strategy of opaqueness. Also, institutional investment managers that are active in U.S.

financial markets are obliged to disclose their quarterly holdings with the SEC. However,

under certain conditions investment managers may use an exemption under Regulation

D to offer and sell securities without having to register the offering with the SEC. In

most cases, those private funds are restricted to accredited investors, i.e. high net worth

individuals or institutional investors.13 To determine whether a fund engages in private

13Regulation D includes three SEC rules — Rules 504, 505 and 506 — that institutional investorscan draw on to sell securities in unregistered offerings. Each rule has specific requirements that thefund must meet. While Rule 504 merely restricts the amount of securities offered to 1 million USD,the other two rules are more stringent and require that the funds’ shareholders are wealthy individualinvestors or trusts directed by specialist managers. A more detailed description of the requirementsare documented in the following investor bulletin: https://www.investor.gov/additional-resources/news-

22

placements or unregistered offerings, we search SEC’s Edgar database for Form D filings

and match them to our sample using investor names.

As evident from Panel A of Table 6, compared to non-secretive positions just above the

publication threshold, the secretive positions originate to a larger degree from hedge funds.

The share of positions from investors registered in a tax haven is also rather low overall,

but there are distinct differences to the left and right of the disclosure threshold. Investors

registered in tax haven countries account for 2.17% of non-secretive positions, but for

6.89% of secretive positions – more than three times as much. There are also economically

sizable differences with respect to investors having no public ownership filings and with

respect to private funds. Investors with no FactSet entry account for 17.61% of all secretive

positions; their share of non-secretive positions is only 2.65%. Similarly, private funds

account for 16.66% of all secretive positions, but their share of non-secretive positions is

only 3.40%. To test whether secretive positions differ according to the size of the investor,

we compare the value of all assets provided in the FactSet database. The natural logarithm

of total assets is slightly smaller for secretive positions than for non-secretive positions,

and the difference between the two is marginally significant at the 10% level. However,

this result should be interpreted with caution because information about portfolio assets is

not available for all investors. In particular, there is less availability for secretive positions

than for non-secretive positions – a direct outcome of the opaqueness of these investors.

Overall, compared to positions just above the publication threshold, positions just

below it are held more by hedge funds, private funds, investors domiciled in tax havens and

investors for whom no public ownership filings are on record. This suggests that secretive

behavior in short selling is part of the investors’ general strategy to conceal company- or

security-related information from the public and to remain largely out of the spotlight.

Besides these investor-specific drivers of avoidance, there may also be stock character-

istics which influence this decision to keep positions below the radar. In particular, an

alerts/alerts-bulletins/investor-bulletin-private-placements-under

23

alternative hypothesis is that investors are concerned about rising borrowing costs or even

that a position disclosure may lead to a stock recall because of action by copy-cat investors.

If this is the case, we would expect investors to avoid disclosure for stocks where the risk

of rising fees or of a recall is likely to be high. We test this borrowing cost hypothesis by

comparing secretive and non-secretive positions on various dimensions of this risk.

Liquidity is crucial for an investor who wants to cover his or her short position at

the right time or who is forced to do so by a recall. If investors avoid disclosure because

they fear a recall induced by publication, we expect avoidance to be stronger for illiquid

than for liquid stocks. Panel A of Table 6, however, shows that secretive positions do

not differ from non-secretive positions in terms of market capitalization, turnover, bid-ask

spread, or the Amihud illiquidity measure. Secretive positions are slightly more volatile

than non-secretive positions, but the magnitude is small and statistically insignificant.

Impediments to short selling arise if there is insufficient supply of lendable stocks.

Moreover, Prado et al. (2016) highlight the importance of ownership structure, in particular

ownership concentration, in the supply of stocks to borrow. In our context, an insufficient

supply of stocks to borrow may result in higher borrowing fees once copy-cat investors

follow. However, comparing positions to the left and right of the disclosure threshold

provides little support for this hypothesis. Namely, secretive positions are similar to

non-secretive positions in terms of institutional ownership – a commonly used proxy for

inventory supply – and the share of lendable stocks reported by Markit. There are also no

significant differences in terms of lender and inventory concentration.

Short squeezes are likely to occur when the percentage of shares on loan relative to loan

supply (utilization) is at a high level. If investors fear short squeezes or rising borrowing

fees after publication, they should avoid disclosure when utilization is high or, by the same

argument, when short-selling fees are already high. As evident from Table 6, secretive

positions are not significantly different from non-secretive positions in terms of the average

24

utilization and lending fee.14 We also do not find any difference in the tail of the fee

distribution as the percentage of stocks trading “on special”, i.e. with a lending fee above

100 bps, is not significantly different between the two types of positions.

D’Avolio (2002) notes that short sellers are not only concerned about the level of

fees, but also require a premium for the volatility of fees, and empirical support for

this hypothesis is provided by Engelberg, Reed and Ringgenberg (2017). Stocks with a

high variance in borrowing fees are associated with higher risk and publicizing a short

position for these stocks might trigger an increase in fees. Following Engelberg, Reed and

Ringgenberg (2017), we calculate different state variables that predict future loan volatility.

The proxies include the standard deviation of loan fees and utilization measured over the

past year and two tail risk measures on loan fees and utilization. The tail risk measures

are defined as the 99th percentile of a normal distribution using the estimated mean and

standard deviation over the past year. Similar to our previous findings, none of the four

short-selling risk proxies differ significantly for secretive and non-secretive positions.15

Taking the results together, we find no evidence that stock liquidity, inventory supply,

concentration of supply, utilization, borrowing fees or short-selling risk are associated with

avoidance by the short sellers of crossing the publication threshold. The avoidance effect,

however, is related to investor characteristics, and particularly to investors’ general policy

of opaqueness.

14We employ the expected borrowing fee for a hedge fund on a given day as defined by Markit. Theyderive a rate using their proprietary analytics and data set. The calculation uses both securities borrowingcosts between agent lenders and prime brokers as well as rates from hedge funds to produce an indicationof the current market rate.

15It is important to note that the size of a short position is also determined endogenously by the costsassociated with borrowing and short selling the stock as shown in Section III.C. In particular, smallpositions may be small (i.e., below the radar) because the stock is difficult to short (e.g., low supply, highfees, high short-selling risk) irrespective of the publication threshold. Consequently, we even expect thatpositions just below the radar will be to some extent associated with higher (but not abnormally higher)frictions than positions just above the publication threshold. However, we do not account for this patternin our tests given that even without adjusting our null hypothesis to a positive value, we do not findeconomically and statistically significant differences between secretive and non-secretive positions in termsof the borrowing costs hypothesis.

25

B. Are secretive investors better informed?

One possible explanation for investors concealing their positions is that they wish

to protect their private information or their proprietary investment strategies. We now

explore this hypothesis by comparing the performance of positions to the left and the right

of the disclosure threshold. If non-disclosure is associated with superior information, we

expect that stocks with secretive short positions to have lower risk-adjusted returns than

stocks with similar but disclosed short positions.

To compare the performance of the two position groups, we form a portfolio of stocks

for each group, weighted by the number of positions with a maximum of 0.4 and 0.5,

respectively. A stock is included in the portfolio if the investor concerned established

a short position greater than 0.20% the day before, and a stock is excluded from the

portfolio if the investor’s position fell below 0.20% the day before. This timing convention

is conservative in that it assumes investors to be trading at the end of each day. We

estimate risk-adjusted returns (alphas) of the two portfolios employing different factor

models including the Capital Asset Pricing Model (CAPM) (Sharpe, 1964; Lintner, 1965),

the Fama and French (1993) three-factor model, and the Carhart (1997) four-factor model.

To estimate standard errors, we follow Newey and West (1987), with the lag length being

selected according to the optimal lag-selection algorithm proposed by Newey and West

(1994).

The results of the performance comparison are depicted in Table 6, Panel B. As is

evident from the alpha estimates, short positions with a maximum of 0.4 have on average

a negative alpha of -4.12 to -4.74 bps per day, which is statistically significant across

all three factor models. In contrast, short positions with a maximum value of 0.5 have

alphas that are not significantly different from zero at any conventional level. Accordingly,

secretive positions on average outperform non-secretive positions by around 5 bps per

day. This difference in mean returns is robust across all factor models and statistically

significant at the 1% level. Since a considerable share of positions remaining just below

26

the disclosure threshold originate from investors who never disclose their positions, our

second step is to narrow down the portfolio to the positions of this subgroup. If secrecy is

associated with having better information about a stock’s future value, we expect these

very secretive positions, as defined by the position and investor maximum, to yield even

better performance. Indeed stocks shorted by these investors show an even stronger price

decline with alphas ranging between -4.79 and -5.58 bps per day, although these results

are statistically weaker due to a substantially reduced sample of positions. Overall, these

findings suggest that secretive positions have an informational advantage over non-secretive

positions, providing support for the private information hypothesis.

C. Secretive short positions and fundamental news

Next, we try to understand more about the sources of secretive investors’ informational

advantage. In particular, if the performance of secretive positions stems from superior

information about impending changes in companies’ fundamentals, we expect that (1)

they will tend to short stocks with future negative changes in fundamentals and (2) their

performance can be largely explained by days when news about fundamentals are released

and investors are able to incorporate this information into their decisions (Engelberg, Reed

and Ringgenberg, 2012; Engelberg, McLean and Pontiff, 2017).

To test these hypotheses, we decompose the performance of secretive positions into

two components: days on which firm-specific information releases were made, including

earnings announcements and ad-hoc corporate disclosures, and all remaining days. In their

quarterly earnings announcements, companies inform investors about their cash flows and

this news serves as one of the main sources of fundamental analysis. In addition, publicly

traded companies in Germany have a statutory obligation to disclose immediately to the

public, via ad-hoc news releases, any facts about their company that could potentially

affect the stock price.16 Ad-hoc news includes only firm-specific information relevant to

16The ad-hoc corporate disclosure regulation in Germany is very similar to the U.S. Form 8-K reportingrequirement. However, it is important to mention some differences. First, although the regulator provides

27

the value of the company, and not information relating to the conditions of the overall

market or to certain industries.

To estimate the magnitude of each component, we use the regression-based generalized

calendar-time portfolio approach proposed by Hoechle, Schmid and Zimmermann (2016)

with Driscoll and Kraay (1998) standard errors. The advantage of this approach is that it

allows multiple explanatory variables to be included in a regression, rather than requiring

us to construct portfolios for each variable of interest. Importantly, in this generalized

approach, standard errors are robust to general forms of cross-sectional dependence,

autocorrelation, and heteroscedasticity.

In Column (1) of Table 7, we first replicate the results of the calendar-time portfolio

approach shown in Panel B of Table 6. When the excess return for each position day

is used as the dependent variable and the asset-pricing factors as explanatory variables,

the Hoechle et al. (2016) estimation procedure yields exactly the same point estimates of

alphas and corresponding standard errors as the portfolio approach.17 We then decompose

the returns in those that are generated on days with fundamental news releases and those

generated on days without observed news. In particular, we set the value of the indicators

to one for all position days with a fundamental news release. To ensure that we also

capture the price reaction to fundamental news released after the trading hours, we also

flag the day following an event. The result of the decomposition is depicted in Columns (2)

to (4) of Table 7.

practical guidelines on publishing corporate ad-hoc news, the German Securities Trading Act containsno conclusive list of events that can be defined as influencing the stock price of a company. The SECis more precise in defining the categories of Forms 8-K than the German regulator. Also, in Germany,corporate ad-hoc news is much shorter and less detailed than in the U.S. Lastly, while the SEC made anumber of adjustments to the categories of ad-hoc news, no similar changes have been made recently tothe German regulation. This may be partially explained, however, by the broad definition of ad-hoc newsin the German Securities Trading Act.

17Following Hoechle et al. (2016), we estimate a weighted least squares (WLS) regression with observationweights matching the implicit weighting scheme of the calendar-time portfolio approach. This estimationprocedure not only enables us to make an exact replication of the results in Panel B of Table 6 but alsoallows a robust decomposition of the return when additional explanatory variables are included.

28

First, the analysis shows that secretive investors take short positions in stocks for which

negative earnings announcements and corporate ad-hoc news are made. In particular,

when the CAPM is used, average daily abnormal return of secretive positions amounts

to economically large −30.21 bps on earnings announcement days and even −69.41 bps

on days on which there is corporate ad-hoc news. The other two models give estimates

of a similar magnitude. This finding strengthens the evidence that secretive investors

possess information about company fundamentals that will be released in future corporate

disclosures. The magnitude of returns is sizable, given that the average return on news

days for a given stock is even significantly positive. Second, although those corporate

news days represent only 4% of trading days in a year, around 50% of the performance

of secretive positions is generated on those days, irrespective of the asset pricing model

used. The average negative return of stocks shorted by these investors is 33 (14) times

larger in absolute terms on ad-hoc news (earnings announcement) days than on non-event

days. These numbers indicate that the collection and production of private information on

company fundamentals plays a key role in the success of secretive positions. Note that the

remaining days may include other fundamental news which short sellers may trade upon

but which is not firm-specific, such as macroeconomic or industry news; this type of news

is, however, not captured in our analysis.

Altogether, evidence on the trading behavior of secretive short sellers around firm-

specific news releases suggests that their concealment of positions is associated with the

possession of superior information about firm fundamentals.

D. Why do secretive investors leave money on the table?

Our evidence so far shows that some investors consistently stay below the disclosure

threshold, which is in line with those investors following a general policy to never disclose

short positions. However, at the same time, the average risk-adjusted returns of those

investors is substantial in percentage terms. At first sight, this seems a puzzling combination

29

of findings given that positions just below are not significantly different from position just

above the threshold in terms of common measures of short-sale constraints. It raises the

question as to why investors maintain their opaqueness and leave money on the table by

not increasing what is typically a profitable short position above the publication threshold.

What are the downsides of disclosing a short position? In this section we discuss potential

explanations and how they relate to our empirical findings.

Although investors with credible information may reduce noise trader risk by disclosing

their short position (Kovbasyuk and Pagano, 2015; Ljungqvist and Qian, 2016), outside

investors can free-ride on this information without incurring the costs of research. A short

position higher above the threshold would yield on average higher profits in dollar terms,

but at the same time it would narrow the return differential to competing funds. For

mutual funds, Frank et al. (2004) have found that copy-cat funds earn after-fee returns

that are statistically indistinguishable from, and possibly even higher than, the actively

managed funds which they are copying. In the case of the EU rule on short position

disclosure, the threat of mimicking strategies is likely to be even more severe as the

disclosure lag is much shorter, being only one day rather than the 60 days required for

the mutual fund holdings studied in Frank et al. (2004). With regard to the new EU

disclosure rules, hedge fund associations have indeed expressed concern that “firms [adopt]

‘copy-cat’ trading strategies - where trading decisions are based solely upon shadowing

other participants’ actions - which may suggest that some market participants are using

the published information to replicate their competitors’ strategies” (AIMA/MFA, 2013).

In addition to the threat of diminishing competitive advantage, a public short position

might also hamper the investors’ ability to produce fundamental research. Namely, some

short sellers reported that they have been excluded from corporate events because of

their public short position (AIMA/MFA, 2013). The burgeoning literature on private

access to management provide evidence that such corporate meetings continue to be

important, despite regulation on fair disclosure (e.g., Green, Jame, Markov and Subasi,

30

2014; Bushee, Jung and Miller, 2011, 2017). In this context, selective disclosure of non-

material information during investor conferences or small-group breakout sessions is legal

and can give an advantage to individual investors by providing them with information

that complements or updates their private information.18 For investors whose superior

performance is based mainly on trading on fundamental news, having only limited access

to corporate management presents a severe impediment for their information production.

Together, these two pieces of empirical evidence - namely that secretive investors are

informed and that their superior performance comes largely from trading on fundamental

news - are consistent with both the notion that investors are maintaining their competitive

advantage and that they are protecting their sources of information. A lack of available

data prevent us from disentangling these non-mutually exclusive explanations which would

require detailed data on how investors generate their proprietary information, which they

are keen to keep private. Indeed, our evidence shows that the investors whom we are

interested in are trying to reveal as little as possible information in official filings.

