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The Impact of Aggressive Orders in an Order Driven Market: A Simulation Approach1 Gunther Wuyts2 University of Leuven January 2011 1 We would like to thank the editor Ingmar Nolte and the anonymous referee for the very helpful and interesting comments and suggestions on an earlier version of the paper. 2 Correspondence can be sent to: [email protected] Postal address: Gunther Wuyts, University of Leuven, Faculty of Business and Economics, Department of Accountancy, Finance and Insurance, Naamsestraat 69, 3000 Leuven, Belgium. Abstract This paper investigates resiliency in an order-driven market. We simulate the e¤ect of a large liquidity shock, measured by a very aggressive market order that uses at least the depth at the three best prices in the book. The simulation is done on basis of a VAR model that captures various dimensions of liquidity and their interactions, it is estimated for data of the Spanish Stock Exchange. We show that, despite the absence of market makers, the market is resilient. All dimensions of liquidity (depth at the best prices, spread and order book imbalances) revert to their steady-state values within 15 orders after the shock. For prices, a long-run e¤ect is found. Furthermore, di¤erent dimensions of liquidity interact. Immediately after a liquidity shock, the spread becomes wider than in the steady state, implying that one dimension of liquidity deteriorates, while at the same time depth at the best prices increases which means an improvement of another dimension of liquidity. In subsequent periods, the spread reverts (declines) back to the steady-state level but also depth decreases. Also, we …nd evidence for asymmetries in the impact of shocks on the ask and bid side. Shocks on the ask side have a stronger impact, compared to shocks on the bid side. Finally, we …nd that resiliency is higher for stocks which are less frequently traded and stocks with a larger relative tick size, in line with theoretical predictions. JEL Classi…cation: G10 Keywords: Liquidity, Liquidity Shock, Resiliency, Limit Order Market, Order Aggressiveness 1 Introduction This paper analyzes resiliency in an order-driven market. Resiliency refers to how fast dimensions of liquidity, such as best prices, depths or duration, recover to their normal (i.e. steady-state) level after the market has been hit by a liquidity shock. Reversion in liquidity following liquidity shocks is especially crucial in order-driven markets since no market makers are present with an obligation to maintain an orderly market by providing liquidity. Can order-driven markets be resilient without their presence? To answer this question, we develop a VAR model that incorporates the di¤erent dimensions of liquidity (prices, depths and duration). The VAR model allows for analyzing jointly these various dimensions of liquidity and capturing the interactions between them. Models such as Rosu (2009) and Parlour (1998) show that bid and ask side of the market do not evolve independently. Also, the ask price cannot move arbitrary far away from the bid price, Engle and Patton (2004) …nd they are cointegrated. Moreover, prices and depths at these prices could interact. If an arriving trader is faced with a long queue of limit orders at the ask, she might prefer to undercut the ask to obtain price priority and probably faster execution. Based on our VARmodel, we analyze resiliency by simulating a liquidity shock. In the literature, such shock is typically implemented via the innovation process of the VAR-model (see e.g. Beltran, Durré and Giot (2009)). The disadvantage of this is that little is said about the speci…c origins of such “general” shock. Therefore, we use an alternative approach by analyzing a well-de…ned liquidity shock having a very speci…c source. More speci…cally, we measure a liquidity shock by a very aggressive order. In particular, a liquidity shock on the ask (bid) side is a very aggressive buy (sell) order that consumes at least all the depth at the three …rst ask (bid) prices in the book and part of the depth at the next price. It is natural to specify a liquidity shock in term of a speci…c type of orders (see also Large (2007) or Degryse et al. (2005)), since in a limit order market, liquidity (and resiliency) is determined by the interaction between limit orders, which supply liquidity, and market orders, which consume it. Ultimately, it is the mix between both types of orders that shapes the liquidity of a limit order market. While VARmodels are regularly used in market microstructure research to model resiliency, other methods have been used as well. They include the intensity model of Large (2007), copula techniques applied to multivariate transaction processes (see e.g. Nolte (2008) or Bien, Nolte and Pohlmeier (2009)) and event study methods (see Degryse et al. (2005)). These methods all are alternatives to the VAR approach, that is used in our paper. Our choice for a VAR model is economically motivated by the theoretical framework of Foucault, Kadan and Kandel (2005) (henceforth FKK05), one of the very few theorical contribution explicitly focussing on resiliency. Their theoretical model de…nes resiliency as the “probability that the spread reverts to its competitive level 1 before the next transaction occurs”. We measure the competitive level of variables, including the spread, by their steady-state value, i.e. their average value over time. Furthermore, FKK05 de…ne a liquidity shock as “a succession of market orders that enlarges the spread”. Our measure of a liquidity shock - a very aggressive market order that uses several levels in the limit order book - is very close to this concept of a series of market orders that enlarge the spread. Moreover, given that FKK05 “have checked numerically that all our implications regarding our measure of market resiliency (for instance Corollary 1) hold for the order-based measure of resiliency as well”(see page 1185 of FKK05), we estimate our VAR model and compute the impulse responses to a liquidity shock in order time. In sum, we favor a VAR approach over the other approaches because it o¤ers a convenient framework for analyzing resiliency in a way that is closely linked to and motivated by theory, and therefore allows an intuitive economic interpretation. We apply our model and simulation framework to a sample of 35 Spanish index stocks over the period July-December 2000 (124 trading days). The Spanish stock market operates as an order-driven market. Our key results can be summarized as follows. First, we show that in general the Spanish stock market is resilient, even though no market makers are present to provide liquidity at all times. The bid-ask spread, depth at the best prices and the duration between order submissions all recover to their steady-state levels within 15 orders after the liquidity shock. For best bid and ask prices, as well as for the midprice, a long-run e¤ect is documented. Secondly, we …nd an interaction and complimenarity between di¤erent dimensions of liquidity. After a liquidity shock, there is a long-run e¤ect on prices as a result of which the spread becomes wider than in the steady state, implying that one dimension of liquidity (spread) deteriorates. However, at the same time depth at the best prices increases which implies an improvement of another dimension of liquidity. In subsequent periods, we observe the opposite evolution: the spread reverts (declines) back to the steadystate level but also depth declines. Thirdly, after a liquidity shock, the limit order book becomes imbalanced. Following a shock on the ask side, depth at the ask side becomes considerably larger than depth at the bid side. It takes around 15 orders for the order book to become balanced again. A similar picture is found after a shock on the bid side. Fourthly, we …nd evidence for asymmetries in the impact of shocks on the ask and bid side. Shocks on the ask side have a larger impact and - depending on the liquidity measure though - it may take longer for the liquidity measure to recover, compared to shocks on the bid side. Finally, we …nd that resiliency is higher for stocks which are less frequently traded and stocks with a larger relative tick size (i.e. tick size/midprice). These …ndings thus con…rm the theoretical predictions in FKK05. The remainder of this paper is organized as follows. In Section 2 we relate our work 2 to the existing literature and elaborate on the di¤erences with and contributions to previous studies. In Section 3, the econometric model is developed. Also, we explain the simulation methodology for studying resiliency. Section 4 presents the dataset used. In Section 5, …rst the estimation results of the VAR model are presented. Subesequently, we discuss in detail our results for resiliency. Section 6 concludes. 2 Related Literature and Contributions In empirical market microstructure research, the use of VAR-models has been pioneered by Hasbrouck (1991). He …nds that the full impact of a trade innovation is not realized instantaneously but with a lag. Moreover, the impact is higher if the stock is more infrequently traded, if the trade size is large and if there exists a wide spread at the moment of the trade. Since this seminal paper, numerous variants and extensions have been developed. Dufour and Engle (2000) investigate the informational role of market activity and show how the dynamics in prices and trades are a¤ected by the information revealed by the time between transactions. In the model of Easley and O’Hara (1992), the time between trades is an indication whether or not a news event has occurred. Uninformed traders use this signal to revise their beliefs about the arrival of news about which some traders might be informed. Dufour and Engle …nd that both larger quote revisions and stronger positive autocorrelation of trades are linked to a higher trading activity. In this case, prices converge faster to the full information value after an unexpected trade. When combining their results with those of Hasbrouck, they conclude that high trading activity goes together with large spreads, high volume and a high price impact of trades. Active markets are then illiquid in the sense that the price impact of trades is higher. Both Hasbrouck (1991) and Dufour and Engle (2000) include the change in the quote midpoint (and the trade direction) as endogenous variables in their VAR-models. Two recent papers, Engle and Patton (2004) and Escribano and Pascual (2006), include both bid and ask quotes in their model and in this way allow trades to have an asymmetric impact on bid and ask prices. They also correct for cointegration between bid and ask. The motivation of Engle and Patton (2004) for including both bid and ask quotes lies in a study by Jang and Venkatesh (1991). The latter show that the most common response by liquidity suppliers to news is no adjustment, but the second preferred response is that only one of both quotes is changed. After a buy, it is more likely for the ask to be changed than for the bid. This means that the dynamics of ask and bid quotes will be di¤erent after a buy order than after a sell order. Engle and Patton (2004) …nd evidence for a strong asymmetric impact on bid and ask prices of buyer and seller initiated trades in the short run. Short-duration and medium-volume trades have the largest impact. 