Are Short Selling Restrictions Effective?

Are Short Selling Restrictions Eﬀective?∗

Yashar H. Barardehi Andrew Bird Stephen A. Karolyi Thomas G. Ruchti

November 30, 2018

Abstract

We exploit SEC Rule 201 to study the price and trading effects of short selling restrictions. The policy requires exchanges to implement an uptick rule until the next day’s market close for stocks that cross a −10% intraday return threshold, generating rare quasi-experimental variation in short selling restrictions. On average, these restrictions increase daily returns by 30.6 bps, reduce seller-initiated volume by 4.5%, and increase off-exchange volume by 1.7%. These direct effects, which contrast with the extant literature, are concentrated in down markets, suggesting that the rule is most effective in periods of most concern to regulators. However, consistent with the substitution of potential short sales, we find significant offsetting spillover effects for peer stocks. Together, our findings yield new and timely policy implications and contribute to our understanding of short seller behavior.

JEL Classiﬁcation: G12, G14. Keywords: short selling, uptick rule, securities regulation, Rule 201, short-sale restrictions

∗We are grateful for comments received from Rui Albuequerque, Torben Andersen, Kelley Bergsma, Dan Bernhardt, Julio Crego, Arthur Denzau, Hans Degryse, Brent Glover, Peter Haslag, Burton Holliﬁeld, Eric Hughson, Olivia Huseman, Tim Johnson, Nikolaos Karagiannis, Daniel Karney, Stefan Lewellen, Zhi Li, Vitaly Meursault, Nate Neligh, Lars Nord´en,Dave Porter, John Ritter, Michael Schneider, Duane Seppi, Timothy Shields, Esad Smajlbegovic (discussant), Dustin Tracy, Marc Weidenmier, Andrew Zhang, and seminar participants at Carnegie Mellon University, Chapman University, Ohio University, Oklahoma, and SAFE Market Microstructure 2018. Barardehi ([email protected]) is at the Argyros School of Business & Economics, Chapman University, and Bird ([email protected]), Karolyi ([email protected]), and Ruchti ([email protected]) are at the Tepper School of Business, Carnegie Mellon University. 1 Introduction

Selling a stock short allows arbitrageurs to exploit privately-held negative information with-

out owning a security. Short sellers drive price discovery, have superior public information

processing skills, and make up almost one-quarter of NYSE trading volume (Hong and Stein

2003; Diether, Lee, and Werner 2009; Engelberg, Reed, and Werner 2012, 2018). Because of

their information advantages, the presence of short sellers may hurt market quality. However,

depending on market conditions, short sellers may also improve market quality by provid-

ing liquidity.1 Determining the net impact of these opposing forces remains an empirical question. Understanding this balance would allow policy makers interested in promoting well-functioning and liquid capital markets to better evaluate the dynamic consequences of regulations that target the prevalence and intensity of short selling activity.

In a world with heterogeneous beliefs, restricting short seller participation forces market prices to reﬂect the views of optimist investors (Miller 1977; Figlewski 1981; Hong and Stein

2007). All over the world, regulators have followed this theoretical argument to restrict short selling activity. In the wake of the 2007-2008 ﬁnancial crisis alone, at least 20 major global capital markets implemented short selling bans.2 In addition to banning short sales, regu-

lators have implemented short selling constraints via margin requirements, failure-to-deliver

restrictions, and uptick rules. In this paper, we study the consequences of this new breed of

short selling restrictions.3

1As Comerton-Forde, Jones, and Putnin.ˇs(2016) point out, short sellers both supply and take liquidity, depending on market conditions. 2See Beber and Pagano (2013). 3The literature has also investigated the connection between short selling constraints and options markets (Figlewski and Webb 1993; Grundy, Lim, and Verwijmeren 2012).

1 To do so, we exploit a rich panel of microstructure data and a threshold-based short selling restriction introduced to U.S. financial markets in 2010, Rule 201 (SEC 2010), using a regression discontinuity design. The design and implementation of the policy allows us to construct a novel methodology centered around rare quasi-random variation in short selling restrictions at the stock-hour level. We contribute a novel and timely policy evaluation as well as new inferences on the causal effects of short selling restrictions on returns, liquidity, and trading platform choice. We also extend our methodology to study novel general equilibrium effects of short selling restrictions, which reveal new inferences about short seller behavior and expand the scope of our policy evaluation.

Our empirical approach takes advantage of the unique cross-sectional nature of Rule 201, the “alternative uptick rule.” In executing Rule 201, exchanges must restrict short selling using the uptick rule once a stock’s intraday returns reach a decline of 10% or greater from the previous day’s close. This short selling restriction lasts until the close of the next trading day. The threshold-based design and short-lived enforcement period of the policy allow us to distinguish the effect of the uptick rule from confounding price and trading effects that would otherwise occur for on days with similarly low returns. Our methodological approach differs from previous studies of short selling restrictions (Alexander and Peterson 2008; Di- ether, Lee, and Werner 2009; Beber and Pagano 2013; Boehmer, Jones, and Zhang 2013) in that we use within stock variation in short selling restrictions, rather than solely time series or cross-sectional variation. As such, instead of the conflating effects that may be driven in general equilibrium, the variation we exploit can clearly be tied to the short selling

2 restriction policy itself.4

In many respects, we find evidence that the direct effects of Rule 201 are in line with policymakers’ expectations and objectives. We find that short selling restrictions substantially reduce seller initiated trading, an indication that the policy successfully restricts short selling.

We also find that off-exchange trading goes up, potentially because of the frictions placed on trading by the restriction. In contrast to much of the extant literature, however, we find significant evidence that short selling restrictions increase daily returns. Compared to stocks with intraday low returns of just above −10% (i.e., unrestricted stocks), stocks with intraday low returns of below −10% (i.e., restricted stocks) have 31 basis points higher daily returns.

This price eﬀect decays within three days, but does not subsequently reverse. This suggests that the type of short selling opportunities that the policy eﬀectively restricts are transient.

Our ﬁndings on price recoveries contrast with the prior literature on short selling restrictions. With few exceptions (e.g., Jones 2012), this literature has provided no evidence that restrictions aﬀect stock prices as would be predicted by theories of disagreement (e.g.,

Miller 1977). Our contrasting evidence follows from our unique setting. Prior empirical work on short selling restrictions have studied restrictions that have been implemented either in response to a market-based stimulus or under speciﬁc market conditions, and have had long- lived enforcement periods. Rule 201 provides such granular within-stock variation that we

4We verify, in unreported results, that the SEC’s price limit rules with similar circuit breakers do not drive our findings. Beginning Sept. 10, 2010, SEC and FINRA required temporary (shorter than 10-minute) trading halts following price declines of 10% or more that realize within 5-minute intervals. The universe of stocks subject to these restrictions expanded from S&P500 stocks to all National Market System stocks by June 23, 2011. The price limit restrictions are sensitive to price movements between 9:45am and 3:35pm. We verify that, if anything, our findings are significantly stronger when short-sale restrictions are triggered outside this window. Brogaard and Roshak (2016) find that price limit restrictions “reduce the frequency and severity of extreme price movements, but induce price underreaction.”

3 can study the local eﬀect of short-lived restrictions across a broad range of market conditions.

Long enforcement periods may encourage short sellers to stop trading or to divert their at- tention to other markets and opportunities, and it is challenging to disentangle enforcement from the stimulus or from policymaker discretion. These limitations exist even for randomized experiments; for example, the pilot program of Regulation SHO randomized short selling restrictions for Russell 3000 stocks during 2005 and 2006. The pilot program aﬀected short selling activity, but had no discernible eﬀect on prices (Diether, Lee, and Werner 2009).

However, the effects of such short selling restrictions may be transient, making them difficult to measure over long horizons. Furthermore, short selling restrictions may be effective only in down markets, and the program constituents experienced a 10.6% return during the period. The methodological flexibility offered by the design and implementation of Rule 201 allows us to evaluate the external validity of other policy effects in a number of dimensions.

Consistent with this local average treatment effect interpretation, we find that the price effects of short selling restrictions are concentrated during down markets. This is also in line with policymaker objectives. Off exchange volume is larger only under these same market conditions, indicating that the price recovery effect is associated with more volume moving off exchange. We also investigate effects across market conditions based on the number of stocks that trigger the uptick rule. We find similar evidence in these tests, which could be driven either by the correlation between market returns and the propensity for individual stocks to cross the −10% return threshold or because short sellers are capital constrained in these conditions.

