How aggressive are high frequency traders?

How aggressive are high frequency traders? Björn Hagströmer, Lars Nordén and Dong Zhang Stockholm University School of Business, S 106 91 Stockholm July 30, 2013 Abstract We study order aggressiveness of market making high frequency traders (HFTs), opportunistic HFTs, and non HFTs. We find that market making HFTs follow their own group's previous order submissions more than they follow other traders orders. Opportunistic HFTs and non HFTs tend to split market orders into small portions submitted in sequence. HFTs submit more (less) aggressive orders when the same side (opposite side) depth is large, and supply liquidity when the bid ask spread is wide. Thus, HFTs adhere strongly to the trade off between waiting cost and the cost of immediate execution. Non HFTs care less about this trade off, but react somewhat stronger than HFTs to volatility. Key words: High frequency trading; Aggressiveness; Order submission; Liquidity; Volatility JEL codes: G14, G18 Corresponding author. Phone: + 46 8 6747139; Fax: +46 8 6747440; E mail: ln@fek.su.se 1

1 INTRODUCTION The limit order book conveys the current state of liquidity supply and demand to its participants. Anyone with an interest in the trading environment, including short and long term traders as well as policy makers, need to understand the determinants of the limit order book, in order to optimize their trading and policy decisions. Such determinants may be regarded at many different levels, but the ultimate building blocks of the limit order book are of course the limit orders. Limit orders can be categorized by their aggressiveness, which the trader chooses by setting the limit price to lead to immediate or more or less delayed expected execution. The aggressiveness of all limit orders collectively forms the supply and demand of liquidity. Order aggressiveness is thus fundamental to the market quality variables that are central to market microstructure research. In modern equity markets, traders differ in technology, sophistication, and strategy. Retail and institutional investors coexist with proprietary traders that use computers to pursue strategies with sub second investment horizons. This paper takes an empirical approach to investigate how order aggressiveness differs between traditional traders and different types of high frequency traders (HFTs). By conditioning order aggressiveness on the state of the order book as well as the actions of other traders, we provide new insights into the functioning of electronic limit order book markets. The theoretical literature shows that order aggressiveness is determined by the tradeoff between waiting costs and the cost of immediate execution. In Parlour (1998), traders choose to submit limit orders or market orders based on their observation of the limit order book depth. Foucault (1999) suggests that market orders are more costly when 2

the asset volatility is higher. Foucault et al. (2005) model how traders' impatience determine their order placement strategies, and Rosu (2008) holds the competition in liquidity supply as a key variable for order aggressiveness. The cost of immediacy is the same for all traders, but waiting costs may differ with the sophistication of the trader. For example, an HFT may have the means to evaluate patterns in order submissions of other traders before deciding what orders to submit, whereas a slow trader does not have the capacity for such an analysis. Empirical evidence of such differences are provided by Hendershott and Riordan (2013), who show that algorithmic traders at the Deutsche Börse have an edge in revising their orders quickly following public news announcements. Several empirical articles analyze how order submission strategies depend on the state of the order book (Griffiths et al., 2000; Handa et al., 2003; Ranaldo, 2004) and the actions of other traders (Biais et al., 1995). Due to data restrictions, most empirical analyses focus on trading and quoting strategies at an aggregate level. As order submissions are increasingly automatic, it is important to understand the differences between human and different types of automatic order submissions. Hendershott and Riordan (2013) study the interaction of order submissions between human traders and algorithmic traders in general. Brogaard (2011a; 2011b; 2012) analyzes the segment of algorithmic traders that do proprietary trading only, referred to as HFTs. His analysis is focused on the difference is order submissions between HFTs and human traders at the NASDAQ. Hagströmer and Nordén (2013), in turn, disaggregate HFTs by their strategies. Using data from NASDAQ OMX Stockholm, they divide HFTs into Market making HFTs and Opportunistic HFTs, and benchmark their results to Non HFTs. 3

The current paper adds to the literature by comparing the aggressiveness of different trader groups, and it is distinguished from the earlier literature in that it has a strong focus on limit orders in general. Most previous papers focus on orders that lead to executions, but we show that executions constitute less than 3% of the message traffic. Limit orders submissions is about 45% of the messages (the rest being cancellations). We access a proprietary database of orders at NASDAQ OMX Stockholm and use the same trader categorization methodology as in Hagströmer and Nordén (2013). The trader classification, which is based on access to trader identities associated with each limit order, allows us to investigate limit order aggressiveness of each trader group. 1 The starting point in our empirical analysis is the well known diagonal effect, first documented by Biais et al. (1995), which refers to the fact that the probability of a particular order type being submitted is higher when the previous order is of the same type. We find that both HFTs and non HFTs contribute to the aggregate diagonal effect. Thus, for all trader groups, market orders tend to be followed by market orders and limit orders tend to be followed by limit orders. Our results on HFT diagonal effects are in line with results presented by Hendershott and Riordan (2013) for algorithmic traders, a much broader specification of traders than our HFT groups. We further investigate whether traders follow traders regardless of trader type, or if the diagonal effect holds only within the trader group. We find that market making HFTs follow its own group's previous order submissions to a larger extent than they follow other traders orders. We also find that opportunistic HFTs and non HFTs tend to split market 1 Brogaard (2012) investigates how volatility affects HFTs' aggressiveness at the NASDAQ, where aggressiveness is tantamount to being on either the liquidity demanding or supplying side of a trade execution. Brogaard (2011b) examines determinants of aggregate HFT buy and sell decisions, again focusing on transactions. Brogaard (2011a) and Brogaard et al. (2012) study HFTs role in liquidity provision and price discovery. They define liquidity demand (supply) as being on the initiating (passive) side of a transaction. Brogaard (2012) and Hagströmer and Nordén (2013) examine the impact of HFTs on intraday volatility. Both studies find that HFTs mitigate volatility. 4

orders into small portions submitted in sequence. This result is consistent with that they slice large market orders to reduce price impact. Next, we study how traders choose their order aggressiveness conditional on the state of market liquidity and volatility. This analysis builds on Ranaldo (2004), who investigates order aggressiveness at the Swiss Stock Exchange. Our analysis is distinguished from his in that we study differences between trader groups, focusing on HFTs and non HFTs, whereas he studies aggregated behavior for all market participants. We apply an ordered probit regression analysis with order aggressiveness as the dependent variable. Our results are qualitatively in line with Ranaldo (2004), but we uncover important differences between trader groups. Both market making HFTs and opportunistic HFTs adhere strongly to the trade off between waiting costs and the cost of crossing the spread. This implies a higher probability of buy side market orders when the buy side depth is high (leading to longer waiting time), when the depth at the opposite side is low, and when the bid ask spread is small. Non HFTs put less emphasis on that trade off, but react somewhat stronger than HFTs to volatility. When volatility in the previous 10 seconds is high, traders price their orders less aggressively. In the next section we present the market and our trader classification methodology. After that, in section 3, we present our data along with descriptive statistics. Section 4 contains our analysis of the diagonal effect of different trader groups, and Section 5 relates order aggressiveness to market conditions. Section 6 concludes. 5

2 MARKET AND TRADERS 2.1 Description of the market We study the trading aggressiveness of different trader groups who are active on the Nasdaq OMX Stockholm exchange (henceforth NOMX St). NOMX St is an electronic limit order book market that is open from 9 am to 5.30 pm every weekday except on Swedish bank holidays. If the day before a Swedish bank holiday is a weekday, trading on that day closes at 1 pm. Opening and closing prices are determined in call auctions. All messages are entered through the INET trading system, which has the capacity to handle more than a million messages per second at an average processing time less than 0.25 milliseconds. To reduce the order processing time further, NOMX St offers co location services, where clients can pay a premium to place their servers at the exchange. Limit orders can be submitted at any price on a grid that is determined by the tick size. At NOMX St the minimum tick size depends on the stock price level. Specifically, the tick size for stocks priced below SEK 50 is SEK 0.01; for stocks priced between SEK 50 and SEK 100 it equals SEK 0.05; and for stocks with a price between SEK 100 and SEK 500 it is SEK 0.10. 2 The tick size rule is important for order aggressiveness, as it puts restrictions on, e.g., the possibilities to compete for order flow by posting orders at the best bid or ask quote. In addition, if the bid ask spread is equal to the minimum tick size, the tick size is binding in the sense that it is not possible to submit aggressive limit orders, undercutting the best quotes in the order book. The market structure at NOMX St has two features that are distinct to most other exchanges. Firstly, the use of hidden liquidity is highly restricted. For the stocks in our 2 The relation between tick size and price level is in accordance with the Federation of European Exchanges (FESE), Table 2, and is applied for the OMXS 30 stocks since October 26, 2009. 6

sample, an order must exceed at least EUR one million in value to be eligible for full nonvisibility (for some of the stocks the threshold is even higher). This restriction is important not only for order management (to hide or not to hide orders) but also for order aggressiveness. Hautsch and Huang (2012) report that, in the U.S. equity markets, hidden liquidity is associated with enormous order activities related to liquiditydetection strategies, which are likely to involve aggressive market orders. The order value restriction does not apply to partially hidden (iceberg) orders. The lack of hidden liquidity at NOMX St is likely to induce less liquidity detection strategies relative, e.g., activities on the U.S. equity markets, which in general should lead to lower aggressiveness. Secondly, the matching of limit orders during the continuous trading session at NOMX St is done using a priority rule that differs from most other exchanges, allowing for internal matching. Internal matching implies that a member firm with an order posted at the best (bid or ask) price is given priority in execution against market orders that come from the same firm. Limit orders at the same price level that are posted by other members do not have priority in this case, even when they are posted earlier in time. Thus, the order of priority is price, internal, time, and visibility. We do not expect this market setup to have a significant influence on order aggressiveness. NOMX St has about one hundred member firms that have the right to submit orders to trade at the stock market. Each member firm may sell the service of trading to clients. The provision of trading services from exchange members to traders may be done via traditional brokers, through direct market access, or through sponsored access. Direct market access gives customers access to the market through the infrastructure of the member firm. In the case of sponsored access, the customer uses its own infrastructure 7