3 The order of magnitude of the e¤ects is in general larger in the lower trade frequency deciles. Also Escribano and Pascual (2006) …nd that the responses of bid and ask quotes to a trade are not necessarily symmetric. They show that the mean impact of an unexpected buy on the ask quote di¤ers from the mean impact of an unexpected sell on the bid quote. Moreover, the sensitivity of the response of the ask to a trade innovation when market conditions are changed, di¤ers from that of the bid quote. The impact of a buy on the ask quote depends e.g. more on the time since the previous trade than the impact of the corresponding sell on the bid quote. However, symmetry is more likely the more informative trades are. Coppejans, Domowitz and Madhavan (2004) also address the issue of liquidity in a limit order market, although they use 5-minute intervals, instead of order time as we do. They use market depth at the buy and sell side as a measure of liquidity and the change in the midquote as a return. With data from the limit order book of the market for Swedish stock index futures, they show that a liquidity shock on the ask (bid) side of the market lowers (increases) returns. The e¤ects are short-lived since almost all the impact occurs during the 10 minutes following the shock. Moreover, they …nd evidence of liquidity clustering since if there is an increase in liquidity1 on one side of the market, this leads to an increase in liquidity at the other side of the market as well. The study most related to ours is Degryse et al. (2005). They also analyze resiliency, but employ an event study instead of a simulation based on a VAR-model. They …nd that depths stay around their mean before and after aggressive orders, whereas spreads return to their mean after about twenty best limit updates. Aggressive orders induce a a long-term price e¤ect. To conclude this paragraph, we would like to remark that our paper does not aim to explain why a trader chooses a certain order type. Ranaldo (2004) discusses the complementary issue of the determinants of the choice of an order type by a trader. We do not model this choice, but take the submission of the order as given and analyze its aftermath. In this sense, Ranaldo focusses on the period before the submission of an order while we investigate the period thereafter. In this way, we shed some light on the consequences of the order choices and how the market responds to them. Note however that we do correct in the regression models for past order ‡ow. How does our paper di¤er from and aim to contribute to the above mentioned literature? First, most papers in the literature employing VAR models only focus on spreads or prices as measures for liquidity, in this way ignoring depth in the market, another important dimension of liquidity. We therefore make a contribution to Dufour and Engle (2000), Engle and Patton (2004) and Escribano and Pascual (2006) by analyzing prices, depth and duration in a unifying VAR framework (in 1 They measure a liquidity shock as a shock to market depth, de…ned as total depth 6 ticks away from the quote midpoint 4 alternative speci…cations we also look at spreads, depth imbalances and midprices), in this way disentangling spread/price e¤ects and depth e¤ects of shocks. Recall from the introduction that other approaches exist, next to VAR models (see e.g. Large (2007) or Bien, Nolte and Pohlmeier (2009)). As argued, we opted for the VAR approach because of its close relation with theory, given the research question of our paper. Further, Engle and Patton (2004) focus on the estimation results of a VAR (VEC) model, and do not consider the impact of liquidity shock over time as we do. Also, these authors consider the NYSE, which is a hybrid market, while we study a pure orderdriven market without market makers that have an obligation to provide liquidity, providing thus a more clear picture of a pure order-driven market. Secondly, our study di¤ers from Coppejans, Domowitz and Madhavan (2004) since we investigate e¤ects in order time, and thus o¤er a more high-frequency, less aggregate analysis. Moreover, we use a clearly identi…able liquidity shock (a very aggressive order) instead of an innovation in the error terms of the VAR model, which is harder to interpret from an economic point of view. Furthermore, our paper also di¤ers from Degryse et al. (2005) in a number of ways. Compared to Degryse et al. (2005), our shock is a much more extreme event, since very aggressive orders are rare (less than 1% of buy or sell orders, see Table 3) but have large price impact. Moreover, given that order types are clustered over time2 , an event study, while having the advantage of looking directly at what happens in the limit order book around aggressive orders, has the potential drawback that multiple events (i.e. liquidity shocks) can occur within the event window. We can isolate one individual shock in our simulation framework. Furthermore, their descriptive approach does not allow for disentangling the e¤ects of order type and order size. Therefore, our paper complements the event study in Degryse et al. (2005) by developing a formal econometric analysis of liquidity, allowing for the accommodation of some drawbacks of the descriptive approach. We are able to correct for the problem of confounding events and can account for the state of the limit order book around aggressive orders. Moreover, we can separate the impact of an aggressive order in itself from other elements such as order size or market environment. Also interactions between dimensions of liquidity are captured in our econometric model, in contrast with an event study. Finally, we motivate the de…nition of our model explicitly by the theoretical literature and in particular Foucault, Kadan and Kandel (2005). We also contribute to the above literature by empirically testing a number of theoretical predications about the determinants of resiliency that emerge from their model. 2 This is the so-called diagonal e¤ect (see Biais, Hillion and Spatt (1995) and Degryse et al. (2005)). An order of a given type is more likely to be followed by an order of the same type, relative to the unconditional probability of the order type. 5 3 Econometric Methodology 3.1 Modeling Prices, Depths and Duration As argued in the introduction, prices and depth at the bid and ask side of the market may not move independently, but rather interact with each other. The same holds for prices and duration between updates of the limit order book. Therefore, we develop in this section an empirical model which is able to capture these elements. In empirical research, vector autoregressive (VAR) models are a popular and convenient methodology for analyzing the interaction between variables of interest and their behavior around shocks. In our study, which makes use of a VAR-model, the variables of interest are the best bid and ask prices in the limit order book, the depth at these best prices and duration. By explicitly modeling both sides of the market, we allow for potential asymmetries between them. This approach is also in line with existing work by e.g. Engle and Patton (2004) and Escribano and Pascual (2006) who consider both bid and ask prices. When analyzing a limit order market, also depth at the best prices needs to be incorporated in the model. Parlour (1998) shows that in an order-driven market the choice between limit and market orders depends on the depth at both sides of the book. Recall that it is precisely the mix between market and limit orders which determines liquidity in a limit order market, since they determine respectively liquidity demand and supply. We include also duration in our model. Theory shows that the time between trades is informative. In the model of Easley and O’Hara (1992), the lack of trades (or in other words, the duration since the last trade) provides a signal about the existence of new information in the market3 . As a result, spreads are shown to decrease as the time between trades increases. Foucault, Kadan and Kandel (2005) show that the resiliency of a limit order market is decreasing in the order arrival rate, i.e. a market having a lower order arrival rate, is more resilient than a fast market. The reasoning is that, when the order arrival rate increases, limit order traders become less aggressive in their price improvements. As a consequence, more orders are needed to bring down the spread to its competitive level, implying resiliency declines. Empirically, Engle and Patton (2004) con…rm that the impact of a trade is di¤erent depending on the time elapsed since the previous trade. They …nd that short duration and medium volume trades have the largest impacts on quote prices. Hence, we de…ne the vector of endogenous variables yt as follows: yt = f ln (At ) ; 3 ln (Bt ) ; ln (ADt ) ; ln (BDt ) ; ln (Durt )g Trades themselves then reveal information about the direction of the information event. 