Informed Trading and Price Discovery Before Corporate Events

ARTICLE IN PRESS JID: FINEC [m3Gdc; June 28, 2017;21:7 ]

Journal of Financial Economics 0 0 0 (2017) 1–28

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Journal of Financial Economics

journal homepage: www.elsevier.com/locate/jfec

Informed trading and price discovery before corporate ✩ events

∗ Shmuel Baruch a, Marios Panayides b, Kumar Venkataraman c, a David Eccles School of Business, University of Utah, Salt Lake City, UT 84112, USA b Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, USA c Edwin L. Cox School of Business, Southern Methodist University, Dallas, TX 75275, USA

a r t i c l e i n f o a b s t r a c t

Article history: Stock prices incorporate less news before negative events than positive events. Further, Received 5 March 2015 informed agents use less price aggressive (limit) orders before negative events and more

Revised 8 June 2016 price aggressive (market) orders before positive events (buy–sell asymmetry). Motivated Accepted 29 June 2016 by these patterns, we model the execution risk that informed agents impose on each other Available online xxx and relate the asymmetry to costly short selling. When investor base is narrow, security

JEL classiﬁcations: borrowing is diﬃcult, or the magnitude of the event is small, buy–sell asymmetry is pro-

G11 nounced and price discovery before negative events is lower. Overall, we show that the G12 strategies of informed traders inﬂuence the process of price formation in ﬁnancial mar- G14 kets, as predicted by theory. G18 ©2017 Elsevier B.V. All rights reserved.

Keywords: Informed trader Insider trading Limit order Short selling Buy–sell asymmetry

1. Introduction

✩ We thank the editor (Bill Schwert) and, in particular, Gideon Saar (the Informed traders play a central role in price formation referee) for many constructive suggestions. For their comments, we thank in ﬁnancial markets. In microstructure models (see Kyle, Amber Anand, Leonce Bargeron, Kerry Back, Indraneel Chakraborty, Jeff

Coles, Kevin Crotty, Dave Denis, Diane Denis, Amy Edwards, Robert En- 1985; Glosten and Milgrom, 1985), informed traders re- gle, Tom George, Hans Heidle, Stacey Jacobsen, Pankaj Jain, Ron Kaniel, ceive a private signal about the security’s value and build Praveen Kumar, Sebastian Michenaud, Bruce Lehman, Ken Lehn, Swami positions before information is widely available. The mar- Kalpathy, Bige Kahraman, Albert Menkveld, Ling Peng, Gideon Saar, Bob ket participants observe the imbalance created by the in- Schwartz, Wing Wah Tham, Erik Thiessen, Shawn Thomas, Rex Thomp- formed order ﬂow and move prices in the direction of the son, Laura Tuttle, Mathijs Van Dijk, Vish Viswanathan, Sunil Wahal, Ingrid

Werner, Chad Zutter, and seminar participants at Arizona State Univer- signal. Thus, the theoretical literature predicts that the ac- sity, Baruch College of the City University of New York, Lehigh Univer- tivities of informed traders influence the informational ef- sity, Rice University, Southern Methodist University, University of Cincin- ficiency of prices before news releases. nati, University of Houston, University of Pittsburgh, University of Toronto, Wilfrid Laurier University, the 2013 Erasmus Liquidity Conference, the 2013 Stern Microstructure Conference, the 2013 Northern Finance Associ- ation Conference, the 2013 European Finance Association Conference, the to Hank Bessembinder for helpful discussions during the development of spring 2015 Conference of the Multinational Finance Society, and US Se- the project. ∗ curities and Exchange Commission. We thank Laurent Fournier and Carole Corresponding author. Huguet of Euronext-Paris for providing data. We are grateful in particular E-mail address: [email protected] (K. Venkataraman). http://dx.doi.org/10.1016/j.jfineco.2017.05.008 0304-405X/© 2017 Elsevier B.V. All rights reserved.

Please cite this article as: S. Baruch et al., Informed trading and price discovery before corporate events, Journal of Financial Economics (2017), http://dx.doi.org/10.1016/j.jﬁneco.2017.05.008 ARTICLE IN PRESS JID: FINEC [m3Gdc; June 28, 2017;21:7 ]

2 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28

In this study, we present an extension of the theory de- purchases, dividend initiations, and dividend terminations scribing informed trader’s strategies and provide relevant for Euronext-Paris stocks. We attribute the change in trad- empirical evidence on the most basic questions about in- ing activity observed before an unscheduled announce- formed trading: First, how do informed traders build posi- ment relative to a control period for the same firm to the tions, and what explains their strategies? Second, how do actions of informed agents. Using the control period to es- their decisions to use aggressive or passive strategies affect timate the shift in order flow before the event reduces the process through which private information is incorpo- the likelihood that the event effect is explained by time- rated into security prices? Third, how do their strategies invariant firm attributes that influence order submission affect the speed of learning before news releases? Under- on non-event days. standing the behavior of informed agents is central both to We present a model of the informed agent’s choice of validating the well-developed theoretical literature that re- market versus limit orders. The intuition for the model is lates trading strategies to price discovery and to designing as follows. Informed agents face a trade-off between trans- better surveillance systems that monitor and detect insider acting with certainty at a current bid or offer price by plac- trading activity. 1 ing a market order versus managing execution risk in an Despite the importance of understanding how informed attempt to get a better price by placing a limit order. In ad- agents build positions, data limitations have left unan- dition to paying the bid-ask spread, market orders tip off swered many important questions about their strategies. market participants about the private signal and increase In the days leading to corporate announcements, such price impact cost. When other informed agents receive the as those related to mergers and acquisitions (M&As) and same signal and trade on the same side of the market, the earnings releases, prior research presents widespread ev- execution risk of a limit order strategy is particularly high. idence of insider trading activity and stock price move- Our model predicts that informed agents use limit orders ments. 2 Many publicly available data sources, such as when sufficient uncertainty exists about the presence of the NYSE Trade and Quote (TAQ) database, report all the other informed agents and use market orders if they are transactions in a market but do not identify the specific certain that other informed agents are present. These pre- trades of informed agents. Some data on transactions are dictions follow the Kaniel and Liu (2006) theoretical work available from regulatory Form 4 filed by corporate in- showing that informed agents could use limit orders if the siders with the US Securities and Exchange Commission mass of informed agents is sufficiently low. (SEC) (see Seyhun, 1986 ), or from the SEC’s case files Informed agents face less competition when the nature of defendants formally charged with insider trading (see of private information conveys a decrease in stock price. Meulbroek, 1992 ). However, these data sets do not con- Corporate insiders face more constraints when they trade tain order-level information that is necessary to describe on bad news than on good news (see Marin and Olivier, the strategies of informed agents. 2008 ). 4 Informed sellers who do not own the stock incur We examine a data set provided by the Euronext-Paris the cost of borrowing shares. When borrowing costs are exchange with information on all orders submitted for all high, these informed sellers are less likely to trade. Consis- stocks. The Euronext data do not directly identify the or- tent with our model, we report a novel empirical regular- ders of informed agents. To identify informed order flow, ity of an asymmetry in informed agents’ order submission we employ a research design based on the methodology strategies before positive and negative events. We find an from Chae (2005), Graham, Koski, and Loewenstein (2006) , increase in price aggressiveness of buy orders before pos- and Sarkar and Schwartz (2009) . Prior studies show that itive events and a decrease in price aggressiveness of sell uninformed traders decrease participation in periods lead- orders before negative events (henceforth, buy–sell asym- ing to news releases with timing that is known in advance, metry). As in Diamond and Verrecchia (1987) , our model such as earnings announcements. In contrast, uninformed relies on short sale constraints to explain the buy–sell traders cannot anticipate unscheduled news events with asymmetry observed in the data. However, in our model, timing that is a complete surprise, but informed traders the asymmetry emerges not only because some informed can, if their information concerns the event. 3 We exam- sellers decide to abstain, but also because informed sellers ine a sample of unscheduled corporate announcements re- become liquidity providers. lated to M&As, seasoned equity offerings (SEOs), stock re- Our model yields cross-sectional predictions in buy–sell asymmetry based on the anticipated competition among informed sellers. Informed sellers can be one of two types; 1 In this study, the term “informed trader” refers to any person with access to valuable, non public information before a corporate announce- the first type already owns the stock and the second type ment. Examples include corporate insiders, such as board members, di- does not. The probability that the informed seller is of the rectors, and employees and well-connected participants such as bankers, first type increases with broadness of investor base. When analysts, lawyers, and institutional investors. investor base is narrow, when the cost of borrowing shares 2 See, for example, Keown and Pinkerton (1981) on price reaction, is large, and when the magnitude of news release is small Meulbroek (1992) on insider trading, and Bodnaruk, Massa, and Simonov

(2009) and Jegadeesh and Tang (2010) on trading by aﬃliated investment such that the potential gains do not justify the borrowing banks and institutional investors before corporate announcements. costs, a limit order equilibrium emerges in which the ﬁrst

3 A June 6, 2013 Wall Street Journal article reports on the increase in trading activity observed before Smithﬁeld’s acquisition announcement:

“When multiple bidders vie for a company, it isn’t unusual for hundreds 4 Insiders in many markets are prohibited from selling short their own of people to know about the possible deal before it surfaces—including stock (e.g., Section 16 of the US Securities Exchange Act of 1934), or sell employees of banks, law ﬁrms, and other outside advisors, not to mention stock holdings that are part of a compensation contract below a certain the people inside the companies themselves.” threshold.

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 3

Positive news Negative news

Informed traders want to buy Informed traders want to sell

Broad investor base, cheap to short sell, Otherwise or event is large

High execution risk Mild execution risk for informed limit orders for informed limit orders

Informede traders Informed traders use use market orders limit orders

Fig. 1. Competition, execution risk, and order submission strategy. This figure shows that short sale constraints decrease the anticipated competition among informed sellers and lower the execution risk of limit orders. This can lead to asymmetry in informed traders’ order submission strategies before positive and negative news releases for short constrained firms. type of agent uses limit orders and the second type ab- ative events. Results are robust to different methods for stains from trade. On the other hand, when investor base is classifying events as positive and negative, as well as al- broad, when borrowing costs are small, or when the mag- ternative model specifications, including panel regressions. nitude of news release is large, the second type of agent Further, we report the novel empirical result that stock borrows the shares, and both types trade. The competition prices incorporate less news before negative events than among informed sellers increases the execution risk of a positive events. Following Biais, Hillion, and Spatt (1999) , limit order strategy and leads to usage of market orders. we estimate the efficiency of price discovery before cor- When the private information conveys an increase in stock porate events using unbiasedness regressions in which we price, informed buyers always anticipate competition and regress the close-to-close return during Days [ −6, + 1] on use market orders. Fig. 1 shows how anticipated competi- the return in the interval [ −6, I ], where I represents half- tion among informed agents can lead to buy–sell asymme- hour snapshots in the interval [ −5, −1]. Barclay and Hen- try before corporate events. dershott (2003) interpret the slope of the unbiasedness Motivated by prior work, our empirical measures of regressions as the signal:noise ratio. In our research de- short sale constraints are stock index membership, avail- sign, as the slope moves closer to one the interpretation ability of exchange-listed stock options, and eligibility for is that the security price before the event reflects the se- Euronext’s Deferred Settlement Service (SRD, Service de curity price after the event with increasing precision. For Règlement Différé). Index stocks have broad investor base, positive and negative events, the slope of the unbiasedness active participation by institutions, and lower borrowing regression at the beginning of the pre-event window is not cost (see D’Avolio, 20 02; Nagel, 20 05 ). Stock options al- statistically different from zero. As the event gets closer low informed sellers to establish equivalent positions at (i.e., Day [ −1]), the slope for positive events is not signif- a lower cost in short constrained stocks (see Battalio and icantly different from one; for negative events, the slope Schultz, 2011; Hu, 2014 ). Euronext’s SRD facility allows is lower (between zero and one) and significantly different short positions in eligible stocks to be established more from one. In addition, consistent with higher price discov- easily (see Foucault, Sraer, and Thesmar 2011 ). ery before positive events, we estimate large opportunity We find strong empirical support for the model’s pre- costs when limit orders go unfilled before positive events dictions. In scenarios in which informed traders antici- but not before negative events, indicating that employing pate competition (i.e., index constituent stocks, stocks with limit orders before positive events is a costly strategy. listed options, SRD-eligible stocks, or large news announce- Results based on subsamples suggest that informed ments), we observe an increase in price aggressiveness for traders’ strategies affect the informational efficiency of buy orders before positive events and for sell orders before prices before corporate events. When informed traders em- negative events. In contrast, when short selling is costly ploy less price aggressive orders (i.e., negative events in (i.e., non-index stocks, stocks without listed options, or non-index stocks, SRD-ineligible stocks, and stocks with- SRD-ineligible stocks) or when news is small, we observe out listed options), the slope of the unbiasedness regres- an asymmetry in the mix of order flow before positive sion toward the end of the pre-event window is between and negative events. Specifically, the price aggressiveness zero and one and is statistically different from one. When of buy orders increases before positive events while the informed traders employ more price aggressive orders (i.e., price aggressiveness of sell orders decreases before neg- negative events with no short sale constraints and all

