Why do Short Selling Bans Increase Adverse Selection? Peter N. Dixon*

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1 Why do Short Selling Bans Increase Adverse Selection? Peter N. Dixon* September, 27 Recent studies document that prohibiting short selling increases adverse selection. This finding is puzzling given the prevailing view of short sellers as informed traders and the lack of theory predicting this outcome. Using a simple rational expectation equilibrium model, I show how a short selling ban may affect adverse selection by decreasing the benefit to becoming informed for investors who do not own the asset. The model predicts an increase in adverse selection during a ban, but only on the sell side of the market. Consistent with this prediction, I find that the observed increase in adverse selection during the 28 US short selling ban is concentrated almost exclusively on the sell side of the market leading sell side effective spreads to increase 5% more than buy side effective spreads. This finding suggests caution when implementing policies that restrict short selling during periods of downward price pressure as they may harm sell side liquidity at the moment it is most needed. JEL Classification: G, G4, G8 Keywords: Adverse Selection, Short Selling, Short Selling Ban, Short Selling Regulation, Liquidity, Transaction Costs, Effective Spread, Price Impact, Realized Spread *Peter Dixon is a Ph.D. candidate at the University of Tennessee-Knoxville. He can be reached at pdixon2@vols.utk.edu or (8) **I would like to extend a special thank you to my advisers, Eric Kelley, Andy Puckett, David Maslar, and Roberto Ragozzino for their invaluable insights and assistance with this paper. I would also like to thank Kyoung-Hun Bae, Chelsea Chen, Kaitlyn Dixon, Ryan Farley, Corbin Fox, Matthew Serfling, Philip Daves, and Tracie Woidtke for their valuable comments and insights.

2 . Introduction During the 28 financial crisis, the US Securities and Exchange Commission imposed a temporary ban on short selling for US listed financial stocks. Boehmer, Jones, and Zhang (23) and Kolasinski, Reed, and Thornock (23) study this event and observe that the ban led to increased levels of adverse selection for those stocks subject to it. Adverse selection in a financial transaction occurs when one party has more precise information about the asset being transacted than does the other. Adverse selection impacts many aspects of finance and financial markets. If unaddressed, adverse selection can cause markets fail (Akerlof (97)). It is a key component of transaction costs and thus liquidity (Kyle (985), Glosten and Milgrom (985)). Adverse selection also plays a role in many firm decisions such as: capital structure (Leland and Pyle (977)), dividend policy (Miller and Rock (985)), contracting (Jullien (2)), management incentives (Ross (977)), investment decisions (Morellec and Schürhoff (2)), banking relationships (Sharpe (99)) and others. The finding that adverse selection increases during a short selling ban is puzzling for a few reasons. First, there is a large body of research characterizing short sellers as informed traders. If this characterization is correct, then removing short sellers would be expected to decrease adverse selection. Second, the increase in adverse selection is not consistent with the theoretical predictions of Diamond and Verrecchia (987). In their model, prohibiting short selling does not affect adverse selection because the prohibition applies to informed and uninformed alike As a result, it leaves unchanged the information of actually observing [a sell]. (p289). See for example: Figlewski (98), Desai et al. (22), Cohen, Diether, and Malloy (27), Boehmer, Jones and Zhang (28), Diether, Lee, & Werner (29), Boehmer, Huszar, and Jordan (2), Karpoff and Lou (2), Christophe, Ferri, and Hsieh (2), Drake, Rees, and Swanson (2), Boehmer and Wu (23), Henry, Kisgen, and Wu (25), Rapach, Ringgenberg, and Zhou (26), Kelley and Tetlock (27) among others.

3 Short selling plays an increasingly prominent role in modern financial markets 2 and is a topic of significant regulatory discussion. 3 Failing to understand why adverse selection increases during a short selling ban leaves financial economists with an incomplete view of the role of short selling in modern financial markets. It also leaves regulators vulnerable to enacting short selling policies which may have unintended and potentially detrimental effects. 4 In this study, I explore how a short selling ban affects adverse selection by first noting that a short selling ban impacts the benefit to becoming informed for investors who do not own the asset because it prevents them from trading on negative information. I model how this effect impacts adverse selection by influencing traders decisions to become informed which subsequently affects the distribution of informed traders in the market. I then test empirically the predictions of the model using data from the 28 short selling ban in the United States. Allowing the fraction of informed investors in the economy to be determined endogenously allows me to consider a perspective not explored by Diamond and Verrecchia (987) who take the faction of informed investors in the economy as exogenous. In the model, an asset takes the equally likely value of either zero or one. A fraction of investors in the economy own the asset and the reminder do not. Any investor can pay a cost to become informed and learn the value of the asset. When short selling is allowed, the benefit to 2 Comerton-Forde, Jones, and Putniņš (26) report in their sample of NYSE and Nasdaq trades that short selling is involved in 39% of all trades. Rapach, Ringgenberg, and Zhou (26) document that average short interest outstanding per stock has been linearly increasing over the past four decades. 3 In the United States, short selling regulations have changed significantly over the past decade or so. Prior to 25, short selling was only allowed on an uptick, this rule was partially removed in 25 and then fully removed in 27. During the financial crisis, short selling was prohibited for a time then reallowed, and more recently the SEC has imposed a modified uptick rule which sets a circuit breaker which restricts short selling to upticks if a stock experiences a severe price decline. Internationally, many nations prohibit short selling, and nations such as China have imposed short selling bans as recently as After the 28 short selling ban, SEC Chairman Christopher Cox remarked to reporters that Knowing what we know now, I believe on balance the commission would not do it again see accessed August, 27 2