A concern with transient, stock level short selling restrictions is that they do not place

4 restrictions on short sellers, only on certain short selling opportunities. To test whether short sellers ﬁnd alternative means of achieving their desired short positions, we analyze the impact of the policy on peer stocks in the same 4-digit SIC industry. Because these peer stocks oﬀer short sellers only an approximation of their desired exposure, substituting short positions across peer stocks is likely costly. In this sense, our analysis reveals the cross-stock elasticity of short selling using the cost imposed by the uptick rule.

We find evidence of economically significant policy spillovers to peer stocks. Whereas the direct effect of the policy increases prices for restricted stocks by 31 basis points per day, the spillover effect for each peer stocks is a negative 7 basis points in daily return. We also

find that off-exchange volume decreases for these stocks, opposite to the effects on triggered stocks. Finally, we find that the proportion of seller-initiated volume goes up for these peer stocks, in keeping with sellers moving their trades to similar stocks. This novel evidence of policy spillovers dramatically change the cost-benefit analysis of short selling restrictions.

Whereas the direct eﬀects generally align with policymaker objectives to curb “excessive downward pressure on individual securities” (Johnson 2010), as cited by SEC chair Mary

Schapiro in the policy introduction, these unanticipated spillover effects offset these benefits.

We make several contributions to the literature. First, we propose a methodology that uses within-stock variation in short selling restrictions, and that measures using intraday returns. Second, we show that Rule 201 was eﬀective in altering short seller trading behavior.

Third, we illustrate the (un)intended ways in which a short selling restriction affects market quality and changes returns for stocks. Our novel approach and findings show that Rule 201 likely affects returns and market quality more than was previously thought (Jain, Jain, and

5 McInish 2012). When considering the spillover eﬀects of the policy, and taking into account its sizable compliance costs, Rule 201 and similar short selling restrictions in other markets may be far from innocuous.

We continue the paper as follows. Section 2 outlines the institutional background of

Rule 201, the data we use, and our empirical methodology. Section 3 details our results on price recoveries and liquidity, moving on to spillover effects and heterogeneity in effects across market conditions. Section 4 discusses identification concerns and Section 5 provides a policy evaluation. Section 6 concludes.

2 Institutional Background and Data

In this section, we describe relevant institutional details for our study, and sketch the debate between the views for and against implementation of Rule 201. We then describe the data.

2.1 Institutional Background

On June 13, 2007, the SEC voted to eliminate the “up-tick” rule on short selling stocks, eﬀective July 6, 2007. Typical short-sale restrictions entail that short selling a stock is only allowed on an uptick. The short must therefore be placed at or above the last traded price of the security (Reg-SHO era NYSE uptick rule), or at or above the last posted bid (Reg-SHO era NASDAQ bid price rule). The removal of short selling restrictions followed a pilot program, beginning May 2, 2005,5 in which 1000 stocks were randomly chosen from the Russell

3000 index to trade without short-sale price tests. Following the pilot program, the SEC

5Securities and Exchange Act Release No. 53684

6 concluded that price tests were not needed, as they upset order ﬂow by distorting short-sale

order placement, and that market quality was not signiﬁcantly aﬀected (SEC 2006; Diether,

Lee, and Werner 2009).6 The SEC then decided to remove short-selling restrictions for all stocks, including those in the pilot program, and further, voted to prohibit any exchange from imposing a price test in the future.

In the wake of the ﬁnancial crisis, public support for short-selling bans mounted, and on April 8, 2009, the SEC sought comment on proposals to restore a modiﬁed version of the uptick rule (SEC 2009). On February 24, 2010, the SEC amended previous short-selling rules to adopt Rule 201, or the “Alternative Uptick Rule”, with the required compliance date of February 28, 2011. This applied to stocks in the National Market System, and would be triggered following an intraday price decline of 10% or more from the previous day’s closing price. The rule imposed a short-selling requirement that short sales be placed above the national best bid at the time of order submission. The short-selling restriction would begin immediately following the breach of the 10% threshold, as determined by the listing exchange,7 and would last through the end of the next trading day. This meant that an uptick rule would be in place for an individual stock for most of two trading days, if the stock saw a price decline of 10% early on in the trading day.

Critics of the alternative uptick rule argued that short-selling had nothing to do with the crisis, and that this new rule had the potential to harm markets by decreasing market eﬃciency and reducing the ability of markets to expose overvalued stocks (Dealbook 2010).

6Boehmer and Wu (2013) show that short sellers improve price discovery. 7https://www.sec.gov/divisions/marketreg/rule201faq.htm

7 The commission estimated startup implementation costs of $1B, and yearly costs of $1B for exchanges to maintain compliance, but senators Ted Kaufman and Johnny Isakson believed the rule would not do enough, “helping only in the worst-case scenarios that could occur during a terrorist attack or ﬁnancial crisis (Johnson 2010).” At the time, there was concern that Rule 201 would reduce market quality through lower volume, poor price eﬃciency, wider bid-ask spreads, and higher intraday volatility (Jain, Jain, and McInish 2012). SEC Chair

Mary Schapiro admitted there were potential beneﬁts to short selling, but stated, “We also are concerned that excessive downward pressure on individual securities, accompanied by the fear of unconstrained short selling, can destabilize our markets and undermine investor conﬁdence in our markets (Johnson 2010).”

2.2 Data

Our sample runs from March 1, 2011 to December 31, 2012, and includes NYSE-, AMEX-, and NASDAQ-listed common shares of U.S.based stocks.8 We obtain daily closing prices, price adjustment factors, and 4-digit SIC industry codes from CRSP. We use trade and quote level data between 9:30AM–4:00PM EST during March 1, 2011–December 31 2012 from Daily TAQ. We obtain information on tick-by-tick prices, transaction sizes, and the exchange at which each transaction took place with millisecond time stamps from the Con- solidated Trades Tape. We match each transaction to the mid-point of the prevailing best bid and oﬀer prices at the end of the previous millisecond. We construct best national bid and oﬀer prices at the millisecond frequency using the Consolidated Quotes Tape and NBBO

8The sample period coincides with the mandatory compliance period that began on February 28, 2011.

8 ﬁles from the Daily TAQ data base. We also drop stocks whose identifying information does

not allow a merge with both CRSP and Daily TAQ.

We calculate various trading outcomes over six equal length, i.e., 65-minute, time inter-

vals each trading day. Returns are calculated using the transaction prices at the beginning

and at the end of each intradaily interval.9 To identify trigger times, using transaction prices, we also calculate intra-bin low returns with respect to the most recent close price. We use the total number of shares traded over each interval to measure trading volume. In Figure 1, we show the timeline of the daily number of triggers throughout our sample period. In the

ﬁgure, we mark Black Monday (August 8, 2011), which saw an outsized number of triggered stocks.10 Similarly, Figure 2 shows a histogram of the number of triggers within our sample as well as a plot of the natural log of the daily number of triggers with daily market returns, suggesting substantial variation.

We measure the extent of seller-initiated order flow using the proportion of seller-initiated dollar volume in each interval. Transactions are classified into buyer- or seller-initiated using the Lee-Ready (1991) algorithm, based on the midpoint of national best quoted prices at the end of the millisecond prior to each transaction. We also calculate average transaction size, dollar-weighted averages of quoted and relative effective spreads,11 and the proportion of

trading volume executed off-exchange. To identify off-exchange trades, we use the trade flag

9Similar to Jain, Jain, McInish (2012), we account for price changes driven by over-night price adjustments. Adding back these changes reflects the fact that Rule 201 is not sensitive to price changes due to such adjustments. 10In untabulated tests, we show that our findings are robust to excluding this date from the sample. 11A transaction’s quoted spread is the difference between national best bid and offer prices at the millisecond a transaction is recorded; relative effective spread is the absolute difference between the transaction price and the midpoint of best quoted prices at the previous millisecond divided by the midpoint of quoted prices.

9 ‘D’ in TAQ data that identiﬁes trades reported to FINRA’s Trade Reporting Facility. We

exclude a stock-day from our sample if trading is absent in at least one 65-minute interval

of the stock within the three-day window around that date.

3 Methodology and identiﬁcation

3.1 Methodology

Our goal is to identify the marginal eﬀects of the Rule 201 “alternative uptick rule” on re-

turns and measures of market quality. While the overall trading environment is changed by

short selling bans (Beber and Pagano 2013), or by pilot programs such as Regulation SHO

(Diether, Lee, and Werner 2009), Rule 201 further places restrictions on short selling in a

way that is time-varying across stocks. That is, the alternative uptick rule requires short

selling to occur only at or above the previous best bid price, but this only occurs following a

−10% return trigger. The policy is triggered when intraday returns pass a 10% decline from

the previous day’s close, and it extends through the end of trading the next day.

