Does Speed Matter? The Role of High-Frequency Trading for Order Book Resiliency

We analyze limit order book resiliency following liquidity shocks initiated by large market orders. Based on a unique data set, we investigate whether high-frequency traders are involved in the replenishment of the order book. Therefore, we relate the net liquidity provision of high-frequency traders, algorithmic traders, and human traders around these market impact events to order book resiliency. While all groups of traders react, our results show that only high-frequency traders reduce the spread within the first seconds after the market impact event. Order book depth replenishment, however, takes significantly longer and is mainly accomplished by human traders' liquidity provision.


I Introduction
Since the emergence of highly automated trading desks and fully electronic securities markets, academics, regulators, and trading firms argue about the direct and indirect consequences of this technological evolution on modern securities markets. Among the most controversially discussed issues is the impact of high-frequency traders (HFTs) on market quality in open limit order books (Haferkorn, 2017). In particular, proponents of high-frequency trading (HFT) argue that automated decision making and low-latency infrastructure favor liquidity provision because information evaluation and the corresponding trading reaction are conducted more efficiently.
Therefore, liquidity increases which leads to a reduction of implicit transaction costs for all market participants. The positive effect of HFTs on liquidity particularly holds for HFTs acting as market makers, which represent the majority of HFTs in terms of trading volume and order messages (Hagströmer and Nordén, 2013).
Various academic studies have shown the positive impact of HFT on spreads and order book depth, which account for the price and quantity dimension of liquidity.
However, very little empirical evidence exists concerning the contribution of HFTs to the third dimension of liquidity, i.e., order book resiliency, which is the dynamic characteristic of liquidity representing the recovery of the order book after a liquidity shock 1 . Especially in case of sudden drops in liquidity, HFTs are able to react quicker and more precisely to such order book changes than other groups of traders.
Consequently, in particular HFTs might contribute to the recovery of liquidity and, thus, foster order book resiliency, which leads to increased price efficiency and lower implicit transaction costs after liquidity shocks.
1 Order book resiliency as the third dimension of liquidity is already described by early papers on market microstructure. Black (1971), Kyle (1985), and also Harris (2003) describe resiliency as the quick recovery of prices after market impact events. Building on this, Foucault et al. (2005) develop a model of order book resiliency which defines market resiliency as the spread reversion to its former level after a liquidity shock.
Based on the outlined debate on the role of HFT for liquidity provision, we study how different types of traders (i.e., HFTs, ATs, and human traders) replenish liquidity in the order book following a large aggressive order leading to market impact and a sudden drop in liquidity. Thereby, we particularly aim to reveal the contribution of HFTs to order book resiliency relative to non-HFT participants. During and after such events, low-latency traders can maximize their speed advantages and benefit from the widened spread and the reduced depth. Given HFTs follow such strategies, other market participants may profit from increased order book resiliency due to HFT. Moreover, a fast recovery of liquidity in terms of spread and depth lowers implicit transaction costs for investors and ultimately the liquidity component of companies' cost of capital. Therefore, we aim to investigate the contribution of different types of traders to order book resiliency by utilizing a sample of large market orders that hit the open limit order book and walk through several order book levels leading to market impact. In particular, we focus on the net liquidity provision of HFTs and non-HFTs around these market impact events to add further evidence on the dynamic aspect of liquidity. We rely on a proprietary data set provided by Deutsche Boerse, which enables us to identify HFT as well as algorithmic trading (AT) activity based on corresponding flags. Thus, we are able to provide detailed insights on order book resiliency in presence of HFTs.
Our results show that HFTs contribute significantly to the replenishment of the open limit order book. Specifically, we find HFTs to be the driving force behind reestablishing tight spreads within short periods of time. In contrast, algorithmic traders (ATs) without low-latency infrastructure and human traders do not significantly support spread resiliency. The recovery of bid-ask spreads is accomplished within the first few seconds after a market impact event, while the largest fraction of the widened spread recovers already within the first second. Human traders, although adapting their submission behavior within the very first seconds after the event, do not significantly affect spread resiliency. When considering the resiliency of order Electronic copy available at: https://ssrn.com/abstract=2603205 The Role of HFT for Order Book Resiliency book depth, however, the results considerably change. HFTs do not sufficiently replenish order book depth as they predominantly submit small volume orders mostly aiming at the top of the order book. This also holds for ATs. Depth resiliency, therefore, is mainly achieved by human traders showing high net liquidity provisions after market impact events. Therefore, fast liquidity provision by HFTs, which is also prevailing after a significant market impact, represents only a very specific and limited contribution to overall order book resiliency. In order to mitigate the price impact of further large orders, order book depth has to be replenished by various limit orders of relevant size. As shown in our analysis, this is mainly achieved with the help of human traders that persistently stay in the order book and offer vast amounts of non-transient liquidity. Therefore, we show that different types of traders, namely HFTs and human traders, pursuing different strategies are needed to accomplish order book resiliency in all dimensions (i.e., spread and depth) in an efficient and fast manner.
The remainder of the paper is structured as follows: Within Section II, related literature on HFT and liquidity as well as order book resiliency as a specific dimension of liquidity is presented. In Section III, we describe our data set and provide descriptive analyses. Section IV and Section V outline the methodological approach as well as the results of our empirical study. Finally, we discuss our results in Section VI and Section VII concludes.

