Arbitrage vs. Informed Short Selling: Evidence from Convertible Bond Issuers* John Hackney University of South Carolina

Transcription

1 Arbitrage vs. Informed Short Selling: Evidence from Convertible Bond Issuers* John Hackney University of South Carolina Tyler R. Henry Miami University, Ohio Jennifer L. Koski University of Washington March 8, 2018 Abstract Prior literature examines the effect of either informed or arbitrage short selling on equity markets. We test the relative importance of informed and uninformed short selling around convertible bond issues and earnings announcements for the same firms over the same time period. Convertible arbitrage short selling is associated with temporary price pressure, consistent with downward sloping demand curves. Earnings announcement short selling is consistent with informed traders who anticipate future returns. Firm-specific characteristics related to the cost of short selling similarly affect both informed and arbitrage short selling. Deal-specific characteristics capturing hedging demand also strongly determine convertible arbitrage short selling. *Henry acknowledges financial support from the Frank H. Jellinek, Jr. Endowed Assistant Professor Chair in Finance. Koski thanks the Kirby L. Cramer Endowed Chair in Finance for financial support. We thank Philip Bond, Jonathan Karpoff, Andreas Stathopoulos, Julie Wu, and seminar participants at the University of Washington for helpful comments, and Jon Kalodimos for valuable research assistance.

2 1. Introduction There is much discussion in the existing short selling literature about why a trader would short sell, what a short sale would imply about the trader s information set, and therefore how a short sale should affect future returns. These relations have critical implications for asset pricing [e.g., Ringgenberg (2014)]. The effect of short selling on returns has its theoretical roots in the models of Miller (1977) and Diamond and Verrecchia (1987), which lay the groundwork for short sellers as informed traders. Empirically, most of this literature has explored the role of short sellers as informed traders. A smaller subset of papers investigates the role of short sellers as uninformed traders executing market-neutral arbitrage strategies. 1 Due to the prevalence of work that takes the former approach, the literature generally concludes that the dominant effect of short selling is to precede negative future returns, implying that short selling contains value-relevant information. However, most of these studies examine the differential motives for short selling in isolation. In this paper, we consider them simultaneously in an effort to distinguish different shorting demand motives and their consequences for price discovery. We test the relative importance of informed and uninformed short selling in a setting that facilitates direct comparison: new convertible bond issues and earnings announcements for the same firms over the same period. We find that short selling on convertible bond issue dates is over twice as large as short selling on earnings announcement dates, suggesting that arbitrage short selling may be large in economic magnitude relative to informed short selling. Given this empirical observation, we ask two fundamental research questions: Does the relation between short selling and stock 1 While the finance literature generally refers to arbitrage as the activity of informed traders enforcing equilibrium values, the short selling literature often refers to arbitrage short selling as a component of long-short strategies implemented by traders without value-relevant fundamental information. It is in this sense that arbitrage short selling is uninformed. Goldstein and Guembel (2008) and others point out that a third group, opportunistic short sellers, may trade manipulatively to distort the informativeness of stock prices. Although our primary focus is on unformed versus uninformed short selling, we present evidence on one type of manipulative short selling which may occur in our setting in Section 3.2, below. 1

3 returns depend on the motivation for short selling? And how do the determinants of uninformed short selling compare to the determinants of informed short selling? We address these questions using a sample of 331 convertible bond offerings made by 301 distinct firms between January 1, 2005, and August 6, 2007, corresponding to the availability of daily short selling data from the Securities and Exchange Commission s Regulation SHO (RegSHO). We also analyze 2,734 earnings announcements for the same firms during this same event window. Our first test explores the relation between short selling and stock returns. If demand curves for shares are downward sloping and convertible arbitrage short selling is uninformed, higher levels of short selling should be related to more negative issue day returns [Scholes (1972)]. These effects would be temporary, so arbitrage short selling should be positively related to future returns as the stock price recovers from price impact. In contrast, if informed short sellers anticipate changes in firm fundamentals or future returns, higher levels of informed short selling should be associated with more negative future returns. For many of our convertible bond offerings, the announcement occurs on the issue date. Therefore, short sellers during this period may be trading on information in the announcement as well as setting up arbitrage positions. We use the predictions for stock returns to examine whether short selling around convertible bond issue dates is relatively more consistent with arbitrage or informed trading. We also test these predictions for short selling around earnings announcements. Our ex ante expectation is that short selling around earnings announcements is more likely to be informed than short selling around convertible bond offerings. Results show that convertible short selling is significantly negatively related to issue-day stock returns and positively related to future returns, consistent with temporary price pressure and subsequent price recovery from arbitrage short selling. In contrast, short selling on earnings announcement dates is negatively related to future returns, consistent with informed short sellers 2