V. Implications for stock prices

In this section we analyze the consequences of investors’ avoidant behavior for price

efficiency. So far, we have observed that the publication requirement for short positions

represents an impediment for some investors in terms of increasing their position, and the

evidence suggests that these secretive investors are informed. According to the literature

on limits to arbitrage, when informed investors are confronted with impediments, this

becomes evident in prices adjusting more slowly in response to private information and

in return predictability due to temporary deviation of prices from fundamental values

(Shleifer and Vishny, 1997; Gromb and Vayanos, 2010).19 In particular, in the rational

18For more details, see the comprehensive survey on this topic by Koch, Lefanowicz and Robinson(2013).

19In general, short-selling risks, such as restrictions or the costs associated with establishing a shortposition, represent one prominent set of factors that works against the elimination of mispricing. Theoretical

31

expectations model developed by Diamond and Verrecchia (1987), in which investors are

defined as either informed or uninformed traders, and as traders with prohibited short

selling and unconstrained traders, prices converge more slowly and the speed of adjustment

to private information decreases as the proportion of prohibited short sellers increases.20

Also, Jones et al. (2016) argue, using the framework of DeMarzo et al. (1998), that when

investors are presented with an impediment to trading - in this instance a disclosure

threshold - this reduces price informativeness.21

If the publication threshold represents a restriction on short selling for informed

investors, we argue that the price discovery process is slower when these secretive investors

are just below the threshold. As a consequence, we expect that these stocks will be

temporarily mis-priced and that return predictability will be particularly pronounced when

investors face this friction.

We rely on the following empirical approach to identify periods in which the disclosure

threshold may prevent secretive investors from further increasing their positions:

Secretive positionjust below threshold i,j,t

=

1 if (Position maximumi,j = 0.4) ∩ (bini,j,t = 0.4)

0 otherwise.

(5)

First, as in the previous section, we use positions that reached the bin just below the

threshold, but never crossed it during our sample period, as a proxy for secretive positions.

Second, the friction is only binding when the position is in the maximum bin of 0.4, just

studies in this area include, for example, Miller (1977), Harrison and Kreps (1978), Diamond and Verrecchia(1987), Duffie, Garleanu and Pedersen (2002), Hong and Stein (2003), and Hong, Scheinkman and Xiong(2006). However, the vast majority of empirical studies use market-wide short-selling restrictions, such asshort-selling bans, or stock-specific characteristics to test for a slower process of price discovery and forreturn predictability.

20Also, Diamond and Verrecchia (1987) argue that in a more general model, in which there are noliquidity short sales or in which there are somewhat informed as well as informed and uninformed traders,the effect of short-selling costs on price efficiency is similar to the effect of short-sale prohibitions.

21DeMarzo et al. (1998) focus on the regulators’ optimal policy in insider trading investigations. Theyargue that the investors’ welfare-maximizing outcome entails investigations of large insider trading volumes,whereas small trades remain unpunished. The result from such a policy is to discourage insiders fromtrading above a certain threshold. Although the authors focus on corporate insiders as their agents ofmain interest, their arguments and findings apply to any group of informed investors.

32

below the threshold. In other words, we flag the investor-stock pair if it has a maximum

reporting bin of 0.4 and this maximum has been reached. Note that the measure is diluted

by noise, because Equation (5) defines only a necessary, but not a sufficient condition

for the friction to be binding. During these position days we expect price adjustments

to negative information to be slower resulting in temporary overpricing and predictable

negative abnormal returns.

A. Publication threshold as a friction

To test the hypothesis of return predictability, we employ a calendar-time portfolio

approach as outlined in Section IV.B. Our first step is to form, on a daily basis, a portfolio

of stocks for which we observe a secretive position that was just below the publication

threshold on the previous day.22 We then measure the average risk-adjusted return of the

portfolio by running time-series regressions of the returns using the risk factor models

introduced in Section IV.B. If the publication threshold represents a friction to secretive

investors, we expect that those particular stocks will have future negative abnormal returns

as a result of slower price adjustment to information.

Column (3) of Panel A, Table 8, shows the average risk-adjusted returns of the portfolio

across the three factor models. Stocks for which investors have secretive positions just

below the publication threshold exhibit predictability of strong and statistically significant,

negative returns. The return predictability is robust across the CAPM, the three-factor

model and the four-factor model, with daily alpha values ranging between -5.46 and -6.13

bps; this translates into a return of around -1% per month.23

22For the majority of these stocks (82%) there is only one secretive investor. For 14% of these stocksthere are two secretive investors, while for the remaining 4%, there are between three and six secretiveinvestors. The portfolio contains on average 32 distinct stocks, with a median of 31, a minimum of 21,and a maximum of 49 stocks.

23In our data, the median time period for which a position is restricted is 16 days and the mean durationis 41 days. To reflect this and to make our results comparable with other studies, we report monthlyabnormal returns.

33

Economically, the predictability effect created by the publication threshold is substantial,

especially considering that these short-position notifications are issued almost always for

highly liquid, large-cap stocks (see Table 1 and Section II). It is important to recall that

the measure for identifying restricted investors is diluted considerably by noise. Thus, the

estimated return effect of around 5 bps per day likely represents a lower bound.

B. Placebo tests

Our finding of abnormal negative returns when short sellers hold positions just below

the disclosure threshold is consistent with the notion of slower price discovery and return

predictability originating from the publication avoidance of investors due to short-sale

impediments. To show that the return predictability effect is unique to positions just

below the disclosure threshold, we employ several placebo tests.

First, we conduct an analysis similar to the one reported in Section V.A and form

calendar-time portfolios, but now we choose hypothetical publication thresholds below and

above the true threshold:

PlaceboAi,j,t =

1 if (Position maximumi,j = p) ∩ (bini,j,t = p)

0 otherwise.

(6)

where p = 0.2, 0.3, 0.5, 0.6. Specifically, we look at positions when they reach their maxi-

mum, but when that maximum is other than 0.4. As before, we include the corresponding

stock into the placebo portfolio whenever a position fulfills the condition in Equation (6).

With this exercise, we want to rule out the possibility that the negative return reported in

the previous section is a finding that applies when short positions generally reach their

maximum. If the publication threshold truly constitutes a trading friction, we should find

the strongest return predictability for stocks with investors present in their 0.4 maximum

interval, but not for the other intervals.

34

Columns (1), (2), (4) and (5) in Panel A of Table 8 report the risk-adjusted average

returns for the other maximum reporting bins, and the same factor models are used

as in the previous analysis. Consistent with our hypothesis that binding short-sale

impediments are imposed by the publication threshold, we find that stocks with investors

in a maximum reporting bin other than 0.4 are not associated with significant negative

future returns. Even the average return for the closest non-public maximum reporting

bin, 0.3, is not significantly negative, and its economic magnitude is only one-fourth of the

return associated with the 0.4 bin. These results suggest that the return effect is unique

to stocks with investors who hold a position just below the disclosure threshold and that

it cannot be generalized to other positions.

Another potential concern is that the result in Column (3) of Panel A may be driven

entirely by informed trading in secretive positions rather than by informed investors being

constrained by the threshold. To determine the constraining effect of the threshold, we

compare the returns of the same investor-stock pair when the disclosure threshold is

binding and non-binding. That is, we look at positions with a maximum bin of 0.4 but

during periods below the maximum:

PlaceboBi,j,t =

1 if (Position maximumi,j = 0.4) ∩ (bini,j,t < 0.4)

0 otherwise.

(7)

If the return just below the disclosure threshold is driven solely by informed trading, we

would expect a return of similar magnitude both inside and outside the maximum bin

phase. As before, we include the stock in the placebo portfolio whenever there is a short

position that fulfills the condition in Equation (7).

The average risk-adjusted return of this portfolio is reported in the shaded column in

Panel B of Table 8. Outside the maximum bin phase the average alpha is negative but not

statistically different from zero. This result suggests that the stock return predictability

that arises when a secretive investor is just below the publication threshold cannot be

35

entirely explained by informed trading in this particular stock. The findings hold across

all factor models and are in line with the hypothesis that there is a slower process of price

discovery because investors are avoiding crossing the publication threshold.

In this context we can also use the other reporting bins as a comparison. Is the

predictability generally stronger inside the maximum bin phase than in the phase outside

the maximum? Interestingly, none of the other maximum reporting bins show a pattern

similar to the interval just below the disclosure threshold. Namely, only for positions with

a maximum of 0.4 can we observe that the return in the maximum bin is negative and

lower than the return of the same positions below the maximum bin. For all other bins,

the average return below the maximum bin is even more negative than the return in the

maximum bin.

Overall, we find negative risk-adjusted returns for secretive positions when the investor

is just below the disclosure threshold. There is no negative return predictability when we

choose various hypothetical publication thresholds below and above the true one. Moreover,

within investor-stock pairs, subsequent negative returns occur mainly when the secretive

position is just below the publication threshold and the constraint originating from it is

binding. Altogether, these results suggest that the evasive behavior of short sellers in

response to the disclosure rule leads to slower price discovery.

VI. Robustness Tests

In this section we briefly summarize the various robustness checks which we carried

out on our analyses. For a detailed description of all additional tests and their results, see

the Internet Appendix.

First, we provide a more detailed description of the distribution pattern of reported short

positions when we include the second digit after the decimal point. We offer an intuition as

to why the frequency of short positions spikes around the reporting thresholds, resulting in

36

a u-shaped pattern within each reporting interval. As previously discussed in Footnote 8,

these mechanically generated spikes posit a challenge to conventional discontinuity tests

as used by Degeorge et al. (1999). Although such a test is not well-suited to our setting, it

still provides evidence that supports the notion of disclosure avoidance.

Second, we conduct different sensitivity analyses to whether investors are actually

avoiding crossing the disclosure threshold. In Section III we document how avoidance is

particularly pronounced when investors approach the publication threshold from below

and for the first time. Specifically, we use a sample split into positions that are at their

record high and positions that are below their record high. As shown in the Internet

Appendix, splitting the sample another way by dividing it simply into previously increased

and previously decreased positions, gives comparable results. This measure is simpler but

noisier given that it is based solely on the investor’s last change of the position instead of

the entire position history.

Additionally, we explore two alternative hypotheses related to the avoidance effect.

First, we investigate whether the effect we found comes from investors being hesitant to

cross the threshold but eventually crossing it after a delay, rather than avoiding doing

so altogether. Second, we examine whether investors jump immediately to abnormally

high positions after crossing the disclosure threshold. The results of our analyses support

neither the hesitance hypothesis nor the large jump hypothesis.

We also conduct a series of sensitivity analyses related to the return predictability

discussed in Section V. We apply several modifications to our calendar-time portfolio

approach. The effect is robust to excluding penny stocks or requiring the duration to be at

least five trading days in the 0.4 bin for the publicaton threshold to be defined as binding.

It is similarly robust when we weight the stocks equally rather than by the number of

positions, and when we use European, rather than German, factor portfolios.

37

VII. Conclusion

Using both public and confidential short-sale notifications, we study how a disclosure

threshold for short positions affects investors’ behavior and security prices. We show

that a considerable share of short sellers seek to avoid crossing the disclosure threshold,

which effectively represents a short-sale impediment for these investors. This publication

avoidance is related to the investors’ general strategy of opaqueness and informed trading

on stock-specific fundamental news. When the short-sale constraint imposed by the

disclosure threshold is potentially binding, stocks subsequently exhibit a negative abnormal

return, consistent with prices adjusting more slowly to private information. These findings

suggest that short sellers’ evasive behavior in response to transparency regulation imposes

a negative externality on the informational efficiency of stock prices.

It is worth noting that the disclosure rule may also have other implications beyond the

effects documented in this paper. Our analysis shows that position disclosure discourages

informed market participants from fully exploiting their information, and that it thereby

reduces price discovery in the market. In the spirit of Grossman and Stiglitz (1980),

the short-sale disclosure rule may also diminish the investors’ incentive to collect and

process information in the first place, resulting in an even greater reduction in stock price

efficiency. Conversely, improvements in liquidity and financial stability as a result of

greater transparency could be argued to have positive effects on the functioning of stock

markets (DeMarzo et al., 1998; Jones et al., 2016). Overall, our insights contribute to

the ongoing debate on the design of position disclosure rules and suggest that greater

transparency should be used with caution.

38

Appendix A. Sample construction

We obtain public and confidential short-sale notifications from the German Federal

Financial Supervisory Authority (BaFin). BaFin’s notification data include the position

holder’s name, address and country, the name and ISIN code of the stock shorted, the net

short position in number of equivalent shares and as a percentage of share issued capital,

and the position and reporting date. To construct a panel of investors’ short positions in

different stocks we first account for the ISIN changes of the stocks. Next, we convert the

original short-sale notifications into reporting intervals of 10 basis points by rounding down

to the first decimal place, as we described in Section I.A. We delete duplicate notifications

(i.e., with the same information in all variables). For a few days, we find multiple short-sale

positions for the same investor-stock pair. For these days, we keep the most recent position

(as identified by the reporting date), which is likely to represent corrections of the previous

values. We omit some stale positions, which occur disproportionately in the first days

after the regulation was put in place. We define a stale position as a position which has

been reported only once, has never changed, and is still open after 600 days.24 From the

notifications, we construct a large daily panel of investors’ short positions in different

stocks. Finally, we identify trading days from the official trading calendar of Frankfurt

Stock Exchange.

We merge the BaFin panel of short positions with stock-level data (static characteristics

and time-series data, such as price, return, and market value data) from Thomson Reuters

Datastream using current ISIN codes. We only consider domestic common equity in

the regulated market. Thus, we keep stocks categorized by Datastream as domiciled in

Germany (variable GEOG = 30), equity (variable TYPE = EQ) and major issuance

(variable MAJOR = Y). We exclude preferred stocks, depositary receipts, real estate

investment trusts, and stocks with other special features by screening the names of the

stocks. We filter out all stock-day observations when a stock is no longer trading (variable

24Other cut-off points, such as 500 or 250 days, lead to similar results.

39

P#T = missing value). We only keep shares admitted to trading on the German regulated

market, using the information from the MiFID database of ESMA.

Noting Ince and Porter’s (2006) concerns about return data from Datastream, we apply

the following filters for daily return data, as proposed by Karolyi et al. (2012) and Griffin

et al. (2010): The return (rt = (RIt/RIt−1) − 1, where RI is the dollar return index)

is set to missing if the current or lagged total return index (RI) is below 0.01. If rt or

rt−1 > 100% and (1 + rt−1)(1 + rt)− 1 < 20%, then both rt and rt−1 are set to missing.

Any return greater than 200% is also set to missing.

To gather additional information on the position holders, we manually research the

corresponding unique investor identification number from FactSet, using the position

holder’s name, address, and country information from the BaFin notification data. For

the identified investors, we then obtain investor characteristics such as investor type.

Securities lending data are obtained from Markit Securities Finance Buyside Analytics

Data Feed (market area equals DE Equity) and merged by using the ISIN.

We obtain the risk-free rate (RF), the market excess return (MKTRF), and the returns

on the factor portfolios small-minus-big (SMB), high-minus-low (HML), and winner-minus-

loser (WML) for the German stock market from Andrea Frazzini’s data library, provided

through AQR’s website.25

The detailed computation and data sources of all variables used in the analysis are

provided in Table A.1.

25See: www.aqr.com/library/data-sets/quality-minus-junk-factors-daily/data

40

Table A.1Definitions of variables

Variable: Description: Source:

Amihud illiquidity |r|/(V C × 1000× P )× 106, where r is the USD return,and V C is the consolidated number of shares tradedacross all German exchanges (in thousands), and P isthe price in USD (Amihud, 2002). We winsorize theAmihud illiquidity ratio at 1% at the upper tail and thenaverage it over the last 250 trading days, requiring atleast 100 valid observations.