II.1 Liquidity Provision by High-Frequency Traders
in terms of spread and order book depth. Thereafter, the following subsection summarizes existing research on order book resiliency.
Research concerning the relation of HFT and liquidity in terms of spread and depth is mostly conducted using time-series regression techniques. Regarding bid-ask spreads, studies have shown that HFTs provide liquidity when spreads are wide and consume liquidity when spreads are tight (Carrion, 2013;Zhang and Riordan, 2011). In line with these results, Brogaard et al. (2014) observe that HFTs are more likely to participate in the order book when bid-ask spreads are wide, trading volume and price volatility are high, and when order book depth is low. Thus, HFTs contribute to decreasing spreads, which is further observed by Hasbrouck and Saar (2013). These results are supported by the observation that HFTs mostly follow market-making strategies and submit passive, i.e., liquidity providing, orders (Hagströmer and Nordén, 2013;Menkveld, 2013). Regarding algorithmic trading in general, Hendershott et al. (2011) find that ATs reduce the bid-ask spread on the New York Stock Exchange. Using a similar data set to our paper, Hendershott and Riordan (2013) confirm this finding.
In contrast to these positive results concerning the impact of HFT on liquidity, Lee (2015) finds that HFT has no effect on liquidity as spread and depth remain unaffected. Goldstein et al. (2018) likewise analyze the contribution of HFTs to overall liquidity and conclude that liquidity provision by HFTs should not be overestimated since they provide liquidity in the opposite direction of order imbalance. Different from our study, the authors focus on regular trading conditions showing how the trading decisions of HFTs depend on and influence order book imbalance. This paper, instead, analyzes the contribution of HFTs to order book resiliency after market impact events especially in light of HFTs' speed advantage in comparison to other traders. Thus, our study contributes to financial market research by revealing how different types of traders react after a market impact event leading to decreased liquidity and, more interestingly, how these traders contribute to the replenishment Electronic copy available at: https://ssrn.com/abstract=2603205 of different dimensions of liquidity, i.e., spread and order book depth resiliency. In contrast to Goldstein et al. (2018), we find evidence that HFTs do not act opportunistic during market impact events but initiate the resiliency process that other non-HFT traders join. Hautsch et al. (2017) find that HFTs tend to consume rather than provide liquidity around scheduled macroeconomic announcements. Our study, in contrast, analyzes market impact events due to sudden, non-news-related excess liquidity demand. In contrast to Hautsch et al. (2017), we provide evidence on how order book resiliency is accomplished by HFTs and human traders in the absence of macroeconomic buy or sell pressure, which affects different market participants differently.

II.2 Order Book Resiliency and High-Frequency Trading
The viability and efficiency of open limit order books depends on public limit orders and quotes standing in the order book, which have to be replenished quickly by traders after market impact events leading to a sharp decrease in liquidity. Order book resiliency represents this dynamic aspect of liquidity, i.e., the recovery of the static liquidity dimensions relative spread and order book depth to their "normal" levels after a liquidity shock. The importance of resiliency is also emphasized by the findings of Obizhaeva and Wang (2013), who show that optimal trading strategies do not depend on static liquidity properties such as relative spread and order book depth but on the speed at which supply of and demand for a security recover after a trade. Foucault et al. (2005) develop a theoretical model of spread resiliency in a limit order book where traders face a trade-off between the spread as a cost of immediacy and the cost of delayed execution. Concerning depth resiliency, Coppejans et al. (2004) are the first to analyze the variation of order book depth over time. They find that electronic order books exhibit high degrees of resiliency as liquidity shocks are resolved quickly. Nevertheless, the variation in order book depth affects trading strategies. These findings are consistent with the observations by Gomber et al. Electronic copy available at: https://ssrn.com/abstract=2603205 (2015), who find that implicit transaction costs of a round trip trade of given size quickly revert to a "normal" level after a liquidity shock and that large orders are timed, meaning they appear when liquidity is unusually high.
This mean reversion of spread and depth around a "normal" level is also shown by Degryse et al. (2005) and regarding the spread already observed by Biais (1995). Kempf et al. (2015) draw on the observation of mean reversion and develop a mean reversion model of liquidity measuring resiliency as the rate of mean reversion in both spread and depth in FTSE 100 stocks over a two-year period. By extending their model with a variable capturing algorithmic trading activity, Kempf et al. (2015) find that algorithmic trading has a positive impact on spread and order book depth resiliency. However, they do not directly infer their conclusions based on the trading behavior of algorithmic traders but rely on the intensity of order cancellations. Moreover, the results are based on five-minute intervals which are too long to infer the behavior of HFTs representing a sub-group of algorithmic traders that react within a fraction of a second. Therefore, our study adds insights to the research gap regarding the role of HFT for order book resiliency by investigating what types of traders replenish liquidity in the order book following a large aggressive order and the associated sudden drop in liquidity. As our proprietary data set includes all order messages by HFTs and non-HFTs time-stamped to a hundredth of a second, we are able to precisely study the contribution of HFTs, ATs, and human traders to order book resiliency. There is only one theoretical paper that provides first evidence regarding HFT and order book resiliency (Leal and Napoletano, 2019). Based on an agent-based model concerning flash crashes, the authors show that HFTs are fundamentally involved both in the cause of a flash crash but also in the liquidity recovery after a shock.