4 who short more in anticipation of lower future returns. In addition to providing evidence on the pricing effects of convertible arbitrage trading in the stock market, these results validate the claim in prior literature that short selling around convertible bond issue dates is arbitrage rather than informed trading. The pricing consequences of short selling in the stock market differ significantly depending on whether the short selling is motivated by arbitrage or information. Not all short selling is the same, and it is important to distinguish the different types. We next examine the determinants of different types of short selling. Extensive prior literature investigates the determinants of informed short selling or short selling in general [e.g., D Avolio (2002)]. Relatively few papers focus on the determinants of arbitrage short selling. We use our setting to examine the determinants of (convertible) arbitrage short selling and compare them to informed short selling. Our main results show that many firm-specific characteristics, in particular those that proxy for the cost of short selling (such as institutional ownership, share price, and firm size), have similar effects on both informed and arbitrage short selling. Several convertible deal characteristics are significantly related to convertible arbitrage short selling. Convertible arbitrage short selling is primarily determined by particular deal characteristics related to hedging demand but is unrelated to convertible bond underpricing itself. It is not the magnitude of the underpricing, per se, that drives the amount of short selling. Rather, short selling serves to hedge out the directional risk of the convertible arbitrage and is associated with the delta hedge. Hedging activity appears to last about two days after the issue date before largely tapering off. Finally, explanatory power is much higher for regressions explaining convertible short selling than it is for informed short selling. Overall, results show firm characteristics that facilitate informed short selling also facilitate arbitrage short selling; however, deal characteristics also play a significant role in the extent to which arbitrage short sellers trade. 3

5 Our results add to the literature providing evidence of downward sloping demand curves. Prior research in this area has focused on positive, non-information motivated demand shocks such as index additions [e.g., Shleifer (1986), Harris and Gurel (1986) and Petajisto (2009)]. Our setting is relatively unique in that we have a quasi-exogenous shock to supply rather than demand [e.g., Ringgenberg (2014)]. We anticipate that, especially for the subsample of events for which the convertible announcement strictly precedes the issue date, convertible arbitrage short selling on the issue date should not be motivated by negative information. We show that convertible arbitrage short selling on convertible bond issue dates is associated with negative temporary price pressure, consistent with downward sloping demand curves. Our paper also contributes to other areas of the literature. First, our paper adds to research that examines the relation between short selling and stock returns. Our paper, however, focuses on this relation for uninformed, arbitrage short selling, rather than the usual focus on informed short selling, and we show that the effects are quite different. Short selling is more nuanced than previously described in the literature. We also extend the literature that looks at the determinants of short selling with a comparison between the determinants of informed versus uninformed short selling. Our tests hold both the sample firms and the time period constant, minimizing concerns that variations in sample selection or across time periods may affect inferences. The remainder of the paper is organized as follows. Section 2 describes our sample. In Section 3 we present results on the relation between short selling and returns. In Section 4, we compare determinants of the two types of short selling. Section 5 concludes. 2. Sample and Data 2.1 Sample of Convertible Bond Events 4

6 We search the Securities Data Corporation (SDC) Global New Issues database for all convertible debt offerings by public, U.S. issuers. Our sample period is January 1, 2005, through August 6, 2007, which corresponds to the availability of short selling data through the RegSHO pilot program (see Section 2.3 for more details on RegSHO). We exclude deals with total principal less than $10 million and require RegSHO data in order to be included in our sample. We also require data for our other control variables (see Section 2.4). The sample consists of 331 offerings, including public, private, and 144A convertible deals made by 301 distinct firms. We verify the issue date and identify the announcement date for each deal using news searches on Factiva. We use the Mergent Fixed Income Securities Database (Mergent FISD) accessed through Wharton Research Data Services (WRDS) to obtain most of our convertible deal characteristics, supplemented with data from SDC. We manually verify deal terms (and fill in any missing observations) from the Securities and Exchange Commission (SEC) filings on Edgar. Unlike seasoned equity offerings in which a pre-offer market value of the security is observable, there is no pre-offer price for newly-issued convertible bonds. Therefore, in order to estimate the issue discount (underpricing), we must have an estimate of the theoretical price of the convertibles. Following the literature [e.g., Chan and Chen (2007), Loncarski, ter Horst, and Veld (2009), and De Jong, Dutordoir, and Verwijmeren (2011)], we use the Tsiveriotis and Fernandes (1998) model to estimate the theoretical value of the convertible bond, and calculate convertible bond issue discounts as Issue Discount = Theoretical Value - Offer Price Theoretical Value (1) For most of the convertible bonds, the offer price is $100 and the theoretical value according to the Tsiveriotis and Fernandes (1998) model is greater than $100. Therefore, larger positive values of the 5