but trade under the member identity of the sponsor. Sponsored access is popular among algorithmic trading firms, in particular HFTs, as it allows for lower latency (order processing time) than direct market access. 2.2 Trader classification We follow Hagströmer and Nordén (2013) and classify market member firms into three broad categories: (1) members who are primarily HFT, i.e., engage in proprietary trading only and who use algorithms in their trading strategies; (2) members who trade for clients only, referred to as non HFTs; and (3) members who engage in both proprietary and client trading. The categorization is carried out with the aid of Nasdaq OMX in house expertise about member activities. 3 Exactly as Hagströmer and Nordén (2013), we classify 29 members as HFT firms, 49 members as non HFT firms, and 22 members as hybrid firms with both proprietary and agency activities. 4 Our data set does not allow us to isolate the activities of HFTs accessing the market through sponsored access. Thus, such activity ends up among the hybrid firms. We also follow the setup of Hagströmer and Nordén (2013) to disaggregate the HFT group into market making and opportunistic strategies, where the latter contains arbitrage and directional strategies. Whether an HFT acts as a market maker or not is determined by its presence at the best bid and offer (BBO). We take snapshots of each order book, each 10 second period, on each trading day, and calculate how often each member firm has an order posted at the BBO. Members who are present at the BBO in more than 20% of the snapshots (on average across days and stocks) are classified as 3 See Hagströmer and Nordén (2013) for details on the classification, and SEC (2010) and Gomber et al. (2011) for definitions of and details on HFT strategies. 4 Confidentiality requirements do not allow us to disclose the categorization, but the complete member list is available publicly online: http://nordic.nasdaqomxtrader.com/membershipservices/membershiplist/ 8

market making HFTs (MM HFTs). All other HFTs are classified as opportunistic HFTs (Opp HFTs). To avoid turn of the second effects in our market maker presence measure we randomize the order book snapshot times so that we get observations each 10 seconds uniformly distributed across increments of 10 seconds. As we use the same data and methodology as in Hagströmer and Nordén (2013), our trader groups are exactly the same as in their study. 3 DATA AND DESCRIPTIVE STATISTICS We have access to all limit order submissions, cancellations, and executions from the trading system INET at NOMX St. All messages carry information on price, volume, time of entry, time in force, side (buy or sell), visibility, and trader identity. The trader identity information includes the MPID, which identifies what exchange member is associated with the message. The data also contains the USERID, which identifies what broker, trader, or workstation at the member firm is responsible for the message. As our trader categorization is done at the exchange member level, MPID is the field we use to distinguish orders from different trader groups. Messages are time stamped to the nanosecond (10 9 second). Each execution involves two messages, one for each side of the trade. To keep the amount of data manageable, we focus our study on two months of data, August 2011 and February 2012, for thirty large cap stocks. The selected stocks are the most traded stocks at NOMX St that together constitute the OMXS 30, the leading Swedish stock index. Our sample is identical to the one used by Hagströmer and Nordén (2013), which facilitates benchmarking to their results. August 2011 is a month of high volatility, primarily due to increasing uncertainty about sovereign debt in Europe and 9

the United States. This month also featured substantial media coverage of HFT activity and its association with market fluctuations. February 2012 is a calmer month in terms of both volatility and trading activity. An important limitation of our data is that NOMX St hosts only 55 65% of the trading volume in OMXS 30 stocks. The largest competitor is BATS Chi X Europe (25 30%), followed by Burgundy and Turquoise (less than 5% each), and we do not access any order book or trading information from those exchanges. 5 Finally, we restrict our analysis to the continuous trading session, representing roughly 97% of all trades and 99% of all limit order submissions. Table 1 provides summary statistics for trading and quoting activity, as well as market quality. Each statistic is based on daily observations across stocks. We report the timeseries mean, median, and standard deviation separately for each of our two sample months. We also perform statistical tests for differences between the two months. Differences in means, medians, and standard deviations are assessed using t tests, Wilcoxon rank sum z tests, and F tests, respectively. The table reports the p value of each test, indicating the probability of the metric in question being equal for the two months. Insert Table 1 here We measure trading activity in terms of monetary value (million Swedish Krona, MSEK), number of shares (millions), and number of trades (thousands), averaged across stocks on each day. As seen in Table 1, the average daily trading volume per stock falls from MSEK 462 in August 2011 to MSEK 301 in February 2012. This sharp drop in trading 5 Market share data are taken from http://www.batstrading.co.uk/market_data/venue/index/omxs/ 10

volume is statistically significant both for the mean and the median, and the same pattern is seen for number of shares and number of trades. The average number of trades (7,480 in August 2011 and 4,930 in February 2012) is large compared with, e.g., Brogaard (2011b) and Brogaard et al. (2013), who report an average trading activity of about 3,000 executions in their respective studies of HFT behavior. The daily volatility of all types of trading volumes is significantly higher in August 2011 than in February 2012. The quoting activity is also significantly higher in August 2011 than in February 2012. We measure the number of visible and hidden limit order submissions and the number of cancellations, averaged across stocks each day. Table 1 shows that the time series average in February 2012 on all these counts is less than a third of the counts for August 2011. On average, in both months, hidden orders constitute less than 1% of all limit order submissions. The reluctance among traders to post hidden orders is probably due to the size restrictions on such order. As a point of comparison, Bessembinder et al. (2009) report that in a sample of 100 stocks at Euronext Paris in April 2003, where there are no size restrictions on hidden orders, 44% of the order volume is hidden. We note from Table 1 that the number of cancellations is higher than the number of limit order submissions. This is because the volume of limit orders is often partially cancelled, meaning that one limit order may be subject to several cancellations. There are no liquidity measures directly available in our data base, but the message bymessage history allows us to reconstruct the full order book at any time of the day. In Table 1 we report the bid ask spread in nominal terms (SEK 0.01), number of ticks, and relative its current midpoint (expressed in basis points). On average, both in terms of means and medians, bid ask spreads are wider in August 2011 than in February 2012. 11

The mean relative spread in February 2012 is 0.09%, which is in the range of relative spreads between medium cap and large cap stocks on the NASDAQ, as reported by Brogaard et al. (2013). The bid ask spread expressed in terms of minimum tick size is on average 1.88 and 1.51 ticks in August 2011 and February 2012, respectively. This implies that the bid ask spread is often equal to the minimum tick size. We also report two measures of the depth dimension of liquidity; how large a purchase or a sale it takes to change the best bid or ask quote at all, and by 0.5%, respectively. On average, in August 2011 (February 2012), a trade worth about MSEK 0.5 (MSEK 0.8) is required to move either the bid quote or the ask quote at all. To move either the bid or ask price by at least 0.5%, on average, a trade worth more than MSEK 6.4 (MSEK 9.4 9.7) is needed. Thus, in terms of average depth, the stocks in our sample are highly liquid, and a substantial fraction of the liquidity rests behind the best bid and ask prices. Finally, Table 1 includes measures of minute by minute returns and realized volatility. The returns are based on log changes of bid ask spread midpoints, expressed in basis points. Realized volatility is the average of squared basis point returns. On both accounts, our results show that volatility is substantially higher in August 2011 than in February 2012. Overall, the statistical tests presented in Table 1 indicate that market quality is significantly higher in February 2012. This result is robust across means and medians of measures of market tightness, market depth, and market volatility (the only exception being the nominal bid ask spread). Insert Table 2 here In Table 2, we present relative statistics on trading and quoting activity for the different trader categories; market making HFTs, opportunistic HFTs, non HFTs, and the hybrids. 12

Panel A contains average fractions of market trading and quoting activities across stockdays. 6 In August 2011 (February 2012), non HFTs' fraction of trading volume is 30.6% (33.3%), while the remaining 69.4% (66.7%) is divided between market making HFTs' 12.6% (14.2%), opportunistic HFTs' 12.6% (8.1%) and hybrids' 44.1% (44.1%). During the more volatile month, August 2011, opportunistic HFTs account for a fraction of marketable limit order submissions twice that of the Market making HFTs, while the fractions of trading volume, non marketable limit order submissions, and cancellations are almost the same, and not significantly different from each other, for the two HFT groups. In contrast, during the calmer month, February 2012, market making HFTs have a significantly larger fraction of trading volume, non marketable limit order submissions, and cancellations than opportunistic HFTs, at the same time as the two HFT groups have an equal fraction of the marketable order submissions. These observations imply that opportunistic HFTs are relatively more active in times of high stock market volatility than market making HFTs. In Table 2, Panel B, we break up the trading volume for each trader category in liquidity demand and liquidity supply. This distinction is based on whether the trader used a marketable order to execute the trade immediately, or a non marketable limit order that was subsequently hit by an incoming marketable order. Consistent with the results in Hagströmer and Nordén (2013), market making HFTs are on the supply side in about 70 79% of the volume, while opportunistic HFTs are supplying liquidity in 33 44% of their total trading volume. Corresponding figures for non HFTs show an almost 50 50 relation between supply and demand of liquidity, whereas hybrids are on the demandside in slightly more than half of their trades. 6 Each entry in Table 2, Panel A, is the average fraction of each trading activity measure, across stocks and days, for each trader group. Significance analyses are based on regressions, as described in the table text. 13