III.1 Data Set
Our study focuses on the most actively traded and largest German stocks, i.e., the constituents of the German blue chip index DAX 30. The data set provided by Deutsche Boerse contains all order book messages of its electronic open limit order book Xetra for the DAX 30 stocks within the two-week time period from August 31 st to September 11 th , 2009 (ten trading days). For every order book message, the data set contains a timestamp, the International Securities Identification Number (ISIN), an order number which allows to identify all other messages related to a certain message (e.g., submissions can be linked to the corresponding (partial) executions or cancellations), whether the respective order was a buy or a sell order, and the price limit and order size. Moreover, the data set contains several flags such as order and message type, which provide further information about each message.
The first flag that makes the data set at hand especially useful for the purpose of this study is the additional AT flag (Algo-flag). It indicates whether a certain message has been generated by an algorithm (Algo-flag = 1) or not (Algo-flag = 0). We will refer to non-algorithmic orders as human traders' orders. The identification of algorithmic traders is possible because Deutsche Boerse implemented a special pricing model for computer generated trades called Automated Trading Program in 2005 to promote algorithmic trading on its electronic trading platform Xetra (Deutsche Boerse, 2004). Traders participating in the Automated Trading Program can take advantage of fee-rebates for transactions that have been submitted by an algorithm if they oblige themselves to exclusively use their Automated Trading User-ID whenever they trade using computer algorithms. In order to be classified as an order triggered by an algorithm, a computer must determine at least two of the following parameters: price (market order or limit of an order), time (time of order entry), and quantity (number of securities) (Deutsche Boerse, 2004). More-Electronic copy available at: https://ssrn.com/abstract=2603205 over, an electronic system must submit or cancel an order independently without manual/human intervention. Since the rebates increase with a customer's number of algorithmic trades per month, it is economically rational for banks and brokers to use their Automated Trading User-ID for every order generated by an algorithm. This is also confirmed by Hendershott and Riordan (2013). Consequently, the Algo-flag appears to be highly reliable and a suitable proxy for algorithmic trading activity.
Since Deutsche Boerse extended the fee reduction program to all Xetra orders in November 2009, it effectively ended the possibility to differentiate between algorithmic and non-algorithmic traders (Deutsche Boerse, 2009). Therefore, a more recent data set is not available.
The second import flag is the Colo-flag, which indicates whether the submitter of an order is co-located at Deutsche Boerse (Colo-flag = 1) or not (Colo-flag = 0).
Hence, we can further differentiate orders submitted by algorithms into the following two groups: Fast algorithmic traders using co-location services, i.e., high-frequency traders (HFTs) and relatively slower ones, i.e., non-HFT algorithmic traders (ATs).
Based on these flags, the data set allows us to distinctively analyze the trading behavior and the respective role for order book resiliency of three different types of traders: HFTs, ATs, and human traders. Electronic copy available at: https://ssrn.com/abstract=2603205 In order to study the role of HFTs, ATs, and human traders for order book resiliency, we only focus on the continuous trading phase since market impacts caused by significant liquidity demands are less prevalent in highly liquid call auctions.
The data set contains 1,243,083 messages logged during continuous trading, thereof 49.1% submissions 2 , 40.9% cancellations, 5.2% executions, 2.7% partial executions, and 2.0% modifications. The number of modifications is rather low compared to the number of submissions and cancellations because only an adjustment of the order's volume leads to a modification while all other changes which affect price-time priority lead to the cancellation of the order and the insertion of the same order as a "new" order with a new timestamp and order number. The remaining 3.2% of all messages represent technical messages generated by the exchange system, which are not relevant for our analysis. Therefore, all messages other than submissions, modifications, cancellations, executions, and partial executions are removed. Moreover, submissions that resulted in a cancellation within the same hundredth of a second are excluded together with their cancellations because they are not liquidity increasing and, therefore, do not contribute to order book resiliency. These modifications lead to a sample of 1,049,212 messages, where most of them are triggered by HFTs.

III.2 Market Impact Events
In order to analyze order book resiliency, we have to identify events in which an order results in high market impact, meaning that the order leads to an immediate and considerable price change by taking significant liquidity away from the market.
Related research investigating order book resiliency typically relies on large orders to determine market impact events (e.g., Large (2007) or Chlistalla (2011)). However, a relatively large order does not necessarily lead to market impact. Gomber et al. (2015), for example, show that large orders are timed, which implies that large orders are often submitted in times of high liquidity to avoid market impact. To circumvent this problem, we directly identify market impact events using a pricebased technique as suggested by Biais (1995). Specifically, we identify market impact events based on the number of order book levels that have been affected by an aggressive order. Since every partial execution in our data set represents the volume traded for a certain price, the number of partial executions shows how many order book levels have been cleared or affected by an order. Consequently, we count the partial executions that follow a each market order to identify market impact events.
We choose market orders instead of limit orders since market orders in general are even more aggressive and are executed for any price available while limit orders are only executed as long as the price is above/below the specified limit. Following this approach, we determine market impact events based an order's relative impact on liquidity resting in the order book and, thus, circumvent the timing issue of large orders.
For our analysis, we take the ten market orders with the highest market impact (i.e., those with the highest number of affected order book levels 3 ) for every stock listed in the German blue chip index DAX 30 during our observation period. Thereby, we are able to identify 300 market impact events. We do not consider any market impact event in our sample that happened 15 minutes before or after an auction as well as circumstances in which two market impact events directly follow each other in order to avoid potential biases from these special trading situations. With this selection process, we are able to ensure that we analyze the most severe market impact events. Since the data set only covers a two-week period, these ten events per stock represent a good compromise between data set size and strength of the market impact. We explicitly search for non-news-related market impact events that are purely order book driven to avoid potential biases due to new information or other exogenous events that might influence traders' decisions. Therefore, every event is checked for companies' ad-hoc disclosures that might have caused the market impact event to rule out that our events are information driven. Moreover, no single earnings announcement date is included in our sample. Concerning other potential information causing these events, we find that 15 company presentations on (industry) conferences often hosted by large investment banks and investor roadshows happened during on one of the observation days. 4 Yet, our results remain robust when we exclude these observations. Thus, our selection of market impact events ensures that our results on order book resiliency are purely liquidity-driven and not biased by exogenous events.
In order to analyze order book resiliency for the identified market impact events, we match order book snapshots retrieved from Thomson Reuters Tick History (TRTH) to the message data provided by Deutsche Borse. Thereby, 33 events were lost in the course of the matching process because the timestamps of both data sources are not synchronized and the corresponding market impact was not visible in the TRTH data. The other events could properly be identified and were double-checked manually. Additionally, we exclude two observations where the market order leading to the market impact event is smaller than the respective stock's Standard Market Size (SMS) as reported by the European Securities and Markets Authority (ESMA) 5 .
Since the stocks in our sample are highly liquid, an order size smaller than SMS leading to a market impact event indicates an unusually illiquid order book, which could bias our results. The distribution of the remaining 265 events over the observation period and over the trading day is provided in Figures A.I and A.II in the appendix. Market orders causing market impact events are almost evenly split be-tween buyer-(133) and seller-initiated (132) orders. However, 91.3% of these orders are submitted by human traders while 6.4% are generated by ATs and only 2.3% by HFTs (see Table 3).
[Insert Table 3 about here.] This finding seems reasonable since ATs regularly slice large orders into smaller parts using limit orders to avoid market impact while human traders might also trade large quantities with market orders, e.g., if they need to fulfill contracts or close positions within a short period of time. Moreover, HFTs predominantly operate on the top of the order book submitting and canceling limit orders within short time frames as shown by Jarnecic and Snape (2014). The following Table 4 depicts the descriptive statistics of the 265 events included in the sample. The descriptive statistics per stock are provided in Table A.1 in the appendix.