7 issue discount correspond to more underpriced convertible bonds, at least relative to this theoretical model. In Panel A of Table 1, we report summary deal statistics for the sample of convertible bond offerings. The average principal amount is about $350 million and average maturity is 14.2 years. The majority (213) of the deals are Rule 144A offerings [see Huang and Ramirez (2010) for more about the 144A market]. In general, private offerings are smaller, with higher coupons and shorter times to maturity. The average convertible bond offering in our sample is underpriced by 8.2 percent, with higher underpricing for private placements and lower underpricing for public and 144A deals. In Panel B of Table 1, we report the number of deals as a function of the length of time between the announcement day (AD) and the issue day (ID). Many of our deals occur on the day they are announced. Therefore, it is challenging to disentangle issue day from announcement effects, and we are careful about this distinction in our tests and interpretations. 2.2 Sample of Earnings Announcements In order to compare arbitrage and informed short selling in the same firms at the same time, we analyze earnings announcements for the 301 firms with convertible bond offerings over our sample period. We acquire earnings announcement dates using the I/B/E/S Summary History database from Thomson Reuters, accessed through WRDS. We are able to obtain earnings announcements for 285 of the distinct 301 firms in our sample, with a total of 2,734 quarterly earnings announcements during our sample period. We expect that informed short selling around earnings announcements may be related to the information content of the announcement. We estimate the information in an earnings announcement 6

8 several different ways. Following Christophe, Ferri, and Angel (2004, p. 1856), we use returns measured over Days [0,1] relative to the announcement day as our proxy for the earnings surprise. We also calculate cumulative abnormal returns over Days [0,1] relative to the CRSP value-weighted index, CAR[0,1]; because short sellers may not react symmetrically to positive and negative abnormal returns in an announcement, we sort CARs into subsets based on the magnitude of the announcement return and use indicator variables to represent the subsets [see Christophe, Ferri, and Hsieh (2010)]. Finally, similar to Boehmer and Wu (2013), we compute earnings surprises as the difference between actual earnings and analyst consensus forecasts (measured using the I/B/E/S average forecast as of the quarter prior to our event window), scaled by the stock price two days before the announcement. We sort firms into deciles based on the scaled decile rankings of these earnings surprises Short Selling Data We use short selling data made available through RegSHO. We collect transactions-level short selling data from all Self-Regulatory Organizations (SROs) for the period January 1, 2005 through August 6, We aggregate the transactions-level data by date and firm, leaving us with a dataset of daily short-sale volume for each firm. We follow de Jong, Dutordoir, and Verwijmeren (2011) and scale short selling by shares outstanding. Our primary short selling variable is short selling divided by shares outstanding, so short selling on day t is defined as SS SSVOL[] t [] t (2) SO SHROUT[] t 2 Summary statistics for the earnings surprise measures are reported in Panel B of Table 2. 3 In June of 2004, the SEC s RegSHO mandated that all SROs make transactions-level short sale data publicly available beginning in January The SROs included the New York Stock Exchange (NYSE), NASDAQ, Amex, NASD ADF, National Stock Exchange, Boston Stock Exchange, Chicago Stock Exchange, Philadelphia Stock Exchange, and Archipelago Exchange (ArcaEX). We collect these data from all SROs for the duration of the RegSHO period. 7

9 where SSVOL[t] is the daily short selling volume on day t, and SHROUT[t] is the number of shares outstanding on day t. In Figure 1, Panel A, we graph average short selling (scaled by shares outstanding) and returns by day relative to Day 0, the convertible bond issue day. There is a significant jump in short selling on Day 0, from an average of about 0.5% of shares outstanding on earlier and later days to over 2.2% on the issue date. Short selling is also high on Day +1, but we find very little evidence of increased short selling before the issue day. Stock returns are very negative (-2.0%) on the issue day. In Panel B of Figure 1, we present the average price level by day relative to the convertible bond issue day. Consistent with returns, price levels fall on the issue day and partially recover, suggesting a combination of arbitrage and informed trading. Figure 2, Panel A reports average daily short selling and returns relative to the earnings announcement Day 0 for the full sample. Short selling increases noticeably, to about 1.1% of shares outstanding on the earnings announcement day. However, this increase is only about half as large in magnitude as the increase in short selling on Day 0 for convertible bond offerings from Figure 1. These results suggest that arbitrage short sellers are large in magnitude relative to informed short sellers, and may have a more significant impact on pricing. Results in Panel B for the subset of firms with negative earnings surprises (measured by announcements with CAR(0,1) < 0) are similar for short selling. By construction, returns are highly negative around these events. There is very little evidence of abnormal short selling before earnings announcement dates. 2.4 Control Variables We obtain data for the firm-specific control variables used in our analysis from several databases, accessed through WRDS. In the Appendix, we provide more detailed definitions of all of our control 8

10 variables. We obtain prices, returns, volume and exchange listing data from the Center for Research in Securities Prices (CRSP). Dividend information comes from Compustat. Institutional ownership data are from Thomson Reuters Institutional (13f) Holdings database. We obtain data on convertible arbitrage hedge fund flows and returns from TASS, and data on options availability from OptionMetrics. All firm-specific control variables are calculated monthly where possible, otherwise quarterly or annually (depending on the reporting frequency of the data, see the Appendix for details). We obtain values for these variables for the 301 distinct firms in our sample from Dec (the month before our first events) through August Therefore, we have monthly values for each firm for each variable. For convertible bonds, we define the event window as [AD-5, ID +5], where AD is the announcement date and ID is the issue date. For earnings announcements, the event window is [AD-5, AD+5], where AD is the earnings announcement date. Regressions use control variables measured as of the last reporting period prior to the start of the event window. In Table 2, Panel A, we report summary statistics for these control variables for our sample of convertible bond offerings. Firm size averages $4.45 billion, and 43% of firms in our sample are listed on the NYSE. Short selling in the prior month (Benchmark Short Selling) averages over 700,000 shares per day, compared to average daily volume of 2.3 million shares. Panel B of Table 2 reports summary statistics for control variables for the earnings announcement sample. Not surprisingly, given these are the same firms over the same time period by construction, summary statistics are similar. 3. Results: Short Selling and Returns 3.1 Short Selling and Stock Returns 4 For variables reported less frequently, we obtain data starting as of the last reporting period of