We also separate the messages of each trader category into three types, with decreasing degree of aggressiveness; marketable limit orders, non marketable limit orders, and limit order cancellations. Interestingly, for all trader categories alike, the message traffic is totally dominated by submissions of limit orders that stay in the book, and cancellations of those, while marketable limit orders are relatively scarce. The fraction of marketable limit orders, in relation to all messages, is 3.1% (7.3%) for non HFTs, 0.7% (1.1%) for market making HFTs, 1.8% (7.3%) for opportunistic HFTs, and 0.7% (1.7%) for hybrids during August 2011 (February 2012). Hence, if the relative usage of marketable limit orders is used as a proxy for aggressiveness, we note that non HFTs are significantly more aggressive than opportunistic HFTs (at least during August 2011), who in turn are significantly more aggressive than market making HFTs. 4 ORDER AGGRESSIVENESS Similar to Biais et al. (1995), we distinguish buy side and sell side orders, and differentiate order types based on their aggressiveness. Whether an order is on the buyor the sell side is directly observable in the data. Order aggressiveness can be determined by relating the limit price to the reconstructed order book. We categorize buy orders by aggressiveness on a scale from (1) to (10). The least aggressive action on the buy side is to cancel an existing buy order, and such messages are assigned type (1) on the aggressiveness scale. Limit orders that do not lead to immediate execution are classified as follows: (2) is a buy order quoted at a price lower than 0.5% below the best bid price; (3) is a buy order quoted below the current best bid price, but less than 0.5% below the current best bid price; and (4) is a buy order posted at the best bid price. Among buy orders that are priced between the best bid and ask prices, we distinguish those that are cancelled if they are not executed immediately (5) from those that are 14

allowed to rest in the order book (6). The remaining buy order categories are marketable limit orders that result in immediate execution: (7) is a marketable limit buy order without price impact; (8) is a marketable limit buy order that is large enough to consume all the available shares quoted at the best ask and withdraws the residual volume, i.e., the volume that is not executed at the best ask; (9) is a price changing marketable limit buy order that posts the residual volume as a limit order in the book; and (10) is a price changing marketable limit order that is walking the book, i.e., is executed at several different price levels. Sell order aggressiveness is assigned in a similar manner, on the scale from (1) to (10). All in all, the categorization leaves us with 20 types of orders; 10 at the buy side, and another 10 at the sell side. Insert Table 3 here 4.1 Order aggressiveness in general Table 3 presents the relative frequencies of orders of different types for both the buy and the sell side, during August 2011 (Panel A) and February 2012 (Panel B), for the different trader groups: non HFTs, market making HFTs, opportunistic HFTs, and hybrids. 7 Concentrating on the results from the volatile month, August 2011, in Panel A of Table 3, it is notable that the most common order type for all groups is cancellations, which varies between 23% and 28% of the total activity on both sides of the market. This is not surprising; given that Hasbrouck and Saar (2009) document that one third of all non marketable limit orders for 100 Nasdaq listed stocks are cancelled. They argue that traders cancel orders as the result of dynamic trading strategies to search for correct market prices or latent liquidity. We find that hybrid traders cancel significantly 7 Each entry in Table 3 is the average relative frequency of each of the 20 order categories, across stocks and days, for each trader group, and separately for buy side and sell side orders. Significance analyses are based on regressions, as described in the table text. 15

more frequently than the non HFTs, on both sides of the market. Differences between each of the two HFT groups and non HFTs are smaller, but still statistically significant. Both market making HFTs and opportunistic HFTs have higher cancellation frequencies than non HFTs on the sell side, but not on the buy side. Opportunistic HFTs cancel both buy orders and sell orders significantly more often than market making HFTs. But in economic terms, the differences between different groups' cancellation rates are very small. This might be surprising, since HFTs often are accused of an order cancellation rate in excess of other types of traders. Our results imply that both HFTs and non HFTs pursue similar trading strategies, at least with respect to cancellation rates, in the words of Hasbrouck and Saar (2009), to infer the correct market prices. Moving up on the aggressiveness scale, we note that non HFTs post passive orders of type (2), i.e., orders with a price more than 0.5% away from the best quotes, with a frequency larger than 7% on both the bid side and the ask side. Both market making and opportunistic HFTs post orders of type (2) very seldom, significantly less frequent than non HFTs, while market making HFTs are posting these passive orders significantly less frequent than opportunistic HFTs. For all the groups except for market making HFTs, the second most frequent order activity is type (3), i.e., posting limit orders priced below the best quotes but within 0.5% from the best quotes. Here, we note that opportunistic HFTs post type (3) orders significantly more frequently than non HFTs, who in turn post this type of order significantly more frequently than market making HFTs. In line with their marketmaking strategy, the market making HFTs is the trader group that submits orders most often at the BBO (type 4) on both sides of the order book. Market making HFTs are also 16

improving the best bid and ask quotes, with order types (5) and (6), significantly more frequently relative both opportunistic HFTs and non HFTs. Marketable limit orders, type (7), (8), (9) and (10), are relatively uncommon. Non HFTs submit marketable limit orders significantly more often than both groups of HFTs. In general, liquidity supplying orders, at aggressiveness levels (2) (6), are much more common than liquidity demanding (marketable) limit orders. This pattern is consistent across all trader groups. Panel B of Table 3 contains order type frequency results for the less volatile month, February 2012. Most of the results are very similar to those for the more volatile month, August 2011. One noteworthy discrepancy is that market making HFTs post significantly less bids and asks within the best quotes than both opportunistic HFTs and non HFTs during February 2012, while the opposite result holds during August 2011. This result is consistent with the notion that market making HFTs use a more aggressive strategy to compete for order flow at the BBO when stock market volatility is high. 4.2 Order aggressiveness conditional on the last order or trade As we are interested in how different types of traders choose aggressiveness levels in the high frequency environment of modern equity markets, the following analysis is focused on how the order choice depends on the aggressiveness of the previous order. Biais et al. (1995) provide a similar analysis, documenting the diagonal effect, i.e., the tendency of an order of a specific type to be followed by an order of the same type. Griffiths et al. (2000) also document a diagonal effect for the Toronto Stock Exchange. Parlour (1998) models a dynamic market and describes the shape of the limit order book when transactions and order submission flows are serially correlated. 17

Table 4 presents the conditional frequencies for each order type at time (t) in the columns of the table, and different aggressiveness levels for the previous order at time 1 are given in the table rows. Panel A shows order type frequencies during August 2011, while Panel B displays corresponding results from February 2012. Given the results from Table 3, that all trader groups rarely use the most aggressive order types (8), (9) and (10), we henceforth present them in aggregated form, referred to as marketable limit orders with price impact. Furthermore, we aggregate spreadimproving orders, (5 6); and depth orders, (2 3). Insert Table 4 here Our August 2011 results in Panel A of Table 4 suggest several implications for the order book dynamics. 8 Following a price changing market order, relative other order types, spread improving orders are more likely on both the buy side and the sell side. 9 This is likely due to that the bid ask spread in normal times is equal to the minimum tick size. The narrowing of the spread following a large marketable order may be seen as either market resiliency or establishment of a new price level. We observe that following a price changing buy order, the spread improvement is more likely to come from the buyside (6.64%) than from the sell side (1.54%). Along the same lines, a price changing sell order is more often followed by a downward spread improvement (6.30%) than an upward spread improvement (1.56%). Thus, our results indicate that the spread is more often narrowed in the direction of the price movement, rather than displaying resiliency. Furthermore, a price changing buy order relative other orders, is often followed by sell 8 The highlighted results for August 2011 appear to be even stronger during February 2012. Thus, we conclude that our results persists irrespective of whether the market volatility is high or low, and focus our comments on the results in Panel A of Table 4. 9 We perform a chi square test of independence, where the null hypothesis is that order submission at time t is independent of the previously submitted order at time 1. For both months in Panel A and B, this hypothesis is strongly rejected at any reasonable significance level. 18

orders above the best ask price (11.18%) and sell order cancellations (38.43%). The same pattern is seen for price changing sell orders, that are followed by buy side limit orders priced lower than the current best bid price (11.46%) or buy side cancellations. We interpret the posting of limit orders in the depths as betting on transitory price impact of subsequent aggressive order. The cancellation, on the other hand, may indicate that traders seek to avoid adverse selection (if the price impact is permanent). For example, if investors with limit sell orders posted in the order book believe that a price changing buy order is information driven; they will cancel their stale orders to avoid adverse selection. 10 Conditional on that the previous event is a marketable order without price impact, the probability of another marketable order (type 8 10 and type 7) is relatively high. This is in line with the diagonal effect discussed by Biais et al. (1995), and indicates that investors split large orders into several smaller orders. Marketable orders without price impact are also followed by opposite side cancellations (43.35% after buyer initiated trades and 44.69% after seller initiated trades) more often than by other order types. Again, this reflects that traders seek to avoid being adversely selected if the price moves. Spread improving orders (5 6) are relatively more likely to be followed price changing orders (8 10). When the spread is narrowed by a buy (sell) order, the probability of the next order consuming that volume is 0.85% (0.84%).Given that the unconditional probability of price changing orders is less than 0.3% on both sides of the book, this result shows that spread improving orders attract impatient orders to take liquidity 10 According to Seppi (1997), limit order submitters worry about stale orders being picked off. In his model, there is a specialist who moves after the limit order submitters, and undercuts stale orders. Moreover, in times when the adversely picked off fee is high, the specialist's participating rate will be high by being able to undercut or jump the queue. This is in line with our finding of the higher rate of priceimproving limit orders conditional on the price changing market orders. Subsequent to market orders potentially driven by information, the limit orders resting in the order book are more prone to be stale and thus have a higher adversely picked off fee. 19

when it is cheap. We also note that order types (5 6) do not display any diagonal effect, probably because the bid ask spread is then often already equal to the minimum tick size. Orders posted at the BBO (type 4) often follow orders of its own type (8.83% on the buyside and 8.80% on the sell side). This is in line with the diagonal effect and may be due to queuing behavior. The diagonal effect also holds for depth orders (2 3) on both sides of the limit order book. Somewhat puzzling, depth orders are also relatively frequently followed by same side cancellations (44.72% on the buy side and 44.67% on the sellside). Overall, both Table 3 and 4 show that the order type frequencies are largely symmetrical between the buy side and the sell side. Furthermore, in spite of durations between order submissions decreasing dramatically in the last twenty years as markets have become increasingly automatic, the diagonal effect remains relevant. Biais et al. (1995) discuss the diagonal effects and explain that similar order types tend to follow each other because: (1) traders strategically split large orders to reduce their market impact; (2) different traders can follow each others' trading behavior, either because they are imitating each other, or because they sequentially react to the same information. In our subsequent analysis we use our access to trader identities to investigate the origin of the diagonal effect. Table 5 provides an in depth analysis of the diagonal effect. Panel A contains results from August 2011 and Panel B contains results from February 2012. Starting with the results in Panel A, we repeat the analysis from Table 4 for each trader group separately, reporting only the diagonal vector, in the panel marked (i). As a point of reference, the diagonal from Table 4, Panel A, is reproduced in the first row (labeled "All"). The results 20

