The Causal Effects of Short-Selling Bans: Evidence from Eligibility Thresholds

Transcription

1 The Causal Effects of Short-Selling Bans: Evidence from Eligibility Thresholds Alan Crane Jones Graduate School of Business Rice University, Houston, TX 77005, U.S.A. Kevin Crotty Jones Graduate School of Business Rice University, Houston, TX 77005, U.S.A. Sébastien Michenaud Driehaus College of Business DePaul University, Chicago, IL 60604, U.S.A. Patricia Naranjo Jones Graduate School of Business Rice University, Houston, TX 77005, U.S.A. Abstract We identify the causal effects of short-selling bans on stock prices using regression discontinuity (RD). We exploit three threshold-based rules that determine a stock s short-selling eligibility on the Hong Kong Stock Exchange. Short-selling bans affect short-selling volume at all thresholds. Despite this, bans do not affect price levels. Stock returns, volatility, and crash risk are not different for banned vs. unrestricted stocks when appropriate counterfactual stocks are used to measure a ban s effects. Our findings suggest that short-selling bans are not as costly as previously argued, but are ineffective at reducing volatility or buttressing prices. We thank Bob Chirinko, Jose Liberti, Jason Sturgess, Kumar Venkataraman, James Weston, and conference/seminar participants at UCLA, UIC, Rice University, the 2015 Lone Star Finance Conference, and the 2016 FMA Conference for helpful comments and suggestions. We thank Bonnie Chan for excellent research assistance. We are responsible for any remaining errors. Tel: (Alan Crane), (Kevin Crotty), (Sébastien Michenaud), (Patricia Naranjo) addresses: alan.d.crane@rice.edu (Alan Crane), kevin.p.crotty@rice.edu (Kevin Crotty), smichena@depaul.edu (Sébastien Michenaud), Patricia.Naranjo@rice.edu (Patricia Naranjo) September 13, 2017

2 1. Introduction We use short-selling eligibility thresholds in Hong Kong to test the causal effects of shortselling bans on prices. We find that short-selling eligibility has no causal effects on stock returns, consistent with the predictions of rational expectations models (e.g., Diamond and Verrecchia, 1987). Our results inform the debate on the effects of short-selling eligibility. Previous studies in this literature reach conflicting conclusions. Chang, Cheng and Yu (2007) find that short-sale eligibility in Hong Kong results in price declines, supporting the overpricing predictions of Miller (1977). On the other hand, recent work by Boehmer, Jones and Zhang (2013) and Beber and Pagano (2013) finds that short-selling bans have no effect on price levels. This conflicting evidence is not surprising given the difficulties associated with exploiting regulatory changes in research design. Regulators often design policy in response to changes in markets or political environments. Therefore, it is not clear whether the estimated treatment effects documented in the literature are due to the implementation of the regulation or to differences between stocks, countries, or time periods. In this paper, we identify causal effects by exploiting exogenous variation in short-selling bans using regression discontinuity (RD). Our analysis relies on three threshold-based rules that determine short-selling eligibility on the Hong Kong Stock Exchange (HKEX). Each quarter, firms are eligible to be shorted if they satisfy cutoffs related to public float, size, and turnover. For firms very close to a given threshold, falling to one side or the other of the cutoff is largely due to chance, providing plausibly exogenous variation in short-selling eligibility. We find that short-selling bans bind. Short-eligible stocks experience discontinuously higher short-selling activity around each threshold, both economically and statistically. The discontinuities in short-selling activity are up to 20% (40%) of the mean (median) shortselling activity for all short-eligible firms in Hong Kong. Despite this, we find that these short-selling bans have no effect on stock prices. Stock returns, volatility, and crash risk are not statistically or economically different for banned vs. unrestricted stocks. Our con- 2

3 clusions do not result from low-powered tests. The signs of the coefficient estimates differ across thresholds, suggesting inference would be unchanged even with lower standard errors. Moreover, our conclusions are unchanged around the financial crisis of 2008, when shortselling bans may be more likely to bind. Our conclusions are robust to alternative regression discontinuity estimation choices as well. Specifically, the results are unchanged using different bandwidths and functional forms around the thresholds, including a simple difference of means in a tight neighborhood of the threshold. We restrict our analysis to firms where the threshold rules are the only binding determinant of short-selling eligibility. A potential concern with this choice is that short-selling demand may be limited to firms that become eligible for other reasons, such as options listing or index inclusion (see Section 3 for all eligibility criteria). Empirically, we find a discontinuous increase in short-selling volume for firms that exceed eligibility thresholds. This fact shows that the thresholds we focus on are a binding constraint to short selling, and that the absence of price effects in our sample is not due to a lack of short-selling demand. Our findings are consistent with rational expectations models that suggest short-selling bans have no effects on price levels (e.g., Diamond and Verrecchia (1987)). Our conclusions contradict Chang, Cheng and Yu (2007), whose finding that short-sale eligibility results in price declines supports the overpricing predictions of Miller (1977). 1 They use all stocks added to (but not deleted from) the short-sale eligibility lists in Hong Kong largely prior to adoption of threshold-based eligibility rules. The differences in our results stem from the fact that, for many of these additions, short-sale eligibility may be endogenous to future returns. This is evident in large price run-ups for firms added to the short-sale eligibility list in Chang et al. (2007). When we analyze all added firms in our sample, we reproduce their finding that added firms have negative returns following addition in our sample period as well. However, additions experience negative returns in short windows preceding the addition date. Prices may move post-addition for the same reasons they fall pre-addition, 1 We discuss theoretical predictions in Section 2. 3