11 Does the relation between short selling and stock returns depend on the motivation for short selling? Scholes (1972) presents three different hypotheses relating to the price effects of trades. Assuming the market views assets of similar risk as perfect substitutes, the price effects of purchases or sales of stock must be very small (the substitution hypothesis ). Uninformed short sellers would be able to trade without price impact, and arbitrage short selling will be unrelated to returns. If the demand curves for shares are downward sloping, uninformed trading may cause temporary price pressure (the price-pressure hypothesis ); prices will decline until the market absorbs the additional supply of shares sold short, and then recover. 5 In this case, higher levels of arbitrage short selling should be associated with more negative issue day stock returns and higher future (post-issue) returns. Finally, informed short selling should cause stock prices to decrease in response to any negative information revealed by the short trades (the information hypothesis ). If markets are efficient and the stock price reacts fully and immediately to any negative information contained in the short sale, this decrease should be permanent. Many prior papers look at the relation between informed short sellers and future returns. 6 The focus of this literature is on whether short sellers anticipate future returns or changes in firm fundamentals. If short sellers are informed about future cash flows, higher levels of short selling should be associated with more negative future returns. In general, the consensus from this literature is that short sellers are, on average, informed traders, and higher short selling typically precedes lower future returns. 5 In Miller (1977). for example, heterogeneous investor beliefs and costly short selling lead to downward sloping demand curves. 6 See, for example, Asquith and Meulbroek (1996), Dechow, Hutton, Meulbroek, and Sloan (2001), Desai, Ramesh, Thiagarajan, and Balachandran (2002), Arnold, Butler, Crack, and Zhang (2005), Boehmer, Jones, and Zhang (2008), Diether, Lee, and Werner (2009), Christophe, Ferri, and Hsieh (2010), Engelberg, Reed, and Ringgenberg (2012), Kolasinski, Reed, and Thornock (2013), and Boehmer, Jones, Wu and Zhang (2018). 10

12 As discussed above, prior research argues that short selling around convertible bond issue dates is primarily (uninformed) arbitrage trading [Choi, Getmansky, and Tookes (2009)]. However, convertible bond announcements may still contain information. As noted earlier, for the majority of our events (233 of 331 convertible deals, or 70% of our sample; see Panel B of Table 1), the convertible bond issuance occurs on the same day the deal is announced. Therefore, short selling around convertible bond offerings may reflect a combination of informed and arbitrage trading. 7 We use the predictions about short selling and stock returns to test whether short selling around convertible bond issue days shows more evidence of arbitrage or information. As discussed above, we also construct a sample of earnings announcements for the same firms over the same time period as our sample of convertible bond offerings. Our expectation is that short selling around earnings announcements is relatively more likely to be informed, and we use this sample to compare the impact of different types of short sellers on stock returns. Prior research tends to focus primarily on one type of short selling, either arbitrage or informed. 8 Our experiment provides a relatively unique opportunity to examine the pricing effects of different types of short selling for the same stocks during the same sample period. Evidence of significantly different price reactions for informed versus arbitrage short selling would suggest that the price pressure effects of short selling may differ distinctly depending on its motive. 7 We note that these two types of short selling are not mutually exclusive, and both types of short sellers may be active in the market. This test will provide evidence as to which type has the greater net effect on prices. 8 Other papers acknowledge the existence of different types of short sellers. For example, Diether, Lee, and Werner (2009) consider whether, rather than being informed, short sellers provide other functions such as voluntary liquidity provision or risk-bearing capacity. Engelberg, Reed, and Ringgenberg (2012) test whether their results may reflect offsetting positions by market makers or liquidity provision rather than informed trading. Savor and Gamboa-Cavazos (2014) compare the relation between short selling and prior returns for valuation shorts and arbitrage shorts (which they proxy according to whether the firm has any convertible securities outstanding). They also analyze the relation between changes in short positions and longer-run future returns, but only for the combined sample of all short positions. Otherwise, we are unaware of other research directly comparing arbitrage to informed short selling for the same firms during the same time period. 11