6 with At (Bt ) the best ask (bid) price at time t, ADt (BDt ) the depth at the best ask (bid) at time t, Durt the duration since the previous order and ln the natural logarithm (in Section 4.2, we provide the details how these variables are measured in our empirical implementation). In this speci…cation, we follow Harris (1990) who considers prices and depth as two separate aspects of liquidity. We take …rst di¤erences of the price series because the null hypothesis of a unit root in both best bid and ask series cannot be rejected. These …rst di¤erence of log prices can be interpreted as the return on the best bid (or ask). The time index t refers to order time, i.e. we record a new observation each time when a new order occurs in the market. This means that the VAR model is speci…ed in event time (as opposed to calendar time). If there are multiple orders at the same 1/100 second, we take the values after the last order. When modeling prices, depths and duration, we account for the characteristics of the order ‡ow. Order ‡ow is modelled by including three sets of exogenous variables. The …rst set describes the degree of aggressiveness of the submitted orders and consists of dummy variables for each order type i = 1; :::; 18. We classify each order according to a scheme which is inspired by the one proposed in Biais, Hillion and Spatt (1995) and also used in other papers, see e.g. Gri¢ ths et al. (2000) or Ranaldo (2004). A de…nition of each order type is provided in Table 1. From this table, it can be seen that we use 9 di¤erent types of buy order, and 9 types of sell order. The orders are presented in descending aggressiveness: M O_B1 can be interpreted as the most aggressive buy order type, Canc_B3 is the least aggressive buy order. The main distinction in our classi…cation is based on the fact whether an order is a market order or marketable limit order (M O), a (non-marketable) limit order (LO) or a cancellation or modi…cation (Canc). From the table, it can be seen that we use a slightly more elaborate version of the Biais, Hillion and Spatt (1995) scheme. First, we added one category of market order - the most aggressive - because we want to measure a liquidity shock by a very aggressive market order M O_B1t and M O_S1t (and our dataset allows doing so, see Section 3.2). Secondly, we also added cancellations and modi…cations. The reason is that, in principle a cancellation can have the same impact as the submission of a market order. For instance, the cancellation of an order at the best ask may cause the best ask to increase, just as an aggressive market order. To make a distinction between market orders and cancellations, we added both in the classi…cation scheme. Please insert Table 1 around here. The second set of order ‡ow variables is related to order size. For market orders, orders with a higher degree of aggressiveness have a larger order size (as can be expected from de…nition), see Table 3. For other order types (limit orders 7 or modi…cation/cancellations), the relation between aggressiveness and order size is not monotonic. Therefore, by including both the degree of aggressiveness and size, we are able to disentangle aggressiveness in itself and order size. Moreover, Easley and O’Hara (1987) show that order size is important in determining price impacts. Hence, OSize_B1t represents the order size of an order of type M O_B1; more speci…cally, the variable is equal to the order size if order t is of type M O_B1, and zero otherwise. For all other order types, the order size variables are de…ned in a similar way. Thirdly, to account for possible intraday patterns in returns and depth4 , we include time of day dummies. We take a separate dummy for the …rst and last 15 minutes of trading because of the more pronounced trading activity during these intervals. Hence, T _01t (T 18t ) equals 1 if the order takes place between 9:00 and 9:15 a.m.. (5:15 and 5:30 p.m.). The remainder of the trading day is divided in intervals of 30 minutes: T 02t is 1 if the order is between 9:15 a.m and 9:30 a.m, ... , T 17t is 1 if the order is between 4:45 p.m and 5:15 p.m and zero otherwise. It needs to be remarked that other frequently used techniques for diurnal adjustments are piecewise linear splines (from the duration literature) or trigonometric functions (from the volatility literature). We have performed a robustness check and diurnally adjusted the endogenous variables and order sizes using piecewise linear splines. Reestimating the VAR and plotting impulse responses with the adjusted variables does not change our results. We therefore use time of day dummies, because it they allow for a more intuitive interpretation. This approach is also in line with other market microstructure papers using VAR models, such as Dufour and Engle (2000), Engle and Patton (2004) or Escribano and Pascual (2006). Hence, the vector of exogenous variables xt is: xt = fM O_B1t ; :::; Canc_S2t ; Size_M O_B1t ; :::; Size_Canc_S2t ; T 01t ; :::T 17t g where we left out Canc_S3t (which is then the reference category for order types) and the dummy for the last interval of the trading day T 18t to avoid perfect multicollinearity in estimation. A …nal point concerns the econometric properties of the series used. Best ask and bid prices not only have a unit root, but can also be expected to be cointegrated. Engle and Patton (2004) …nd empirical evidence of the presence of cointegration. In our model, the cointegrating term has a simple interpretation, being the log spread, hence: LSpreadt = ln (At ) ln (Bt ). This means that the VAR-model is speci…ed in error correction form. We do not impose other cointegrating relations since only bid and ask prices are found to be integrated of order 1 or I (1). Depths and duration are I (0). 4 This e¤ect might e.g. be due to the U-shaped pattern of trading activity during the day (see Biais, Hillion and Spatt (1995) for an illustration of this phenomenon on the Paris Bourse). 8 Bringing all of the above together, our VAR-model is speci…ed as follows: yt = L X l=1 Al y t l + A0 M X Bm xt m + LSpreadt 1 + ut (1) m=0 with ut the error term which is assumed to be white noise and A0 , Al , Bm and the coe¢ cient matrices to be estimated. Note that for the endogenous variables, only lags are included, while for the vector of exogenous variables, also the contemporaneous values are considered. 3.2 Resiliency Resiliency, a crucial aspect of liquidity in order-driven markets, refers to the ability of a trading system to cope with liquidity shocks hitting the market. Earlier, we de…ned resiliency as “the speed of recovery to their steady-state levels of di¤erent measures of liquidity (i.e. prices, depths and duration) after a liquidity shock hits the market”. It then remains to be speci…ed what comprises such liquidity shock. Most of the market microstructure literature uses a “general” shock, implemented via the error terms in a VAR-model (in our case this would be ut in equation (1)). In contrast, our paper proposes an alternative approach by using a clearly identi…able and concrete event. More speci…cally, we measure a liquidity shock on the ask (bid) side as a type M O_B1 (type M O_S1) order. From Table 1, it is clear that such orders are the most aggressive market buy (sell) orders. Such shock widens the bid-ask spread and consumes all the depth at the …rst three prices and some of the depth behind the third price. Note that a distinction is made between a shock on the buy and sell side of the market to investigate potential asymmetries. This measure is also in line with the one in the model of Foucault, Kadan and Kandel (2005), who de…ne a liquidity shock as “a succession of market orders that enlarges the spread”. Our measure of a liquidity shock - a very aggressive market order that uses several levels in the limit order book - is very close to this concept of a series of market orders that enlarge the spread. To investigate resiliency, we start from the estimation results of the VAR model in Equation (1). We then implement a simulation of the impact of a liquidity shock (a type M O_B1 or M O_S1 order) on each of the endogenous variables. We then are able to study resiliency by comparing these impulse responses of the endogenous variables with their steady-state values, and more in particular how fast - expressed in number of orders - variables return to their steady-state level after the shock. This methodology is also in line with theory. Given that Foucault, Kadan and Kandel (2005) “have checked numerically that all our implications regarding our measure of market resiliency (for instance Corollary 1) hold for the order-based measure of resiliency as well”(see page 9 1185 of their paper), we follow their theoretical model and estimate our VAR model and compute the impulse responses to a liquidity shock in order time. For the full technical discussion of our simulation methodology, we refer to Appendix A. Finally, it should be noted that we can only compute steady-state levels in a meaningful way for variables that are stationary (hence not for prices). 