show that the diagonal effect is present for each trader type in isolation. Market making HFTs, opportunistic HFTs, and non HFTs all tend to be more aggressive conditional on that the previous order is also aggressive. 11 Their aggressiveness level is also lower if the previous order aggressiveness level is low. 12 In the panel marked (i), we report the p value from a chi square test of the null hypothesis that each group's diagonal effect is not different from the overall diagonal effect (labeled "All"). This null hypothesis is rejected for each trader group. Accordingly, the diagonal effect in marketable limit orders without price impact (type 7) is largely due to the behavior of non HFTs (14.61% on the buy side and 11.46% on the sell side). This may reflect usage of execution algorithms aimed at reducing price impact by ordersplitting. For limit orders posted at the BBO (type 4), market making HFTs seem to drive the diagonal effect, with 18.51% of the buy side BBO orders being followed by a marketmaking HFT BBO order (symmetrical results hold for the sell side). This may reflect competition among market makers. Insert Table 5 here In order to investigate the reason behind the diagonal effect, we further disaggregate the results of Table 4 with respect to trader groups. In Table 5, Panel A, we present the August 2011 diagonal effect for market making HFTs (ii), opportunistic HFTs (iii), and Non HFTs (iv). For each of these groups, aggressiveness is conditioned on the previous order aggressiveness as well as the previous order origin (by trader group). For example, the first row of the panel marked (ii) displays the diagonal effect for market 11 As the hybrid trader group is a mixture of HFT and client driven activity, it is excluded from further analysis. 12 For each of the trader groups, we perform a chi square test of independence (not reported), where the null hypothesis is that order submission at time t is independent of the previously submitted order at time 1. This hypothesis is strongly rejected at any reasonable significance level, for all trader groups. 21

making HFTs conditional on that the previous order was also made by a market making HFT. In addition, for each panel (ii), (iii), and (iv), we report the p value from a test of the null hypothesis that the diagonal effect is independent of which trader group that posted the previous order. For example, in the panel marked (ii), the null hypothesis is that the frequencies reported are equal to those reported for MM HFT in panel (i). Each and every one of these hypotheses are firmly rejected. The results clearly indicate that all trader groups have higher propensities to submit order type (7) at time (t) conditional on that they did the so on the same side at 1. This implies that they all tend to submit several small market orders in sequence, consistent with order splitting strategies aimed at reducing the price impact. Thus our result that the diagonal effect in type (7) messages is due to non HFTs comes from their relatively intense usage of market orders (see Table 2). Market making HFTs post depth orders (type 2 3) more often when the previous message was also a depth order posted by a market making HFT. For other order types where we observe diagonal effects, however, we do not find that the diagonal effect is a within group effect. For example, market making HFTs tend to post type (4) orders after another type (4) order has been posted, regardless of who posted that previous message. To sum up the order aggressiveness analysis so far, our results show that the diagonal effect exists in general and to some extent also within trader groups. 13 All trader groups have a tendency to slice their marketable limit orders in order to reduce price impact when they demand liquidity. In liquidity supply we find less evidence of self following within trader groups. The quoting at BBO is done independent of which trader group submitted the previous order, suggesting queuing behavior. 13 The results for February 2012, displayed in Table 5, Panel B, are similar to those for August 2011. 22

5 ORDER AGGRESSIVENESS CONDITIONAL ON MARKET CONDITIONS According to Parlour (1998), traders choose to submit limit orders or market orders based on their observation of the limit order book depth. Foucault (1999) suggests that submitting market orders is more costly when the asset volatility is high. Roşu (2008) concludes that when the bid ask spread is at its minimum, traders may use more fleeting limit orders. In the empirical literature, several studies analyze how order submission strategies depend on the state of the order book, e.g., Griffiths et al. (2000), Handa et al. (2003), Ranaldo (2004), and Brogaard (2011b). In this section we analyze how order submission strategies of the different trader groups relate to market conditions. We consider two dimensions of market quality: liquidity and volatility. 5.1 Ordered probit regression analysis In line with Foucault et al. (2005) and Roşu (2008), a trader arriving at the market decides what order to submit based on the trade off between waiting costs and the cost of immediate execution. The waiting cost is determined by the length of the queue at the side (buy side or sell side) of the order book where the trader would like to submit an order. One way of measuring the waiting cost is market depth. The cost of immediate execution is commonly measured with the bid ask spread. According to Foucault (1999), volatility is a key determinant of the mix between order types. Increased volatility leads to an increased risk for limit orders to be picked off. For that reason, Foucault (1999) argues, liquidity providers require larger compensation in times of high volatility. This reasoning implies that aggressive orders are more expensive in times of high volatility, as liquidity providers charge liquidity demanders 23

wider spreads. Furthermore, aggressive non marketable limit orders have higher pickoff risk than otherwise. To investigate the order choice empirically, we assume that a trader arrives to the market with either a buying interest or a selling interest. Depending on the trade off between waiting costs, immediate execution costs and picking off risk, he chooses the type of order to submit. We specify an ordered probit regression model to investigate the relationship between the order choices and limit order book conditions. As the number of limit orders in the thirty large cap stocks during our two sample months is immense, we randomly select one limit order submission for each stock from each minute of continuous trading. This sampling procedure ensures that our sample consists of independent observations, which would not be the case had we chosen to use all limit order submissions in subsequent analyses. With 8.5 hours of continuous trading each day, we retrieve roughly 500 observations for each stock on each day, resulting in around 22000 observations for each stock over the 44 trading days. We bunch observations from different stocks together, but disaggregate the random sample by the side of the book (buy side or sell side), by trader group, and by month. For August 2011, our random sampling of buy side (sell side) orders results in 30602 (30602) observations for the market making HFTs, 12788 (13396) for the opportunistic HFTs and 33541 (32219) for the non HFTs. In February 2012, the corresponding number of observations is 36351 (37234), 8580 (7217), and 21626 (21182), respectively. 14 Each of the resulting subsamples is analyzed in isolation. More specifically, for each subsample, for an order submission i, the ordered probit regression model is specified as: 14 Note that we discard the observations retrieved for the hybrid traders. 24

,,,,,,,,,,,, where g denotes trader group (MM HFT, Opp HFT or Non HFT), d indicates whether the order was submitted on the buy side or sell side of the order book, and m represents month (August 2011 or February 2012). The dependent variable,,, is defined in relation to the aggressiveness measurement,,, partitioned at five different levels in line with the categories analyzed in Tables 4 and 5, as follows: 15 1 when 1 2 i. e, order type 2 3 2 when 1 2,, 2 3 i. e, order type 4,, 3 when 2 3,, 3 4 i. e, order type 5 6 4 when 3 4,, 4 5 i. e, order type 7 5 when,, 4 5 i. e, order type 8 10 where γ to γ are the intercepts for the cumulative probabilities of the occurrence of orders with different aggressiveness levels, also known as threshold parameters or cutoff points. As explanatory variables, representing different order book and market conditions, we use buy side depth (,, ), which is the logged SEK volume available at the best buy price, sell side depth (,, ), which is the logged SEK volume available at the best sell price, relative bid ask spread (,, ), which is the prevailing relative spread when the order is entered into the order book, calculated as the difference between the best sell and buy quotes and divided by the midpoint of these quotes 15 As limit order cancellations [(1) on our aggressiveness scale] differ in nature from submissions, we exclude cancellations from this analysis. 25

(expressed in basis points), and realized volatility (,, ), measured as the average squared second by second basis point returns (midpoint quote changes) during the 10 whole seconds prior to the order submission. With whole seconds we mean that for an order submitted at 09:30:00.352, we measure volatility over the interval 09:29:50 to 09:30:00. The ordered probit specification largely follows the analysis of Ranaldo (2004), who investigates order aggressiveness in relation to market conditions at the Swiss Stock Exchange. While Ranaldo (2004) does not analyze order aggressiveness of different trader types, using aggregated order submission data, we study how the order aggressiveness of market making HFTs, opportunistic HFTs, and non HFTs is influenced by the state of the order book, liquidity, and market volatility. In addition, we run separate regressions for our two sample months in order to study whether aggressiveness of the different trader types differs between the volatile month (August 2011) and the relatively calm month (February 2012). Insert Table 6 here Table 6 presents the results from the estimations of the ordered probit regressions for the three trader groups. Panel A shows the results for August 2011, and Panel B contains corresponding results for February 2012. 16 The results show that both buy side and sellside depth are significant determinants of buy side aggressiveness, with opposite signs, for all trader groups and during both months. Evidently, for all trader types alike, the thicker the buy side depth is, the more aggressive buy side limit orders they tend to use. Similarly, the thicker the sell side depth, the less aggressive buy side orders are used. 16 We note that the results for buy side and sell side aggressiveness are very similar. Thus, to get a more concise presentation, and to save space, Table 6 only contains buy side results. Sell side results are available in the appendix. 26