Because Rule 201 short selling restrictions occur during the course of the trading day and necessarily follow very negative returns, it is diﬃcult to understand the incremental eﬀects of

Rule 201 without accounting for intraday price and trading dynamics. Speciﬁcally, if a stock is triggered earlier in the day, there are nearly two days of trading of that stock that will take place under short selling restrictions (the remainder of the triggering day, and the entirety of the next day). Contrastingly, if a stock is triggered later in the day, there is roughly only one day of trading of that stock that will take place under short selling restrictions (the neg- ligible remaining portion of the triggering day, but primarily the entirety of the next day).

10 Because we must also control for intraday dynamics, it is important to employ an empirical

design that both includes controls that account for changes in trading over the course of the

trading day and accounts for the discontinuous eﬀect of the policy at −10% returns.

First, we address the intraday dimension of trading through our sample and variable construction. In particular, trading happens over the course of the day, but we must strike a balance between granularity—how ﬁne our measurement is—with data we can draw inference from–trading observations. We choose to break up the day into six equal bins, 65 minutes each in length.12 For each stock day and for each bin, we calculate returns (or our other dependent variables of interest) from the end of that bin to the end of the following trading day. In the case of returns, and for bin 1 of the trading day (out of 6), this would be from the end of bin 1 through the end of bin 6 of the next day (what we label as bin 12).

Figure 3 illustrates the way in which we split up bins. In the ﬁgure, we illustrate the bins that are aﬀected or treated by the alternative uptick rule, given an intraday low reaching

−10%. In the ﬁgure, we show an example of the bins aﬀected if a 10% intraday decline in the stock’s value during day t from the value at close of day t−1 is reached at noon. Because

12:00 p.m. is between 11:40 a.m., and 12:45 p.m., the trigger occurs in our third of six 65 minute bins during the day. In our notation below in equation (1), we denote the period of

12In particular, we aggregate trading, returns, volume, etc. according to 9:30–10:35 a.m., 10:35–11:40 a.m., 11:40 a.m.–12:45 p.m., 12:45–1:50 p.m., 1:50–2:55 p.m., and 2:55–4:00 p.m.

11 measurement using the superscripted [x+, 12], for intraday returns and triggers in bin x.

[x+,12] x x∗ x x∗ yjt = y0 + α0TRGjt + α1lrjt + α2(TRGjt × lrjt ) 6 X x + λiI(x=i) + ﬁxed eﬀects + εjt, (1) i=1 x∗ x x ∈ {1,..., 6} and lrjt = [lrjt + 10%] ∈ (−2%, 2%)

In equation (1), we address the discontinuous eﬀect of the policy at −10% with a regres-

[x+,12] sion discontinuity design. We regress our dependent variable, yjt , for stock j, on date t

+ x for bins x through 12, on TRGjt, whether stock j was triggered in bin x of day t, and a running variable, or a linear function of returns on either side of the discontinuity. Namely, we control for any local eﬀects of intraday low returns on the subsequent returns (or another outcome variable) for the remainder of that day, through the next day. This is shown by the

x∗ x x∗ x∗ independent coefficients for lrjt , and its interaction with the trigger, TRGjt ×lrjt . lr is the intraday low return for bin x on day t. This means that the variation we are using is localized to the difference in our outcome variables that is induced by the discontinuous nature of the policy: triggers occur only at or below an intraday decline of 10% from the previous day’s close.13 Therefore, this design measures the effect of the policy, controlling for any effects the intraday low for a stock should have on subsequent returns. Using our bin structure, we also include indicator variables I(x=i) where i = 1,..., 6. This enables us to control for each intraday measure that corresponds with the same time-of-day trigger (whether bin 1, 2, etc.).

Otherwise, we include month and time-of-day ﬁxed eﬀects. Because we use a local linear polynomial design, we restrict to intraday low returns within a 2% bandwidth of the discontinuity

13 Centering the running variable at the threshold −10% allows α0 to capture the exact magnitude of the x discontinuity in the dependent variable when lrjt = −10%.

12 in question, from −12% to −8%. It is important to note here that our results are qualitatively

similar for smaller bandwidths, and with quadratic controls on each side of the discontinuity.

We also conduct additional tests of the eﬀects of Rule 201 across varying market and trig-

ger conditions. We look at daily measures of equally-weighted market returns and the total

number of triggered stocks. We identify the bottom and top 20% in the entire time-series

of daily observations in our sample. These produce three indicator variables to categorize

trading days into low, medium, and high, which are denoted by the subscripts `, m, and h. In market condition tests, we include three indicators for market conditions, one for the bottom quintile, another indicator for the middle three quintiles, and a third for the top quintile. For example, MKTω,t equals 1 if date t market return is in the quintile(s) “X”, and 0 otherwise, where ω = `, m, h denotes X = {ﬁrst, second through fourth, ﬁfth}, respectively. NTRGω,t is a similar measure for the number of market wide triggers.

In equation (2), below, we interact the trigger and intraday low return running variables with market conditions, so as to uncover the relative eﬀects across these markets. Here,

Condition is either MKT , market returns, or NTRG, the number of triggers that same day.

` ` m m m h h h As such, our coefficients of interest are α0 = α , α0 = α − y0 , and α0 = α − y0 . Of note, this design does not imply that coefficients from regressions using this model should add up to coefficients in the pooled regression.14 Here, as above, ω = `, m, h correspond to market

14This is due to the inclusion of interaction terms with the local linear polynomial controls as well as differing intercept coefficients, and the fact that the number of intraday observations are different across the quintiles of the aggregate market/trigger conditions.

13 conditions. Fixed eﬀects and bandwidths are the same as above in equation (1).

[x+,12] X ω X ω x yjt = y0 + y0 Conditionω,jt + α (TRGjt × Conditionω,jt) ω∈{m,h} ω∈{`,m,h} 6 x∗ x x∗ X ω x + α1lrjt + α2(TRGjt × lrjt ) + λi I(x=i) + ﬁxed eﬀects + εjt, (2) i=1 x∗ x x ∈ {1,..., 6} , lrjt = [lrjt + 10%] ∈ (−2%, 2%) , ω ∈ {`, m, h} ,

and Condition ∈ {MKT,NTRG}

We are also interested in measuring the spillover of these eﬀects to other stocks. In particular, we are interested in how short selling restrictions may change trading behavior and lead traders to engage in broader strategies across stocks. To this end, we study spillovers for stocks in the same 4-digit SIC industry. Here, we run regressions similar to equation (1), but using left hand side variables calculated for peer stocks. That is, we want to identify the extent to which Rule 201 incrementally leads traders to engage in diﬀerent strategies on peer stocks, so we investigate the same discontinuity on the right hand side as before.

This is shown in equation (3), where each (right-hand-side) stock j on date t is paired with some (left-hand-side) stock(s) k on the same day—in our ﬁnal sample the median number of industry-peer stocks per day is 16.

[x+,12] x x∗ x x∗ ykt = y0 + β0TRGkjt + β1lrkjt + β2(TRGkjt × lrkjt) 6 X x + γiI(x=i) + ﬁxed eﬀects + εjkt, (3) i=1 x∗ x ∗ x ∈ {1,..., 6} and lrkjt = [lrkjt − R ] ∈ (−2%, 2%)

We are also interested in the longer-run eﬀects of the policy. For Rule 201 to have meaningful eﬀects, policymakers may be concerned both with price reversals, such that any

14 meaningful positive return eﬀects of the trigger are undone, or any persistent market quality eﬀects. In equation (4), we run a regression similar to equation (1) above, but now following the stock for up to 8 days after the trigger.

k k x k x∗ k x x∗ yj,t+k = y0 + α0TRGjt + α1lrjt + α2(TRGjt × lrjt ) 6 X k x + λi I(x=i) + ﬁxed eﬀects + εj,t+k, (4) i=1 x∗ x ∗ x ∈ {1,..., 6} , k ∈ {1,..., 8} , and lrjt = [lrjt − R ] ∈ (−2%, 2%)

We regress returns (or another outcome measure), through the end of trading on day t + k, where in our ﬁgures t = 0 is the trigger/control day. All control variables are the same, except we include indicators so that treatment and control are compared across the

k same day, coeﬃcient λi , where i = 1,..., 6 bins, and k = 1,..., 8 days.