4 4.1 Data Sample This paper uses data from the Spanish Stock Exchange SIBE, an exchange which operates essentially as a pure order-driven market. For the institutional details of SIBE and a description of its main features, we refer to Pardo and Pascual (2007). The sample contains 35 stocks that were part of the IBEX35 stock index during the sample period. The IBEX35 is composed by the 35 most liquid and active stocks, traded on the exchange. Our sample period ranges from July 2000 - December 2000 and thus spans 124 trading days. The data on the limit order book contain the …ve best bid and ask prices and the displayed depth at each of these ten prices. Moreover, we have data on all trades that were executed during the continuous trading session. Preopening or postclosing orders are not included since the trading mechanism during this period is di¤erent from the one during the trading day. All changes in the book (i.e. submitted orders) are timestamped to 100th of a second. The trading data show price and size of each trade. The index numbers and time stamps allow for a perfect matching of trade and limit order book data. Since the sample period is before 2001, we do not have to take into account the presence of volatility auctions (see Pardo and Pascual (2007)). These auctions were only introduced at May 14, 2001. Finally, we …ltered the database to exclude items that contain errors (e.g. registers out of sequence, increases in the accumulated volume over the day that are negative, ...). Table 2 presents the summary statistics of each of the stocks in our sample. The …rst column shows the code of the stock. Columns 2 and 3 present the market capitalization (expressed in 1000 euro) at the end of 2000, and the total trading volume (in 1000 euro) during 2000, respectively. The next four columns show the average daily number of trades, the average trade size (in shares), the average duration (in seconds) between orders, the average bid-ask spread and the average midprice. All these average are computed over the whole sample period. From this table, it can be seen that there is substantial variation between the stocks with respect to market cap, trading volume and spreads. As a …nal remark, it should be noted that the tick size for all stocks is 1 cent (0.01 euro). Hence, bid-ask spreads expressed in cents give the same results as 10 when expressed in number of ticks. Please insert Table 2 around here. 4.2 De…nition and Summary Statistics of Endogenous and Exogenous Variables Table 3 presents the summary statistics for the endogenous and exogenous variables that are used in our VAR model, speci…ed in Section 3.1. We now provide their empirical de…nition and the unit of measurement. All endogenous variables, as well as log order sizes and log durations are winsorized at the 99.5% level to account for extreme outliers. In Panel A, we …rst show the mean, median and standard deviation for the …ve endogenous variables. For all stocks, the returns on the best ask and bid, expressed in % and denoted ln (At ) ; ln (Bt ), are small on average. This is due to the fact that for a majority of the orders, there is no change in the best price (see the de…nitions in Table 1), hence the return is zero for these observations. Subsequently, the log of depths at the best bid and ask ln (ADt ) ; ln (BDt ) are shown. Depths ADt (BDt ) are measured in euros and obtained by multiplying depth in shares at the best ask (bid) with the prevailing best ask (bid price). Note that the average depth at the best ask is larger than average depth at the best bid. The average log of duration ln (Durt ) is the next variable, Durt is computed as the time in seconds between order t 1 and order t. The second part of Panel A contains summary statistics of variables that will be used in transformations of our main model (see Sections 5.2.2 and 5.2.3). Spread is the bid-ask spread in cents, it is on average 6.36 cents. The second variable, ln (BADR) is the log of the ratio of depth at the best bid and ask (in euro) and can be interpreted as a measure for the imbalance of the limit order book. Its value is close to zero, implying on average a balanced book. Next, ln (M ) is the return on the midprice in % and ln (BAD_Avg) is the log of the average of depth (in euro) at the best bid and ask. Panel B presents the frequency (in %) of occurring of the di¤erent order types, the average order size in shares and the log of order size per type (which are the size variables in our VAR model), the left part of the table for buy order, the right part for sell orders. The results reveal that the most aggressive buy and sell orders (type M O_B1 and M O_S1) have the smallest frequency of occurring across order types. So when these two types are used as measures for a liquidity shock, we are looking at relatively rare events but with a large impact as they consume depth at at least the …rst three price levels in the order book. The most frequent order type are the market orders 11 that are …lled completely and have no price impact (type M O_B3 and M O_S3). All frequencies are in line with the …ndings of Biais, Hillion and Spatt (1995) or Degryse et al. (2005) for the Paris Bourse and of Gri¢ ths et al. (2000) for the Toronto stock exchange5 . Furthermore, it can be seen that in general more aggressive market orders are also larger, with the largest orders being types M O_B1 and M O_S1. At …rst sight, this …nding may seen to be expected from their de…nition since these are the most aggressive orders, consuming all depth at one or more prices. However, a priori it could also be true that orders are classi…ed as aggressive because they are submitted at times when depths in the book are small. The fact that the average order size of aggressive market orders is large and moreover considerably larger than the average depth shows that this is not the case. For limit order types and cancellations/modi…cations, the relation between aggressiveness and order size is not monotonic, but there are no theoretical reasons to a priori expect such a monotonic relation (e.g. there is no reason why a cancellation should be smaller than a limit order). This is our motivation for including both the type and size of an order in the econometric model, in this way we distinguish both e¤ects. Please insert Table 3 around here. 5 Empirical Results 5.1 Model Estimation Before estimating the model, we verify the econometric properties of the series. Augmented Dickey-Fuller tests (not-reported) reveal that log best prices ln (At ) and ln (Bt ) contain a unit root, while log depth at the best ask and bid and log duration between orders are stationary. As stated in Section 3, we take this into account in the model speci…cation. During the estimation of the model in equation (1), we included …ve lags of the endogenous variables (L = 5) and zero lags of the exogenous variables (M = 0). We aimed to make the speci…cation of the VAR as concise as possible, while on the other hand also optimizing the AIC criterion. Our choice of L = 5 and M = 0 balances both points and it is also in line with the literature, see e.g. Engle and Patton (2004). The VAR model is estimated for each of the 35 stocks separately with least squares and Newey-West standard errors are computed. Recall that the de…nition of the variables is explained in Section 3 and the units of measurement are shown in Section 4.2, we do not repeat them here. All endogenous variables, as well 5 Recall though that these papers use a slightly less detailed classi…cation scheme, see Section 3.1. 12 as log order sizes and log durations are winsorized at the 99.5% level to account for extreme outliers. Finally, it should be noted that all results for resiliency (see the next section), are robust to alternative speci…cations of the VAR-model (1). Neither adding more lags of endogenous and exogenous variables, nor leaving out certain exogenous variables (e.g. estimating the VAR only with order type dummies, and leave out order sizes) do not change the main conclusions obtained in the resiliency section. Table 4 present the estimation results of the VAR model in Equation (1) with the vector of endogenous variables yt = f ln (At ) ; ln (Bt ) ; ln (ADt ) ; ln (BDt ) ; ln (Durt )g and the vector of exogenous variables xt = fM O_B1t ; :::, Canc_S2t , ln (Size_M O_B1t ), :::, ln (Size_Canc_S2t ), T 01t ; :::T 17t g. The …rst column in the table gives the righthand-side variables, the next columns are the …ve equations in the VAR, the header shows the endogenous variable. For each coe¢ cient, we give the unweighted average value of the coe¢ cient across the 35 stocks, followed - between brackets - by the number of stocks out of 35 for which the coe¢ cient is signi…cantly positive (…rst element) and negative (second element) at the 5% level. For instance, the …rst element in the table, 0:0980 (0; 35), should be interpreted as follows: the average coe¢ cient across the 35 stocks of the variable ln (At 1 ) in the equation for ln (At ) is 0:0980. For 0 stocks, the coe¢ cient is signi…cantly positive, for 35 stocks it is signi…cantly negative. For 0 stocks (the di¤erence between the 35 stocks in our sample and the sum of the two elements 0+35), it is insigni…cant. To save space, we do not report results in the table for the log order size variables and time-of-day dummies, but they are included in the estimation (and later in the simulation). Below the table, the average adjusted R2 across stocks are reported for the di¤erent equations. As the main interest of our analysis is in resiliency (see next subsection), we discuss the estimation results in a relatively concise way and just highlight the main points. We consider coe¢ cients to be signi…cant if they are so for a majority of the stocks (see the numbers between brackets). Table 4 clearly provides evidence for the existence of a number of relationships between the endogenous variables. First, the estimates show a relation between both sides of the market. Ask returns are signi…cant in the bid return equation and the other way around. Depth at the ask (bid) side of the market is positively related to lagged depth at the bid (ask) side, in line with the theory in Parlour (1998) who shows that traders look at both sides of the market when determining their order choice between market and limit orders (and this choice determines liquidity in a limit order market). Secondly, our results also demonstrate an interaction between the dimensions of liquidity, as argued by Harris (1990). This can be seen by noting that ln (AD) has a negative sign in the ask- and bidreturn-equations, while ln (BD) has a positive sign. The intuition is as follows. Suppose depth at the best ask is high and a seller arrives. Since the execution probability of an additional 13 sell limit order joining the queue at the best ask is small, she will not submit such order. She will either improve the best ask (implying a negative return on the ask) or submit a market order. If in the latter case all depth at the best bid is consumed, this implies a negative return on the bid. Similarly, if depth at the best bid is higher, ceteris paribus, a buyer will either submit a market order (increasing the best ask if all depth at the best ask in consumed), or improve the best bid, implying a positive return on the best bid. Furthermore, we …nd signi…cant coe¢ cients of returns in the equations for depth, positive for the ask return, negative for the bid return. The intuition is that an undercutting of the best ask by a limit order, implying a negative return on the best ask, will lower depth at the best ask (since the size of the order becomes the