4 which cannot be attributed to short selling. Our research design eliminates this bias by comparing market outcomes for similar firms that happen to be on either side of the shortsale eligibility thresholds. Our results regarding price levels are consistent with both Boehmer et al. (2013) and Beber and Pagano (2013). Boehmer, Jones and Zhang (2013) find that stock price levels are not affected by the 2008 SEC ban in U.S. stock markets, but that stock market quality is heavily affected for all but the smallest firms. Using a cross-country setting, Beber and Pagano (2013) find a negative effect of short-selling bans on market quality and price discovery, as well as an increase in stock market volatility in 30 countries that imposed short sales restrictions during the financial crisis. Unlike Boehmer et al. (2013) who find strongest effects for large stocks, Beber and Pagano (2013) find that the strongest results are concentrated in smaller capitalization stocks. Bris, Goetzmann and Zhu (2007) analyze an international panel of short-selling regulations and find that countries without short-selling restrictions exhibit improved price efficiency, but more negative market return skewness. 2 These studies document important regularities concerning short-selling eligibility, but they also acknowledge the empirical difficulty of disentangling the effects of short-selling eligibility from extreme stock market conditions and non-random selection of stocks, time periods, or countries for regulation. Our conclusions differ from both Boehmer et al. (2013) and Beber and Pagano (2013) with regard to volatility. We find no effect, while they find that bans harm volatility, albeit for stocks of different sizes (large stocks in Boehmer et al. (2013); small stocks in Beber and Pagano (2013)). Our findings corroborate their policy conclusions that the use of shortsale bans by regulators is ineffective at buttressing price levels or reducing volatility, which is important given that Battalio and Schultz (2011) document adverse unintended consequences 2 Using firm-specific equity lending supply and fees to proxy for short-sale restrictions, Saffi and Sigurdsson (2011) also find that looser short-selling restrictions are associated with more negative skewness, but the effect comes from fewer occurrences of extreme price increases rather than from an increase in the number of extreme price decreases. Moreover, they find no evidence that short-sale restrictions affect downside risk or total volatility. 4

5 of the U.S. ban in equity option markets due to regulatory uncertainty. Our setting has several distinct advantages relative to previous studies of short-selling bans/eligibility. First, RD is a quasi-experimental framework that helps alleviate concerns about endogeneity that other studies on short-selling bans face. Under the assumption of local continuity of potential outcomes, we can interpret our local average treatment effects causally (Roberts and Whited, 2013). Second, our estimation is based on a panel dataset exploiting 52 quarterly updates to the short-selling eligibility list. This panel covers more than a decade of data and spans periods of bull and bear markets, thus allowing us to test the effects of bans under varying economic conditions. Finally, we can estimate the average treatment effects of a short-selling ban/eligibility across three different thresholds, which demonstrates the robustness of our findings across different size groups. 3 These advantages potentially come at a cost. By definition, identification at the eligibility thresholds measures a local treatment effect. Our conclusions should therefore be viewed as applying to those firms around these thresholds. The rules we exploit allow for unbiased estimates of treatment effects on the sixth largest stock market in the world (HKEX). The HKEX has around 1,500 ordinary stocks, almost 700 of which were eligible for short selling as of 2013 year end. Short-selling activity is prevalent in Hong Kong, averaging 9% of traded volume during 2013 conditional on eligibility and non-zero shorting. 4 Previous studies of short selling in HKEX find strong effects of short sales on stock prices and other outcome variables (Chang et al. (2007), Massa, Qian, Xu and Zhang (2015), and Massa, Zhang and Zhang (2015)). 5 Our results also contribute more generally to the literature on the effects of short-selling on stock market outcomes. A large literature finds that short selling is negatively associated 3 The mean market capitalization differs across thresholds. For example, the mean market capitalization for the market capitalization threshold sample is about HK$860 million while it is much higher (over HK$2,000 million) for the turnover velocity threshold sample. 4 Our short volume data does not include short sales by market makers, which may understate the magnitude of observable shorting activity in Hong Kong relative to the U.S. 5 On the other hand, Hong Kong has also been used to show what short selling cannot explain such as the weekend effect (Gao et al., 2015). 5