3.2 Identiﬁcation

Our approach is based on inference made around the −10% threshold deﬁned in the Rule

201 policy. Any short selling restriction or ban will have effects on trader behavior. One may be concerned that traders, anticipating the threshold, will alter their behavior in a manner that biases our estimates of the policy’s effects. We now investigate potential anticipation of the threshold by traders and the implications of this anticipation. We find evidence of a response that is consistent with traders attempting to complete their orders before the uptick rule takes effect. While there are momentary effects for returns, these effects disappear within seconds. Because our specifications are based on 65-minute intervals, and treatment is assigned only in bins subsequent to the triggering return, these effects are unlikely to be

15 driving our results. Because we rely on the discontinuity surrounding −10%, one may be

concerned that what we may ﬁnd is driven by trends in price that are not accounted for in

our speciﬁcations. To show that our results are not spurious, we also provide falsiﬁcation

tests using diﬀerent cutoﬀs of −6% and −14%, which we discuss in Section 4.2.

We investigate the existence of manipulation around the −10% threshold using McCrary

(2008) test statistics. In Table 1, we find evidence consistent with manipulation in the first column. However, evidence for this goes away once we exclude trades in the 30 seconds following the realization of the minimum return with respect to the preceding day’s closing price. In column 2, under this restriction, we find no increase in the density to the left of the threshold.

This is represented graphically in Figure 4. In the ﬁrst subﬁgure, one can see an abnormal mass of minimum returns just below the trigger threshold. This mass to the left of the threshold is consistent with short sellers competing to place their before the stock price reaches the −10% return threshold. If short selling costs are higher under an uptick rule, short sellers will have incentive to place their order before the trigger point is hit.15 An- ticipating this, traders supplying liquidity would account for the adverse selection of being paired with these traders, leading to wider spreads and lower sell price executions. This last moment rush could itself push prices lower, potentially driving reversals for these stocks.

However, this mass appears to go away in the second subﬁgure after removing the trades immediately following the intraday minimum. This shows that any downward price pressure

15This intuition diﬀers from that of a model in which a single informed trader trades with noise traders in the presence of a boundary. Instead of pushing against the boundary, a single trader would internalize the externalities of doing so and may instead even manipulate away from the boundary to avoid the short selling restriction.

16 is gone just thirty seconds later. We argue that these effects are due to microstructure and reduced liquidity offering terms to likely short sellers, rather than concerted price manipulation around the threshold. Moreover, our measurement is in 65-minute bins, and we assign treatment only for bins following the stock hitting the intraday low of −10%. Because we measure outcomes in this way, it is highly unlikely that these transient microstructure effects— disappearing in seconds—are driving returns results at least a half an hour later, on average.

We demonstrate more acutely how transient these effectas are in Figure 5. In this figure, we estimate the McCrary (2008) test coefficient removing trades at an increasing number of seconds from the time of the intraday minimum. While the test coefficient disappears at 30 seconds, it is nearly indistinguishable from zero at only five seconds, indicating that, if anything, the order book quickly recovers following an intraday minimum. These results show that our

ﬁndings are unlikely to be driven by manipulation around the threshold, and, if anything, there are some short-lived microstructure eﬀects at the crossing of the -10% trigger threshold.

4 Short selling restrictions, returns, and trading

We begin our empirical analysis by providing visual evidence of discontinuities in returns, seller-initiated volume, and off-exchange volume. We contrast conditional distributions of mean 65-minute returns for intervals that span over days of short-sale restrictions to those that do not. We plot the linear fit of bin returns and proportions of seller-initiated volume against the most recent low returns within a 2% bandwidth of the −10% cutoff for low returns. Figure 6 shows discontinuity evidence suggesting that the regulation impacts both trading behavior and price dynamics. There is a significant jump in average bin returns as

17 short-sale restrictions go into effect. Importantly, this is coupled with a substantial drop in the proportion of seller-initiated volume, suggesting that differences in trading behaviors un- derlie the differences in price dynamics. We bolster our identification strategy with placebo tests and discuss the effects of short selling restrictions for liquidity.

4.1 Price recoveries and trading eﬀects

To more systematically investigate the incremental effects of a Rule 201 short selling restriction on returns, we estimate equation (1) with returns as the dependent variable. Because we divide all dependent variables by the number of bins measured (for a bin 1 trigger, divided by 11, the remaining five bins of the first day, and six bins of the day after), our estimates are for 65 minute returns in all of our tests. In table 2, we show that Rule 201 has a 5.10 basis points positive abnormal return for stocks that just trigger the cutoff when compared to stocks that do not. This aggregates to a daily return effect of roughly 31 basis points, and a total abnormal return of 44 basis points on average for the full trigger period.16 We show in column (2) that our findings are robust to including firm fixed effects. Further, in column (3) we instead use a quadratic polynomial control on either side of the cutoff, and in column (4) decrease the bandwidth we use and obtain quantitatively similar results. The latter two columns demonstrate that our findings are not simply driven by functional form surrounding the policy cutoff.

Next, we investigate the eﬀects of Rule 201 on trading behavior. If short sellers are sig- niﬁcant market participants, especially in down markets, restrictions should be expected to

16This calculation is based on the number of bins that are exposed to the “alternative uptick rule” which is, on average, 8.6 bins or about 1.4 trading days, multiplied by the 65 minute returns eﬀect of 5.39 basis points.

18 reduce seller-initiated volume. Critics argued that short-sellers would evade the “alternative uptick rule” by moving their trading off-exchange (Dealbook 2010). Here, we also consider the proportion of seller-initiated trading and off-exchange trading using the specification in equation (1). Our results are shown in Table 3.

We find that restrictions on short-selling have meaningful effects on the proportion of Lee and Ready (1991)-categorized seller-initiated volume. In particular, seller-initiated volume for triggered stocks falls by 4.48%. These results indicate that short selling restrictions disproportionately remove seller initiations of trades. Additionally, we find that off-exchange volume increases by 1.65%, suggesting that the removal of short sellers reduces the overall share of informed trading—volume that is less likely to take place on-exchange (Zhu 2014;

Bloomfield, O’Hara, and Saar 2015). Zhu (2014) studies the role of dark pools in price discovery when informed traders’ information is short lived. Because informed traders are more likely to pursue on-exchange execution to avoid execution risk, dark pools help price discovery. Bloomfield, O’Hara, and Saar (2015) find that liquidity and informed traders re- act differently to changes in the extent of market transparency: liquidity traders trade more aggressively in opaque markets; in contrast, informed investors trade more aggressively in transparent markets. If short selling is in fact informed, these insights are consistent with our finding that restrictions on short selling reduces the share of trading in on-exchange venues (transparent markets), increasing the share of off-exchange volume, possibly due to a higher share of trading in dark pools (opaque markets).17 As before, these findings are robust to inclusion of firm fixed effects, and different polynomial and bandwidth controls.

17In other words, the informed trading volume from short sellers would be substituted by uninformed volume that is likely routed to oﬀ-exchange venues.

19 While our results on reduced selling are broadly consistent with past studies, our finding that short selling restrictions have a positive effect on returns contrasts with the existing literature. In particular, recent papers have found no effect of these restrictions in support- ing prices, whether the restrictions were in the form of policy experiments such as Reg SHO

(Diether, Lee, and Werner 2009) or wholesale bans during the ﬁnancial crisis (Beber and

Pagano 2013; Boehmer, Jones, and Zhang 2013).18 There are several reasons our ﬁndings may depart from past studies.

Our setting provides time series variation in short selling restrictions within stocks. As such, our tests suffer neither from general equilibrium effects between treatment and control stocks, as with Reg SHO, nor from selection bias, as in blanket short selling bans in response to shocks to the financial system. These issues would make it difficult for an empirical strategy to isolate the effects of the policy from other factors. Our setting, however, provides quasi-random assignment of short selling restrictions across stocks and over time. This means that our approach does not require assumptions about the relationships between covariates to treatment and outcome variables (Lee and Lemieux 2010). This feature of the setting allows us to conduct analysis across market conditions. In Section 5, we explore market conditions under which these effects matter most and potential spillovers of the policy to other stocks.

4.2 Placebo tests

Our identiﬁcation focuses on variation surrounding the −10% threshold for triggering return events. Speciﬁcally, we are interested in isolating trading patterns that are driven by Rule

18A notable exception is Jones (2012), which ﬁnds that three short selling restrictions in the U.S. in the 1930s were associated with positive returns.

20 201 uptick rule eﬀects. To do so, we wish to control for any trends in intraday loan price that

would otherwise drive returns. We show that our results are robust to time and ﬁrm ﬁxed

eﬀects, a second order polynomial, and tighter bandwidths; however, one may still be con-

cerned that our results are driven by features of returns that are not accounted for in these

specifications. We now investigate placebo cutoffs to address such misspecification concerns.