4 becoming informed is the same for both investors who do and do not own the asset since both can trade on positive and negative information. Consequently, an equal fraction of both types of investors choose to become informed. However, when a ban is imposed, investors who do not own the asset have less benefit to becoming informed because of they cannot trade on negative information. Consequently, during a ban fewer investors who do not own the asset choose to become informed. In equilibrium, the decline in investors who do not own the asset becoming informed leads to an increase in investors who do own the asset becoming informed. During a short selling ban, only investors who own the asset are allowed to sell, and a larger fraction of these investors are informed relative to when a ban is not in force. Therefore, during a short selling ban there is a greater probability that a sell order comes from an informed trader. Market makers know this and increase transaction costs on the sell side to account for this increased adverse selection risk. Consequently, the model predicts that a short selling ban will be associated with an increase in adverse selection but only on the sell side of the market. I test this prediction using trade and quote data from the 28 short selling ban imposed by the Securities and Exchange Commission (SEC) on US listed financial stocks. Each stock subject to the ban is matched to a control stock following a procedure similar to that used by Boehmer, Jones, and Zhang (23). For each stock and its matched control, I compute the daily average effective spread and decompose it into its adverse selection and realized spread components. Effective spreads, adverse selection, and realized spreads are computed both in aggregate and for the buy and sell sides of the market separately. I employ difference-in-difference-in-difference (DDD) regressions to measure the effect of the ban on buy and sell side adverse selection. I also perform this same analysis for effective spreads and realized spreads. 3

5 The results of the empirical analysis are consistent with the predictions of the model. I find that the increase in adverse selection documented by Boehmer, Jones, and Zhang (23) and Kolasinski, Reed, and Thornock (23) during the short selling ban is concentrated almost exclusively on the sell side of the market. This increase in sell side adverse selection is the single largest component leading to increased effective spreads during the ban and causes effective spreads to increase 5% more for seller initiated trades than for buyer initiated trades during the ban. To further test the implications of the model, I hypothesize that the asymmetry predicted by the model is likely to be more pronounced for stocks with a more competitive environment for information. This hypothesis is derived from the fact that a key assumption in the model is that the market for information is competitive. Consequently, I expect the model s predictions to be more pronounced in situations where its assumptions are more nearly satisfied. To proxy for a stock s information competitiveness I use institutional holdings. Consistent with this hypothesis, I document in cross sectional tests that the abnormal increase in sell side adverse selection during the short selling ban is larger for stocks with higher institutional ownership. I also document asymmetry in the other component of the effective spread the realized spread. The realized spread is the portion of the spread that market makers earn after adverse selection losses are accounted for. It compensates market makers for the non-adverse selection costs of market making such as inventory and processing costs and provides the market maker s profit. When analyzing the effects of the ban on realized spread I find that that realized spreads increase during the ban although not as much as adverse selection costs and that this increase is concentrated on the buy side of the market. 4

6 The increase in buy side realized spread is consistent with the suggestion of Boehmer, Jones, and Zhang (23) that the ban hurts liquidity because short sellers are important liquidity providers and prohibiting them acts as a negative shock to liquidity supply. Less competition to provide liquidity allows the remaining liquidity suppliers to charge higher spreads in the form of higher realized spreads. However, since short sellers only provide liquidity by trading passively at the buyer initiated side of the market, the shock to liquidity supply should be concentrated on the buy side of the market consistent with the effect I document. The analysis in this study has implications for multiple aspects of finance. First, the finding that the short selling ban leads spreads to increase significantly more on the sell side of the market suggests caution when enacting regulations which restrict short selling during periods of downward price pressure. Maintaining sell side liquidity during periods of downward price pressure is a necessary component of maintaining market stability (Huang and Wang (28)). Regulations which restrict short selling during periods of downward price pressure may have the unintended effect of diminishing sell side liquidity at the moment when it is most needed. In addition, this study has implications for how researchers approach the study of the determinates of liquidity. The asymmetry documented in this study suggests that studying the determinates of liquidity using measures which aggregate the buy and sell side may fail to capture important effects and thus provide an incomplete analysis of the topic being examined. Further, the result that the increase in adverse selection costs during the ban is larger than the increase in realized spread costs highlights the need to better understand the impact of short selling on financial markets from an information economics perspective. Prior studies linking short selling to liquidity have tended to concentrate on exploring how short selling affects the supply and 5