Datastream

Bid-ask spread (PA− PB)/P , expressed in percentage terms, where Pis the stock’s price, PA is the ask price, and PB is thebid price, all provided by Datastream. We winsorize thebid-ask spread at 1% at the upper tail and then averageit over the last 250 trading days, requiring at least 100valid observations.

Datastream

Book-to-market ratio Calculated as PTBV −1, where PTBV is the price-to-bookvalue provided by Datastream. The book-to-market ratiois set to missing if it is below 0.

Datastream

Daily turnover V C/NOSH, expressed in percentage terms, where V Cis the consolidated number of shares traded across allGerman exchanges (in thousands), and NOSH are thecompanies’ shares outstanding (in thousands).

Datastream

Dummy: “on special” Dummy variable that equals 1 if the indicative fee (p.a.)to borrow a stock is above 100 bps (Prado et al., 2016).

Markit

Dummy: Bank Dummy variable that equals 1 if the investor is a bank. BaFin, own re-search

Dummy: European holder Dummy variable that equals 1 if the investor is domiciledin a European country.

BaFin

Dummy: Earnings an-nouncement

Event dummy variable that equals 1 if there is an earningsannouncement for that specific stock on that day or theprevious day.

Datastream

Dummy: Ad-hoc news Event dummy variable that equals 1 if there is ad-hocnews for that specific stock on that day or the previousday.

DGAP (part ofthe EQS Group)

Dummy: Futures or listedoptions

Dummy variable that equals 1 if futures or listed optionsexist for the underlying stock.

Datastream

Continued on next page

41

Table A.1 – Continued from previous page

Variable: Description: Source:

Dummy: Hedge fund Dummy variable that equals 1 if the investor is definedby FactSet as a hedge fund or has no entry in Factset(similar to the selection criterion of Brunnermeier andNagel (2004)).

BaFin, FactSet

Dummy: No FactSet entry Dummy variable that equals 1 if the investor is notincluded in the FactSet Ownership database. The owner-ship information in FactSet originates from public filings,so a non-appearance is indicative of no public record.

FactSet

Dummy: Private fund Dummy variable that equals 1 if the investor files FormD with the SEC and seeks private placements underRegulation D. Private placements are not subject to someof the laws and regulations designed to protect investors,such as the comprehensive disclosure requirements thatapply to registered offerings.

EDGAR by SEC

Dummy: Tax haven Dummy variable that equals 1 if the investor is domiciledin a tax haven as defined by OECD (2000)

BaFin, OECD

Dummy: US holder Dummy variable that equals 1 if the investor is domiciledin the United States.

BaFin

Fee tail risk The 99th percentile of a normal distribution using theestimated mean and standard deviation of the indicativefee (see below) over the last 250 trading days (Engelberg,Reed and Ringgenberg, 2017). We requiring at least 100valid observations for mean and standard deviation com-putation: mean of fee + 2.33× standard deviation of fee

Markit

Share of lendable stocks Ratio, expressed in percentage terms, between lendablevalue and the market capitalization of the stock. We useMarkit’s lendable value adjusted for inventory which isnot being actively made available for lending.

Markit

Indicative fee The expected securities borrowing cost, in percentageper year terms, for a hedge fund on a given day, whichis derived by Markit.

Markit

Institutional ownership Percentage of shares held by institutional investors inthe previous quarter.

FactSet

Inventory concentration Herfindahl–Hirschman Index (HHI) scaled between 0 and100 to measure inventory concentration.

Markit

Lender concentration Herfindahl–Hirschman Index (HHI) scaled between 0 and100 to measure lender concentration.

Markit

Market value Market capitalization (in USD million) provided by theDatastream variable MV .

Datastream

Continued on next page

42

Table A.1 – Continued from previous page

Variable: Description: Source:

Return volatility Standard deviation of return computed over the last 250trading days, requiring at least 100 valid observations.Expressed in percentage terms.

Datastream

Short interest Ratio, expressed in percentage terms, between the valueof securities on loan (with dividend trading and financingtrades removed) and the market capitalization of thestock.

Markit

Standard deviation of fee Standard deviation of the indicative fee (see above) overthe last 250 trading days, requiring at least 100 validobservations.

Markit

Standard deviation of uti-lization

Standard deviation of utilization (see below) over thelast 250 trading days, requiring at least 100 valid obser-vations.

Markit

Total assets Market capitalization (in USD million) of the investor’slong holdings as provided by FactSet.

FactSet

Utilization Percentage of actively lendable securities in lending pro-grams which are currently out on loan, calculated as thevalue of assets on loan from lenders divided by the activelendable value

Markit

Utilization tail risk The 99th percentile of a normal distribution usingthe estimated mean and standard deviation of utiliza-tion (see above) over the last 250 trading days (En-gelberg, Reed and Ringgenberg, 2017). We requireat least 100 valid observations for mean and stan-dard deviation computation and we limit utilizationtail risk to 100%: min(mean of utilization + 2.33 ×standard deviation of utilization; 100%)

Markit

43

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Hong, H., Scheinkman, J. and Xiong, W. (2006), ‘Asset float and speculative bubbles’,The Journal of Finance 61(3), 1073–1117.

46

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47

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48

(a) Overall sample

Public disclosure threshold

010

2030

4050

Freq

uenc

y (in

%)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Reporting bins

(b) Sample split

Public disclosure threshold

010

2030

4050

Freq

uenc

y (in

%)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Reporting bins

Positions below their record highPositions at their record high

Figure 1.Distribution of open short positionsThis figure shows the distribution of days with open short positions (investor-stock-day observations)across reporting intervals. Reporting intervals are in 10 bps steps, starting from 0.2%. Positions above0.2% but below 0.5% are reported to the regulator but not disclosed to the public; positions of 0.5% andhigher are disclosed to the public. Figure 1(a) shows the relative frequency of days with an open positionfor each interval for the overall sample. Figure 1(b) reports the relative frequency separately for shortpositions at their record high and for positions below their record high. Reporting intervals greater than1.5% are truncated for readability. The sample contains all German domestic equity in the regulatedmarket from November 5, 2012, to March 31, 2015.

49

Public disclosure threshold

05

1015

2025

Freq

uenc

y (in

%)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Position maximum

Position maximum ≠ investor's maximumPosition maximum = investor's maximum

Figure 2.Distribution of open short positions according to the maximum bin reachedThis figure shows the distribution of short position days (investor-stock-day observations) according tothe maximum bin reached by the position. Positions that never cross the disclosure threshold (positionswith a maximum of 0.4) account for the largest group (22.8%) of short position days. The red coloringindicates the share of positions where the position maximum is also the investor’s maximum. Reportingintervals greater than 1.5% are truncated for readability. The sample contains all investors with shortposition notifications in German domestic equity in the regulated market from November 5, 2012, toMarch 31, 2015.

50

Table 1Summary statistics:Stocks with short position notifications/disclosures vs. all stocksThis table shows summary statistics for the various stock characteristics of stocks with at least one shortposition notification and for all stocks in the regulated market. Short positions must be reported to theregulator if the position is greater than or equal to 0.2% of the issued share capital of the company shortedand must be publicly disclosed if the position is greater than or equal to 0.5%. Column (1) contains thesummary statistics for the entire population of stocks in the German regulated market, Column (2) reportsstocks that have at least one public or confidential short position notification, Column (3) includes stockswith at least one public short position, and Column (4) refers to stocks with at least one confidential butno public short position notification. The table reports time-series averages of cross-sectional medians.The sample consists of common equity in the German regulated stock market from November 5, 2012,until March 31, 2015. For details on calculation of the stock characteristics, see Table A.1.

(1) (2) (3) (4)

Stocks withAll stocks short position notifications/disclosures

All Public Confidential

Share of stocks 19.9% 8.3% 11.6%

Median values:

Market value (millions USD) 102.1 2,225.3 1,986.6 2,401.2Book-to-market ratio 0.65 0.53 0.55 0.52Daily turnover (%) 0.12 0.32 0.37 0.29Amihud illiquidity 0.456 0.004 0.004 0.004Bid-ask spread (%) 3.10 0.64 0.65 0.63Return volatility (%) 2.47 1.96 2.16 1.85Institutional ownership (%) 3.86 29.21 29.85 29.00Share of lendable stocks (%) 2.42 13.59 12.87 14.31Indicative fee (p.a. %) 0.66 0.53 0.56 0.51

51

Table

2Sum

mary

stati

stic

sT

his

table

conta

ins

sum

mar

yst

atis

tics

for

the

inve

stor

-sto

ckp

anel

wit

hop

ensh

ort

pos

itio

nnot

ifica

tion

sab

ove

0.2%

ofth

eis

sued

shar

eca

pit

al.

The

sum

mar

yst

atis

tics

incl

ude

the

num

ber

ofob

serv

atio

ns

(N),

mea

n,

stan

dar

ddev

iati

on(S

D),

and

the

10th

,25

th,

50th

,75

than

d90

thp

erce

nti

les.

The

sam

ple

consi

sts

ofco

mm

oneq

uit

yin

the

Ger

man

regu

late

dst

ock

mar

ket

from

Nov

emb

er5,

2012

,unti

lM

arch

31,

2015

.F

ordet

ails

onth

eca

lcula

tion

ofth

eva

riab

les,

see

Tab

leA

.1.

Per

centi

les:

Var

iab

leN

Mea

nSD

10th

25th

50th

75th

90th

Mar

ket

valu

e(m

illion

sU

SD

)278,6

49

5,4

43.3

711,8

65.4

5323.6

2845.1

02,1

13.8

15,3

42.1

310,4

67.8

5B

ook

-to-

mar

ket

rati

o276,1

47

0.8

93.2

10.2

60.3

70.5

50.8

61.3

0D

aily

turn

over

(%)

273,5

36

0.5

00.3

10.1

80.2

60.4

30.7

10.9

2A

mih

ud

illiquid

ity

273,5

36

0.0

71.0

10.0

00.0

00.0

00.0

10.0

3B

id-a

sksp

read

(%)

276,8

60

0.7

30.5

00.3

40.4

20.6

40.8

91.2

0R

eturn

vola

tility

(%)

276,8

60

2.2

50.9

21.4

21.7

12.0

82.6

13.0

6In

stit

uti

onal

own

ersh

ip(%

)278,4

75

34.3

717.5

013.0

821.9

331.5

045.8

161.2

1D

um

my:

Fu

ture

sor

list

edop

tion

s(%

)278,6

49

38.3

9Sh

ort

inte

rest

(%)

278,5

70

4.3

53.6

50.7

81.6

03.3

26.2

29.0

8U

tiliza

tion

(%)

278,6

30

33.3

029.5

83.7

39.0

022.9

650.1

884.1

6In

dic

ativ

efe

e(%

p.a

.)278,5

43

2.0

45.7

10.5

00.5

00.5

01.0

06.0

0D

um

my:

Hed

gefu

nd

(%)

278,6

49

76.2

2D

um

my:

Ban

k(%

)278,6

49

1.8

1D

um

my:

Euro

pea

nhol

der

(%)

278,6

49

47.4

1D

um

my:

US

hol

der

(%)

278,6

49

45.3

5D

um

my:

Tax

hav

en(%

)278,6

49

6.1

4T

otal

asse

ts(m

illion

sU

SD

)206,8

23

78,3

95

232,6

84

72

755

4,3

6730,4

66

134,2

92

Dum

my:

No

Fac

tSet

entr

y(%

)278,6

49

9.7

3D

um

my:

Pri

vate

fund

(%)

217,0

36

8.3

6

52

Table

3P

robabilit

yof

ash

ort

posi

tion

incr

ease

This

table

show

sth

ees

tim

ated

pro

bab

ilit

yof

incr

easi

ng

ash

ort

pos

itio

n,

condit

ional

oncu

rren

tly

hav

ing

ap

osit

ion

ina

spec

ific

rep

orti

ng

bin

.Shor

tp

osit

ions

are

rep

orte

din

bin

sof

10bp

s,st

arti

ng

from

0.2%

ofth

eis

sued

shar

eca

pit

alof

the

com

pan

ysh

orte

d.

Pos

itio

ns

abov

e0.

2%b

ut

bel

ow0.

5%are

rep

ort

edto

the

regula

tor

but

not

dis

close

dto

the

public;

posi

tions

of

0.5

%and

ab

ove

are

dis

close

dto

the

public.

The

0.2

bin

den

ote

sth

ebin

rangi

ng

from

0.20

%to

0.29

%,

the

0.3

bin

from

0.30

%to

0.39

%,

the

0.4

bin

from

0.40

%to

0.49

%,

and

sofo

rth.

Rep

orti

ng

bin

sgr

eate

rth

anor

equal

to1.

0%ar

esu

mm

ariz

edin

one

grou

p.

Inad

dit

ion

toth

epro

bab

ilit

ies

ofin

crea

sing

ash

ort

pos

itio

n,

the

table

also

dis

pla

ys

the

diff

eren

cein

pro

bab

ilit

yof

row

(3)

rela

tive

toro

w(k

),th

e0.4

rep

ort

ing

bin

just

bel

owth

ep

ub

lica

tion

thre

shold

(shad

edin

gra

y),

and

thep-v

alu

efo

rth

ediff

eren

ces

inm

ean

s.T

he

tab

ledis

pla

ys

pro

bab

ilit

ies

for

the

over

all

sam

ple

and

for

two

subsa

mple

s,w

her

ew

esp

lit

the

sam

ple

into

shor

tp

osit

ion

sat

thei

rre

cord

hig

han

dp

osit

ion

sb

elow

thei

rre

cord

hig

h.

*,**

,an

d***

ind

icate

signifi

can

ceat

the

10%

,5%

,and

1%

leve

ls,

resp

ecti

vely

.

Posi

tions

Posi

tions

Ove

rall

at

thei

rre

cord

hig

hb

elow

thei

rre

cord

hig

hP

robab

ilit

yD

iffer

ence

Pro

babilit

yD

iffer

ence

Pro

babilit

yD

iffer

ence

Bin

ofin

crea

sero

w(3

)-

(k)

p-v

alu

eof

incr

ease

row

(3)

-(k

)p-v

alu

eof

incr

ease

row

(3)

-(k

)p-v

alu

e

undis-

closed

(1)

0.2

0.36

4−

0.01

0(0

.469)

0.3

47

−0.

010

(0.5

81)

0.3

80

−0.

001

(0.9

47)

(2)

0.3

0.39

1−

0.03

7**

(0.0

14)

0.4

23

−0.0

85***

(0.0

00)

0.3

60

0.018

(0.4

16)

(3)

0.4

0.35

40.3

38

0.3

79

disclosed

(4)

0.5

0.40

8−

0.05

4***

(0.0

07)

0.5

14

−0.

176***

(0.0

00)

0.3

02

0.076***

(0.0

09)

(5)

0.6

0.47

6−

0.12

2***

(0.0

00)

0.5

62

−0.2

25***

(0.0

00)

0.3

95

−0.

017

(0.6

24)

(6)

0.7

0.44

0−

0.08

6***

(0.0

01)

0.6

04

−0.2

66***

(0.0

00)

0.3

08

0.071**

(0.0

48)

(7)

0.8

0.44

9−

0.09

5***

(0.0

01)

0.6

48

−0.3

10***

(0.0

00)

0.2

66

0.113***

(0.0

06)

(8)

0.9

0.47

7−

0.12

3***

(0.0

00)

0.7

02

−0.3

64***

(0.0

00)

0.2

79

0.100**

(0.0

32)

(9)≥

1.0

0.47

4−

0.12

0***

(0.0

00)

0.6

82

−0.3

45***

(0.0

00)

0.2

75

0.103***

(0.0

00)

53

Table

4D

ura

tion

inre

port

ing

bin

sT

his

table

show

sth

eav

erag

eti

me

spen

tin

each

rep

orti

ng

bin

.Shor

tp

osit

ions

are

rep

orte

din

bin

sof

10bps,

star

ting

from

0.2%

ofis

sued

shar

eca

pit

alof

the

com

pany

short

ed.

Posi

tions

ab

ove

0.2

%but

bel

ow0.5

%are

rep

ort

edto

the

regula

tor

but

not

dis

close

dto

the

public;

posi

tions

of

0.5

%and

hig

her

are

dis

clos

edto

the

public.