4 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 positive events), the slope of the unbiasedness regression ders before positive and negative events. In Section 4 , we is positive and not statistically different from one. Collec- present a model that explains the results and provides new tively, our results provide support for the well-established testable predictions. We test the model’s cross-sectional theoretical literature that links informed traders’ strate- predictions in Section 5 and present robustness analyses gies to level of competition and, further, to the process of in Section 6 . Section 7 presents the study’s conclusions. price formation in financial markets ( Holden and Subrah- manyam, 1992 ). 2. Sample and data In the Diamond and Verrecchia (1987) and also Saar (2001) framework, informed traders trade upon arrival; in We examine the Euronext-Paris Base de Donnees de other words, they do not employ limit orders. In fact, most Marche (BDM) database for the year 2003. The BDM theoretical work posits that informed agents exclusively database contains detailed information on the charac- use market orders to exploit their information advantage. 5 teristics of all orders submitted for all stocks listed on Novel exceptions are Kumar and Seppi (1994), Chakravarty Euronext-Paris: the stock symbol, the date and time of or- and Holden (1995), Kaniel and Liu (2006), Goettler, Parlour, der submission, whether the order is a buy or a sell, the and Rajan (2009), Boulatov and George (2013) , and Rosu total size of the order (in shares), the displayed size (in (2014) . In these models, informed traders do find it opti- shares), an order type indicator for identifying market or mal under certain conditions to submit limit orders. How- limit orders, a limit price in the case of a limit order, and ever, none of these theoretical papers relates strategies of instructions on when the order expires. informed agents to the direction of the private signal and, We examine the 2003 sample period because more re- further, to asymmetry in competition that is introduced by cent order-level data purchased from the Euronext mar- costly short selling. ket have important inaccuracies. Orders that never get ex- In a recent work, Collin-Dufresne and Fos (2015) study ecuted and orders with a hidden size that are partly ex- a sample of trades reported in the Schedule 13D filings by ecuted do not get reported to the database. The omis- activist investors. The study shows that activist investors sion affects the accuracy of the reconstructed limit or- time their trades when liquidity is high and use limit order book, the analysis of order submission strategies, ders when public disclosure of their positions is not immi- and the construction of control variables used in some nent. These results support the Kaniel and Liu (2006) pre- specifications. diction that informed traders with long-lived information The growth in the alternative trading venues in the last use limit orders. 6 Other experimental and empirical pa- decade has caused equity markets in the United States and pers also suggest that informed traders use limit orders Europe to be highly fragmented. In a fragmented market, (e.g., Barclay, Hendershott, and McCormick (2003), Bloom- an analysis of the informed traders’ strategies must con- field, O’Hara, and Saar (2005, 2015 ), Anand, Chakravarty, sider the choice of the trading venue to execute an order, and Martell (2005), Hautsch and Huang (2012) , and Zhang which introduces a layer of complexity due to the inter- (2013) ). market priority rules and the make-take pricing arrange- Our study points to an unintended consequence of the ment at each trading venue. During our sample period, the widespread ban on short selling by regulators around the vast majority of trading activity (over 90%) in French stocks world in response to the 2007–09 financial crisis. Beber was observed on Euronext-Paris. Thus, the market struc- and Pagano (2013) find that the short sale ban lowers the ture in 2003 provides a simple laboratory to test theoreti- information efficiency of prices, particularly surrounding cal predictions on informed trader strategies. events with negative information. Because the short sale The Euronext database does not provide information on ban reduces competition among sellers, our model predicts trader identity. To identify informed order flow, we exam- that informed sellers who already own the stock use less ine trading activity before unscheduled corporate events. aggressively priced orders, which impedes the flow of neg- The timing of information release for scheduled events, ative private information into prices. Our study offers a such as earning releases, is publicly available in advance of specific mechanism by which short sale constraints impede announcement. Chae (2005), Graham, Koski, and Loewen- the price discovery process, as shown by Boehmer and Wu stein (2006) , and Sarkar and Schwartz (2009) show that, (2013) . although traders do not know in advance the information The rest of the paper is organized as follows. contained in scheduled events, those traders with some Section 2 describes the sample, data sources, and sum- discretion on timing of trades alter activity prior to these mary statistics. In Section 3 , we present evidence of buy– events. For example, Lee, Mucklow, and Ready (1993) find sell asymmetry in order price aggressiveness, price dis- that market makers widen bid-ask spreads and lower covery, and opportunity cost of non-execution of limit or- inside depth before earnings releases. In comparison, informed agents alone are aware of the pending news release for unscheduled (surprise) events in which the 5 See Kyle (1985) and Glosten and Milgrom (1985) for studies of strategic trading in a dealer setting and Glosten (1994), Rock (1996), Seppi timing of the information release is not known publicly (1997) and Back and Baruch (2013) for strategic trading in a limit order in advance. Sarkar and Schwartz (2009) show that trading book setting. activity before unscheduled events is characterized by 6 Evidence on limit order usage in Collin-Dufresne and Fos (2015) is in- one-sided markets, which is consistent with the presence direct because Schedule 13D filings do not require investors to disclose of informed agents. Following the prior literature, we what type of orders they use. The study matches transaction data dis- closed in Schedule 13D filings with TAQ data and uses the Lee and Ready attribute the abnormal trading activity that is observed (1991) algorithm to identify limit orders. before unscheduled events to informed agents.

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 5

Table 1 Abnormal returns surrounding unscheduled corporate events. The table reports the cumulative abnormal returns (CARs) surrounding unscheduled corporate events, namely, acquisitions, targets, seasoned equity offerings (SEOs), repurchases, dividend initiations, and dividend termination, for a sample of Euronext-Paris stocks in 2003. The sample consists of 95 Euronext-Paris stocks with 101 events. Daily abnormal return is calculated by subtracting the daily index (CAC 40) close-to-close returns from the daily event’s close-to-close returns. We classify events as positive and negative news based on the CAR observed over Days [0, + 1], with Day 0 denoting the event day. Reported are the cross-sectional mean and median for the full sample and the subsample by event type. In Panel A, we report the CARs over Days [0, + 1]; in Panel B, the CARs over Days [ −5, + 1]. Panel C reports the CAR ratio, which is deﬁned as the event’s CARs over Days [0, + 1] divided by the event’s CARs over Days [ −5, + 1].

Positive Negative

Type of event Total Number of Mean Median Number of Mean Median events events

Panel A: Cumulative abnormal returns [DAYS 0 to + 1] Overall 101 58 4.84% 2.74% 43 −4.53% −2.57% Acquisitions 35 26 3.61% 2.56% 9 −3.88% −4.15% Targets 25 16 9.52% 7.12% 9 −7.73% −2.65% SEOs 22 8 3.41% 3.42% 14 −4.53% −3.08% Repurchases 14 6 2.88% 1.59% 8 −1.83% −1.82% Dividend initiations 4 2 2.32% 2.32% 2 −5.34% −5.34% Dividend terminations 1 −−− 1 −1.82% −1.82% Panel B: Cumulative abnormal returns [DAYS −5 to + 1] Overall 101 58 6.59% 4.25% 43 −4.98% −3.38% Acquisitions 35 26 4.81% 3.96% 9 −5.03% −4.66% Targets 25 16 12.29% 7.72% 9 −8.10% −7.35% SEOs 22 8 4.63% 4.99% 14 −4.63% −3.67% Repurchases 14 6 2.07% 1.55% 8 −1.68% −1.85% Dividend initiations 4 2 5.66% 5.66% 2 −5.34% −5.34% Dividend terminations 1 −−− 1 −6.84% −6.84% Panel C: CAR ratio of abnormal returns [DAYS 0 to + 1] / abnormal returns [DAYS −5 to + 1] Overall 101 58 44.83% 56.15% 43 73.52% 56.53%

We identify unscheduled events using the Securities accounts on average for 44.83% of the Days [ −5, + 1] CAR, Data Company (SDC) database compiled by Thomson implying that the stock price reflects 55.17% of the news Financial Securities Data and the Amadeus database pro- before positive events. In comparison, the stock price re- vided by Bureau van Dijk. We focus on five types of flects 26.48% of the news before negative events. unscheduled events: M&As, SEOs, repurchases, dividend The descriptive statistics in Table 2 , Panel A suggest that initiations, and dividend terminations. We use Bloomberg the positive event sample has larger market capitalization, and Factiva search engines to identify the date of the first higher stock price, lower return volatility, and smaller bid- news announcement about the event (Day [0]). We elim- ask spread than the negative event sample. The median inate Euronext-Paris stocks that switch from continuous percentage bid-ask spread is approximately 0.80%, indicat- trading to call auctions (or vice versa) or were de-listed ing that the benefit of using limit orders instead of market from Euronext during Days [ −30, + 10] surrounding the orders is economically large. event. The final sample consists of 101 unscheduled Panel B presents descriptive statistics for buy orders be- corporate events for 95 unique stocks. fore positive events and sell orders before negative events. In microstructure models, informed agents build posi- Statistics based on daily averages are reported for event tions in the direction of the private signal before the in- Days [ −5, −1], control Days [ −30, −10], and tests of the dif- formation is widely available. We classify events as posi- ference between event and control days. 7 We report the tive and negative news based on the announcement (Days total number of orders (marketable and non-marketable), [0, + 1]) cumulative abnormal returns (CARs), with CAC 40 the order size, the percentage of marketable to non- index return serving as the benchmark. In Table 1 , Panel A, marketable orders (henceforth, market:limit ratio), and the the 58 positive events have a mean (median) Days [0, + 1] percentage of limit orders with a hidden size. A higher CAR of 4.84% (2.74%) and the 43 negative events have a (lower) market:limit ratio on event days relative to control mean (median) Days [0, + 1] CAR of −4.53% ( −2.57%). We days suggests that informed traders use more (less) aggres- observe positive and negative news for all event types with sively priced orders to build positions before events. the exception of dividend termination. In Table 1 , Panel B, we examine the stock’s price move- ments over a five-day window before the event. For all 7 For a sample of French M&A announcements, Aktas, de Bodt, De- event types, the magnitude of Days [ −5, + 1] CAR in Panel clerck, and Ven Oppens (2007) report that trading volume spikes in the B is larger than Days [0, + 1] CAR in Panel A, implying the five days preceding a merger announcement and that trading volume stock price moves before the event in the direction of the and bid-ask spreads increase for both acquirers and targets in the Days news. The results in Panel C suggest that the stock price [ −65, −6] before announcement. Informed trading in the control period incorporates more information before positive events than reduces the power of our research design to detect informed trading. To minimize the impact of leakage, we delete events with rumors reported + negative events. For positive events, the Days [0, 1] CAR in press articles based on a Factiva search before the news release.

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Table 2 Descriptive statistics on the sample and the order flow before corporate events. Panel A reports the descriptive statistics on the Euronext-Paris sample firms associated with unscheduled corporate events: acquisitions, targets, seasoned equity offerings, repurchases, dividend initiations, and dividend termination. The sample consists of 95 Euronext-Paris stocks with 101 events. We classify events into positive and negative news based on the two-day (Day [0, + 1]) cumulative abnormal returns, with Day 0 denoting the event day. In Panel A, we report market capitalization (in millions of euros, as of January 2003), daily trading volume (shares), quoted bid ask spread (percent), volatility (percent) and stock price (euros) on control Days [ −30, −10] before the event. Panel B reports daily statistics on order flow activity on Days [ −5, −1] and control Days [ −30, −10] before the event. Reported are the daily number of orders and the average order size based on non-marketable and marketable orders, the percentage of marketable orders to limit orders and the percentage of limit orders with a hidden size. We calculate the statistics for each firm event and report the (cross-sectional) statistics across all firm events. ∗∗∗, ∗∗ and ∗ indicate that tests of differences are statistically significant at the 1%, 5%, and 10% level, respectively.