7 demand for liquidity. 5 These effects will primarily affect liquidity through the channel of realized spread. While I find evidence consistent with increased realized spread during the ban, these effects appear to have smaller effect on spreads than the informational effects of the ban on adverse selection costs. Lastly, the model s prediction that the inability to short sell will influence the characteristics of the investors who choose to become informed may have implications for monitoring. If fewer outside investors choose to become informed because of an inability to trade on negative information, then the role of outside investors as monitors of the firm is diminished. Fang, Huang, and Karpoff (25) find evidence consistent with this notion. They document that easing short selling restrictions is associated with an increase likelihood of a firm being caught for misdeeds which occurred before the easing took place. 2. Background information a. Adverse selection, price impact, and liquidity In the context of financial markets, adverse selection represents the risk that one party in a transaction knows more about the asset than the other. This information asymmetry causes the market maker to lose money when they trade with informed traders. Losses occur because informed traders only trade when the asset is mispriced. When the fraction of informed traders increases, so too do the adverse selection losses. To remain in business, market makers charge higher spreads to all traders in order to recoup the losses due to trading with informed traders. 5 See for example: Diether, Lee, and Werner (29), Boehmer and Wu (23), Beber and Pagano (23), Boehmer, Jones, and Zhang (23), Kaplan, Moskowitz, and Sensoy (23), and Comerton-Forde, Jones, & Putniņš (26) 6

8 Consequently, adverse selection has a direct impact on liquidity. A large literature has grown studying the relation between adverse selection and liquidity. 6 In models such as Kyle (985) and Glosten and Milgrom (985) the price impact of a trade is direct measure of adverse selection. In these models, the market maker sets the price equal to the expected value of the asset given order flow. Since informed traders only trade when the asset is mispriced, order flow provides a signal about the value of the asset. After observing a trade, the market maker computes the new expected value of the asset given the arrival of the new trade and updates the price. When adverse selection increases, the strength of the signal obtained from order flow is stronger, and the subsequent price change or price impact increases. The connection between adverse selection as measured by price impact and transaction costs can be seen clearly by decomposing the effective spread. The effective spread paid on trade i which occurs at time t is presented in equation (). It is the signed (s i ) proportional distance between the trade price (P i ) and the prevailing midpoint (M t ). It represents the cost that an active trader pays to the market maker to transact. Effective Spread it = 2 s i (P i M t ) M t () By adding and subtracting the prevailing midpoint at some future time t + Δt, as shown in equation (2), the effective spread can be decomposed into two components. The first component is the price impact of the trade and measures the proportional distance that the midpoint moves after the trade. It is an empirical measure of adverse selection costs and numerous empirical 6 See for example: Glosten and Milgrom (985), Kyle (985), Glosten and Harris (988), Stoll (989), Rubin (27), Chung, Elder, and Kim (2), Riordan and Storkenmaier (22), and Fotak, Raman, and Yadav (24) 7

9 studies use the terms price impact and adverse selection interchangeably. 7 The second component is the realized spread. It is the portion of the spread that the market maker realizes after adverse selection costs are accounted for. The realized spread compensates the market maker for all nonadverse selection related costs as well as provides the market maker profit. Effective Spread i = 2 s i (P i M t + M t+δt M t+δt ) M t Effective Spread i = 2 s i (M t+δt M t ) M t + 2 s i (P i M t+δt ) M t (2) Effective Spread i = Adverse Selection it + Realized Spread it Decomposing effective spreads into adverse selection and realized spread components provides a method for testing the economic channels through which an event may impact overall liquidity. Events that increase adverse selection will be associated with an increase in the effective spread through the channel of price impact. Events that affect non-adverse selection related market maker costs, as well as competition among market makers will affect spreads through the channel of realized spread. b. Diamond and Verrecchia (987) The most relevant theoretical work on short selling and adverse selection is Diamond and Verrecchia (987) (hereafter DV). DV study the effect of a short selling ban on the bid-ask spread in the context of a Glosten and Milgrom (985) model. In their model, the bid and ask prices are 7 See for example: Sandås (2), Barclay and Hendershott (24), and Hendershott, Jones, and Menkveld (2) among others 8

10 set equal to the expected value of the asset given the history of trades. When a trade arrives, the market maker updates prices in proportion to the expected amount of information contained in the trade. As adverse selection increases i.e. the probability that the market maker faces an informed trader increases the price impact of a given trade will also increase. As the market maker observes more trades, he becomes more confident about the true value of the asset. This confidence causes spreads narrow and prices to converge to fundamentals. DV study the effect of two types of short selling restrictions on the bid-ask spread. The first is a short selling ban. The second is a restriction on the use of the proceeds from a short selling transaction. As this study and the two cited at the beginning of this study focus on the 28 short selling ban, I will focus my discussion exclusively on the short selling ban case. In their model, a short selling ban affects the bid-ask spread by converting some trading rounds that would have experienced a sell into rounds where no trade occurs. A no trade event is less informative to the market maker than a trade. Consequently, the expected speed at which spreads narrow and prices converge to fundamentals slows. Although it takes longer for spreads to narrow and prices to converge a short selling ban does not affect the adverse selection faced by the market maker. This is because the ban prohibits informed and uninformed trades in the same proportion. Consequently, the information contained in given trade and thus adverse selection is unaffected (p.289). Converting this effect into an empirical prediction suggests that price impact measures of adverse selection may actually go down during a ban. Prices converge to fundamentals in the model due to the accumulated price impact of all the trades which have arrived. As fewer trades 9