6 with stock returns, consistent with Miller (1977) (e.g. Lamont and Thaler (2003), Danielsen and Sorescu (2001), Jones and Lamont (2002), Chang, Cheng and Yu (2007), Cohen, Diether and Malloy (2007), and Grullon, Michenaud and Weston (2015)). On the other hand, a large literature finds no effect on stock returns consistent with the argument in Diamond and Verrecchia (1987) that, in equilibrium, rational investors counteract any overvaluation by optimists (e.g., Battalio and Schultz (2006), Diether, Lee and Werner (2009), Beber and Pagano (2013), and Kaplan, Moskowitz and Sensoy (2013)). We contribute to this literature by providing estimates of causal effects of short-selling eligibility using a novel identification strategy. Our work is also related to a number of studies that investigate the causal effects of altering costs associated with short selling. Diether, Lee and Werner (2009), Alexander and Peterson (2008), and Grullon, Michenaud and Weston (2015) study the Regulation SHO randomized experiment conducted by the SEC from 2005 to The experiment repealed the uptick rule for a set of Pilot stocks. Kaplan, Moskowitz and Sensoy (2013) study the effects of a lending shock to randomly selected stocks of a large portfolio manager. These studies differ from ours because they investigate changes in short-selling costs rather than short-selling eligibility. This distinction is important; theory suggests that the effects of cost changes may differ from those of eligibility (Diamond and Verrecchia, 1987), because bans and restrictions may affect the relative composition of informed and uninformed investors differently. 6 Since it is unlikely that regulators will soon run a randomized experiment on short-sale eligibility, our RD evidence is a relevant and useful contribution to the existing literature. The remainder of the paper is organized as follows. Section 2 briefly reviews the theoretical predictions of the effects of short-selling eligibility. Section 3 describes our empirical 6 Diamond and Verrecchia (1987) argue that short-selling bans eliminate short sales by informed and uninformed traders. In contrast, short-selling restrictions decrease short-selling by relatively uninformed investors more than short-selling by informed investors. Kolasinski, Reed and Thornock (2013) provide empirical support for these theoretical implications. 6

7 setting and data. Section 4 presents our primary analysis, the estimation of causal effects of short-selling on asset prices using regression discontinuity. In Section 5, we compare our results to previous findings concerning short-sale eligibility in Hong Kong. Section 6 provides robustness tests relating to alternate econometric choices, and Section 7 investigates heterogeneous treatment effects. Section 8 concludes. 2. Theoretical Predictions of Short-sale Eligibility Theoretical predictions of the effect of short-selling bans on stock prices are mixed. Miller (1977) argues that if investors have differences of opinion about a stock s value, the price will reflect the optimistic investors valuation in the absence of short-sale eligibility. Thus, shortsale bans help support prices by eliminating pessimistic investors shorting activities. In the absence of short selling, security prices should be overvalued. Therefore, allowing shortselling should lead to stock price declines. The intuition of Miller is formalized in Chen, Hong and Stein (2002), which relates differences of opinion to breadth of ownership. In their model, securities can become overvalued even if only a subset of investors is constrained from short selling. Hong and Stein (2003) add another prediction of short-sale constraints under differences of opinion. In their model, market crashes can result from short-sale constraints as negative information fails to be gradually incorporated into prices. Unrevealed bad news accumulates until previously optimistic investors abandon the market, leading to large negative price adjustments. The model predicts short-sale prohibitions to be associated with a greater prevalence of extreme downward price movements. Diamond and Verrecchia (1987) model short-sale bans in a rational expectations framework. Because market makers account for the availability of short-selling in valuing a stock, the stock is not overvalued in their model. However, overvaluation due to short-sale prohibitions is possible even in rational models if investors value the option to sell to another trader with a different expectation of value as in Harrison and Kreps (1978). For instance, differences of opinion on asset valuation arise due to overconfidence in Scheinkman and Xiong 7

8 (2003). In their dynamic setting, traders are willing to purchase a security for a price above their valuation in the hopes of selling to another buyer, generating a bubble under short-sale restrictions. The bubble is accompanied by increased volume and volatility. If short-sale restrictions prevent these bubbles, short-sale bans should reduce volatility and volume. Allen, Morris and Postlewaite (1993) show that overpricing can result from short-sale bans as a result of private information in a finite-horizon rational expectations equilibrium if agents do not know other agents beliefs. This allows the backward induction argument eliminating overpricing to fail. Therefore, short-sale eligibility may push stock prices down and increase volume and volatility, even in rational expectations models of short-selling bans/eligibility. 3. Empirical Setting and Data HKEX initially allowed short-selling in 1994 for 17 stocks designated Pilot Stocks. Over the following years, HKEX modified the eligible list 11 times to eventually include over 200 stocks by the end of These initial list changes were somewhat haphazard and dependent on market conditions; see Chang et al. (2007) (hereafter CCY) for details. By 2001, HKEX utilized several threshold-based rules, among other requirements, for inclusion to the Designated Securities List. Eligibility rules include criteria such as index inclusion, whether options are traded on the stock, and criteria related to size and turnover. The eligibility criteria as of the last quarter of 2001, when our sample starts, are the following: 1. all constituent stocks of indices which are the underlying indices of equity index products traded on the Exchange; 2. all constituent stocks of indices which are the underlying indices of equity index products traded on Hong Kong Futures Exchange Limited; 3. all underlying stocks of stock options traded on the Exchange; 4. all underlying stocks of Stock Futures Contracts (as defined in the rules, regulations and procedures of Hong Kong Futures Exchange Limited) traded on Hong Kong Futures Exchange Limited; 8