The

0.2

bin

den

otes

the

bin

rangi

ng

from

0.20

%to

0.29

%,

the

0.3

bin

from

0.30

%to

0.39

%,

the

0.4

bin

from

0.40

%to

0.49

%,

and

sofo

rth.

Rep

orti

ng

bin

sgr

eate

rth

anor

equal

to1.

0%ar

esu

mm

ariz

edin

one

grou

p.

The

table

rep

orts

the

mea

nan

dm

edia

nnum

ber

oftr

adin

gday

ssp

ent

inea

chre

por

ting

bin

(Pan

els

Aan

dB

,re

spec

tive

ly).

Inaddit

ion,

itd

isp

lays

the

diff

eren

cein

mea

n(m

edia

n)

dura

tion

of

row

(3)

rela

tive

toro

w(k

),th

e0.4

rep

ort

ing

bin

just

bel

owth

ep

ublica

tion

thre

shold

(shad

edin

gra

y),

an

dth

ep-v

alu

efo

rdiff

eren

ces

inm

eans

(med

ian

s).

Eac

hpan

eldis

pla

ys

pro

bab

ilit

ies

for

the

over

all

sam

ple

and

for

two

subsa

mple

s,w

her

ew

esp

lit

the

sam

ple

into

shor

tp

osit

ions

atth

eir

reco

rdhig

han

dp

osit

ion

sb

elow

thei

rre

cord

hig

h.

*,**

,an

d***

ind

icate

signifi

can

ceat

the

10%

,5%

,and

1%

leve

ls,

resp

ecti

vely

.

Panel

A:

Mean

dura

tion

wit

hin

rep

ort

ing

bin

intr

ad

ing

days

Posi

tions

Posi

tions

Ove

rall

at

thei

rre

cord

hig

hb

elow

thei

rre

cord

hig

hM

ean

Diff

eren

ceM

ean

Diff

eren

ceM

ean

Diff

eren

ceB

indura

tion

row

(3)

-(k

)p-v

alu

edu

rati

on

row

(3)

-(k

)p-v

alu

ed

ura

tion

row

(3)

-(k

)p-v

alu

e

undis-

closed

(1)

0.2

18.3

2.2**

(0.0

19)

22.3

3.6**

(0.0

12)

14.0

−2.4

**

(0.0

39)

(2)

0.3

17.0

3.6***

(0.0

00)

21.3

4.6***

(0.0

02)

12.6

−1.0

(0.3

76)

(3)

0.4

20.6

26.0

11.7

disclosed

(4)

0.5

14.3

6.2***

(0.0

00)

16.7

9.3***

(0.0

00)

11.8

−0.1

(0.9

19)

(5)

0.6

13.7

6.8***

(0.0

00)

17.4

8.5***

(0.0

01)

9.9

1.8

(0.2

38)

(6)

0.7

13.3

7.3***

(0.0

00)

15.8

10.

1***

(0.0

01)

11.2

0.5

(0.7

72)

(7)

0.8

13.6

7.0***

(0.0

01)

17.2

8.8***

(0.0

08)

10.0

1.6

(0.3

79)

(8)

0.9

11.9

8.7***

(0.0

00)

14.1

11.

8***

(0.0

02)

9.7

2.0

(0.3

55)

(9)≥

1.0

12.6

8.0***

(0.0

00)

16.6

9.4***

(0.0

00)

8.6

3.1***

(0.0

04)

Continued

onnextpage

54

Tab

le4

–Continued

from

previouspage

Panel

B:

Media

ndura

tion

wit

hin

rep

ort

ing

bin

intr

ad

ing

days

Posi

tions

Posi

tion

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undis-

closed

(1)

0.2

61***

(0.0

04)

73***

(0.0

00)

50

(0.1

82)

(2)

0.3

61***

(0.0

03)

82***

(0.0

07)

50

(0.8

24)

(3)

0.4

710

5

disclosed

(4)

0.5

52***

(0.0

00)

73***

(0.0

04)

41

(0.3

64)

(5)

0.6

52***

(0.0

00)

64***

(0.0

00)

41

(0.3

31)

(6)

0.7

43***

(0.0

00)

46***

(0.0

00)

41

(0.2

78)

(7)

0.8

43***

(0.0

00)

55***

(0.0

00)

32***

(0.0

09)

(8)

0.9

43***

(0.0

00)

55***

(0.0

00)

32*

(0.0

53)

(9)≥

1.0

43***

(0.0

00)

55***

(0.0

00)

32***

(0.0

00)

55

Table 5Probability of increase: Regression approach with fixed effectsThis table shows estimates from the linear probability model

yi,j,t+1 = α0 + β1 Just below thresholdi,j,t +∑k

βk k bini,j,t + γ′ Xi,t + αt + εi,j,t+1,

yi,j,t+1 = α0 + β1 Just below thresholdi,j,t +∑k

βk k bini,j,t + αi,t + αj,t + εi,j,t+1.

with yi,j,t+1 = 1 (bini,j,t > bini,j,t−1). Just below threshold is equal to 1 if investor j has a short position instock i in the bin 0.4. k bini,j,t−1 is equal to 1 if investor j has a short position in stock i in the bin k. Theomitted benchmark bin is 0.3, i.e. k ∈ {0.2, 0.5, 0.6+}, where 0.6+ indicates position bins greater or equalto 0.6. Xi,t represents a vector of control variables related to short selling activity. αt, αi,t, and αj,t denoteday, stock-day, and investor-day fixed effects, respectively. Panel A reports the regression coefficientsPanel B shows the differences in probability of increase between the bin just below the disclosure thresholdand the neighboring bins. The unconditional probability of increasing a short position to enter the nextbin (estimated by the sample average of yi,j,t+1) is 2.0%. The estimated coefficients are scaled to reflectchanges in percentage points. Standard errors are clustered at the investor-stock and time level. Thet-statistics are given in parentheses, and *, **, and *** indicate significance at the 10%, 5%, and 1%levels, respectively. For details on the calculation of the variables, see Table A.1.

(1) (2) (3)

Panel A: Regressions with reporting bin dummies

0.2 bin −0.43∗∗∗ (−3.41) −0.42∗∗∗ (−3.26) −0.41∗∗∗ (−2.76)0.3 bin − − − − − −0.4 bin (Just below threshold) −0.54∗∗∗ (−3.67) −0.59∗∗∗ (−3.88) −1.08∗∗∗ (−5.40)0.5 bin 0.64∗∗∗ (2.74) 0.59∗∗ (2.50) −0.16 (−0.54)≥0.6 bin 1.22∗∗∗ (4.82) 1.13∗∗∗ (4.64) 1.02∗∗∗ (4.18)ln(market value) −0.16∗∗ (−2.07)ln(return volatility) 1.55∗∗∗ (5.83)ln(Amihud illiquidity) −0.37 (−1.25)ln(bid-ask spread) −0.46∗∗ (−2.04)Dummy: stock with listed futures or options 0.50∗∗∗ (3.47)Share of lendable stocks 0.04∗∗∗ (3.92)Inventory concentration −0.02∗∗ (−2.53)Indicative fee 0.01 (0.48)Standard deviation of fee −0.07∗∗∗ (−2.67)

Fixed effects:Time Yes Yes NoStock × time No No YesInvestor × time No No Yes

R2 (%) 0.60 0.78 38.08Within R2 (%) 0.20 0.37 0.14Number of observations 278,003 272,340 202,057

Panel B: Differences in the probability of increase

Just below threshold – 0.2 bin −0.11 (−0.86) −0.17 (−1.23) −0.67∗∗∗ (−3.35)Just below threshold – 0.3 bin −0.54∗∗∗ (−3.67) −0.59∗∗∗ (−3.88) −1.08∗∗∗ (−5.40)Just below threshold – 0.5 bin −1.18∗∗∗ (−5.04) −1.18∗∗∗ (−4.96) −0.92∗∗∗ (−2.89)Just below threshold – (≥ 0.6 bin) −1.76∗∗∗ (−7.31) −1.72∗∗∗ (−7.41) −2.10∗∗∗ (−8.51)

56

Table 6Comparison of positions just below with positions just above the disclosurethresholdFor each investor-stock pair we determine the maximum bin reached in the sample period. We comparepositions which never have been public but have reached the 0.4 bin at least once (position maximum:0.4 bin) with positions that have just exceeded the public disclosure threshold (position maximum: 0.5bin). In Panel A we compare the different positions along several investor and stock characteristics,reporting means, the difference in means ∆ and the respective p-value, clustering standard errors atthe investor-stock level. N denotes the number of observations (investor-stock-days) in each group. InPanel B we compare the performance of the two groups. For details on the calculation of the variables,see Table A.1. Additionally, we investigate the performance of positions that remain below the disclosurethreshold which originate from investors who have always remained just below the disclosure threshold(position and investor maximum: 0.4 bin). To measure performance, we form equal-weighted portfolios ofthe respective positions and regress the portfolio excess returns on market excess return (MKTRF), thesize (SMB) and value (HML) factors, and the momentum factor (WML), depending on the factor model.The table reports alphas (in bps per day) of the time-series regression, omitting the factor loadings forthe sake of brevity. The t-statistics are computed with Newey–West standard errors and are shown inparentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

(1) (2) (3) (4) (5) (6)

Panel A: Stock and investor characteristics

Position max.: Position max.:0.4 bin 0.5 bin Diff. in means

Variable N Mean N Mean ∆ p-value

Investor characteristics:Dummy: Investor max. = position max. (%) 63,454 39.94 20,801 10.99 28.95∗∗∗(0.000)Dummy: Hedge fund (%) 63,454 81.51 20,801 72.80 8.71∗ (0.092)Dummy: Tax haven (%) 63,454 6.89 20,801 2.17 4.72∗∗ (0.020)Dummy: No FactSet entry (%) 63,454 17.61 20,801 2.65 14.96∗∗∗(0.000)Dummy: Private fund (%) 45,107 16.66 17,897 3.40 13.26∗∗∗(0.004)ln(total assets) 40,535 22.06 16,536 22.78 −0.72∗ (0.095)

Stock characteristics:ln(market value) 63,454 7.60 20,801 7.68 −0.08 (0.626)ln(turnover) 62,705 −5.55 20,345 −5.47 −0.08 (0.332)ln(Amihud illiquidity) 62,705 −5.93 20,345 −6.10 0.17 (0.452)ln(bid-ask spread) 62,990 −5.06 20,801 −5.14 0.08 (0.176)ln(return volatility) 62,990 0.75 20,801 0.70 0.05 (0.155)Institutional ownership (%) 63,454 33.07 20,801 35.61 −2.55 (0.212)Share of lendable stocks (%) 63,451 15.95 20,801 16.77 −0.82 (0.365)Dummy: Futures or listed options (%) 63,454 39.94 20,801 34.28 5.66 (0.276)Inventory concentration (HHI, 0-100) 63,451 15.20 20,801 14.16 1.04 (0.126)Lender concentration (HHI, 0-100) 63,451 21.35 20,801 20.82 0.53 (0.665)Utilization (%) 63,451 31.68 20,801 28.94 2.74 (0.343)Indicative fee (%) 63,439 1.61 20,800 1.30 0.31 (0.139)Dummy: “on special” (%) 63,454 23.02 20,801 20.91 2.11 (0.603)Standard deviation of fee (%) 62,957 0.69 20,793 0.59 0.10 (0.319)Standard deviation of utilization (%) 62,957 12.75 20,793 13.00 −0.25 (0.784)Fee tail risk (%) 62,957 3.11 20,793 2.54 0.57 (0.139)Utilization tail risk (%) 62,957 53.69 20,793 51.46 2.24 (0.487)

Continued on next page

57

Table 6 – Continued from previous page

(1) (2) (3) (4) (5) (6)

Panel B: Performance (in bps per day)

Positions max.: 0.4 bin Positions max.: 0.5 bin Diff. in means

Model α t-stat. α t-stat. ∆ t-stat.

CAPM -4.15* (-1.72) 1.34 (0.57) -5.49*** (-2.86)Fama–French -4.74*** (-2.66) 0.68 (0.39) -5.42*** (-2.89)Carhart -4.12** (-2.36) 0.75 (0.41) -4.87*** (-2.72)

Positions and investormax.: 0.4 bin Positions max.: 0.5 bin Diff. in means

Model α t-stat. α t-stat. ∆ t-stat.

CAPM -4.82 (-1.50) 1.34 (0.57) -6.16** (-2.57)Fama–French -5.58** (-2.39) 0.68 (0.39) -6.27*** (-2.66)Carhart -4.79** (-2.14) 0.75 (0.41) -5.54*** (-2.58)

Table 7Secretive short positions and fundamental newsThis table reports the average risk-adjusted daily return of stocks associated with secretive positions aswell as the decomposition of the return into returns generated on days when firm-specific fundamentalnews are released and days when we do not observe news. To measure performance, we regress theexcess return of each position day on the market excess return (MKTRF), the size (SMB) and value(HML) factors, and the momentum factor (WML), depending on the factor model. We employ theHoechle et al. (2016) regression framework that allows an exact replication of the calendar-time portfolioapproach. The table reports alpha estimates (in bps per day), omitting the factor loadings for the sakeof brevity. The t-statistics are computed with Driscoll and Kraay (1998) standard errors and are shownin parentheses. The estimates in Column (1) correspond to those reported in Panel B of Table 6 whentime-series regressions with Newey–West standard errors are used. Columns (2) to (4) report the averagereturns on earnings announcement days, firm-specific ad-hoc news days, and days on which we do notobserve news, respectively. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively

(1) (2) (3) (4)

Days with

Earnings No observedannounce- Ad-hoc firm-specific

All days ments news news

CAPM −4.15∗ −30.21 −69.41∗∗∗ −2.05(−1.72) (−1.47) (−3.32) (−0.98)

Fama–French −4.74∗∗∗ −27.82 −68.64∗∗∗ −2.76∗

(−2.66) (−1.40) (−3.21) (−1.67)Carhart −4.12∗∗ −27.21 −67.84∗∗∗ −2.15

(−2.36) (−1.35) (−3.31) (−1.32)

N 63,390 2,013 1,169 60,390

58

Table 8Short sellers’ avoidance and predictability of stock returnsThis table shows the average risk-adjusted returns of different portfolios constructed on the basis ofdifferent maximum reporting bins (Column (1) to (5)). For each investor-stock pair, we determine themaximum reporting interval reached during the sample period. In Panel A, for each maximum binwe report the average risk-adjusted return of portfolios that include all stocks for which we observe aposition at its maximum reporting bin. In Panel B, for each maximum bin interval we report the averagerisk-adjusted return of portfolios that include all stocks for which we observe a position that is outsidethe maximum reporting bin. In other words, it is the average return of the stocks not generated in themaximum bin phase. We form an position-weighted portfolio of stocks for each test. We then regressthe portfolio returns on market excess return (MKTRF), the size (SMB) and value (HML) factors, andthe momentum factor (WML), depending on the factor model. The table reports alphas (in bps perday) of the time-series regression, omitting the factor loadings for the sake of brevity. The t-statisticsare computed with Newey–West standard errors and are shown in parentheses. *, **, and *** indicatesignificance at the 10%, 5%, and 1% levels, respectively.