new depth and this is most likely smaller than the depth that was present before the order). This in turn leads to a positive correlation between ln (A) and ln (AD). Turning to duration, we …nd a no relation between lagged duration and returns or depth. This is in line with Engle and Patton (2004) and the predictions in Easley and O’Hara (1992) that long durations do not reveal information. In the duration equation, we …nd signi…cant coe¢ cients for returns, and for the …rst lag of depth. Finally, in line with the literature, all endogenous variables are autocorrelated, the coe¢ cients of their own …ve lags are signi…cant. However, their magnitude quickly decreases. For returns the autocorrelations are negative, while for depths and duration they are positive. Secondly, as in Engle and Patton (2004), we …nd evidence of cointegrating behavior, since the lagged log spread LSpreadt 1 is signi…cant in the return equations. Its sign is as expected. If the spread after the previous period was large, the ask can be expected to decrease and/or the bid to increase at the next order. This causes the spread to become narrower and return to its equilibrium value. Also, if the spread is larger, it is easier to undercut the best prices in the limit order book. Our results con…rm this intuition since the lagged spread has a negative sign in the ask return equation and a positive sign in the bid return. In the duration equation, the spread has a negative sign, meaning that when the lagged spread was larger, the duration between orders will become smaller. The signs of the order type variables in the return equations are as can be expected from their de…nition. Focusing on the types that will be used as measures for shocks, we …nd that type M O_B1 orders have a positive sign in the ask return equation, implying a large positive ask return of 0.4339% (recall this is on an order by order basis), while type M O_S1 orders have a negative sign in the bid return equation, i.e. a decrease in the best bid by 0.4078%. Now turning the e¤ect of di¤erent order types on the depth at the best prices, we …nd that type M O_B1 orders have a positive sign in the AD equation, while type M O_S1 orders have a positive sign in the BD equation. This can be interpreted as evidence that the limit order book behind the three …rst prices 14 is deep. Finally, the type of the order has only a limited impact on the duration since only few coe¢ cients of order types are signi…cant in the duration equation. Please insert Table 4 around here. 5.2 Resiliency In this section, we discuss the results for resiliency. As explained in Section 3.2, resiliency is analyzed by simulating the paths of di¤erent dimensions of liquidity after a liquidity shock. This simulation is performed on basis of the estimated VAR-model in equation (1). We do the simulation separately for each stock and then compute the median, and 5% and 95% percentile across the 35 stocks in our sample. In the discussion, we make a distinction between a shock occurring on the ask side of the market and one occurring on the bid side. Such shock is measured by a type M O_B1 order on the ask side and a type M O_S1 order on the bid side. We …rst discuss results for our main model. Next, we transform the model to analyze the behavior of the bid-ask spread and depth imbalance after a liquidity shock. A third subsection investigates midprice returns and average depth. In a …nal subsection, we make a distinction between more and less frequently traded stocks, and stocks with a large and small relative tick size. 5.2.1 Responses a Liquidity Shock Figure 1 presents the impulse responses of di¤erent variables after a liquidity shock, during a period of 15 orders (x-axis) after the shock. We de…ne a liquidity shock as an order of type M O_B1 in Panel A (which measures a shock on the ask side), and as an order of type M O_S1 in Panel B (measuring a shock on the bid side). The …rst graph in each panel draws the impact of such shock on the return (in %) on the best ask price ln (A), the second graph the impact on the return (in %) on the best bid price ln (B). The third and fourth graph display the impact of the shock on the log depth in euro at the best ask and best bid price, ln (AD) and ln (BD) respectively. The …fth graph shows the impact on log duration (in seconds) ln (Dur). The simulation for the impulse responses is done for each stock separately according to the procedure outlined in Appendix A, full lines in the graphs represent the median value of the responses across the 35 stocks in our sample, the upper (lower) dashed lines are the 95% (5%) percentile across stocks. The dotted straight lines are the steady-state levels, measured as the average value of the variable over the sample period. In our discussion below, we focus mainly on the median value (full line), if not stated explicitly otherwise, all statements should be interpreted in this way. 15 Please insert Figure 1 around here. The return graphs demonstrate that a liquidity shock has a long-term e¤ect on the best prices in the book. This e¤ect is however realized very quickly. More speci…cally, after a type M O_B1 order, there is a positive return on the best ask, but in the periods after this initial impact of the shock, there is a small reversal: in subsequent periods, returns on the best ask are slightly negative. A similar response is found for a shock at the bid side M O_S1: a negative return on the best bid immediately after the shock, followed by a small reversal. One interpretation for this long-run e¤ect on prices is the presence in the market of informed traders that are trading on perishable information. We further …nd some evidence that the impact of a shock also a¤ects the other side of the market than where the shock occurred. There is a small positive return on the best bid following a type M O_B1 order, while after an aggressive sell order (type M O_S1) a small negative return on the best ask is found. These small e¤ects disappear after some periods. They o¤set part of the e¤ect on the own side of the market on the spread6 . The e¤ect on the other side of the market is con…rming the empirical predictions of the model of Rosu (2009). The impact of a liquidity shock on log depths is found mainly at the side of the market at which the shock occurs. More speci…cally, depth increases at that side of the market: after an M O_B1 order, ln (AD) increases. After this initial increase, however, ln (AD) moves gradually back to its steady state, which it achieves around 15 orders after the shock. A symmetric result applies for ln (BD) after a M O_S1 order. An interpretation can be given to this result. At …rst, just after the shock, the limit order book behind the best prices is deep. In subsequent periods new liquidity (in the form of new limit orders) is provided to the market after it has been consumed by the aggressive order. These orders slighty improve the best prices, while the depth of these orders becomes the new depth at the best prices. At the other side of the market, depth remains more ‡at and the impact of the shock is small since median log depths do not move far away from their steady state. The last graphs in Figure 1 show that the duration between orders declines in the periods immediately after the shock. However, very quickly duration increases and stabilizes again around its steady state value. Furthermore, our results demonstrate the interaction and complementarity between di¤erent dimensions of liquidity. Right after the shock, there is a long-run e¤ect on prices as a result of which the spread becomes wider than in the steady state, such that one aspect of liquidity (spread) deteriorates. However, at the same time depth increases which implies an improvement of another dimension of liquidity. In later periods, we 6 A negative return on the ask means an improvement of the best ask. On the other hand, a positive return on the bid points to an improvement of the best bid. Both imply a narrower spread. 16 have the opposite evolution: depth declines to its steady-state, but also the spread reverts and becomes smaller. Also, we …nd evidence for asymmetries in the impact of shocks. Shocks on the ask side of the market have a larger impact than shocks on the bid side. This can be seen by comparing the responses of ln (A), ln (AD) and ln (Dur) in Panel A with ln (B), ln (BD) and ln (Dur) in Panel B. The median values in Panel A are always larger, in other words, a shock resulting from an aggressive buy order has a larger impact than a shock resulting from an aggressive sell order. The speed of recovery of the variables, or resiliency, is very similar, however. Escribano and Pascual (2006) also report asymmetric adjustments of ask and bid prices and asymmetric impacts of buyer and seller initiated trades. We show that this conclusions extends to other dimensions of liquidity such as depth and duration. 5.2.2 Spread and Depth Imbalances An interesting transformation of our model allows for analyzing the behavior after a liquidity shock of the bid-ask spread Spread (in cents) and the log depth imbalance, ln (BADR), de…ned as the log of the ratio of depth at the best bid and ask (in euro) ln (AD=BD). ln (BADR) = 0 can then be interpreted as a balanced limit order book (i.e. depth at best bid and ask are equal), ln (BADR) > 0 means that there is an imbalance at the bid side (i.e. larger depth at the bid side, compared to the ask side) and ln (BADR) < 0 implies an imbalance at the ask side. We estimate a similar model as Equation (1), but rede…ne the vector of endogenous variables as yt = fSpreadt ; ln (BADRt ) ; ln (Durt )g The vector of exogenous variables xt , number of lags and estimation procedure remain the same as before. Impulse responses after a liquidity shock are computed using the procedure outlined in Appendix A. Figure 2 draws these impulse response functions during a period of 15 orders (x-axis) after the shock. Liquidity shocks are again measured by an order of type M O_B1 in Panel A (shock on the ask side), and by an order of type M O_S1 in Panel B (shock on the bid side). The …rst graph in each panel draws the impact of such shock on bid-ask spread Spread (in cents), the second graph the impact on ln (BADR), the log of the ratio of depth at the best bid and ask (in euro) ln (AD=BD). The third graph shows the impact on log duration (in seconds) ln (Dur). The simulation for the impulse responses is done for each stock separately, full lines in the graphs represent the median value of the responses across stocks, the upper (lower) dashed lines are the 95% (5%) percentile across stocks. The dotted straight lines are the steady-state values, measured as the average value of the variable over the sample period. 