about here.]
Although we have not explicitly searched for the largest orders to identify order book situations with large market impact, the volume of the market orders that initiated the market impact events covered in this study are on average 12.39 (median 9.92) times larger than the SMS of the respective stock. Moreover, the average market impact 6 of 17.10 bps (median 13.87 bps) is quite significant given that we study the most liquid German stocks. Also, more than six price levels are on average affected by the market orders leading to market impact events. This shows that these orders significantly walk through the book and consume liquidity, which needs to be replenished. 7 6 Market impact is defined as the absolute difference between the first and the last price level affected by an aggressive, i.e., liquidity-consuming, order. To ensure comparability across stocks with different price levels, we divide the absolute market impact in euro by the volume-wheighted average price of the trades resulting from the aggressive market order.
7 These descriptive results also show the economic relevance of our research on order book resiliency. Due to the consumed liquidity and the related market impact, implicit transaction costs for orders executed at the top of the order book increase by 171% compared to a mean spread of 9.99 bps averaged across all stocks and over the ten trading days in our data set. If the order book was not resilient and liquidity would not revert to the pre-market impact event level, all market participants and orders demanding immediacy would have to bear these additional costs. Therefore, For the resiliency analyses based on the identified market impact events, we focus on each group of traders' activity and related net liquidity provision before and after the event by investigating their submission (liquidity providing) and cancellation (liquidity withdrawing) behavior. In a first step, we analyze the submission and cancellation behavior five and ten seconds before and after the 265 market impact events. These time intervals appear to be appropriate given that we simultaneously analyze HFTs, ATs, and human traders' activity, which differs in speed and reaction time. Table 5 reports the mean number of submissions and cancellations for each group of traders within five (ten) seconds before and after a market impact event.
These figures give a first impression how the different groups of traders react to market impact events. Relative activity is calculated by aggregating the number of submissions and cancellations for each group of traders divided by all submissions and cancellations in the respective time interval. Both tables clearly indicate that HFTs, ATs, and human traders react to the market impact event by changing their submission and cancellation behavior. All three groups of traders increase their submissions by at least 310% compared to the pre-event number. Since the number of cancellations rises to a lesser degree, the intensified limit order submissions imply an increase in net liquidity provision. In both observation periods, especially human traders increase their limit order submissions relative to the pre-event number. In absolute terms, HFTs show the highest number of limit order submissions, however, they also exhibit the highest number of limit order cancellations.
[Insert Table 5 about here.] The increasing commitment of liquidity by all trader types is also supported by the observations reported in Figure I which depicts the mean euro order volume of HFTs, ATs, and human traders five and ten seconds before and after the market impact event. All traders increase their average order size after the market impact order book resiliency can be seen as a key component of liquidity ensuring consistently low implicit transaction costs and trading possibilities at appropriate spreads. event thereby providing additional liquidity. Moreover, the chart shows that human traders submit significantly larger order sizes than ATs and HFTs. Their mean order size across all 265 events amounts to 29,012 euro (33,239 euro) in the five (ten) seconds interval before the market impact event and 44,185 euro (43,982 euro) in the five (ten) seconds interval after the market impact event. ATs submit the smallest mean order sizes of all groups of traders with 7,084 euro (10,432 euro) before and 11,032 euro (11,717 euro) after the market impact event. The mean order sizes of HFTs are in between with on average 16,440 euro (17,528 euro) before and 19,956 euro (19,665 euro) after the market impact event.
[Insert Figure I about here.]

III.3 Liquidity around Market Impact Events
Before investigating the contributions of ATs, HFTs, and human traders to order book resiliency, we provide descriptive statistics regarding the liquidity development around the market impact events analyzed in this study. Figures II and III visualize changes in relative spreads and order book depth before and after the market impact event. The bars depict the one-second average relative spread respectively order book depth five seconds before until ten seconds after the market impact event as well as the relative spread (order book depth) right after the execution of the market order (time interval 0). The line represents the average relative spread (order book depth) for the 30 DAX constituents included in our sample over the ten trading days under investigation in this study. We do not use the pre-event window as benchmark since previous research has shown that large orders are timed and tend to be submitted when the liquidity level is abnormally high (Gomber et al., 2015). Therefore, the pre-event window is not the best benchmark to study and visualize the resiliency process. Moreover, research shows that liquidity follows a mean-reversion process (Kempf et al., 2015). Consequently, the ten trading days' average of spread and depth appear to be the appropriate benchmark to visualize the resiliency process. We measure order book depth using the Depth(10) measure Electronic copy available at: https://ssrn.com/abstract=2603205 proposed by Degryse et al. (2015), which sums up all volumes in euro quoted ten basis points around the midpoint. [Insert Figures II and III about here.] Several observations can be made in this high-level aggregation. First, a significant drop in liquidity is visible after the market order has hit the order book. Regarding the relative spread depicted in Figure II, there is an extreme increase of the mean relative spread to 24.29 bps directly after the market impact event, which is also significantly larger than the ten days average of 9.99 bps across all DAX 30 constituents. Second, the relative spread seems to recover quite fast. While the strongest recovery occurs within the first second after the event, it takes further four seconds until the relative spread is not significantly different from the ten days average. After five seconds following the initial impact, no significant changes in average relative spreads are observable. The differences between the average relative spread in each second and the ten-day average as well as the test statistics for significance are provided in Table 6. Third, the relative spreads in the seconds prior to the market impact event are significantly lower than their average over the whole investigation period meaning that liquidity is provided cheaper at the top of the order book. As the market orders leading to market impact events are considerably larger than the SMS of the respective stock, lower relative spreads prior to the market impact event support previous findings that large orders are timed when liquidity is unusually high.
Turning now to the second liquidity measure, i.e., order book depth measured by Depth(10), depicted in Figure III, the picture looks slightly different. First, there is also a significant dry up of liquidity in terms of depth, which is reduced to as low as 77,357 euro after the market impact event compared to an average depth of 254,520 euro in our observation period. However, order book depth needs additional time to reach a similar constant level as the relative spread. Even though the largest Electronic copy available at: https://ssrn.com/abstract=2603205 recovery contribution is within the first second, it takes up to eight more seconds to establish a constant level. Different from the relative spread, the recovery of order book depth takes longer and does not reach the "normal" level within ten seconds after the event as indicated by the significant differences compared to the ten-day average provided in Table 6. Nevertheless, the differences to the average depth remain stable from the eighth second after the market impact event onwards.
Therefore, our proposed observation periods of five and ten seconds after the market impact event are supported by this high-level analysis. Moreover, and contrary to relative spreads, there is no evidence for the timing of large orders by looking at order book depth.
[Insert Table 6 about here.] To provide further robustness of our results, we repeat our analysis using Depth (5) as measure for order book depth, which only considers quoted volumes closer to the midpoint, i.e., five basis points around the midpoint 8 . The descriptive results are qualitatively similar for order book depth measured by Depth(5) as shown in Table 6 and Figure A.III in the appendix.