(1) (2) (3) (4) (5)

Panel A: Performance during the maximum bin phaseMaximum reporting bin reached

0.2 0.3 0.4 0.5 0.6

CAPM 0.30 −0.59 −5.46∗∗ 6.37 0.80(0.14) (−0.34) (−2.00) (1.64) (0.21)

Fama–French −0.36 −1.09 −6.13∗∗∗ 6.30∗ −0.22(−0.21) (−0.59) (−2.83) (1.71) (−0.05)

Carhart −0.09 −1.22 −5.66∗∗ 6.02 −1.37(−0.05) (−0.87) (−2.57) (1.58) (−0.36)

Panel B: Performance outside the maximum bin phaseMaximum reporting bin reached

0.2 0.3 0.4 0.5 0.6

CAPM – −4.69 −1.70 0.69 −4.83(−1.58) (−0.64) (0.28) (−1.50)

Fama–French – −5.23∗∗ −2.02 −0.22 −5.62∗∗

(−2.16) (−1.01) (−0.12) (−2.26)Carhart – −4.67∗ −1.43 −0.18 −5.20∗∗

(−1.86) (−0.69) (−0.09) (−2.09)

59

Internet Appendix accompanying

Flying Under the Radar:

The Effects of Short-Sale Disclosure Rules on

Investor Behavior and Stock Prices

March 9, 2018

This appendix contains supplemental material for the paper “Flying Under the Radar: The

Effects of Short-Sale Disclosure Rules on Investor Behavior and Stock Prices.” We provide

additional descriptive statistics, and results of robustness tests, and analyses corroborating

the findings in the main text.

The roadmap is as follows: In Sections A and B we show additional figures describing

the stock universe underlying our analyses. Sections C, D, and E provide further evidence

of investors’ avoidance to disclose their position publicly using alternative estimation

procedures. In Sections F and G we test two alternative hypotheses related to the

disclosure threshold. Section H contains additional descriptive statistics and robustness

tests related to the documented return predictability using the calendar-time portfolio

approach.

Contents

A Additional sample characteristics ........................................................ 2

B Distribution of short position notifications ......................................... 3

C Alternative sample split: Positions approaching the disclosure thresh-

old from below ...................................................................................... 4

D Testing for discontinuity in the distribution of short positions.......... 5

E Fixed-effects regressions: Alternative model specifications................ 8

F Is there hesitance before eventually crossing the disclosure thresh-

old?........................................................................................................ 11

G Do investors jump to large short positions once they cross the

disclosure threshold? ............................................................................ 13

H Additional analyses to the calender-time approach ............................ 14

References ............................................................................................. 38

1

A. Additional sample characteristics

As described in the main text (see page 11), the vast majority (73.5%) of stocks with

short positions are in the highest market capitalization quartile, and almost all stocks

with short position notifications (95.8%) appear above the median value of the market

capitalization distribution. Figure IA.1(a) provides further details by plotting the frequency

of stocks with an open short position across the four quartiles of market capitalization.

The quartile breakpoints are defined according to the overall sample of stocks in the

German regulated stock market. As is evident from the figure, the distribution is highly

right-skewed irrespective of whether stocks have confidential or public short position

notifications. Similar findings emerge when plotting the distribution across the four

quartiles of institutional ownership, as in Figure IA.1(b). Also, stocks with short position

notifications are highly liquid as evident from Figure IA.1(c) (Amihud illiquidity measure)

and Figure IA.1(d) (bid-ask spread). Finally, stocks with short position notifications are

held by a considerable share of institutional investors indicating a sufficiently large supply

of stocks to borrow (Nagel, 2005).

The descriptive statistics in Table 1 of the main text show that almost 20% of all

German stocks in the regulated market have at least one short position notification over

the sample period. Figure IA.2(a) illustrates this share measured at each point in time. As

is evident from the blue line, the share of stocks with at least one short position notification

increases from 15% at the beginning of the sample to around 25% at the end of the sample

period. We also observe a slight increase of the stocks with at least one public short

position notification from around 7% to 10% of the overall stock universe (red line). As

suggested by Figure IA.2(b), the relative increase of stocks with short position notifications

is driven by both an increase in the absolute number of short position notifications and a

decline of the overall number of stocks in the regulated market.

2

B. Distribution of short position notifications

As discussed in the main text, we sort the short positions into bins of 10 basis points

(bps) each. The reason is that the exact (two-digit precision) value of the short position is

only recorded on the day at which the position crosses the respective thresholds at 0.20,

0.30, 0.40%, ... . This feature of the reporting rule mechanically generates a pattern in

the data, as illustrated in Figure IA.3. In this histogram we report the frequency of the

short position notifications with a bin width of 0.01%, i.e. at two-digit precision. The

histogram shows frequency spikes occurring at regular distance always at low and high

second decimal places.

For a better understanding as to why this pattern emerges, we report the frequency of

decimal places occurring in the short position notifications in Figure IA.4(a). It shows that

the u-shaped pattern within the reporting bins originates from two processes overlaying

each other: Positions that come from below are more likely to enter the reporting bin at

low second decimal places. Positions that come from above are more likely to enter the bin

at high second decimal places. The slightly asymmetric u-shape is due to a lower number

of decreases in the sample. Figure IA.4(b) displays the two conditional distributions of

second decimal places, showing a very symmetrical picture. Conditional on the positions

coming from below (increase), the likelihood of reporting a zero as a second decimal is

35.4%, whereas the corresponding likelihood of a nine as a second decimal place is only

2.3%. The mirror image emerges when conditioning on the positions coming from above

(decrease): The likelihood of reporting a short position with a zero as a second decimal

place is 2.7%, in contrast to a probability of 37.9% for a nine as a second decimal place.

The pattern around high and low second decimal places of short sale notifications, as

shown in Figures IA.3, IA.4(a), and IA.4(b), is the main reason why we collect positions

into reporting bins. Because of these“spikes”, it is unfeasible to compare density forecasts of

the true underlying distribution around the disclosure threshold. In the way the reporting

is set up, the share of positions with a reported value of 0.49 does not represent the true

3

fraction of positions with that value. In other words, investors’ short position is essentially

measured at one-digit precision.

C. Alternative sample split: Positions approaching the dis-

closure threshold from below

To uncover avoidance of investors to cross the disclosure threshold, we rely in our main

analyses on a sample split into positions at and positions below their record high. As

discussed in Section III, the avoidance to pass the disclosure threshold should be particularly

pronounced for positions at their record high relative to positions below their record high.

We repeat our main empirical tests from Figure 1(b), and those in Table 3 and Table 4

of the main text with a slightly different definition for the sample split. Specifically, we

divide all observations into position-days for which the last change was an increase, and

positions previously decreased.

The two measures relate to two extremes in terms of considered data history: The

measure in the main text is determined by the running maximum of the entire history of

the short position. The alternative measure is determined by the shortest possible window

of past position values, namely the maximum of the current and previous position value.

Related to the 0.4 bin, “previously increased” positions include position days, which were

never public in the past but also positions which were public prior to the last increase.

Because of the latter positions, we expect that the alternative sample split results in a

weaker avoidance effect relative to the “at-the-record-high” subsample from the main text.

Figure IA.5 plots the frequency of days with open short positions for the two subsamples.

Similar to the findings in the main text in Figure 1(b), our alternative sample split also

provides descriptive evidence for investors’ avoidance to cross the disclosure threshold.

Only for the “previously-increased” subsample we observe an accumulation of observations

in the 0.4 bin.

4

Table IA.1 re-conducts the analysis of Table 3 by using the alternative sample split.

In line with our main findings, Table IA.1 shows that the low probability of an increase

in the 0.4 bin is entirely driven by positions approaching the threshold from below. In

relative terms, for the subsample of previously increased positions, in the bin just below

the disclosure threshold it is 14% and 26% less likely to increase a short position than in

the two neighboring intervals. Comparing these results with findings of Table 3 with a

reduction between 20% and 34%, we observe that the avoidance for previously increased

positions is only slightly lower than for positions at the record high, corroborating the

robustness of our results.

Table IA.2 re-conducts the duration analysis of Table 4, but uses the alternative sample

split. In line with our main findings, the table shows that the abnormal long duration in

the 0.4 bin is unique to the sample of previously increased positions while avoidance is not

evident for the positions previously decreased (and public). In relative terms, the mean

duration in the bin just below the disclosure threshold is 27% and 55% longer than in

the two neighboring intervals. The corresponding reduction in Table 4 was 22% to 55%.

Results for median durations in Panel B are comparable.

Overall, we confirm our main findings from Sections III.A and Section III.B by using

only the last position change instead of the entire history of the short position evolution

as the sample split variable.

D. Testing for discontinuity in the distribution of short posi-

tions

If short positions accumulate below the disclosure threshold, one would expect to find a

jump or discontinuity in the distribution of short positions at or close to this point. A

common test to detect strategic behavior of investors around a given threshold is suggested

by Degeorge, Patel and Zeckhauser (1999).

5

When using this test in our setting, a critical feature of the data should be kept in

mind. As we pointed out in Section III and in more detail in Section A, although short

positions are reported with two-digit precision in principle, these positions are still measured

imprecisely: once a given position enters a reporting bin, say the 0.4 interval [0.40, 0.49),

it is no longer observed until it leaves this particular bin. This feature may give rise to

relatively few observations in the middle of each reporting bin, while observations near the

interval boundaries (0.20, 0.30 and so on) may be overrepresented. Therefore, the u-shaped

pattern may induce any statistical test to find evidence for a discontinuity at more than

one point in the support of the distribution. Thus, to detect strategic behavior of investors

around the 0.5 publication threshold, we compare the outcomes of the discontinuity test

around 0.5 to the results for the two neighboring boundaries, 0.4 and 0.6. While our

main interest is to test for a jump in the distribution below the disclosure threshold, the

two neighboring boundaries help us to disentangle investors’ strategic behavior from the

mechanical u-pattern within each interval. If possible discontinuities in the distribution

are only driven by the u-shaped reporting pattern described above, a powerful test may

detect discontinuities for any of these thresholds. If investors avoid publication of their

short positions, we expect evidence for a discontinuity to be even more pronounced below

the disclosure threshold.

Given this setup, we briefly review the testing procedure and discuss the outcomes

of the test. Let x be a random variable with probability density function f . For a given

random sample of this random variable, let x0, x1, . . . , xn, xn+1 be a set of n+ 2 equidistant

points. Let p (xi) be the proportion of observations that lie in the interval or bin [xi, xi+1),

which can be viewed as an estimate of f (xi), i = 0, . . . , n. Under the null hypothesis,

the density is smooth at a given point in the support of the distribution, while under the

6

alternative hypothesis the distribution may display a discontinuity at this point. To test

this null hypothesis, Degeorge et al. (1999) suggest the following test statistic:

τi =

∆p (xi)− meanxj∈Ri(r),xj 6=xi

{∆p (xj)}

s.d.xj∈Ri(r),xj 6=xi

{∆p (xj)}, (IA.1)

where ∆p (xi) = p (xi)−p (xi−1) is the first difference of the observed proportions, Ri (r) =

{xi−r, . . . , xi, . . . , xi+r} is a symmetric region around xi with radius r, and mean{·}, s.d.{·}

denote the empirical mean and standard deviation taken over selected points in this region.

To motivate this statistic, note that if f is smooth, the first derivative is continuous at

xi, and there are no jumps in the vicinity of this point. Hence, under the null hypothesis, if

∆p (xi) serves as an estimate of f ′ (xi), we expect ∆p (xi) not to be substantially different

from nearby ∆p (xj). Therefore, we reject the null hypothesis of smoothness for large

values of this statistic. Note that Degeorge et al. (1999) suggest to exclude xi itself when

computing the mean of the ∆p (xj) to increase the power of the test.

Although the test is intuitively appealing and imposes relatively few assumptions on

the data generating process, a disadvantage of the test is that the finite-sample or limiting

distribution of the statistic τ is not derived rigorously by Degeorge et al. (1999). Rather,

they conjecture that the statistic follows a t-distribution if ∆p (xi) is Gaussian in the

region R, although the number of degrees of freedom remain unspecified. Degeorge et al.

(1999) consider the standard ±2 critical values, and we highlight these benchmarks in

the figures below. Furthermore, this non-parametric test requires the user to specifiy the

radius r and the interval width of the bins [xi, xi+1). We consider an interval width of 0.01

percentage points as a natural choice, and provide results for several values of r in the

following application.

The top panel in Figure IA.6 shows the empirical distribution of short positions between

0.35% and 0.65%. These histograms can be viewed as close-ups of the histograms displayed

in Figure IA.3 over the relevant region.

7

We find that the frequency of short position notifications with the magnitude of 0.48

and 0.49 are larger than the frequency of positions just above the threshold of 0.50. This

pattern is unique to the disclosure threshold, given that for the two neighboring thresholds

we observe higher frequencies for positions just above the threshold. The bottom panel

presents the test statistic τ for each point in this range, where a radius of r = 0.06 is chosen.

It turns out that for xi = 0.48, the test provides the strongest evidence for rejecting the

null hypothesis of smoothness. The test statistic has a value of 5.1, which is substantially

larger than the second largest statistic of 3.6 at xi = 0.58, while there is no evidence for a

discontinuity around the 0.40 threshold.

Finally, Figures IA.7 and IA.8 repeat this testing procedure for r = 0.04 and r = 0.08,

yielding similar results. Overall, this exercise suggests that there is a discontinuity closely

below the disclosure threshold of 0.50, lending support for the evidence provided in

Section III.

E. Fixed-effects regressions: Alternative model specifications

Controlling for additional reporting bins separately. The results from the linear

probability model (LPM) from Table 5 document an abnormally low probability of increase

in the bin just below the publication threshold. In the regression specification of the main

text, we collect all position days with a position size of 0.6 and above in one reporting bin

to ensure a sufficient number of observations for each dummy variable. In this section,

we extend the number of reporting bins and include the intervals 0.7, 0.8, 0.9, and 1.0+

in the LPM, where 1.0+ denotes all positions shorting 1% or more of the stock’s shares

outstanding. This extension comes at the expense of a low number of observations for the

bins above 0.6. Despite this shortcoming, our main result of short sellers’ avoidance to

cross the publication threshold remains essentially the same.

8

In Table IA.3 we report regression results in line with the findings in the main text. In

particular, the probability of a position increase when the position is in the bin just below

the publication threshold is significantly lower relative to the corresponding probabilities in

the two neighboring bins. This result holds even when we account for different dimensions

of unobserved effects. For example, in the most saturated specification, controlling for both

time-varying stock and time-varying investor fixed effects, we find that the probability of

a position increase is the lowest among all reporting bins.

Fixed-effects regression with at-record high interactions. Throughout Section III

we document that avoidance to cross the disclosure threshold is particularly strong for

positions at their record high. To account for this difference in our fixed-effects regression

model from Equation (2b), we interact all bin dummies with a dummy variable indicating

positions at their record high. The indicator variable Record high is defined according to

Equation (1) of the main text. Formally, we estimate the following model:

yi,j,t+1 = β0 + β1 Just below thresholdi,j,t +∑k

βk k bin i,j,t

+ β1 Just below thresholdi,j,t × Record high i,j,t

+∑k

βk k bin i,j,t × Record high i,j,t

+ γ Record high i,j,t + ui,j,t+1. (IA.2)

where we control for all reporting bins up to 1.0+ separately, and estimate the model using

different specifications of ui,j,t+1 to account for unobserved stock and investor effects as in

Table IA.3.

Similar to Panel B of Table IA.3, in Table IA.4 we report the probability of increase for

the bin just below the publication threshold relative to all other reporting bins. Consistent

with the findings presented in the main text, we find evidence on avoidance only for

positions at their record high. The probability of position increase in the 0.4 bin is

9

significantly lower than in the neighboring bins for positions at their record high across

all specifications. For positions below their record high, in contrast, this difference is

insignificant or significantly positive.

Comparison: “increase”, “decrease” and “no change”. In our analysis we focus

on the probability of a position increase. Analyzing this event is a natural choice because we

are interested in investors’ potential avoidance to cross the disclosure threshold. Naturally,

at any given day, an investor has three options: increasing, decreasing, and not changing

its short position. Essentially, our analysis in the main text compares the event “increase”

against the events “decrease” and “no change”. In the following we shed more light on the

other two events. To do so, we follow our modeling approach of Equation (2b) from the

main text and define our three dependent variables as follows:

yincreasei,j,t = 1 (bini,j,t > bini,j,t−1) , (IA.3)

yno changei,j,t = 1 (bini,j,t = bini,j,t−1) , and (IA.4)

ydecreasei,j,t = 1 (bini,j,t < bini,j,t−1) . (IA.5)

where bini,j,t denotes the reporting bins (0.2, 0.3, 0.4, 0.5, ...). In case of avoidance, we

expect that the probability of not changing the short position in the bin 0.4 is higher than

in the two neighboring bins 0.3 and 0.5. Moreover, given the longer duration in bin 0.4

(see Table 4 in the main text), we expect that the probability of decrease in the bin just

below the publication threshold is lower than in the two neighboring bins.