Descriptive statistics Positive events Negative events

Mean Median Mean Median

Panel A: Sample ﬁrms Market capitalization (millions of euros) 5114 425 2805 227 Daily volume (shares) 454,347 6034 996,291 45,526 Quoted spreads (percent) 1.32 0.78 1.45 0.88 Daily return volatility (percent) 0.18 0.13 0.25 0.16 Stock price (euros) 33.3 27.2 24.1 18.0

Buy orders, Sell orders, positive events negative events

Daily descriptive statistics Mean Median Mean Median

Panel B: Market activity Number of marketable and non-marketable orders Days [ −5, −1] before corporate event 808.8 ∗∗ 63.9 ∗ 995.5 ∗ 117.0 ∗ Control period 638.5 50.7 898.6 87.6 Average order size Days [ −5, −1] before corporate event 1358 ∗ 461.7 2031 ∗ 1107 Control period 1004 436.6 1771 1045 Percentage marketable or market orders to limit orders Days [ −5, −1] before corporate event 48.1% ∗∗∗ 46.1% ∗∗∗ 49.4% 49.0% ∗ Control period 45.1% 44.3% 50.0% 51.7% Percentage of limit orders with hidden size Days [ −5, −1] before corporate event 18.8% 14.8% 17.1% ∗ 16.2% Control period 18.4% 15.3% 17.6% 16.3%

The results indicate that informed trades are active be- [ −5, + 1] and control Days [ −30, −10]. The control period fore unscheduled events. For both positive and negative provides a benchmark measure of the order submission events, the daily number of orders and the order size are process for the firm, absent the event. By holding trading higher on event days relative to control days. The mar- activity on control days in a firm as its own benchmark, ket:limit ratio increases before positive events (significant our research design reduces the influence of time-invariant at the 1% level) and decreases marginally (significant at the firm attributes on the variation in trading strategies across 10% level) before negative events, suggesting that informed firms. agents use a different mix of order flow based on the di- The null hypothesis is that the event has no impact rection of the news. The percentage of limit orders with a on order flow or that the event effect is zero. The event’s hidden size is similar on event and control days. impact is captured by day coefficients that measure the change in dependent variable on the event days relative 3. Analysis of price aggressiveness, price discovery, and to the control days. Extensions of the original Kyle model opportunity cost of non-execution generate different predictions about the trading intensity of informed agents before news releases (e.g., Kyle, 1985; Why does the stock price incorporate more information Back, Cao, and Willard, 20 0 0; Baruch, 20 02; Sastry, Smith, before positive events than negative events? Is price dis- and Thompson, 2014 ). Because theory does not predict that covery influenced by the informed agent’s choice of active trading intensity is uniform, we estimate separate coeffi- versus passive strategies? We further explore these ques- cients for each day in the event period (Days [ −5, −1]). tions by modeling the order submission strategy in a mul- This approach allows individual day effects to differ be- tivariate regression framework that controls for order at- fore news releases since informed agents can be active on tributes and the market conditions at the time of arrival of any of the five days before the event. We then calculate an order. the combined effect of informed trading with a cumulative measure that sums up the individual day coefficients. 3.1. Methodology When interpreting the results, we focus on both the individual day effects as well as the cumulative effect, and The multivariate regressions are estimated on an event- the associated t -statistics. In Section 6 , we demonstrate by-event basis using all orders submitted on event Days

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 7 robustness with a speciﬁcation that considers a single co- To render the results more comparable across stocks, eﬃcient to capture the event’s impact on Days [ −5, −1]. we normalize the continuous (non-dummy) variables by We present results that are aggregated across events dividing the actual observation by the median for the stock using the Bayesian framework attributable to DuMouchel on control days. OrderExposure equals one if the order Oit (1994) and implemented by Bessembinder, Panayides, and that arrives at time t has a hidden size and equals zero Venkataraman (2009) . Similar to Harris and Piwowar otherwise. TotalOrderSize is total (displayed plus hidden)

(2006), the method assigns larger weight in the cross- size of the order Oit divided by median order size during sectional aggregation to those events parameters estimated the control period. more precisely. Further, the method allows variation in the The variables describing market conditions at time of true parameter estimates across events, thus accommodat- order submission are defined as follows. Spread is the per- ing the theoretical prediction that informed trader strate- centage bid-ask spread at time t divided by the median gies are influenced by firm characteristics, such as short percentage spread during the control period. DepthSame is sale constraints. Details of the aggregation methodology the displayed depth at the best bid (ask) when Oit is a buy are provided in Appendix A . The events are not clustered (sell) order divided by the median depth during the con- in calendar time and thus are viewed as cross-sectionally trol period. DepthOpp is the displayed depth at the best ask independent. We present robustness analyses based on al- (bid) when Oit is a buy (sell) order divided by the median ternate model specifications, including panel regressions, depth during the control period. BookOrderImbalance is the in Section 6 . percentage difference between displayed liquidity in the best five prices on the same side versus the opposite side

3.2. Price aggressiveness of informed traders before positive of order Oit in the limit order book divided by the median and negative events percentage difference during the control period. Volatility is the standard deviation of quote midpoint returns over

We examine the informed agents’ preference of market the preceding hour divided by the median volatility during versus limit orders based on a regression analysis of order the control period. WaitTime is the average elapsed time price aggressiveness. The regression speciﬁcation accounts between the prior three order arrivals on the same side

as the order Oit divided by the median time during the for the impact of market conditions on an order Oit that arrives at time of submission t for event i , as follows: control period. TradeFreqHour is the number of transactions during the previous hour of trading divided by the median P riceAggressi v e it = γ0 + γ1 DayMinus 5 it + γ2 DayMinus 4 it number of transactions for the previous hour of trading during the control period. We also include control vari- + γ3 DayMinus 3 it + γ4 DayMinus 2 it + γ5 DayMinus 1 it ables based on recent transactions observed before sub- + γ Day 0& P lus 1 + γ DayP lus 2 + γ Order Exposur e 6 it 7 it 8 it mission of the order Oit . TradesSize is the size of the most + γ + γ + γ 9 Tot al OrderSizeit 10 Spreadit 11 DepthSameit recent transaction divided by the median trade size during

+ γ12 DepthOp p it + γ13 BookOrderImbalanc e it the control period. HiddenOppSide is the size of the hidden depth at the best ask (bid) revealed in the prior transac- γ14 V ol atil it y it + γ15 W aitT im e it + γ16 T radeF reqHou r it

tion when Oit is a buy (sell) order divided by the median + γ + γ 17 PriceAggressiveit−1 18 DisplayedOrderSizeit−1 hidden depth (of the opposite side) revealed in control pe- + γ19 T rad eSiz e it−1 + γ20 Hid d enOppSid e it−1 riod. DisplayedOrderSize is the exposed size of the previous order ( O ) divided by median exposed size of all orders + γ21 F irstHou r it + γ22 LastHou r it + γ23 Mkt.V ol atil it y it it-1 submitted during the control period. + γ Ind.V ol atil it y (1) 24 it Finally, we include control variables that capture indus- Following Biais, Hillion, and Spatt (1995) and try volatility, market volatility, and time-of-the-day effects. Bessembinder, Panayides, and Venkataraman (2009) , FirstHour ( LastHour ) is an indicator variable that equals one PriceAggressive is an ordinal variable that takes the value for orders submitted in the first (last) hour of the trad- of one when Oit is classified in the most aggressive cat- ing day and equals zero otherwise. Ind.Volatility is the re- egory and takes a value of seven when Oit is classified turn volatility of the portfolio of all Euronext-Paris stocks in the least aggressive category. The first four categories belonging to the same industry, and Mkt.Volatility is the represent orders that demand liquidity from the limit order book and the last three categories represent orders order. Category 4 represents buy (sell) orders with the limit price equal 8 that supply liquidity to the book. to the inside ask (bid) and with order size less than those displayed in the inside ask (bid). These orders are expected to immediately execute in full. Category 5 represents orders with limit prices that lie within the

8 The most aggressive orders (Category 1) represents buy (sell) orders inside bid and ask prices. Category 6 represents buy (sell) orders with with order size greater than those displayed in the inside ask (bid) and limit price equal to the inside bid (ask). Finally, Category 7 represents with instructions to walk up (down) the book until the order is fully exe- buy (sell) orders with limit price less (greater) than the inside bid (ask). cuted. Category 2 represents buy (sell) orders with order size greater than Following Liu and Agresti (2005) and Gelman and Hill (2007) , we select those displayed in the inside ask (bid) and with instructions to walk up a linear specification over a nonlinear specification (ordered probit) be- (down) the book, but the order specifies a limit price such that the or- cause the dependent variable represents a large number of price aggres- der is not expected to execute fully based on displayed book. Category 3 siveness (seven) categories. When fitting a proportional odds model, little represents buy (sell) orders with the limit price equal to the inside ask gain in efficiency is achieved when using more than four levels of the (bid) and with order sizes greater than those displayed in the inside ask category variable over an ordinary least squares. Further, a linear regres- (bid). Orders in Category 2 and Category 3 could execute fully due to hid- sion specification allows an easy estimation of the economic significance den liquidity but could also clear the book and convert to a standing limit of day-indicator variables and the cumulative measure.

8 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 return volatility of the CAC 40 index in the prior hour the news. The asymmetry in informed trader strategies be- of trading, both divided by the median volatility numbers fore positive and negative events is a novel contribution of during the control period. 9 The last two variables help our study. account for commonality in economic fundamentals (see In terms of economic significance, the cumulative ef- Chordia, Roll, and Subrahmanyam, 20 0 0 ). fect coefficient in linear specification is interpreted as the Columns 1 and 2 of Table 3 report the coefficients of change in price aggressiveness on Days [ −5, −1] relative the price aggressiveness regression along with correspond- to control Days [ −30, −10] after accounting for other de- ing t -statistics, estimated on an event-by-event basis and terminants of price aggressiveness. Focusing on all posi- then aggregated across events using the Bayesian Aggre- tive events (Column 1), the cumulative coefficient −0.56 gation described in Appendix A . The coefficients on the implies that, relative to the average price aggressiveness control variables are consistent with those reported in the of 5.18 observed on control days, price aggressiveness in- prior studies. Traders submit less aggressively priced or- creases on Days [ −5, −1] by 10.8%. For negative events, a ders (i.e., choose limit orders over market orders) when similar analysis indicates a decrease in price aggressive- (1) the inside bid-ask spread is wide, (2) same side book ness of 4.8%. We also examine the distribution of the seven depth is thin, which signals less competition, (3) opposite categories of price aggressiveness on event days relative to side book depth is deep or the last trade does not reveal control days. The observed changes in price aggressiveness the presence of hidden orders, both of which signal ac- point to a 8.12% increase in the frequency of aggressive or- tive counterparties, (4) volatility is high, consistent with a ders (Category 1 to Category 4) on Days [ −5, −1] for posi- volatility capture strategy (see Handa and Schwartz, 1996 ), tive news versus a 4.67% decrease in the frequency of sim- (5) book imbalance signals less competition on same side ilar aggressive orders on Days [ −5, −1] for negative news. relative to opposite side of the book, and (6) the limit price of the previous order (a proxy for omitted market condi- 3.3. The speed of price discovery before positive and negative tions) is less aggressive. The impact of market volatility events and industry volatility is not significant. We focus on the coefficient estimates of indicator Microstructure models predict that stock prices incor- variables, DayMinus5 to DayMinus1 . Note that the least porate more information when informed agents use ag- aggressive order is categorized as 7 and the most aggres- gressive orders before news releases. In this subsection, sive order is categorized as 1. Thus, a negative (positive) we investigate asymmetry in learning and price discov- DayMinus3 coefficient supports the hypothesis that order ery before positive and negative events using unbiasedness flow observed on event Day [ −3] is more (less) price ag- regressions following Biais, Hillion, and Spatt (1999) . For gressive than those observed on control days for the same each half-hour time period ( i ) in interval Days [ −5, −1], we firm. Because the research design attributes abnormal regress the return from close on Day [ −6] to close on Day order flow on Day [ −3] to informed agents, a negative [ + 1] on the return from close on Day [ −6] to end of time DayMinus3 coefficient suggests that informed agents use period I , as follows: more aggressively priced orders to build the positions. r et − , + = α + β . r et − , + ε . (2) For buy orders submitted before positive events (Col- [ 6 1] [ 6 I] i umn 1), all five coefficients corresponding to Days [ −5, −1] We separately estimate the cross-sectional regression are negative, and DayMinus3 and DayMinus1 coefficients for each time period I and calculate confidence intervals have t -statistics below −2.0. Overall, the cumulative effect based on the standard error of the slope. Barclay and Hen- coefficient is −0.56 (see Panel B, t -statistic = −2.71), imply- dershott (2003) interpret the slope of the unbiasedness re- ing that informed traders submit more aggressively priced gressions as a signal:noise ratio. According to the learning buy orders before positive events. For sell orders submitted hypothesis, the slope will move closer to one as the pre- before negative events (Column 2), four of the five coeffi- event security price reflects the post-event price with in- cients corresponding to Days [ −5, −1] are positive and the creasing precision. DayMinus5 coefficient is statistically significant ( t -statistic Fig. 2 presents the slope and the confidence intervals = 2.23). The lack of a clear pattern of price aggressiveness for positive and negative events. At the beginning of inter- between Day [ −5] and Day [ −1] points to the possibility val [ −5, −1] for both types of events, the slope is not sig- that informed agents are not certain about the exact tim- nificantly different from zero. In the case of positive events, ing of the news release. The cumulative effect coefficient toward the end of the interval [ −5, −1], the slope is signif- of 0.24 ( t -statistic = 1.65) suggests that informed traders icantly different from zero and not significantly different submit less aggressively priced sell orders before nega- from one. Thus, we cannot reject the learning hypothesis tive events. The “t -statistic of the difference between posi- that informational efficiency of the pre-event stock price is tive and negative events” tests the null hypothesis that the no different from the post-event stock price before positive event effects for positive and negative news are the same. events. Interpretations are similar from the bar chart that The highly significant t -statistic ( = −3.16) suggests that in- shows the ratio of the root mean square error (RMSE) of formed traders strategies are influenced by the direction of the unbiasedness regression to the unconditional standard deviation of return from close on Day [ −6] to close on Day + [ 1]. As the announcement day gets closer, the bar chart 9 For the first hour of trading, we construct volatility measures based shows that the ratio declines. on all available information at the time of the order (i.e., using time win- dows less than an hour). Deleting the first hour of trading does not alter In the case of negative events, the slope of the unbi- our results. asedness regression is significantly lower than one and, in

