Why Do Short Selling Bans Increase Adverse Selection and Decrease Price Efficiency?

Why Do Short Selling Bans Increase Adverse Selection and Decrease Price Efficiency? Dixon, Peter N 2021-02-15 00:00:00 Abstract When short selling is costly, owners of an asset have greater incentive to become informed than nonowners because trading on negative information is easier for them. Thus, information acquisition concentrates among investors owning the asset. A short selling ban restricts selling to only the relatively more informed investors who own the asset, increasing adverse selection but only on the sell side of the market. Price efficiency declines due to less overall information acquisition because a ban magnifies the disincentive to gather information for investors not owning the asset. Empirical evidence from the 2008 U.S. short selling ban is consistent with these theoretical predictions. This study explores the link between short selling, adverse selection, and price efficiency. Adverse selection occurs when one party has more precise information about an asset’s value than the other. It is a key determinate of liquidity and affects many other aspects of finance.1 Prior empirical research links short selling and adverse selection by documenting that increased adverse selection appears to be a key driver of diminished liquidity during short selling bans (Boehmer, Jones, and Zhang 2013; Marsh and Payne 2012; Kolasinski, Reed, and Thornock 2013). This finding is not intuitive. Short sellers are generally viewed as informed traders.2 Consequently, a short selling ban would be expected to decrease adverse selection by removing informed traders from the market. And, specifically, it should do so on the sell side of the market, where informed short sellers transact.3 The link between short selling and price efficiency is better understood. Going back to Miller (1977) and Diamond and Verrecchia (1987) (hereafter DV), it has been understood that restricting short selling harms price efficiency by preventing certain information from becoming incorporated into prices. Empirical work has borne out this relation consistently.4 What is not understood is the seemingly counterintuitive result that a ban both increases adverse selection—indicating that trades are more informative—at the same time it decreases price efficiency—indicating that prices are less informative. I explore the link between a short selling ban, adverse selection, and price efficiency theoretically by modifying the standard setup of DV to allow for endogenous information acquisition. The model shows how a short selling ban can simultaneously increase adverse selection and decrease price efficiency. Additionally, and somewhat counter to initial expectations, the model predicts that a ban will increase adverse selection only on the sell side of the market. The intuition for these results is straightforward. Adverse selection on one side of the market (say on sell orders) increases when the ratio of informed investors to liquidity traders in the pool of investors trading on that side increases. When short selling is allowed but costly, information acquisition concentrates among investors owning the asset. This occurs because the expected cost of transacting on information is less for them since they do not have to pay a short selling cost to trade on negative information. Consequently, the mass of informed investors in the market has relatively more investors who own the asset than who do not. Imposing a short selling ban prevents both informed and liquidity investors who do not own the asset from selling; this action lowers both the numerator and the denominator of the ratio of informed to liquidity traders on the sell side of the market. However, since the population of informed traders is skewed toward investors who own the asset, while the population of liquidity traders is not, the drop in the numerator of the ratio of informed to liquidity traders is smaller than the drop in the denominator, thereby increasing the overall ratio of informed to uninformed traders on the sell side of the market. In contrast adverse selection on the buy side of the market decreases because a short selling ban only reduces the mass of informed buyers—lowering the ratio of informed to liquidity buyers. This occurs because sophisticated investors who do not own the stock have even less incentive to become informed during a ban due to their inability to trade on negative information and so even fewer of them do so. At the same time, a ban does not reduce the mass of liquidity buyers. Thus, a ban increases adverse selection on the sell side and reduces it on the buy side. Overall, price efficiency declines because the drop in the informativeness of buy market orders along with the convergence of some trades that would have arrived as sell orders in the absence of a ban to less informative no trade events more than offsets the increase in the informativeness of sell market orders. Empirical analysis from the 2008 short selling ban in the United States (hereafter the ban or the short selling ban) provides results consistent with the predictions of the model. The ban decreases price efficiency. It also increases adverse selection, but only on the sell side of the market. This asymmetry is economically meaningful as I show that increased sell side adverse selection is the dominate factor contributing to increased transaction costs during the ban; that is, the ban disproportionately harms sell side liquidity leading transaction costs for sellers to increase 50% more than for buyers. An alternative explanation for an increase in sell side adverse selection is found in DVs analysis of a short selling restriction. While their model predicts that a prohibition will be associated with no change in sell side adverse selection—because it removes both informed and uninformed traders alike, leaving unchanged the overall fraction of informed traders in the market—a restriction in their model produces an increase in sell side adverse selection. A restriction differs from a prohibition in their setting in that it only prevents traders from accessing the proceeds of a short sell, it does not outright prohibit short selling. Consequently, liquidity traders who would have shorted to raise funds cease doing so while informed traders continue to short sell. Consequently, DV predicts that a restriction increases sell side adverse selection because it only removes uninformed short sellers on the sell side of the market. However, in a DV restriction, the removal of only uninformed sellers increases the information content of sell trades leading to an overall increase in price efficiency. Thus, a DV restriction can explain an increase in sell side adverse selection, but not a simultaneous decline in price efficiency. Further analysis of DV’s model reveals that it predicts that the ban will have a stronger effect on sell side adverse selection for stocks for which investors may have been able to circumvent the ban, perhaps by using options, making the ban more closely resemble a restriction. Counter to the predictions of DV, I find that the ban had a stronger impact on stocks without listed options. Consequently, the main empirical results in this paper are unlikely to be explained by DV. To further explore the implications of the model I test the model’s prediction that the increase in sell side adverse selection will be greater for stocks with a higher concentration of institutional investors. I test this hypothesis using a procedure similar to Nagel (2005) and find that stocks with higher residual institutional ownership experience greater abnormal sell side adverse selection during the ban. This study contributes to multiple areas of finance. First, it shows how a short selling ban simultaneously affects adverse selection and price efficiency through its impact on which traders choose to become informed and which traders are allowed to trade. It also highlights the magnitude and asymmetric nature of the link between short selling and adverse selection and provides a potential explanation for why that link and asymmetry may exist. The analysis also helps to fill a gap in the literature linking short selling and liquidity. The existing literature in this area primarily links short selling to liquidity through its impact on the supply and demand of liquidity provision.5 As stated by Boehmer, Jones, and Zhang (2013, p. 1366), “[a] shorting ban could hurt market quality if short sellers are important liquidity providers. Banning short sellers could reduce competition in liquidity provision, worsening the terms of trade for liquidity demanders.” While doing much to illuminate the role of short sellers as liquidity providers, this literature does very little to link short selling to liquidity through adverse selection. And given that I find that adverse selection is the dominate factor negatively affecting transaction costs during the 2008 U.S. short selling ban it is important to understand this channel. In an additional contribution to the literature linking short selling to liquidity I explore a heretofore untested implication of that literature: that the effect of a ban on liquidity through liquidity supply also should be asymmetric and concentrated on the buy side of the market. This occurs because short sellers only provide liquidity when they trade passively with buyers. Consequently, their removal only decreases the supply of liquidity on the buy side of the market, allowing the remaining liquidity providers to increase the cost of liquidity—in the form of increased realized spread—for buyers. Consistent with this prediction, I find that increase in realized spread during the ban appears to be concentrated on the buy side of the market. The model has a few additional implications. First, the model’s prediction that the inability to short sell will influence the characteristics of the investors who become informed has implications that go beyond liquidity. If fewer outside investors become informed because of an inability to trade on negative information, then their role as monitors of the firm diminishes when short selling is restricted. Fang, Huang, and Karpoff (2015) find evidence consistent with this notion. They document that easing short selling restrictions increases the likelihood of a firm being caught for misdeeds that occurred before the easing took place, suggesting that when short selling restrictions are relaxed, more outside investors become informed. Second, the finding that the ban disproportionally harms sell side liquidity has regulatory implications and suggests caution when implementing policies which restrict short selling during down markets. Maintaining sell side liquidity during periods of downward price pressure is important to preserving market stability (Huang and Wang 2008). And the finding that sell side liquidity is harmed more than buy side liquidity during a ban suggests that restricting short selling during periods of downward price pressure may have the unintended effect of diminishing sell side liquidity when it is most needed. 1. Model The model is an adaptation of a one-period DV model where information acquisition is endogenous.6 In the economy an asset takes the equally likely value of zero or one. Market makers observe order flow but do not know the identity of the trader originating a given trade and they set the bid and ask price equal to the expected value of the asset conditional on the arrival of a buy or sell trade. The economy has two types of investors: sophisticated and liquidity. The fraction η of investors are sophisticated. Sophisticated traders trade only on information. If a sophisticated trader does not become informed then they abstain from trading. The remaining 1-η of investors trade for liquidity reasons and buy or sell/short with equal probability. The fraction γ of investors—sophisticated and liquidity—own one share of the asset. Sophisticated investors can pay a cost c to learn the value of the asset. The mass of sophisticated investors who become informed is determined in equilibrium such that the expected benefit of becoming informed is equal to the cost. The two endogenous variables are λe and λn which are the fraction of sophisticated investors who do and do not own the asset that become informed, respectively. Traders who do not own the asset but would like to short sell must pay a cost k to do so. k is assumed to be positive, but sufficiently small that it does not prevent liquidity traders from short selling.7 All traders transact exactly one share. Trading occurs in one round; then the value of the asset is revealed, and the asset is liquidated. As in DV, Glosten and Milgrom (1985) and others, market makers are perfectly competitive and have no other frictions to market making. Consequently, the bid ask spread in this model is driven exclusively by adverse selection and the implications of the model are only applicable to the adverse selection component of the bid ask spread. The model is solved for two cases: the baseline case in which short selling is costly but allowed (Section 1.1) and for a short selling ban (Section 1.2). These cases are then compared in Section 1.3. 1.1 Baseline: Costly short selling is allowed Two assumptions are needed to characterize the equilibrium presented in the baseline and short selling ban cases. These are presented below as Assumptions 1 and 2. Assumption 1 ensures that the equilibrium fraction of investors who do not own the asset that become informed (⁠ λn ⁠) is constrained by zero and one.8 Assumption 2 ensures that short selling is not so costly that it prevents traders from ever short selling. Assumption 2 also ensures that short selling is somewhat costly. Costly short selling is critical to the model as it drives the differential behavior of sophisticated traders who do and do not own the asset that characterizes the equilibrium presented in Proposition 1. 1-η2<c+k2<1-η21-η+ηγAssumption 1 0<k<2cAssumption 2 When short selling is allowed, a market maker may observe 16 possible events yielding three outcomes: a buy trade, a sell/short trade, or no trade. Figure 1 illustrates these events along with their accompanying probabilities. In Figure 1, a buy corresponds to events 1, 3, 5, 7, 13, and 15; a sell/short trade corresponds to events 6, 8, 9 ,11, 14, and 16; and no trade corresponds to events 2, 4, 10, and 12. Figure 1 Open in new tabDownload slide Outcome tree for model when short selling is allowed Probabilities are listed below each event. The entries on the far right indicate the market outcome from the given branch of the probability tree. Figure 1 Open in new tabDownload slide Outcome tree for model when short selling is allowed Probabilities are listed below each event. The entries on the far right indicate the market outcome from the given branch of the probability tree. Market makers know the probabilities of the given events as depicted in Table 1. Given these probabilities, the market maker sets the bid and ask price equal to the expected value of the asset conditional on a buy or sell/short trade arriving. The bid and ask prices are denoted as AskSS and BidSS with the subscript SS indicating the regime where short selling is allowed (NoSS indicates the short selling ban regime). If a buy arrives, the expected value of the asset is simply the expected value given the buyer is informed (which is one because informed traders will only buy if the asset value is one) multiplied by the probability that the buy originates from an informed trader plus the expected value of the asset given that the buyer is uninformed (which is one-half because an uninformed trader has no information so the expected value conditional on an uninformed trade is simply the unconditional expected value) multiplied by the probability that the buy originates from an uninformed trader. After simplifying the ask price is as shown in Equation (1). The bid price is similarly derived. AskSS=EVBuy=1-12*1-ηηγλe+1-γλn+1-η (1) BidSS= EVSell or Short=12*1-ηηγλe+1-γλn+1-η(2) Table 1 Probability of various events when short selling is allowed Outcome . Event number . Probability . Informed buy 1, 3 12ηγλe+1-γλn Uninformed buy 5, 7, 13, 15 1-η2 Informed sell 9 12ηγλe Uninformed sell 6, 14 1-ηγ2 Informed short 11 η1-γλn2 Uninformed short 8, 16 1-η1-γ2 No trade 2, 4, 10, 12 ηγ1-λe+η(1-γ)(1-λn) Outcome . Event number . Probability . Informed buy 1, 3 12ηγλe+1-γλn Uninformed buy 5, 7, 13, 15 1-η2 Informed sell 9 12ηγλe Uninformed sell 6, 14 1-ηγ2 Informed short 11 η1-γλn2 Uninformed short 8, 16 1-η1-γ2 No trade 2, 4, 10, 12 ηγ1-λe+η(1-γ)(1-λn) This table presents the various events that may occur in the model given that short selling is allowed. The leftmost column indicates the outcome observed by the market maker; the middle column indicates the events from Figure 1 that correspond to the observed outcome; and the rightmost column indicates the probability of the given outcome occurring. Open in new tab Table 1 Probability of various events when short selling is allowed Outcome . Event number . Probability . Informed buy 1, 3 12ηγλe+1-γλn Uninformed buy 5, 7, 13, 15 1-η2 Informed sell 9 12ηγλe Uninformed sell 6, 14 1-ηγ2 Informed short 11 η1-γλn2 Uninformed short 8, 16 1-η1-γ2 No trade 2, 4, 10, 12 ηγ1-λe+η(1-γ)(1-λn) Outcome . Event number . Probability . Informed buy 1, 3 12ηγλe+1-γλn Uninformed buy 5, 7, 13, 15 1-η2 Informed sell 9 12ηγλe Uninformed sell 6, 14 1-ηγ2 Informed short 11 η1-γλn2 Uninformed short 8, 16 1-η1-γ2 No trade 2, 4, 10, 12 ηγ1-λe+η(1-γ)(1-λn) This table presents the various events that may occur in the model given that short selling is allowed. The leftmost column indicates the outcome observed by the market maker; the middle column indicates the events from Figure 1 that correspond to the observed outcome; and the rightmost column indicates the probability of the given outcome occurring. Open in new tab Knowing the bid and ask prices, sophisticated traders choose whether to pay c to become informed. Equations (3) and (4) present the expected trading benefit to becoming informed for investors who do and do not own the asset, referred to as Bsse and Bssn ⁠, respectively. If the asset value equals one, sophisticated investors who do and do not own the asset will buy the asset at the value of AskSS earning a benefit of 1-AskSS ⁠. If the asset is worth zero, then investors who own the asset will sell it at BidSS ⁠, thereby preventing them from selling at zero when the true value is revealed. If they do not own the asset, they can pay k and short sell by selling at BidSS and covering their short at zero when the true value is revealed earning the investor BidSS-0-k ⁠. The likelihood of the asset equaling zero or one is one-half: EBsse=121-AskSS+12BidSS-0=1-η2(ηγλe+η1-γλn+1-η),(3) EBssn=121-AskSS+12BidSS-0-k=1-η2(ηγλe+η1-γλn+1-η)-k2.