The relative bid ask spread has a significantly positive effect on order aggressiveness (at the 5% level) for all trader groups and during both months. Thus, when the bid ask spread is wide, and liquidity is low, each type of trader tend to be more aggressive in their order submissions, relative to the case when the spread is narrow, and liquidity is high. From these results alone, we cannot infer whether each of the different trader types improve or worsen liquidity, by being more aggressive in response to a wider bidask spread. In this sense, increased aggressiveness can, e.g., imply submitting a limit order inside the bid ask spread rather than in the depth, and thereby increasing liquidity, or submitting a marketable limit order, rather than a non marketable limit order, and thereby decreasing liquidity. We investigate this issue further in the next section. The results from the dependence of traders' aggressiveness to liquidity are by and large in line with the trade off between waiting costs and costs of immediate execution. In our analysis, we separate between buy side and sell side depth. The empirical findings indicate that traders of all groups have a larger propensity to submit aggressive orders when the depth is abundant on the same side of the book (the buy side). The opposite side (sell side) depth also matters, with orders being less aggressive when the opposite side of the limit order book is deep, and vice versa. When the spread is wide, all trader groups are more prone to submit aggressive orders to reduce the waiting time. The ordered probit regression results for both months suggest that volatility has a significantly negative effect on order aggressiveness for all trader groups. This implies that traders submit less aggressive orders when the market is more volatile. Interestingly, the volatility has a negative effect on traders' order aggressiveness both in August 2011, when the overall market volatility was high, and in February 2012, when 27

the market exhibited considerably less erratic price movements. Thus, the results so far suggest that neither HFTs nor non HFTs can be accused of amplifying volatility by submitting more aggressive orders (e.g., market orders) when the market is volatile. 5.2 Marginal effects of the market conditions To interpret our regression results in economic terms we use the estimated coefficients from Table 6 to calculate probabilities that, for each trader group, each order type is used under a specific market condition. Omitting the superscripts denoting trader group, buy side or sell side submission, and sample month, respectively, the probability that an order is submitted at an aggressiveness level 1, 2, 3, 4, or 5, conditional on the explanatory variables, representing market conditions, can be written as: 1 Φ Φ Φ for l = 2, 3, 4 5 1 1 2 3 4 where is a vector with the explanatory variables, and and are vectors containing the estimated regression coefficients. The vector contains the unconditional sample means of the explanatory variables, and Φ denotes the cumulative normal distribution. This set of probabilities constitute the base case in the analysis. We define a marginal effect of an explanatory variable on the choices of order aggressiveness as the change in the probabilities 1,..., 5 following a onestandard deviation increase in the explanatory variable in question, while the other explanatory variables are held constant at the unconditional mean level. Table 7 reports the base case probabilities and the marginal effects for the aggressiveness of buy side 28

orders. 17 The column denoted "Predicted" contains the probabilities when all explanatory variables are equal to their unconditional sample means, while the column labeled "Actual" contains corresponding actual frequencies for the order types in our data set. Each marginal effect is obtained when each of the explanatory variables, one at a time, is increased by one standard deviation from the mean. Probabilities and marginal effects are calculated for market making HFTs, Opportunistic HFTs, and non HFTs respectively. Panel A contains results for August 2011, and Panel B for February 2012. Insert Table 7 here For both Panel A and Panel B, when comparing the base case probabilities derived from the regression coefficients and the actual frequencies, the levels are very close. This implies that the ordered probit regression model does well in predicting the probabilities of different order types. Consistent with section 4, the non marketable limit orders account for the majority of the order addition for all trader groups. In Panel A of Table 7, containing the results for August 2011, we note that following a one standard deviation increase in same side depth, all types of traders exhibit a lower probability of submitting a buy order below the best bid (order type 1 in table 7), and higher probabilities to submit more aggressive buy orders (types 2 to 5). On the contrary, when a corresponding increase in the opposite side depth is incurred, all trader types experience a higher probability to submit a buy order below the best bid, and lower probabilities for more aggressive buy orders. These results are in line with Parlour (1998), in that an incoming buyer submits aggressive buy orders when the buyside is thick, and the sell side is thin, in the order book. Ranaldo (2004) also documents 17 Corresponding results for the aggressiveness of sell side orders can be found in the appendix. 29

similar empirical results with opposite marginal reactions to same side and oppositeside depth for limit order and market order submissions. In addition, we observe noteworthy differences among trader types' reactions to changes in same side depth. Market making HFTs are 14.5% less likely to submit a buy order below the best bid, 4.1% more likely to submit a limit order at the best quote, and 8.6% more likely to improve the best quote after an increase in same side depth. Corresponding marginal effects for opportunistic HFTs are smaller, implying a smaller effect on aggressiveness following a change in same side depth relative market making HFTs. Moreover, Non HFTs have a very small marginal reaction to a change in same side depth. Comparing the marginal effects from a change in same side depth to a corresponding change in opposite side depth for all aggressiveness levels, HFTs react stronger to a change in same side depth than to opposite side depth, while the reverse is true for non HFTs. Our results suggest that HFTs, and in particular market making HFTs, monitor the market more carefully than non HFTs, and adjust their order submission aggressiveness in response to depth changes. Evidently, HFTs are behaving more in line with the expectations according to Parlour (1998) relative non HFTs. Subsequent to a one standard deviation increase in the relative bid ask spread, all trader types demonstrate a reduced probability of submitting buy side orders below the best bid quote, and increased probabilities of submitting more aggressive orders. This result supports the queue jumping story in that when the bid ask spread widens, traders submit more aggressive orders for a better chance of execution. Buy orders queuing below the best bid will have a smaller chance of execution in this situation. As for changes in depth, market making HFTs increase their order aggressiveness more 30

than opportunistic HFTs following a wider bid ask spread, by being 2.5% more likely to submit orders at the best quotes, and 3.5% more likely to improve the best price, relative the base case. Thus, we find that HFTs, in particular market making HFTs, improve liquidity by posting relatively more orders at the best quotes, and inside the best quotes, when the bid ask spread is wide, i.e., liquidity is low. Put differently, the results are consistent with the assertion of Brogaard (2011a), that HFTs supply liquidity when it is expensive. In August 2011, the effect of increasing realized volatility is to increase the probability of submitting orders below the best bid price but to decrease the probability of submitting more aggressive orders for all trader groups. This result is in agreement with the suggestion in Foucault (1999), that, when volatility increases, liquidity providers demand a larger compensation and they lower their reserved bid prices accordingly. When volatility is high, aggressive orders are more costly and, thus, less likely to be used. With respect to volatility, we find very small differences between the trader groups. If anything, non HFTs react stronger to volatility changes than HFTs. 18 Even in the volatile month of August 2011, we find evidence supporting the notion that non HFTs as well as HFTs mitigate volatility by submitting less aggressive orders when the market is volatile. The mitigating effect of HFTs on volatility is in line with the results in Hagströmer and Nordén (2013). Turning to Panel B of Table 7, we observe quite similar results for the less volatile month, February 2012. Comparing the results for the volatile month (August 2011) with 18 Seppi (1997) suggests that when volatility is high, the cost of being adversely picked off is also high, and, as a result, the specialist will be undercutting more. In our context, HFT groups who monitor the market better will update their orders more promptly and avoid their stale orders being picked off. On the contrary, non HFTs who don't monitor the market as well are more vulnerable to such price changes. In our empirical results, we indeed document that non HFTs react stronger to volatility. 31

those for the calmer month (February 2012), we note that all marginal effects, for all trader groups, have the same signs during both months. However, the differences between the trader groups are overall slightly smaller. In particular, we find that market making HFTs marginal effects are in general much larger in magnitude when the market is more volatile, while the opportunistic HFTs marginal effects increase somewhat in the less volatile month. Also, non HFTs marginal effects are very small in magnitude in the more volatile month. These results indicate that HFTs, in particular market making HFTs, monitor the market conditions more closely, and adjust their strategies to a larger extent, when the market volatility is high, relative non HFTs. Overall, our results suggest that all trader groups enter more (less) aggressive orders when the same side (opposite side) queue is long. HFTs are more concerned with the same side depth, while non HFTs are more concerned with the opposite side depth. A wider spread induces more order submissions at and within the BBO. HFTs adjust their aggressiveness more to changes in the bid ask spread when the market is volatile than non HFTs. Between HFT groups, market making HFTs react stronger to spread changes in the volatile month than opportunistic HFTs. Higher volatility implies less aggressive orders, indicating a soothing effect on volatility for both HFTs and non HFTs. 6 CONCLUDING REMARKS In today's equity markets, traders differ in technology, sophistication, and strategy. Conventional retail and institutional investors coexist with proprietary traders that use computers to pursue strategies with investment horizons that span only fractions of seconds. This paper studies how order aggressiveness differs between traditional traders and HFTs. By conditioning order aggressiveness on the state of the order book as 32

well as the actions of other traders, we provide new insights into the functioning of electronic limit order book markets. Our dataset contains the full order book activity for the OMXS 30 index stocks at Nasdaq OMX Stockholm. The data period covers two months, August 2011 and February 2012. During the former month, the market is more volatile and less liquid relative the latter month. Following Hagströmer and Nordén (2013), we classify traders into HFTs and non HFTs. HFTs are further classified into market making HFTs and opportunistic HFTs. Inspired by Biais et al. (1995), but with more detailed data, we classify orders and trades into finer categories according to their aggressiveness and whether they are on the buy side or the sell side (a total of 20 aggressiveness categories). The most common order types are cancellations and limit orders posted behind the best buy and sell prices. Market orders, with or without price impact, constitute less than 1% of all messages. We analyze the order choice by conditioning aggressiveness on the previous message entered into the system. In line with Biais et al. (1995), we find a diagonal effect for several order types, including market orders without price impact and limit orders posted at or behind the BBO. In addition, both HFTs and non HFTs contribute to the aggregate diagonal effect. Thus, for all trader groups, market orders tend to be followed by market orders and limit orders tend to be followed by limit orders. To improve the understanding of the diagonal effect in order choice, we also condition order aggressiveness on who posted the previous order. This analysis allows us to investigate whether the diagonal effect has its origin within the trader groups, or if traders from different groups also follow each other. We find that market making HFTs follow its own group's previous order submissions to a larger extent than they follow 33

other traders orders. Opportunistic HFTs and non HFTs slice market orders and submit these small portions successively to the limit order book in order to reduce price impact. We also study how different trader groups choose their order aggressiveness conditional on the state of market liquidity and volatility within an ordered probit regression model, with order aggressiveness as the dependent variable. The findings suggest that market making HFTs and opportunistic HFTs submit more (less) aggressive orders when the same side (opposite side) depth is large. When the bid ask spread widens, they tend to supply liquidity and quote more often at and within the BBO. This implies that both types of HFTs submit orders considering the trade off between waiting cost and the cost of crossing the spread, while non HFTs care less about this trade off than non HFTs. With respect to volatility, non HFTs are more sensitive to changes in volatility than HFTs. Even in the volatile month of August 2011, we find evidence supporting the notion that non HFTs as well as HFTs mitigate volatility by submitting less aggressive orders when the market is more volatile. The mitigating effect of HFTs on volatility is in line with the results in Hagströmer and Nordén (2013). Acknowledgements We would like to thank NASDAQ OMX for providing the data, and Petter Dahlström and Frank Hatheway for numerous discussions about the data and market structure. Remaining errors are our own. All three authors are grateful to the Jan Wallander and Tom Hedelius foundation and the Tore Browaldh foundation for research support. 34