The results of this extended analysis, using the most saturated fixed-effects model,

are shown in Table IA.5. As in Panel B of Table IA.3, and Table IA.4, we report the

estimates for the bin just below the publication threshold relative to all other reporting

bins. Column (1) shows the relative probability of increase, which corresponds to our

previous analysis shown in Table IA.3, Panel B, Column 5. Column (2) of Table IA.5

10

displays the results for the relative probability of not changing the bin on the next day.

Coefficients of all bins are significantly positive. This result implies that the probability

of staying in the same bin is significantly higher just below the threshold compared to

all other reporting bins. The difference in the probability is economically sizable when

compared to the neighboring bins, amounting to 1.51 to 2.42 percentage points. Since

investors are avoidant to cross the disclosure threshold, they stay longer in the 0.4 bin.

This result reflects our finding from Section III.B of the main text: The duration in the

0.4 bin is the longest among all reporting bins.

In Column (3) we observe that the probability of a position decrease is lower in the

0.4 bin compared to its neighboring bins. This finding can be explained by the longer

duration in the 0.4 bin. In particular, days with a position decrease decline in relative

terms because investors increase the days they stay in the 0.4 bin.

F. Is there hesitance before eventually crossing the disclosure

threshold?

Our results from the main text present strong evidence for investors’ avoidance of crossing

the disclosure threshold. In this section we strive to better understand whether this finding

is driven by positions that do not cross the publication threshold (“absolute avoidance”)

or by positions that eventually cross the publication threshold some time in the future

(“hesitance”).

The analysis of Table 3 in the main text already shows that there is an absolute

avoidance to cross the disclosure threshold. In particular, in this exercise we eliminate the

duration dimension: Instead of looking at the probability of a position increase on the next

day, we investigate the probability that the next position change in the future is an increase.

The low probability of this event in the 0.4 bin shows that investors absolutely avoid

to cross the threshold and that there is not merely a hesitance followed by an eventual

11

position increase. This result is line with Figure 2 of the main text, which shows that

positions that reach the reporting bin below the publication threshold but never crossing

it subsume the largest group of position-days. Moreover, the results of Table 6 suggest

that this absolute avoidance is strongly investor-specific, with investors sticking to their

decision either to cross the threshold or not to cross the threshold.

Nevertheless, there may still exist hesitance to cross the threshold present among those

investors that eventually cross the threshold. We investigate this alternative hypothesis by

repeating the duration analysis of Table 4 but focusing on the subsample of positions that

eventually increase their position value with the next change. If hesitance is present before

crossing the disclosure threshold, we expect a longer duration in the 0.4 bin compared to

its neighboring bins.

The results of this exercise are shown in Table IA.6 and provide no clear support for the

hypothesis that investors are hesitant before eventually crossing the disclosure threshold.

The mean duration (Panel A) in the 0.4 bin is only slightly larger compared to the duration

in the bin 0.3 and 0.5, respectively, but the difference is insignificant. We find similar

results when conditioning on positions at their record high, for which we previously found

the strongest avoidance effect. The median duration, which is more robust to extreme

observations of the highly right-skewed duration distribution, are shown in Panel B. Here

we find that the median time spent in the 0.4 bin is identical to the duration spent in

the neighboring bins. Taken together, these results support the notion that investors’

avoidance is driven by the “absolute avoidance” to cross the publication threshold rather

than investors being hesitant before eventually crossing the threshold.

12

G. Do investors jump to large short positions once they cross

the disclosure threshold?

The main result of the paper is that a sizable share of investors are avoidant to cross

the disclosure threshold. A question that arises in this context is how investors behave if

they have decided to cross the disclosure threshold. A possible behavior when crossing

the threshold could be that investors immediately try to establish an abnormally large

position. The rationale may be as follows: If the investor’s targeted position is above but

not much larger than the publication threshold, the investor might prefer a position just

below the threshold. The costs of a position publication exceed the potential benefits of

the larger targeted short position. As a consequence, only investors that target a very large

position (associated with higher benefits) are willing to tolerate publication and increase

their position accordingly. If so, we would expect that a position increase is particularly

large when the increase was initiated from the bin just below the publication threshold.

We explore this conjecture by looking at future position changes across all reporting

bins. Specifically, we compute the average position change, given that a position increase

occurs. Then, we compare the average position increase across the various reporting bins

from where they were initiated. Evidence in Table IA.7 does not support this “large jump

hypothesis”. The average position increase initiated from the 0.4 bin is 0.114%, which is

not significantly larger than the increase from any other bin. There is also no unusual

pattern when conditioning on positions at their record high or positions below their record

high. Next, we not only look at the mean increase, but at various percentiles of position

increases. As apparent from Table IA.8, the median increase is 0.1 and identical across all

starting bins including the 0.4 bin. Also, when looking at higher percentiles, we find no

abnormal patterns for the bin just below the disclosure threshold even in the tails of the

distribution. No other insights arise from the sample split of positions at or below their

13

record high. Overall, the results do not support the conjecture that investors immediately

jump to very high positions once they decided to cross the disclosure threshold.

H. Additional analyses to the calender-time approach

In Section V.A of the main text we find that a portfolio consisting of stocks with secretive

positions just below the publication threshold yields on average a significant abnormal

return of -5.46 to -6.13 bps per day. In this section of the Appendix we briefly illustrate

the composition of the portfolio over time.

As indicated on page 33 in the main text, the average number of stocks in this portfolio

is 32 ranging from 21 up to 49 stocks on a given day. In Figure IA.9 we plot the number

of distinct stocks in the portfolio over time. In addition, the figure includes the time series

of positions in this portfolio. The number of positions is slightly higher given that there

can be more than one secretive position that is just below the publication threshold for

the same stock by different investors. Two notable findings emerge from the figure. First,

the number of stocks and positions in the portfolio only slightly varies, with an increasing

trend during our sample period. Second, the majority of positions come from distinct

stocks, suggesting that investors’ publication avoidance and its consequences for price

efficiency documented in this study are prevalent effects in the financial market.

In this section we conduct a number of variations to our sample and variable definitions

to test the robustness of the results from Section V.A. Table IA.9 reports the average

abnormal returns of the benchmark model from Panel A of Table 8 and those of our

sensitivity analyses.

In the main analysis we include a stock into the portfolio if we observe a secretive

position that is in the bin just below the publication threshold. Consequently, the returns

within the portfolio are weighted by the number of positions. The rationale is that we

expect overpricing to be positively related to investors’ avoidance and to the number of

14

positions that are possibly constrained. As a robustness test, we now use equal weighting.

That is, we include a stock in the portfolio if we observe one or more secretive positions

that are in the bin just below the publication threshold. As is evident from Panel B of

Table IA.9, employing the alternative, less powerful, portfolio weighting yields only slightly

lower returns in absolute terms relative to the benchmark result in Panel A.

In our second robustness test, we exclude all short positions for which the stock price on

the day before crossing the reporting threshold of 0.2% is below 1 EUR. Such a restriction

ensures that our main overpricing results are not driven by small-cap and illiquid stocks. As

already noted in Section II, the sample of stocks with open short positions consists almost

entirely of stocks above the median market capitalization of the German stock universe.

As a consequence, the exclusion of penny stocks only marginally affects our sample size.

Using the 1 EUR filter, we drop merely four stocks from our sample. Accordingly, the

alphas in Panel C are virtually the same as in the benchmark model in Panel A.

In Panel D we conduct another change in our sample by defining investors to be avoidant

to cross the publication threshold if they spend at least five days in their maximum bin of

0.4. In comparison, in the main analysis we require only a minimum of two days spent in

the maximum bin of 0.4. With the more conservative definition of being avoidant using

restrictions on the shorting period, we expect to better identify avoidance, short-selling

impediments, and, as a result, more accurate estimates. In line with this expectation, we

indeed find that the standard errors of the abnormal returns decrease and the statistical

significance of the effect increases across all asset pricing models compared to the baseline

model in Panel A, despite a slight decrease in the economic magnitude.

Our main results on overpricing are also robust to changes in the asset pricing factors.

Namely, in Panel E of Table IA.9, we use European factor portfolios, which are also

obtained from Andrea Frazzini’s data library, provided through AQR’s website.1 Using

European factors results in economically comparable, but noisier alpha estimates. This

1See: www.aqr.com/library/data-sets/quality-minus-junk-factors-daily/data

15

result is in line with Griffin (2002) who documents that local factor portfolios are generally

better suited for performance evaluation.

16

(a) Market capitalization

020

4060

80Fr

eque

ncy

(in %

)

1 2 3 4

AllConfidentialPublic

Short-sale notifications:

(b) Institutional ownership

020

4060

80Fr

eque

ncy

(in %

)

1 2 3 4

AllConfidentialPublic

Short-sale notifications:

(c) Amihud illiquidity

020

4060

80Fr

eque

ncy

(in %

)

1 2 3 4

AllConfidentialPublic

Short-sale notifications:

(d) Bid-ask spread

020

4060

80Fr

eque

ncy

(in %

)

1 2 3 4

AllConfidentialPublic

Short-sale notifications:

Figure IA.1:Distribution of stocks with open short-position notifications across size, insti-tutional ownership, and illiquidityThis figure displays the distribution of stock-days with open short-sale notifications across quartiles ofmarket capitalization (Figure IA.1(a)), institutional ownership (Figure IA.1(b)), the Amihud illiquiditymeasure (Figure IA.1(c)), and the bid-ask spread (Figure IA.1(d)). The quartile breakpoints are definedaccording to the overall sample of stocks in the German regulated stock market. All short-sale notifi-cations subsume stocks with either public or confidential short-sale notifications, confidential short-salenotifications consist of stocks with positions above 0.2% but below 0.5% of issued share capital, and publicshort-sale notifications consist of stocks with at least one short position of 0.5% or higher. The overallsample contains all German domestic equity in the regulated market from November 5, 2012, to March 31,2015.

17

(a) Percentages

05

1015

2025

30S

hare

of s

tock

s (in

%)

Jan-2013 July-2013 Jan-2014 July-2014 Jan-2015

Stocks with short position notificationsStocks with public short position notifications

(b) Number of stocks

020

040

060

0N

umbe

r of s

tock

s

Jan-2013 July-2013 Jan-2014 July-2014 Jan-2015

All stocksStocks with short position notificationsStocks with public short position notifications

Figure IA.2:Stocks with short position notifications over timeFigure IA.2(a) displays the percentage of stocks that have at least one short position notification belowthe publication threshold (≥ 0.2%) and the percentage of stocks that have at least one short positionnotification above the publication threshold (≥ 0.5%) over time, respectively. Figure IA.2(b) shows thesame statistics over time in absolute terms as well as the overall number of stocks in our sample. Theoverall sample contains all German domestic equity in the regulated market from November 5, 2012, toMarch 31, 2015.

18

05

1015

Freq

uenc

y (in

%)

0.20 0.30 0.40 0.50 0.60 0.70Reported short position (in % of issued share capital)

Figure IA.3:Detailed histogram of reported short positionsThis figure displays the detailed frequency histogram of reported short positions with a bin width of0.01%. Positions greater than 0.70% are truncated for readability. The sample contains all short positionnotifications in the German regulated equity market from November 5, 2012, to March 31, 2015.

19

(a) Overall distribution

05

1015

2025

Freq

uenc

y (in

%)

0 1 2 3 4 5 6 7 8 9Second decimal

Position coming from belowPosition coming from above

(b) Conditional distribution

010

2030

40Fr

eque

ncy

(in %

)

0 1 2 3 4 5 6 7 8 9Second decimal

Position coming from belowPosition coming from above

Figure IA.4:Second decimal places of the short position notificationFigure IA.4(a) displays the relative frequency of second decimal places of short-position notifications.Figure IA.4(b) shows the frequency distribution conditional on positions coming from above or below. Thesample contains all short position notifications in the German regulated equity market from November 5,2012, to March 31, 2015.

20

Public disclosure threshold

010

2030

4050

Rel

ativ

e fre

quen

cy (%

)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Reporting bins

Previously increased positionsPreviously decreased positions

Figure IA.5:Distribution of open short positionsThis figure displays the relative frequency separately for short positions that previously increased andpreviously decreased, respectively. Reporting intervals greater than 1.6% are truncated for readability.The overall sample contains all German domestic equity in the regulated market from November 5, 2012,to March 31, 2015.

21

Reporting Threshold

01

23

4

Freq

uenc

y (in

%)

.35 .36 .37 .38 .39 .4 .41 .42 .43 .44

Reported short position (in % of issued share capital)

-5-4

-3-2

-10

12

34

5

Test

Sta

tistic

.35 .36 .37 .38 .39 .4 .41 .42 .43 .44

Reported short position (in % of issued share capital)

Disclosure Threshold

0.3

7.7

41.

111.

481.

85

Freq

uenc

y (in

%)

.45 .46 .47 .48 .49 .5 .51 .52 .53 .54

Reported short position (in % of issued share capital)

-5-4

-3-2

-10

12

34

5

Test

Sta

tistic

.45 .46 .47 .48 .49 .5 .51 .52 .53 .54

Reported short position (in % of issued share capital)

Reporting Threshold

0.1

68.3

36.5

04.6

72.8

4

Freq

uenc

y (in

%)

.55 .56 .57 .58 .59 .6 .61 .62 .63 .64

Reported short position (in % of issued share capital)

-5-4

-3-2

-10

12

34

5

Test

Sta

tistic

.55 .56 .57 .58 .59 .6 .61 .62 .63 .64

Reported short position (in % of issued share capital)

Figure IA.6:Testing for discontinuity in the distribution of short positionsThe top panel displays the histogram of reported short positions with a bin width of 0.01 percentagepoints for a range of positions between 0.35% and 0.65%. These histograms are close-ups of the relevanthistograms in figure IA.3. The bottom panel shows the test statistic suggested by Degeorge et al. (1999),based on a radius of r = 0.06, see Equation (IA.1). Under the null hypothesis, the density function ofshort positions is smooth. Large values of the statistic provide evidence for the alternative hypothesis andhence a discontinuity in the distribution. Critical values of ± 2 are highlighted as a benchmark.

22

Reporting Threshold

01

23

4

Freq

uenc

y (in

%)

.35 .36 .37 .38 .39 .4 .41 .42 .43 .44

Reported short position (in % of issued share capital)

-5-4

-3-2

-10

12

34

5

Test

Sta

tistic

.35 .36 .37 .38 .39 .4 .41 .42 .43 .44

Reported short position (in % of issued share capital)

Disclosure Threshold

0.3

7.7

41.

111.

481.

85

Freq

uenc

y (in

%)

.45 .46 .47 .48 .49 .5 .51 .52 .53 .54

Reported short position (in % of issued share capital)

-5-4

-3-2

-10

12

34

5

Test

Sta

tistic

.45 .46 .47 .48 .49 .5 .51 .52 .53 .54

Reported short position (in % of issued share capital)

Reporting Threshold

0.1

68.3

36.5

04.6

72.8

4

Freq

uenc

y (in

%)

.55 .56 .57 .58 .59 .6 .61 .62 .63 .64

Reported short position (in % of issued share capital)

-5-4

-3-2

-10

12

34

5

Test

Sta

tistic

.55 .56 .57 .58 .59 .6 .61 .62 .63 .64

Reported short position (in % of issued share capital)

Figure IA.7:Testing for discontinuity in the distribution of short positionsThe top panel displays the histogram of reported short positions with a bin width of 0.01 percentagepoints for a range of positions between 0.35% and 0.65%. These histograms are close-ups of the relevanthistograms in figure IA.3. The bottom panel shows the test statistic suggested by Degeorge et al. (1999),based on a radius of r = 0.04, see Equation (IA.1). Under the null hypothesis, the density function ofshort positions is smooth. Large values of the statistic provide evidence for the alternative hypothesis andhence a discontinuity in the distribution. Critical values of ± 2 are highlighted as a benchmark.