(4) In equilibrium sophisticated investors become informed until the expected benefit to becoming informed is equal to the cost. That is until Equations (3) and (4) both equal c. However, setting (3) and (4) equal to c and then solving for λe and λn is not possible because (3) is always greater than (4). This is easy to see as EBsse-k2=EBssn ⁠. Consequently, another method is used to determine the equilibrium. Specifically, both sophisticated investors who do and do not own the asset pay the same cost to become informed, but investors who own the asset have a higher expected benefit because they do not pay any short selling cost if the value of the asset turns out to be equal to zero. For the market to be in equilibrium the cost to becoming informed must equal the expected benefit of information for the marginal investor. Since both investors have the same cost to becoming informed but sophisticated traders owning the asset have a larger benefit, they are initially the marginal investors and will become informed until either EBsse=c or until all are informed (⁠ λe=1) ⁠. If the former, then none of the sophisticated traders not owning the asset ever become informed. If the latter, then there still may be benefit to becoming informed remaining after all the sophisticated traders owning the asset become informed, at which point sophisticated traders not owning the asset become the marginal investor and will become informed until c=EBssn ⁠. Assumption 1 ensures that the equilibrium outcome presented here falls in the latter case in which λe=1 and λn is selected such that c=EBssn ⁠. This process yields the equilibrium value of λn, which is then inserted into Equations (1) and (2) to yield Proposition 1. Proposition 1 Under Assumptions 1 and 2 there exists an equilibrium where the values of λeSS ⁠, λnSS ⁠, AskSS ⁠, BidSS ⁠, and SpreadSS are given by Equations (5) through (8): λeSS^*=1, λnSS^*=1-ηη2c+k1-γ-1-η+ηγη1-γ,(5) AskSS*=1-c-k2,(6) BidSS*=c+k2,(7) SpreadSS*=1-2c-k.(8) Equations (6) and (7) indicate that the bid and ask prices are independent of the fraction of sophisticated traders in the economy and are functions of the costs that sophisticated traders not owning the asset pay to transact on information: k and c ⁠. This occurs because when Assumption 1 is true the fraction of informed traders relative to the cost of becoming informed is such that there always will be enough sophisticated traders in the economy to ensure that the expected benefit to becoming informed is equal to the cost for the marginal investor (i.e., sophisticated investors who do not own the asset). Thus, only the expected benefit and cost to becoming informed for the marginal investor determine the equilibrium. Equations (6) and (7) also indicate that when short selling is allowed the bid ask spread is symmetric around the value of one-half, indicating that adverse selection is the same on both sides of the market. Equations (5), (6), (7), and (8) provide a baseline with which to compare adverse selection when short selling is prohibited. Other configurations of c and k may result in other equilibrium. However, in all equilibrium λe≥λn ⁠. That is the fraction of informed traders owning the asset who become informed will always be weakly greater than the fraction of informed traders not owning the asset. These other cases would appear less interesting. For instance, if c+k2 is sufficiently large then no sophisticated investors who do not own the asset would ever become informed. Such an outcome would seem to run contrary to the large empirical literature (see footnote 2) documenting the informed nature of short sellers (outside investors). Additionally, if c+k2 is sufficiently small, then all sophisticated traders who do and do not own the asset will become informed and there would be no variation in λn to study. Consequently, I focus on what I consider the most realistic and interesting equilibrium where λe=1 and λn varies between zero and one. This equilibrium imposes that all sophisticated investors owning the asset become informed. This may not be unrealistic in practice as it would be unlikely that a sophisticated trader, whose business it is to trade on information, will choose to not be informed about the value of the assets that they hold. 1.2 Short selling is prohibited A short selling ban produces two key changes to the economy relative to the baseline case.9 The first is that since short selling is not allowed, the market maker now knows that all sell orders originate from an investor who owns the asset. Consequently, the probability that a sell trade originates from an informed trader is the probability of an informed sell (event 9) divided by the probability of observing any sell (events 6,9,14). And the probability that an observed sell trade originates from an uninformed trader is the probability of an uninformed sell (events 6,14) divided by the probability of observing any sell (events 6,9,14). Consequently, the market maker updates their bid price as shown in Equation (9). BidNoSS= EVSell or Short=12*1-ηηλe+1-η(9) Since there are no restrictions on buying the asset during a short selling ban, the expression indicating the ask price does not change relative to the baseline case presented in Equation (1). AskNoSS=1-12*1-ηηγλe+1-γλn+1-η(10) The second change during a short selling ban is that the expected benefit of becoming informed diminishes for investors who do not own the asset since they can no longer trade on negative information. This change is reflected in Equations (11) and (12): EBNoSSe=121-AskNoSS+12BidNoSS-0 EBNoSSe=12-2ηγλe+2η1-γλn+1-η4ηγλe+η1-γλn+1-η+1-η4ηλe+1-η,(11) EBNoSSn=121-AskNoSS EBNoSSn=12-2ηγλe+2η1-γλn+1-η4ηγλe+η1-γλn+1-η.(12) As in the baseline case, the equilibrium fraction of investors who become informed is found by setting λeNoSS=1 and then finding the value of λeNoSS that equates EBNoSSn=c ⁠. The outcome of this equilibrium is presented as Proposition 2.10 Proposition 2 Under Assumptions 1 and 2, when short selling is not allowed there exists an equilibrium where the values of λeNoSS ⁠, λnNoSS ⁠, AskNoSS ⁠, BidNoSS ⁠, and SpreadNoSS are given by Equations (13) through (16): λeNoSS*=1, λnNoSS*=1-η+4c-14cη1-γ,(13) AskNoSS*=1-2c,(14) BidNoSS*=1-η2,(15) SpreadNoSS*=1-2c-1-η2.(16) Proposition 2 is intuitive. During a ban the ask price is determined by the marginal investor, that is, sophisticated investors who do not own the asset. And their entire benefit to becoming informed derives from the case in which the value of the asset equals one. So in expectation, for the expected benefit to becoming informed to equal the expected cost for these investors, it must be that AskNoSS*=1-2c ⁠. Also, since only investors who own the asset can sell, the bid price is determined simply by the fraction of liquidity traders in the market. From Equations (14) and (15), the short selling ban clearly affects adverse selection such that the bid ask spread is no longer symmetric. The next section presents the comparison of the baseline case in which short selling is allowed but costly to the case in which it is prohibited. 1.3 The effect of the ban Comparing the outcome of the model when short selling is and is not permitted produces the following propositions, the proofs of which are included in the appendix. Proposition 3a When short selling is prohibited, fewer investors who do not own the asset choose to become informed, that is, λnNoSS*<λnSS*. This result is intuitive. Investors who do not own the asset have less incentive to become informed when they are unable to trade on negative information and so the fraction who become informed decreases. Proposition 4 implies that information acquisition increasingly concentrates among investors owning the asset during a ban. Proposition 3b When short selling is allowed but costly fewer investors who do not own the asset will choose to become informed as the cost of short selling increases. Proposition 3b intuitively states that as transacting on negative information becomes more costly for investors who do not own the asset, fewer of these investors will choose to become informed. So even when short selling is allowed, if it is costly it will affect the distribution of investors who become informed in the market causing information acquisition to concentrate among investors owning the asset. Proposition 4 The bid price lowers during a short selling ban indicating increased adverse selection on the sell side of the market, that is, BidNoSS*<BidSS*. Proposition 4 indicates that the bid price lowers during a short selling ban indicating increased adverse selection on the sell side of the market. Intuitively, Proposition 4 is driven by the fact that the ratio of informed to liquidity investors owning the asset is greater than the ratio for investors not owning the asset. In the model the mass of investors that own the asset that become informed is γηλe while the mass of liquidity traders that own the asset is γ1-η ⁠. Thus, the ratio of informed to uninformed investors who own the asset is Re=ηλe1-η ⁠. Similarly, the mass of investors that do not own the asset that become informed is 1-γηλn while the mass of liquidity traders who do not own the asset is 1-γ1-η ⁠. Thus, the ratio of informed to uninformed investors not owning the asset is Rn= ηλn1-η ⁠. Since λn<λe ⁠, both when short selling is and is not allowed, it follows that Rn<Re and the investors not owning the asset are always the less informed of the two groups of investors. When a short selling ban is imposed it removes investors not-owning the asset—the less informed group—from the sell side of the market and leaves only the relatively more informed investors owning the asset. Consequently, a ban increases the likelihood that a sell trade originates from an informed trader—increasing sell side adverse selection. Proposition 5 the ask price declines during a short selling ban indicating less adverse selection on the buy side of the market, that is, AskNoSS*<AskSS* ⁠. Proposition 5 indicates that the ask price declines during a short selling ban indicating less adverse selection on the buy side of the market. Since no traders are prevented from buying the asset during a ban, adverse selection on the buy side is determined by the overall fraction of informed traders in the economy. Equations (5) and (13) indicate that λe does not change during a ban and Proposition 4 indicates that λnNoSS*<λnSS* consequently, the overall fraction of informed traders in the economy decreases leading to a decline in buy side adverse selection. Proposition 6 When η>1-2k then SpreadNoSS*>SpreadSS* ⁠. Proposition 6 states that when either η or k are relatively large, a ban increases overall adverse selection in the market. As seen from Equation (15), BidNoSS* is decreasing in η indicating that sell side adverse selection is increasing in η ⁠. When η becomes sufficiently large, the ban’s impact on sell side adverse selection will dominate its impact on buy side adverse selection causing overall adverse selection to increase. A high k affects the ban’s impact on adverse selection by discouraging sophisticated traders who do not own the asset from becoming informed in the baseline case in which short selling is allowed; thus, k diminishes adverse selection when short selling is allowed. Consequently, when k is high, the ban induced increase (decrease) in sell (buy) side adverse selection is relatively larger (smaller). Consequently, when k is sufficiently high the ban leads to an increase in total adverse selection. Proposition 7a Except when k and c are simultaneously near their maximum feasible values under Assumptions 1 and 2, a short selling ban will result in a decline in price efficiency, that is, ENoSSΔp>ESSΔp ⁠. Proposition 7a states that a short selling ban will be associated with a decline in price efficiency except when k and c are simultaneously near their maximum feasible values. Price efficiency is measured as the absolute deviation in the expected value of the asset after trading occurs from its true value as shown in Equation (17), where p1 is the conditional expected value of the asset after trading occurs. When EΔp is lower, price efficiency is higher. This measure is similar in spirit to the measure used in DV.11 EΔp=.5*E1-p1|v=1+.5*Ep1-0|v=0(17) Price efficiency declines because even though the ban increases the information content of sell trades (Proposition 4), it decreases the information content of buy trades (Proposition 5) and converts some trades that would have arrived on the sell side of the market into less informative no-trade events. In aggregate these effects cause trading to be less informative about the stock price during a short selling ban. Proposition 7b When short selling is allowed but costly price efficiency declines as the cost of short selling increases, that is, δESSΔpδk>0 ⁠. Proposition 7b states that in the baseline case in which short selling is allowed but costly, an increase in the cost of short selling (k) will lead to lower price efficiency. This occurs because as short selling becomes more costly, fewer sophisticated traders not owning the asset become informed. This has two impacts on price efficiency. First, fewer investors becoming informed means a buy or sell trade contains less information. Second, it means that it is more likely that a less informative no trade event occurs. 1.4 Extension: Large versus small increases in short selling costs Equation (8) implies that when short selling is costly but permitted then the amount of adverse selection in the market decreases as the cost of short selling increases. This outcome is potentially consistent with some of the findings of Kaplan, Moskowitz, and Sensoy (2013), who document in some of their specifications that spreads decrease when short selling is made more costly. In contrast, other studies associate short selling restrictions (as opposed to bans) implemented during the financial crisis with wider spreads, which may indicate increased adverse selection.12 These seemingly contradictory findings can be reconciled through a simple extension of the model. This extension produces the prediction that small increases in short selling costs will decrease adverse selection while large increases will increase adverse selection. Suppose there exists a threshold 0<τ<2c ⁠, where if the cost of short selling (k) exceeds then liquidity traders quit short selling. This modification creates three distinct short selling regimes: Unrestrained Short Selling: If k<τ ⁠, then both liquidity traders and sophisticated traders will short sell and the outcome is described in the baseline version of the model described in Section 1.1. Restricted Short Selling: If τ<k<2c then liquidity traders will not short sell, but some sophisticated traders will continue to do so. Banned Short Selling: If k>2c ⁠, then neither sophisticated nor liquidity traders short sell, resulting in an effective ban on short selling as described in Section 1.2. Case 2, where high short selling costs prevent liquidity traders, but not sophisticated traders, from transacting, is analogous to the portion of the DV model where they study the impact of the inability to reinvest the proceeds of a short sell. This restriction in their model prevents liquidity traders, but not informed traders, from short selling. I refer to this portion of the DV model as a DV restriction. The equilibrium outcomes for this regime can be found following a similar procedure as is presented in the paper. These outcomes are not presented here due to their complexity. However, it can be shown in this case that, relative to the unrestrained short selling regime, sell side adverse selection is unambiguously greater during the restricted short selling regime. The increase in sell side adverse selection occurs because the loss of liquidity traders on the sell side of the market means that there is a greater likelihood that a sell trade originates from an informed trader and thus sell side adverse selection increases. Consequently, there is a nonmonotonic relation between short selling costs and sell-side adverse selection. If the increase in short selling costs occurs within the unrestrained short selling regime, then that increase will result in a decline in adverse selection because it will dissuade some sophisticated traders from becoming informed. However, if the increase in short selling cost moves the market from the unrestrained short selling regime to the restricted short selling regime, then the restriction will be associated with an increase in adverse selection because it removes liquidity traders from the market. Also, in this case the information content of short sales will be greater, since all short sales will originate from informed traders. This is consistent with the findings of Kolasinski, Reed, and Thornock (2013). 2. Empirical Analysis 2.1 Sample The event that I use to study the effects of short selling on adverse selection is the 2008 short selling ban imposed by the U.S. Securities and Exchange Commission (SEC). As the financial crisis deepened in August and September 2008 the SEC and other policy makers came under increasing pressure by various market participants to put a stop to what was believed to be “manipulative” short selling. After the collapse of Lehman Brothers on September 15 and the subsequent stock market decline, the SEC prohibited short selling by all nonregistered market makers for 799 U.S. financial stocks. The ban began on September 19 and lasted through October 8. As the ban went on, nonfinancial stocks, such as General Electric, were included leading to a total of 931 stocks subject to the ban. The primary data source for this study is the NYSE Daily Trade and Quote (DTAQ) database for the months of August–October 2008.13 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. WRDS Intraday Indicators provides the variance ratios used in Section 3. Of the 931 stocks tickers that the SEC posted as being subject to the ban, I remove those that do not match to a permno in CRSP as well as those that ambiguously match to multiple permnos leaving 910 tickers. 