11 arrive, the time it takes in expectation for the price to converge slows down. Implying that the price is expected to move less over the same time period relative to when a ban is in place. Empirical measures of price impact keep the time period constant. Consequently, the slowing of the market due to the ban combined with no change in the information content of trades should cause the price to move less in expectation over the same period of time during a ban. Consequently, a careful analysis of DV indicates that their model actually predicts that price impact measures of adverse selection should decrease during a short selling ban. This prediction is contrary to the empirical observation that price impact increases during a short selling ban. 3. The Model a. Setup The intuition central to this simple model is that a short selling ban decreases the benefit to becoming informed for investors who do not own the asset. This decrease occurs because if short selling is prohibited then an investor that does not own the asset runs the risk that upon becoming informed, they may not be able to trade on their information, if the information is negative. This restriction does not apply to endowed investors who are free to sell their asset. To explore how this dynamic affects adverse selection I model an economy with one asset which has a value of either zero or one v ε[,] with each value being equally likely. There exists a continuum of traders and perfectly competitive market makers. All trade occurs in one round, and then the asset is liquidated. Some fraction γ of these traders own the asset. The traders can pay a cost c to learn the value of the asset prior to trading. The fraction of investors who choose to become informed is endogenous and the fraction λ of investors which own the asset choose to

12 become informed, and the fraction λ 2 of the investors which own the asset choose to become informed. Market makers are perfectly competitive and thus set the bid and the ask prices such that they are equal to the expected value of the asset given that a buy or sell order arrives. Uninformed traders will buy or sell with equal probability. Informed traders always buy if the asset value is equal to one and sell (or short) if the asset value is equal to zero. Market makers cannot distinguish which traders are informed and which are not, but they do know the distribution of traders in the economy. Traders and market makers are risk neutral and transact one share. b. The Baseline Model Where Short Selling is Allowed In the absence of a short selling ban traders can buy and sell regardless of whether they own the asset. The initial ask price is equal to the expected value of the asset given that the order to arrive is a buy order. There are four types of trader which may transact: informed investors who own the asset, uninformed investors who own the asset, informed investors who do not own the asset, and uninformed investors who do not own the asset. The probability that a given market maker transacts with these four categories of investors is presented below as π, π 2, π 3, and π 4. Type of Seller Probability of Event Informed owning the asset π = γλ Uninformed owning the asset π 2 = γ( λ ) Informed not owning the asset π 3 = ( γ)λ 2 Uninformed not owning the asset π 4 = ( γ)( λ 2 )

13 Prior to the start of trading, the expected value of the asset is simply.5. The market maker knows that uninformed traders will buy and sell randomly, and their trades convey no information. The informed traders will only buy if the value of the asset is equal to one. Consequently, the ask price will be equal to the expected value of the asset given a buy arrives as shown in equation (3). Ask = E[v uninformed Buy] P(uninformed trader) + E[v informed Buy] P(informed trader) = 2 (π 2 + π 4 ) + (π + π 3 ) (3) = 2 [γ( λ ) + ( γ)( λ 2 )] + [γλ + ( γ)λ 2 ] = 2 [γ( + λ ) + ( γ)( + λ 2 )] The initial bid price can be likewise determined as shown in equation (4). Bid = E[v uninformed Sell] P(uninformed trader) + E[v informed Sell] P(informed trader) = 2 (π 2 + π 4 ) + (π + π 3 ) (4) = 2 [γ( λ ) + ( γ)( λ 2 )] If an investor chooses not to become informed, then the investor will on average earn a negative profit equal to one half the bid ask spread. A natural question to ask is why would the uninformed traders transact in the first place. This question is similar in spirit to the question that fund managers 2

14 must ask when deciding whether or not to be a passively or an actively managed fund. A passive fund that perfectly tracks a given index will earn a benchmark adjusted return equal to zero minus transaction costs. If there is a market for passively managed funds then managers of such funds will still find it beneficial to remain in business, even though their benchmark adjusted returns are somewhat negative. A fund may seek to acquire information and improve their stock selection, but doing so requires that the fund spend resources gathering information. If markets are competitive then managers should be indifferent between the two choices. Consequently, in this model, I assume that all traders who choose to participate earn an outside benefit equal to the half the bidask spread which makes them indifferent between trading and not trading. Prior to making the choice to become informed, traders know that there is a ½ probability that the asset will be worth one and a one and a ½ probability that the asset will be worth zero. If the asset is worth zero the traders can either sell the asset if they are endowed with it, or they can short sell the asset if they are not endowed with the asset. The benefit to becoming informed will be equal to the probability that the asset is worth one multiplied by the liquidation value of the asset less the cost of purchasing the asset at the ask price. This value is added to the benefit of being informed if the asset is worth zero. Which is the price received from selling the asset at the bid minus the liquidation value of the asset which is equal to zero multiplied by the probability that the asset is worth. The benefit to becoming informed is displayed below in equation (5). 3