IV.1 Research Approach
Based on the descriptive analyses of the market impact events in our sample and corresponding the resiliency process, we now turn to the statistical evaluation of the role HFTs, ATs, and human traders for order book resiliency. In this section, we first focus on the reaction of HFTs, ATs, and human traders to non-news-related market impact events. Thereafter, we evaluate each trader types' contribution to order book resiliency within Section V. In order to study the reaction to the sudden drop in 8 In order to provide a deeper understanding of the Depth(x) measure, Table A.2 in the appendix provides an overview of how many order book levels are regularly considered for the calculation of both depth measures based on our sample and observation period. While Depth(5) in almost 80% of the cases captures the euro volume quoted on the first order book level, Depth(10) more often also considers the volume on deeper order book levels.
liquidity, we analyze whether the traders change their liquidity provision behavior in response to the market impact event. Specifically, we relate each group of traders' net liquidity provision following a market impact event to the respective five-and tensecond interval before the large market order hits the order book. Measuring the net liquidity provision of each type of traders is important since especially HFTs and ATs cancel a large proportion of their orders thereby withdrawing liquidity provision from the market. We define net liquidity provision as the difference between submitted limit order volume and canceled limit order volume (both denoted in euro). Equation (1) shows the formal definition of the net liquidity provision measure (N LP ). We calculate each group of traders' (g) net liquidity provision for each pre-and postevent observation interval i based on all submitted limit orders l.
Consequently, a positive net liquidity provision of group g indicates that this group of traders submitted more limit order volume to the book than it canceled within the five-or ten-second interval i. A negative net liquidity provision means that the respective group of traders removed a larger limit order volume from the order book than it provided during the same period. If a group of traders neither submitted nor canceled orders within the five or ten seconds window, the measure is set to zero. For the following analysis, the net liquidity provision behavior of each group of traders within five and ten seconds before and after the market impact event is obtained and evaluated in a cross-sectional regression setup. The estimated regression model is based on the following Equation (2): Electronic copy available at: https://ssrn.com/abstract=2603205 Within the regression model, all five-second (ten-second) net liquidity provisions (N LP ) before as well as after the market impact event are explained and compared according to their respective characteristics. Consequently, the number of observations is increased by the factor six to 1,590 since each of our 265 events has a preand a post-event observation and is calculated for HFTs, ATs, and human traders.
HF T (AT ) is a dummy variable indicating that the respective net liquidity provision corresponds to HFTs (ATs). The dummy variable P reP ost equals zero if the net liquidity provision is measured based on five (ten) seconds before the market impact event and switches to one if N LP is measured after the event. The interaction terms P reP ost · HF T , P reP ost · AT and P reP ost · Human indicate the changes in the respective HFTs', ATs', and human traders' net liquidity provision before and after the market impact event. Additionally, we apply control variables capturing further idiosyncratic differences in net liquidity provision. Foremost important is the overall activity level, which is computed by counting all submissions and cancellations in the specific five (ten) seconds observation window. Moreover, the net liquidity provision may systematically be different for each stock in our sample. Therefore, we apply stock-specific controls by including a dummy variable for each of the analyzed stocks. For the purpose of this study, we are most interested in the estimated coefficients of P reP ost · HF T , P reP ost · AT , and P reP ost · Human that provide indications about a systematic change of each group's behavior after market impact events.
Electronic copy available at: https://ssrn.com/abstract=2603205 Besides traders' net liquidity provision and to provide further robustness of our results, we also consider each group of traders' net limit order submissions (N LOS) reflecting traders' activity in terms of liquidity provision. As shown in Equation (3), the number of net limit order submissions for each group of traders is computed by the number of limit order submissions minus the number of limit order cancellations by the respective group g in a given time interval i independent of the order volume connected to an order.

IV.2 Results
The results of the regression model described in the previous subsection are provided in Table 7, which includes the estimates based on both net liquidity provision (N LP ) and net limit order submissions (N LOS) for the five-as well as the ten-second aggregation period. From a general perspective, HFTs and ATs exhibit significantly lower net liquidity provisions and net limit order submissions compared to human traders as shown by the negative coefficients HF T and AT in the pre-event phase. Most important for our research on order book resiliency, however, is the change in liquidity provision after the market impact event, which is depicted by the coefficients of the P reP ost interaction terms. Regarding the mere submission and cancellation activity captured by the net limit order submissions (N LOS), all groups of traders react to the market impact event by submitting significantly more limit orders relative to limit order cancellations compared to the pre-event period. In particular, HFTs and human traders increase their net limit order submissions the most by submitting 3.68 (4.28) respectively 4.58 (5.52) more limit orders minus potential cancellations in the five (ten) seconds after the market impact event. The net limit order submissions of ATs, in contrast, increase by only 1.07 respectively 1.41 orders in the same observation windows.