123 Tickers that are not common stocks (CRSP share codes 10 and 11) are removed leaving 787 tickers. Of these 787 tickers 33 are not listed on NYSE or NASDAQ and are removed leaving 754. Stocks must also have complete CRSP volume and returns data for December 2007–July 2008 as well as DTAQ data from August 2008–October 2008 leaving a total of 711 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 19, 2008, and the remaining 58 were added to the ban later. Each banned stock is identified as a large, small, or microcap stock based on its market cap (from CRSP) as of December 31, 2007. Following Fama and French (2008), large stocks are those stocks that are in the five largest NYSE size deciles as of December 31, 2007, small stocks are 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 139 large stocks, 118 small stocks, and 454 microcap stocks. I focus my analysis on large and small stocks and omit microcap stocks from my analysis.14 Each banned stock is matched—with replacement—to a control stock based on market cap (calculated from CRSP) as of December 31, 2007, dollar trading volume in the first seven months of 2008 (calculated from CRSP), listing exchange (from CRSP), and options status (from Options Metrics). This matching procedure is based on the procedure used in Boehmer, Jones, and Zhang (2013) and Brogaard, Hendershott, and Riordan (2017). For each banned stock a control stock is found by taking the universe of CRSP common stocks (share codes 10 and 11) which have complete DTAQ data for August-October 2008, and complete CRSP data for 2007 and 2008, as well as the same listing exchange and the same options status as the banned stock in question and calculating a distance measure between the banned stock and a potential control. The distance measure is the sum of the absolute proportional distance between the banned stock (i) and the potential control stock (j) based on market cap and dollar volume as shown in Equation (18). The control stock with the smallest distance measure becomes the assigned control stock for the given banned stock. This process is repeated for each banned stock and sampling is done with replacement. Table 2 presents descriptive statistics for the banned and control stocks used in this study. Distancei,j=Mktcpi-MktcpjMktcpi+Dvoli-DvoljDvoli(18) Table 2 Summary statistics for the matched sample . Total . Large . Small . N 257 139 118 Average distance 0.142 0.171 0.108 Banned Matched Banned Matched Banned Matched Average monthly Dollar volume (millions) 2,838 2,421 5,046 4,271 260 259 t-statistic (0.75) (0.81) (0.02) p-value .451 .421 .981 Market cap (millions) 12,547 13,049 22,363 23,301 1,081 1,075 t-statistic (−0.16) (−0.16) (0.15) p-value .876 .87 .881 . Total . Large . Small . N 257 139 118 Average distance 0.142 0.171 0.108 Banned Matched Banned Matched Banned Matched Average monthly Dollar volume (millions) 2,838 2,421 5,046 4,271 260 259 t-statistic (0.75) (0.81) (0.02) p-value .451 .421 .981 Market cap (millions) 12,547 13,049 22,363 23,301 1,081 1,075 t-statistic (−0.16) (−0.16) (0.15) p-value .876 .87 .881 This table presents descriptive statistics for the 257 stocks used in the regression analysis. Each stock subject to the ban is matched, with replacement, to a stock not subject to the ban that has the same listing exchange and options status. The match is based on market cap as of December 31, 2007, and average dollar trading volume over the first 7 months of 2008 based on the distance measure: Distancei,j=Mktcpi-MktcpjMktcpi+Dvoli-DvoljDvoli ⁠. Stocks are divided into size groups based on their market cap as of December 31, 2007. Large stocks are those stocks with market caps in the top five NYSE deciles, small stocks are those stocks with market caps in NYSE deciles 3–5. Results are provided both in aggregate and by size group. Average dollar volume and market cap statistics are reported for the total as well as for each of the three size groups separately. t-statistics and p-values for a t-test on the difference between the banned and matched stocks are provided below. Open in new tab Table 2 Summary statistics for the matched sample . Total . Large . Small . N 257 139 118 Average distance 0.142 0.171 0.108 Banned Matched Banned Matched Banned Matched Average monthly Dollar volume (millions) 2,838 2,421 5,046 4,271 260 259 t-statistic (0.75) (0.81) (0.02) p-value .451 .421 .981 Market cap (millions) 12,547 13,049 22,363 23,301 1,081 1,075 t-statistic (−0.16) (−0.16) (0.15) p-value .876 .87 .881 . Total . Large . Small . N 257 139 118 Average distance 0.142 0.171 0.108 Banned Matched Banned Matched Banned Matched Average monthly Dollar volume (millions) 2,838 2,421 5,046 4,271 260 259 t-statistic (0.75) (0.81) (0.02) p-value .451 .421 .981 Market cap (millions) 12,547 13,049 22,363 23,301 1,081 1,075 t-statistic (−0.16) (−0.16) (0.15) p-value .876 .87 .881 This table presents descriptive statistics for the 257 stocks used in the regression analysis. Each stock subject to the ban is matched, with replacement, to a stock not subject to the ban that has the same listing exchange and options status. The match is based on market cap as of December 31, 2007, and average dollar trading volume over the first 7 months of 2008 based on the distance measure: Distancei,j=Mktcpi-MktcpjMktcpi+Dvoli-DvoljDvoli ⁠. Stocks are divided into size groups based on their market cap as of December 31, 2007. Large stocks are those stocks with market caps in the top five NYSE deciles, small stocks are those stocks with market caps in NYSE deciles 3–5. Results are provided both in aggregate and by size group. Average dollar volume and market cap statistics are reported for the total as well as for each of the three size groups separately. t-statistics and p-values for a t-test on the difference between the banned and matched stocks are provided below. Open in new tab 2.2 Computation of empirical metrics 2.2.1 Adverse selection and price impact The primary empirical measure of adverse selection used in this study is the adverse selection component of the effective spread, which is also referred to as the price impact portion of the effective spread.15 The link between adverse selection and price impact originates with models such as Kyle (1985) and Glosten and Milgrom (1985). In these models, the presence of informed traders means that order flow conveys information about the value of the asset. Market makers respond to this information by adjusting subsequent prices based on the signal obtained from past order flow. When adverse selection increases—implying a greater fraction of informed traders in the market—the information contained in a trade increases, causing a trade’s price impact to also increase. As discussed in Appendix C, the effective spread can be decomposed into two components: adverse selection (i.e., price impact) and realized spread. This decomposition provides a method for testing the economic channels through which an event or situation affects financial markets. Events that affect the information environment will influence financial markets primarily through the adverse selection component, whereas events that affect nonadverse selection related elements of the market, such as competition among market makers, affect effective spreads through the realized spread. 2.2.2 Estimating adverse selection For the empirical tests in this study, the effective spread and its constituent components of adverse selection and realized spread are computed using DTAQ data for all qualifying trades during August - October 2008.16 Trades are signed using the Lee and Ready (1991) algorithm with a one millisecond lag as the reference midpoint. Decomposing the effective spread into adverse selection and realized spread requires adding and subtracting some future midpoint to the effective spread. Unfortunately, guidance in the literature is scarce as to what the appropriate time horizon should be. Perhaps the most common time horizon employed in the literature is 5 minutes, however, as O’Hara (2015) points out, 5 minutes in modern markets is a “lifetime.” Consequently, in my analysis I vary the time horizon used to measure adverse selection from 1 to 5 minutes. After computing the effective spread, adverse selection, and realized spread for each trade, I aggregate these measurements into equally weighted daily averages. These daily averages are computed in two ways. 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—regardless of the sign—yielding one observation per stock per day. In specifications where the objective is to measure the differential effect of the ban on adverse selection or spreads for buy and 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 stock per day—one for each side of the market. The equally weighted daily average values of adverse selection, realized spread, and effective spreads are converted to basis points for all analysis. 2.3 Empirical results The primary empirical methodology used to determine the effects of the ban on adverse selection , realized, and effective spreads is difference-in-differences (DD) regressions when estimating the overall effect of the ban, and difference-in-difference-in-differences (DDD) regressions for the signed analysis. In these regressions, the dependent variable is the difference in equally weighted daily average adverse selection (or realized spread or effective spread) between a banned stock and its matched control. This effectively places the first difference in the DD, or DDD regressions on the left-hand side of the equation and allows the use of stock pair fixed effects in the model to control for systematic differences in the dependent variable between each banned stock and its matched control. 2.3.1 The effect of the ban on adverse selection One of the primary predictions of the model presented in Section 1 is that prohibiting short selling may lead to an overall increase in adverse selection, but that such an increase will be concentrated on the sell side of the market. To test this prediction, I use the DD and DDD regressions in Equations (19) and (20): ASi,tB,Δt-ASi,tC,Δt=η0+η1Bant+ΓXi,t+νi+εi,t,(19) ASi,t,sB,Δt-ASi,t,sC,Δt=ξ0+ξ1Bant+ξ2SIi,s+ξ3Bant*SIi,s+ΓXi,t,s+νi+εi,t,s.(20) AS indicates adverse selection. The superscript B or C indicate banned and control, the subscript i indexes the banned stock/control stock pair, t indexes the day and Δt indicates the time horizon used to measure adverse selection (1 to 5 minutes). In Equation (20), the subscript s indicates whether the observation refers to the buy or sell sides of the market. SIi,s equals one if the given observation for stock pair i occurs on the sell side of the market and zero otherwise. The coefficient η1 from Equation (19) identifies the total effect of the ban on adverse selection. Equation (20) is a DDD regression identifying the differential effect of the short selling ban on the buyer and seller-initiated sides of the market. The coefficient ξ1 from Equation (20) identifies the effect of the ban on buyer-initiated adverse selection, and the sum of ξ1+ξ3 identifies the ban’s effect on adverse selection for seller-initiated trades. Xi,t and Xi,t,s are matrices of control variables.17 All models include stock pair fixed effects and standard errors are clustered at the date level. Table 3 presents the regression estimates for the coefficient η1 from Equation (19). In these specifications, the results for adverse selection are computed using horizons of 1, 2, 3, 4, and 5 minutes, and are presented in columns 1 through 5 of Table 3, respectively. Panel A presents the results for large stocks, and panel B presents the results for small stocks. In both instances, the regressions reveal that the short selling ban is associated with a statistically significant increase in adverse selection. For large stocks, the measured increase in adverse selection is about 2.5–3.5 basis points, depending on the time horizon used. The pattern of results in panel B for small stocks is similar with adverse selection costs increasing by about 5–7 basis points. These results confirm the findings of Boehmer, Jones and Zhang (2013) and Kolasinski, Reed, and Thornock (2013) that the ban is associated with an increase in adverse selection costs, and are consistent with the model’s prediction that a short selling ban can increase overall adverse selection. Table 3 Effect of the ban on adverse selection A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (η1) 2.536*** 3.092*** 3.138*** 3.161*** 3.416*** (.000) (.000) (.000) (.000) (.000) N 8,000 8,000 8,000 8,000 8,000 R2 .257 .238 .228 .205 .187 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (η1) 4.500*** 5.876*** 6.209*** 6.604*** 7.032*** (.000) (.000) (.000) (.000) (.000) N 8,000 8,000 8,000 8,000 8,000 R2 .395 .389 .397 .392 .371 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (η1) 2.536*** 3.092*** 3.138*** 3.161*** 3.416*** (.000) (.000) (.000) (.000) (.000) N 8,000 8,000 8,000 8,000 8,000 R2 .257 .238 .228 .205 .187 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (η1) 4.500*** 5.876*** 6.209*** 6.604*** 7.032*** (.000) (.000) (.000) (.000) (.000) N 8,000 8,000 8,000 8,000 8,000 R2 .395 .389 .397 .392 .371 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes This table presents the results from DD regressions indicating the effect of the short selling ban on adverse selection for large stocks (panel A) and small stocks (panel B) using 1- to 5-minute time horizons to compute adverse selection in basis points. Small stocks are those stocks that have a market cap in NYSE deciles 3–5, and large stocks are those stocks subject to the short selling ban and that have a market cap in the five largest NYSE deciles as of December 31, 2007. Each banned stock is matched to a control stock based on listing exchange, options status, dollar volume, and market cap. Equally weighted adverse selection is computed for each stock each day. Then the difference in daily average adverse selection between a banned stock and its matched control is computed and is the dependent variable used in the following DD regression: ASi,tB,Δt-ASi,tC,Δt=η0+η1Bant+ΓXi,t+νi+εi,t ⁠. Presented in the table are the estimated coefficients from the above regression for the effect of the short selling ban on 1- to 5-minute adverse selection in columns 1 through 5, respectively. In this specification, the coefficient η1 indicates the effect of the short selling ban aggregate realized spread. p-values testing the hypothesis that η1is equal to zero are presented in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 3 Effect of the ban on adverse selection A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (η1) 2.536*** 3.092*** 3.138*** 3.161*** 3.416*** (.000) (.000) (.000) (.000) (.000) N 8,000 8,000 8,000 8,000 8,000 R2 .257 .238 .228 .205 .187 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (η1) 4.500*** 5.876*** 6.209*** 6.604*** 7.032*** (.000) (.000) (.000) (.000) (.000) N 8,000 8,000 8,000 8,000 8,000 R2 .395 .389 .397 .392 .371 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (η1) 2.536*** 3.092*** 3.138*** 3.161*** 3.416*** (.000) (.000) (.000) (.000) (.000) N 8,000 8,000 8,000 8,000 8,000 R2 .257 .238 .228 .205 .187 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (η1) 4.500*** 5.876*** 6.209*** 6.604*** 7.032*** (.000) (.000) (.000) (.000) (.000) N 8,000 8,000 8,000 8,000 8,000 R2 .395 .389 .397 .392 .371 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes This table presents the results from DD regressions indicating the effect of the short selling ban on adverse selection for large stocks (panel A) and small stocks (panel B) using 1- to 5-minute time horizons to compute adverse selection in basis points. Small stocks are those stocks that have a market cap in NYSE deciles 3–5, and large stocks are those stocks subject to the short selling ban and that have a market cap in the five largest NYSE deciles as of December 31, 2007. Each banned stock is matched to a control stock based on listing exchange, options status, dollar volume, and market cap. Equally weighted adverse selection is computed for each stock each day. Then the difference in daily average adverse selection between a banned stock and its matched control is computed and is the dependent variable used in the following DD regression: ASi,tB,Δt-ASi,tC,Δt=η0+η1Bant+ΓXi,t+νi+εi,t ⁠. Presented in the table are the estimated coefficients from the above regression for the effect of the short selling ban on 1- to 5-minute adverse selection in columns 1 through 5, respectively. In this specification, the coefficient η1 indicates the effect of the short selling ban aggregate realized spread. p-values testing the hypothesis that η1is equal to zero are presented in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 4 presents the results from the DDD regressions from Equation (20) examining the differential effect of the short selling ban on adverse selection on the buy and sell sides of the market. The results presented in Table 4 are consistent with the predictions of the model as the effect of the short selling ban on adverse selection appears concentrated almost exclusively on the sell side of the market. For large stocks, there is not a single instance in which the regressions indicate that the ban is associated with a statistically significant increase in buy side adverse selection, yet every time frame at which adverse selection is measured indicates a statistically significant increase in adverse selection costs of 4–6 basis points on the sell side of the market. Table 4 Effect of the ban on signed adverse selection A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ξ1 ⁠) 0.386 1.051 0.528 0.534 0.666 (.656) (.336) (.674) (.722) (.706) Seller (⁠ ξ1+ξ3 ⁠) 4.340*** 5.232*** 5.874*** 5.702** 6.065* (.000) (.000) (.000) (.000) (.000) Difference (⁠ ξ3 ⁠) 3.954** 4.181* 5.319** 5.168 5.399 (.019) (.056) (.050) (.114) (.163) N 18,904 18,904 18,904 18,904 18,904 R2 .035 .035 .032 .030 .027 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ξ1 ⁠) 2.166*** 2.616** 2.217 2.316 2.554 (.009) (.034) (.146) (.262) (.299) Seller (⁠ ξ1+ξ3 ⁠) 7.747*** 10.393*** 12.135*** 12.936*** 14.284** (.030) (.014) (.015) (.008) (.043) Difference (⁠ ξ3 ⁠) 5.581*** 7.777*** 9.918*** 10.62** 11.73** (.001) (.004) (.003) (.019) (.025) N 16,000 16,000 16,000 16,000 16,000 R2 .171 .144 .126 .108 .095 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ξ1 ⁠) 0.386 1.051 0.528 0.534 0.666 (.656) (.336) (.674) (.722) (.706) Seller (⁠ ξ1+ξ3 ⁠) 4.340*** 5.232*** 5.874*** 5.702** 6.065* (.000) (.000) (.000) (.000) (.000) Difference (⁠ ξ3 ⁠) 3.954** 4.181* 5.319** 5.168 5.399 (.019) (.056) (.050) (.114) (.163) N 18,904 18,904 18,904 18,904 18,904 R2 .035 .035 .032 .030 .027 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ξ1 ⁠) 2.166*** 2.616** 2.217 2.316 2.554 (.009) (.034) (.146) (.262) (.299) Seller (⁠ ξ1+ξ3 ⁠) 7.747*** 10.393*** 12.135*** 12.936*** 14.284** (.030) (.014) (.015) (.008) (.043) Difference (⁠ ξ3 ⁠) 5.581*** 7.777*** 9.918*** 10.62** 11.73** (.001) (.004) (.003) (.019) (.025) N 16,000 16,000 16,000 16,000 16,000 R2 .171 .144 .126 .108 .095 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes This table presents the results from DDD regressions indicating the effect of the short selling ban on signed adverse selection for large stocks (panel A) and small stocks (panel B) using time horizons of one minute to five minutes to compute adverse selection in basis points presented in columns 1 through 5, respectively. Small stocks are those stocks that have a market cap in NYSE deciles 3–5, and large stocks are those stocks subject to the short selling ban and that have a market cap in the five largest NYSE deciles as of December 31, 2007. Each banned stock is matched to a control stock based on listing exchange, options status, dollar volume, and market cap. The equally weighted adverse selection is computed for each stock each day. Then the difference in daily average adverse selection and adverse selection between a banned stock and its matched control is computed and is the dependent variable used in the DDD regressions. Presented in the table are the estimated coefficients from the below regression for the effect of the short selling ban on adverse selection: ASi,t,sB,Δt-ASi,t,sC,Δt=ξ0+ξ1Bant+ξ2SIi,s+ξ3Bant*SIi,s+ΓXi,t,s+νi+εi,t,s. In this specification, the coefficient ξ1 indicates the effect of the short selling ban on buyer-initiated adverse selection, the sum of coefficients ξ1+ξ3 indicates the seller-initiated effect, and the coefficient ξ3 indicates the difference between the buyer- and seller-initiated effect. p-values testing the hypothesis that the relevant coefficients are equal to zero are presented in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 4 Effect of the ban on signed adverse selection A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ξ1 ⁠) 0.386 1.051 0.528 0.534 0.666 (.656) (.336) (.674) (.722) (.706) Seller (⁠ ξ1+ξ3 ⁠) 4.340*** 5.232*** 5.874*** 5.702** 6.065* (.000) (.000) (.000) (.000) (.000) Difference (⁠ ξ3 ⁠) 3.954** 4.181* 5.319** 5.168 5.399 (.019) (.056) (.050) (.114) (.163) N 18,904 18,904 18,904 18,904 18,904 R2 .035 .035 .032 .030 .027 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ξ1 ⁠) 2.166*** 2.616** 2.217 2.316 2.554 (.009) (.034) (.146) (.262) (.299) Seller (⁠ ξ1+ξ3 ⁠) 7.747*** 10.393*** 12.135*** 12.936*** 14.284** (.030) (.014) (.015) (.008) (.043) Difference (⁠ ξ3 ⁠) 5.581*** 7.777*** 9.918*** 10.62** 11.73** (.001) (.004) (.003) (.019) (.025) N 16,000 16,000 16,000 16,000 16,000 R2 .171 .144 .126 .108 .095 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ξ1 ⁠) 0.386 1.051 0.528 0.534 0.666 (.656) (.336) (.674) (.722) (.706) Seller (⁠ ξ1+ξ3 ⁠) 4.340*** 5.232*** 5.874*** 5.702** 6.065* (.000) (.000) (.000) (.000) (.000) Difference (⁠ ξ3 ⁠) 3.954** 4.181* 5.319** 5.168 5.399 (.019) (.056) (.050) (.114) (.163) N 18,904 18,904 18,904 18,904 18,904 R2 .035 .035 .032 .030 .027 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ξ1 ⁠) 2.166*** 2.616** 2.217 2.316 2.554 (.009) (.034) (.146) (.262) (.299) Seller (⁠ ξ1+ξ3 ⁠) 7.747*** 10.393*** 12.135*** 12.936*** 14.284** (.030) (.014) (.015) (.008) (.043) Difference (⁠ ξ3 ⁠) 5.581*** 7.777*** 9.918*** 10.62** 11.73** (.001) (.004) (.003) (.019) (.025) N 16,000 16,000 16,000 16,000 16,000 R2 .171 .144 .126 .108 .095 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes This table presents the results from DDD regressions indicating the effect of the short selling ban on signed adverse selection for large stocks (panel A) and small stocks (panel B) using time horizons of one minute to five minutes to compute adverse selection in basis points presented in columns 1 through 5, respectively. Small stocks are those stocks that have a market cap in NYSE deciles 3–5, and large stocks are those stocks subject to the short selling ban and that have a market cap in the five largest NYSE deciles as of December 31, 2007. Each banned stock is matched to a control stock based on listing exchange, options status, dollar volume, and market cap. The equally weighted adverse selection is computed for each stock each day. Then the difference in daily average adverse selection and adverse selection between a banned stock and its matched control is computed and is the dependent variable used in the DDD regressions. Presented in the table are the estimated coefficients from the below regression for the effect of the short selling ban on adverse selection: ASi,t,sB,Δt-ASi,t,sC,Δt=ξ0+ξ1Bant+ξ2SIi,s+ξ3Bant*SIi,s+ΓXi,t,s+νi+εi,t,s. In this specification, the coefficient ξ1 indicates the effect of the short selling ban on buyer-initiated adverse selection, the sum of coefficients ξ1+ξ3 indicates the seller-initiated effect, and the coefficient ξ3 indicates the difference between the buyer- and seller-initiated effect. p-values testing the hypothesis that the relevant coefficients are equal to zero are presented in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab For small stocks, the pattern of results is similar. Across all time horizons there is a statistically significant increase in adverse selection costs on the sell side of the market of between 8 and 14 basis points. The results identifying the effect of the ban on buy side adverse selection (⁠ ξ1 ⁠) indicate an increase of only about 2 basis points, which is not statistically significant in three of the five specifications. To highlight the economic magnitude of the effect of the ban on adverse selection costs, I note that the average effective spreads (of which adverse selection is a key component) paid by traders outside the ban for large (small) stocks is approximately 7 (18) basis points. Consequently, the increase in sell side adverse selection costs of 4–6 (8–12) basis points for large (small) stocks represents an increase in transaction costs equal to approximately 60%–85% (50%–90%) of total transaction costs paid outside the ban. Figure 2 presents a graphical description of the regressions results presented in Tables 3 and 4. Each point in each series indicates the observed value of coefficient η1 ⁠, ξ1 ⁠, or the sum of coefficients ξ1+ξ3 from a DD or DDD regressions corresponding to Equations (19) and (20) and for a given time horizon used to compute adverse selection. Time horizons vary from 30 to 300 seconds. The vertical axis represents the magnitude of the effect in basis points, and the horizontal axis represents the time horizon used to compute adverse selection. The dashed line in the figure represents the effect of the short selling ban on sell side adverse selection (coefficients ξ1+ξ3 from Equation (20)). The fine dotted line represents the effect of the ban on buy side adverse selection (coefficient ξ1 from Equation (20)), and the solid line represents the aggregate effect of the ban on adverse selection (⁠ η1 from Equation (19)). This figure graphically illustrates the effect of the ban on adverse selection, which is documented in Tables 2 and 3. For every time horizon used to measure adverse selection, the effect of the ban on adverse selection is concentrated almost exclusively on the sell side of the market. Figure 2 Open in new tabDownload slide Regression results for the impact of the short selling ban on adverse selection This figure presents the regression coefficients from regressions estimating the effect of the short selling ban on adverse selection. Adverse selection is measured from DTAQ data employing time horizons from 60 to 300 seconds as described in Section 2.2. The effect of the ban on aggregate and buyer and seller-initiated adverse selection is estimated using Equations (19) and (20). Coefficients from these regressions are saved and plotted in this figure. The effect of the ban on aggregate adverse selection is indicated by the coefficient η1 from Equation (19), is plotted as the solid line. The effect of the ban on buyer-initiated adverse selection is indicated by the coefficient ξ1 from Equation (20) and is represented by the fine dotted line. The effect of the ban on seller-initiated adverse selection is the sum of coefficients ξ1+ξ3 from Equation (20) and is represented by the dashed line. The horizontal axis represents the time frame used to measure adverse selection, and the vertical axis represents the observed value of the indicated coefficients in basis points. Panel A presents the results for large stocks, and panel B presents the results for small stocks. Figure 2 Open in new tabDownload slide Regression results for the impact of the short selling ban on adverse selection This figure presents the regression coefficients from regressions estimating the effect of the short selling ban on adverse selection. Adverse selection is measured from DTAQ data employing time horizons from 60 to 300 seconds as described in Section 2.2. The effect of the ban on aggregate and buyer and seller-initiated adverse selection is estimated using Equations (19) and (20). Coefficients from these regressions are saved and plotted in this figure. The effect of the ban on aggregate adverse selection is indicated by the coefficient η1 from Equation (19), is plotted as the solid line. The effect of the ban on buyer-initiated adverse selection is indicated by the coefficient ξ1 from Equation (20) and is represented by the fine dotted line. The effect of the ban on seller-initiated adverse selection is the sum of coefficients ξ1+ξ3 from Equation (20) and is represented by the dashed line. The horizontal axis represents the time frame used to measure adverse selection, and the vertical axis represents the observed value of the indicated coefficients in basis points. Panel A presents the results for large stocks, and panel B presents the results for small stocks. 2.3.2 Realized spread The other component of the effective spread paid by the liquidity demanders is the realized spread. This is the portion of the spread that compensates market makers for non-adverse-selection costs and provides their profit. The literature examining the link between short selling and liquidity has primarily concentrated on studying the role that short sellers play as liquidity providers. As articulated by Boehmer, Jones, and Zhang (2013, p. 1366), the effect that a short selling ban may have on liquidity through the liquidity provision channel comes because “banning short sellers could reduce competition in liquidity provision, worsening the terms of trade for liquidity demanders.” A decline in competition among liquidity providers allows the remaining liquidity providers to charge higher rents. These higher rents should be discernable in the data through an increase in the realized spread portion of the effective spread. However, this liquidity provision channel comes with the heretofore untested prediction that the increase in realized spread during a short selling ban will be concentrated on the buy side of the market. This asymmetry comes because short sellers only provide liquidity when they trade passively with buyers, so the decline in competition due to prohibiting short sellers is likely to be concentrated on the buy side of the market, thereby increasing buy side realized spread. I examine the asymmetric effects of the short selling ban on buy and sell side realized spread employing DD and DDD regressions presented in Equations (21) and (22) similar to those employed in the previous section, where i indexes the banned stock. RESP indicates daily average realized spread. All super- and subscripts are the same as those used in Equations (19) and (20). Equation (21) is used to determine the total effect of the short selling ban on realized spread and in this specification, the coefficient κ1 indicates this overall effect. Equation (22) is used to study the differential effect of the short selling ban on realized spread for the buy and sell sides of the market. In Equation (22), the coefficient ρ1 indicates the effect of the short selling ban on buyer-initiated trades whereas the sum of coefficients ρ1+ρ3 indicates the effect of the short selling ban on seller-initiated trades. In all specifications, the matrices of control variables Xi,t and Xi,t,s contain the same controls as those employed in the regressions in the prior analysis. All models include stock pair fixed effects, and standard errors are clustered at the date level. RESPi,tB,Δt-RESPi,tC,Δt=κ0+κ1Bant+ΓXi,t+νi+εi,t(21) RESPi,t,sB,Δt-RESPi,t,sC,Δt=ρ0+ρ1Bant+ρ2SIi,s+ρ3Bant*SIi,s+ΓXi,t,s+νi+εi,t,s(22) Table 5 presents the regression estimates for the coefficient κ1 from Equation (21) at various horizons, which indicate the total effect of the short selling ban on realized spread. The results of the DD regressions indicate that for both large and small stocks, the short selling ban is associated with a statistically significant increase in realized spread at all time horizons used to compute the realized spread, except for the 5-minute realized spread for large stocks. For large stocks, the increase is around 1 basis point. For small stocks, the increase in realized spread is approximately 5 to 6 basis points. Table 5 Effect of the ban on the realized spread A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (⁠ κ1) 1.646*** 1.023*** 1.028** 1.013** 0.837 (0.000) (0.005) (0.019) (0.036) (0.101) N 9,452 9,452 9,452 9,452 9,452 R2 .175 .135 .111 .095 .080 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (⁠ κ1) 6.722*** 5.483*** 5.169*** 4.819*** 4.455*** (0.000) (0.000) (0.000) (0.000) (0.000) N 8,000 8,000 8,000 8,000 8,000 R2 .257 .238 .228 .205 .187 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (⁠ κ1) 1.646*** 1.023*** 1.028** 1.013** 0.837 (0.000) (0.005) (0.019) (0.036) (0.101) N 9,452 9,452 9,452 9,452 9,452 R2 .175 .135 .111 .095 .080 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (⁠ κ1) 6.722*** 5.483*** 5.169*** 4.819*** 4.455*** (0.000) (0.000) (0.000) (0.000) (0.000) N 8,000 8,000 8,000 8,000 8,000 R2 .257 .238 .228 .205 .187 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes This table presents the results from DD regressions indicating the effect of the short selling ban on signed realized spread for large stocks (panel A) and small stocks (panel B) using 1- to 5-minute time horizons to compute the realized spread in basis points. Small stocks are those stocks that have a market cap in NYSE deciles 3–5, and large stocks are those stocks subject to the short selling ban and that have a market cap in the five largest NYSE deciles as of December 31, 2007. Each banned stock is matched to a control stock based on the listing exchange, options status, dollar volume, and market cap. The equally weighted realized spread is computed for each stock each day. Then the difference in daily average realized spread between a banned stock and its matched control is computed and is the dependent variable used in the DD regressions: RESPi,tB,Δt-RESPi,tC,Δt=κ0+κ1Bant+ΓXi,t+νi+εi,t ⁠. Presented in the table are the estimated coefficients from the above regression for the effect of the short selling ban on 1- to 5-minute realized spread in columns 1 through 5, respectively. In this specification, the coefficient κ1 indicates the effect of the short selling ban aggregate realized spread. p-values testing the hypothesis that κ1is equal to zero are presented in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 5 Effect of the ban on the realized spread A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (⁠ κ1) 1.646*** 1.023*** 1.028** 1.013** 0.837 (0.000) (0.005) (0.019) (0.036) (0.101) N 9,452 9,452 9,452 9,452 9,452 R2 .175 .135 .111 .095 .080 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (⁠ κ1) 6.722*** 5.483*** 5.169*** 4.819*** 4.455*** (0.000) (0.000) (0.000) (0.000) (0.000) N 8,000 8,000 8,000 8,000 8,000 R2 .257 .238 .228 .205 .187 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (⁠ κ1) 1.646*** 1.023*** 1.028** 1.013** 0.837 (0.000) (0.005) (0.019) (0.036) (0.101) N 9,452 9,452 9,452 9,452 9,452 R2 .175 .135 .111 .095 .080 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Ban (⁠ κ1) 6.722*** 5.483*** 5.169*** 4.819*** 4.455*** (0.000) (0.000) (0.000) (0.000) (0.000) N 8,000 8,000 8,000 8,000 8,000 R2 .257 .238 .228 .205 .187 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes This table presents the results from DD regressions indicating the effect of the short selling ban on signed realized spread for large stocks (panel A) and small stocks (panel B) using 1- to 5-minute time horizons to compute the realized spread in basis points. Small stocks are those stocks that have a market cap in NYSE deciles 3–5, and large stocks are those stocks subject to the short selling ban and that have a market cap in the five largest NYSE deciles as of December 31, 2007. Each banned stock is matched to a control stock based on the listing exchange, options status, dollar volume, and market cap. The equally weighted realized spread is computed for each stock each day. Then the difference in daily average realized spread between a banned stock and its matched control is computed and is the dependent variable used in the DD regressions: RESPi,tB,Δt-RESPi,tC,Δt=κ0+κ1Bant+ΓXi,t+νi+εi,t ⁠. Presented in the table are the estimated coefficients from the above regression for the effect of the short selling ban on 1- to 5-minute realized spread in columns 1 through 5, respectively. In this specification, the coefficient κ1 indicates the effect of the short selling ban aggregate realized spread. p-values testing the hypothesis that κ1is equal to zero are presented in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 6 presents the DDD regression results indicating the effect of the short selling ban on realized spread for the buyer and seller-initiated sides of the market from Equation (22). The coefficient ρ1 from Equation (22) measures the impact of the ban on buy side realized spread, while the sum of coefficients ρ1+ρ3 indicates the effect of the ban on sell side realized spread. Panel A of Table 6 presents the results for large stocks, and panel B presents the results for small stocks. Table 6 Effect of the ban on the signed realized spread A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ρ1 ⁠) 2.914*** 2.506** 2.982** 2.888* 2.709 (0.001) (0.021) (0.018) (0.056) (0.127) Seller (⁠ ρ1+ρ3 ⁠) 0.878 0.002 −0.449 −0.421 −0.817 (0.000) (0.021) (0.239) (0.460) (0.817) Difference (⁠ ρ3 ⁠) −2.036 −2.504 −3.431 −3.309 −3.526 (0.210) (0.251) (0.207) (0.312) (0.362) N 18,904 18,904 18,904 18,904 18,904 R2 .012 .010 .010 .009 .009 