23

Reporting Threshold

01

23

4

Freq

uenc

y (in

%)

.35 .36 .37 .38 .39 .4 .41 .42 .43 .44

Reported short position (in % of issued share capital)

-5-4

-3-2

-10

12

34

5

Test

Sta

tistic

.35 .36 .37 .38 .39 .4 .41 .42 .43 .44

Reported short position (in % of issued share capital)

Disclosure Threshold

0.3

7.7

41.

111.

481.

85

Freq

uenc

y (in

%)

.45 .46 .47 .48 .49 .5 .51 .52 .53 .54

Reported short position (in % of issued share capital)

-5-4

-3-2

-10

12

34

5

Test

Sta

tistic

.45 .46 .47 .48 .49 .5 .51 .52 .53 .54

Reported short position (in % of issued share capital)

Reporting Threshold

0.1

68.3

36.5

04.6

72.8

4

Freq

uenc

y (in

%)

.55 .56 .57 .58 .59 .6 .61 .62 .63 .64

Reported short position (in % of issued share capital)

-5-4

-3-2

-10

12

34

5

Test

Sta

tistic

.55 .56 .57 .58 .59 .6 .61 .62 .63 .64

Reported short position (in % of issued share capital)

Figure IA.8:Testing for discontinuity in the distribution of short positionsThe top panel displays the histogram of reported short positions with a bin width of 0.01 percentagepoints for a range of positions between 0.35% and 0.65%. These histograms are close-ups of the relevanthistograms in figure IA.3. The bottom panel shows the test statistic suggested by Degeorge et al. (1999),based on a radius of r = 0.08, see Equation (IA.1). Under the null hypothesis, the density function ofshort positions is smooth. Large values of the statistic provide evidence for the alternative hypothesis andhence a discontinuity in the distribution. Critical values of ± 2 are highlighted as a benchmark.

24

020

4060

80N

umbe

r of p

ositi

ons/

stoc

ks

Jan-2013 July-2013 Jan-2014 July-2014 Jan-2015Date

Number of positionsNumber of distinct stocks

Secretive positions just below threshold

Number of positions and distinct stocksin calendar-time portfolio:

Figure IA.9:Number of stocks with secretive positions just below the publication thresholdThis figure shows the number of secretive positions that are just below the publication threshold overtime (green line). The red line is the corresponding number of distinct stocks with at least one secretiveposition that is just below the publication threshold. The overall sample contains all German domesticequity in the regulated market from November 5, 2012, to March 31, 2015.

-

25

Table

IA.1

:P

robabilit

yof

short

posi

tion

incr

ease

:A

ltern

ati

ve

sam

ple

split

This

table

rep

eats

the

anal

ysi

sof

Tab

le3

usi

ng

anal

tern

ativ

esa

mple

split

ofsh

ort

pos

itio

ns

pre

vio

usl

yin

crea

sed

and

pos

itio

ns

pre

vio

usl

ydec

reas

ed.

The

table

rep

orts

the

pro

bab

ilit

yof

incr

easi

ng

ash

ort

pos

itio

n(i

.e.,

chan

ging

toa

hig

her

rep

orti

ng

bin

),gi

ven

that

anin

vest

orcu

rren

tly

has

ap

osit

ion

ina

spec

ific

bin

.In

addit

ion,

itd

ispla

ys

the

diff

eren

cein

pro

babilit

yof

row

(3)

rela

tive

toro

w(j

),th

e0.4

rep

ort

ing

bin

just

bel

owth

epu

blica

tion

thre

shol

d(s

had

edin

gray

),an

dth

ep-

valu

efo

rth

ediff

eren

ces

inm

eans.

*,**

,an

d**

*in

dic

ate

sign

ifica

nce

atth

e10

%,

5%,

and

1%le

vels

,re

spec

tive

ly.

Posi

tion

sP

osi

tions

Ove

rall

pre

vio

usl

yin

crea

sed

pre

vio

usl

ydec

rease

d

Pro

bab

ilit

yD

iffer

ence

Pro

babilit

yD

iffer

ence

Pro

babilit

yD

iffer

ence

Bin

ofin

crea

sero

w(3

)-

(j)

p-v

alu

eof

incr

ease

row

(3)

-(j

)p-v

alu

eof

incr

ease

row

(3)

-(j

)p-v

alu

e

undis-

closed

(1)

0.2

0.36

4−

0.01

0(0

.469)

0.3

72−

0.0

10

(0.5

24)

0.3

45−

0.012

(0.6

37)

(2)

0.3

0.39

1−

0.03

7**

(0.0

14)

0.4

22−

0.0

60***

(0.0

01)

0.3

28

0.005

(0.8

46)

(3)

0.4

0.35

40.3

62

0.3

33

disclosed

(4)

0.5

0.40

8−

0.05

4***

(0.0

07)

0.4

87−

0.1

25***

(0.0

00)

0.2

63

0.071**

(0.0

37)

(5)

0.6

0.47

6−

0.12

2***

(0.0

00)

0.5

73−

0.2

11***

(0.0

00)

0.3

13

0.020

(0.6

06)

(6)

0.7

0.44

0−

0.08

6***

(0.0

01)

0.5

61−

0.1

99***

(0.0

00)

0.2

47

0.086**

(0.0

36)

(7)

0.8

0.44

9−

0.09

5***

(0.0

01)

0.6

04−

0.2

42***

(0.0

00)

0.1

75

0.158***

(0.0

01)

(8)

0.9

0.47

7−

0.12

3***

(0.0

00)

0.6

67−

0.3

05***

(0.0

00)

0.1

88

0.146***

(0.0

05)

(9)≥

1.0

0.47

4−

0.12

0***

(0.0

00)

0.6

49−

0.2

87***

(0.0

00)

0.2

14

0.120***

(0.0

00)

26

Table

IA.2

:D

ura

tion

wit

hin

rep

ort

ing

bin

s:A

ltern

ati

ve

sam

ple

split

This

table

rep

eats

the

dura

tion

analy

sis

of

Table

4usi

ng

an

alt

ernati

ve

sam

ple

split

of

short

posi

tions

pre

vio

usl

yin

crea

sed

and

posi

tions

pre

vio

usl

ydec

reas

ed.

The

tab

lere

por

tsth

em

ean

and

med

ian

num

ber

oftr

adin

gd

ays

spen

tin

each

dis

clos

ure

bin

(Pan

els

Aan

dB

,re

spec

tive

ly).

Inad

dit

ion

,it

dis

pla

ys

the

diff

eren

cein

mea

n(m

edia

n)

dura

tion

ofro

w(3

)re

lati

veto

row

(j),

the

0.4

rep

orti

ng

bin

just

bel

owth

epu

blica

tion

thre

shol

d(s

had

edin

gray

),an

dth

ep-v

alu

efo

rdiff

eren

ces

inm

eans

(med

ians)

.*,

**,

an

d***

indic

ate

sign

ifica

nce

at

the

10%

,5%

,an

d1%

leve

ls,

resp

ecti

vely

.

Panel

A:

Mean

dura

tion

wit

hin

rep

ort

ing

bin

intr

ad

ing

days

Posi

tions

Posi

tions

Ove

rall

pre

vio

usl

yin

crea

sed

pre

vio

usl

ydec

rease

d

Mea

nD

iffer

ence

Mea

nD

iffer

ence

Mea

nD

iffer

ence

Bin

du

rati

onro

w(3

)-

(j)

p-v

alu

edu

rati

on

row

(3)

-(j

)p-v

alu

edu

rati

on

row

(3)

-(j

)p-v

alu

e

undis-

closed

(1)

0.2

18.3

2.2**

(0.0

19)

19.4

3.8***

(0.0

01)

15.6

−3.

4**

(0.0

27)

(2)

0.3

17.0

3.6***

(0.0

00)

18.3

4.9***

(0.0

00)

13.3

−1.

1(0

.429)

(3)

0.4

20.6

23.2

12.2

disclosed

(4)

0.5

14.3

6.2***

(0.0

00)

15.0

8.3***

(0.0

00)

12.8

−0.

7(0

.690)

(5)

0.6

13.7

6.8***

(0.0

00)

15.3

7.9***

(0.0

00)

10.7

1.4

(0.4

51)

(6)

0.7

13.3

7.3***

(0.0

00)

14.6

8.6***

(0.0

00)

11.0

1.2

(0.5

70)

(7)

0.8

13.6

7.0***

(0.0

01)

15.1

8.1***

(0.0

03)

10.0

2.1

(0.3

73)

(8)

0.9

11.9

8.7***

(0.0

00)

11.8

11.

5***

(0.0

00)

9.4

2.7

(0.2

96)

(9)≥

1.0

12.6

8.0***

(0.0

00)

14.9

8.3***

(0.0

00)

8.2

3.9***

(0.0

02)

27

Table

IA.2

–C

onti

nued

Panel

B:

Media

ndura

tion

wit

hin

rep

ort

ing

bin

intr

adin

gdays

Posi

tion

sP

osi

tions

Ove

rall

pre

vio

usl

yin

crea

sed

pre

vio

usl

ydec

rease

d

Med

ian

Diff

eren

ceM

edia

nD

iffer

ence

Med

ian

Diff

eren

ceB

indu

rati

onro

w(3

)-

(j)

p-v

alu

edu

rati

on

row

(3)

-(j

)p-v

alu

ed

ura

tion

row

(3)

-(j

)p-v

alu

e

undis-

closed

(1)

0.2

61***

(0.0

04)

72***

(0.0

00)

50*

(0.0

96)

(2)

0.3

61***

(0.0

03)

72***

(0.0

00)

50

(0.9

84)

(3)

0.4

79

5

disclosed

(4)

0.5

52***

(0.0

00)

63***

(0.0

00)

41

(0.9

34)

(5)

0.6

52***

(0.0

00)

54***

(0.0

00)

41

(0.3

93)

(6)

0.7

43***

(0.0

00)

54***

(0.0

00)

32

(0.1

16)

(7)

0.8

43***

(0.0

00)

54***

(0.0

00)

23***

(0.0

07)

(8)

0.9

43***

(0.0

00)

54***

(0.0

00)

32*

(0.0

54)

(9)≥

1.0

43*

**

(0.0

00)

45***

(0.0

00)

32***

(0.0

00)

28

Table IA.3:Probability of increase: Regression approach with fixed effectsThis table shows estimates from the linear probability model

yi,j,t+1 = β0 + β1 Just below thresholdi,j,t +∑k

βk k bini,j,t + ui,j,t+1,

with yi,j,t+1 = 1 (bini,j,t+1 > bini,j,t), and ui,j,t+1 models various fixed effects and an error term. k bini,j,t

is equal to 1 if investor j has a short position in stock i in the bin k at day t, with k ∈ {0.2, 0.5, 0.6, . . . , 1.0+},where 1.0+ indicates position bins greater or equal to 1.0. The unconditional probability of increasing ashort position to enter the next bin (estimated by the sample average of yi,j,t) is 2.0%. Panel A showscoefficient estimates using the 0.3 bin as omitted reference category. Panel B tests for differences inthe probability of increase between the bin just below the threshold and all other bins. The estimatedcoefficients are scaled to reflect changes in percentage points. Standard errors are clustered at the investor-stock and time level. The t-statistics are given in parentheses, and *, **, and *** indicate significance atthe 10%, 5%, and 1% levels, respectively.

(1) (2) (3) (4) (5)

Panel A: Regression with reporting bin dummies

0.2 bin -0.43*** -0.16 -0.63*** -0.29** -0.41***(-3.41) (-1.30) (-4.72) (-2.20) (-2.76)

0.3 bin – – – – –

0.4 bin (Just below threshold) -0.54*** -0.92*** -0.68*** -0.61*** -1.08***(-3.66) (-5.72) (-4.23) (-3.55) (-5.40)

0.5 bin 0.64*** -0.20 0.45* 0.27 -0.16(2.74) (-0.87) (1.85) (1.10) (-0.53)

0.6 bin 1.26*** 0.65** 1.37*** 0.99*** 0.68*(3.70) (2.03) (4.05) (2.61) (1.85)

0.7 bin 0.92** 0.61* 0.97*** 0.91** 0.37(2.18) (1.87) (2.73) (2.52) (1.02)

0.8 bin 0.69 0.78* 0.69 1.65*** 1.07**(1.35) (1.79) (1.58) (3.57) (2.22)

0.9 bin 1.36* 0.91* 0.93 1.68*** 0.94*(1.90) (1.92) (1.39) (3.76) (1.87)

≥ 1.0 bin 1.42*** 0.74** 1.44*** 2.40*** 1.61***(3.90) (2.20) (4.59) (6.11) (4.46)

Fixed effects:Time Yes Yes No No NoStock No Yes No No NoInvestor No Yes No No NoStock × time No No Yes No YesInvestor × time No No No Yes Yes

R2 (in %) 0.61 2.56 15.71 19.58 38.09Within R2 (in %) 0.20 0.08 0.22 0.22 0.15Number of observations 278,003 277,999 255,274 228,358 202,057

Continued on next page

29

Table IA.3 – Continued from previous page

(1) (2) (3) (4) (5)

Panel B: Differences in the probability of increase

Just below threshold – 0.2 bin -0.11 -0.76*** -0.05 -0.31** -0.66***(-0.85) (-4.70) (-0.31) (-1.99) (-3.34)

Just below threshold – 0.3 bin -0.54*** -0.92*** -0.68*** -0.61*** -1.08***(-3.66) (-5.72) (-4.23) (-3.55) (-5.40)

Just below threshold – 0.5 bin -1.18*** -0.72*** -1.13*** -0.88*** -0.92***(-5.04) (-2.92) (-4.49) (-3.38) (-2.89)

Just below threshold – 0.6 bin -1.81*** -1.57*** -2.05*** -1.60*** -1.76***(-5.43) (-4.85) (-6.10) (-4.22) (-4.69)

Just below threshold – 0.7 bin -1.47*** -1.53*** -1.65*** -1.52*** -1.45***(-3.52) (-4.60) (-4.77) (-4.25) (-3.98)

Just below threshold – 0.8 bin -1.23** -1.70*** -1.37*** -2.26*** -2.15***(-2.44) (-3.86) (-3.09) (-4.79) (-4.30)

Just below threshold – 0.9 bin -1.91*** -1.83*** -1.61** -2.28*** -2.02***(-2.68) (-3.90) (-2.43) (-5.24) (-4.18)

Just below threshold – (≥ 1.0 bin) -1.96*** -1.66*** -2.12*** -3.01*** -2.68***(-5.53) (-5.03) (-6.75) (-7.64) (-7.40)

30

Table IA.4:Probability of increase: Fixed-effects regression approach with at-record-highinteractionsThis table repeats the analysis of Table IA.3 but interacts all coefficients with a dummy variable indicatingwhether positions are at the record high or not. The estimated coefficients are differences in the probabilityof increase between the bin just below the threshold and all other bins. Standard errors are clustered atthe investor-stock and time level. The t-statistics are given in parentheses, and *, **, and *** indicatesignificance at the 10%, 5%, and 1% levels, respectively.