15 Benefit to being informed = 2 [ Ask] + [Bid ] 2 = 2 [ 2 [γ( + λ ) + ( γ)( + λ 2 )]] + 2 [ 2 [γ( λ ) + ( γ)( λ 2 )]] (5) = 2 [γ( λ ) + ( γ)( λ 2 )] To solve for the optimal values of λ and λ 2 given that we have one equation and two unknowns, we note that in the absence of a short selling ban there is no difference in the value of becoming informed between those traders endowed with the asset and those not endowed with the asset. Consequently, I assert that in such a case the same fraction of investors who do and do not own the asset choose to become informed i.e. λ = λ 2 λ. In this case, the benefit to becoming informed simplifies to the expression in equation (6). Benefit to being informed = [γ( λ) + ( γ)( λ)] 2 = λ 2 (6) Markets are competitive, thus the benefit to becoming informed must equal the cost of becoming informed making investors indifferent between being informed and not informed, thus λ is a function of the cost of becoming informed as shown in equation (7). cost of becoming informed = Benefit to being informed c = λ 2 λ = 2c (7) 4

16 This expression for the optimal fraction of investors to become informed can be inserted into the bid and ask prices from equations () and (2) to find the equilibrium ask and bid prices, and the bid-ask spread in effect in a trading environment where short selling is allowed as presented in equation (8). Ask = c Bid = c (8) From equation (8) the bid and ask prices are a function of the cost of becoming informed. This is the case because the cost of becoming informed determines what fraction of investors choose to become informed. If the cost of becoming informed were then all investors will become informed and a buy or sell order would reveal perfectly what the true value of the asset it and consequently the bid and ask prices will be set to and. c. Short Selling Ban A short selling ban will change the dynamics of trade by prohibiting those sellers who do not own the asset from transacting at the bid. Consequently, the market makers know that if a sell arrives then it must come from an investor that already owns the asset. That is only the events corresponding to probabilities π (informed investor endowed with the asset) and π 2 (uninformed investor endowed with the asset) are possible. In this setting, the probability that a market maker faces an informed trader at the bid changes from π + π 3 in the case where short selling is allowed to π π +π 2, and the probability that a market maker faces an uninformed trader at the bid changes from π 2 + π 4 in the case where short selling is allowed to price during a short selling ban accordingly as presented in equation (9). π 2 π +π 2. Market makers update the bid 5

17 Bid ban = E[v uninformed Sell] P(uninformed trader) + E[v informed Sell] P(informed trader) π 2 π = + 2 π + π 2 π + π 2 (9) = γ( λ ) 2 γ( λ ) + γλ = λ 2 Since there are no restrictions on buying during a short selling ban, the probability that a market maker faces an informed trader at the ask does not change. The bid and ask prices in force during a short selling ban are presented in equation (). Ask ban = 2 [γ( + λ ) + ( γ)( + λ 2 )] Bid ban = λ 2 () The effect of a short selling ban on the bid-ask spread is determined by the parameters λ and λ 2. During a short selling ban the inability to trade on negative information diminishes the value to becoming informed for investors who do not own the asset. Equations () and (2) present the value of becoming informed for both the investors who own the asset and those investors who do not own the asset when investors cannot short sell. 6

18 Benefit to being informed endowed,ban = 2 [ Ask] + [Bid ] 2 = 2 [ 2 [γ( + λ ) + ( γ)( + λ 2 )]] + 2 [ λ 2 ] () = 4 [γ( + λ ) + ( γ)( λ 2 )] Benefit to being informed not endowed,ban = [ Ask] 2 = 2 [ 2 [γ( + λ ) + ( γ)( + λ 2 )]] (2) = 4 [γ( λ ) + ( γ)( λ 2 )] It is clear to see from equations () and (2) that the value to becoming informed is greater for those investors endowed with the asset since both types of investor receive the same profit if the value turns out to be equal to one, but only the endowed investors profit when the value of the asset is equal to zero. What is left is to determine the new equilibrium fractions of investors that become informed. Since the value of becoming informed is different for those endowed with the asset and those investors not endowed with the asset it can no longer be imposed that λ = λ 2. However, markets are still competitive, and thus the value of becoming informed must still be equal to the cost of becoming informed for both the endowed and not endowed investors. This gives rise to two equations and two unknowns presented in equations (3) and (4). 7

19 c = Benifit to being informed endowed,ban c = 4 [γ( + λ ) + ( γ)( λ 2 )] (3) c = Benifit to being informed not endowed,ban c = 4 [γ( λ ) + ( γ)( λ 2 )] (4) The solution to the above system of equations is presented in equation (5). λ =, λ 2 = γ + 4c γ (5) In the case where investors were allowed to short sell the fraction of investors who do and do not own the asset that choose to become informed is equal to 2c. However, as equation (5) shows, when short selling is prohibited the fraction of investors that do not own the asset who choose to become informed decreases from 2c to γ+4c 8. In equilibrium, as fewer investors γ who do not own the asset become informed they are replaced by investors who do own the asset and the fraction of investors who own the asset who choose to become informed increases from λ = 2c when everyone can short sell to a value of λ =. It is important to note that this solution may not be an equilibrium for some values of γ and c. The fraction of informed investors cannot be less than zero, and thus only when c < γ will the solution provided in equation (5) yield a feasible outcome in which λ 2. In the case that c > 4 8 Proof: The fraction of investors who do not own the asset that choose to become informed decreases if 2c > γ+4c γ+4c. The term on the RHS can be rewritten = + 4c. By subtracting one from both sides the question γ γ γ can be restated as 2c > 4c 2. Divide both sides by 2c to restate the question <. Moving the γ to γ the other side of the inequality and subtracting from both sides makes the truth of the inequality obvious γ <. γ 8