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ρ1 ⁠) 7.510*** 7.013*** 7.328*** 7.200*** 7.024*** (0.000) (0.000) (0.000) (0.001) (0.007) Seller (⁠ ρ1+ρ3 ⁠) 6.571*** 4.060** 2.462 1.910 .0681 (0.001) (0.002) (0.008) (0.007) (0.025) Difference (⁠ ρ3 ⁠) −0.939 −2.953 −4.866 −5.290 −6.343 (0.563) (0.206) (0.111) (0.193) (0.192) N 16,000 16,000 16,000 16,000 16,000 R2 .099 .082 .063 .053 .046 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ρ1 ⁠) 2.914*** 2.506** 2.982** 2.888* 2.709 (0.001) (0.021) (0.018) (0.056) (0.127) Seller (⁠ ρ1+ρ3 ⁠) 0.878 0.002 −0.449 −0.421 −0.817 (0.000) (0.021) (0.239) (0.460) (0.817) Difference (⁠ ρ3 ⁠) −2.036 −2.504 −3.431 −3.309 −3.526 (0.210) (0.251) (0.207) (0.312) (0.362) N 18,904 18,904 18,904 18,904 18,904 R2 .012 .010 .010 .009 .009 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ρ1 ⁠) 7.510*** 7.013*** 7.328*** 7.200*** 7.024*** (0.000) (0.000) (0.000) (0.001) (0.007) Seller (⁠ ρ1+ρ3 ⁠) 6.571*** 4.060** 2.462 1.910 .0681 (0.001) (0.002) (0.008) (0.007) (0.025) Difference (⁠ ρ3 ⁠) −0.939 −2.953 −4.866 −5.290 −6.343 (0.563) (0.206) (0.111) (0.193) (0.192) N 16,000 16,000 16,000 16,000 16,000 R2 .099 .082 .063 .053 .046 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes This table presents the results from DDD regressions indicating the effect of the short selling ban on signed realized spread for large stocks (panel A) and small stocks (panel B) using 1- to 5-minute time horizons to compute the realized spread in basis points presented in columns 1 through 5, respectively. Small stocks are those stocks that have a market cap in NYSE deciles 3–5, and large stocks are those stocks subject to the short selling ban and that have a market cap in the five largest NYSE deciles as of December 31, 2007. Each banned stock is matched to a control stock based on listing exchange, options status, dollar volume, and market cap. Equally weighted adverse selection and the realized spread are computed for each stock each day. Then the difference in daily average adverse selection and realized spread between a banned stock and its matched control is computed and is the dependent variable used in the DDD regressions. Presented in the table are the estimated coefficients from the below regression for the effect of the short selling ban on realized spread: RESPi,t,sB,Δt-RESPi,t,sC,Δt=ρ0+ρ1Bant+ρ2SIi,s+ρ3Bant*SIi,s+ΓXi,t,s+νi+εi,t,s ⁠. In this specification, the coefficient ρ1 indicates the effect of the short selling ban on buyer-initiated realized spread, the sum of coefficients ρ1+ρ3 indicates the seller-initiated effect, and the coefficient ρ3 indicates the difference between the buyer- and seller-initiated effect. p-values testing the hypothesis that the relevant coefficients are equal to zero are presented in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 6 Effect of the ban on the signed realized spread A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ρ1 ⁠) 2.914*** 2.506** 2.982** 2.888* 2.709 (0.001) (0.021) (0.018) (0.056) (0.127) Seller (⁠ ρ1+ρ3 ⁠) 0.878 0.002 −0.449 −0.421 −0.817 (0.000) (0.021) (0.239) (0.460) (0.817) Difference (⁠ ρ3 ⁠) −2.036 −2.504 −3.431 −3.309 −3.526 (0.210) (0.251) (0.207) (0.312) (0.362) N 18,904 18,904 18,904 18,904 18,904 R2 .012 .010 .010 .009 .009 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ρ1 ⁠) 7.510*** 7.013*** 7.328*** 7.200*** 7.024*** (0.000) (0.000) (0.000) (0.001) (0.007) Seller (⁠ ρ1+ρ3 ⁠) 6.571*** 4.060** 2.462 1.910 .0681 (0.001) (0.002) (0.008) (0.007) (0.025) Difference (⁠ ρ3 ⁠) −0.939 −2.953 −4.866 −5.290 −6.343 (0.563) (0.206) (0.111) (0.193) (0.192) N 16,000 16,000 16,000 16,000 16,000 R2 .099 .082 .063 .053 .046 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes A. Large stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ρ1 ⁠) 2.914*** 2.506** 2.982** 2.888* 2.709 (0.001) (0.021) (0.018) (0.056) (0.127) Seller (⁠ ρ1+ρ3 ⁠) 0.878 0.002 −0.449 −0.421 −0.817 (0.000) (0.021) (0.239) (0.460) (0.817) Difference (⁠ ρ3 ⁠) −2.036 −2.504 −3.431 −3.309 −3.526 (0.210) (0.251) (0.207) (0.312) (0.362) N 18,904 18,904 18,904 18,904 18,904 R2 .012 .010 .010 .009 .009 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes B. Small stocks 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) Buyer (⁠ ρ1 ⁠) 7.510*** 7.013*** 7.328*** 7.200*** 7.024*** (0.000) (0.000) (0.000) (0.001) (0.007) Seller (⁠ ρ1+ρ3 ⁠) 6.571*** 4.060** 2.462 1.910 .0681 (0.001) (0.002) (0.008) (0.007) (0.025) Difference (⁠ ρ3 ⁠) −0.939 −2.953 −4.866 −5.290 −6.343 (0.563) (0.206) (0.111) (0.193) (0.192) N 16,000 16,000 16,000 16,000 16,000 R2 .099 .082 .063 .053 .046 Stock FE Yes Yes Yes Yes Yes Date clustered SE Yes Yes Yes Yes Yes This table presents the results from DDD regressions indicating the effect of the short selling ban on signed realized spread for large stocks (panel A) and small stocks (panel B) using 1- to 5-minute time horizons to compute the realized spread in basis points presented in columns 1 through 5, respectively. Small stocks are those stocks that have a market cap in NYSE deciles 3–5, and large stocks are those stocks subject to the short selling ban and that have a market cap in the five largest NYSE deciles as of December 31, 2007. Each banned stock is matched to a control stock based on listing exchange, options status, dollar volume, and market cap. Equally weighted adverse selection and the realized spread are computed for each stock each day. Then the difference in daily average adverse selection and realized spread between a banned stock and its matched control is computed and is the dependent variable used in the DDD regressions. Presented in the table are the estimated coefficients from the below regression for the effect of the short selling ban on realized spread: RESPi,t,sB,Δt-RESPi,t,sC,Δt=ρ0+ρ1Bant+ρ2SIi,s+ρ3Bant*SIi,s+ΓXi,t,s+νi+εi,t,s ⁠. In this specification, the coefficient ρ1 indicates the effect of the short selling ban on buyer-initiated realized spread, the sum of coefficients ρ1+ρ3 indicates the seller-initiated effect, and the coefficient ρ3 indicates the difference between the buyer- and seller-initiated effect. p-values testing the hypothesis that the relevant coefficients are equal to zero are presented in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 6 documents evidence consistent with the prediction that the increase in realized spread will be concentrated on the buy side of the market. On the buy side of the market, large stocks experience an increase in realized spread of approximately 3 basis points. For small stocks the increase is approximately 7 basis points. Whereas on the sell side of the market the effect of the ban on realized spread is not clear. For large stocks, the sum of coefficients ρ1+ρ3 indicating the effect of the short selling ban on sell side realized spread is not significant in any specification, and negative in three of them. For small stocks, the effect of the ban on sell side realized spread is positive and significant when employing time horizons of 1 and 2 minutes but attenuates and is statistically indistinguishable from zero at longer time horizons. Recall that outside the ban, the average effective spreads paid by traders for large and small stocks is 7 and 18 basis points, respectively. Consequently, the increase in buy side realized spread of approximately 3 and 7 basis points for large and small stocks represents an increase in transaction costs equal to approximately 40% or 45% of total transaction costs paid outside the ban for large and small stocks, respectively. This is an economically meaningful increase, but smaller than the observed increase in adverse selection presented in the prior section, a difference that will be explored in greater depth in Section 2.3.3. Figure 3 presents a graphical description of the regression results presented in Tables 5 and 6 and is similar to Figure 2 in the prior section. Each point in each series indicates the observed coefficient κ1 ⁠, ρ1 ⁠, or the sum of coefficients ρ1+ρ3 from the DD or DDD regressions corresponding to Equations (21) and (22) for a given time horizon used to compute the realized spread. Time horizons are varied from 60 to 300 seconds. The vertical axis represents the magnitude of the effect in basis points, and the horizontal axis represents the time horizon used to compute the realized spread. The dashed line represents the effect of the short selling ban on sell side realized spread (coefficients ρ1+ρ3 from Equation (22)). The fine dotted line represents the effect of the ban on buy side realized spread (coefficient ρ1 from Equation (22)), and the solid line represents the aggregate effect of the ban on realized spread (⁠ κ1 from Equation (21)). Figure 3 illustrates that the effect of the ban on buy side realized spread is positive and stable across all time horizons for both large and small stocks. Figure 3 Open in new tabDownload slide Regression results for the impact of the short selling ban on realized spread This figure presents the coefficients from regressions estimating the effect of the short selling ban on realized spread. Realized spread is measured from DTAQ data employing time horizons from 60 to 300 seconds as described in Section 2.2. The effect of the ban on aggregate and buyer and seller-initiated realized spread is estimated using Equations (21) and (22). Coefficients from these regressions are plotted in this figure. The effect of the ban on aggregate realized spread is indicated by the coefficient κ1 from Equation (21), is plotted as the solid line. The effect of the ban on buyer-initiated realized spread is indicated by the coefficient ρ1 from Equation (22) and is represented by the fine dotted line. The effect of the ban on seller-initiated realized spread is the sum of coefficients ρ1+ρ3 from Equation (22) and is represented by the dashed line. The horizontal axis represents the time frame used to measure realized spread, and the vertical axis represents the observed value of the indicated coefficients in basis points. Panel A presents the results for large stocks, and panel B presents the results for small stocks. Figure 3 Open in new tabDownload slide Regression results for the impact of the short selling ban on realized spread This figure presents the coefficients from regressions estimating the effect of the short selling ban on realized spread. Realized spread is measured from DTAQ data employing time horizons from 60 to 300 seconds as described in Section 2.2. The effect of the ban on aggregate and buyer and seller-initiated realized spread is estimated using Equations (21) and (22). Coefficients from these regressions are plotted in this figure. The effect of the ban on aggregate realized spread is indicated by the coefficient κ1 from Equation (21), is plotted as the solid line. The effect of the ban on buyer-initiated realized spread is indicated by the coefficient ρ1 from Equation (22) and is represented by the fine dotted line. The effect of the ban on seller-initiated realized spread is the sum of coefficients ρ1+ρ3 from Equation (22) and is represented by the dashed line. The horizontal axis represents the time frame used to measure realized spread, and the vertical axis represents the observed value of the indicated coefficients in basis points. Panel A presents the results for large stocks, and panel B presents the results for small stocks. The finding that the increase in realized spread during the ban appears to be concentrated on the buy side of the market is consistent with the notion that removing short sellers is likely to hurt liquidity because short sellers provide liquidity when they trade passively with a liquidity demanding buyer. Consequently, the removal of passive—liquidity-providing—short sales during the ban negatively shocks liquidity supply on the buy side of the market resulting in wider realized spreads for buyers. 2.3.3 Comparing the adverse selection and realized spread channels The prior two sections document that the ban was associated with an increase in both adverse selection and realized spread. In this section, I provide an analysis comparing the magnitude of these two effects with one another. The purpose of this analysis is to highlight the economic magnitude—and thus relevance—of the relatively unexamined adverse selection channel linking short selling and liquidity. Empirically, effective spreads can be affected through one of four channels: adverse selection on the buy and sell sides of the market and realized spread on the buy and sell sides of the market. Figure 4 displays the economic magnitude of the effect of the ban on each of these four channels with respect to one another by combining Figures 2 and 3, which plot the effect of the ban on adverse selection and realized spread using DD and DDD regressions. Figure 4 Open in new tabDownload slide Comparing the adverse selection and realized spread channels This figure combines Figures 2 and 3 to compare the effect of the ban on transaction costs through both the adverse selection and realized spread channels. Each point represents the estimated coefficient indicating the effect of the short selling ban on one of the given channels obtained from DD and DDD regressions estimated from Equations (19) through (22). The time horizon used to measure adverse selection and realized spread varies from 60 to 300 seconds as indicated on the horizontal axis, the vertical axis indicates the magnitude of the observed effect in basis points. The lines with x markers represent the effect of the ban on adverse selection, and the lines without x markers represent the effect of the ban on realized spread. The solid lines represent the aggregate effect of the ban; the dashed lines represent the effect on the seller-initiated side of the market; the fine dotted lines represent the effect of the ban on the buyer-initiated side of the market. Panel A presents the results for large stocks, and panel B presents the results for small stocks. Figure 4 Open in new tabDownload slide Comparing the adverse selection and realized spread channels This figure combines Figures 2 and 3 to compare the effect of the ban on transaction costs through both the adverse selection and realized spread channels. Each point represents the estimated coefficient indicating the effect of the short selling ban on one of the given channels obtained from DD and DDD regressions estimated from Equations (19) through (22). The time horizon used to measure adverse selection and realized spread varies from 60 to 300 seconds as indicated on the horizontal axis, the vertical axis indicates the magnitude of the observed effect in basis points. The lines with x markers represent the effect of the ban on adverse selection, and the lines without x markers represent the effect of the ban on realized spread. The solid lines represent the aggregate effect of the ban; the dashed lines represent the effect on the seller-initiated side of the market; the fine dotted lines represent the effect of the ban on the buyer-initiated side of the market. Panel A presents the results for large stocks, and panel B presents the results for small stocks. Figure A1 Open in new tabDownload slide Impact of a short selling ban on price efficiency This figure shows the impact of a short selling ban on price efficiency for various values of c and k. In both panels, the shaded region represents the feasible region given Assumptions 1, and 2, the constraint that λnNoSS*>0 ⁠, and the given values of η and γ ⁠. The black-shaded region indicates the region where a ban decreases price efficiency, and the gray region represents the region where price efficiency increases during a short selling ban. Figure A1 Open in new tabDownload slide Impact of a short selling ban on price efficiency This figure shows the impact of a short selling ban on price efficiency for various values of c and k. In both panels, the shaded region represents the feasible region given Assumptions 1, and 2, the constraint that λnNoSS*>0 ⁠, and the given values of η and γ ⁠. The black-shaded region indicates the region where a ban decreases price efficiency, and the gray region represents the region where price efficiency increases during a short selling ban. What becomes apparent from this figure is that the largest single effect that the ban appears to have on transaction costs comes through sell side adverse selection. For large stocks, this effect is nearly twice as large as the second largest effect, that of buy side realized spread. This finding is important, because most of the literature linking short selling to liquidity highlights the liquidity provision role of short sellers, and Figure 4 shows that, in the context of the 2008 short selling ban, these effects were secondary in magnitude compared to the effect of the ban on adverse selection. To test the hypothesis that the informational effect of the ban on transaction costs, through its effect on adverse selection, is greater than the realized spread channel, I use DDD regressions. In these regressions, the data set employed to test the effect of the ban on aggregated adverse selection, presented in Table 3, is combined with the data set employed to test the effect of the ban on aggregated realized spread, presented in Table 5. DDD regression are used to test whether the effect of the ban on transaction costs through the adverse selection channel is greater than its effect through the realized spread channel. I omit the full results for brevity’s sake, and because the coefficients, indicating the differential effect of the ban can be obtained by simply subtracting the results in Table 3 from those in Table 5. What is of interest is the test of significance for the coefficient indicating the difference between the two economic channels. For both large and small stocks, the measured effect of the ban on adverse selection is larger than the effect of the ban on realized spread in every case except for small stocks at the 1-minute horizon. This difference is statistically significant across every time horizon employed to measure adverse selection and realized spread for large stocks. For small stocks the effect of the ban on adverse selection is statistically greater than the effect on adverse selection for time horizons longer than 2 minutes. With time horizons shorter than 2 minutes, the difference is statistically insignificant. These tests document that during the 2008 short selling ban, the effect of the ban on liquidity through adverse selection appears to dominate the ban’s effect on liquidity through the realized spread. 