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Gomber, P., Arndt, B., Lutat, M., and Uhle, T. (2011). High frequency trading. Working paper, University of Frankfurt. Griffiths, M., Smith, B., Turnbull, D., and White, R. W. (2000). The costs and the determinants of order aggressiveness. Journal of Financial Economics 56, 65 88. Hagströmer, B., and Nordén, L. (2013). The diversity of high frequency traders. Journal of Financial Markets (Forthcoming). Handa, P., Schwartz, R. A., and Tiwari, A. (2003). Quote setting and price formation in an order driven market. Journal of Financial Markets 6, 461 489. Hasbrouck, J., and Saar, G. (2009). Technology and liquidity provision: the blurring of traditional definitions. Journal of Financial Markets 12, 143 172. Hautsch, N., and Huang, R. (2012). On the dark side of the market: identifying and analyzing hidden order placements. Discussion Paper 2012 14, CRC 649, Humboldt Universität zu Berlin. Parlour, C. (1998). Price dynamics in limit order markets. Review of Financial Studies 11, 789 816. Ranaldo, A. (2004). Order aggressiveness in limit order book markets. Journal of Financial Markets 7, 53 74. Roşu, I. (2008). A dynamic model of the limit order book. Review of Financial Studies 22, 4601 4641. 36

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Table 1: Daily market quality and trading activity statistics August, 2011 February, 2012 Test for difference Statistic Mean Median St. Dev. Mean Median St. Dev. t test z test F test Trading volume (MSEK) 462.74 409.56 164.29 300.73 295.79 47.71 0.000 0.000 0.000 Trading volume (millions of shares) 5.00 4.31 1.80 2.97 2.90 0.49 0.000 0.000 0.000 Trades (thousands) 7.48 6.70 2.61 4.93 4.77 0.85 0.000 0.000 0.000 Visible limit order submissions (thousands) 257.58 256.43 81.29 80.86 83.17 10.04 0.000 0.000 0.000 Hidden limit order submissions (thousands) 2.50 2.35 1.10 0.70 0.70 0.16 0.000 0.000 0.000 Limit order cancellations (thousands) 301.10 300.07 97.35 96.69 101.12 13.57 0.000 0.000 0.000 Nominal bid ask spread (SEK 0.01) 12.65 12.26 1.19 12.14 12.12 0.39 0.062 0.294 0.000 Number of ticks between best bid and ask quote 1.88 1.76 0.28 1.51 1.50 0.05 0.000 0.000 0.000 Relative bid ask spread (basis points) 10.65 10.26 1.28 8.77 8.71 0.25 0.000 0.000 0.000 SEK required to change best bid quote (MSEK) 0.46 0.45 0.08 0.84 0.82 0.09 0.000 0.000 0.561 SEK required to change best ask quote (MSEK) 0.47 0.47 0.09 0.85 0.84 0.08 0.000 0.000 0.458 SEK required to change best bid quote by 0.5% (MSEK) 6.39 6.51 1.07 9.45 9.47 0.74 0.000 0.000 0.106 SEK required to change best ask quote by 0.5% (MSEK) 6.43 6.47 1.07 9.72 9.64 0.73 0.000 0.000 0.095 Absolute one minute returns (basis points) 0.56 0.52 0.26 0.15 0.15 0.02 0.000 0.000 0.000 Realized volatility (basis points squared) 4.02 3.34 2.63 0.80 0.81 0.18 0.000 0.000 0.000 Table 1 reports market quality and trading activity statistics, averaged across stock days, i.e., all trading days in August, 2011, and February, 2012, respectively, and the stocks included in the OMXS 30 index at that time. The bid ask spread is reported in nominal terms, number of ticks, and relative its midpoint. Limit order book depth is reported as the trade size (SEK) required to move the best bid or ask by one tick or 0.5%. Absolute one minute returns is the absolute value of the change in the logarithm of the midpoint price. Realized volatility is the intraday realized stock return volatility, using the log midpoint changes in one minute intervals. Each statistic is observed for each minute of continuous trading, except the first and last such minute in the trading day, for each stock in the OMXS30 index, each day in February 2012. Reported statistics are thus based on pooled time series across stocks. The last three columns contain p values from a t test for equality between means, a Wilcoxon rank sum z test for equality between medians and an F test for equality between variances across the two months. 38

Table 2: Relative daily trading and quoting activity statistics for different trader groups Panel A: Non HFT MM HFT Opp HFT Hybrid Wald Test Statistic ( ) ( ) ( ) ( ) ( ) August, 2011 Trading volume 0.306 0.126 0.126 0.441 0.000 (0.000) (0.000) (0.000) (0.841) Marketable limit orders 0.295 0.101 0.201 0.404 0.100 (0.000) (0.000) (0.000) (0.000) Non marketable limit orders 0.178 0.131 0.123 0.568 0.008 (0.000) (0.000) (0.000) (0.225) Limit order cancellations 0.159 0.107 0.113 0.620 0.006 (0.000) (0.000) (0.000) (0.356) February, 2012 Trading volume 0.333 0.142 0.081 0.441 0.059 (0.000) (0.000) (0.000) (0.000) Marketable limit orders 0.320 0.120 0.110 0.450 0.010 (0.000) (0.000) (0.000) (0.124) Non marketable limit orders 0.109 0.248 0.047 0.596 0.201 (0.000) (0.000) (0.000) (0.000) Limit order cancellations 0.088 0.227 0.043 0.642 0.184 (0.000) (0.000) (0.000) (0.000) 39

Table 2: Relative daily trading and quoting activity statistics for different trader groups Panel B: Non HFT MM HFT Opp HFT Hybrid Wald Test Statistic ( ) ( ) ( ) ( ) ( ) August, 2011 Liquidity demand volume / 0.449 0.207 0.563 0.590 0.356 Total trading volume (0.000) (0.000) (0.000) (0.000) Liquidity supply volume / 0.551 0.793 0.437 0.410 0.356 Total trading volume (0.000) (0.000) (0.000) (0.000) Marketable limit orders/ 0.031 0.007 0.018 0.007 0.011 All messages (0.000) (0.000) (0.000) (0.000) Non marketable limit orders/ 0.493 0.518 0.493 0.442 0.035 All messages (0.000) (0.000) (0.000) (0.000) Limit order cancellations/ 0.476 0.474 0.498 0.550 0.024 All messages (0.206) (0.000) (0.000) (0.000) February, 2012 Liquidity demand volume / 0.500 0.301 0.670 0.529 0.369 Total trading volume (0.000) (0.000) (0.000) (0.000) Liquidity supply volume / 0.500 0.699 0.330 0.471 0.369 Total trading volume (0.000) (0.000) (0.000) (0.000) Marketable limit orders/ 0.073 0.011 0.073 0.017 0.062 All messages (0.000) (0.836) (0.000) (0.000) Non marketable limit orders/ 0.500 0.507 0.487 0.455 0.020 All messages (0.000) (0.000) (0.000) (0.000) Limit order cancellations/ 0.427 0.482 0.441 0.528 0.041 All messages (0.000) (0.000) (0.000) (0.000) For the stocks included in the OMXS 30 index, Table 2 reports relative trading activity statistics for each group of traders. In Panel A, the fractions are reported for market making HFTs (MM HFT), opportunistic HFTs (Opp HFT), non HFTs (Non HFT), and hybrids (Hybrid), displaying groups' average fractions of each total trading activity measure over stock days. Trade statistics are based on share volumes, whereas order entry statistics are based on message counts. In the following regression equation:,,,,,, denotes the fraction of each trading activity measure, for stock i, on day t, for Non HFTs, MM HFTs, and Opp HFTs (Hybrids are omitted since their corresponding fraction is redundant),, (, ) is equal to one when the fraction is observed for MM HFTs (Opp HFTs), and zero otherwise, and, is a residual. The regression coefficients form fractions of each trading activity measure for Non HFTs ( ), MM HFTs ( ), Opp HFTs ( ), and Hybrids ( ). Note that 1. Each parenthesis below a reported average fraction contains a p value for a test that 0 (for MM HFTs), 0 (for Opp HFTs), and 0 (for Hybrids), respectively. Each Wald test is a test for the difference between MM HFTs' and Opp HFTs' fraction of each trading activity measure, which boils down to a test of the hypothesis 0. Panel B reports relative trading activity for each group of traders. Fractions are reported for all trader groups, displaying groups' average fractions, within each group of traders, over stock days. All messages denotes the sum of marketable limit orders, non marketable limits, and limit order cancellations. In the following regression equation:,,,,,,, denotes the fraction of each trading activity measure, for stock i, on day t, for each trader group. The regressors and tests are similar to Panel A. 40