In Table 4, we investigate placebo cutoffs of −6% in Panel A, and −14% in Panel B. Of the three outcomes we study, across these two placebo cutoffs, none come up as statistically significant.19 Because returns are more likely to have intraday lows in the −6% cutoff range, and less likely in the −14% cutoff range, compared to −10%, we have evidence that it is not simply noise driving insignificance, but the coefficients themselves appear to be muted in proportion to the power of the respective tests. Of particular interest are returns. We

find a coefficient estimate that is markedly smaller for both cutoffs than in our actual Rule

201 tests. We plot graphical evidence of this falsification in Figure 7. In it, we plot the linear fit of returns, proportion of seller-initiated volume, and off-exchange volume against intraday low returns within a 2% bandwidth of our placebo cutoffs -6% and -14%, shading in corresponding 95% confidence intervals for the predicted variable of interest.

4.3 Eﬀects of the policy on liquidity

Past studies ﬁnd that short selling restrictions harm market quality (Diether, Lee, and

Werner 2009; Boehmer, Jones, and Zhang 2013; Beber and Pagano 2013). In keeping

19In untabulated tests, we also investigate placebo cutoffs for transaction size, volume, effective spreads, and quoted spreads, and find only one statistically significant result across the 14 variable-placebo cutoff combinations.

21 with these ﬁndings, short sellers may provide liquidity when other market makers are not

(Comerton-Forde, Jones, and Putnin.ˇs2016). If instead short sellers hold private information and trade on it (Aitken, Frino, McCorry, and Swan 1998;), then a short selling restriction could be beneficial for liquidity. In fact, different short selling restrictions may have effect on different types of short selling behavior. In the example of Reg SHO, short selling restrictions may have made it too costly for some liquidity providers to provide as much liquidity as they were before. In our setting, these liquidity providers would have no reason to exit a stock because the temporary uptick rule would likely expire in a few trading days. Conversely, private information is inherently short lived, and so a temporary short selling restriction for a stock may disproportionately affect informed short sellers.

In Table 5, we investigate the effects of triggers on trade size, volume, trade-weighted relative effective spreads, and trade-weighted quoted spreads. We do not see any changes to mean transaction size, in contrast with Diether, Lee, and Werner (2009), and volume also appears to be relatively unaffected. However, both effective spreads and quoted spreads fall, indicating that the limitations imposed by Rule 201 affect traders with private information.

Further, this improvement in market quality happens despite our finding that a larger proportion of trading volume moves off exchange. While we provide no evidence of short sellers providing necessary liquidity to markets, we believe that ex ante the policy is most likely to affect short sellers with private information. These findings illustrate potential value of this policy, from a regulatory perspective, to that of previous short selling restrictions. In untabulated tests, we investigate these effects across markets, but do not find statistically significant differences if market-wide returns are high or if they are low.

22 5 Long-run eﬀects, cross-sectional variation, and spillovers

We have shown that short selling restrictions are associated with with an expected reduction in seller-initiated volume, more off-exchange trading (potentially because short sellers are trading less in these stocks), and higher abnormal returns. Due to the short-lived nature of these restrictions, policymakers would be interested in how long the effects last and whether or not they reverse. Because this policy is directed at curbing excessive downward price pressure, it is important to understand how these short selling restrictions apply across market conditions. Further, while short selling restrictions increase the costs of short selling, the incentive to short does not go away. In this section, we investigate long-run effects of the uptick rule, variation across time in the effects of the policy, and the degree to which price pressure is redirected to related stocks.

5.1 Long-run eﬀects

We next show that the price recovery and liquidity effects of the policy are short-lived, barely extending to trading days past the short selling restriction. We do so by estimating equation (4) for trading outcomes observed up to 7 trading days after the last treatment date, i.e., k = {2,..., 8}.20 Figure 8 demonstrates that the differences in 65-minute returns re- main positive for one trading day, before flattening out at k = 3 and remaining insignificant afterwards. The proportion of seller-initiated volume follows the opposite pattern, as there is a decrease in this proportion on the full trading day that is triggered, but there are no effects after the triggering period. Share of off-exchange volume sees a positive increase for

20Note that setting k = 1 in equation (4) yields the same results as in equation (1).

23 a day, but this also decays. These results are presented in Table 6.

What we find is consistent with there being no reversal of the price effects. This implies that short sellers are more likely trading on transient market movements, rather than on fundamental information. Further, these tests indicate that there are no lingering effects of short selling restrictions in these markets that may contaminate our results or limit the generalizability of our findings.

5.2 Market returns and same-day triggers

Since the primary goal of introducing Rule 201 was to curb “excessive downward pressure on individual securities” as suggested by SEC chair Mary Schapiro in 2010, one would imagine that regulators may be most worried about the policy’s efficacy in down markets. Because short sellers behave differently under different short selling restrictions (Geczy, Musto, and

Reed 2002; Diether, Lee, and Werner 2009), this may apply to overall market conditions as well. In this subsection, we address the dynamics of markets under short selling restrictions interacted with other market conditions. We first investigate the effect of Rule 201 interacted with low quintile vs. high quintile market-wide returns. We then investigate the effects on returns and market quality of the “alternative uptick rule” interacting with low quintile vs. high quintile numbers of market-wide triggers. Overall, we find that Rule 201 was most effective in the markets regulators may care the most about: low markets, and markets with a large number of triggers.

In Table 7, we study the differential effects of Rule 201 by market-wide returns. We find that while the policy is most effective in down markets (markets that have a 20th percentile

24 or lower return), it is only statistically insigniﬁcantly eﬀective when the market is in the highest quintile, or the middle three. Overall, in the bottom quintile of market return days,

Rule 201 has a positive 54 basis points effect on subsequent returns over the rest of that trading day, and through the next trading day. However, the proportion of seller initiated volume falls by roughly 4-5%, regardless of market-wide returns. This finding is in keeping with the trigger period having meaningful effects on the dynamics of order execution and trading behavior. We see that the proportion of trading that moves off exchange increases by 2.8% in down markets, but there is no substitution except in these down markets.

Regulators may also be concerned about the effects of Rule 201 when the market expe- riences different numbers of simultaneous triggers. In Table 8, we find that triggered stocks see statistically significant positive returns on days with a high number of triggers (80th percentile or above). Effects for the bottom four quintiles of the distribution see insignificantly positive returns. Similarly, the proportion of seller initiated volume decreases, regardless of the number of simultaneous triggers, and trading moves off exchange only when there is a high number of triggers. Our findings for number of triggers mirror those in Table 7, indicating that Rule 201 is most effective in down markets. There is, however, limited impact of the policy on returns except in more extreme market conditions.

Overall, these findings are consistent with the uptick rule only having effects when the market is otherwise down. This is true either when there are low market returns, or when the number of stocks facing very low returns (that are therefore triggered) is higher than normal. Down markets may offer short sellers greater opportunity to engage in shorting behavior. As such, the policy appears to have bite when short sellers do not have the time

25 to otherwise employ short-lived informational advantages. As such, they are more reliant on the trading technology.

5.3 Spillover eﬀects of short selling restrictions

Short selling restrictions may increase the costs of short selling, but they do not remove the impetus to short a stock. Rule 201 focuses on relieving excessive downward pressure, but if short sellers are less able to achieve their positions due to a trigger, this downward price pressure may be shunted oﬀ to other stocks. Given there is no obvious rebound in price for triggered stocks following the trigger period, it is natural to think that short sellers may instead short related stocks to take advantage of whatever transient information advantage they have.

We now explore the extent to which there are spillovers to peer stocks when there is a short selling restriction on a focal stock. In particular, we estimate equation (3) for stocks that are in the same 4-digit SIC industry as the focal stock, and identify the spillovers due to the discontinuous implementation of Rule 201. In Table 9, we ﬁnd that there are indeed negative spillovers to stocks in the same 4 digit SIC code industry, on average. This ﬁnd- ing is robust to the use of quadratic polynomial and to a narrower bandwidth restriction.

Graphical evidence for these eﬀects identiﬁed at the threshold is presented in Figure 9.

When a focal stock is triggered, peer stocks see returns fall by roughly one basis point, which is magniﬁed by the number of peer stocks of the median (15) and average (36) triggered stock. This eﬀect may appear to be large, when compared to results for focal stocks in Table

2, but this may simply reﬂect the fact that shorting a similar stock is a poor proxy for the focal stock. In Table 10, we corroborate these ﬁndings by showing, in Panel A, that seller initiated

26 volume increases for peer stocks of triggered stocks and, in Panel B, that trade is moved back on exchange. Our results are similar using quadratic polynomials or restricting the bandwidth in our tests. This evidence, paired with our results in previous tables, is consistent with short sellers reacting to these restrictions by selling peer stocks, resulting in lower returns for those stocks. These spillovers make the overall eﬀects of the policy theoretically ambiguous.