9 5. stocks that meet the minimum liquidity requirement for the issuance of basket derivative warrants (i.e. market capitalization of public float of not less than HK$1 billion, being maintained for the 60 days qualifying period); 6. stocks with market capitalization of not less than HK$1 billion and an annual turnover to market capitalization ratio of not less than 40%; 7. Tracker Fund of Hong Kong and other Exchange Traded Funds approved by the Board in consultation with the Commission; and 8. all securities traded under the Pilot Programme. Effective July 3, 2012, HKEX altered the sixth eligibility requirement. In particular, they increased the market capitalization requirement to HK$3 billion from HK$1 billion and increased the turnover-to-market capitalization ratio (henceforth, turnover velocity) requirement to 50% from 40%. The turnover velocity threshold was subsequently raised to 60% in In this study, we exploit the three thresholds identified in the fifth and sixth requirements to identify exogenous variation in the probability of short-sale eligibility: float-adjusted market capitalization (public float), market capitalization, and turnover velocity. In our discontinuity analysis, we exclude firms that may be on the list due to other eligibility criteria such as index inclusion or options/futures listing. These other eligibility criteria are not met randomly, and therefore may be endogenous to return characteristics. 7 Therefore, for each threshold, we analyze only firms where a given threshold is the only one that affects short-sale eligibility. Specifically, the float-adjusted market capitalization threshold sample only includes firms that do not satisfy both the market capitalization and turnover velocity thresholds. For the turnover velocity threshold, the sample contains firms that are not included in the Designated List under the float-adjusted market capitalization rule and 7 For instance, Mayhew and Mihov (2004) find that exchanges tend to list options for stocks with high trading volume, volatility, and market capitalization. Therefore, including short-sale additions due to option listing may confound potential effects of short-selling eligibility with the underlying reason for option listing. The analysis in Section 5 of all eligibility additions suggests this is the case. 9

10 where the market capitalization threshold is satisfied. Similarly, for the market capitalization threshold, the sample includes firms that are not included in the Designated List under the float-adjusted market capitalization rule and where the turnover velocity threshold is satisfied. Apart from eligibility, Hong Kong also has relatively strict short-selling regulations. During our sample, short sales were subject to a tick test. 8 Naked short-selling was also not allowed. Disclosure of short positions to the regulator, the Securities and Futures Commission (SFC), were required beginning in Sample construction The current list of short-sale eligible securities is available on the Hong Kong Stock Exchange website. To construct the historical list, we start with the designated security list as of November 5, 2014 and work backwards in time using additions and deletions. Firms being added or removed from the short sale eligibility list are identified in periodic HKEX press releases. 9 Press releases are available online for all quarterly evaluations since 2001 as well as additions intermediate to the quarterly evaluations. We hand collect these additions and deletions to create the history of the eligible security list. Our daily data on HKEX stocks is from Bloomberg and includes information on prices, returns, market capitalization, shares outstanding, float outstanding, total volume, short volume, and bid/ask prices. We have quarterly list additions and deletions from HKEX s press releases beginning in We start the sample in December 2001 when the eligibility criterion were revised to include market capitalization and turnover thresholds. Our sample runs from 2001 to Float data is only available from 2006 on; therefore, tests using the float-adjusted market capitalization use data from 2006 to The tick test was briefly lifted from 1996 to A proposal to remove the tick test in 2007 was ultimately dropped in One exception is for deletions due to acquisition or delisting. We manually correct for this by identifying any firms not on our historical list as short-sale eligible if they experience shorting volume at any point over the sample (prior to acquisition or delisting). 10 When forming the turnover velocity and market capitalization threshold samples prior to 2006, we 10

11 In general, HKEX evaluates the Designated Securities List on a quarterly basis. However, the evaluation is not conducted at regular intervals, nor does HKEX disclose the date on which eligibility is determined (i.e., when market capitalization is evaluated as above or below the threshold), which we refer to as the HKEX measurement date. The timing irregularity is evident in Table 1, which reports the quarterly effective dates in our sample. There is substantial variation in the effective date across years for a given quarter. To construct the thresholds, we evaluate whether a firm has met a given threshold using end-of-month data from two months prior to the month of the updated list s effective date. For example, we use data as of the last trading day of March 2005 for the May 17, 2005 effective date. We refer to the date on which we measure the threshold variable as the measurement date and distinguish this from the actual HKEX measurement date, which is unobservable. We use the minimum float-adjusted market capitalization over the 60 trading days preceding the measurement date to evaluate if the firm met the basket derivative warrants threshold. For turnover velocity, we use the aggregate dollar volume traded over the 365 calendar days preceding the measurement date, divided by the market capitalization as of the measurement date. 11 Market capitalization is the closing market value as of the measurement date. The use of lagged data to create the forcing variable is critical to our analysis. If we measure the threshold variables at the quarterly announcement dates or effective dates, there are no observed discontinuities in eligibility. This supports our identifying assumption. The fact that calculating the threshold at other times results in no jump in eligibility suggests that firms near the threshold are more or less randomly assigned to a specific side as of the HKEX measurement date and that at another time they could fall on the other side of the threshold. To account for the noise in the discontinuity due to not knowing the HKEX measurement date exactly, we employ a fuzzy regression discontinuity approach that we assume the float-adjusted capitalization is the same as the unadjusted market capitalization for the filtering associated with float-adjusted capitalization. 11 To be included in our analysis, we require a firm trade on at least 200 trading days over the annual window. 11