V.1 Research Approach
Although different in the specific magnitude, each group of traders' reaction to the market impact event appears to be positive for order book resiliency since they significantly increase their net liquidity provision or at least their net limit order submissions. How this increase actually contributes to order book resiliency is the focus of this section. Therefore, we aim to evaluate whether and how the different groups of traders affect order book resiliency in the post-event phase. Hence, we Electronic copy available at: https://ssrn.com/abstract=2603205 propose an intuitive regression approach, which relates the post-event change in spreads and order book depth to the specific net liquidity provision of each group of traders within the five-and ten-second periods following the market impact event.
Hence, the stronger both measures recover after the market impact event (i.e., spread reductions and depth improvements), the more efficient the resiliency dynamic is assumed. 9 We explicitly do not rely on any pre-event or average benchmark to analyze the resiliency process but investigate which groups of traders contribute to liquidity recovery compared to the decreased liquidity level directly after the market impact event. Thereby, we are able to identify which trader type systematically contributes to different dimensions of liquidity recovery. We estimate the following regression model shown in Equation (4) ery will result in a larger spread reduction (depth improvement) from the event to 9 We do not restrict or depend our analysis to require a full recovery of liquidity since our sample, which focuses on significant order book impact events only, already justifies at least a temporal price impact right after the event. While we tried to rule out any exogenous events that might lead to a permanent price impact, our analysis, therefore, is not biased if the price after some events does not fully recover after ten seconds. the the post-event period. In order to reveal which group of traders is responsible for order book resiliency, we relate the liquidity recovery to the respective N LP i measure of HFTs, ATs, and human traders in the five and ten seconds after the market impact event. If a positive or negative expected overall liquidity recovery in terms of spread or depth can regularly be associated with the net liquidity contribution of one specific group of traders, then a regression setup can estimate such a significant relation. In contrast, if a specific group of traders regularly exhibits a high net liquidity provision but order book recovery is small, the contribution of this group of traders to order book resiliency must be doubted. Again, we control for the overall activity level measured by the sum of all submissions and cancellations within the five and ten seconds after the market impact event. In addition, we control for differences in the pre-event liquidity level by including the pre-event spread, order book depth (Depth(10)), and order book imbalance 10 all based on the one-second pre-event average. Also, we apply stock-specific controls. The resiliency regression is run separately for liquidity recovery in terms of relative spreads and order book depth (Depth(10) and Depth (5)) and for both the five-and ten-second periods. To provide further robustness of our results, we repeat the regression considering only one group of traders' net liquidity provision (i.e., HF T , AT , and Human) at a time and additionally perform the regression based on N LOS for the spread resiliency since order volumes are not important for spread determination.

V.2 Results
The results provided in Table 8 reveal that HFTs show a significant and robust relationship between their net liquidity provision and relative spread recovery. Across all models (1), (2), (5), and (6), we observe a negative and significant effect of HFTs' net liquidity provision on spread changes from the event to the post-event interval indicating spread improvements. Therefore, HFTs recover the widened relative 10 Similar to Chordia et al. (2002), we compute order book imbalance as |Depth(10) Ask −Depth(10) Bid | Depth (10) for each order book snapshot. In particular, Goldstein et al. (2018) have shown that order book imbalance influences the trading decisions of HFTs. spread after a market impact event when providing additional liquidity to the order book. In contrast, ATs' and human traders' liquidity provision after market impact events does not lead to spread improvements. Although human traders exhibit the strongest increase in net liquidity provision after market impact events, they do not contribute to the recovery of the relative spread. The positive effect of HFTs for spread resiliency is robust for both the five-as well as the ten-second observation interval. Yet, the effect size is almost identical indicating that HFTs accomplish the spread resiliency within the very first seconds after a market impact event, which is further supported by Figure II.

about here.]
Since the relative spread is independent of the volume connected to submitted and canceled limit orders, we repeat the spread resiliency regression using net limit order submissions (N LOS) instead of the net liquidity provision to provide further robustness of our results. Based on the net limit order submissions of the three groups of traders as dependent variables, we obtain similar results, which are reported in Table A.3 in the appendix. Again, HFTs' net limit order submissions contribute most to the spread improvements after a market impact event while human traders' and ATs' order submissions do not have a significant effect. We also perform an Ftest for the full models of the spread resiliency regressions to investigate whether the spread improvement coefficient of HFTs is significantly different from the coefficients of the two other groups of traders. For both liquidity provision measures N LP and N LOS and both analyzed time intervals, the results of the F-test confirm that the contribution of HFTs to spread resiliency is significantly higher than that of human traders and ATs. Consequently, the analysis reveals that order book resiliency in terms of bid-ask spreads is accomplished by HFTs only within the first few seconds after a market impact event.
Electronic copy available at: https://ssrn.com/abstract=2603205 Concerning the recovery of order book depth measured by Depth(10) and Depth (5) as proposed by Degryse et al. (2015), the three groups of traders' contributions to order book resiliency give a different impression. As depicted in Table 9, HFTs do not significantly contribute to the recovery of order book depth measured by Depth (10) despite their increased net liquidity provision in the post-event period. This also holds for ATs, although we find a significant effect on depth replenishment when only considering their net liquidity provision. Yet, the effect vanishes in the full models with all traders' net liquidity provision measures being considered as explanatory variables. Thus, even if HFTs' net liquidity provision recovers the relative spread within the first seconds after a market impact event, their actual order sizes are too low in order to achieve a significant increase in order book depth.
In contrast, we find that human traders and their net liquidity provision recover Depth(10) as indicated by the positive and significant coefficient in all models (1), (4), (5), and (8). Consequently, even within five seconds after the market impact event, human traders' net liquidity provision leads to order book resiliency in terms of order book depth. With respect to order book depth closer around the midpoint as measured by Depth(5), we find qualitatively similar effects (see Table 10). Yet, as Depth (5) is mostly based on the first order book level in our sample, the contribution of HFTs to Depth(5) recovery is higher than for Depth(10) recovery and also significant in model (6).
The results concerning order book depth resiliency also remain robust if we additionally control for the size of the market order that caused the market impact event thereby consuming varying amounts of quoted volumes. 11 Yet, we cannot confirm that human traders' depth improvement coefficient is significantly different from that of HFTs based on an F-test (both for Depth(10) and for Depth(5)).
Consequently, although HFTs' contribution to order book depth is smaller, mostly insignificant, and noisier than that of human traders, the results for order book depth resiliency less clearly reveal one single group of traders as being responsible for depth resiliency as the results for spread resiliency do. Nevertheless, the analysis provides strong support that human traders and not HFTs are the main contributors to depth resiliency.
[Insert Tables 9 and 10 about here.] Human traders' positive impact on order book depth resiliency can be explained by their submission (and non-cancellation) of relatively large order sizes (see Figure I within the descriptive analysis). In the ten seconds before and after a market impact event, human traders submit on average orders sizes two times larger than the size of HFTs' orders and three times larger than the size of ATs' orders. The strong increase in net liquidity provision of human traders as revealed by the first regression analysis (see Table 7) combined with the large order sizes are the key components for depth recovery. HFTs and ATs, on the other hand, contribute less to the recovery of order book depth due to their transient liquidity commitment and relatively small order sizes.
In summary, our results show that HFTs are mainly responsible for liquidity recovery in terms of bid-ask spreads while human traders are the main contributors to order book depth resiliency. From an overall liquidity resiliency perspective, the spread is often seen as the most important liquidity dimension since it influences the implicit transaction costs for both large and small orders. Order book depth, however, is highly relevant for larger orders in order to minimize market impact. To shed further light on the relative importance of these two liquidity measures for order book resiliency, we repeat our analysis using the Exchange Liquidity Measure (XLM) proposed by Gomber et al. (2015), which measures the cost of a roundtrip trade of given size. Consequently, this measure accounts for both, the implicit transaction Electronic copy available at: https://ssrn.com/abstract=2603205 costs associated with the bid-ask spread as well as the implicit costs due to market impact by walking through deeper levels of the order book.
The analysis provided in Table A.4 in the appendix shows that HFTs are mainly responsible for the recovery of XLM10k after a market impact event, i.e., the reduction of implicit transaction costs associated with an order size of 10,000 euro as shown by the negative and significant coefficients for the net liquidity provision of HFTs. Since the spread is the main factor determining implicit transaction costs for such smaller order sizes, this result is in line with HFTs being responsible for the recovery of bid-ask spreads. Yet, human traders' contribution becomes increasingly important for larger order sizes (XLM20k and XLM50k), which also consume liquidity from deeper order book levels so that this liquidity dimension gains importance for implicit transaction costs.