6 Conclusion

In 2010, the Securities and Exchange Commission proposed and implemented a modiﬁed

Rule 201, the “Alternative Uptick Rule”, to reduce the perceived negative effects of short selling behavior. The primary concern was the role of short sellers in perpetuating and even amplifying daily firesales in individual stocks. As a result, the new regulation would trigger the implementation of an uptick rule on a stock-by-stock basis once a stock exceeded an intraday decline of 10%. This uptick rule, which remains in effect, requires that short sales be completed at or above the previous best bid for the remainder of the day on which the rule is triggered and until the market close on the subsequent day. Market participants generally feared that the policy would harm markets by reducing liquidity and price efficiency and increasing price volatility, overpricing, and retreat by long-sellers (Jain, Jain, and McInish

2012), but the policy’s proponents believed that it was necessary for investor protection.

As SEC Chair Mary Schapiro (2010) stated at the time, “it is a rule that is designed to pre- serve investor confidence . . . recognizing short selling can potentially have both a beneficial and harmful impact on the market.” In this paper, we address this tradeoff empirically, which allows us to evaluate the policy based on its direct and indirect effects and to draw infer-

27 ences about short seller behavior based on their policy-induced absence. Whereas other short selling regulations implement blanket restrictions that affect all or large subsets of exchange- traded stocks at the same time, this policy targeted only securities experiencing significant price declines. The dynamic and threshold-based nature of the policy is well-suited for causal inference regarding the direct effects of short selling restrictions on prices, liquidity, and trading behavior in affected stocks. We introduce panel data structure that breaks each stock- day into six trading intervals, which allows us to precisely measure policy implementations and trading effects on an intraday basis, and we exploit the intraday return implementation- threshold of −10% using a regression discontinuity design. On average, we find that dynamic short selling restrictions significantly reduce seller-initiatied trades, increase daily returns by

31 bps, and moderately improve market quality, measured by eﬀective and quoted spreads.

However, the dynamic, stock-speciﬁc implementation of the policy also introduces a new set of general equilibrium eﬀects that may be of concern. We investigate time-series and stock-level heterogeneity using aggregate market returns and implementation frequency.

These measures provide a basis to understand whether dynamic short selling restrictions are most effective when market-wide returns are poor, or when short seller capital is constrained. For example, the direct return effects exist in down markets, but are statistically insignificantly effective in up markets. These results suggest that the policy is effective in markets that regulators may believe to be of greater concern, but that the policy is relatively ineffective otherwise. Since short seller capital is unlikely to leave the market in response to dynamic, stock-specific policy implementations, another potential general equilibrium effect may be spillovers to peer stocks. We find that short selling restrictions are associated with

28 the selling of peer stocks. These two general equilibrium effects that we analyze question the efficacy of the policy. We find that the policy has negative spillover effects to related stocks.

Given the SEC’s estimated costs of compliance are roughly $1B for Rule 201, and the mixed outcomes of the policy across market conditions, it is unclear the overall value of Rule 201 to markets.

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33 Tables and Figures

Table 1: McCrary tests of date t low returns calculated z seconds after realization of minimum return. For every stock-day in the sample, intraday return at z seconds after the z realization of minimum return with respect to preceding closing price, lrt , is calculated. Density z magnitudes of lrt are calculated as the relative frequency of observations in 1-basis-point bins, giving rise to a total of 400 bins in the overall sample. Density magnitudes are regressed on the magnitudes of bin upper-limits based on quadratic specifications. Specifications are flexible on the two sides of the cutoff R∗ = −10% used to define the treatment indicator variable. TRGz equals z ∗ 1 when lrt is less than or equal to the cutoff R , and equals 0 otherwise. Table reports estimation results given z ∈ {0, 30}. The sample period is 03/01/2011–12/30/2012. Symbols ∗, ∗∗, ∗∗∗ reflect statistical significance given 10%, 5%, and 1% type one error, respectively.

Panel A: McCrary tests z=0 z=30 Dependent Variable: lrjt density lrjt density TRGz 0.101∗∗∗ −0.001 (0.02) (0.02) Adjusted-R2 (%) 78.9 84.7 Observations 400

Table 2: Price recoveries driven by Rule 201 short-sales restrictions. The table presents estimation results for 65-minute returns (R), in basis points, using equation (1), given R∗ = −10%. Estimates account for time (month, day-of-week, and time-of-day) fixed-effects. The last three columns present robustness of estimates to (i) inclusion of stock fixed effects, (ii) specifying a quadratic functional from for running variable, and (iii) use of a tighter (1.5%) bandwidth around the −10% cutoff. Sample period is 03/01/2011–12/30/2012. Standard errors are clustered at the stock level. Symbols ∗, ∗∗, ∗∗∗ reflect statistical significance given 10%, 5%, and 1% type one error, respectively.

Dependent Variable: Rjt TRG 5.10∗∗∗ 4.92∗∗∗ 5.77∗∗ 4.92∗∗ (1.82) (1.87) (2.57) (2.01) Time FE Yes Yes Yes Yes Firm FE No Yes No No Polynomial degree 1 1 2 1 Bandwidth 2% 2% 2% 1.5% R2 (%) 8.7 25.7 8.7 9.3 Observations 34169 23432

34 Table 3: Impacts of short-sales restrictions on seller-initiated trade intensity and choice of trading venue. The table presents estimation results for natural logs of 65-minute proportions of seller-initiated volume (ln(PSL)) and off-exchange volume (ln(OFEX)), using equation (1), given R∗ = −10%. Estimates account for time (month, day-of-week, and time-of-day) fixed-effects. The last three columns present robustness of estimates to (i) inclusion of stock fixed effects, (ii) specifying a quadratic functional from for running variable, and (iii) use of a tighter (1.5%) bandwidth around the −10% cutoff. The last three columns replicate results from the first column with the restriction that observations whose running variable magnitudes fall within a range δ of the cutoff R∗ = 10% are excluded. Sample period is 03/01/2011–12/30/2012. Standard errors are clustered at the stock level. Symbols ∗, ∗∗, ∗∗∗ reflect statistical significance given 10%, 5%, and 1% type one error, respectively.

Panel A: Proportion of seller-initiated volume Dependent Variable: ln(PSL)jt TRG −4.48∗∗∗ −3.69∗∗∗ −4.30∗∗∗ −4.30∗∗∗ (0.32) (0.33) (0.46) (0.36) Time FE Yes Yes Yes Yes Firm FE No Yes No No Polynomial degree 1 1 2 1 Bandwidth 2% 2% 2% 1.5% R2 (%) 4.7 28.0 4.7 4.9 Observations 34169 23432

Panel B: Proportion of oﬀ-exchange volume Dependent Variable: ln(OFEX)jt TRG 1.65∗ 2.86∗∗∗ 2.75∗∗ 2.27∗∗ (0.91) (0.63) (1.34) (1.05) Time FE Yes Yes Yes Yes Firm FE No Yes No No Polynomial degree 1 1 2 1 Bandwidth 2% 2% 2% 1.5% R2 (%) 14.4 69.8 14.5 14.7 Observations 34169 23432

35 Table 4: Price recoveries and impacts on proportions of seller-initiated and off- exchange volume at placebo cutoffs. The table presents estimation results for average 65-minute return (R), in basis points, and the natural logs of 65-minute proportions of seller- initiated volume (ln(PSL)), and the proportion of off-exchange volume (ln(OFEX)) using equation (1), given R∗ ∈ {−6%, −14%}. Coefficients on natural log variables are re-scaled by 100. Estimates account for month, day-of-week, and time-of-day fixed-effects. The sample period is 03/01/2011–12/30/2012. Standard errors are clustered at the stock level. Symbols ∗, ∗∗, ∗∗∗ reflect statistical significance given 10%, 5%, and 1% type one error, respectively.