12 explain in detail in Section 4. In our primary discontinuity analyses, we consider all quarterly evaluations of the Designated Securities List from Q to Q We exclude changes that occur outside of the regular quarterly evaluation as these changes are not based on the standard threshold rules and are therefore not plausibly exogenous. To avoid confounding effects of other reasons for list inclusion, our RD analysis in Section 4 excludes all firms that are members of various indices or that are the underlying securities for options or futures. 12 We also exclude from our analyses any time windows in which a stock appears not to trade, as evidenced by a return standard deviation of exactly zero. 13 In Section 5, where we compare our results to previous findings concerning short-sale eligibility in Hong Kong, we use all additions to the list consistent with prior literature, regardless of whether the addition occurred at a quarterly evaluation or not Summary statistics Table 2 reports summary statistics of stock-quarter observations for the three regression discontinuity samples. Panels A, B, and C present summary statistics for the float-adjusted market capitalization, turnover velocity, and market capitalization threshold samples, respectively. For each firm-quarter, the float-adjusted market capitalization, turnover velocity, and market capitalization are month-end values, measured two months prior to a given quarterly effective date. These variables are the threshold values determining short-sale eligibility for a particular effective quarter and are measured as discussed above. Average daily returns and standard deviation of daily returns are measured over the 250 trading days preceding a quarterly effective date. The summary statistics indicate that the threshold firms differ across the samples. This 12 We exclude all firms that are member of the Hang Seng, Hang Seng Composite, Hang Seng LargeCap, Hang Seng MidCap, Hang Seng SmallCap, and the Hang Seng China Enterprise indices. We obtain historical index constituent lists from the Hong Kong Stock Exchange website. 13 Our results are not sensitive to this screen, and non-trade days do not increase as a function of short-sale eligibility. 12

13 is helpful for our overall conclusions. Regression discontinuity estimates are inherently local. Therefore, there are always valid concerns about the external validity of any inference. In our case, such concerns are mitigated by virtue of the fact that we have three different samples with different sets of firms. For example, the turnover velocity sample consists of larger firms relative to the other samples. This is not surprising since the market-capitalization threshold must be satisfied for the turnover threshold to bind. On the other hand, the market capitalization sample has the smallest average market capitalization. 4. Causal Effects of Short-Selling Eligibility 4.1. Methodology To establish the causal effects of short selling, we examine outcomes for firms immediately within the vicinity of one of the three thresholds that make the firm eligible for short selling. For example, consider the market capitalization threshold. When a firm surpasses the HK$1 billion threshold in market capitalization (prior to 2012), it is eligible to be shorted provided the firm also meets the turnover velocity threshold. Within the set of firms satisfying the turnover velocity threshold, firms that fall just short of the market capitalization threshold should be similar to those firms that just exceed that threshold. As such, an unbiased treatment effect, τ, can be estimated using regression discontinuity by comparing the outcomes of firms just above and just below the threshold. We compare the treated firms to their counterfactual firms for each of the thresholds. These firms that fall on the other side of a threshold are still counterfactually similar on all other dimensions, such as pre-period performance. The only assumption we require is continuity in potential outcomes around the threshold. This assumption requires that there should be no discontinuity in outcomes if there were no difference in treatment. In other words, within a small bandwidth around the threshold, short-sale eligibility should be quasi-random. 14 While this assumption is fundamentally untestable (we cannot observe 14 Related work on short-selling bans has used differences-in-differences for identification. Differences-in- 13

14 the treated outcomes of untreated firms), the nature of the Hong Kong eligibility criteria suggests this assumption is satisfied provided that firms do not have precise control over the forcing variable. Manipulation by firms or other market participants seems unlikely. Two of the thresholds are based on rolling averages, which would be hard to manipulate. The quarterly effective dates are irregular across years as well (see Table 1), and unknown to firms before the fact, which would further complicate manipulation. Moreover, any manipulation would likely result in discontinuities in population density around the thresholds. We find no evidence of such discontinuities under the McCrary (2008) density test. The p-values for discontinuities in the forcing variable for the float-adjusted market capitalization, turnover velocity, and market capitalization samples are 0.45, 0.17, and 0.44, respectively. Finally, we might expect to see pricing differences prior to the evaluation date in the presence of manipulation. We see no evidence of pre-treatment differences across the threshold (see discussion of Figure 3 in Section 5). While we observe both the announcement and eligibility dates, we do not perfectly observe the underlying forcing variables because the exact date on which the Hong Kong Stock Exchange determines eligibility (the HKEX measurement date) is not known. To account for this, we estimate a fuzzy regression discontinuity following Lee and Lemieux (2010). Estimation is by two-stage least squares where the first stage estimates the probability of treatment as a function of the threshold: N N D i,t = ω 0 +φ1(x i,t c t > 0)+ γ j (X i,t c t ) j + ω j 1(X i,t c t > 0)(X i,t c t ) j +η i,t. (1) j=1 j=1 D i,t is an indicator equal to one if firm i is included on the short-sale eligibility list at time t differences is used to control for the fact that firms are not randomly assigned to treatment, and therefore are likely to be different on various dimensions. The identifying assumption in differences-in-differences is that trends in treatment and control firms are similar across groups. In contrast, RD considers treatment to be essentially random close to the threshold, so there should be no ex ante differences across treated and control groups. For discussions of both methodologies, see Roberts and Whited (2013), Atanasov and Black (2016), or Angrist and Pischke (2009). 14