VI Discussion
The analysis of order book resiliency is of interest for researchers, market participants, and regulators alike since our data highlights the economic relevance of market impact events and the necessary replenishment of the order book. After the market impact events included in our sample, implicit transaction costs for orders executed at the top of the order book increase by 171% compared to the mean relative spread.
Further, they would stay at this high level if there was no resiliency or if the order book was only resilient at a very slow pace. Consequently, order book resiliency is a key component of liquidity ensuring consistently low implicit transaction costs.
In this study, we focus on the contribution of different types of traders to order book resiliency, which differs from the general analysis of a market's resiliency as in Foucault et al. (2005).
This paper contributes to the discussion on liquidity provision by HFTs by revealing which types of traders are most relevant for the recovery of different dimensions of liquidity based on non-news-related and sudden market impact events that are trig-Electronic copy available at: https://ssrn.com/abstract=2603205 gered by large incoming market orders. Thereby, and different from, e.g., Hautsch et al. (2017), our results provide a clear picture on order book resiliency that is not biased by any changes in trading strategies due to exogenous events.
Our results show that speed does in fact leverage one characteristic of order book resiliency, which is the recovery of relative spreads. In particular, we find that spread resiliency is determined by HFTs, i.e., participants relying on trading algorithms and co-location services. Relative spread recovery is particularly strong if HFTs contribute liquidity to the open limit order book and happens within the first five seconds after a market impact event. However, our results reveal that HFTs and also ATs do not substantially restore order book depth, which is the second important characteristic of order book resiliency. The recovery of order book depth is mainly achieved by human traders contributing with a high net liquidity provision combined with large order sizes. This process consumes additional time compared to the relative spread recovery, providing further indications that HFTs as well as ATs do not predominantly participate in the resiliency of order book depth. Therefore, our conclusions are twofold. First, liquidity provision of HFTs contributes mainly to a very distinct dimension of order book resiliency, i.e., the recovery of relative spreads. Consequently, the speed of trading indeed matters for order book resiliency since the recovery of a tight bid-ask spread needs only the submission of one precise order at best. Second, in order to absorb further liquidity demands, order book depth has to be replenished by various orders of relevant size. As shown in our analysis, this is mainly achieved by human traders that persistently stay in the order book and submit orders of relevant size. One potential explanation for our findings is that, within the category of human traders (besides retail and other traders), there is also a variety of proprietary banks' and brokers' trading desks whereof a majority has larger risk limits and trading volumes than specialized HFT firms that focus on specific sectors or liquidity classes operating close to their risk Electronic copy available at: https://ssrn.com/abstract=2603205 limits. 12 Consequently, differences in higher risk limits and their lower utilization might explain why human traders rather than HFTs mainly recover liquidity in terms of order book depth.
In contrast to Kempf et al. (2015), who use five-minute aggregation intervals and find that algorithmic trading in general is responsible for order book resiliency, we show that rather HFTs as a subgroup of ATs are responsible for spread resiliency since speed matters regarding this dimension of liquidity. Moreover, we find that mainly human traders and not HFTs or ATs significantly contribute to order book depth resiliency. Furthermore, our results are in line with the observations made by Haferkorn and Zimmermann (2014), who show that HFTs mainly impact bid-ask spreads and not order book depth. However, they analyze general trading activity and static liquidity dimensions whereas our study focuses on order book resiliency, i.e., the dynamic aspect of liquidity, in non-standard market conditions due to market impact events initiated by large market orders.
Some limitations are present in our analysis. On the one hand, our data set, which includes ten trading days, covers a rather short period of time. Therefore, one might argue that not enough remarkable market impact events are included in the analysis. Nevertheless, the mean market impact of 17.10 bps for the market impact events included in this study as shown in Table 4 appears to be quite substantial given that we analyze the most liquid German stocks. This is further supported by more than six price levels that are on average affected by the liquidity demanding market orders leading to the analyzed events. On the other hand, a second limitation relates to the precise attribution of the order submissions and cancellations to the respective trader types. Although market participants conducting algorithmic trading have a high incentive to participate in the Automated Trading Program offered by Deutsche Boerse, they are not obliged to do so. Therefore, not all messages sent by trading algorithms might be flagged as such. Nonetheless, the unique flag for algorithmic trading activity in the data set used in this study seems to be the best proxy available. Moreover, our analysis is based on blue chips stocks that are characterized by high levels of liquidity and heterogeneity of trading participants. Therefore, our results may not be generalizable to small cap or other illiquid stocks where less algorithmic and high-frequency trading takes place.
Our results have important implications for academics, regulators, and market participants alike. From an academic perspective, our findings contribute to the research on HFT and its impact on liquidity in financial markets. While there exist several academic studies that provide evidence for a positive effect of HFT on liquidity in terms of spread and depth at the top of the book, the contribution of HFT to order book resiliency is still an open question. We add to this research gap by showing that HFTs indeed recover one dimension of liquidity, i.e., the bid-ask spread. However, liquidity provision by HFTs should not be overestimated with respect to resiliency of order book depth. After market impact events and the associated drops in liquidity, human traders provide meaningful amounts of liquidity thereby contributing to order book depth resiliency. While HFTs are the ones who tighten the enlarged relative spread within the first seconds after a market impact event, human traders are the main contributors to order book depth resiliency.
From a regulatory point of view, the results reveal that HFTs play a crucial role for at least one dimension of order book resiliency by ensuring that enlarged spreads almost instantaneously revert to previous levels. With respect to ongoing discussions regarding the regulation of HFT, these results should be taken into consideration to ensure resilient financial markets. Putting our findings in the perspective of market participants, this study shows that neither HFTs nor ATs replenish large quantities of liquidity deeper in the order book. Thus, especially institutional investors should be aware that they cannot rely on these types of traders to fulfill their liquidity demands after market impact events.