Panel A: Placebo cutoﬀ −6% Dependent Variable: Rjt ln(PSL)jt ln(OFEX)jt TRG 0.18 0.12 −0.38 (0.58) (0.12) (0.42) R2 (%) 5.1 0.7 13.9 Observations 278655

Panel B: Placebo cutoﬀ −14% Dependent Variable: Rjt ln(PSL)jt ln(OFEX)jt TRG 1.50 −0.92 −0.38 (5.57) (0.76) (1.91) R2 (%) 11.1 1.2 10.8 Observations 6634

Table 5: Impacts of Rule 201 short-sales restrictions on measures of market quality. The table presents estimation results for natural logs of 65-minute mean trade size (ln(TRS)), trading volume (ln(VOL)), trade-weighted relative effective spreads (ln(PESP )), and trade-weighted quoted spreads (ln(QSP )) using equation (1), given R∗ = −10%. Coefficients are re-scaled by a factor of 100. Estimates account for month, day-of-week, and time-of-day fixed-effects. The sample period is 03/01/2011–12/30/2012. Standard errors are clustered at the stock level. Symbols ∗, ∗∗, ∗∗∗ reflect statistical significance given 10%, 5%, and 1% type one error, respectively.

Dependent Variable: ln(TRS)jt ln(VOL)jt ln(PESP )jt ln(QSP )jt TRG 1.17 −1.23 −12.59∗∗∗ −6.84∗∗∗ (0.93) (3.73) (2.73) (1.90) R2 (%) 5.2 2.3 2.1 3.6 Observations 34169

36 Table 6: Long-term effects of short-sale constraints. The table illustrates the dynamic effects of short-sales restrictions on prices, seller-initiated volume, and the choice of trading venue several trading days after constraints are reset. Mean differences between trading outcomes of the treated and controlled stocks are estimated using equation (4). Point estimates and standard errors are presented for the day of and 7 trading days after the trigger date, i.e., k ∈ {1,..., 8}. Estimates account for month, day-of-week, and time-of-day fixed-effects. The sample period is 03/01/2011–12/30/2012. Standard errors are clustered at the stock level. Symbols ∗, ∗∗, ∗∗∗ reflect statistical significance given 10%, 5%, and 1% type one error, respectively.

Panel A: Long-term eﬀects on returns (Rjt) Number of days since trigger date 1 2 3 4 5 6 7 8 TRG 5.10∗∗∗ 3.01∗ −0.19 1.95 −0.96 0.29 −1.30 −1.53 (1.82) (1.76) (1.82) (1.73) (1.68) (1.75) (1.78) (1.60) R2 (%) 8.7 18.4 3.2 5.8 5.4 10.7 13.0 6.9 Observations 34169

Panel B: Long-term eﬀects on proportions of seller-initiated volume (ln(SPLjt)) Number of days since trigger date 1 2 3 4 5 6 7 8 TRG −4.48∗∗∗ −0.04 0.62 0.17 0.28 −0.06 0.21 0.39 (0.32) (0.34) (0.37) (0.37) (0.36) (0.37) (0.38) (0.38) R2 (%) 4.7 2.6 0.6 1.3 0.9 1.3 0.9 1.4 Observations 34169

Panel C: Long-term eﬀects on proportions of oﬀ-exchange volume (ln(OFEXjt)) Number of days since trigger date 1 2 3 4 5 6 7 8 TRG 1.65∗ −1.19 −0.92 1.16 −0.07 −0.94 −1.26 −0.38 (0.91) (1.01) (1.00) (1.02) (1.07) (1.04) (1.06) (1.04) R2 (%) 14.4 10.0 11.1 9.6 10.3 8.0 9.8 9.7 Observations 34169

37 Table 7: Price recoveries and impacts on proportions of seller-initiated and off- exchange volume by overall market condition. The table presents estimation results for average 65-minute return (R), in basis points, and the proportion of off-exchange volume (ln(OFEX)) using equation (2), given R∗ = −10% and Z = MKT . Coefficients on natural log variables are re-scaled by 100. Estimates account for month, day-of-week, and time-of-day fixed-effects. The sample period is 03/01/2011–12/30/2012. Standard errors are clustered at the stock level. Symbols ∗, ∗∗, ∗∗∗ reflect statistical significance given 10%, 5%, and 1% type one error, respectively.

Dependent Variable: Rjt ln(PSL)jt ln(OFEX)jt ∗∗∗ ∗∗∗ ∗∗∗ TRG × MKT` 6.28 −4.29 2.79 (1.90) (0.33) (1.01) ∗∗∗ TRG × MKTm 2.34 −5.05 −0.50 (2.62) (0.45) (1.14) ∗∗∗ TRG × MKTh 4.59 −4.01 −0.05 (3.89) (0.69) (1.79) R2 (%) 9.2 4.8 15.0 Observations 34169

Table 8: Price recoveries and impacts on proportions of seller-initiated and off- exchange volume by the daily number of stocks with short-sale constraints. The table presents estimation results for average 65-minute return (R), in basis points, proportions of seller-initiated volume (ln(PSL)), and the proportion of off-exchange volume (ln(OFEX)) using equation (2), given R∗ = −10% and Z = NTRG. Coefficients on natural log variables are re-scaled by 100. Estimates account for month, day-of-week, and time-of-day fixed-effects. The sample period is 03/01/2011–12/30/2012. Standard errors are clustered at the stock level. Symbols ∗, ∗∗, ∗∗∗ reflect statistical significance given 10%, 5%, and 1% type one error, respectively.

Dependent Variable: Rjt ln(PSL)jt ln(OFEX)jt ∗∗∗ ∗∗∗ ∗∗∗ TRG × NTRGh 5.71 −4.09 2.79 (1.86) (0.32) (0.98) ∗∗∗ TRG × NTRGm 4.10 −5.40 −0.43 2.53 0.46 1.17 ∗∗∗ TRG × NTRG` 1.81 −4.30 −2.20 (6.49) (1.14) (2.61) R2 (%) 8.7 4.8 14.9 Observations 34169

38 Table 9: Industry price spillover effects driven by Rule 201 short-sales restrictions. The table presents estimation results for 65-minute returns (R), in basis points, using equation (3), given R∗ = −10%. Estimates account for time (month, day-of-week, and time-of-day) fixed-effects. The last three columns present robustness of estimates to (i) specifying a quadratic functional from for running variable, and (ii) use of a tighter (1.5%) bandwidth around the −10% cutoff. Sample period is 03/01/2011–12/30/2012. Standard errors are clustered at the stock level. Symbols ∗, ∗∗, ∗∗∗ reflect statistical significance given 10%, 5%, and 1% type one error, respectively.

x∗ x∗ Dependent Variable= Rjt lrjt ∈ (−2%, 2%) lrjt ∈ (−1.5%, 1.5%) TRG −1.21∗∗∗ −1.87∗∗∗ −1.69∗∗∗ (0.23) (0.31) (0.26) Quadratic polynomial No Yes No R2 (%) 9.3 9.3 10.2 Observations 1219378 829655 Median & mean number of peer stocks per day: 15 & 36

Table 10: Industry spillover effects of short-sales restrictions on sheller-initiated trade intensity and choice of trading venue. The table presents estimation results for natural logs of 65-minute proportions of seller-initiated volume (ln(PSL)) and off-exchange volume (ln(OFEX)), using equation (3), given R∗ = −10%. Estimates account for time (month, day-of-week, and time-of-day) fixed-effects. The last three columns present robustness of estimates to (i) inclusion of stock fixed effects, (ii) specifying a quadratic functional from for running variable, and (iii) use of a tighter (1.5%) bandwidth around the −10% cutoff. Sample period is 03/01/2011–12/30/2012. Standard errors are clustered at the stock level. Symbols ∗, ∗∗, ∗∗∗ reflect statistical significance given 10%, 5%, and 1% type one error, respectively.

Panel A: Proportion of seller-initiated volume x∗ x∗ Dependent Variable= ln(PSL)jt lrjt ∈ (−2%, 2%) lrjt ∈ (−1.5%, 1.5%) TRG 0.15∗∗ 0.08 0.17∗∗ (0.07) (0.08) (0.07 ) Quadratic polynomial No Yes No R2 (%) 1.2 1.2 1.2 Observations 1219378 829655

Panel B: Proportion of oﬀ-exchange volume x∗ x∗ Dependent Variable= ln(OFEX)jt lrjt ∈ (−2%, 2%) lrjt ∈ (−1.5%, 1.5%) TRG −2.14∗∗∗ −2.28∗∗∗ −2.23∗∗∗ (0.29) (0.30) (0.29) Quadratic polynomial No Yes No R2 (%) 6.2 6.2 6.2 Observations 1219378 829655

39 Figure 1: Number of stocks subject to Rule 201 restrictions. The ﬁgure presents temporal changes the daily number of stocks, from the entire universe of NYSE-, AMEX-, and NASDAQ-listed common shares in the period 03/01/2011–12/31/2012, that are subject to Rule 201 restrictions. The vertical axis features a break—identiﬁed by the thik dashed line—that excludes magnitudes falling between 550 and 1250.