15 and zero otherwise, and 1(X i,t c t > 0) is an indicator function equal to one if the value of the forcing variable, X i,t (for example, market cap), exceeds the threshold value for inclusion, c t. In our setting, the unknown HKEX measurement date results in measurement error in both the forcing variable and in the sample screen (i.e., the measurement of the other threshold variables). Such measurement error, due solely to our observation of characteristics on different days than the exchange, should not be systematically related to outcome variables such as returns or volatility. Nonetheless, it can result in mis-classifications of predicted short-sale eligibility. Such mis-classification will result in a jump in the probability of shortsale eligibility of less than 1 (i.e., φ < 1). We discuss these issues and how the fuzzy RD accounts for them in detail in Appendix A. RD measures the treatment effect at the threshold (i.e., where X i,t c t = 0), but the estimation requires the use of observations within some bandwidth around the threshold. Within this bandwidth, outcome variables of interest may vary systematically with the forcing variable. Therefore, Equation (1) allows for a flexible functional form on either side of the threshold in order to measure an unbiased causal effect, as is standard. We control for the distance a firm is from the threshold, X i,t c t, as well as the interaction between the distance and the indicator function, 1(X i,t c t > 0). Thus, the relationship between D i,t and the distance to the threshold may have different slopes on either side of the cutoff. Higher-order polynomials of both the distance and the interaction are also included to allow for non-linear effects. In our primary specification, we report results for N=3. We consider alternative specifications in Section 6.1. Intuitively, the fuzzy RD accounts for the fact that observed short-selling eligibility is not perfectly predicted by the threshold rule (i.e., φ < 1), but that the probability of short-sale eligibility jumps at the threshold (i.e., φ > 0). Thus, one can use whether a firm is above the eligibility threshold, 1(X i,t c t > 0), as an instrument for short-sale eligibility and estimate 15

16 the treatment effect τ in a second-stage equation: y i,t = θ 0 + τ D N i,t + β j (X i,t c t ) j + N j=1 j=1 θ j Di,t (X i,t c t ) j + ε i,t (2) where y i,t is some outcome variable of interest (e.g., returns) and D i,t is the predicted jump in the probability of treatment at the cutoff c t, estimated from the first stage equation (1). 15 The coefficient τ represents the causal effect of short-selling eligibility on the outcome variable and is the estimate of interest in our analysis. We estimate equations (1) and (2) for the three thresholds described in Section 3, excluding firms that may be on the list due to index inclusion or options/futures listing. For each threshold, we only estimate the results for firms where a given threshold is the only one that will affect short-sale eligibility (for details, see Section 3). For example, when considering the float-adjusted market capitalization threshold, we estimate equations (1) and (2) for firms that do not satisfy both the market capitalization and turnover velocity thresholds. We consider fixed bandwidths around the centered threshold variables. These are +/ 100% of the capitalization thresholds for both the float-adjusted market capitalization and market capitalization samples and +/ 50% for the turnover velocity sample. These bandwidths are chosen to include all firms to the left of the thresholds. We show in Section 6.1 that our results are insensitive to bandwidth choice. The float-adjusted market capitalization threshold sample contains approximately 14,000 firm-quarter observations, the turnover velocity threshold sample contains about 3,000 firmquarter observations, and the market-capitalization threshold sample contains approximately 11,000 firm-quarter observations. Panels A, B, C of Table 2 report summary statistics for these samples. Note that certain eligibility criteria, such as index inclusion or option trading, occur disproportionately in larger stocks. Additionally, since two thresholds are based on 15 The interaction terms Di,t (X i,t c t ) j are instrumented by 1(X i,t c t > 0)(X i,t c t ) j in separate first-stage regressions. 16