13 First, we examine the contemporaneous relation between short selling and stock returns. Specifically, we estimate the following regression: SS VOL RETi[] t 1 [] t 2 [] t i SO SO (3) where RET[t] is the daily return on day t relative to event day 0. Following Christophe, Ferri, and Angel (2004) and others, we include contemporaneous volume scaled by shares outstanding, VOL [] t, as a control variable. We estimate equation (3) for Days t = -1, 0, and +1. This range of SO dates allows some time for the market to react. Day -1 is of particular interest for the subset of convertible events for which the announcement strictly precedes the issuance. If similar assets are substitutes, there should be no price pressure associated with short selling on the event day and 1 should be zero. Either temporary price pressure due to arbitrage short selling or negative news revealed by informed short sellers will result in lower contemporaneous returns, implying that 1 should be negative. To explore the relation between short selling and post-event-day returns, we estimate the following regression: 9 SS VOL RETi [ t 1, t 2] 1 [ t] 2RET[ t] 3 [ t] i SO SO (4) where RET [ i t, ] 1 t 2 is the average daily return from trading days 1 to 2 after event day t. We estimate this regression for several different windows of short selling and returns. As additional VOL control variables, we include returns (RET[t]) and volume ( [] t ) measured on the same day as SO 9 Christophe, Ferri and Angel (2004, Eq. 2) run a similar regression, but in their specification pre-announcement short selling is the dependent variable and the post-announcement return is an explanatory variable. For robustness we also run their version and inferences are similar. 12

14 short selling. If short selling around convertible bond issue dates is arbitrage, the recovery from temporary price pressure should result in 1 > 0. If markets react fully and efficiently to the information contained in the short sale, any initial price reaction should be permanent and 1 = 0. Alternatively, if short selling occurs in assets that have perfect substitutes, there should be no price reaction and 1 = 0. Finally, if short selling around earnings announcements is informed and short sellers are trading because they anticipate negative future returns, we expect 1 < 0. Results for the sample of convertible bonds are reported in Table 3. Panel A reports results of tests of equation (3), measuring the contemporaneous relation between short selling and returns. Panel B reports results for the relation between short selling and future returns (equation (4)). As noted earlier, for many of the convertible bond offerings, the announcement and issuance occur on the same day. To separate announcement from issue day effects, we separately report results for the full sample and for subsamples based on whether or not the announcement date equals the issue date. Results in Panel A show that short selling around convertible bond issue dates is significantly negatively related to contemporaneous returns; the coefficient 1 is significantly negative in columns (1) and (2). The effect is present for short selling before and on the issue day, but not on the day after ( 1 is not significant in column (3)). For the subsample with AD = ID, the coefficient 1 is significantly negative only when measured on Day 0 (column (5)). For the subset with AD ID, the relation between short selling and contemporaneous returns is marginally significantly negative on both Days -1 and 0 (columns (7) and (8)). These results are consistent with the assertion that convertible arbitrageurs can only establish hedging positions after the deal has been announced. They are also consistent with short sellers reacting to negative news in the announcement. 13

15 Results in Panel B of Table 3 show that convertible arbitrage short selling is positively associated with future returns ( 1 0 ); this relation is significant only for short selling measured on Day 0 (the issue day) for the full sample (column (2)). When we partition the sample according to whether or not the announcement date is the same as the issue date, 1 is significantly positive on Day 0 for the subsample with AD = ID, and on Day +1 for the subsample with AD ID. The relation is not significant for pre-issue short selling. Collectively, these results are consistent with temporary price pressure resulting from uninformed arbitrage short selling. 10 Greater arbitrage short selling around convertible bond issue dates is associated with higher price impact and larger, post-issue price recovery. These results validate the claim in prior literature that short selling around convertible bond issue dates is predominantly arbitrage rather than informed trading, even for events for which the announcement and issue dates are the same. Our results, especially for the subsample for which the announcement date strictly precedes the issue date (AD ID), also provide empirical evidence of downward sloping demand curves. Empirical challenges in attempting to test for the presence of downward sloping demand curves are twofold. The first challenge is finding a setting where one would expect downward sloping demand curves because investors do not hold diversified portfolios. Brown, Grundy, Lewis and Verwijmeren (2012) show that convertible arbitrageurs provide over 70 percent of the financing for new convertible issues. Convertible arbitrage hedge funds are not diversified in that they specialize in a 10 In untabulated results, we repeat the analysis from Table 3 using CARs rather than raw returns as the dependent variable. Our main inferences are robust to this alternative measure of returns. We also replicate the analysis from Table 3 redefining Day 0 as the announcement date rather than the issue date. Our main results are present only for the subsample with AD = ID, suggesting that the effects we document are related to the actual issuance rather than the announcement. This finding provides further support for our conclusion that these effects reflect temporary price pressure rather than negative news in the announcement. 14