1400 Black Monday 1300 500 400 300 200 Daily number of triggers 100 0 03/01/2011 07/21/2011 12/12/2011 05/22/2012 10/12/2012 Date

40 Figure 2: Number of stocks subject to Rule 201 restrictions and overall market performance. The plot in the left displays the histogram of the daily number of stocks, from the entire universe of NYSE-, AMEX-, and NASDAQ-listed common shares in the period 03/01/2011– 12/31/2012, subject to rule 201 restrictions (horizontal axis feature a break—identified by the thik dashed line—that excludes magnitudes falling between 550 and 1250). The plot on the right shows the association between natural log of the number of stocks affected by rule 201 and the corresponding overall (equally-weighted) market return. The vertical and horizontal dashed lines represent the first and the forth quintile statistics of the relevant variable in the period 03/01/2011–12/31/2012.

Daily number of triggers: histogram Number of triggers vs. market return 8

.05 Bottom 20% Top 20% .04 6

.03 Top 20% 4 Density .02 2

.01 Black Monday Bottom 20% 0 Natural log of daily number triggers 0 0 100 200 300 400 500 1300 1400 −8 −6 −4 −2 0 2 4 Daily number of triggers Daily market return (%)

41 Figure 3: “Alternative uptick rule”-treated bins as a result of an intraday return of −10% reached at 12:00 p.m. on day t The figure illustrates our panel data setup and which bins are treated as the result of a trigger. In particular, the six 65 minute bins that cover the trading day are 9:30–10:35 a.m., 10:35–11:40 a.m., 11:40 a.m.–12:45 p.m., 12:45–1:50 p.m., 1:50–2:55 p.m., and 2:55–4:00 p.m. As an example, we say the stock reaches an intraday low of −10% at 12:00 p.m., which lies in the third bin. This means that all bins the remainder of the day (four through six), and the six bins the next day are treated by the “alternative uptick rule,” Rule 201. The figure illustrates the stock’s trading bins that are not subject to the uptick rule using white boxes. The box that is split between white and black along the diagonal represents the trading bin in which the stock triggers the uptick rule. The figure illustrates the stock’s trading bins that are subject to the uptick rule using black boxes.

Day t – 1 Day t Day t + 1

Bin: 1

Bin: 2

Bin: 3

Bin: 4

Bin: 5

Bin: 6

Time

Control: Trigger: Treated:

42 Figure 4: McCrary tests of date t low returns calculated z seconds after realization of minimum return. For every stock-day in the sample, intraday return at z seconds after the z realization of minimum return with respect to preceding closing price, lrt , is calculated. Kernel z densities of lrt given probability mass estimates over 1-basis-point bins are estimated on the two sides of the R∗ − 10% threshold. Predicted values and 95% conﬁdence intervals of kernels are used to test the null of “no density break” at the hypothesized threshold.

z = 0 z = 30 .8 .8 .6 .6 .4 .4 Density Density .2 .2 0 0 −12 −11 −10 −9 −8 −12 −11 −10 −9 −8 Intraday low return (%) Intraday low return (%)

43 Figure 5: McCrary tests of date t low returns calculated z seconds after realization of minimum return. For every stock-day in the sample, intraday return at z seconds after the z realization of minimum return with respect to preceding closing price, lrt , is calculated. Density z magnitudes of lrt are calculated as the relative frequency of observations in 1-basis-point bins, giving rise to a total of 400 bins in the overall sample. Density magnitudes are regressed on the magnitudes of bin upper-limits based on quadratic specifications. Specifications are flexible on the two sides of ∗ z the cutoff R = −10% used to define the treatment indicator variable. TRG equals 1 when lrt is less than or equal to the cutoff R∗, and equals 0 otherwise. Sample period is 03/01/2011–12/30/2012. Point estimates and 90% confidence intervals of TRG’s coefficient are plotted against z. .16 .12 .08 .04 0 McCrary test coefficient −.04

−.08 0 1 2 5 10 30 60 300 600 Seconds after intraday low return

44 Figure 6: Average bin return and the corresponding 95% confidence intervals around the −10% intraday low return threshold. The figures illustrate regression discontinuity in returns (left) and proportions of seller-initiated volume (right). 65-minute returns and proportions if seller-initiated volume are averaged over 5-basis-point increments of the running variable, previous bin’s low return. The scatter plots present these averages against the running variable. Linear estimates provide the OLS fits and the corresponding 95% intervals for predicted variable of interest within a 2% bandwidth on each side of the −10% threshold.

Return Seller-initiated volume Oﬀ-exchange volume .5 .51 .36 .5 .4 .34 .49 .3 .48 .2 .32 .47 .1 Average 65−minute return (%) .46 Proportion of off−exchange volume Proportion of seller−initiated volume .3 0 −12 −11 −10 −9 −8 −12 −11 −10 −9 −8 −12 −11 −10 −9 −8 Intradaily low return (%) Intradaily low return (%) Intraday low return (%)

45 Figure 7: Average 65-minute return, proportions of seller-initiated and off-exchange volume and the corresponding 95% confidence intervals around placebo −6% and −14% intraday low return thresholds. The figures illustrate absence of any regression discontinuity in returns (left), proportions of seller-initiated volume (center), and proportions of off-exchange volume (right) at −6% (top) and −14% (bottom) placebo thresholds of the running variable. 65-minute trading outcomes are averaged over 5-basis-point increments of the running variable, previous bin’s low return. The scatter plots present these averages against the running variable. Linear estimates provide the OLS fits and the corresponding 95% intervals for predicted variable of interest within a 2% bandwidth on the two sides of placebo thresholds −6% and −14%.

Panel A: Placebo cutoff R∗ = −6% Return Seller-initiated volume Off-exchange volume .2 .34 .515 .15 .51 .32 .1 .3 .505 .05 Average 65−minute return (%) Proportion of off−exchange volume .5 Proportion of seller−initiated volume 0 .28 −8 −7 −6 −5 −4 −8 −7 −6 −5 −4 −8 −7 −6 −5 −4 Intradaily low return (%) Intradaily low return (%) Intraday low return (%) Panel B: Placebo cutoff R∗ = −14% Return Seller-initiated volume Off-exchange volume .6 .5 .38 .49 .4 .36 .48 .34 .2 .47 Average 65−minute return (%) Average 65−minute return (%) .32 Proportion of off−exchange volume .46 0 −16 −15 −14 −13 −12 −16 −15 −14 −13 −12 −16 −15 −14 −13 −12 Intradaily low return (%) Intradaily low return (%) Intraday low return (%)

46 Figure 8: Long-term effects of short-sale constraints. The figures illustrates the dynamic effects of short-sales restrictions on prices, seller-initiated volume, and the choice of trading venue several trading days after constraints are reset. Mean differences between trading outcomes of the treated and controlled stocks are estimated using equation (4). k Point estimates and 90% confidence intervals for α0 are plotted against the number days after trigger date k ∈ {1,..., 8}. Estimates account for month, day-of-week, and time-of-day fixed-effects. The sample period is 03/01/2011–12/30/2012. Standard errors are clustered at the stock level.

Panel A: Return 9 6 3 0 −3 Average 65−miute return (bps) −6 1 2 3 4 5 6 7 8 k

Panel B: Share of seller-initiated volume 2 0 −2 −4 −6

Log share of seller−initiated volume 1 2 3 4 5 6 7 8 k

Panel C: Share of oﬀ-exchange volume 4 3 2 1 0 −1 −2 −3 −4 Log share of off−exchange volume 1 2 3 4 5 6 7 8 k

47 Figure 9: Average bin return and shares of seller-initiated and off-exchange volume of industry peer stocks around focal stocks’ −10% intraday low return threshold. The figure illiustrates discontinuities in returns and shares of seller-initiated and off-exchange volume of industry peers stocks as short-sales constrains are imposed on a focal stock. Each trading outcome for peer stocks is averaged over 5-basis-point increments of the running variable, the focal stocks’ previous bin’s low return. The scatter plot present these averages against the running variable within a 2% bandwidth on each side of the −10% threshold. Linear estimates provide the OLS fits and the corresponding 95% confidence intervals for predicted values of each trading outcome.

Returns Seller-initiated volume Oﬀ-exchange volume .2 .52 .36 .15 .34 .515 .1 .51 .32 .3 .05 .505 0 Peers’ average 65−minute return (%) .5 Peers’ share of off−exchange volume .28 Peers’ share of seller−initiated volume −12 −11 −10 −9 −8 −12 −11 −10 −9 −8 −12 −11 −10 −9 −8 Intraday low return (%) Intraday low return (%) Intraday low return (%)