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 9

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10 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28

100% 100% events

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S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 11

Fig. 2. The speed of learning before positive and negative events. This figure plots the speed of price discovery before corporate events based on the coefficients from an unbiasedness regression specification, following

Biais, Hillion, and Spatt (1999) . For each half-hour time period ( i ) in the interval Days [ −5, −1], we regress the close-to-close return ( ret cc ) in interval Days [ −6, + 1] on return from the close on Days [ −6] to the end of time period i ( ret ci ). For both positive and negative events, we estimate the unbiasedness regressions cross-sectionally for each time period. The figure plots the beta coefficient and the confidence intervals (dotted line) based on standard error of the beta coefficient. The bar graph shows the ratio of the root mean square error (RMSE) of each unbiasedness regression to the unconditional standard deviation of the close-to-close return ( ret cc ). fact, does not reach one by the close on Day [ −1]. Simi- sectional regression of the event i ’s CAR_ratio , defined as larly, the bar chart indicates that residual variance relative CAR [0, + 1] / CAR [ −5, + 1], on event i ’s cumulative ef- to return variance from close on Day [ −6] to close on Day fect coefficient ( AGG_CumEffect ) from the event-by-event [ + 1] remains high. Thus, security prices incorporate less regression [Eq. (1)] . A higher CAR_ratio indicates that stock news before negative events than positive events. prices incorporate less news before the event. A higher In a related analysis that links informed trader strate- value of AGG_CumEffect indicates that informed traders gies to the speed of price discovery, we estimate a cross- employ less price aggressive orders before the event. The

12 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 regressions results are: possibly at a less advantageous price. The opportunity cost, which captures the cost of the delayed execution, is C AR _rat i o i = α + β AGG _CumE f fect i + ε i positive if the stock price moves higher (lower) after a 0 . 557 0 . 449 (3) buy (sell) limit order is placed. The results in Columns − . . t stat ( 3 17) ( 2 13) 7 and 8 suggest that hidden orders are associated with The positive coefficient on AGG_CumEffect suggests that smaller opportunity costs. This result is consistent with stock prices incorporate more news when informed agents Bessembinder, Panayides, and Venkataraman (2009) , who employ more price aggressive orders before news release. show that hidden orders are primarily used by uninformed traders to control order exposure risk. 3.4. Opportunity costs of non-execution of limit orders before Results in Table 3 on opportunity costs suggest that em- positive and negative events ploying limit orders on Days [ −5, −1] before positive events is costly. For buy orders (Column 7), the cumulative ef- The price discovery analysis indicates that stock prices fects coefficient is 0.32 ( t -statistic = 2.17), implying that in- drift more in the direction of news before positive events formed traders face a higher cost when a limit order goes than negative events. This result has important implica- unfilled before a positive event relative to control days. The tions for the informed trader’s choice of a market order finding is consistent with the price discovery pattern that versus a limit order. A drift in stock price in the direction the stock price incorporates a portion of the good news be- of the signal lowers the informed traders’ probability of fore positive events. For sell orders (Column 8), the oppor- execution of a limit order because prices tend to gravitate tunity cost is negative, implying that the stock price does away from the limit price. To prevent limit orders from be- not gravitate away from the limit price before negative coming stale, the informed trader has to keep offering bet- events. The difference in opportunity costs between pos- ter prices, implying it is more costly to employ limit orders itive and negative events ( t -statistic of difference = 2.79) before positive events than negative events. leads to a difference in implementation shortfall costs ( t - In this analysis, we estimate the cost of non-execution statistic = 2.62) reported in Columns 3 and 4. of a limit order before positive and negative events using the implementation shortfall framework proposed by 4. Modeling an informed trader’s strategy Perold (1988) and implemented by Harris and Hasbrouck (1996) and Griffiths, Smith, Turnbull, and White (20 0 0) . The results thus far point to an asymmetry in order Prior studies note that each order is associated with two flow before positive and negative events. Before positive cost components: (1) the effective spread cost, which re- events, the proportion of aggressively priced orders is in- lates to the portion of the order that is executed, is mea- creasing; before negative events, the proportion is decreas- sured as the appropriately signed difference between the ing. 10 Further, when a limit order goes unfilled, we esti- fill price and the quote midpoint at the time of order sub- mate large opportunity costs prior to positive events but mission, and (2) the opportunity cost, which relates to the not negative events, indicating that employing an aggres- portion of the order that goes unfilled, is the appropriately sive strategy before positive events is reasonable. The goal signed difference between the closing price on order expi- of this section is to provide a falsifiable economic rationale ration or cancellation date and quote midpoint at the time for these results; that is, to provide a model that matches of order submission. The implementation shortfall cost for the findings and offers novel empirical predictions that are an order is the weighted sum of effective spread and op- outside our initial findings. portunity cost, in which weights are the proportion of or- The natural candidate for an explanation of any form of der size that is filled and unfilled, respectively. asymmetry in trading patterns between positive and nega- Table 3 presents regression coefficients of implementa- tive news is costly short selling. This is our starting point. tion shortfall costs on the prevailing market conditions and In Kaniel and Liu (2006) , the lower the probability that the order attributes. For a limit order that goes unfilled, the next trader is informed, the more likely the current (in- effective spread cost is zero. Thus, the effective spread re- formed) trader submits a limit order. We believe that an gression (Columns 5 and 6) includes only orders with ei- amalgam of the economics that underlies Kaniel and Liu ther partial or full execution (fill rate > 0%). Consistent (2006) together with buy–sell asymmetry in competition with Harris and Hasbrouck (1996) , we find that orders that that is introduced by costly short selling, as in Diamond are more aggressively priced are associated with higher ef- and Verrecchia (1987) , is a good foundation to build our fective spread cost. After controlling for price aggressive- framework. ness, the incremental effective spread cost on Days [ −5, −1] We study a two-period Glosten and Milgrom relative to control days, as reflected in the cumulative ef- (1985) model with competitive market makers. In the fect coefficient, is not statistical significant. Thus, we do first round of trading, the active (whether noise or in- not find evidence that trading costs, conditional on execu- formed) trader can submit a limit order or a market order. tion, are significantly higher before unscheduled events. We next focus on coefficients of opportunity cost regressions reported in Columns 7 and 8. For an order that 10 A related literature on block trading examines buy-sell price impact is fully executed, the opportunity cost is zero; thus, the asymmetry; that is, the well-known result that block purchases of securities convey more information than block sales of securities (see Kraus analysis considers only orders with partial or full non- and Stoll, 1972, Keim and Madhavan, 1996 ). Saar (2001) motivates the < execution (fill rate 100%). When a limit order goes un- idea that informed sellers could trade for liquidity reasons while informed filled, the informed trader would need to transact later, buyers do not, which is a source of price impact asymmetry.

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 13

Because the asset liquidates after the second round, there whether or not the traders belong to the firm’s investor is no point in submitting a limit order in the second base. Unconstrained investors already own the stock be- round. Informed traders have identical information and fore the event period. Constrained investors do not own trade in the same direction; that is, buy if the event is the stock and can sell only when they pay the borrowing positive and sell if the event is negative. The probability costs associated with short selling. of execution of informed limit order is inversely related to To simplify our analysis, we assume constrained in- the mass of informed trading. Kaniel and Liu show that formed traders are not present in the first round. This as- if the mass of informed trading in the second round is sumption can be interpreted as information leakage. Ini- sufficiently small, then an informed trader in round one tially (in the first round of trading), information is acquired finds it optimal to submit limit orders. Our model relies by traders who are interested in the stock. Later (in the on costly short selling to replicate the result in Kaniel second round of trading), the information leaks to traders and Liu (2006) in a non symmetric manner. When the who are not part of the firm’s investor base; i.e., con- event is positive, all informed traders in the second round, strained traders. That said, this model is not about infor- constrained or not, are active. When the event is negative, mation leakage, and the assumption is made for simplifi- informed sellers can choose to abstain if the borrowing cation. 12 costs are high or the event is small. It is natural to assume that the mass of each group of traders is related to the size of the firm’s investor base. 4.1. The model We let β ∈ ( 0 , 1 ) be a measure of the size of the investor base. In each trading round, the mass of noise traders who We consider an event period that contains two trading submit market orders is 2 βz, and each of these traders rounds. The timing of the model is as follows: Market mak- is equally likely to buy or sell. In the first round of traders post bid and ask prices for the first round of trading. A ing, the mass of noise traders who submit limit orders is trader is picked at random from a large pool of potential 2 βl, and each of these traders is equally likely to submit traders, and submits an order (either a market or a limit a buy or a sell limit order. We assume that noise limit order). When round two commences, market makers re- order traders are absent from the second round of trad- 13 fresh their quotes. A second trader is then picked at ran- ing. The total mass of informed traders in the first round dom and submits a market order. The asset liquidates. is βμ, consistent with our assumption that only uncon- We denote the asset value by v˜ and assume it is a 0–1 strained informed traders are present in the first round. 11 The total mass of informed traders in the second round random variable. We let H 0 denote the history of trade up to the start of the event period and let depends on whether or not constrained informed traders participate. We write the mass of informed traders in the ≡ = ≡ ≡ | = = | p 0 P0 ( v˜ 1) E0 v˜ E[v ˜ H0 ] P( v˜ 1 H0 ) (4) second round as − − be the prior. Before the history of trades unfolds, p itself μ = μ + μ = μ + − μ , 0 ˜ I{v ˜ =1 } I{v ˜ =0} v˜ ( 1 v˜) (5) is a random variable. However, during the event period, where μ− has to be determined in equilibrium. If con- the prior, p 0 , is common knowledge and, for the remain- strained informed traders choose to abstain, then μ− = der of this subsection, we treat p 0 as a parameter. βμ μ− = μ A positive event is { v˜ = 1} , and a negative event is , and if they short sell, then .

{ v˜ = 0} . We say that an event is small when the magnitude Let ai and bi be the posted ask and bid prices in the ith round of trading, i ∈ { 1 , 2} . We let O denote the order in of v˜ − p 0 is small. That is, a positive event is small when i round i , p 0 is close to one, and a negative event is small when p 0 is close to zero. When the event is small, the potential gains O 1 ∈ {M B, M S, ( LB ; P B ), ( LS; P S )} (6) of informed traders are small. As in all probability selection models, we need to spec- and ify the types of potential traders and their respective O 2 ∈ {M B, M S} , (7) masses. All together, our model has four groups of potential traders. There are two groups of noise traders: mar- where M B , M S, LB , and LS represent a market buy, market ket order traders and limit order traders. There are also sell, limit buy, and limit sell, respectively, and P B and P S two groups of informed traders: unconstrained and con- are limit buy and limit sell prices, respectively. strained informed traders. The distinction is according to Our notion of equilibrium requires that the following conditions, Eqs. (8) –(13) and Eqs. (18) –(22) hold. First are

11 The two point distribution simplifies our analysis and is common in the literature. However, this assumption is a deviation from Kaniel and 12 In Kaniel and Liu, there is a positive probability of information leak- Liu, who assume that the asset value is drawn from a continuous and age, though they assume that in such a case everyone learns the informa- symmetric distribution. In Kaniel and Liu (2006) , informed traders use tion. limit orders when the asset value is sufficiently close to the unconditional 13 Noise limit orders provide camouflage to the informed traders’ limit expected value of the asset (i.e., in equilibrium, informed traders use limit orders. Limit orders placed in the second round never execute, so we orders when the value is between the bid and ask price, or barely outside choose to turn off the presence of noise limit order traders in the last the quotes ). Also in our model, informed traders end up using limit or- round. Kaniel and Liu choose to assume that in the last round of trading, ders if the value is sufficiently close to the expected value of the asset the mass of noise limit order traders is added to the mass of noise mar- (though an artifact of the two point distribution assumption is that the ket order traders, which increases the proportion of noise trading in the asset value is always outside the quotes). Thus, the choice of support is last round. Qualitatively, the choice of assumption has no impact on the benign. asymmetry between positive and negative events.