16 particular trading strategy. If they are the marginal investors, it is reasonable to anticipate that their demand curves may be downward sloping. The second challenge for documenting downward sloping demand curves is that we must rule out trading on new information. As noted earlier, the convertible bond announcement occurs on the issue day for a substantial portion (70 percent) of our events. However, for the remaining 30 percent, the announcement occurs before the issue date. Convertible arbitrage trading on issue dates for this subsample is unlikely to be information motivated. As we document more fully in subsequent tests, these trades are driven by hedging demand, not information. We find evidence that convertible arbitrage short selling on convertible bond issue dates is associated with negative temporary price pressure even for this subsample, consistent with downward sloping demand curves. In Table 4, we repeat this analysis for earnings announcements. Results for the full sample show that short selling on the earnings announcement date is unrelated to announcement day returns (column (2) of Panel A). 11 This result is in sharp contrast to the relation between short selling and returns on convertible bond issue days, and is consistent with the substitution hypothesis. Short selling on earnings announcement days is not associated with negative price pressure for the full sample. Boehmer and Wu (2013, p. 303) argue that it is hard to interpret changes in short selling after positive surprises. To address this concern, in columns (4) through (6) of Panel A, we repeat our analysis for the subsample of events with negative earnings surprises (measured by events with CAR(0,1) < 0). The coefficient 1 is significantly negative for this subsample in column (5), consistent with either temporary price pressure or negative news revealed by informed short sellers. 11 The coefficients on short selling in columns (1),(3), and (4) of Panel A are significantly positive, suggesting a positive relation between short selling and returns on the days before and after the announcement date. These results are puzzling. 15

17 Ringgenberg (2014) finds that short sales in general exert significant price pressure. We show that his results extend to shorts motivated by both arbitrage and (negative) information. Results in Table 4, Panel B, also show that short selling on the earnings announcement date is significantly negatively related to post-announcement returns for both the full sample (column (3)) and for the subsample with negative earnings surprises (column (7)). Short selling on the day after the announcement date is also weakly negatively related to future returns for the full sample (column (4) of Panel B). Higher levels of short selling around the announcement date are associated with more negative future returns, suggesting that informed short sellers anticipate negative returns after earnings announcements. Our results are in line with Boehmer and Wu (2013), who show that short sellers react to negative earnings surprises after the announcement and that the increased shorting is accompanied by lower future returns as short sellers exploit the well-documented post-earningsannouncement drift [PEAD, e.g., Ball and Brown (1968)] in the weeks following the announcement. In columns (1) and (5) of Table 4.B, we also examine the relation between pre-issue short selling on Day -1 and announcement returns RET(0,1). This test is similar to that proposed in Christophe, Ferri and Angel (2004, Eq. 2). We find no evidence that short sellers trade before the earnings announcement to anticipate information in the announcement. Our results are relatively more consistent with Engelberg, Reed and Ringgenberg (2012), who find that short sellers trading advantage comes from their ability to process information contained in the public announcement, rather than an ability to anticipate news events. Overall, convertible arbitrage short selling is associated with negative contemporaneous stock returns and positive future returns, consistent with downward sloping demand curves and price pressure from uninformed selling. Short selling on the earnings announcement day is negatively related to future returns, suggesting that informed traders around earnings announcements anticipate 16

18 poor future return performance. We highlight that the effect of short selling on stock returns differs significantly for arbitrage versus informed short selling and therefore depends critically on the motive for the short sales. 3.2 Short Selling and Convertible Issue Discounts Our main focus is distinguishing the price effects of informed from arbitrage short selling. However, Goldstein and Guembel (2008) point out that a third type of short seller may trade opportunistically to distort prices. In this section, we examine one particular manipulative short selling strategy that may affect convertible issue discounts. This analysis allows us to examine the impact of equity short selling on returns in the convertible bond market. Gerard and Nanda (1993) present a theoretical model in which short sellers trade before a seasoned equity offering to manipulate the informativeness of net order flow and prices, leading to larger issue discounts. 12 Convertible bond offerings are also underpriced on the issue date [e.g., Chan and Chen (2007), Loncarski, ter Horst, and Veld (2009), and De Jong, Dutordoir, and Verwijmeren (2011)]. Does manipulative, pre-issue short selling also affect the magnitude of convertible issue discounts? To address this question, we estimate the following regression of convertible bond issue discounts on short selling before the issue date: SS ' Issue Discounti 0 1( [ t 1, t 2]) b ( Control Variables) i (5) SO where Issue Discount i is the issue discount (defined as the percentage difference between the theoretical model value and the actual offer price, see equation (1)). As noted previously, larger 12 See Safieddine and Wilhelm (1993), Corwin (2003), Kim and Shin (2004), Henry and Koski (2010) among others for empirical tests of this model. 17