VII Conclusion
We study the liquidity provision and the respective contribution to order book resiliency of high-frequency traders (HFTs), algorithmic traders (ATs), and human traders around market impact events caused by large market orders. Order book resiliency as the dynamic dimension of liquidity is a key determinant of market quality that ensures consistently low implicit transaction costs in securities markets. Our results show that spread resiliency is accomplished by HFTs, who replenish the top of the order book within five seconds after the market impact event. Liquidity recovery in terms of order book depth, however, takes considerably longer and is mainly accomplished by liquidity providing orders of human traders. In contrast, HFTs and ATs do not significantly contribute to order book depth resiliency. Consequently, our results show that the speed of trading only matters for one dimension of order book resiliency. HFTs and their low-latency infrastructure are responsible for spread resiliency since the recovery of a tight bid-ask spread needs only the submission of one precise order at best. Resiliency in terms of order book depth, however, that is necessary for a market to absorb further liquidity demands of larger orders, is mainly achieved by human traders, who persistently stay in the order book with relevant order volumes.
(1) Electronic copy available at: https://ssrn.com/abstract=2603205  (4)) conducted for the five-and ten-second interval respectively. Variables HF T , AT , and Human refer to the coefficient of the respective net liquidity provision (N LP ) of that group within five and ten seconds after the market impact event. Activity accounts for the overall activity level measured by the sum of submissions and cancellations in the considered post-event period. Pre-event spread (Spread pre ), order book depth (Depth pre ), and order book imbalance (OIB pre ) are included to control for differences in the liquidity level right before the market impact event. Stock specific controls and heteroskedastic robust variance estimators are applied. We report standardized beta coefficients and t-statistics in parentheses; * p < 0.10, * * p < 0.05, * * * p < 0.01.

Relative Spread -5 seconds
Relative Spread -10 seconds (1) (3) Electronic copy available at: https://ssrn.com/abstract=2603205 Table 9: Results of the Depth(10) resiliency regression (Equation (4)) conducted for the five-and ten-second interval respectively. Variables HF T , AT , and Human refer to the coefficient of the respective net liquidity provision (N LP ) of that group within five and ten seconds after the market impact event. Activity accounts for the overall activity level measured by the sum of submissions and cancellations in the considered post-event period. Pre-event spread (Spread pre ), order book depth (Depth pre ), and order book imbalance (OIB pre ) are included to control differences in the liquidity level right before the market impact event.
Depth (10)  Electronic copy available at: https://ssrn.com/abstract=2603205  (4)) conducted for the five-and ten-second interval respectively. Variables HF T , AT , and Human refer to the coefficient of the respective net liquidity provision (N LP ) of that group within five and ten seconds after the market impact event. Activity accounts for the overall activity level measured by the sum of submissions and cancellations in the considered post-event period. Pre-event spread (Spread pre ), order book depth (Depth pre ), and order book imbalance (OIB pre ) are included to control differences in the liquidity level right before the market impact event.
Stock specific controls and heteroskedastic robust variance estimators are applied. Observations with zero Depth(5) before and after the event are not considered in the analysis. We report standardized beta coefficients and t-statistics in parentheses; * p < 0.10, * * p < 0.05, * * * p < 0.01.

X Figures
Human Before ATs Before HFTs Before Human After ATs After HFTs After Electronic copy available at: https://ssrn.com/abstract=2603205 after the event (time 0), and its recovery ten seconds after the market impact event.
Electronic copy available at: https://ssrn.com/abstract=2603205 Time Interval (in seconds) Depth(10) (in 1,000 euro) Figure III: Depth(10) five seconds before the market impact event, directly after the event (time 0), and its recovery ten seconds after the market impact event.
Electronic copy available at: https://ssrn.com/abstract=2603205  (5) and Depth(10) for the order book snapshots from five seconds before to ten seconds after the 265 analyzed market impact events.

XI Appendix
Order Book Levels Depth (5) Depth (10) (4)) conducted for the five-and ten-second interval respectively. Variables HF T , AT , and Human refer to the coefficient of the number of net limit order submissions (N LOS) of each group within five and ten seconds after the market impact event. Activity accounts for the overall activity level measured by the sum of submissions and cancellations in the considered post-event period. Pre-event spread (Spread pre ), order book depth (Depth pre ), and order book imbalance (OIB pre ) are included to control for differences in the liquidity level right before the market impact event. Stock specific controls and heteroskedastic robust variance estimators are applied. We report standardized beta coefficients and t-statistics in parentheses; * p < 0.10, * * p < 0.05, * * * p < 0.01.