14 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 the rationality conditions for the market makers quotes in nonrandom limit prices, limit prices do not contain infor- the first trading round. mation. Thus, we do not lose any generality if we assume that the first round order, O 1 , is in the set { M B, M S, LB, LS} a = E [ ˜ | O = MB ] (8) 1 0 v 1 and rewrite Eqs. (10) and (11) as and P S = E 0 [v ˜ | O 1 = LS, O 2 = MB] (14) = | = b1 E0 [v˜ O1 MS] (9) and Next, we require that limit prices satisfy P B = E 0 [ v˜ | O 1 = LB, O 2 = MS] . (15) = | = ( ; ), = PS E0 [v˜ O1 LS PS O2 MB] (10) The second part of the lemma says that limit orders and cannot be strictly optimal for informed traders. This means that whenever informed traders use limit orders, they = | = ( ; ) , = PB E0 [v˜ O1 LB PB O2 MS] (11) might as well use market orders. Let m p and m n be the probabilities that an informed trader submits market or- To see why these conditions are natural, consider ders when the event is positive and negative, respectively. Eq. (10) , which corresponds to the offer (ask) side. If the The probabilities that an informed trader submits limit trader posts at a price strictly higher than the conditional orders for positive and negative events are 1 − m and expectation, then market makers will undercut and the p 1 − m , respectively. Because limit orders cannot be strictly limit order will never execute. If the trader posts at a price n optimal, Lemma 1 implies that we do not lose any gener- strictly lower than the conditional expectation, it would be ality if we replace (12) and (13) with a needless concession. Therefore, condition (10) is natural. 14 A similar argument justifies condition (11). βz We also require that, in round one, an informed trader ( 1 − a 1 ) ≥ ( 1 − P B ) with > only if m p = 1 2 βz + μ optimally chooses between a market order and a limit order, taking into account the execution risk of the limit or- (16) der. That is, in a positive event, an informed trader prefers and a buy market (resp. limit) order over a buy limit (resp. βz market) order at PB only if b ≥ P S with > only if m n = 1 . (17) 1 2 βz + μ− βz ( 1 − a ) ≥ ( 1 − P B ) ( resp. ≤) (12) The quotes in the second round of trading should de- 1 2 βz + μ pend on the type of order that was submitted in the and, in a negative event, an informed trader prefers a sell first round, and we therefore denote them by a 2 ( O 1 ) and market (resp. limit) order over a sell limit (resp. market) b 2 ( O 1 ) . We require that order at PS only if a 2 ( O 1 ) = E 0 v˜ | O˜ 1 = O 1 , O 2 = MB (18) βz b ≥ P S ( resp. ≤) (13) and 1 2 βz + μ− b ( O ) = E v˜ | O˜ = O , O = MS . (19) The fraction that appears on the right hand side of 2 1 0 1 1 2 (12) (resp. (13) ) is the execution probabilities of a buy The above is consistent with conditions (14) and (15) ;

(resp. sell) limit order, conditional on positive (resp. neg- namely, a 2 ( LS ) = P S and b 2 ( LB ) = P B . The subtle point is ative) event. that if O 1 = LS, then a 2 ( LS ) is a limit order trader’s quote and b ( LS ) is the market makers’ quote. Similarly, if O = Lemma 1 . Consider the first round of trading. If informed 2 1 LB , then b ( LB ) is a limit order trader’s quote and a ( LB ) traders use limit orders, then informed traders and noise 2 2 is the market makers’ quote. If O is a market order, then traders use the same limit prices, and informed traders are 1 both quotes are the market makers’ quotes. Conditions indifferent between limit orders and market orders. (18) and (19) state that regardless who is quoting, the The proof, found in Appendix B , relies only on mutual quotes satisfy the standard rationality condition in round consistency between conditions (8) –(13) . Thus, the lemma two. is a partial equilibrium result. The first part of the lemma Finally, during a negative event, constrained investors implies that, to find the equilibrium, we need to find a sin- are present only if the bid is greater than the borrowing gle pair of deterministic limit prices: P S and P B . Moreover, costs. To emphasize the dependency of the mass of in- because both noise and informed traders use the same formed trading during negative event on the posted bid, − we write μ ( b 2 ) . We denote the borrowing costs by c and require that

14 The limit prices that satisfy (10) and (11) are the ones that minimize − the expected losses from trade of the group of noise limit order traders, b 2 > c ⇒ μ ( b 2 ) = μ (20) subject to the constraint that the limit order is the best quote in the second round. Kaniel and Liu also posit the same price, though they also − verify a participation constraint; that is, a noise limit order trader should b 2 < c ⇒ μ ( b 2 ) = βμ (21) not prefer market orders. In their Lemma 6, Kaniel and Liu show the constraint is never binding. Also, here the participation constraint is never and binding, and we choose not to include it as part of our deﬁnition of equi- − librium. b 2 = c ⇒ μ ( b 2 ) ∈ [βμ , μ] . (22)

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 15

Condition (22) is relevant only in a knife-edge situation, 1. Unconditionally ( i.e. , without reference to the realization in which the constrained investors are indifferent. In that of p˜ 0 ), the probability of observing a sell limit order when − case, any value for μ ( b 2 ) in the interval [ βμ, μ] is ac- the event is negative is as high as the probability of ob- ceptable. serving a buy limit order when the event is positive. Hereafter, an equilibrium is a tuple 2. [Asymmetry] Consider small events ( i.e. v˜ − p˜ is close to 0 − zero). If borrowing costs are sufficiently high and the in- a , b , m , m , a ( ·) , b ( ·), P B, P S, μ ( ·) , 1 1 p n 2 2 vestor base is sufficiently small, then the probability of ob- such that, for every O 1 ∈ { M B, M S, LB, LS} , the elements of serving a sell limit order in a negative event is strictly the tuple greater than the probability of observing a buy limit or- − der in a positive event. , , , , ( ) , ( ), , , μ ( ( ) ) a1 b1 mp mn a2 O1 b2 O1 PB PS b2 O1 3. [Symmetry] When the investor base is large, events are satisfy conditions (8) –(13) and (18) –(22). large, or borrowing costs are small, then the probability Lemma 2 shows that our model is not vacuous. If bor- of observing a sell limit order in a negative event is sim- rowing costs are high, the investor base is narrow, and the ilar to the probability of observing a buy limit order in a event is small and negative, then informed traders may positive event. submit sell limit orders (i.e., m < 1 ), while constrained in- n Both the proof of Lemma 3 and the proof of formed traders abstain. Theorem 1 are in Appendix B . Lemma 2 . Assume the event is negative. Our model predicts that short sale constraints lead to asymmetry in informed traders’ strategies before positive < 1. If borrowing cost is large or event is small, such that p0 and negative events. The empirical literature (see Harris c, then constrained informed traders abstain in the second and Hasbrouck, 1996; Bloomfield, O’Hara, and Saar, 2005; μ−( ( ) ) = βμ round (i.e., b2 LS ). Hopman, 2007; Bershova, Stephens, and Waelbroeck, 2014 ) < μ/ ( + μ) 2. If event is small such that p0 z 2 , constrained shows that the price impact of a market order is signifi- μ−( ( ) ) = βμ informed traders abstain (i.e., b2 LS ), and in- cantly larger than the price impact of a limit order. This β vestor base is narrow ( i.e. , is sufficiently small), then evidence is consistent with the patterns in Fig. 2 , in which informed traders in the first round use limit orders ( i.e. , stock prices incorporate more news before positive events < m n 1). than negative events. That is, the usage of more aggressive

The proof of Lemma 2 is in Appendix B . informed traders’ strategies before positive events leads market participants to incorporate more news before positive events than negative events. We posit the following 4.2. Empirical predictions prediction that relates short sale constraints to price efficiency asymmetry before events: Recall that p = E[ v˜ | H ] , the prior, depends on the re- 0 0 4. [Price efficiency asymmetry] The stock price incorpo- alization of the history up to the start of the event win- rates more news before positive events than negative events, dow. Our empirical prediction is based on the assumption particularly when event is small, investor base is narrow, and that the prior is a symmetric random variable, p˜ . That is, 0 borrowing costs are high. positive events are as likely as negative events, and small positive events are as likely as small negative events. In particular, E v˜ = 1 / 2 . Thus, the only source of asymmetry 5. Cross-sectional evidence on order submission between positive and negative events in our model is the strategies, price discovery, and opportunity cost need of constrained informed traders to borrow the shares during negative events. Prior research has identified a number of firm at- To emphasize the dependency of the equilibrium on tributes that are associated with the ease of short sell- the realization of p˜ 0 , we write the equilibrium as ( a 1 ( p 0 ) , ing. We test our model’s predictions using three cross- b 1 ( p 0 ) , m p ( p 0 ) , m n ( p 0 ) , a 2 ( p 0 , O 1 ) , b 2 ( p 0 , O 1 ) , P B ( p 0 ) , P S sectional measures of short sale constraints. The first mea- − ( p 0 ) , μ ( b 2 ( p 0 , O 1 ) )) for every O 1 ∈ { M B, M S, LB, LS} . sure is the stock’s membership in an index, which influ- In preparation for our Theorem 1 , in Lemma 3 we com- ences the broadness of the investor base. Index firms tend pare the probability of informed sell market orders dur- to be larger, actively traded, and attract attention from an- ing negative events and informed buy market orders dur- alysts and buy-side institutions ( Nagel, 2005 ). Index stocks ing positive events. To control for the size of the event, are also easier to borrow because index funds are active the comparison is carried at symmetric values of the prior. lenders of securities. We classify stocks based on member-

That is, we compare m n ( p 0 ) with m p ( 1 − p 0 ) . ship in the SBF 120 index, which represents a broader cross section of stocks than the CAC 40 index ( Bessembinder and = Lemma 3. Consider the equilibria that correspond to p˜0 p0 Venkataraman, 2004 ). = − and to p˜0 1 p0 . Then, The second measure is the availability of exchange- listed options contracts in a stock. Battalio and Schultz 1. m n ( p 0 ) ≤ m p ( 1 − p 0 ) . − (2011) show that traders build equivalent short positions 2. If both ( μ ( b 2 ( p 0 , LS ) ) < μ and ( m n ( p 0 ) < 1 hold, then using option contracts when short selling is diﬃcult. Be- m n ( p 0 ) < m p ( 1 − p 0 ) ; i.e., the inequality is strict. cause options market makers enjoy special exemptions

Theorem 1 . Assume that p˜ 0 is drawn from a symmetric dis- on inventory-hedging stock trades, they can assume short tribution. positions in the underlying stock at low cost and, via

16 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 this mechanism, exchange-listed options lower short sale 5.1. The cross section of informed traders’ strategy on price constraints. Hu (2014) shows that options market mak- aggressiveness ers hedge the inventory risk by short selling the underlying stock. Data on the availability of exchange-listed op- Table 4 presents univariate statistics on daily mar- tions for sample firms are obtained from the Euronext- ket:limit ratio on event and control days. For all LO events, Paris BDM database. we observe a decrease in the market:limit ratio. As an ex- The third measure is based on a unique institutional ample, in Column 4 of Panel A, the percentage of mar- feature on Euronext-Paris that affects the ease of short ket:limit orders declines from 51.5% on control days to selling. For certain eligible stocks, the Deferred Settlement 47.4% on events days, indicating that informed traders em- Service allows investors the convenience to take long and ploy a higher percentage of limit orders relative to market short positions with deferred settlement of the trade un- orders. Similar patterns are observed for other LO events til the end of the month (see Foucault, Sraer, and Thesmar, reported in Column 8 of Panel A and Columns 4 and 8 of 2011 ). Stocks that are eligible for SRD facility are selected Panel B. In contrast, for all MO events, the market:limit ra- by the exchange. An investor who wishes to sell short an tio increases from control days to the event days indicating SRD-eligible stock must flag the order as deferred execu- that informed traders employ a higher percentage of mar- tion. On executing the short sale, the broker effectively acts ket orders relative to limit orders. These results provide as a lender of the stock until the end of the month. In preliminary support for the cross-sectional predictions of our setting, the SRD facility offers informed sellers a con- the model. venient way to short sell an SRD-eligible stock. 15 Foucault, Table 4 reports the number of trades on control days Sraer, and Thesmar (2011) report that short selling a stock and the percentage change (and the associated test of dif- that is not eligible for Euronext’s SRD facility is cumber- ference) in number of trades on the event days relative to some because short sellers need to locate shares they want control days. The increase in trading activity on the event to sell in advance of executing a short sale. Information on days relative to control days is smaller for LO events rel- SRD-eligibility for sample stocks in 2003 was made avail- ative MO events. As an example, the increase in trades able by Euronext-Paris. for negative events in non-index firms is 11.9% (Column Our model predicts that informed traders’ strategy de- 4 of Panel A) and the increase in trades in Columns 1– pends on the magnitude of the event. Informed sellers 3 of Panel A exceeds 20%. These patterns are consistent have incentives to locate difficult-to-borrow shares when with the model’s assumption that constrained informed negative news is large. When the negative news is small, sellers abstain from trading when borrowing shares is dif- the benefits from short selling might not outweigh the bor- ficult, or the benefits of short selling do not outweigh the rowing costs. We classify events as large when the absolute costs. value of announcement day return exceeds 5%. 16 In Table 4 , we also report the cumulative effects co- Table 4 presents the main results on the cross-sectional efficient based on an event-by-event price aggressiveness analysis of events. Panel A reports the results for index regression and then aggregated using the Bayesian frame- membership and SRD-eligibility, and Panel B reports the work described in Appendix A . The results provide strong results for options listing and announcement return. The support for the model predictions. For all MO events, the model predicts that informed traders employ more aggres- cumulative effects coefficient is negative, which indicates sive strategies for all positive events (Columns 1, 3, 5, and that informed order flow is associated with more price 7 in Panels A and B), negative events without short con- aggressive orders. In nine out of 12 columns, the coeffi- straints (Column 2 in Panels A and B and Column 6 in cients are statistically significant at the 5% level and, in Panel A), and large negative events (Column 6 in Panel B). two columns, the coefficients are significant at the 10% In addition, the model predicts that informed traders em- level. ploy less price aggressive strategies before negative events For all LO events, we observe a positive cumulative ef- in short constrained stocks (Column 4 in Panels A and fects coefficient, which indicates that informed order flow B and Column 8 in Panel A) and small negative events is associated with less price aggressive orders. In two of (Column 8 in Panel B). For ease of exposition, we refer four columns, the coefficients are statistically significant at to the former category as market order (MO) equilibrium the 5% level. For the remaining two columns, the coeffi- events and the latter category as limit order (LO) equilib- cients are significant at the 10% level. rium events. In addition, in the case of short sale constrained firms, we find support for a buy–sell asymmetry in order submission before positive and negative events. Table 4 reports