19 values of the discount correspond to relatively more underpriced convertible bond offerings. To test whether manipulative pre-issue short selling affects issue discounts, we estimate equation (5) with SS SS pre-issue short selling measured before the issue date (either [ 5, 1] or [ 1] SO SO ). If higher 18 levels of short selling are associated with larger issue discounts, the coefficient, 1, should be positive. We include two types of control variables in these regressions: firm-specific variables and deal-specific variables (please see the Appendix for specific definitions of these variables). These variables are motivated by the literature on underpricing around seasoned equity offerings [see, e.g., Altincilic and Hansen (2003) and Corwin (2003)] as well as prior literature on underpricing in the bond market in general [Cai, Helwege, and Warga (2007)], and underpricing of convertible bonds [Loncarski, ter Horst, and Veld (2009) and de Jong, Dutordoir and Verwijmeren (2011)]. Issue discounts may be larger for firms with higher levels of asymmetric information [e.g., Corwin (2003) and Cai, Helwege, and Warga (2007)]. To proxy for asymmetric information, we include the natural log of one plus the firm s average daily market capitalization during the prior month (LnMktCap) and stock return volatility (Volat), measured as the daily return standard deviation during the last calendar month before the start of our event window. We include an indicator for NYSE-listed firms (NYSE) to capture differences in market structure. Since we are interested in the relation between short selling and issue discounts, we include several control variables related to the cost of short selling. Arbitrage activity should be more difficult in less liquid securities [Hirshleifer, Teoh, and Yu (2011); Choi, Getmansky and Tookes (2009); de Jong, Dutordoir, and Verwijmeren (2011); Calamos (2003)], which we proxy with the Amihud (2002) illiquidity measure (Amihud). We also include institutional ownership (IO), which affects short selling through the supply of shares available to short [D Avolio (2002)]. As noted

20 earlier, all firm-specific control variables are measured as of the last reporting period prior to the start of the event window for each offering. Deal-specific control variables include the relative offer size (RelOfrSize), defined as the total dollar principal of the convertible bond offering divided by firm equity market capitalization the day before the announcement, to capture price pressure related to the market s ability to absorb new shares. Here, although the new security being offered is a convertible bond rather than new shares of stock, arbitrage short sales in the stock market may increase the supply of shares on the issue day. Since liquidity may be lower for private deals, we include indicators (Public and D144A) for the other two types of convertible deals. de Jong, Dutordoir, and Verwijmeren (2011) show that underpricing is lower for convertible bonds with simultaneous repurchases, so we include an indicator (RepoFlag) for these types of deals. We include the option delta (Delta) for the option embedded in the convertible; Loncarski, ter Horst, and Veld (2009) show that underpricing is greater for more equity-like convertibles. Finally, we include time to maturity (Maturity); according to Duca, Dutodoir, Veld and Verwijmeren (2012), bonds with longer maturities are assumed to be more equity-like. Table 5 reports results of the regression in equation (5). Results show that pre-issue short selling has no effect on convertible issue discounts. One potential explanation is that short selling takes place in the stock market, but issue discounts are set in the convertible bond market. Unlike SEOs, short sellers are therefore not able to profit by covering their short position at a discounted price in the same market in which the security is issued. In addition to extending the literature on the relation between pre-issue short selling and issue discounts, this result helps establish that short selling around convertible deals is not manipulative. Our evidence suggests that there are multiple 19

21 types of uninformed short sellers. Convertible arbitrage short selling is distinctly different from manipulative short selling before SEOs. Coefficients on the control variables in Table 5 are generally of the predicted sign. Underpricing is greater for firms with more asymmetric information as measured by volatility. Consistent with univariate results, underpricing is lower for public and 144A deals relative to private placements. Similar to de Jong, Dutordoir and Verwijmeren (2011), underpricing is lower for deals with simultaneous repurchases in most specifications, although the difference is not significant. As predicted, underpricing is also positively related to Delta. Underpricing is negatively related to the maturity of the bond, which is the opposite of predictions if longer-maturity bonds are more equitylike. Duca, Dutodoir, Veld and Verwijmeren (2012) also find that maturity is (insignificantly) negatively related to stock returns around announcements of convertible debt. Our overall conclusion from this analysis is that pre-issue short selling does not result in larger convertible bond issue discounts. Although short selling is associated with temporary price pressure in the stock market, it does not cause larger discounts in the convertible bond market. We extend the literature that studies the effect of short selling on new issue discounts to a new class of securities, convertible bonds. 4. Results: Determinants of Short Selling 4.1 Choice of Determinants Several papers discuss the general determinants of short selling. 13 Christophe, Ferri, and Angel (2004), Desai, Krishnamurthy, and Venkataraman (2006), Boehmer and Wu (2013), Drake, Myers, Myers, and Stuart (2015), Massa, Zhang, and Zhang (2015), Akbas (2016) and others discuss 13 See, for example, D Avolio (2002), Calamos (2003), Asquith, Pathak and Ritter (2005), Nagel (2005), and Hirshleifer, Teoh and Yu (2011). 20