20 γ, the equilibrium is found by imposing λ 4 2 =, and then solving from equation (3) the value of λ that makes the benefit to becoming informed for those investors who own the asset equal to the cost, and then verifying with the new solution of λ that the investors not endowed with the asset are better off not becoming informed because the benefit to becoming informed is less than the cost. This turns out to be true so long as c > γ, which is the range that this equilibrium is designed to describe. In the case where c > γ the equilibrium solution is given as in equation (6). 4 4 λ = 2 γ + ( 2c), λ 2 = (6) Like the previous equilibrium the fraction of investors who do not own the asset who choose to become informed falls. In this case the decline is from a value of 2c in the case where short selling is allowed to a value of. It is also clear that the fraction of investors who own the asset that choose to become informed increases since 2 γ+ >. Thus, in both solutions the outcome is the same. The ban leads fewer investors who do not own the the asset to choose to become informed which causes more investors who do own the asset to choose to become informed. Since both solutions yield the same intuition, for simplicity, I will continue using only the equilibrium solutions presented in equation (5) to determine the equilibrium bid and ask prices in force during a short selling ban. To find the equilibrium bid and ask prices in force during the short selling ban, the solutions for λ and λ 2 from equations (5) is inserted into the bid and ask prices prevailing during the short selling ban from equation (). The solution is presented in equation (7). 9

21 Ask ban = 2c Bid ban = (7) It is clear in equation (7) that the price impact of a sell is more severe during a short selling ban than is the price impact of a sell when short selling is allowed. When short selling is allowed, the arrival of a sell changed the expected value of the asset from a value of ½ to a value of c. Thus, the price impact is equal to c. When the ban is in place, the market maker knows that all of 2 the investors who own the asset are informed and they are the only investors allowed to sell. Consequently, observing a sell order during a short selling ban reveals to the investor that the value of the asset is equal to. Thus, the price impact of a sell during a short selling ban is equal to /2. In sum, the model predicts that a short selling ban will have an asymmetric effect on adverse selection and will cause adverse selection to increase on the sell side of the market. This asymmetry comes because a short selling ban decreases benefit to becoming informed for investors who do not own the asset leading fewer of them to choose to become informed. This leads more investors who do own the asset to choose to become informed. Since only investors who own the asset are allowed to sell during a short selling ban, and more of these investors are informed relative to when short selling is not prohibited, adverse selection increases on the sell side of the market. 2

22 4. Empirical Analysis a. Sample Data for this study comes primarily from the NYSE Daily Trade and Quote (DTAQ) database for the moths of August October 28. Data from the DTAQ database offers an improvement over data from the NYSE Monthly Trade and Quote (MTAQ) database employed in prior studies. 9 As demonstrated in Holden and Jacobsen (24) these differences can have a significant effect on the results obtained from empirical analysis. Specifically, Holden and Jacobsen (24) document that compared to the more accurate DTAQ results, computations using MTAQ data can produce effective spreads that are 5% larger than the effective spreads computed using DTAQ. Consequently, where our analysis overlaps with that of Boehmer, Jones, and Zhang (23) the pattern of results is similar, but the magnitudes presented here are smaller. Other data sources include OptionMetrics from which I obtain data about the options status of the firm, and CRSP where I obtain stock specific data such as listing exchange, shares outstanding, and stock return data. The total number of stocks subject to the ban, either initially or added later is 93. Tickers that do not match to a permno in CRSP are removed as are tickers that ambiguously match to multiple permnos leaving 9 tickers that pass the initial filter. 23 Tickers that are not common stocks (CRSP share codes and ) are removed leaving 787 tickers that pass the second filter. Of these 787 tickers 33 are not listed on NYSE or NASDAQ and are removed leaving 754. Stocks must 9 The key differences between the MTAQ database and the DTAQ database are that the trade and quotes in the DTAQ database are time stamped at the millisecond whereas the MTAQ database is timestamped at the second. Also, the DTAQ database provides the national best bid and offer prices (NBBO) prices time stamped to the millisecond, whereas the MTAQ database requires the user to estimate the NBBO prices from the quotes database which are time stamped to the second. 2