15 For a typical retail order in June 2001, Foucault, Sraer, and Thesmar the t-statistic of the difference in cumulative effects coeffi- (2011) report that online brokers charge an additional fee of 0.20% of the cient between positive and negative events. We find that order (with a minimum amount of 6.2 euros) for orders with deferred the difference is highly significant for non-index stocks, execution. In comparison, the median announcement returns for negative events reported in Table 1 is −2.57%. non-SRD-eligible stocks, stocks without listed options, and

16 In a robustness analysis, we divide the absolute value of the stock’s events with small announcement returns. In contrast, the announcement returns by the stock’s average bid-ask spread on control difference is not statistically significant for index stocks, days, and use this measure to classify events as large (above median) and SRD-eligible stocks, stocks with listed options, and events small (below median). This measure helps incorporate the trade-off be- with large announcement returns. Thus, we observe a buy– tween using market orders and paying the spread versus using limit orders and receiving the spread. The sign (and statistical significance) of sell asymmetry in order flow for stocks that are difficult regression coefficients are similar to those reported in the study. to short sell but observe a symmetry in order flow for

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 17

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and

deﬁnitions orders and

from

regression

eligible period.

below period,

∗

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events book,

orders

cost reports

differences

an Events 2.19) orders, market 24

(1) Yes Yes

and Variable

0.3583 919.1 46.3% −

(2.25) 48.4% 0.4327 ( on 21.3% control − or on 1–4),

limit

trader

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table

membership

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the

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The limit report

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and price opportunity Columns

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estimated informed from orders and

marketable

on on

A, tests returns

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SBF120 −

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and

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percent marketable

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The

Dependent Cumulative Number Cumulative Days Days Percentage (t-statistic) Panel Number Control Control t t Control Cumulative (t-statistic) t t Control Cumulative period controls or The Table surrounding stock between opportunity number for the

18 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28

∗∗

events

∗∗∗

2.21) orders, (8) Yes Yes 30

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0.2479 8.9% ( 49.4% −

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≤

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absolute negative

≥

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period

return

∗∗∗ ∗∗∗

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∗∗

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0.2052 45.3% −

(2.36) 0.4368 8.7% ( 39.6% − Coeﬃcient Sell

negative

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from

without ∗∗

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positive

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negative

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Options 1.67

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magnitude

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regression

with the

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cost

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limit Coeﬃcient Buy

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orders

on on

Exchange-listed DayMinus1

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between between between between of or

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before

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1] 1]:

and and and and of of of of period

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of of

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variables period period variables

5, 5,

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control positive positive DayMinus1 positive positive -statistic -statistic -statistic -statistic

Number Days Cumulative Days Percentage Control Cumulative t t Panel Number Control Control Cumulative Cumulative (t-statistic) t Control (t-statistic) t Continued. Table

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 19 stocks that are easier to short sell. These results provide 5.2. Short sale constraints and the speed of price discovery strong empirical support for the novel predictions of the model. We investigate the impact of short sale constraints The economic significance of these results is large. As on learning and price discovery before corporate events. an example, for large positive events, we estimate an in- We estimate cross-sectional unbiasedness regressions for crease of 27.78% in buy order aggressiveness on event days different subsamples, and calculate confidence intervals relative to control days, which reflects a 43.59% increase based on the standard error of the slope. Fig. 3 reports in the frequency of aggressive buy orders (Categories 1–4). the slope and the confidence intervals for four subsam- The corresponding statistics are 6.37% and 4.67%, respec- ples based on SRD eligibility: (1) positive events for SRD- tively, for small positive events. For small negative events, eligible firms, (2) negative events for SRD-eligible firms, (3) the positive cumulative coefficient translates into a de- positive events for SRD-ineligible firms, and (4) negative crease of 4.78% in sell order price aggressiveness and a events for SRD-ineligible firms. Similar to Biais, Hillion, and 4.78% decrease in frequency of aggressive sell orders. Spatt (1999) , we plot the ratio of the root mean square We also examine trading activity in the options market error (RMSE) of each unbiasedness regression to the un- for stocks with listed options. While we observe no sig- conditional standard deviation of the close-to-close return nificant change in daily options trades relative to control ( ret cc ). days prior to positive events, we observe an increase in For the MO events [i.e., (1), (2), and (3)], the slope of daily options trades prior to negative events. Options ac- the unbiasedness regression by the end of the pre-event tivity is nearly twice as large and statistically different on interval is not significantly different from one. We cannot Day [ −1], which points to informed sellers using options reject the learning hypothesis that informational efficiency to build short positions (see Battalio and Schultz, 2011 ). of the pre-event stock price is no different from post-event Our results provide empirical support for several theo- stock price. In contrast, for LO events [i.e., (4) ], the slope is retical papers that model a dynamic limit order book with significantly less than one and, in fact, not significantly dif- strategic traders. For example, Goettler, Parlour, and Ra- ferent from zero. These results suggest that LO events in- jan (2009) predict that informed traders use limit orders corporate less news before announcement than MO events. when volatility is low and Rosu (2014) predicts that in- The patterns for samples based on index membership and formed traders use limit orders when realized signals are exchange-listed options are similar to Fig. 3 but are not re- close to their expected value. In support of these predic- ported in the interest of brevity. tions, and consistent with our model, we find that in- The analysis of the regression residuals also point to formed traders use limit orders before negative events lower price discovery for LO events relative to MO events. with small announcement effects. However, consistent For MO events, the ratio drops substantially at the end of with our model and inconsistent with Goettler, Parlour, the interval [ −5, −1], indicating that the security price in- and Rajan (2009) and Rosu (2014) , we show that informed corporates the informed traders’ private information before traders use market orders before positive events with small the event. For LO events, the ratio does not drop substan- announcement effects. That said, when event is small, the tially at the end of the interval [ −5, −1]. We are unable orders that the informed traders submit are less aggressive to reject the hypothesis that noise trading dominates the than the orders when event is large. trading process. Stocks with small investor base and high borrowing costs can be less liquid. Informed traders face a smaller ex- 5.3. Short sale constraints and opportunity cost of plicit cost of using market orders (bid-ask spread) in liquid non-execution of limit orders stocks. However, the higher price impact of market orders as compared with limit orders can increase the total cost The patterns in Fig. 3 suggest that stock prices incorpo- of building a position. To investigate the interplay between rate more news before MO events than LO events. These short sale constraints and liquidity, we separately exam- patterns raise the possibility that using limit orders before ine informed trader behavior for liquid and illiquid stocks. MO events is costly because if the limit order goes unfilled, We classify a stock as liquid (illiquid) if it is placed in the the informed trader will transact later at a less advanta- lowest (highest) tercile of stocks based on percentage bid- geous price. To empirically estimate the cost of an unfilled ask spreads in the control period. In unreported results, we limit order, we report cumulative effects coefficients of the find evidence of buy–sell asymmetry in informed trader opportunity cost regressions in Table 4 . strategies for stocks that are difficult to short sell in both For all MO events (with the exception of Column 2 in the highest and lowest liquidity terciles. Panel B), we estimate a positive cumulative effects coef- Table 4 reports the number of events for each subsam- ficient, which indicates that the stock price moves higher ple. Many index stocks have exchange-listed options and before positive MO events (Columns 1, 3, 5, and 7 of Pan- are eligible for the SRD facility. We find that the overlap els A and B) and moves lower before negative MO events leaves sufficient room for independence across these cuts (Columns 2 and 6 of Panel A and Column 6 of Panel B). of the data. For example, for index stocks, ten among 24 In seven out of 12 columns, the MO coefficients are sta- positive event stocks and five among 16 negative event tistical significant at the 5% level and, in one column, the stocks do not trade with listed options. Similarly, for stocks coefficient is significant at the 10% level. These results sug- without listed options, 13 among the 44 positive events gest that the stock price tends to gravitate away from the and nine among 28 negative events are eligible for SRD limit price and that limit orders face a higher risk of be- facility. coming stale. For all LO events, we estimate a negative

20 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28

Fig. 3. Short sale constraints and the speed of learning before corporate events. This figure plots the speed of price discovery before corporate events based on the coefficients from an unbiasedness regression specification, following

Biais, Hillion, and Spatt (1999) . For each half-hour time period ( i ) in the interval Days [ −5, −1], we regress the close-to-close return ( ret cc ) in interval Days [ −6, + 1] on return from the close on Day [ −6] to the end of time period i ( ret ci ). The figure plots the beta coefficient and the confidence intervals (dotted line) based on standard error of the beta coefficient. The bar graph shows the ratio of the root mean square error (RMSE) of each unbiasedness regression to the unconditional standard deviation of the close-to-close return ( ret cc ). The model predicts that informed traders use less aggressive order in short constrained stocks before negative events. The proxy for short sale constraint is eligibility for Euronext’s Deferred Settlement Service (SRD) facility. cumulative effects coefficient, although only one of four nificant for index stocks, SRD-eligible stocks, stocks with coefficients is statistically significant. The results do not listed options, and large events. support that stock prices gravitate away from limit price, Overall, the results in Section 5 provide empirical sup- suggesting that using limit orders to build positions be- port for the important theoretical prediction that the fore LO events is a reasonable strategy. In addition, the dif- strategies of informed traders affect the process of price ference in cumulative effects coefficients between positive formation in financial markets. When informed traders and negative events is statistically significant for non-index anticipate competition from other informed traders, they stocks, non-SRD-eligible stocks, stocks without listed op- tend to employ aggressive strategies, which are easier to tions, and small event returns, and is not statistically sig- detect by market participants. This causes the stock price

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 21

Fig. 3. Continued to move in the direction of the news before the public an- events are classified as positive and negative news using nouncement. When faced with less competition, informed longer period (Days [ −5, + 1]) CARs. We also classify events agents employ passive strategies, which are more difficult based on the abnormal imbalance in order flow using both to detect by market participants, and leads to a smaller nonmarketable and marketable orders. That is, we aggre- stock price adjustment before the public announcement. gate the displayed order size each day across all buy or- Our study documents the mechanism that links the activi- ders and all sell orders and then calculate the average daily ties of informed traders to the price discovery process. difference during event and control periods, respectively. Events are classified as positive when abnormal imbalance 6. Robustness analysis is greater than zero and negative when abnormal imbalance is less than zero. We observe a significant overlap The analysis thus far classifies events as positive and between the classifications based on announcement period negative news using announcement period (Days [0, + 1]) CAR and order imbalance (87 of the 101 events) and near cumulative abnormal returns (CARs). Results are similar if perfect overlap based on longer period CARs and order im-