2.3.4 Effective spread Adverse selection and realized spread sum to equal the effective spread, which is the total cost paid to execute a trade and provides one of the primary indicators of liquidity in financial markets. The prior sections document that the ban’s impact on the adverse selection portion of the effective spread is concentrated on the sell side of the market and that the ban’s effect on the realized spread portion is concentrated on the buy side. In this section, I explore how these two effects aggregate to affect the total transaction costs paid by liquidity demanders during the short selling ban. I explore the effect of the ban on effective spreads using the same basic DD and DDD regression frameworks that have been used previously. In these models, the dependent variable is the difference in equally weighted daily average effective spread between a banned stock and its matched control for a given day. In Equation (23), which measures the aggregate effect of the ban, effective spreads are averaged across all trades regardless of the sign. In Equation (24), effective spreads are averaged across the buy and sell sides of the market separately allowing me to study the differential effect that the ban has on the buy and sell sides of the market. All super and subscripts are the same as those use in previous regressions. The same control variables are also used as in the prior sections, and both specifications include stock pair fixed effects and standard errors are clustered at the date level. ESPi,tB-ESPi,tC=γ0+γ1Bant+ΓXi,t+νi+εit,(23) ESPi,t,sB-ESPi,t,sC=β0+β1Bant+β2SIi,s+β3Bant*SIi,s+ΓXi,t,s+νi+εi,t,s.(24) The coefficient identifying the aggregate effect of the short selling ban on effective spreads from Equation (23) is γ1 ⁠, the coefficient identifying the buy side effect is β1 from Equation (24) and the sum of coefficients β1+β3 (from Equation (24)) indicate the effect of the ban on seller-initiated effective spreads. Table 7 presents the results from these regressions. Table 7 Effect of the ban on effective spread A. Aggregate effect Large stocks(1) Small stocks(2) Total effect (⁠ γ1 ⁠) 4.770*** 12.66*** (0.000) (0.000) N 9,452 8,000 R2 .618 .469 Stock FE Yes Yes Date clustered SE Yes Yes B. Signed effect Large stocks(1) Small stocks(2) Buyer-initiated effect (⁠ β1 ⁠) 3.773*** 10.11*** (0.000) (0.000) Seller-initiated effect (⁠ β1+β3 ⁠) 5.596*** 15.317*** (0.000) (0.000) Difference (⁠ β2 ⁠) 1.823*** 5.207*** (0.000) (0.000) N 18,904 16,000 R2 .581 .434 Stock FE Yes Yes Date clustered SE Yes Yes A. Aggregate effect Large stocks(1) Small stocks(2) Total effect (⁠ γ1 ⁠) 4.770*** 12.66*** (0.000) (0.000) N 9,452 8,000 R2 .618 .469 Stock FE Yes Yes Date clustered SE Yes Yes B. Signed effect Large stocks(1) Small stocks(2) Buyer-initiated effect (⁠ β1 ⁠) 3.773*** 10.11*** (0.000) (0.000) Seller-initiated effect (⁠ β1+β3 ⁠) 5.596*** 15.317*** (0.000) (0.000) Difference (⁠ β2 ⁠) 1.823*** 5.207*** (0.000) (0.000) N 18,904 16,000 R2 .581 .434 Stock FE Yes Yes Date clustered SE Yes Yes This table presents the results for regressions testing the effect of the short selling ban on effective spreads for large and small stocks. The effective spread is computed as the equally weighted daily average effective spread. The total effect of the short selling ban on effective spreads is estimated using the difference-in-differences regression from Equation (23). In this regression, the dependent variable is the difference in daily average effective spread between a banned stock and its matched control. The effect of the short selling ban on buyer- and seller-initiated effective spread is estimated using the following difference-in-difference-in-differences regression from Equation (24). In this regression, the equally weighted average effective spread is computed daily for buyer and seller-initiated trades, where trades are signed using the Lee and Ready (1991) algorithm. The dependent variable is the difference in equally weighted average effective spread between a banned stock and its matched control on a given day for either all buy or sell trades. This table presents only the coefficients indicating the effect of the short selling ban on effective spreads. The coefficient γ1from Equation (23) indicates the total effect of the short selling ban on transaction costs. The coefficient β1 from Equation (24) indicates the effect of the ban on buyer-initiated trades, and the sum of β1+β2 indicates the effect of the ban on seller-initiated trades. Significance for the seller-initiated effect is determined by an F-test of joint significance. Panel A presents the aggregate effect of the ban on effective spread, and panel B presents the signed effect of the ban on effective spread. p-values are provided in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 7 Effect of the ban on effective spread A. Aggregate effect Large stocks(1) Small stocks(2) Total effect (⁠ γ1 ⁠) 4.770*** 12.66*** (0.000) (0.000) N 9,452 8,000 R2 .618 .469 Stock FE Yes Yes Date clustered SE Yes Yes B. Signed effect Large stocks(1) Small stocks(2) Buyer-initiated effect (⁠ β1 ⁠) 3.773*** 10.11*** (0.000) (0.000) Seller-initiated effect (⁠ β1+β3 ⁠) 5.596*** 15.317*** (0.000) (0.000) Difference (⁠ β2 ⁠) 1.823*** 5.207*** (0.000) (0.000) N 18,904 16,000 R2 .581 .434 Stock FE Yes Yes Date clustered SE Yes Yes A. Aggregate effect Large stocks(1) Small stocks(2) Total effect (⁠ γ1 ⁠) 4.770*** 12.66*** (0.000) (0.000) N 9,452 8,000 R2 .618 .469 Stock FE Yes Yes Date clustered SE Yes Yes B. Signed effect Large stocks(1) Small stocks(2) Buyer-initiated effect (⁠ β1 ⁠) 3.773*** 10.11*** (0.000) (0.000) Seller-initiated effect (⁠ β1+β3 ⁠) 5.596*** 15.317*** (0.000) (0.000) Difference (⁠ β2 ⁠) 1.823*** 5.207*** (0.000) (0.000) N 18,904 16,000 R2 .581 .434 Stock FE Yes Yes Date clustered SE Yes Yes This table presents the results for regressions testing the effect of the short selling ban on effective spreads for large and small stocks. The effective spread is computed as the equally weighted daily average effective spread. The total effect of the short selling ban on effective spreads is estimated using the difference-in-differences regression from Equation (23). In this regression, the dependent variable is the difference in daily average effective spread between a banned stock and its matched control. The effect of the short selling ban on buyer- and seller-initiated effective spread is estimated using the following difference-in-difference-in-differences regression from Equation (24). In this regression, the equally weighted average effective spread is computed daily for buyer and seller-initiated trades, where trades are signed using the Lee and Ready (1991) algorithm. The dependent variable is the difference in equally weighted average effective spread between a banned stock and its matched control on a given day for either all buy or sell trades. This table presents only the coefficients indicating the effect of the short selling ban on effective spreads. The coefficient γ1from Equation (23) indicates the total effect of the short selling ban on transaction costs. The coefficient β1 from Equation (24) indicates the effect of the ban on buyer-initiated trades, and the sum of β1+β2 indicates the effect of the ban on seller-initiated trades. Significance for the seller-initiated effect is determined by an F-test of joint significance. Panel A presents the aggregate effect of the ban on effective spread, and panel B presents the signed effect of the ban on effective spread. p-values are provided in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Among large and small stocks, the total effect (⁠ γ1 ⁠) of the ban on effective spreads amounts to a statistically significant increase of 4.8 and 12.7 basis points, respectively. Relative to the average effective spreads paid outside the ban, these magnitudes indicate that the ban is associated with an increase in effective spread of 68% and 84% for large and small stocks, respectively. When the effect of the short selling ban on effective spread is divided into its effect on the buy and sell sides of the market in Equation (24), the results indicate that among both large and small stocks, seller-initiated trades experience an increase in effective spread that is approximately 50% larger than the increase experienced by buyer-initiated trades. This asymmetry is to be expected given the prior findings that the ban’s effect on adverse selection appears to dominate the ban’s effect on realized spread, and that the increase in adverse selection is concentrated on the sell side of the market. For large stocks average seller (buyer) initiated effective spread increases by 5.6 (3.7) basis points. For small stocks, the effect of the ban on seller (buyer) initiated effective spread is equal to 15.3 (10.1) basis points. For large (small) stocks, this amounts to an increase in the cost of transacting of 70% and 53% (102% and 80%) on the sell and buy sides of the market, respectively.18 The cost of transacting is a key indicator of liquidity in financial markets, and the finding that the short selling ban deteriorates sell side liquidity significantly more than buy side liquidity has potential regulatory implications. Maintaining sell side liquidity—particularly during periods of downward price pressure—is important to preserving market stability (Huang and Wang 2008). Consequently, regulations that restrict short selling during periods of downward price pressure may have the unintended effect of diminishing sell side liquidity when it is most needed. 3. DV Restriction A potential alternative explanation for the increase in sell side adverse selection during the ban is provided by DV. DV study the impact of a short selling restriction and short selling prohibition on the information content of prices. In their model, a prohibition prevents all traders from short selling and a restriction prevents traders from accessing the proceeds of a short sale. A DV restriction only prevents liquidity traders from short selling. In a DV prohibition there is no change in adverse selection because “the prohibition applies to informed and uninformed alike, implying that it leaves the fraction of informed traders remaining in the pool of ‘sell-or-short’ transactions unchanged. As a result, it leaves unchanged the information content of actually observing a ‘sell-or-short’” (p. 289). On the other hand, a restriction in DV leads to an increase in sell side adverse selection, because when investors cannot use the proceeds from a short sale, then short selling is no longer a means of raising capital for liquidity traders and as a result uninformed short sellers no longer transact. Informed traders however do not require access to the proceeds of a short sale to profit from their information and so a restriction does not limit their trading. Consequently, a restriction in DV only removes uninformed short sellers from the market increasing the likelihood that a sell-or-short trade originates from an informed trader. A DV restriction is analogous to the intermediate case of my model presented in Section 1.4. Empirically differentiating between the predictions in my model and those of DV in terms of their predictions for adverse selection requires determining whether the 2008 ban resembled a DV type ban or restriction. If informed short sellers were able to circumvent the ban by trading in options markets, as argued by Kolasinski, Reed, and Thornock (2013), then the ban may be characterized by a DV restriction. In contrast, Battalio and Schultz (2011, p. 2015) argue that their study “refute[s] the argument that short sale restrictions, or indeed many regulations, can be circumvented by trading in the options markets.” To differentiate between these two possibilities, I begin by noting that in DV, the more the market is characterized by a restriction, compared to a ban, the greater will be the impact on adverse selection. To see this effect in DV, consider a one-period DV model. The bid price is set equal to the expected value of the asset given that a sell/short trade arrives.19 Equation (25) shows the bid price in the one-period DV model. In DV, all investors face one of three short selling regimes: no restriction, a restriction, or a ban. A restriction prevents uninformed traders, but not informed traders, from short selling, whereas a ban prevents all traders from short selling. The likelihood that a given investor faces no restriction or a restriction is defined as c1, and c2 ⁠. The likelihood that an investor faces a ban is simply 1-c1-c2. Unrestricted short selling occurs when c1=1 and c2=0 ⁠. All investors face a restriction when c2=1 and c1=0. A ban is characterized by c1=0 and c2=0 ⁠. γ represents the likelihood a given investor owns the asset and λ is the exogenous fraction of informed traders in the economy. Equation (26) presents the DV bid price when there are no short selling constraints. Equation (27) presents the DV bid price during a short selling ban, and Equation (28) presents the DV bid price when there is a short selling restriction. BidDV=121-λγ+1-λ1-γc1γ+1-γc1+λ1-γc2,(25) BidDVNo Constraints=121-λ,(26) BidDVBan=121-λ,(27) BidDVRestriction=12γ1-λλ+γ1-λ.(28) To explore how adverse selection on the sell side of the market is affected in DV as the market becomes more characterized by a ban instead of a restriction, I assume that all investors face either a short selling restriction or a ban, that is, c1=0 and 0≤c2≤1 ⁠. Equation (29) presents the DV bid price for this scenario: BidDVRest or Ban=121-λγγ+λ1-γc2(29) In Equation (29), when c2 equals zero the market is characterized by a ban, as c2 increases to one, the market becomes more characterized by a restriction. In Equation (29), as c2 increases, the denominator clearly gets bigger and so BidDV decreases. This indicates that, in the context of DV, sell side adverse selection increases the more an event becomes characterized by a restriction, as opposed to a ban. I explore this prediction empirically in the context of the 2008 short selling ban by testing whether the ban affected stocks with and without listed options differently. Compared to stocks with listed options it would be more difficult to circumvent the ban for stocks without listed options. Consequently, the 2008 short selling ban is closer to a DV restriction for stocks with listed options and closer to a ban for stocks without. Consequently, in this test, DV predicts that the ban will have a stronger effect on sell side adverse selection among stocks with listed options, that is, stocks for which the ban more closely resembles a restriction. Two factors may bias this test against finding a result. First, I cannot rule out the possibility that investors were able to use over-the-counter options to circumvent the ban for stocks without listed options. In this case, differentiating stocks based on options status would not provide a valid test since one could argue that investors could circumvent the ban for both groups of stocks causing both groups to be characterized by a DV restriction. Second, during the ban, the SEC issued guidance prohibiting options market makers from executing a trade if they knew that the counterparty was building an economic short position. To the extent that this guidance was effective at preventing investors from using options to create short positions, investors would not have been able to circumvent the ban in options markets. Consequently, there would be little to differentiate the effect of the ban on stocks with and without listed options. I concentrate exclusively on small stocks for this test because nearly all large stocks (96%) have listed options, and so making meaningful statistical comparisons for large stocks is econometrically dubious. Among small stocks the ratio is approximately one-third do not have listed options and two-thirds do have listed options. To create a sample of stocks with listed options that is as similar as possible to the sample without listed options I match without replacement each stock subject to the ban without listed options to a stock subject to the ban with listed options based on listing exchange, market capitalization and dollar trading volume. Market capitalization and dollar trading volume are computed using averages from August 1, 2008, to September 18, 2008 (the day before the ban). I then use the same distance measure as employed in Section 2 to match a stock without listed options to a stock that is listed on the same exchange with listed options.20 To determine whether the ban affects adverse selection differently for stocks with and without listed options, I split the sample into the buy and sell sides of the market and estimate two separate DDD regressions, similar to those estimated in Table 4, which determine whether the ban’s impact on adverse selection is greater for stocks with compared to without listed options. As shown in Equation (30), the dependent variable in these regressions is the same as employed in Table 4. Independent variables include an indicator for whether the ban is in force on a given day, an interaction between an indicator variable for listed options and the ban and a matrix of control variables that are the same as those included in the regressions presented in Table 4. The regressions include firm-pair fixed effects and standard errors are clustered at the date level. Adverse selection is measure using time horizons of from 1 to 5 minutes. ASi,t,sB,Δt-ASi,t,sC,Δt=ξ0+ξ1Bant+ξ2Bant*Optionsi,s+ΓXi,t,s+νi+εit(30) In Equation (30), the coefficient ξ1 indicates the effect of the ban on stocks without listed options while the sum of coefficients ξ1+ξ3 provide the ban’s impact on stocks with listed options. ξ3 tests the differential effect of the ban on stocks with and without options. The results in Table 8 indicate that the ban had a significantly stronger impact on sell side adverse selection for stocks without listed options, a finding that is opposite to the predictions of DV. This difference is economically meaningful as panel A of Table 8 shows that for stocks without listed options, the ban’s impact on sell side adverse selection is approximately twice as large as it is for stocks with listed options and is statistically significant in every specification. Table 8 Options and adverse selection during the ban A. Options status and sell side adverse selection during the ban 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) No options (⁠ ξ1) 12.04*** 15.87*** 19.40*** 20.76*** 22.60*** (0.000) (0.000) (0.000) (0.000) (0.000) Options (⁠ ξ1+ξ3) 5.75*** 7.74*** 9.42*** 9.53*** 11.02*** (0.001) (0.000) (0.000) (0.002) (0.001) Difference (ξ3) −6.294*** −8.130*** −9.980*** −11.23*** −11.58*** (0.000) (0.000) (0.000) (0.000) (0.000) N 5,144 5,144 5,144 5,144 5,144 R2 .413 .389 .409 .399 .407 Date clustered SE Yes Yes Yes Yes Yes Firm-pair FE Yes Yes Yes Yes Yes B. Options status and buy side adverse selection during the ban 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) No options (⁠ ξ1) 3.241* 3.941** 2.201 2.586 2.771 (0.060) (0.033) (0.348) (0.290) (0.315) Options (⁠ ξ1+ξ3) 0.81 1.44 1.04 0.8 0.92 (0.58) (0.363) (0.557) (0.707) (0.684) Difference (ξ3) −2.436 −2.503 −1.161 −1.785 −1.853 (0.230) (0.277) (0.652) (0.511) (0.551) N 5,144 5,144 5,144 5,144 5,144 R2 .463 .477 .463 .474 .457 Date clustered SE Yes Yes Yes Yes Yes Firm-pair FE Yes Yes Yes Yes Yes A. Options status and sell side adverse selection during the ban 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) No options (⁠ ξ1) 12.04*** 15.87*** 19.40*** 20.76*** 22.60*** (0.000) (0.000) (0.000) (0.000) (0.000) Options (⁠ ξ1+ξ3) 5.75*** 7.74*** 9.42*** 9.53*** 11.02*** (0.001) (0.000) (0.000) (0.002) (0.001) Difference (ξ3) −6.294*** −8.130*** −9.980*** −11.23*** −11.58*** (0.000) (0.000) (0.000) (0.000) (0.000) N 5,144 5,144 5,144 5,144 5,144 R2 .413 .389 .409 .399 .407 Date clustered SE Yes Yes Yes Yes Yes Firm-pair FE Yes Yes Yes Yes Yes B. Options status and buy side adverse selection during the ban 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) No options (⁠ ξ1) 3.241* 3.941** 2.201 2.586 2.771 (0.060) (0.033) (0.348) (0.290) (0.315) Options (⁠ ξ1+ξ3) 0.81 1.44 1.04 0.8 0.92 (0.58) (0.363) (0.557) (0.707) (0.684) Difference (ξ3) −2.436 −2.503 −1.161 −1.785 −1.853 (0.230) (0.277) (0.652) (0.511) (0.551) N 5,144 5,144 5,144 5,144 5,144 R2 .463 .477 .463 .474 .457 Date clustered SE Yes Yes Yes Yes Yes Firm-pair FE Yes Yes Yes Yes Yes This table describes the impact of the ban on adverse selection separately for small stocks with and without listed options. Each small stock without listed options subject to the ban is matched without replacement to a stock subject to the ban with listed options based on listing exchange size and dollar trading volume. DDD regressions are estimated for the buy and sell sides of the market separately determining whether the ban affects adverse selection differently for stocks with and without listed options. Regressions for the sell side of the market are in Panel A, and the buy side of the market is in Panel B. Columns 1 through 5 of panels A and B estimate adverse selection costs using a 1- to 5-minute time horizon, respectively. p-values are included in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 8 Options and adverse selection during the ban A. Options status and sell side adverse selection during the ban 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) No options (⁠ ξ1) 12.04*** 15.87*** 19.40*** 20.76*** 22.60*** (0.000) (0.000) (0.000) (0.000) (0.000) Options (⁠ ξ1+ξ3) 5.75*** 7.74*** 9.42*** 9.53*** 11.02*** (0.001) (0.000) (0.000) (0.002) (0.001) Difference (ξ3) −6.294*** −8.130*** −9.980*** −11.23*** −11.58*** (0.000) (0.000) (0.000) (0.000) (0.000) N 5,144 5,144 5,144 5,144 5,144 R2 .413 .389 .409 .399 .407 Date clustered SE Yes Yes Yes Yes Yes Firm-pair FE Yes Yes Yes Yes Yes B. Options status and buy side adverse selection during the ban 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) No options (⁠ ξ1) 3.241* 3.941** 2.201 2.586 2.771 (0.060) (0.033) (0.348) (0.290) (0.315) Options (⁠ ξ1+ξ3) 0.81 1.44 1.04 0.8 0.92 (0.58) (0.363) (0.557) (0.707) (0.684) Difference (ξ3) −2.436 −2.503 −1.161 −1.785 −1.853 (0.230) (0.277) (0.652) (0.511) (0.551) N 5,144 5,144 5,144 5,144 5,144 R2 .463 .477 .463 .474 .457 Date clustered SE Yes Yes Yes Yes Yes Firm-pair FE Yes Yes Yes Yes Yes A. Options status and sell side adverse selection during the ban 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) No options (⁠ ξ1) 12.04*** 15.87*** 19.40*** 20.76*** 22.60*** (0.000) (0.000) (0.000) (0.000) (0.000) Options (⁠ ξ1+ξ3) 5.75*** 7.74*** 9.42*** 9.53*** 11.02*** (0.001) (0.000) (0.000) (0.002) (0.001) Difference (ξ3) −6.294*** −8.130*** −9.980*** −11.23*** −11.58*** (0.000) (0.000) (0.000) (0.000) (0.000) N 5,144 5,144 5,144 5,144 5,144 R2 .413 .389 .409 .399 .407 Date clustered SE Yes Yes Yes Yes Yes Firm-pair FE Yes Yes Yes Yes Yes B. Options status and buy side adverse selection during the ban 1 minute(1) 2 minutes(2) 3 minutes(3) 4 minutes(4) 5 minutes(5) No options (⁠ ξ1) 3.241* 3.941** 2.201 2.586 2.771 (0.060) (0.033) (0.348) (0.290) (0.315) Options (⁠ ξ1+ξ3) 0.81 1.44 1.04 0.8 0.92 (0.58) (0.363) (0.557) (0.707) (0.684) Difference (ξ3) −2.436 −2.503 −1.161 −1.785 −1.853 (0.230) (0.277) (0.652) (0.511) (0.551) N 5,144 5,144 5,144 5,144 5,144 R2 .463 .477 .463 .474 .457 Date clustered SE Yes Yes Yes Yes Yes Firm-pair FE Yes Yes Yes Yes Yes This table describes the impact of the ban on adverse selection separately for small stocks with and without listed options. Each small stock without listed options subject to the ban is matched without replacement to a stock subject to the ban with listed options based on listing exchange size and dollar trading volume. DDD regressions are estimated for the buy and sell sides of the market separately determining whether the ban affects adverse selection differently for stocks with and without listed options. Regressions for the sell side of the market are in Panel A, and the buy side of the market is in Panel B. Columns 1 through 5 of panels A and B estimate adverse selection costs using a 1- to 5-minute time horizon, respectively. p-values are included in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab I also explore another prediction of a DV restriction. Since a DV restriction only removes uninformed traders from the market in their model “short-restrictions actually improve the information content of each period of trade and improve informational efficiency” (p. 293). In contrast, Proposition 7a states that in the context of my model a short selling ban will generally decrease the informativeness of stock prices. I test these competing predictions using a variance ratio test. For each banned and control stock I use intraday variance ratios using the ratio of 15- to 5-second variances VR15\5=Var15second3Var5second-1 and the ratio of 60- to 15-second variances VR60\15=Var15second3Var5second-1 ⁠. I then estimate regressions exactly analogous to those in Tables 5 and 3, except that the dependent variable is the difference in variance ratios between a banned stock and its matched control on a given day. Table 9 presents the results, which indicate, consistent with my model and prior literature, that for both large and small stocks and for both VR15\5 and VR60\15 variance ratios increase during the ban, indicating diminished price efficiency during the ban for banned stocks. Table 9 Impact on price efficiency: Variance ratio tests . Large stocks . Small stocks . . 15- to 5-second variance ratio . 60- to 15-second variance ratio . 15- to 5-second variance ratio . 60- to 15-second variance ratio . . (1) . (2) . (3) . (4) . Ban 0.0395*** 0.0194** 0.0896*** 0.0883*** (0.000) (0.019) (0.000) (0.000) N 8,797 8,797 7,400 7,400 R2 .150 .094 .271 .142 . Large stocks . Small stocks . . 15- to 5-second variance ratio . 60- to 15-second variance ratio . 15- to 5-second variance ratio . 60- to 15-second variance ratio . . (1) . (2) . (3) . (4) . Ban 0.0395*** 0.0194** 0.0896*** 0.0883*** (0.000) (0.019) (0.000) (0.000) N 8,797 8,797 7,400 7,400 R2 .150 .094 .271 .142 This table presents the results from difference-in-differences regressions estimating the impact of the short selling ban on intraday variance ratios. In columns 1 and 3 variance ratios are computed using 5- and 15-second time intervals. Columns 2 and 4 compute variance ratios using 15- and 60-second time horizons. Columns 1 and 2 indicate the ban's impact on large stocks, and columns 3 and 4 indicate the same for small stocks. Variance ratios are the absolute value of the difference between the scaled ratios and one. The dependent variable is the difference in variance ratios on a given day between a banned stock and its matched control. The indicator Ban indicates the ban's impact on variance ratios for those stocks subject to it. Control variables have been omitted for brevity. Each regression uses firm-pair fixed effects and clusters standard errors at the date level. p-values are included in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 9 Impact on price efficiency: Variance ratio tests . Large stocks . Small stocks . . 15- to 5-second variance ratio . 60- to 15-second variance ratio . 15- to 5-second variance ratio . 60- to 15-second variance ratio . . (1) . (2) . (3) . (4) . Ban 0.0395*** 0.0194** 0.0896*** 0.0883*** (0.000) (0.019) (0.000) (0.000) N 8,797 8,797 7,400 7,400 R2 .150 .094 .271 .142 . Large stocks . Small stocks . . 15- to 5-second variance ratio . 60- to 15-second variance ratio . 15- to 5-second variance ratio . 60- to 15-second variance ratio . . (1) . (2) . (3) . (4) . Ban 0.0395*** 0.0194** 0.0896*** 0.0883*** (0.000) (0.019) (0.000) (0.000) N 8,797 8,797 7,400 7,400 R2 .150 .094 .271 .142 This table presents the results from difference-in-differences regressions estimating the impact of the short selling ban on intraday variance ratios. In columns 1 and 3 variance ratios are computed using 5- and 15-second time intervals. Columns 2 and 4 compute variance ratios using 15- and 60-second time horizons. Columns 1 and 2 indicate the ban's impact on large stocks, and columns 3 and 4 indicate the same for small stocks. Variance ratios are the absolute value of the difference between the scaled ratios and one. The dependent variable is the difference in variance ratios on a given day between a banned stock and its matched control. The indicator Ban indicates the ban's impact on variance ratios for those stocks subject to it. Control variables have been omitted for brevity. Each regression uses firm-pair fixed effects and clusters standard errors at the date level. p-values are included in parentheses. * p < .1; ** p < .05; *** p < .01. Open in new tab Both the findings that the increase in sell side adverse selection during the ban is greater for stocks without listed options and that price efficiency decreases during the ban are inconsistent with the predictions of a DV restrictions. Consequently, it is unlikely that DV explains the outcomes observed in this study. Two key differences between my model and DV’s model, despite their similarities, account for the different predictions. The primary difference is that in my model the fraction of informed investors is determined in equilibrium. In DV the fraction of informed traders in the economy is exogenous and does not vary depending on whether the investor does or does not own the asset, that is, in DV by assumption λe=λn=1 ⁠. Thus, when a ban is imposed, adverse selection is not affected because the ban affects sophisticated and liquidity traders the same. The second key difference is that our models make somewhat different comparisons. My model compares the baseline equilibrium in which both liquidity and informed traders are active with a moderate cost of short selling with that of a ban. DV compares the baseline equilibrium with costless short selling to one where short selling is either banned or restricted. Costly short selling is a key part of my model in the baseline case as it drives the sophisticated traders who do and do not own the asset to behave differently. This friction is absent in DV. Taken together these two differences account for the different predictions between my model and DV. 4. Model Extensions: Institutional Ownership and Adverse Selection This section tests the hypothesis that the impact of the ban on overall and sell side adverse selection will be greater for stocks with a higher concentration of institutional ownership. To generate this hypothesis, consider how both the overall bid ask spread during the ban and the ban’s impact on sell side adverse selection are affected by η (the fraction of sophisticated traders). From Equation (16) SpreadNoSS=1-2c-1-η2 ⁠, one clearly sees that the spread during a ban is increasing in η ⁠. Similarly, the bid price during a short selling ban from Equation (15) which is BidNoSS=1-η2 is decreasing in η ⁠. Consequently, the model predicts that both total and sell side adverse selection will be increasing in η during a ban. I use institutional ownership as a proxy for η and estimate cross-sectional regressions linking institutional ownership to overall and sell side adverse selection during the short selling ban. Like the sophisticated traders in the model, institutional traders tend to be in the market for information and are willing to short sell. However, institutional ownership is correlated with other variables that may affect how the stock responds to the ban (Gompers and Metrick 2001). Thus, I follow Nagel (2005) and identify residual institutional ownership from a predictive regression as a measure of institutional holdings presented in Equation (31). This regression is estimated using the entire universe of merged CRSP and Compustat data. InstOwni,q=α+β1Sizei,q+β2Sizei,q2+β2MtBi,q+β4Illiqi,q+β5Reti,q12+ηsic2i+νq+εi,q(31) i indicates the firm, q indicates the quarter (e.g., 2002:q1), InstOwni,q is the quarterly institutional ownership for a given stock based on 13f filings and is defined as the fraction of shares outstanding held by 13f reporting institutions. Size and book-to-market are measured quarterly from Compustat following Lemmon, Roberts, and Zender (2008). Illiqi,q is the Amihud (2002) illiquidity measure and is calculated quarterly (i.e., daily illiquidity averaged across a quarter). Reti,q12 is the past 12 months return from CRSP. Specifically, for quarter one in 2002 the past 12-month return is measured as the return from March 2001 through February 2002. The model includes fixed effects at the 2 digit SIC and year level. εi,q is the residual institutional ownership for stock i during quarter q.  εi,q is divided by its standard deviation for ease in interpreting the regression coefficients. I then select the most recent value of the standardized εi,q for each banned stock as its measure of abnormal institutional ownership at the time of the ban yielding one observation of institutional ownership per banned stock for use in the cross-sectional regressions. The primary dependent variable in these tests is the average abnormal adverse selection experienced throughout the duration of the ban. This is computed for each stock both overall (that is, for buy and sell trades combined) and for buy and sell trades separately yielding either one or two observations per banned stock for use in the cross-sectional regressions. Average abnormal adverse selection is computed by first estimating the relation between the daily difference in 1-minute adverse selection between a banned and a control stock (which I define as define ΔASi,t ⁠) and a host of control variables for each stock pair from August through October 2008, while omitting days that the ban was in force.21 This regression is estimated individually for each banned stock-control stock pair. The coefficients from these regressions are saved and applied to the observations during the short selling ban to yield the expected difference in adverse selection between a banned stock and its control during the ban. These expected differences are compared to the observed differences yielding abnormal adverse selection experienced by a stock on a given day during the ban. I then compute the average of daily abnormal adverse selection across the ban. This procedure is followed to produce overall unsigned average abnormal adverse selection, yielding one observation per banned stock, and also signed average abnormal adverse selection, yielding two observations per banned stock one for the buy and sell sides of the market. I then estimate the regressions presented in Equations (32) and (33) to examine the cross-sectional relation between average abnormal adverse selection and residual institutional ownership. In Equation (32), the dependent variable Abnormal ASi is the unsigned average abnormal adverse selection for a given banned stock. In Equation (33), the dependent variable Abnormal ASi,s is the signed average abnormal adverse selection for a given banned stock. In Equation (33), there will be two observations per banned stock (one for the buy and sell sides of the market), while in Equation (32) there will be one observation only: Abnormal ASi=β0+β1Inst Hldngsi+ΓXi+εi,(32) Abnormal ASi,s=γ0+γ1Inst Hldngsi+γ2Inst Hldngsi*SIi,s+γ3SIi,s+ΓXi,s+εi.(33) In these specifications the subscript i indicates the given banned stock while the subscript s in Equation (33) indicates the sign. β1 from Equation (32) identifies the effect of a one-standard-deviation increase in residual institutional ownership on abnormal adverse selection. Equation (33) measures the relation between average abnormal adverse selection on the buy and sell sides of the market and residual institutional ownership. The hypothesis that during the ban sell side adverse selection will be greater among stocks with higher institutional ownership suggests the sum γ1+γ3 will be statistically greater than zero. Table 10 presents the results from these tests. 22 Table 10 Residual institutional ownership and abnormal adverse selection . (1) . (2) . (3) . (4) . Total effect (β1) 1.782*** 1.583** (0.009) (0.023) Buyer effect γ1 −3.460 −3.540 (0.196) (0.198) Seller effect (γ1+γ2) 7.18*** 7.10** (0.008) (0.01) Difference (γ2) 10.64*** 10.64*** (0.005) (0.005) N 255 255 510 510 R2 0.027 0.099 0.019 0.024 Control variables No Yes No Yes . (1) . (2) . (3) . (4) . Total effect (β1) 1.782*** 1.583** (0.009) (0.023) Buyer effect γ1 −3.460 −3.540 (0.196) (0.198) Seller effect (γ1+γ2) 7.18*** 7.10** (0.008) (0.01) Difference (γ2) 10.64*** 10.64*** (0.005) (0.005) N 255 255 510 510 R2 0.027 0.099 0.019 0.024 Control variables No Yes No Yes This table presents results from cross-sectional regressions indicating the effect of institutional holdings on abnormal adverse selection during the ban. Abnormal adverse selection is estimated following the process described in Section 4. Institutional ownership is estimated using data from 13f filings and is standardized so that it indicates the number of standard deviations above or below the mean a given stock’s level of institutional ownership is. Columns 1 and 2 present the effect of institutional ownership on aggregate adverse selection. Columns 3 and 4 present the effect of institutional ownership on signed adverse selection. Adverse selection is measured in basis points employing a 60-second horizon. p-values are provided in parentheses. For the seller effect, an F-test of joint significance of the variables γ1+γ2 from Equation (33) is reported. Even-numbered columns include control variables, whereas odd-numbered columns do not. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 10 Residual institutional ownership and abnormal adverse selection . (1) . (2) . (3) . (4) . Total effect (β1) 1.782*** 1.583** (0.009) (0.023) Buyer effect γ1 −3.460 −3.540 (0.196) (0.198) Seller effect (γ1+γ2) 7.18*** 7.10** (0.008) (0.01) Difference (γ2) 10.64*** 10.64*** (0.005) (0.005) N 255 255 510 510 R2 0.027 0.099 0.019 0.024 Control variables No Yes No Yes . (1) . (2) . (3) . (4) . Total effect (β1) 1.782*** 1.583** (0.009) (0.023) Buyer effect γ1 −3.460 −3.540 (0.196) (0.198) Seller effect (γ1+γ2) 7.18*** 7.10** (0.008) (0.01) Difference (γ2) 10.64*** 10.64*** (0.005) (0.005) N 255 255 510 510 R2 0.027 0.099 0.019 0.024 Control variables No Yes No Yes This table presents results from cross-sectional regressions indicating the effect of institutional holdings on abnormal adverse selection during the ban. Abnormal adverse selection is estimated following the process described in Section 4. Institutional ownership is estimated using data from 13f filings and is standardized so that it indicates the number of standard deviations above or below the mean a given stock’s level of institutional ownership is. Columns 1 and 2 present the effect of institutional ownership on aggregate adverse selection. Columns 3 and 4 present the effect of institutional ownership on signed adverse selection. Adverse selection is measured in basis points employing a 60-second horizon. p-values are provided in parentheses. For the seller effect, an F-test of joint significance of the variables γ1+γ2 from Equation (33) is reported. Even-numbered columns include control variables, whereas odd-numbered columns do not. * p < .1; ** p < .05; *** p < .01. Open in new tab Table 10 presents findings consistent with the hypothesis that during the ban both overall and sell side sell side adverse selection will be increasing in the fraction of institutional traders. Specifically, a one-standard-deviation increase in residual institutional ownership is associated with a 1.6- to 1.8-basis-point increase in overall abnormal adverse selection costs during the ban. This increase comes exclusively from the sell side of the market where the effect of institutional ownership on adverse selection is 7.1–7.2 basis points. On the buy side of the market, there is no statistically identifiable relation between adverse selection and institutional ownership, which is consistent with the model since η does not affect AskSS* or AskNoSS* ⁠. 5. Conclusion This study explores the link between short selling, adverse selection and price efficiency. In a simple rational expectations equilibrium model I show how a short selling ban affects price efficiency and adverse selection through its impact on the value of information for different types of investors. Costly short selling means that investors who do not own the asset have less incentive to gather information and thus information acquisition concentrates among investors who already own the asset. When a short selling ban is imposed investors owning the asset are the only investors allowed to sell, and since they are more informed than the average investor the likelihood that a market maker trades with an informed trader on the sell side of the market increases leading to increased sell side adverse selection. Additionally, a ban further dissuades investors not owning the asset from becoming informed leading to less overall information acquisition and thus worse price efficiency. Consistent with these predictions the effect of the 2008 short selling ban in the United States on adverse selection is asymmetric and concentrated almost exclusively on the sell side of the market and is the dominate factor contributing to increased transaction costs during the ban leading the ban to disproportionately harm sell side liquidity. I also document that price efficiency declines for stocks subjects to the ban. This analysis contributes to multiple areas of finance. First, it shows how a short selling ban simultaneously affects adverse selection and price efficiency through a trader’s decision to become informed. It also highlights the magnitude and asymmetric nature of the link between short selling and adverse selection and provides a potential explanation for why this link and asymmetry may exist. Doing so also fills a gap in the literature linking short selling and liquidity. Also, the finding that the ban disproportionately harms sell side liquidity has regulatory implications, suggesting that policies which restrict short selling during down markets may have the unintended consequence of harming sell side liquidity when markets most need it. Lastly, the model’s prediction that the inability to short sell influences the characteristics of investors who become informed has implications beyond liquidity. If fewer outside investors become informed because of an inability to trade on negative information, then the role of outside investors as monitors of the firm may diminish when short selling is restricted. Footnotes 1 Adverse selection affects liquidity because market makers lose money when they trade with informed traders and compensate for these losses by making it more expensive to transact. Based on this idea, a large literature of both theoretical and empirical work has grown examining the role of adverse selection as a key component of liquidity (see, e.g., Copeland and Galai 1983; Kyle 1985; Glosten and Milgrom 1985; Diamond and Verrecchia 1987; Glosten and Harris 1988; Stoll 1989; Eom, Ok, and Park 2007; Chung, Elder, and Kim 2010; Riordan and Storkenmaier 2012; Fotak, Raman, and Yadav 2014). Other prominent studies examining the impact of adverse selection on various other aspects of financial markets and financial decisions include Akerlof 44(1970), Leland and Pyle (1977), Miller and Rock (1985), Jullien (2000), Ross (1977), Morellec and Schürhoff (2011), and Sharpe (1990), among others. 2 See, for example, Figlewski (1981), Desai et al. (2002), Cohen, Diether, and Malloy (2007), Boehmer, Jones, and Zhang (2008), Diether, Lee, and Werner (2009), Boehmer, Huszar, and Jordan (2010), Karpoff and Lou (2010), Christophe, Ferri, and Hsieh (2010), Drake, Rees, and Swanson (2011), Kecskés, Mansi, and Zhang (2013), Boehmer and Wu (2013), Henry, Kisgen, and Wu (2015), Rapach, Ringgenberg, and Zhou (2016), Comerton-Forde, Jones, and Putniņš (2016), Kelley and Tetlock (2017), Nezafat, Schroder, and Wang (2017), and Boehmer, Duong, and Huszár, (2018), among others. 3 The term sell (buy) side of the market refers to the side of the market where the active trader is a seller (buyer). 4 See, for example, Senchack and Starks (1993) and Stambaugh, Yu, and Yuan (2012), among others. 5 Prominent studies in this literature linking short selling to liquidity include: Diether, Lee, and Werner (2009), Boehmer and Wu (2013), Boehmer, Jones, and Zhang (2013), Beber and Pagano (2013), Kaplan, Moskowitz, and Sensoy (2013), and Comerton-Forde, Jones, and Putniņš (2016) among others. 6 DV is in turn an adaptation of the model presented in Glosten and Milgrom (1985). 7 This assumption is not altogether unrealistic as investors without firm-specific information may be willing to pay the cost to short sell for hedging purposes. Exact constraints on k are presented in Assumptions 1 and 2. Section 1.4 presents a case in which k is large enough to prevent liquidity traders from short selling. 8 c+k2 is the expected cost of trading on information for sophisticated investors who do not own the asset, that is, the marginal informed investor. 1-η2 is related to the fraction of liquidity traders in the market, that is, the traders from whom the sophisticated traders profit. Consequently, 1-η2 provides an indication of the total possible trading profits available to sophisticated traders. 1-η21-η+ηγ is related to the ratio of liquidity traders to liquidity and sophisticated traders who own the asset (i.e., all traders who are not marginal investors). 1-η21-η+ηγ ⁠, it provides a measure of how much benefit to information remains after the sophisticated traders who own the asset are taken into account. In order for 0<λn<1 the expected cost to trading on information for sophisticated traders not owning the asset must be low enough that it is profitable to trade and high enough to prevent λn from exceeding 1. 9 A short selling ban in my model does not require that all short selling goes to zero. Market makers can still short sell in the model as part of their market making activities without affecting any of the implications. 10 Given Assumptions 1 and 2, λnNoSS will always be less than one; however, it is possible for λnNoSS to be negative. In this case the equilibrium is found by imposing λn=0 and solving. This case is considered in Appendix B. All main results presented in the main body of the paper hold in this case as well. 11 see their Corollary 1. 12 See, for example, Bris (2008), Boulton and Braga-Alves (2010), Beber and Pagano (2013), and Kolasinski, Reed, and Thornock (2013). However, none of these studies nor Kaplan, Moskowitz, and Sensoy (2013) decompose the bid-ask spread into adverse selection and the realized spread (see Appendix C). Thus whether the impact of the restrictions on spreads is due to adverse selection is not certain. 13 The DTAQ data set offers an improvement over the NYSE Monthly Trade and Quote (MTAQ) database employed in prior studies. 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 time stamped 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, which are time stamped to the second, from the quotes database. As demonstrated in Holden and Jacobsen (2014), these differences can have a significant effect on the results obtained from empirical analysis. Most relevant to this study, Holden and Jacobsen (2014) document that compared to the more accurate DTAQ results, computations using MTAQ data can produce effective spreads that are 50% larger than the effective spreads computed using DTAQ. Consequently, where my analysis overlaps with that of Boehmer, Jones, and Zhang (2013), the pattern of results is similar, but the magnitudes presented here are smaller when using DTAQ instead of MTAQ data. 14 Microcap stocks are omitted from the analysis for the following reasons: First, the analysis requires signing order flow. Microcap stocks trade infrequently, and the time between quote revisions can be significant. Consequently, signing order flow using algorithms, such as that of Lee and Ready (1991), is likely to be highly noisy. Second, Boehmer, Jones, and Zhang (2013) show that smaller stocks are lightly shorted and the effects of the ban on them is muted. Lastly, trading in microcap stocks accounts for only a fraction of total trading volume, and given the large number of microcap stocks, including them may cause the study to lack generalizability. 15 See, for example, Sandås (2001), Barclay and Hendershott (2004), and Hendershott, Jones, and Menkveld (2011), among others. 16 To be included in the sample, a trade must not have a non-normal trade code. Non-normal trades include those trades in the field tr_scond, which have a value of J, L, N, O, P, T, Z, U, or Q. Also, Reg NMS requires that brokers route orders to the best quote price, and so trades outside the current NBBO prices should not occur and may be indicative of 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 30% in the millisecond prior to the trade. The computation of adverse selection and realized spread require the use of a midpoint at some future time Δt after the trade. 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 30%. Lastly, trades associated with locked or crossed quotes are eliminated. These filters eliminate approximately 4% of trades from the sample. 17 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. 18 Outside of the ban, I am unable to find systematic differences between buy and sell side transaction costs. 19 In DV, the coefficient a indicates the exogenous fraction of informed traders in the economy, and h indicates the fraction of investors who own the asset. To maintain consistency with the model presented in this study, I have substituted λ for a and γ for h. 20 Matching without replacement makes the match dependent on how the stocks without listed options are sorted prior to the match. For the results presented in the Table 8, I order stocks without listed options in ascending order by market cap prior to performing the match. However, the results are effectively the same regardless of whether I sort ascending or descending or by market capitalization, dollar volume, or permno. The results are also robust to using sampling with replacement. The primary drawback to sampling with replacement is that one stock with listed options is matched to eight stocks without listed options somewhat diluting the representativeness of the matched sample. Additionally, the results are robust to not computing a matched sample and instead simply comparing stocks with listed options to those without listed options. 21 Control variables include price, dollar volume, price volatility, return, and market cap. For each of these variables I include as controls both the level of the given variable for the banned stock and the difference between the banned stock and its matched control. 22 Nearly all stocks subject to the ban had a computed residual institutional ownership as of 2008 Q3. Two cases had missing data for these dates; however, both cases had values of residual institutional ownership in the few quarters prior. Missing data occur because Lemmon, Roberts, and Zender (2008) trim their data at the 1% level. Acknowledgments I 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 also thank Kyoung-Hun Bae, Chelsea Chen, Nicole Choi, Philip Daves, Kaitlyn Dixon, Amy Edwards, Ryan Farley, Corbin Fox, Michael Goldstein, Pawan Jain, John Ritter, Matthew Serfling, Eric Sirri, Ingrid Werner, and Tracie Woidtke for their valuable comments and insights. I also express gratitude to Thierry Foucault (editor) and an anonymous referee for their valuable comments and suggestions. The Securities and Exchange Commission disclaims responsibility for any private publication or statement of any SEC employee or Commissioner. This article expresses the author’s views and does not necessarily reflect those of the Commission, the Commissioners, or other members of the staff. Send correspondence to Peter N. Dixon, peter.nephi.dixon@gmail.com. Appendix A. Proofs of Propositions 3–7 Appendix B. Equilibrium when λnNoSS=0 When λnNoSS*=1-η+4c-14cη1-γ<0 the equilibrium bid and ask prices are found by inserting λe=1 and λn=0 into Equations (9) and (10) from the text resulting in the following bid and ask prices when short selling is not allowed. AskNoSS*=1-1-η21-η+ηγ(B1) BidNoSS*=1-η2(B2) SpreadNoSS*=1-1-η21-η+ηγ-1-η2(B3) Inserting (B1) and (B2) into the expected benefit to becoming informed for investors who own the asset from Equation (11) reveals that EBNoSSe>c when λn=0 and λe=1 ⁠. Thus even when λnNoSS*=0 the equilibrium value for λeNoSS*=1. Note that the bid does not change relative to the case presented in the body of the text because λn does not affect the bid since investors who do not own the asset are not able to transact on that side of the market. So the difference between this case and that presented in the text is in the Ask. Proposition 3a holds in this scenario because λnSS*>0=λnNoSS and thus it is easy to see that the fraction of sophisticated traders in the economy who become informed will decrease. Proposition 3b holds because it is not affected by a ban so the proof is unchanged. Proposition 4 holds because the bid price is not affected by λnNoSS ⁠. Proposition 5 holds because it is straightforward to show that AskNoSS* from Equation (B1) is less than AskSS* from Equation (6). This can be seen by showing that AskNoSS*=1-1-η21-η+ηγ<1-c-k2=AskSS* ⁠, which reduces to c+k2<1-η21-η+ηγ ⁠, which is true by Assumption 1. Proposition 6 changes somewhat as the range where the spread widens to: 1-η41-η1-γ+1-η4<c+k2 ⁠. However, the same intuition holds in this case. The left-hand side of the inequality is declining in η thus as η gets larger the likelihood that spreads widen increases. The RHS is the expected cost of transacting on information for investors who do not own the asset. As this increases, the likelihood that spreads widen increases. Proposition 7a is also true in this case. Using a process exactly analogous to that described in the proof of Proposition 7a yields that in this case EΔpNoSS=1-η1-η+2ηγ41-η+ηγ+1+η1-ηγ4+1-γ1+η-γ-ηγ+6c-2cη+2cηγ-2cγ+2η48c-4cγ-1+η ⁠. Showing that this expression is greater than EΔpSS is done numerically; however, in this case there is never an instance in which Assumptions 1 and 2 are satisfied and for which this equilibrium is the appropriate case where a short selling ban does not lead to a decrease in price efficiency when η=.65 and γ=.2 ⁠. This outcome is generally true for the other values of η and γ examined. Proposition 7b is true because the expression EΔpNo does not change relative to the proof presented in Appendix A. Appendix C. Decomposition of the Effective Spread into Adverse Selection and Realized Spread The connection between adverse selection (measured by price impact) and liquidity is seen by decomposing the effective spread—one of the primary measures of liquidity—into its constituent components of price impact and realized spread. The effective spread is the signed (⁠ si) proportional distance between the trade price (⁠ Pi) and the prevailing midpoint at the time of the trade (⁠ Mt) ⁠. It is the cost that an active trader pays to the market maker to execute a trade as shown in Equation (C1). Effective Spreadi,t=2*si*Pi-MtMt(C1) By adding and subtracting the midpoint at some future time t+Δt ⁠, as shown in Equation (C2), the effective spread can be decomposed into its two components. The first component 2*si*Mt+Δt-MtMt 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 and the literature uses the terms price impact and adverse selection interchangeably to refer to this portion of the effective spread. The second component 2*si*Pi-Mt+ΔtMt 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 non-adverse-selection-related costs as well as provides the market maker’s profit. 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