(1) (2) (3) (4)

Just below threshold – 0.2 bin 0.07 0.96** 0.71** 0.57(0.22) (2.42) (2.29) (1.60)

Just below threshold – 0.3 bin 0.05 0.37 0.57* 0.31(0.17) (0.99) (1.82) (0.88)

Just below threshold – 0.5 bin 0.82** 0.80* 0.56 0.77(2.29) (1.88) (1.34) (1.54)

Just below threshold – 0.6 bin -0.79 -0.62 -1.00 -0.61(-1.53) (-0.99) (-1.59) (-0.89)

Just below threshold – 0.7 bin 0.11 0.67 0.79* 1.02**(0.29) (1.24) (1.69) (2.15)

Just below threshold – 0.8 bin 0.24 0.73 0.14 0.22(0.41) (1.10) (0.21) (0.29)

Just below threshold – 0.9 bin 0.52 0.42 0.22 0.49(0.96) (0.61) (0.35) (0.63)

Just below threshold – (≥ 1.0 bin) 0.36 0.20 -0.47 0.41(0.76) (0.39) (-0.78) (0.68)

Record high × (Just below threshold – 0.2 bin) -0.94*** -1.05** -1.15*** -1.37***(-2.86) (-2.54) (-3.32) (-3.40)

Record high × (Just below threshold – 0.3 bin) -1.21*** -1.11*** -1.41*** -1.68***(-3.67) (-2.73) (-3.92) (-3.96)

Record high × (Just below threshold – 0.5 bin) -2.26*** -2.55*** -1.88*** -2.37***(-4.94) (-4.98) (-3.63) (-3.93)

Record high × (Just below threshold – 0.6 bin) -1.01 -1.77** -0.58 -1.59*(-1.59) (-2.36) (-0.78) (-1.91)

Record high × (Just below threshold – 0.7 bin) -2.65*** -3.35*** -3.59*** -4.20***(-3.73) (-4.17) (-4.97) (-4.89)

Record high × (Just below threshold – 0.8 bin) -2.92*** -2.79*** -3.45*** -3.59***(-3.42) (-3.14) (-3.75) (-3.42)

Record high × (Just below threshold – 0.9 bin) -3.46*** -2.66** -3.50*** -3.36***(-3.84) (-2.21) (-3.64) (-3.38)

Record high × (Just below threshold – (≥ 1.0 bin)) -2.86*** -3.08*** -3.49*** -4.42***(-5.41) (-5.08) (-4.87) (-6.18)

Record high 1.31*** 2.30*** 1.89*** 2.15***(4.51) (6.02) (6.05) (5.86)

Fixed effects:Time Yes Yes Yes NoStock Yes No No NoInvestor Yes No No NoStock × time No Yes No YesInvestor × time No No Yes Yes

R2 (in %) 2.62 15.86 19.67 38.17Within R2 (in %) 0.14 0.39 0.33 0.28Number of observations 277,999 255,274 228,358 202,057

31

Table IA.5:The probability of increasing, decreasing, and not changing a positionFollowing the regression approach of Table 5, this table explores the probability of increasing, decreasing ornot changing a short position in the bin just below the publication threshold relativ to other reporting bins.The results of Column 1 coincide with those of Table IA.3, Panel A, Column 5. The estimated coefficientsare scaled to reflect changes in percentage points. Standard errors are clustered at the investor-stock andtime level. The t-statistics are given in parentheses, and *, **, and *** indicate significance at the 10%,5%, and 1% levels, respectively.

(1) (2) (3)Probability of

increase no change decrease

Just below threshold – 0.2 bin -0.66*** 0.44 0.22(-3.34) (1.33) (1.06)

Just below threshold – 0.3 bin -1.08*** 1.51*** -0.44**(-5.40) (4.85) (-2.15)

Just below threshold – 0.5 bin -0.92*** 2.42*** -1.50***(-2.89) (4.82) (-4.54)

Just below threshold – 0.6 bin -1.76*** 3.21*** -1.45***(-4.69) (5.70) (-3.51)

Just below threshold – 0.7 bin -1.45*** 3.06*** -1.62***(-3.98) (4.80) (-3.65)

Just below threshold – 0.8 bin -2.15*** 4.31*** -2.16***(-4.30) (5.35) (-4.14)

Just below threshold – 0.9 bin -2.02*** 3.29*** -1.27**(-4.18) (4.14) (-2.40)

Just below threshold – (≥ 1.0 bin) -2.68*** 4.38*** -1.70***(-7.40) (6.92) (-3.94)

Fixed effects:Stock × time Yes Yes YesInvestor × time Yes Yes Yes

R2 (in %) 38.09 41.63 40.86Within R2 (in %) 0.15 0.24 0.11Number of observations 202,057 202,057 202,057

32

Table

IA.6

:D

ura

tion

wit

hin

rep

ort

ing

bin

s:Is

there

hesi

tance

befo

recr

oss

ing

the

dis

closu

rebin

?T

his

table

rep

eats

the

dura

tion

anal

ysi

sof

Tab

le4

condit

ionin

gon

pos

itio

ns

that

even

tual

lyin

crea

seon

the

nex

tch

ange

.T

he

table

rep

orts

the

mea

nan

dm

edia

nnum

ber

oftr

adin

gday

ssp

ent

inea

chdis

clos

ure

bin

(Pan

els

Aan

dB

,re

spec

tive

ly).

Inad

dit

ion,

itdis

pla

ys

the

diff

eren

cein

mea

n(m

edia

n)

du

rati

onof

row

(3),

the

0.4

rep

orti

ng

bin

just

bel

owth

epub

lica

tion

thre

shol

d(s

had

edin

gray

),re

lati

veto

row

(j),

and

thep-v

alue

for

diff

eren

ces

inm

ean

s(m

edia

ns)

.*,

**,

and

***

ind

icat

esi

gnifi

cance

at

the

10%

,5%

,and

1%

level

s,re

spec

tivel

y.

Panel

A:

Mean

dura

tion

wit

hin

rep

ort

ing

bin

intr

ad

ing

days

Posi

tion

sP

osi

tions

Ove

rall

at

thei

rre

cord

hig

hb

elow

thei

rre

cord

hig

h

Mea

nD

iffer

ence

Mea

nD

iffer

ence

Mea

nD

iffer

ence

Bin

dura

tion

row

(3)

-(j

)p-v

alu

edu

rati

on

row

(3)

-(j

)p-v

alu

edu

rati

on

row

(3)

-(j

)p-v

alu

e

undis-

closed

(1)

0.2

13.9

−0.

2(0

.883)

16.7

−0.

3(0

.862)

11.4

−1.

2(0

.339)

(2)

0.3

12.5

1.2

(0.2

88)

14.5

1.9

(0.3

00)

10.3

−0.

2(0

.901)

(3)

0.4

13.8

16.4

10.1

disclosed

(4)

0.5

11.8

1.9

(0.2

09)

13.1

3.3

(0.1

52)

9.7

0.5

(0.7

69)

(5)

0.6

10.0

3.8**

(0.0

24)

10.8

5.7**

(0.0

34)

8.9

1.2

(0.4

39)

(6)

0.7

10.9

2.9

(0.1

34)

10.9

5.5*

(0.0

59)

10.9

−0.

7(0

.708)

(7)

0.8

8.8

4.9**

(0.0

26)

9.2

7.2**

(0.0

25)

7.9

2.3

(0.3

54)

(8)

0.9

10.9

2.9

(0.2

42)

9.0

7.5**

(0.0

33)

15.0

−4.

9(0

.121)

(9)≥

1.0

9.6

4.1***

(0.0

01)

10.0

6.4***

(0.0

00)

8.7

1.5

(0.3

24)

33

Table

IA.6

–C

onti

nued

Panel

B:

Media

ndura

tion

wit

hin

rep

ort

ing

bin

intr

adin

gdays

Posi

tion

sP

osi

tions

Ove

rall

at

thei

rre

cord

hig

hb

elow

thei

rre

cord

hig

h

Med

ian

Diff

eren

ceM

edia

nD

iffer

ence

Med

ian

Diff

eren

ceB

indu

rati

onro

w(3

)-

(j)

p-v

alu

edu

rati

on

row

(3)

-(j

)p-v

alu

ed

ura

tion

row

(3)

-(j

)p-v

alu

e

undis-

closed

(1)

0.2

6−

1(0

.467)

7−

1(0

.244)

5−

1(0

.775)

(2)

0.3

50

(0.7

89)

60

(0.9

93)

40

(0.5

29)

(3)

0.4

56

4

disclosed

(4)

0.5

50

(0.8

61)

60

(0.9

21)

40

(0.7

38)

(5)

0.6

41**

(0.0

49)

33***

(0.0

06)

40

(0.9

97)

(6)

0.7

32

(0.1

15)

33*

(0.0

70)

40

(0.5

02)

(7)

0.8

41**

(0.0

12)

42**

(0.0

23)

31*

(0.0

53)

(8)

0.9

41*

(0.0

74)

42**

(0.0

19)

5−

1(0

.912)

(9)≥

1.0

32***

(0.0

01)

42***

(0.0

00)

31

(0.5

30)

34

Table

IA.7

:A

vera

ge

posi

tion

change

giv

en

that

ap

osi

tion

incr

ease

occ

urs

This

table

show

sth

eav

erage

posi

tion

changes

,giventhatapositionincrease

occurred

,acr

oss

diff

eren

tre

port

ing

bin

sfr

om

whic

hth

ep

osi

tion

was

incr

ease

d(s

tart

ing

bin

).In

addit

ion,

itd

ispla

ys

the

diff

eren

ces

inm

eans

ofro

w(3

),th

e0.

4re

por

tin

gb

inju

stb

elow

the

pu

blica

tion

thre

shol

d(s

had

edin

gra

y),

rela

tive

toro

w(j

),and

thep-v

alu

efo

rth

ediff

eren

ces

inm

eans.

The

table

dis

pla

ys

posi

tion

changes

for

the

over

all

sam

ple

and

for

two

subsa

mple

s,in

whic

hw

esp

lit

the

sam

ple

into

shor

tp

osit

ions

atth

eir

reco

rdhig

han

din

top

osit

ions

bel

owth

eir

reco

rdhig

h.

*,**

,an

d**

*in

dic

ate

sign

ifica

nce

atth

e10

%,

5%,

and

1%le

vels

,re

spec

tivel

y.

Posi

tion

sP

osi

tions

Ove

rall

at

thei

rre

cord

hig

hb

elow

thei

rre

cord

hig

h

Mea

nM

ean

posi

tion

Mea

nSta

rtin

gp

osit

ion

Diff

eren

cep

osi

tion

Diff

eren

cep

osi

tion

Diff

eren

cebin

chan

gero

w(3

)-

(j)

p-v

alu

ech

ange

row

(3)

-(j

)p-v

alu

ech

ange

row

(3)

-(j

)p-v

alu

e

undis-

closed

0.2

(1)

0.11

10.0

03

(0.3

94)

0.1

09

0.007

(0.1

47)

0.1

12−

0.001

(0.8

30)

0.3

(2)

0.11

10.0

03

(0.3

78)

0.1

12

0.005

(0.3

31)

0.1

10

0.001

(0.8

82)

0.4

(3)

0.11

40.1

17

0.1

11

disclosed

0.5

(4)

0.12

1−

0.007*

(0.0

88)

0.1

16

0.001

(0.8

94)

0.1

30−

0.019***

(0.0

05)

0.6

(5)

0.12

3−

0.009**

(0.0

37)

0.1

21−

0.004

(0.5

03)

0.1

27−

0.016**

(0.0

11)

0.7

(6)

0.12

2−

0.007

(0.1

33)

0.1

24−

0.008

(0.2

75)

0.1

17−

0.006

(0.3

06)

0.8

(7)

0.12

6−

0.012**

(0.0

18)

0.1

23−

0.006

(0.3

60)

0.1

35−

0.024***

(0.0

04)

0.9

(8)

0.13

1−

0.017***

(0.0

04)

0.1

21−

0.004

(0.5

88)

0.1

56−

0.045***

(0.0

00)

≥1.

0(9

)0.

119−

0.005

(0.3

68)

0.1

13

0.003

(0.6

64)

0.1

31−

0.020**

(0.0

23)

35

Table

IA.8

:A

ddit

ional

sum

mary

stati

stic

sfo

rp

osi

tion

changes

giv

en

that

ap

osi

tion

incr

ease

occ

urs

This

table

show

sri

ght-

hand

per

centi

les

of

posi

tion

changes

,giventhatapositionincrease

occurred

,acr

oss

diff

eren

tre

port

ing

bin

sfr

om

whic

hth

ep

osit

ion

was

incr

ease

d(s

tart

ing

bin

).T

he

table

dis

pla

ys

pos

itio

nch

ange

sac

ross

the

diff

eren

tp

erce

nti

les

for

the

over

all

sam

ple

and

for

two

subsa

mple

s,in

wh

ich

we

split

the

sam

ple

into

shor

tp

osit

ions

at

thei

rre

cord

hig

hand

into

posi

tions

bel

owth

eir

reco

rdh

igh.

Posi

tion

sP

osi

tions

Ove

rall

at

thei

rre

cord

hig

hb

elow

thei

rre

cord

hig

h

Sta

rtin

gP

erce

nti

les

Per

centi

les

Per

centi

les

bin

50th

75th

90th

95th

50th

75th

90th

95th

50th

75th

90th

95th

undis-

closed

0.2

(1)

0.1

0.1

0.1

0.2

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.2

0.3

(2)

0.1

0.1

0.1

0.2

0.1

0.1

0.1

0.2

0.1

0.1

0.1

0.1

0.4

(3)

0.1

0.1

0.1

0.2

0.1

0.1

0.2

0.2

0.1

0.1

0.1

0.2

disclosed

0.5

(4)

0.1

0.1

0.2

0.2

0.1

0.1

0.2

0.2

0.1

0.1

0.2

0.4

0.6

(5)

0.1

0.1

0.2

0.2

0.1

0.1

0.2

0.2

0.1

0.1

0.2

0.3

0.7

(6)

0.1

0.1

0.2

0.2

0.1

0.1

0.2

0.2

0.1

0.1

0.1

0.3

0.8

(7)

0.1

0.1

0.2

0.2

0.1

0.1

0.2

0.2

0.1

0.1

0.2

0.2

0.9

(8)

0.1

0.1

0.2

0.3

0.1

0.1

0.2

0.2

0.1

0.2

0.3

0.3

≥1.

0(9

)0.

10.1

0.2

0.2

0.1

0.1

0.2

0.2

0.1

0.1

0.2

0.3

36

Table IA.9:Robustness tests: Calendar-time portfolio approachThis table shows the performance of stocks for which there is at least one secretive short seller just belowthe publication threshold. The analysis is the same as in Table 8 with different sample specifications. InPanel A, we report the baseline results of Panel A of Table 8. In Panel B, we weight the stocks equallyrather than by the number positions that are secretive and just below the publication threshold. In PanelC, we report results when we exclude penny stocks with a price below 1 EUR. In Panel D, we exclude astock from the portfolio if a secretive short seller stays in the bin just below the publication threshold forless than five days. In Panel E, we use European asset pricing factors instead of local. To account for riskfactors, we regress the portfolio excess return on the market excess return (MKTRF), the size (SMB) andvalue (HML) factors, and the momentum factor (WML). For brevity, the table reports only the alphas(in bps per day) of the time-series regression. The t-statistics are computed with Newey-West standarderrors and are shown in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% levels,respectively. Returns are daily and the sample period is November 5, 2012 to March 31, 2015.

(1) (2) (3)

CAPM Fama-French Carhart

Panel A: Baseline result from Table 8

Alpha -5.46** -6.13*** -5.66**(-2.00) (-2.83) (-2.57)

Panel B: Equal-weighted portfoliojust below the threshold

Alpha -4.82** -5.42*** -5.17***(-1.98) (-3.02) (-3.01)

Panel C: Stocks above 1 EUR

Alpha -5.35* -6.01*** -5.55**(-1.96) (-2.77) (-2.52)

Panel D: At least 5 days just below threshold

Alpha -5.32** -5.97*** -5.58***(-2.06) (-2.99) (-2.72)

Panel E: European pricing factors

Alpha -4.76 -5.45* -5.81*(-1.57) (-1.87) (-1.95)

37

References

Degeorge, F., Patel, J. and Zeckhauser, R. (1999), ‘Earnings management to exceedthresholds’, The Journal of Business 72(1), 1–33.

Griffin, J. M. (2002), ‘Are the Fama and French factors global or country specific?’,Review of Financial Studies 15(3), 783–803.

Nagel, S. (2005), ‘Short sales, institutional investors and the cross-section of stockreturns’, Journal of Financial Economics 78(2), 277–309.

38