22 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 balance (97 of the 101 events). For limit order events clas- that 28 out of 36 coefficient estimates are statistically sig- sified using announcement period CARs, the overlap with nificant at the 5% level and that six estimates are signifi- other classifications is near perfect. 17 Thus, the important cant at the 10% level. For all limit order events, the cumu- result that informed agents use limit orders when they an- lative effects coefficient is positive, which indicates that in- ticipate less competition is not sensitive to the classifica- formed order flow is associated with less price aggressive tion scheme. orders. Six of the 12 coefficients are statistically significant In Table 5 , we present robustness analyses based on at the 5% level, and three more coefficients are significant several alternative specifications of the price aggressive- at the 10% level. In addition, for all subsamples of short ness regression. In the first set of analyses, the event’s im- constrained firms and for events with small announcement pact is captured by a single event day coefficient, which effects, we find support for buy–sell asymmetry in trading equals one for orders submitted over the interval [ −5, −1] strategy before positive and negative events. and equals zero otherwise. In comparison with estimating The alternative model specifications of the opportunity separate event day coefficients, a single coefficient imposes cost regressions yield results that are similar to those re- the constraint that informed trading intensity is the same ported in Table 4 . In the interest of brevity, these results on each of the five days before the news release. We esti- are not reported in Table 5 but are available upon request. mate the model for each separate event and aggregate coefficients across events using the Bayesian framework described in Appendix A . 7. Conclusions When sample events are not clustered in calendar time, the event study literature commonly estimates the model This study extends the theory on the impact of com- on an event-by-event basis (see Binder, 1985; Thompson, petition among informed traders on the choice of aggres- 1985, 1995 ). This is because forecast errors are expected to sive versus passive trading strategies before news releases. be uncorrelated across events, and the efficiency gain from It further shows that the strategies of informed traders af- a panel specification, which imposes additional constraints fect the process of price discovery before corporate events. on parameters, is expected to be small. Since our sam- The intuition for the model is as follows. The compe- ple period of one year is relatively short, we present ro- tition among informed agents increases the execution risk bustness analyses based on panel regression specifications on informed limit orders, which leads an informed agent using individual day coefficients for the interval [ −5, −1]. to preempt and use market orders. Absent competition, an Table 5 reports the cumulative effects coefficient and the t - informed agent could prefer a limit order to a market or- statistics based on robust standard errors with event fixed der to lower the cost of building a position. We extend the effects and clustered standard errors by date. In unreported Kaniel and Liu (2006) framework by incorporating short analysis, we find that results are similar in a panel specifi- sale constraints that leads to an asymmetry in competi- cation using a single event day coefficient for the interval tion among informed agents before positive and negative [ −5, −1]. events. When short selling is costly and the magnitude of Table 5 also reports the cumulative effects coefficient negative news is small, our model predicts that informed estimated separately for a pooled sample of events that are agents use limit orders. When news is positive, short sell- similar in terms of the direction of news and the proxy for ing is not expensive, or the magnitude of negative news is the degree of competition among informed sellers. Pool- large, informed agents anticipate competition and use mar- ing similar events helps incorporate the theoretical predic- ket orders. tion that true event effects vary by firm attributes, such For a sample of Euronext-Paris stocks, we show that the as short sale constraints, and event attributes, such as the order mix of market and limit orders is influenced by an- magnitude of the announcement. It also helps alleviate to ticipated competition among informed agents. We present some extent the difficulty in panel analysis to disentangle empirical evidence of an asymmetry in price aggressive- the effect of true variation in parameter estimates across ness of informed order flow before positive and negative events from the variation that is attributable to estima- events. When short selling is costly, when the magnitude tion error. We also estimate the panel regression using the of news is small, or when investor base is not broad, in- full sample of events and restrict the individual day coef- formed sellers anticipate less competition and use limit ficients for the interval [ −5, −1] to be the same for similar orders before negative events. In all other scenarios, in- events. formed traders anticipate competition and use market or- Results in Table 5 suggest that the theoretical predic- ders before news releases. tions are strongly supported in the alternative model spec- We further show that informed traders’ strategies af- ifications. For all market order events (Columns 1–3 and fect the informational efficiency of prices. In scenarios in 5–7 in Panels A and B), we obtain a negative cumulative which informed agents use aggressive orders, we are un- effect coefficient, which indicates that informed order flow able to reject the learning hypothesis that informational ef- is associated with more price aggressive orders. We find ficiency of the pre-event security price is no different from the post-event security price. In contrast, when informed agents use less aggressive orders, we are able to reject that 17 For limit order events, the overlap in classification based on an- stock prices incorporate the news before announcement nouncement period CAR and the order imbalance is 18 of the 19 events date. The key finding is that stock prices incorporate less for SRD-ineligible stocks, 26 of the 27 events for non-index stocks, and

26 of the 28 events for stocks without listed options. The results using news before negative events than positive events, particu- alternative classiﬁcation schemes are available upon request. larly in short constrained stocks.

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 23

four

single effects

control

page.

options on a

events

estimated to

cumulative orders, (8) 19 Yes

Yes Yes

next ﬁxed is (1.92)

(2.43) (2.48)

0.1312

with 0.6872 0.5539 speciﬁcations

events the

on Coeﬃcient Sell

that

The negative

relative event

SDR-ineligible 1] 3.21 2.88 2.95

−

− − −

presents 5, exchange-traded

continued

(negative) companies

−

from

include speciﬁcation

[

variables.

a also has

events speciﬁcation

orders, 2.10) on 1.89) 33 2.23) (7) Yes Yes Yes Days

term 0.4051 0.6026 0.0845

Events −

−

positive table ( 5–8), ( ( −

− −

on Coeﬃcient Buy

positive The based

speciﬁcations before regression

Columns

interaction

This observed (2009)

(1994)

panel

orders

events

using coeﬃcients

types. in 4.31) orders, 24 4.24) 2.22)

(6)

Yes Yes Yes (Panel

0.1047 (sell) 0.6560 0.6696

−

( ( ( − − − events.

Coeﬃcient Sell DuMouchel event buy

negative

obtained

Venkataraman facility of aggressiveness SDR-eligible 16 regression

for

coeﬃcient are 2.15 0.70 2.20

negative

and the

from order companies

and reports Services results in

events

dummy

framework

orders, 1.81) each 25 2.50) 2.84) (5) Yes Yes Yes Events

1] 0.2762 0.2636 0.0636 table −

− −

(

( ( Panayides, −

− − − report

for

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[

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Bayesian

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and

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Days

between book.

separately measures) facility

reports

Deferred

Bessembinder,

using

events

positive

order

(four 27 orders, (4) (SRD) Yes Yes Yes

of Columns

table

and

(1.87) (1.92) (2.30)

0.0972 0.4264 0.4066

individual difference

Coeﬃcient estimated

Sell limit

on The

negative

is Euronext’s the

Service

companies

aggregated (2007)

and measure SBF120

(Panel 3.35 3.88 4.28

for

that

in − − − based

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from 5%

sale

not

for

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eligible events

basis -statistic

Panayides t short conditions

below Events orders,

4.21) 34 3.63) 2.43) is

(3) Yes Yes Yes measure

(16

0.1066 0.9251 0.8202

−

− −

on by ( ( ( − or corporate −

− the

speciﬁcation

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1–4), type positive

Deferred

effect market

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based

above report

event

event-by-event we aggregated

regression

by Columns

strategies. unscheduled return an Euronext’s

A, regression attributes,

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cumulative

on for aggregated

panels 16 1.86) orders, 4.30) 4.44) panel

(2) Yes Yes Yes

the 0.1293 0.9576 0.8778 −

−

the trader a ( ( ( before −

−

− all order

Coeﬃcient (Panel

Sell regression in

regression

abnormal

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companies

eligibility estimated

index regression

presents 0.84 2.89 3.29 SBF120

informed panel pooled

date.

strategies and

are from

speciﬁcation, 120 on

coeﬃcient

table event

cumulative

events

SBF

Events orders, 1.91) panel 24 2.09) 2.48) the (1) traders’ Yes Yes Yes

0.2177 aggressiveness

0.2084 0.0664 errors −

−

( ( ( − − − coefficients, coefficients, dummy Coefficient

coeﬃcients Buy membership

each

constraints

absolute positive 1]

price

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events

DayMinus5 DayMinus5 the sample

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constraints robustness of of of DayMinus5 DayMinus5 DayMinus5

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for 1–4),

difference difference difference whether

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coeﬃcient negative negative negative from sale

standard

based on

the the the

the ﬁxed effect effect

effect effect effect

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−

of for Short variables variables variables

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based dummy coeﬃcient event 30,

B, table −

measure 5

[

cluster DayMinus1 positive positive positive

-statistic -statistic -statistic

The Cumulative Cumulative Single Panel Number Cumulative Control (t-statistic) Cumulative Control (t-statistic) (t-statistic) Cumulative Control t t t Days effect Robustness Table (Panel and samples include dummy separately

24 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28

events

orders, (8) Yes Yes 30 Yes

(1.37)

(1.02) (1.59) 0.3170 0.0374 0.2203 Coeﬃcient 5% Sell

absolute

negative ≤

2.02 2.34 2.44

− − −

period

return

events

orders, 1.97) 39 2.83) 2.05) (7) Yes Yes Yes Event

0.1936 0.0612 0.2430 −

− −

( ( ( − − − Coeﬃcient Buy positive

events

(2009)

1.32) 13 orders, 3.53) 3.58) (6) Yes Yes Yes

0.7428 0.6778 0.0950

−

− −

( ( ( − − − Coeﬃcient 5% Sell

absolute

negative ≥

0.13

0.41 0.79 −

period

return Venkataraman

events

orders, 1.70) 19 2.72) 2.05) (5) Yes Yes Yes Event

and 0.1071 0.5624 0.4895 −

−

( ( ( − − − Coeﬃcient Buy positive

Panayides,

events

orders, 28 (4) Yes Yes Yes

(1.99) (2.50) (2.28) 0.5313 0.0887 0.3662 Coeﬃcient Sell

companies negative Options

4.58 4.93 3.44

Bessembinder,

− − −

from

and measures)

events without

5.14) orders, 44 4.81) 2.38) (3) Yes Yes Yes

0.7563 0.7981 0.0946 Events −

− −

(four ( ( (

− − − (2007) Coeﬃcient

Buy positive

measure

types)

return Panayides

sale

events

(16

15 1.39) orders, 3.99) 4.29) on (2) Yes Yes Yes

0.1263 0.6910 0.7290 −

− −

( ( ( period − − short −

type Coeﬃcient Sell

by companies negative based

Options

2.15 0.77 2.60 event

from

with

events

aggregated announcement orders, 2.15) 1.97) 14 2.37)

(1) Yes Yes Yes

aggregated 0.2317 0.0540 0.2382 Events

−

( of ( ( − − −

Coeﬃcient Buy positive regression

regression

panel magnitude

events events events

pooled the

event

negative negative negative options

coeﬃcients,

coeﬃcients, and and and

individual

1], −

5, positive positive positive −

DayMinus1

[

DayMinus1 Exchange-listed to

DayMinus1 DayMinus1 DayMinus1

to to to are Days

between between between

for

events DayMinus5

regressions regressions regressions DayMinus5

constraints of DayMinus5 DayMinus5 DayMinus5

in in in

difference difference difference

coeﬃcient sale

the the the effect

effect effect effect corporate effect

of of of

Short variables variables variables

dummy

-statistic -statistic -statistic

Cumulative Cumulative Control Single Cumulative Cumulative t Panel Number Control (t-statistic) (t-statistic) Cumulative (t-statistic) t Control t Continued. Table

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 25

βˆ Although our study focuses on informed trading in a N i i =1 2 + σ 2 ( s ˆ . . ) centralized limit order market, our theory has implica- βˆ = i m l e (25) N 1 tions for informed trading in fragmented markets, in which = i 1 ( s 2 + σˆ 2 ) the strategy space includes the choice of trading plat- i m.l.e forms with different levels of transparency. Some trad- Assuming independence across firms, the variance of ing platforms such as Dark Pools are designed to offer the aggregate estimate is lower cost but with lower fill rates (see Zhu, 2014; Buti, 1 Rindi, and Werner, 2017 ). In the case of Dark Pools func- V ar βˆ = , (26) N 1 tioning as a crossing network, the probability of execu- i =1 ( 2 + σ 2 ) si ˆm.l.e tion decreases as the number of traders participating on where σˆ 2 is the maximum likelihood estimator of σ 2 . the same side of the market increases. In our theoretical m.l.e model, this scenario is captured by anticipated competi- The aggregate t-statistic is based on the aggregated coef- tion among informed traders. As some informed traders ficient estimate relative to the standard error of the ag- recognize the low rate of execution in the crossing net- gregate estimate. This method allows for variation across β work, they route their orders to the transparent exchange, stocks in the true i and also for cross-sectional differences β 18 despite the higher cost of execution. The price impact of in the precision with which i is estimated. their orders in the transparent exchange increases the execution cost for informed traders remaining in the crossing Appendix B. Proofs of Lemmas 1–3 and Theorem 1 network because the Dark Pool crossing price is based on quotations from the transparent exchange. Thus, informed B.1. Proof of Lemma 1 traders in fragmented markets face a risk-return trade-off affected by competition that is similar to the one that we Consider the first part of the lemma. Assume by means have modeled in a centralized market. of contradiction that informed traders post limit orders Our study points to a specific mechanism by which re- and their limit prices are different than the limit prices of strictions on short selling impede the flow of private neg- noise limit order traders. Then, the only price that satisfies ative information into prices (see Beber and Pagano, 2013 ). conditions (10) –(11) is P S = v˜ . But, then, optimality condi- A short sale ban lowers competition among informed sell- tions (12) –(13) imply that market orders are preferable ers and leads to a limit order equilibrium, which makes it to limit orders which is a contradiction to the assumption difficult to detect informed order flow. This leads to lower that informed traders use limit orders. price discovery before negative news relative to positive Consider now the second part of the lemma. Assume news. Our study is relevant for regulators interested in that informed traders strictly prefer buy limit orders over the efficacy of short sale regulation, particularly in markets buy market orders. That is, the right-hand side of (12) is around the world that continue to restrict or impede short strictly greater than its left-hand side. The right-hand side sales in one form or another. is strictly smaller than 1/2. If noise traders submit buy market orders only in round one, the left-hand side of (12) is a 1 = 1 / 2 , and a contradiction arises. In a similar Appendix A. Aggregation method manner, we show that informed traders cannot strictly prefer sell limit orders over sell market orders. Our aggregation method relies on a Bayesian framework attributable to DuMouchel (1994) and implemented B.2. Proof of Lemma 2 by Panayides (2007) and Bessembinder, Panayides, and Venkataraman (2009) . The method assumes that, for each Consider the first part. From the equilibrium condition estimated firm i coefficient, β, (21) it follows that we only need to show that

βˆ | β ∼ . . . β , 2 b 2 ( LS ) < c. (27) i i i d N i si (23) From equilibrium condition (10) , we know and b ( LS ) = P ˜ = 1 | O˜ = LS, O = MS < E ˜ = p . (28) 2 2 0 v 1 2 0v 0 βi ∼ i.i.d.N β, σ (24) where the inequality is because the order ﬂow contains in- − where N is the Gaussian distribution. The Newey-West cor- formation. Thus, p 0 < c implies μ ( b 2 ( LS ) ) = βμ. rected standard errors, si , are estimated using generalized We turn our attention to the second part of the lemma. method of moments (GMM) with a Bartlett kernel and a By way of contradiction, assume that in equilibrium m n = maximum lag length of 10, and σ 2 is estimated by maxi- 1 . So, the left-hand side of the equilibrium condition mum likelihood. (17) is Harris and Piwowar (2006) emphasize the desirability of assigning larger weights in the cross-sectional aggrega- 18 The aggregated β estimate deals with the error-in-variable issue. It tion to those securities whose parameters are estimated also corrects for the variability in the sample selection through σˆ 2 . more precisely. Consistent with the study’s recommenda- m.l.e The method does not control for dependence of estimation errors across β tion, the aggregated is obtained from N individual ﬁrm events. We believe that this dependence should be small because the estimates as events are not clustered in time.