23 also have complete CRSP volume and returns data for December 27-July 28 as well as DTAQ data from August 28 October 28 leaving a total of 7 usable tickers from the published list of banned stocks from the SEC. Of these 653 are on the original list published by the SEC on September 9, 28, and the remaining 58 were added to the ban later. Each banned stock is identified as either a large, small, or microcap based on its market cap as of December 3, 27. Following Fama and French (28), large stocks are defined as those stocks that are in the largest 5 NYSE size deciles as of December 3, 27, small stocks are defined as those stocks that are in NYSE size deciles 3-5, and microcap stocks are those stocks that are in the smallest two NYSE deciles. This methodology results in 39 large stocks, 8 small stocks, and 454 microcap stocks. The analysis focuses only on the large and small stocks for a variety of reasons. First, measuring adverse selection and spreads on each side of the market requires accurately signing order flow. Microcap stocks trade infrequently, and the time between quote revisions can be significant. Consequently, signing order flow using algorithms which match trades to prior quotes such as the Lee and Ready (99) algorithm for microcap stocks is likely to be highly noisy. Second, as Boehmer, Jones, and Zhang (23) document, smaller stocks are lightly shorted and thus the effects of the short selling ban on smaller stocks is muted. Lastly, trading in microcap stocks accounts for only a tiny fraction of total trading volume, and a study whose results are strongly influenced by microcap stocks may lack generalizability. To estimate the effect of the short selling ban on adverse selection and spreads, each banned stock is matched with replacement to a control stock based on market cap (calculated from CRSP) as of December 3, 27, dollar trading volume in the first six months of 28 (calculated from CRSP), listing exchange (from CRSP), and options status (from Options Metrics). This 22

24 matching procedure is similar to that employed by Boehmer, Jones, and Zhang (23) and Brogaard, Hendershott, and Riordan (27). To match stocks subject to the ban to a control stock, I employ a distance measure like the one employed by Boehmer, Jones, and Zhang (23) and Brogaard, Hendershott, and Riordan (27). As shown in equation (8) where i indexes the banned stock, and j indexes the potential match, the distance between a banned stock and a potential control stock is the sum of the proportional distance between the banned stock and the control stock based on market cap and dollar volume. Distance i,j = Mktcp i Mktcp j Mktcp i + Dvol i Dvol j Dvol i (8) For a stock to be considered as a match it must have complete CRSP volume and return data from December 27-July 28, as well as TAQ data for September and October 28. The matched stock for a given banned stock is the stock that has the smallest distance measure among those stocks with the same listing exchange and options status as the banned stock. Table presents descriptive statistics for the banned stocks and the control stocks used in this study. <Insert Table Here: Descriptive Statistics> b. Computation of Adverse Selection and Spread Measures The primary empirical measures used in this study are the effective spread and its constituent components realized spread and adverse selection. These measures are computed from DTAQ data. To be included in the sample of trades I require that a trade not have a non-normal trade code. Also, Reg NMS requires that brokers route orders to the best quote price, and so trades outside the national best bid and offer (NBBO) prices should not occur and may be indicative of Non-normal trades include those trades in the field tr_scond which have a value of J, L, N, O, P, T, Z, U, and Q. 23

25 errors in the data. Consequently, I remove trades where the posted trade price is more than one cent outside of the NBBO prices in the millisecond prior to the trade. To eliminate trades associated with erroneous quotes I remove trades corresponding to quoted spreads (computed from the NBBO file) that are greater than 3% in the millisecond prior to the trade. The computation of adverse selection and realized spread require the use of a midpoint at some point Δt after the initial midpoint which occurs at time t. I eliminate trades in my computation of realized spread and adverse selection that are associated with quoted spreads at time t + Δt that are greater than 3%. Lastly, trades associated with locked or crossed quotes are eliminated. These filters eliminate approximately 4% of trades from the sample. For each remaining trade in the DTAQ database the effective spread, realized spread, and adverse selection measures are computed as displayed in equations (9) through (2). In these equations i indexes a given trade, s i indexes the sign of the given trade as assigned by the Lee and Ready (99) algorithm ( indicates a buyer initiated trade and - indicates a seller initiated trade) using the prevailing NBBO midpoint in the millisecond prior to the trade provided by DTAQ as the reference midpoint in the algorithm. P i,t is equal to the transaction price for trade i which occurred at time t. M t is the prevailing NBBO midpoint in the millisecond prior to trade i. M t+δt is the prevailing NBBO midpoint at some time Δt after the arrival of the given trade. Adverse selection and realized spread are computed with Δt ranging from one second to five minutes depending on the specification. Effective Spread i = 2 s i(p i,t M t ) M t (9) 24

26 Realized Spread i,δt = 2 s i(p i,t M t+δt ) M t (2) Adverse Selection i,δt = 2 s i(m t+δt M t ) M t (2) Equally weighted daily averages for each of the three metrics are computed and these metrics are the primary dependent variables in the empirical analysis. If the empirical specification is analyzing the total effect of the ban on adverse selection or spreads, then the dependent variable will be the equally weighted daily average across all trades irrespective of sign. In this case there will be one observation stock per day. If the specification studies the differential effect of the ban on adverse selection or spreads for buy or sell sides of the market, then the dependent variable will be the equally weighted daily average across all buy or sell trades producing two observations per banned stock per day. c. Empirical Results The key empirical methodology used to determine the effects of the ban on adverse selection and spreads is difference-in-difference (DD) regressions for the unsigned analysis, and differencein-difference-in-difference (DDD) regressions for the signed analysis. In these regressions, the dependent variable is the difference between a banned stock and its matched control for the variable of interest. Doing this effectively places the first difference in the DD, or DDD analysis on the left-hand side of the regression. i. Effective Spread I first turn attention to the effect of the short selling ban on effective spreads. Figure plots the time series of effective spreads for large and small stocks around the 28 short selling ban. 25