17 Please insert Figure 2 around here. We …nd that the spread increases directly after the shock, to 11 cents (or ticks, since tick size in 1 cent for all stocks), which is almost double the value of the steady-state spread. This shows again that our measure for a liquidity shock indeed models indeed a signi…cant event. Also, the order book becomes imbalanced: after a shock on the ask (bid) side, ln (BADR) becomes negative (positive), implying an larger depth at the ask (bid) side. The market is resilient, however. Both spread and depth imbalance revert to their steady-state values within around 15 orders after the liquidity shock. For log duration the results are in line with the main model above. 5.2.3 Midprice Returns and Average Depth In a next subsection, we implement another transformation of our model. More speci…cally, denote the return (in %) on the midprice M (the average of ask and bid) as ln (Mt ), and let ln (BAD_Avgt ) be the log of the average depth at the best ask and bid price. We then rede…ne the vector of endogenous variables as follows: yt = f ln (Mt ) ; ln (BAD_Avgt ) ; ln (Durt )g The vector of exogenous variables xt , number of lags, estimation procedure and computation of impulse responses remains the same as before. Figure 3 presents the impulse response functions, the interpration of this …gure is identical to the one in the previous subsection. Please insert Figure 3 around here. From this …gure, it can be seen that a liquidity shock has a log-run impact on midprices. After a liquidity shock on the ask, the midprice increases. In subsequent periods, returns are slightly negative meaning a small reversal of midprices. After a shock in the bid side, a symmetric result is found, which is slightly smaller in magnitude. Further, a liquidity shock induces an increase in the log average depth ln (BAD_Avg). It returns relatively quickly (within 15 orders) to its steady-state after a shock at the bid side, but it takes longer after a shock on the ask side. This con…rms earlier …ndings on asymmetries, i.e. that shocks on the ask side have a stronger impact. 5.2.4 Trading Frequency and Relative Tick Size While the percentiles in the …gures above already provided an idea of the di¤erences in impact of liquidity shocks across stocks, we discuss this issue more in detail in this 18 subsection. More in particular, we …rst divide the 35 stocks in our sample …rst on basis of their trading activity, i.e. the average daily number of trades (see Table 2). The most frequently traded subsample M ost_F req contains the 10 stocks that are most frequently traded, the least frequently traded subsample Least_F req then comprises the 10 stocks who are least frequently traded (the 15 middle stocks are not considered). The distinction between frequently and less frequently traded stocks motivated by the model of Foucault, Kadan and Kandel (2005), who show that resiliency is decreasing in the order arrival rate. The reasoning is that, when the order arrival rate increases, limit order traders become less aggressive in their price improvements. As a consequence, more orders are needed to bring down the spread to its competitive level, implying resiliency declines.We use trading frequency, i.e. the average number of daily trades, as a proxy for the arrival rate. Spierdijk (2004) shows that considerable di¤erences exist between the price impact of trades for frequently and infrequently traded stocks. For both subsamples, we repeat the same estimation and simulation as above. Important to stress is that the steady-state level is computed seperately for the two subsamples. The reason is that we are interested in reversion of liquidity dimensions to their normal level (steady state) and this level can be di¤erent across subsamples. To save space, we do not report the estimation results or plots of the impulse responses, but just discuss the main …ndings. The results are available upon request. The key result of this analysis con…rms the result in the model of Foucault, Kadan and Kandel (2005): we …nd a negative relation between resiliency and trading frequency. Although almost all liquidity dimensions7 (i.e. spread, depth8 , depth imbalance, average depth) do revert to their steady state within at maximum 30 periods, we …nd that reversion to the steadystate occurs much faster, i.e. it takes less orders after the shock, for less frequently traded stocks. Given our and Foucault et al.’s de…nition of resiliency, this implies that resiliency is thus higher for less frequently traded stocks. Only for duration, we …nd little di¤erence. Secondly, we …nd some di¤erences in magnitude. The impact of a shock on returns is larger for stocks in the Least_F req group, but still realized quickly. The impact on depth however is smaller for these stocks, compared to frequently traded stocks. The explanation for these …ndings is as follows. For frequently traded stocks, the second best price in the book and those beyond are closer to the best one, while for the Least_F req stocks, the di¤erence between the subsequent prices in the book is larger. Furthermore, depth is more evenly distributed in the book for Least_F req stocks than for M ost_F req stocks for which depth beyond the best prices is larger. For duration, the impact of a shock is larger for Least_F req stocks. Important to note is that while the recovery of variables, is expressed in number of orders for the two subsamples, this takes much more time expressed in seconds for Least_F req stocks 7 8 Recall that we do not investigate reversal for prices, as they are non-stationary. The only exception to this result is ln (BD) : 19 than in the case of M ost_F req stocks, since the time between orders is larger for the latter. In other words the period of 15 orders is much longer (in seconds) for these Least_F req stocks, since the duration between orders is larger. Next, we create two subsamples based on relative tick size. The relative tick size Rel_tick for each stock is de…ned as the ratio of the tick size (in cent) to the average price midpoint (in euro): Rel_ts = tick size average midprice Creating separate groups based on the minimum price variation is in line with the model of Foucault, Kadan and Kandel (2005). They show that there exists a link between the resiliency of an order-driven market and tick size. More speci…cally, a smaller tick size reduces resiliency9 . The reasoning is that when the tick size is larger, traders need to improve prices by more than they would with a smaller tick size in order to obtain price priority. This spread improvement e¤ect causes the bid-ask spread to narrow faster between transactions, making the market more resilient. The subsample Small_T ick contains the 10 stocks with the smallest relative tick size, the subsample Large_T ick the 10 stocks with the smallest relative tick size (the 15 middle stocks are again not considered). Again, we compute the steady-state level separately for the two subsamples. To save space, we do not report the estimation results or plots of the impulse responses, but discuss the main …ndings. We …nd that - as predicted theoretically by Foucault - that resiliency is higher for stocks with a larger relative tick size. For the Large_T ick subsample, all liquidity dimensions (i.e. spread, depth, depth imbalance, average depth) return faster to their respective steady-state levels, compared to the Small_T ick subsample. Secondly, we also …nd some di¤erences in magnitude. The results show that the impact of an aggressive order on returns is found to be much larger for large tick stocks. Secondly, the impact of aggressive orders on depth is also larger for large tick stocks. This is the case both at the side of the market at which the aggressive order was submitted as on the other side. This comparison between both groups for returns and depth suggests that the larger relative tick size is a binding constraint for this group of stocks. These results are in line with the literature that investigates tick size. When faced with a smaller tick size, traders use more intermediate prices, but the depth at these prices is lower. Finally, the impact of a shock on duration is comparable for stocks with large and small tick size. 9 To be precise, they prove that a market having a minimum price variation is more resilient that a market without. 