Panel A: August 2011 Table 3: Order type frequencies by trader type Non HFT MM HFT Opp HFT Hybrid Wald Test Event type ( ) ( ) ( ) ( ) ( ) Buy side (10) Market order walking the book 0.05 0.00*** 0.01*** 0.01*** 0.01*** (9) Price changing market order + residual volume as a limit order 0.13 0.07*** 0.08*** 0.03*** 0.01 (8) Price changing market order that withdraws residual volume 0.33 0.09*** 0.32 0.15*** 0.24*** (7) Market order without price impact 1.10 0.21*** 0.50*** 0.17*** 0.29*** (6) Bid within the best quotes 1.05 5.75*** 0.57*** 0.16*** 5.18*** (5) Bid within the best quotes, automatically cancelled if not executed 0.12 0.35*** 0.06** 0.04*** 0.29*** (4) Bid at the BBO 3.43 12.13*** 5.16*** 1.71*** 6.97*** (3) Bid below the BBO, within 0.5% from the best bid price 12.55 7.02*** 17.35*** 16.79*** 10.33*** (2) Bid below the BBO, more than 0.5% from the best bid price 7.92 0.30*** 1.02*** 3.14*** 0.73*** (1) Cancellation of bid 24.39 23.83** 24.85* 27.16*** 1.02*** Sell side (10) Market order walking the book 0.05 0.00*** 0.01** 0.01*** 0.01*** (9) Price changing market order + residual volume as a limit order 0.13 0.07*** 0.08*** 0.04*** 0.01 (8) Price changing market order that withdraws residual volume 0.33 0.09*** 0.32 0.16*** 0.23*** (7) Market order without price impact 0.95 0.21*** 0.50*** 0.17*** 0.28*** (6) Ask within the best quotes 0.97 5.83*** 0.59*** 0.16*** 5.24*** (5) Ask within the best quotes, automatically cancelled if not executed 0.12 0.33*** 0.06** 0.04*** 0.27*** (4) Ask at the BBO 3.09 12.28*** 5.36*** 1.78*** 6.92*** (3) Ask above the BBO, within 0.5% from the best ask price 12.28 7.15*** 17.51*** 16.59*** 10.36*** (2) Ask above the BBO, more than 0.5% from the best ask price 7.62 0.31*** 0.73*** 3.83*** 0.42*** (1) Cancellation of ask 23.40 23.99** 24.92*** 27.87*** 0.94*** 41

Table 3: Order type frequencies by trader type Panel B: February 2012 Non HFT MM HFT Opp HFT Hybrid Wald Test Event type ( ) ( ) ( ) ( ) ( ) Buy side (10) Market order walking the book 0.05 0.00*** 0.01*** 0.01*** 0.01*** (9) Price changing market order + residual volume as a limit order 0.24 0.04*** 0.19*** 0.06*** 0.15*** (8) Price changing market order that withdraws residual volume 0.50 0.12*** 2.89*** 0.27** 2.77*** (7) Market order without price impact 3.17 0.36*** 1.27*** 0.53*** 0.91*** (6) Bid within the best quotes 1.50 1.08*** 0.86*** 0.28*** 0.21** (5) Bid within the best quotes, automatically cancelled if not executed 0.31 0.08*** 0.42*** 0.04*** 0.34*** (4) Bid at the BBO 7.84 13.51*** 5.17*** 3.98*** 8.34*** (3) Bid below the BBO, within 0.5% from the best bid price 13.07 9.20*** 13.60* 16.41*** 4.40*** (2) Bid below the BBO, more than 0.5% from the best bid price 1.81 1.29*** 3.14*** 1.84 1.86*** (1) Cancellation of bid 21.49 24.01*** 24.36*** 26.47*** 0.35 Sell side (10) Market order walking the book 0.05 0.00*** 0.01*** 0.01*** 0.01*** (9) Price changing market order + residual volume as a limit order 0.22 0.04*** 0.20 0.06 0.17*** (8) Price changing market order that withdraws residual volume 0.55 0.12*** 2.71*** 0.23*** 2.60*** (7) Market order without price impact 2.60 0.39*** 1.16*** 0.55*** 0.77*** (6) Ask within the best quotes 1.65 1.17*** 0.93*** 0.29*** 0.24* (5) Ask within the best quotes, automatically cancelled if not executed 0.35 0.08*** 0.37 0.05 0.30*** (4) Ask at the BBO 7.99 13.61*** 4.44*** 3.95*** 9.18*** (3) Ask above the BBO, within 0.5% from the best ask price 13.29 9.39*** 12.04*** 16.71*** 2.65*** (2) Ask above the BBO, more than 0.5% from the best ask price 1.60 1.21** 3.44*** 1.73 2.23*** (1) Cancellation of ask 21.71 24.32*** 22.79** 26.55*** 1.53*** For the stocks included in the OMXS 30, Table 3 reports the relative frequency of the 20 categories of orders, which add up to 100%. Panel A reports the results for August 2011, and panel B reports February 2012. Market order is short for marketable limit order. Frequencies are reported for market making HFTs (MM HFT), opportunistic HFTs (Opp HFT), non HFTs (Non HFT), and hybrids (Hybrid), displaying groups' average fractions, within each group of traders, over stock days. In the regression:,,,,,,, denotes the frequency for each event type (row), for stock i, on day t, for Non HFTs, MM HFTs, Opp HFTs, and Hybrids,, (, ) is equal to one when the frequency is observed for MM HFTs (Opp HFTs), and zero otherwise,, is equal to one when the frequency is observed for Hybrids, and zero otherwise, and, is a residual. The regression coefficients form frequencies for Non HFTs ( ), MM HFTs ( ), Opp HFTs ( ), and Hybrids ( ). For each event type (row), a test that 0 (for MM HFTs), 0 (for Opp HFTs), and 0 (for Hybrids), respectively, is carried out. Also, a Wald test for the difference between MM HFTs' and Opp HFTs' frequencies is carried out, which boils down to a test of the hypothesis 0. Statistical significance is denoted at the 5% level (*), 1% level (**), and 0.1% level (***). 42

Table 4: Order type frequencies conditional on the type of the previous order Panel A: August 2011 All Buy side orders (t) Sell side orders (t) Previous event type ( 1) (8 10) (7) (5 6) (4) (2 3) (1) (8 10) (7) (5 6) (4) (2 3) (1) Buy side (8 10) Price changing market order 0.12 0.13 6.64 8.19 7.83 18.94 0.83 0.42 1.54 5.77 11.18 38.43 (7) Market order without price impact 4.67 5.33 1.88 10.07 6.07 18.53 0.11 0.19 0.14 2.84 6.82 43.35 (5 6) Bid within the best quotes 0.14 0.09 0.34 4.92 15.62 57.01 0.85 0.34 0.55 2.29 4.24 13.60 (4) Bid at the BBO 0.50 0.53 2.06 8.83 13.33 41.63 0.06 0.25 0.81 2.30 6.70 22.99 (2 3) Bid below the BBO 0.17 0.26 1.00 2.95 23.55 44.72 0.24 0.28 0.61 2.15 7.58 16.48 (1) Cancellation of bid 0.11 0.17 1.24 3.93 41.28 36.58 0.14 0.16 0.47 1.87 4.31 9.74 Sell side (8 10) Price changing market order 0.80 0.43 1.56 6.29 11.46 39.67 0.13 0.13 6.30 7.50 7.46 18.28 (7) Market order without price impact 0.10 0.19 0.14 2.68 7.18 44.69 4.89 5.27 1.69 9.29 5.81 18.09 (5 6) Ask within the best quotes 0.84 0.37 0.42 2.20 4.11 13.85 0.15 0.09 0.34 4.93 15.32 57.37 (4) Ask at the BBO 0.06 0.27 0.79 2.15 6.55 23.04 0.52 0.51 2.00 8.80 13.19 42.13 (2 3) Ask above the BBO 0.23 0.30 0.62 2.12 7.16 16.79 0.18 0.24 1.00 2.98 23.71 44.67 (1) Cancellation of ask 0.14 0.17 0.47 1.84 4.63 8.79 0.11 0.17 1.22 3.97 41.80 36.69 43

Panel B: February 2012 Table 4: Order type frequencies conditional on the type of the previous order All Buy side orders (t) Sell side orders (t) Previous event type ( 1) (8 10) (7) (5 6) (4) (2 3) (1) (8 10) (7) (5 6) (4) (2 3) (1) Buy side (8 10) Price changing market order 0.12 0.09 5.34 9.83 5.85 15.75 0.46 0.25 1.43 4.19 20.56 36.14 (7) Market order without price impact 4.56 7.58 0.95 12.85 4.28 15.52 0.10 0.31 0.11 4.67 6.46 42.60 (5 6) Bid within the best quotes 0.13 0.10 0.59 6.82 21.02 39.47 1.85 0.68 0.71 3.62 5.73 19.28 (4) Bid at the BBO 0.60 0.94 0.82 12.15 10.32 38.20 0.09 0.55 0.56 3.92 7.13 24.73 (2 3) Bid below the BBO 0.23 0.49 0.59 4.98 19.22 43.28 0.36 0.66 0.53 3.91 8.55 17.22 (1) Cancellation of bid 0.15 0.38 0.60 6.54 34.32 37.92 0.23 0.35 0.42 3.56 4.88 10.64 Sell side (8 10) Price changing market order 0.48 0.26 1.52 4.24 19.82 37.30 0.07 0.09 5.03 9.93 5.95 15.30 (7) Market order without price impact 0.10 0.35 0.11 4.49 6.78 45.71 4.47 6.77 0.79 11.58 4.11 14.75 (5 6) Ask within the best quotes 2.13 0.74 0.62 3.37 5.79 18.61 0.13 0.08 0.31 6.59 20.82 40.81 (4) Ask at the BBO 0.09 0.60 0.53 3.78 7.39 24.68 0.55 0.85 0.88 11.82 10.30 38.53 (2 3) Ask above the BBO 0.41 0.71 0.52 3.97 8.32 17.62 0.22 0.48 0.64 5.05 18.61 43.45 (1) Cancellation of ask 0.25 0.39 0.41 3.62 5.25 10.44 0.15 0.41 0.65 7.03 34.58 36.81 For all the stocks included in the OMXS 30 index at that time, Table 4presents the conditional frequencies for each order type. Panel A presents the result for August 2011, and panel B presents February 2012. Order submissions at time (t) are given in the columns, and different aggressiveness levels for the previous order at time (t 1) are given in the table rows. The buy side and sell side are considered separately. The trader contains all the trader groups. The most aggressive order types (8), (9) and (10) are rarely used in the dataset, we henceforth present them in aggregated form as price changing market order. Furthermore, we aggregate order types (5 6) as bid/ask within the best quotes. Order types (2 3) are aggregated as bid below the BBO/ask above the BBO. 44