27 In this figure, each stock subject to the initial ban is paired with a control stock not subject to the ban as discussed in section 3 (a). For each stock pair, each day the difference in equally weighted daily average effective spread between the banned stock and its matched control stock is computed. These differences are then averaged across stocks in the same size group each day to produce a single time series representing the average difference in effective spread between the banned stocks and their matched controls. Because some stocks were added after the initial imposition of the ban only data from those stocks on the initial list are included in the graphs. The series is computed from August, 28-October 3, 28. Panels A, B, and C of figures and 2 show the average difference in effective spread between banned stocks and their matched counterparts for large stocks while panels D, E, and F present the same analysis for small stocks. Insert Figure Here: Effective Spread Large Stocks Panel A and D present the time series for the difference in aggregate effective spreads for banned stocks and their matched controls for large and small stocks respectively. The pattern revealed in panels A and D is similar to what is observed in Boehmer, Jones, and Zhang (23), however due to using DTAQ instead of MTAQ data the magnitudes of the effect of the ban are smaller. Panels A and D confirm that for large and small stocks, the short selling ban appears to be associated with significant increases in effective spread for those stocks subject to the ban relative to their matched counterparts, and that after the ban is lifted the increased spreads decline. Panels B and E of figure document that the increase in transaction costs during the ban appears to be asymmetric. In panels B and E, effective spreads are computed exactly as before, but with the sample of trades separated into buyer and seller initiated trades according to the Lee and Ready (99) algorithm yielding two series. Prior to the ban, and after the lifting of the ban 26

28 there does not appear to be any discernible difference between buyer and seller initiated effective spreads. However, during the short selling ban the difference in effective spreads for banned and control stocks appears to be larger for seller initiated trades than for buyer initiated trades. The asymmetry is more readily apparent in panels C and F of Figure. This figure computes the difference between the buyer and seller initiated series presented in panels B and E of the same figure. In essence, panels C and F present an informal difference-in-difference-in-difference analysis of the short selling ban on seller initiated trades relative to buyer initiated trades. These graphs indicate that the effect of the ban on effective spreads is more severe for seller initiated trades, and that this asymmetry disappears as soon as the ban is lifted. The figures presented above suggest that the short selling ban led to increased effective spreads, and that the increase in effective spread is larger on the sell side of the market. To formally test this hypothesis, I use DD and DDD regressions. To determine the overall effect of the short selling ban on effective spreads I estimate the DD regression presented in equation (22). In this specification, the dependent variable is the difference in equally weighted daily average effective spread between a banned stock and its matched control stock for a given day. The independent variables include an indicator variable for whether or not the short selling ban is in effect on a given day and a host of control variables. The coefficient identifying the effect of the short selling ban on realized spreads from equation (22) is γ. ESP B i,t ESP C i,t = γ + γ Ban t + ΓX it + ν i + ε it (22) Control variables include the difference between banned and control stocks on dimensions of value weighted average price, market cap, dollar volume, number of trades, price volatility, and daily return, as well as the return on the CRSP value weighted index and level of the value weighted average price, market cap, dollar volume, number of trades, daily return, and price volatility for the banned stock. 27

29 ESP B i,t,s C ESP i,t,s = β + β Ban t + β 2 SI s + β 3 Ban t SI s + ΓX it + ν i + ε it (23) Equation (23) presents the model used to identify the differential effect of the short selling ban on seller initiated effective spread. The dependent variable in these specifications is difference in equally weighted daily average effective spreads between a banned stock and its matched control for buyer and seller initiated sides of the market. In the regression corresponding to equation (23), each stock pair will have two observations each day, one for the difference in buyer initiated effective spread between the banned stock and its matched control, and the other for the difference in seller initiated effective spread between the banned stock and its matched control. The independent variables include an indicator for whether the ban is in effect for stock pair i on a given day, an indicator for whether the given observation is from the buyer or seller initiated side of the market, and an interaction term between the ban indicator and the seller initiated indicator. Lastly, I include the same control variables as are included in equation (22). For both specifications, I include stock pair fixed effects, and I cluster standard errors at the date level. The specification in equation (23) identifies the effect of the short selling ban on buyer and seller initiated trades separately. In this specification, the coefficient β indicates the effect of the short selling ban on buyer initiated trades, and the sum of coefficients β + β 3 indicates the effect of the short selling ban on seller initiated trades. Table 2 presents the results from these regressions. Insert Table 2 here: Effective spread results These results indicate that among large stocks the total effect (γ ) of the ban on effective spreads amounts to a statistically significant increase in the effective spread of 4.8 basis points. Small stocks likewise experience a statistically significant increase in average effective spreads of 2.7 basis points during the ban. For perspective, the average effective spread outside of the short 28