17 size, there is correlation between the sample filters that require the other thresholds to not be satisfied. As a result, using a fixed bandwidth results in more observations away from the threshold on the left (ineligible) compared to the right for our two market capitalizationbased thresholds. This is not a problem because the distance controls, including interactions, are included to ensure that measured treatment effects are due to differences at the threshold rather than a result of the bandwidth used. An alternative approach is to consider tighter bandwidths, which we do in Section Short-Sale Eligibility We first present evidence that the threshold-based rules create discontinuities in inclusion in the short-sale eligibility list. Panel A of Figure 1 plots the probability of list inclusion relative to the centered forcing variables. 16 The forcing variables are minimum float-adjusted market capitalization over the 60 days preceding the measurement date, turnover velocity over the year preceding the measurement date, and market capitalization as of the measurement date. We also plot the predicted list inclusion value estimated from equation (1) along with 90% confidence bands. For all three thresholds, there is a clear discontinuity in short-sale eligibility at the threshold. The corresponding estimates from equation (1) are tabulated in the left-hand panel of Table 3 (labeled First Stage). As shown in the plots, list inclusion is significantly associated with a firm satisfying a given threshold. The increased probability (φ) ranges from 35% for the turnover velocity threshold to almost 50% for the float-adjusted market capitalization threshold. 16 In the plots, we bin firms that are the same distance away from each threshold and take an average. For the turnover velocity threshold, the data are binned to the nearest half percentage difference from the threshold value. For the market value thresholds, the bins are to the the nearest quarter (half) percentage difference to the right (left) of the threshold. 17

18 4.3. Short-Sale Activity An important question for our setting is whether eligibility is, in fact, associated with short-selling activity. It is possible that our sample, which contains firms for which eligibility depends only on the threshold-based rules, does not contain firms for which there is actually shorting demand. For instance, if options are endogenously listed for all firms for which there is shorting demand, there would be no discontinuity in short selling around the thresholds. To assess whether the threshold-based short-sale eligibility is a binding constraint, we estimate equation (2) with shorting activity as the outcome variable. We measure shorting activity by short volume as a fraction of total volume over the 30 trading days following each quarterly effective date, denoted RELSS. The results are tabulated in Table 3 and plotted in Panel B of Figure 1. The results provide clear evidence that shorting activity is higher for firms to the right of each of the three thresholds. The float-adjusted market capitalization threshold is associated with an 87 basis point increase in shorting as a fraction of total volume. The effect is even larger for the turnover velocity threshold; RELSS increases by 102 basis points around this threshold. The increase in shorting is smaller for the market capitalization threshold, at 25 basis points. At first glance, these discontinuities in actual shorting activity seem relatively modest. However, conditional on being eligible, the average RELSS in Hong Kong over our sample period is 4.6%; the median RELSS is 2.5%. This means that discontinuities of approximately 1% (i.e., that of the float-adjusted market capitalization and turnover samples) represent about 20% of the mean and 40% of the median RELSS for all short-eligible firms in Hong Kong, which are large relative increases. Our actual short-selling effects are all larger in magnitude than those found by CCY. While they find large asset pricing effects for additions to the short-eligible list, the average (median) RELSS in their sample is a modest 0.175% (0.00%) as reported in Table IV of CCY. Our estimated discontinuities should be more than sufficient to draw inference regarding the effects of short-sale eligibility. 18

19 4.4. Returns In this section, we examine the effects of short-selling eligibility on asset prices in our regression discontinuity setting. We evaluate several aspects of stock returns for the 30, 60, and 90 day windows following the quarterly effective dates. Table 4 presents estimates of equation (2) for average returns, cumulative returns, return volatility, return skewness, and the prevalence of extreme downside returns (defined as the number of days with a return more than two standard deviations below the mean for a given period). 17 We also show the effect on actual short selling for the same horizon. RELSS is higher in all instances, but the asset pricing results provide no evidence that short selling causes downward pressure on prices, increased volatility, more negative skewness, or increased prevalence of extreme negative returns. The lack of causal effects of short-selling eligibility around the thresholds on asset prices is shown graphically in Figure 2. The figure shows the return variables of interest as a function of the centered forcing variables. It is clear from the plots that there is no discontinuity at the threshold for the return variables. These results are inconsistent with those found in Hong Kong by CCY. We discuss differences in our analyses in the next section. How does the Hong Kong evidence compare to evidence from short-selling bans during the financial crisis? In terms of the level of prices, our results are generally consistent with those of Boehmer et al. (2013) and Beber and Pagano (2013) that short-selling bans did not affect the level of prices. The former focuses on pricing analysis of firms added to the US banned list after the initial announcement to avoid confounding effects of the contemporaneous TARP announcement. For these subsequently banned stocks, Boehmer et al. (2013) find no evidence of a boost in prices associated with banned short-selling. Similarly, Beber and Pagano (2013) find no evidence of changes in returns in their international panel, except in the U.S., perhaps due to the TARP announcements. Our result that exogenous short-sale 17 We present results for raw returns. Results are unchanged if returns are measured in excess of the market return (untabulated). 19