20 6 Conclusion In this paper we analyze resiliency in an order-driven market. We develop a VARmodel that captures di¤erent dimensions of liquidity, being prices, depth, duration. Our econometric model allows for taking into account relations between bid and ask sides of the market, as well as between liquidity dimensions. We used the estimated VAR to simulate liquidity shocks, measured by very aggressive buy and sell orders that at least consume all depth at the …rst three ask and bid prices in the book. A liquidity shock is found to have a permanent e¤ect on prices at the side of the market at which the shock occurred, but the impact is realized almost instantaneously. However, in line with Rosu (2009), we also document an e¤ect - though smaller in magnitude - on the best price at the other side of the market, which partly o¤sets the e¤ect of the own side. Depth at the best prices increases after a liquidity shock, but mainly at the side of the market of the shock. Duration declines just after a negative shock, but increases quickly again to converges within a few orders to its average value value. Our results clearly demonstrate the importance of incorporating di¤erent dimensions of liquidity in the analysis. After a liquidity shock, we …nd a permanent e¤ect on prices, with returns (in absolute value) of initially around 0.4% (realized on an order by order basis) and a widening of the spread (almost doubling compared to its steadystate value). On the other hand, depth at the best prices increases, initially with up to 20%. This implies on the one hand an derioration of liquidity since the spread widens, but at the same time, another dimension of liquidity improves since depth at the best prices increases. In subsequent periods, we observe the opposite evolution: the spread reverts (declines) back to the steady-state level but also depth declines. These results demonstrate the need to account for interaction and complementarity between di¤erent dimensions of liquidity. The Spanish market is found to be resilient, since all dimensions of liquidity revert to their steady-state level within around 15 orders after the shock. Furthermore, an analysis of liquidity should also allow for asymmetries in dynamics at bid and ask side of the market, since we …nd that shocks at the ask side have a larger impact compared to stocks on the bid side. These …ndings thus comprise relevant recommendations for theoretical modeling and empirical research. Furthermore, some di¤erences between groups of stocks are found. The e¤ect of shocks on both returns and depth is larger for stocks with a larger relative tick size. This may indicate that tick size is a binding constraint for these stocks. The impact of a shock on returns is also larger for less frequently traded stocks, but still realized relatively quickly. The impact on depth however is smaller for these stocks. Concluding, the analysis in this paper indicates that despite the absence of market makers with an obligation to maintain an orderly market and provide liquidity, pure order-driven markets seem able to cope with large liquidity shocks. They recover 21 quickly from the impacts of such shocks. In other words, the limit order book is able to provide su¢ cient liquidity to the market. 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Nolte, I., 2008, Modeling a Multivariate Transaction Process, Journal of Financial Econometrics, 6, pp. 143-170. Pardo, A., R. Pascual, 2007, On the Hidden Side of Liquidity, Unpublished Working Paper. Parlour, C., 1998, Price Dynamics in Limit Order Markets, Review of Financial Studies, 11, pp. 789-816. Ranaldo, A., 2004, Order Aggressiveness in Limit Order Book Markets, Journal of Financial Markets, 7, pp. 53-74. Rosu, I., 2009, A Dynamic Model of the Limit Order Book , Review of Financial Studies, 22, pp. 4601-4641. Spierdijk, L., 2004, An Empirical Analysis of the Role of the Trading Intensity in Information Dissemination on the NYSE, Journal of Empirical Finance, 11, pp. 163184. 24 25 M O_B1 M O_B2 M O_B3 LO_B1 LO_B2 LO_B3 Canc_B1 Canc_B2 Canc_B3 Sell orders are classi…ed symmetrically in the same way as buy orders from M O_S1 to Canc_S3: Panel B: Sell Orders market buy order that consumes at least all depth until the 3th ask price (or a further price) and part of subsequent level market buy order that consumes minimum all depth at the best ask price and maximum part of the depth at the 3th ask price market buy order that consumes part of the depth at the best ask price limit buy order that improves the best bid price limit buy order that increases depth at the best bid price limit buy order that queues in the book beyond the best bid price cancellation or modi…cation of buy order that consumes all depth at the best bid price cancellation or modi…cation of buy order that consumes part of the depth at the best bid price1 cancellation or modi…cation of buy order beyond the best bid Notation De…nition Panel A: Buy Orders Note: This table gives an overview of the various order types. Panel A (Panel B) presents the various buy (sell) order types. The notation is given in the …rst column, the de…nition of the type in the second column. Table 1: De…nition of the Variables Table 2: Sample: Descriptive Statistics Note: This table presents the descriptive statistics of the sample. The …rst column gives the code of the stock, while columns 2 and 3 in the table present the market capitalization (in 1000 euro) at the end of the year 2000 and the total trading volume (in 1000 euro) during 2000. The next four columns show the average daily number of trades, the average trade size (in shares), the average duration (in seconds) between orders, the average bid-ask spread and the average midprice, where averages are computed over the sample period. For all stocks, the tick size is equal to 0.01 euro. Market Cap Annual Trading # Trades Trade Size Duration Spread Midprice ACE 2,590,264 1,362,467 342 1751 48.93 3.02 8.99 ACR 1,153,006 866,086 370 802 41.62 3.17 9.3 ACS 1,607,952 1,801,030 249 664 51.61 13.7 27.11 ACX 1,925,285 2,518,999 329 650 40.52 13.07 32.09 AGS 1,818,759 887,916 233 875 59.01 6.63 14.19 ALB 1,969,448 1,288,164 189 910 58.35 19.03 27.55 ALT 5,040,279 7,958,527 773 1832 20.93 4.05 16.31 AMS 4,663,754 6,940,124 925 1552 16.58 2.84 10.23 ANA 2,583,331 2,135,196 288 531 45.54 14.68 38.48 BBVA 50,654,255 61,753,870 2024 3944 8.58 1.71 16.07 BKT 2,709,682 5,406,253 559 490 26.33 11.73 44.19 CAN 2,252,616 2,861,239 148 1191 79.40 12.06 20.97 CTG 600,639 782,829 369 1316 34.48 7.29 18.94 DRC 1,999,276 1,979,024 440 1853 33.82 3.6 9.94 ELE 19,216,351 28,783,198 1496 2549 11.52 2.45 20.8 FCC 2,426,060 1,637,996 323 695 41.43 8.63 19.56 FER 1,907,601 1,144,835 397 538 40.02 4.96 13.92 IBE 12,035,682 12,600,314 758 3451 21.08 2.57 13.8 IDR 1,486,405 2,358,084 531 654 28.35 5.87 17.81 MAP 1,228,587 921,525 117 1493 101.95 12.12 18.27 NHH 1,565,881 1,780,277 232 2022 57.40 6.26 13.09 POP 8,056,418 6,826,078 464 1092 29.63 8.57 34.72 PRS 3,851,100 3,369,875 555 883 27.40 7.95 23.68 REE 1,359,464 1,075,761 280 662 51.85 4.49 10.66 REP 20,779,096 30,377,832 1655 2655 10.45 2.41 20.32 SCH 51,476,555 52,786,425 2962 3804 6.24 1.34 11.45 SGC 2,037,499 4,146,904 546 451 23.93 12.24 33.37 SOL 2,034,392 1,309,640 293 1199 49.64 4.7 10.92 TEF 76,396,509 152,323,837 6609 3505 2.70 1.56 21.9 TPI 2,098,936 5,192,664 1009 1384 15.35 2.41 8.83 TPZ 563,465 3,708,955 848 1915 19.48 1.6 4.92 TRR 7,206,684 32,774,256 4597 814 3.52 4.75 34.53 UNF 5,956,481 6,864,353 414 2159 36.33 4.4 20.47 VAL 836,328 914,042 254 1580 59.31 3.01 6.71 ZEL 1,989,150 5,817,857 1776 594 8.35 4.25 34.95 26 Table 3: Model Variables: Descriptive Statistics Note: Panel A presents the descriptive statistics of the endogenous variables, i.e. their mean, median and standard deviation across the stocks in our sample. ln (A) and ln (B) are the returns of the best ask and bid in %, ln (AD) and ln (BD) the log of depth in euro at the best ask (bid), ln (Dur) the log of duration in seconds since the previous order. Spread is the bid-ask spread in cents, ln (BADR) is the log of the ratio of depth at the best bid and ask, ln (M ) is the return on the midprice in % and ln (BAD_Avg) is the log of the average of depth in euro at the best bid and ask. Panel B shows the frequency of occurring, in % of the total number of orders, of the di¤erent order types, and the average order size (in shares and in logs) of each order type. In both panels, all statistics are computed after winsorizing at the 99.5% level. Panel A: Endogenous Variables ln(At ) ln(Bt ) Mean Median S.d. -0.0004 0.0000 0.0945 0.0002 0.0000 0.0943 Mean Median S.d. Spreadt 6.3600 4.9100 4.4200 ln(BADRt ) 0.0150 0.0103 1.7770 ln(ADt ) ln(BDt ) ln(Durt ) 9.4985 9.6060 1.2895 9.5134 9.6235 1.2684 1.7706 2.3428 2.5158 ln(Mt ) ln(BAD_Avgt ) -0.0001 9.5060 0.0000 9.6147 0.0772 1.2790 Panel B: Exogenous Variables Buy Orders Notation M O_B1t M O_B2t M O_B3t LO_B1t LO_B2t LO_B3t Canc_B1t Canc_B2t Canc_B3t Freq Size 0.06% 11069 5.76% 2687 15.17% 1050 8.24% 2104 5.55% 1789 6.32% 1487 2.12% 1494 1.07% 1557 6.10% 1541 Sell Orders ln(Size) Notation 8.423 6.514 5.773 6.582 6.618 6.468 6.400 6.485 6.582 M O_S1t M O_S2t M O_S3t LO_S1t LO_S2t LO_S3t Canc_S1t Canc_S2t Canc_S3t 27 Freq Size 0.08% 10845 6.00% 2836 17.10% 833 7.14% 1956 4.98% 1795 6.08% 1381 1.87% 1451 0.90% 1530 5.47% 1572 ln(Size) 8.455 6.534 5.543 6.516 6.555 6.371 6.316 6.403 6.543 Table 4: Estimation Results VAR-model Note: P5 This table present the estimation results of equation (1): yt = A0 + A y + B x + LSpread + u . The vector of endogenous variables is yt = 0 t t 1 t l=1 l t l f ln (At ) ; ln (Bt ) ; ln (ADt ) ; ln (BDt ) ; ln (Durt )gwith ln (At ) ( ln (Bt )) the return on the best ask (bid) price in % at time t, ln (ADt ) (ln (BDt )) the log of depth in euro at the best ask (bid) at time t, ln (Durt ) the log of duration in seconds since the previous order and ln the natural logarithm. The vector of exogenous variables is xt = fM O_B1t ; :::; Canc_S2t ; ln (Size_M O_B1t ) ; :::; ln (Size_Canc_S2t ) ; T 01t ; :::T 17t g. The de…nition of the order types M O_B1t ; :::; Canc_S2t can be found in Table 1; the next set of variables in xt are the corresponding log of order sizes (in number of shares); T 01t ; :::T 17t are time-of-dummies, equal to one if the order is in period 1,...,17 of the day, respectively, and zero otherwise. LSpreadt 1 = ln (At ) ln (Bt ). Ai , Bi and are the coe¢ cient matrices to be estimated. Estimations are done per stock using least squares, Newey-West standard errors are computed. The …rst column shows the right-hand-side variables, the next columns the VAR equations (endogenous variables are shown in the header). For each variable, we show the unweighted average value of the coe¢ cient across stocks, followed - between brackets - by the number of stocks out of 35 for which the coe¢ cient is signi…cantly positive (…rst element) and negative (second element) at the 5% level. All endogenous variables, log order sizes and log durations are winsorized at the 99.5% level. ln(At ) ln(Bt ) ln(ADt ) ln(BDt ) ln(Durt ) ln(At 1) -0.0980 (0,35) 0.0220 (35,0) 0.4030 (35,0) 0.0510 (16,0) -1.0560 (0,35) ln(At 2) -0.0540 (0,35) 0.0110 (33,0) 0.2730 (35,0) 0.0630 (16,0) 0.6410 (35,0) ln(At 3) -0.0370 (0,35) 0.0060 (23,0) 0.1960 (35,0) 0.0530 (12,0) 0.4310 (30,0) ln(At 4) -0.0250 (0,35) 0.0050 (18,0) 0.1470 (33,0) 0.0500 (18,0) 0.3520 (28,0) ln(At 5) -0.0170 (0,35) 0.0040 (20,1) 0.0650 (24,0) 0.0290 (10,0) 0.2130 (21,0) ln(Bt 1) 0.0220 (35,0) -0.0990 (0,35) -0.0600 (0,17) -0.3970 (0,35) 0.9840 (35,0) ln(Bt 2) 0.0110 (32,0) -0.0530 (0,35) -0.0840 (0,18) -0.2660 (0,34) -0.6750 (0,34) ln(Bt 3) 0.0070 (28,0) -0.0360 (0,35) -0.0690 (0,15) -0.1830 (0,33) -0.4680 (0,31) ln(Bt 5) 0.0030 (15,1) -0.0230 (0,35) -0.0530 (0,13) -0.1350 (0,33) -0.4130 (0,35) ln(Bt 5) 0.0020 (14,0) -0.0160 (0,35) -0.0380 (0,9) -0.0500 (0,13) -0.2710 (0,29) ln(ADt 1) 0.0020 (35,0) 0.0010 (29,1) 0.7680 (35,0) -0.0080 (0,27) -0.0400 (0,31) ln(ADt 2) -0.0010 (0,28) 0.0000 (0,4) 0.0430 (35,0) 0.0040 (11,0) 0.0080 (5,6) ln(ADt 3) 0.0000 (0,16) 0.0000 (1,2) 0.0170 (35,0) 0.0020 (7,0) 0.0100 (8,2) ln(ADt 4) 0.0000 (0,10) 0.0000 (1,3) 0.0140 (35,0) 0.0020 (6,0) 0.0070 (2,1) ln(ADt 5) -0.0010 (0,24) 0.0000 (0,2) 0.0230 (35,0) 0.0040 (16,0) 0.0020 (3,2) ln(BDt 1) -0.0010 (0,28) -0.0020 (0,35) -0.0080 (0,27) 0.7530 (35,0) -0.0530 (0,32) ln(BDt 2) 0.0000 (3,4) 0.0010 (26,0) 0.0040 (12,0) 0.0450 (35,0) 0.0170 (11,4) ln(BDt 3) 0.0000 (3,3) 0.0000 (11,0) 0.0020 (7,1) 0.0170 (34,0) 0.0100 (5,0) ln(BDt 4) 0.0000 (2,4) 0.0000 (9,0) 0.0020 (8,0) 0.0150 (35,0) 0.0040 (4,1) ln(BDt 5) 0.0000 (5,0) 0.0000 (17,0) 0.0040 (18,0) 0.0230 (35,0) 0.0080 (7,1) ln(Durt 1) 0.0000 (2,7) 0.0000 (11,1) -0.0010 (1,11) 0.0000 (0,6) 0.0170 (23,6) ln(Durt 2) 0.0000 (1,12) 0.0000 (16,0) 0.0000 (1,5) 0.0000 (3,2) 0.1080 (35,0) ln(Durt 3) 0.0000 (0,11) 0.0000 (10,0) 0.0000 (0,7) 0.0000 (2,1) 0.0700 (35,0) ln(Durt 4) 0.0000 (0,10) 0.0000 (15,1) 0.0000 (2,4) 0.0000 (2,3) 0.0700 (35,0) ln(Durt 5) 0.0000 (0,4) 0.0000 (7,1) 0.0000 (2,5) 0.0000 (2,4) 0.0560 (35,0) 0.0140 (34,0) -0.0160 (0,33) 1.2550 (35,0) 1.3770 (35,0) 1.9090 (35,0) C 28 Table 4 (continued) ln(At ) ln(Bt ) ln(ADt ) ln(BDt ) ln(Durt ) M O_B1t 0.4339 (35,0) -0.0002 (0,0) 1.3310 (34,0) -0.0230 (0,0) -0.3433 (0,6) M O_B2t 0.1734 (35,0) 0.1071 (35,0) 0.5631 (29,6) -0.2867 (0,34) -0.8168 (0,35) M O_B3t -0.0005 (0,0) 0.0020 (7,0) -0.5087 (0,35) 0.0188 (11,0) -0.5793 (0,35) LO_B1t 0.0068 (35,0) 0.1004 (35,0) -0.0012 (0,2) -0.0288 (20,14) -1.0720 (0,35) LO_B2t 0.0032 (28,0) 0.0005 (0,0) 0.0009 (2,0) 1.0883 (35,0) -1.3744 (0,35) LO_B3t 0.0019 (6,0) 0.0029 (22,0) 0.0032 (2,0) -0.0235 (0,18) -0.7196 (0,35) Canc_B1t 0.0017 (0,0) -0.1502 (0,35) 0.0142 (0,0) 0.0145 (14,20) -0.0318 (3,4) Canc_B2t 0.0018 (0,0) 0.0006 (0,0) 0.0126 (0,0) -0.7161 (0,35) 0.0234 (2,2) Canc_B3t 0.0024 (15,0) 0.0022 (8,0) 0.0026 (0,0) 0.0049 (3,0) -0.0366 (0,6) M O_S1t -0.0005 (0,0) -0.4078 (0,35) 0.0018 (0,0) 1.2596 (34,0) -0.4278 (0,6) M O_S2t -0.1061 (0,35) -0.1664 (0,35) -0.2856 (0,35) 0.5306 (29,5) -0.8299 (0,35) M O_S3t 0.0007 (3,0) 0.0024 (12,0) 0.0104 (6,0) -0.5284 (0,35) -0.4818 (0,35) LO_S1t -0.1027 (0,35) -0.0046 (0,31) -0.0204 (20,14) -0.0036 (0,2) -1.2030 (0,35) LO_S2t 0.0019 (5,0) -0.0007 (0,0) 1.1220 (35,0) 0.0006 (2,1) -1.3410 (0,35) LO_S3t -0.0005 (0,1) 0.0006 (0,0) -0.0233 (0,16) 0.0053 (2,0) -0.5815 (0,35) Canc_S1t 0.1604 (35,0) 0.0008 (1,0) -0.0029 (15,20) 0.0188 (1,0) -0.0143 (8,2) Canc_S2t 0.0013 (2,0) 0.0009 (0,0) -0.7542 (0,35) 0.0161 (0,0) 0.0461 (3,0) Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes -1.7336 (0,35) 1.7459 (35,0) -2.1463 (0,18) -0.6536 (5,7) -51.6209 (1,34) ln(Size_M O_B1t ) ... ln(Size_Canc_S2t ) T 01t ... T 17t LSpreadt Adj R2 1 0.50543 0.50961 0.71097 29 0.69507 0.10115 30 Panel A: Responses to Liquidity Shock on the Ask Side M O_B1 Note: This …gure presents the impulse responses of a number of variables after a liquidity shock, during a period of 15 orders (x-axis) after the shock. This shock is de…ned as an order of type M O_B1 in Panel A (measuring a shock on the ask side), and as an order of type M O_S1 in Panel B (measuring a shock on the bid side). The …rst graph in each panel draws the impact of such shock on the return on the best ask price ln (A), the second graph the impact on the return on the best bid price ln (B). The third and fourth graph display the impact of the shock on the log of depth in euro at the best ask and best bid price, ln (AD) and ln (BD) respectively. The …fth graph shows the impact on log of duration (in seconds) ln (Dur). The simulation for the impulse responses is done for each stock separately, full lines in the graphs represent the median value of the responses across stocks, the upper (lower) dashed lines are the 95% (5%) percentile across stocks. The dotted straight lines are the steady-state values, measured as the average value of the variable over the sample period. The computational details for the impulse responses can be found in Appendix A. Figure 1: Impulse Responses after a Liquidity Shock 31 Panel B: Responses to Liquidity Shock on the Bid Side M O_S1 Figure 1 (continued) Figure 2: Spread Model: Impulse Responses after a Liquidity Shock Note: This …gure presents the impulse responses of a number of variables after a liquidity shock, during a period of 15 orders (x-axis) after the shock. This shock is de…ned as an order of type M O_B1 in Panel A (measuring a shock on the ask side), and as an order of type M O_S1 in Panel B (measuring a shock on the bid side). The …rst graph in each panel draws the impact of such shock on bid-ask spread Spread (in cents), the second graph the impact on ln (BADR), the log of the ratio of depth at the best bid and ask (in euro) ln (AD=BD). The third graph shows the impact on log of duration (in seconds) ln (Dur). The simulation for the impulse responses is done for each stock separately, full lines in the graphs represent the median value of the responses across stocks, the upper (lower) dashed lines are the 95% (5%) percentile across stocks. The dotted straight lines are the steady-state values, measured as the average value of the variable over the sample period. The computational details for the impulse responses can be found in Appendix A. Panel A: Responses to Liquidity Shock on the Ask Side M O_B1 Panel B: Responses to Liquidity Shock on the Bid Side M O_S1 32 Figure 3: Midprice Model: Impulse Responses after a Liquidity Shock Note: This …gure presents the impulse responses of a number of variables after a liquidity shock, during a period of 15 orders (x-axis) after the shock. This shock is de…ned as an order of type M O_B1 in Panel A (measuring a shock on the ask side), and as an order of type M O_S1 in Panel B (measuring a shock on the bid side). The …rst graph in each panel draws the impact of such shock on the return (in %) on the midprice ln (M ), with M de…ned as the average of the best ask and bid. The second graph plots the impact on the log of the average of depth at the best bid and ask (in euro) ln (BAD_Avg). The third graph shows the impact on log of duration (in seconds) ln (Dur). The simulation for the impulse responses is done for each stock separately, full lines in the graphs represent the median value of the responses across stocks, the upper (lower) dashed lines are the 95% (5%) percentile across stocks. The dotted straight lines are the steady-state values, measured as the average value of the variable over the sample period. The computational details for the impulse responses can be found in Appendix A. Panel A: Responses to Liquidity Shock on the Ask Side M O_B1 Panel B: Responses to Liquidity Shock on the Bid Side M O_S1 33 Appendix A: Simulation Methodology: Computation of the Impulse Response Functions Using the VAR model in Equation (1), the resiliency of the market can be investigated by simulating a liquidity shock on basis of this model. More speci…cally, we start from an order of type i, i 2 fM O_B1, M O_S1g, and compute the evolution of returns, depths and duration during a period of h = 1::15 orders after the submission of the initial order. In the simulation procedure, which is inspired by Escribano and Pascual (2006), it is assumed that an aggressive order of type i is submitted in interval 9 (this is between 12h45 and 13h15). After having estimated the VAR model in (1), the simulation procedure proceeds through the following steps: 1. As stated, a liquidity shock will be measured by an order of type i in interval 9 of the day. This is simulated by setting the relevant order type and time of day dummies equal to one. So, T 09t = 1, and either M O_B1 or M O_S1 = 1, depending on the value of i. The corresponding order size is set equal to the average order size of type i. 2. In a second step, we need to compute the initial values for the lags of the endogenous variables (yt l ; l = 1::L), as well as the lags of the exogenous variables (xt m , m = 1::M )10 . They are equated to their mean, conditional upon the submission of an order of type i in period t. In this way, we consider in our simulation the average market conditions around a liquidity shock.11 3. For each of the exogenous variables, a predicted value needs to be computed for h = 1::15 periods after the shock (recall that one period refers to a trade). For predicting the order type and order size variables, we calculate the average value of each of these variables in period t + h, h = 1::15, conditional upon the submission of a type i order in interval 9, which is indexed by t. Finally, we need predicted values for the last group of exogenous variables, being the time of day dummies. For them, we assume that the 15 orders following an aggressive order, fall entirely in the ninth interval of the day (i.e. between 12h45 and 13h15), such that T 09t+h = 1; h = 1::15. The summary statistics on duration indicate that this is a plausible assumption. Moreover, it is not a restrictive assumption since, as will turn out later, the coe¢ cients of the time of day dummies often are not signi…cant, neither econometrically, nor from an economic point of view. 10 The values for x0 are those of the initial shock and are determined in step 1. As a robustness check, we also take the unconditional mean over the sample period. The interpretation of this alternative is that in this way the system starts from a “stationary”or “steadystate”situation, after which an unexpected shock arrives. The result are unchanged and are available upon request. 11 34 4. On the basis of the VAR in Equation (1) and the necessary data computed in the previous three steps, we are able to compute the impulse response functions for bid and ask returns, depth at best bid and ask and duration for each period h = 1; :::; 15 after the liquidity shock, i.e. the submission of the order of type i. Note that for each period h, the value of Spread is updated in the following way: Spreadt+h = Spreadt+h 1 + ln At+h ln Bt+h . 35