22 determinants of informed short selling around earnings announcements. What are the determinants of arbitrage short selling, and how do they compare to those of informed short selling? As argued above, short selling around convertible issue dates shows relatively more evidence of being uninformed arbitrage trading, while short selling around earnings announcements is consistent with informed trading. Based on this insight, we use this setting as a natural experiment to explore the determinants of arbitrage short selling and compare them to the determinants of informed short selling. To our knowledge, we are the first to directly compare determinants of these two types of short selling in the same firms over the same time period. Several prior studies discuss the determinants of convertible arbitrage short selling, either explicitly or as controls in other tests. 14 All of these studies include issuer characteristics to control for the general costs of short selling and issue characteristics to control for the attractiveness of the arbitrage opportunity. However, there is little consistency in the specific determinants chosen. Based on the literature, we identify three different sets of variables that may affect informed and/or arbitrage short selling: firm-specific, deal-specific, and supply of capital variables. The following firm-specific variables are included in regressions as potential determinants of both arbitrage and informed short selling. D Avolio (2002) shows that short selling is more constrained for small, illiquid stocks with low price levels and low institutional ownership, so we include control variables to measure firm size (LnMktCap), illiquidity (Amihud), institutional ownership (IO), and an indicator for firms with an average stock price below $5/share (LowPrice). Short selling may be higher in firms with higher trading activity in general, so we include benchmark volume 14 Examples include Calamos (2003), Choi, Getmansky and Tookes (2009), de Jong, Dutordoir and Verwijmeren (2011), Duca, Dutordoir, Veld and Verwijmeren (2012), Brown, Grundy, Lewis and Verwijmeren (2012, 2013), and de Jong, Dutordoir, van Genuchten and Verwijmeren (2012). 21

23 (LnBenchVolume) as a control. 15 Following Choi, Getmansky, and Tookes (2009) and de Jong, Dutordoir, and Verwijmeren (2011), convertible bond arbitrageurs may prefer more volatile stocks that do not pay dividends, so we include return volatility (Volat) and an indicator for dividend paying stocks (Div). The existence of options markets presents an alternative venue to establish effective short positions and also allows traders the opportunity to hedge short positions, so we include an indicator equal to one for firms with traded options (OptionFlag). Hirshleifer, Teoh, and Yu (2011) argue that the constraints of short arbitrage vary by exchange, so we include an indicator for firms listed on the NYSE. Again, firm-specific control variables are measured as of the last reporting period ending before the start of the event window for each event. To explore determinants of arbitrage short selling, we also include several variables related to the convertible offering. We begin with the deal-specific variables introduced in Section 3.2 as potentially related to issue discounts: RepoFlag, Delta, RelOfrSize, Public, D144A, and Maturity. These variables may affect arbitrage short selling, either indirectly (if they are associated with higher discounts which in turn attract more short selling) or directly. For example, de Jong, Dutordoir, and Verwijmeren (2011) show that (open market) short selling is lower for deals with simultaneous repurchases, because, although these deals are designed to facilitate arbitrage-related short selling, this short selling is privately arranged and does not show up in open market data. Similarly, Choi, Getmansky, and Tookes (2009) note that arbitrageurs will have to short sell more shares to hedge convertibles with higher deltas because of their larger equity exposure. We include several additional deal-specific characteristics which are motivated by the literature as potentially related to arbitrage short selling. According to Calamos (2003) and Choi, 15 Arbitrage short selling may also be higher in stocks with higher benchmark short selling. We note that the correlation between benchmark volume and benchmark short selling is very high (0.9856). We do not have benchmark short selling from the prior month for the deals announced in January 2005, since our short selling data starts in January Therefore, we include benchmark volume as the control variable. Inferences are very similar if we estimate these regressions using benchmark short selling for events with these data. 22

24 Getmansky, and Tookes (2009), arbitragers may prefer stocks with lower conversion premiums (ConvPrem) because they imply lower interest rates and credit risk. Following de Jong, Dutordoir, and Verwijmeren (2011), we include the number of shares that need to be shorted to obtain a deltaneutral hedge (NumSharesDelta). 16 They also include lnproceeds, since arbitrageurs may have to short sell more shares for larger deals. Therefore, both of these variables should be positively related to arbitrage short selling. In some specifications, we include the issue discount as defined in equation (1) above. We are interested whether arbitrage short selling is driven more strongly by characteristics related specifically to hedging, or whether arbitrage short sellers are attracted to relatively more underpriced convertible bonds. Several of the variables included above (such as Delta, NumSharesDelta, and LnProceeds) should be directly related to the magnitude of the hedging short position. We compare the explanatory power of these deal characteristics to that of underpricing to identify the primary motivation for arbitrage short selling. Finally, following the literature, we also include two variables that are related more generally to the supply of capital [e.g., Duca, Dutordoir, Veld, and Verwijmeren (2012) and Choi, Getmansky, Henderson, and Tookes (2010)]. These variables are the monthly return to convertible arbitrage hedge funds (VW Return) and the flow of capital into funds (Total Flow). Summary statistics for these variables are provided in Panel C of Table 2. Arbitrage should be easier when more capital is available to convertible arbitrage hedge funds. In regressions with short selling around earnings announcements as the dependent variable, our main deal-specific variable is the earnings surprise, which should reflect the (unexpected) information content of the announcement. As discussed in Section 2.2, we use several alternate 16 NumSharesDelta is defined as (Number of Convertibles Issued)x(Face Value)x(Delta)/(Conversion Price). See de Jong, Dutordoir, and Verwijmeren (2011), equation (3). 23