26 S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28

b 1 = E 0 [ v˜ = 1 | O˜ 1 = MS] are given by βz βz p 2 βz+ βμ+2 βl p0 2 βz+ βμ+2 βl 0 = f ( p 0 , m ) = , (38) βz βz+ m βμ βz βz+ mβμ + n ( − ) p + ( 1 − p ) 2 βz+ βμ+2 βl p0 2 βz+ βμ+2 βl 1 p0 2 βz+ βμ+2 βl 0 2 βz+ βμ+2 βl 0 z p 0 βl = . (29) 2 βz+ βμ+2 βl p0 z p 0 + ( z + μ) ( 1 − p 0 ) g ( p , m ) = , (39) 0 βl βl+ ( 1 −m ) βμ p + ( 1 − p ) The right-hand side of the same equilibrium condition, 2 βz+ βμ+2 βl 0 2 βz+ βμ+2 βl 0 (17) , is and β + μ βz z β + μ p1 βz P S = E 0 [v ˜ | O 1 = LS, O 2 = MB] − 2 z β + μ−( ( ) ) h p , μ, μ = × . 2 z b2 LS 1 βz+ μ βz β + μ− + ( − ) 2 z 2 βz+ μ p1 2 βz+ μ− 1 p1 = E 0 [v ˜ | O 2 = MB]

βz+ μ (40)

2 βz+ μ p0 βz = × β + μ β − It is clear that (one does not even have to differentiate z z 2 βz + μ ( b ( LS ) p 0 + − ( 1 − p 0 ) 2 20 2 βz+ μ 2 βz+ μ ( b 2 ( LS ) ) explicitly to conclude the monotonicity) ( βz + μ)z p ∂ f < 0 , (41) = 0 2 βz ( μp 0 + 2 z ) + μ( μp 0 + ( 1 + p 0 )z ) z p → 0 ∂ 2 g > 0 , (42) β→ 0 μp 0 + ( 1 + p 0 )z μ and > < . b1 for p0 (30) ∂ h > 0 ∂ h > 0 ∂ h < 0 . (43) z + 2 μ 1 2 3 We are now ready to prove the lemma. By way of con- The second equality holds because, under the assump- tradiction, assume either tion that m n = 1 , a limit sell order in round one can come only from a noise limit order trader. Observing a limit sell m p ( 1 − p 0 ) < m n ( p 0 ) (44) in round one is uninformative. or β Thus, for sufficiently close to zero, equilibrium condi- − ( − ) = ( ) < μ ( , ( ) ) < μ. tion (17) is violated and a contradiction results. mp 1 p0 mn p0 1 and p0 b2 LS (45) We show that either assumption leads to a contra- B.3. Proof of Lemma 3 diction. A contradiction under assumption ( 44 ) proves the first part of the lemma; i.e., m p ( 1 − p 0 ) ≥ m n ( p 0 ) . − Given an arbitrary choice of scalars m p , m n , μ , and b, A contradiction under assumption (45) proves that if − the equilibrium conditions (8) , (9) , (14) , and (15) dictate μ ( p 0 , b 2 ( LS ) ) < μ and m n ( p 0 ) < 1 , then m p ( 1 − p 0 ) = ( ) what values a 1 , b 1 , P S, P B , and b 2 ( LS ) are consistent with mn p . Together with the proof of the first part (i.e., to- − 19 the arbitrary choice of m p , m n and μ . It is convenient gether with [ m p ( 1 − p 0 ) ≥ m n ( p 0 ) ], contradiction under to express these values as (45) constitutes a proof of the second part of the lemma. Under either (44) or (45) , we have ( 1 − a 1 ) = f ( 1 − p 0 , m p ), (31) ( 1 − a 1 ( 1 − p 0 ) ) = f ( p 0 , m p ( 1 − p 0 ) ) by ( 31 ) ≥ f ( p , m ( p ) ) because ∂ f < 0 b 1 = f ( p 0 , m n ) , (32) 0 n 0 2 = b 1 ( p 0 ) by ( 32 ) βz βz − ( − ) = ( − , ), μ , μ , ≥ P S ( p 0 ) by ( 17 ) 1 PB h g 1 p0 mp (33) β + μ−( ( , ) ) 2 βz + μ 2 z b2 p0 LS = h (g ( p 0 , m n ( p 0 ) ), and − μ, μ ( ( , ) ) ) ( ) b2 p0 LS by 34 βz − P S = h g ( p , m n ) , μ, μ . (34) (46) 2 βz + μ− 0 where Bayes rule dictates the functions ≥ v h ( g ( p 0 , m n ( p 0 ) ) , μ, μ) because ∂ 3 h < 0

f : [0 , 1] × [0 , 1] → [0 , 1] , (35) ≥ h ( g ( p 0 , m p ( 1 − p 0 ) ) , μ, μ) because ∂ 1 h > 0 ,

∂ 2 g > 0 ≥ ( ( , ( − ) ) , g : [0 , 1] × [0 , 1] → [0 , 1] , (36) h g p0 mp 1 p0 (47) − μ ( b 2 ( p 0 , LB ) ) , μ) because ∂ 2 h > 0 and βz + + = ( 1 − P B ( 1 − p ) ) by ( 33 ) h : [0 , 1] × R × R → [0 , 1] (37) 0 2 βz + μ

− 19 In equilibrium, μ depends on the realized order at period one. Thus, 20 The functions f and g also depend on μ. Because f and g do not − − − in equilibrium, (33) holds with μ = μ ( b 2 ( LB ) ) , and (26) holds with depend on μ , the dependency on μ is of no consequence to our analysis, − − μ = μ ( b 2 ( LS ) ) . so we keep it implicit.

S. Baruch et al. / Journal of Financial Economics 0 0 0 (2017) 1–28 27

Now, if assumption (44) holds, then the inequalities de- Bershova, N. , Stephens, R. , Waelbroeck, H. , 2014. The impact of visible and noted with (46) are both strict. If (45) holds, then the in- dark orders. Alliance Bernstein, New York, NY Unpublished working paper . equality (47) is strict. Either way, we get Bessembinder, H. , Panayides, M. , Venkataraman, K. , 2009. Hidden liquid-

β ity: an analysis of order exposure strategies in automated markets. z Journal of Financial Economics 94, 361–383 . ( 1 − a 1 ( 1 − p 0 ) ) > ( 1 − P B ( 1 − p 0 ) ) , (48) 2 βz + μ Bessembinder, H. , Venkataraman, K. , 2004. Does an electronic stock exchange need an upstairs market? Journal of Financial Economics 73, which implies [see equilibrium condition (16) ] that m p = 1 . 3–36 . This is a contradiction because both (44) and (45) imply Biais, B. , Hillion, P. , Spatt, C. , 1995. An empirical analysis of the limit order book and the order ﬂow in the Paris Bourse. Journal of Finance 50, ( − ) < mp 1 p0 1. 1655–1689 . Biais, B. , Hillion, P. , Spatt, C. , 1999. Price discovery and learning during the

pre-opening period in the Paris Bourse. Journal of Political Economy B.4. Proof of Theorem 1 107, 1218–1248 . Binder, J. , 1985. On the use of the multivariate regression model in event studies. Journal of Accounting Research 23, 370–383 . Under the assumption that p˜ 0 is a symmetric random variable, the first part of the theorem follows from the first Bloomfield, R., O’Hara, M., Saar, G., 2005. The “make or take” decision in an electronic market: evidence on the evolution of liquidity. Journal part of Lemma 3 . of Financial Economics 75, 165–199 .

For the second part, let p 0 be such that Bloomfield, R., O’Hara, M., Saar, G., 2015. Hidden liquidity: some new light on dark trading. Journal of Finance 70, 2227–2274 . μ Bodnaruk, A. , Massa, M. , Simonov, A. , 2009. Investment banks as insiders p < min c, . (49) 0 z + 2 μ and the market for corporate control. Review of Financial Studies 22, 4989–5026 . This condition holds if the event is sufficiently small Boehmer, E. , Wu, J. , 2013. Shock selling and the price discovery process. Review of Financial Studies 26, 287–322 . < and borrowing costs are sufficiently high. Because p0 c, Boulatov, A. , George, T. , 2013. Hidden and displayed liquidity in securities − Lemma 2 implies that μ ( b 2 ( p 0 , LS ) ) = βμ. Because p 0 < markets with informed liquidity providers. Review of Financial Stud- ies 26, 2096–2137 . μ/ ( z + 2 μ) , Lemma 2 also implies that m n ( p 0 ) < 1 . From Buti, S. , Rindi, B. , Werner, I. , 2017. Dark pool trading strategies, market the second part of Lemma 3 , it follows that m ( p ) < n 0 quality, and welfare. Journal of Financial Economics 124 (2), 244–265 . m p ( 1 − p 0 ) . Thus, the probability of observing a sell mar- Collin-Dufresne, P. , Fos, V. , 2015. Do prices reveal the presence of in- ket order during a small negative event is strictly smaller formed trading? Journal of Finance 70, 1555–1582 . than the probability of observing a buy market order dur- Chae, J., 2005. Trading volume, information asymmetry, and timing information. Journal of Finance 60, 412–442 . ing a small positive event. This proves the second part of Chakravarty, S. , Holden, C. , 1995. An integrated model of market and limit the theorem. orders. Journal of Financial Intermediation 4, 213–241 .

We now consider the third part of the theorem. If β = Chordia, T., Roll, R., Subrahmanyam, A., 2000. Commonality in liquidity. Journal of Financial Economics 56, 3–28 .

1, then there are no constrained investors and the model D’Avolio, G. , 2002. The market for borrowing stock. Journal of Financial is symmetric, that is, m p ( 1 − p 0 ) = m n ( p 0 ) . By a continu- Economics 66, 271–306. ity argument, it follows that also for β close to one, these Diamond, D. , Verrecchia, E. , 1987. Constraints on short selling and asset price adjustment to private information. Journal of Financial Eco- probabilities are similar. nomics 18, 277–311 . In addition, these probabilities are identical whenever DuMouchel, W. , 1994. Hierarchical Bayes Linear Models for Meta-Analysis. constrained investors do not abstain. According to equilib- National Institute of Statistical Sciences, Research Triangle Park, NC Technical report 27 . rium condition (20), this is the case whenever the bid in Foucault, H. , Sraer, D. , Thesmar, D. , 2011. Individual investors and volatil- round 2 is greater than the cost of borrowing. This is the ity. Journal of Finance 66, 1369–1406 . case when cost of borrowing is near zero, or p is near Gelman, A., Hill, J., 2007. Data Analysis Using Regression and Multi- 0 one and borrowing cost is less than one; i.e., the event is level/Hierarchical Models. Cambridge University Press, New York, NY. Glosten, L. , 1994. Is the electronic open limit order book inevitable? Jour- negative and large. nal of Finance 49, 1127–1161 . Glosten, L. , Milgrom, P. , 1985. Bid, ask, and transaction prices in a special-

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Please cite this article as: S. Baruch et al., Informed trading and price discovery before corporate events, Journal of Financial Economics (2017), http://dx.doi.org/10.1016/j.jﬁneco.2017.05.008