20 eligibility is not related to subsequent returns is thus consistent with the evidence from the financial crisis bans literature. The evidence is less consistent when turning to an examination of volatility of prices. In our setting, we find no evidence that volatility is affected by short-sale eligibility. On the other hand, both Boehmer et al. (2013) and Beber and Pagano (2013) find substantial increases in volatility for banned securities. Short-sale bans are often implemented by regulators in times of extreme volatility and for the most affected firms. Our result, using a different identification strategy, suggests that volatility may be unaffected by short-sale eligibility alone. 5. Analysis of All Hong Kong Additions CCY find that stocks that are added to the Hong Kong short-sale eligibility list experience negative abnormal returns, increased volatility and prevalence of extreme negative returns, and less positive skewness in returns subsequent to being added to the eligibility list. Their sample period runs from 1994 to 2003; the threshold rules we analyze in Section 4 were in effect only at the tail end of this sample. In this section, we analyze all firms added to the short-sale eligibility list as in CCY and compare their identification strategies to our RD setting. Our sample period of 2001 to 2014 contains a total of 1,528 addition events. Note that while we use quarterly effective dates in Section 4, the analysis in this section uses all effective dates, including dates falling between the quarterly dates. In Table 5, we use all additions and present average and cumulative market-adjusted returns for both short (10 trading days) and long (250 trading days) windows preceding and following the event date. For the long window, we also report additional return characteristics: standard deviation, skewness, and prevalence of extreme negative returns. Panel A (B) presents means (medians). Subsequent to becoming eligible for shorting activity, firms added to the list experience large negative abnormal returns. These are economically large and statistically significant except for the 20

21 mean returns for the 10-day window following addition. For the short window of 10 days, the mean (median) cumulative abnormal return (in excess of the HK value-weighted market return) is 92 bps ( 154 bps). For the 250 day window, the mean (median) cumulative abnormal return is 15% ( 22%). This is consistent with the findings in CCY, who find average (median) cumulative returns of 4.5% ( 2.3%) over a 10-day window (CCY Table II, Panel B). Over a longer horizon of 280 days, CCY find average (median) returns of 12 ( 9) bps per day (CCY Table VI). The identification strategies used by CCY depend on the horizon of the test. For the short horizon tests, the tests use a tight window around the event and adjust returns for market movements. Inference in such short horizon tests relies on a null hypothesesis of zero market-adjusted returns, which is generally reasonable for sufficiently tight windows. However, this is not the case in our sample. Both the mean and median cumulative return for newly-eligible firms over the 10 days preceding the event date are significantly negative as well. For this horizon, our pre-period results differ from those found in CCY. In drawing inference about the effects of short selling bans in their long horizon tests (CCY Table VI), CCY calculate pre- and post-eligibility differences, so the counterfactual is implicitly a firm s own performance in the pre-eligibility period. However, firms being added to the list have significant positive abnormal returns in the 250 days preceding the addition effective date. In the CCY sample, the mean (median) daily return over the (-280,- 31) window is 14 (11) bps. The same is true in our sample where the mean (median) average daily return is 15 (9) basis points, and the mean (median) cumulative return is 33% (7.5%). Therefore, in order to conclude that the effects measured in the post-eligibility period are due to short selling, one must believe that the large positive pre-period performance was likely to continue absent being added to the list. We believe this unlikely. It is therefore difficult to distinguish the effects of short-selling eligibility from those of recent performance which is abnormally positive over a long horizon and has subsequent reversals over the near term preceding list addition. More generally, abnormal performance 21

22 in the pre-addition period highlights the fact that short-sale eligible firms are quite different from ineligible firms. Additional evidence that this is true can be found in Table 6, which reports summary statistics of stock-quarter observations for firms that are ineligible or eligible for shorting. It is immediately clear that firms that are eligible for shorting are different from those that are not eligible. Eligible stocks are dramatically larger firms. Not surprisingly, smaller, short-ineligible stocks have higher return volatility than the larger, short-eligible securities. 18 The differences in Panel A and B demonstrate the need for careful selection of appropriate counterfactuals to compare short eligible and short ineligible firms that are otherwise identical firms. Results from our sample period differ from those in CCY with respect to return volatility. Using one-year windows, they find that return standard deviation is significantly higher subsequent to list inclusion (CCY Table VI). In our sample, we find that the mean (median) daily return volatility is actually 72 (40) basis points lower in the 251 days following short sale eligibility. One possible explanation for CCY s findings is the Asian crisis. Out of the 519 addition events studied by CCY, 129 occur on May 1, 1997, so the one-year window following this addition date includes the height of the Asian financial crisis. Finally, we confirm in our sample the results of CCY for skewness and the prevalence of extreme negative returns (defined as the number of days with a return more than two standard deviations below the mean for a given period). Return skewness is less positive following the initiation of short-sale eligibility. This difference is statistically significant. Moreover, the average prevalence of extreme negative returns increases from 1.5% to 1.9% following addition to the short-sale eligibility list. With the exception of return volatility, the results of CCY hold up remarkably well in our out-of-sample analysis. However, the results also highlight the potential pitfalls in studying 18 Since firms can be removed from the short-sale eligibility list, some of the ineligible securities may have experienced shorting activity over the preceding year. However, the vast majority of the short ineligible securities have experienced no shorting activity over the year preceding a given quarterly effective date. For short-sale eligible securities, the average (median) amount of shorting as a fraction of total volume is 4.6% (2.5%). 22