Table 5: Order type frequencies for different trader groups, conditional on previous order's type and origin Panel A: August 2011 Buy side orders (t) Sell side orders (t) Chi square test Trader type (8 10) (7) (5 6) (4) (2 3) (1) (8 10) (7) (5 6) (4) (2 3) (1) p value (i) Diagonal effect across trader types All 0.12 5.33 0.34 8.83 23.55 36.58 0.13 5.27 0.34 8.80 23.71 36.69 0.0000 MM HFT 0.00 2.93 0.31 18.51 8.73 22.28 0.00 3.15 0.34 18.84 9.15 22.46 0.0000 Opp HFT 0.13 5.68 0.65 11.82 25.01 36.44 0.15 5.74 0.67 12.00 24.72 35.98 0.0000 Non HFT 0.18 14.61 0.91 7.74 29.06 32.15 0.23 11.46 0.73 6.71 29.10 31.56 0.0000 (ii) Diagonal effect of MM HFT conditional on the trader group posted at 1 MM HFT 0.00 8.85 0.16 18.91 18.95 15.26 0.00 9.15 0.16 19.36 20.25 15.67 0.0000 Opp HFT 0.00 2.85 1.69 18.96 6.91 32.66 0.00 3.14 1.79 19.05 7.37 32.45 0.0000 Non HFT 0.00 0.86 0.29 16.33 3.83 30.67 0.01 0.83 0.38 16.55 4.20 30.15 0.0000 (iii) Diagonal effect of Opp HFT conditional on the trader group posted at 1 MM HFT 0.02 8.82 0.26 12.63 18.10 35.12 0.03 9.52 0.26 12.55 17.99 34.88 0.0000 Opp HFT 0.18 8.79 1.80 6.54 25.20 34.56 0.18 8.24 1.80 7.25 25.46 33.99 0.0000 Non HFT 0.18 2.05 0.32 13.29 21.80 34.93 0.19 2.25 0.33 13.60 21.16 35.81 0.0000 (iv) Diagonal effect of Non HFT conditional on the trader group posted at 1 MM HFT 0.06 2.09 0.49 5.49 12.36 36.31 0.00 2.06 0.45 4.55 11.47 35.23 0.0000 Opp HFT 0.12 4.72 2.40 5.83 14.17 42.46 0.12 4.55 1.79 4.60 14.08 40.89 0.0000 Non HFT 0.36 21.40 0.84 12.33 36.26 29.17 0.58 17.49 0.69 11.97 36.86 28.61 0.0000 45

Table 5: Order type frequencies for different trader groups, conditional on previous order's type and origin Panel B: February 2012 Buy side orders (t) Sell side orders (t) Chi square test Trader type (8 10) (7) (5 6) (4) (2 3) (1) (8 10) (7) (5 6) (4) (2 3) (1) p value (i) Diagonal effect across trader types All 0.12 7.58 0.59 12.15 19.22 37.92 0.07 6.77 0.31 11.82 18.61 36.81 0.0000 MM HFT 0.02 4.16 0.26 23.57 15.93 29.51 0.01 4.46 0.32 23.53 15.97 29.32 0.0000 Opp HFT 0.37 7.73 0.79 5.39 20.13 28.12 0.38 6.30 0.64 5.18 17.58 28.74 0.0000 Non HFT 1.61 25.19 4.03 10.98 11.22 23.99 0.31 18.57 1.91 10.83 11.28 23.83 0.0000 (ii) Diagonal effect of MM HFT conditional on the trader group posted at 1 MM HFT 0.04 16.64 0.28 23.61 25.55 26.98 0.03 17.14 0.36 23.74 24.22 26.77 0.0000 Opp HFT 0.00 3.12 1.13 23.19 10.21 30.84 0.00 2.40 0.92 22.75 13.97 30.46 0.0000 Non HFT 0.03 0.90 0.06 21.04 6.91 35.48 0.01 0.98 0.13 20.61 6.71 35.26 0.0000 (iii) Diagonal effect of Opp HFT conditional on the trader group posted at 1 MM HFT 0.00 7.23 0.89 5.79 18.98 35.28 0.00 6.87 0.80 5.43 19.17 35.77 0.0000 Opp HFT 0.05 25.10 0.88 3.87 15.35 17.88 0.00 18.56 0.81 4.15 19.92 19.82 0.0000 Non HFT 1.20 2.95 0.49 4.98 25.36 37.99 1.58 2.76 0.26 4.86 8.36 30.84 0.0000 (iv) Diagonal effect of Non HFT conditional on the trader group posted at 1 MM HFT 0.00 8.87 0.61 10.15 10.37 29.71 0.00 9.09 1.12 9.87 11.30 28.55 0.0000 Opp HFT 0.08 8.07 2.58 10.22 10.09 41.33 0.08 6.99 2.30 10.33 8.41 38.57 0.0000 Non HFT 0.78 33.78 1.34 13.68 8.49 9.65 0.79 26.73 2.86 13.97 8.67 9.64 0.0000 For all the stocks included in the OMXS 30 index, Table 5presents the conditional frequencies for each order type at time (t) in the columns of the table, and different conditions at time (t 1) are given in the table rows. Panel A presents the results for August 2011, and panel B presents February 2012. Part(i) conditions only on the previous order type as in table 4. We present the diagonal numbers for all traders, market making HFTs, opportunistic HFTs and non HFTs. For trader All, part (i) is simply the diagonal numbers from table 4. Part (ii) (iii) and (iv) not only condition on the previous order type, but also which trader group submits that order. We report the p value from a test of the null hypothesis that the diagonal effect is independent of which trader group that posted the previous order. Under this null hypothesis, the numbers in a row in, e.g., part (ii), are equal to the numbers in the corresponding row for MM HFTs in part (i). 46

Table 6: Ordered probit regressions on buy side orders Panel A: August 2011 MM HFT Opp HFT Non HFT Buy side depth 0.297 (53.1) 0.226 (23.3) 0.040 (6.2) Sell side depth 0.066 ( 12.8) 0.190 ( 22.1) 0.119 ( 19.5) Relative spread 0.028 (23.7) 0.018 (10.2) 0.006 (4.3) Realized volatility 0.002 ( 5.5) 0.003 ( 2.5) 0.006 ( 6.7) 2.947 (37.0) 1.256 (9.3) 0.069 (0.7) 4.231 (52.1) 2.336 (17.2) 0.561 (5.9) 5.409 (65.0) 2.558 (18.8) 0.819 (8.6) 5.838 (68.5) 2.852 (20.9) 1.374 (14.3) Observations 30602 12788 33541 Panel B: February 2012 MM HFT Opp HFT Non HFT Buy side depth 0.252 (45.2) 0.218 (16.6) 0.075 (11.2) Sell side depth 0.084 ( 16.3) 0.233 ( 22.9) 0.147 ( 23.3) Relative spread 0.003 (1.9) 0.012 (3.6) 0.016 (7.5) Realized volatility 0.005 ( 5.0) 0.015 ( 2.8) 0.012 ( 4.2) 1.783 (20.7) 0.522 (2.8) 0.677 ( 6.6) 3.913 (44.7) 1.369 (7.2) 0.164 (1.6) 4.389 (49.7) 1.528 (8.1) 0.367 (3.6) 4.934 (54.4) 1.782 (9.4) 1.355 (13.2) Observations 36351 8580 21626 The table presents the estimates of the ordered probit regressions. The dependent variable is buy order aggressiveness defined on a scale from (1) to (5), where (1) is for orders posted below the best buy price; (2) is for orders posted at the best buy price; (3) is for spread improving orders; (4) is for market order without price impact; and (5) is for market orders with price impact. The probit threshold above order type i is denoted. The explanatory variables include Buy side depth and Sell side depth (the SEK volume available at the best buy and sell prices); Relative spread (the basis point spread between the best sell and buy prices); and Realized volatility (squared basis point second by second returns averaged across the 10 whole seconds preceding the order). For each coefficient estimate, the t statistic is given in parentheses. We run one regression for each trader group (MM HFT, Opp HFT, and Non HFT) and each month. Panel A holds results for August 2011 and Panel B for February 2012. 47

Table 7: Base case and marginal probabilities of buy side orders Panel A: August 2011 Base case probability Order type Predicted Actual MM HFT Buy side depth Marginal effects Sell side Relative depth Spread Realized Volatility 1 0.427 0.434 0 0.145 0.035 0.067 0.020 2 0.437 0.410 0 0.041 0.016 0.025 0.009 3 0.124 0.139 0 0.086 0.016 0.035 0.009 4 0.008 0.012 0 0.011 0.002 0.004 0.001 5 0.003 0.006 0 0.007 0.001 0.002 0.000 Opp HFT 1 0.736 0.726 0 0.105 0.075 0.039 0.017 2 0.221 0.221 0 0.070 0.056 0.027 0.012 3 0.017 0.019 0 0.011 0.007 0.004 0.002 4 0.014 0.016 0 0.011 0.006 0.004 0.001 5 0.013 0.018 0 0.014 0.006 0.004 0.002 Non HFT 1 0.844 0.842 0 0.013 0.035 0.009 0.027 2 0.090 0.089 0 0.006 0.017 0.004 0.013 3 0.027 0.028 0 0.002 0.006 0.002 0.005 4 0.029 0.029 0 0.003 0.008 0.002 0.006 5 0.010 0.011 0 0.002 0.004 0.001 0.003 48

Panel B: February 2012 Base case probability Order type Predicted Actual MM HFT Buy side depth Marginal effects Sell side Relative depth Spread Realized Volatility 1 0.337 0.352 0.109 0.041 0.005 0.013 2 0.619 0.599 0.070 0.032 0.004 0.010 3 0.029 0.031 0.022 0.006 0.001 0.002 4 0.011 0.013 0.012 0.003 0.000 0.001 5 0.003 0.005 0.005 0.001 0.000 0.000 Opp HFT 1 0.731 0.717 0.100 0.090 0.017 0.031 2 0.197 0.196 0.053 0.057 0.010 0.019 3 0.019 0.021 0.009 0.008 0.002 0.003 4 0.022 0.024 0.013 0.010 0.002 0.004 5 0.030 0.043 0.025 0.016 0.004 0.006 Non HFT 1 0.555 0.555 0.039 0.074 0.026 0.030 2 0.281 0.276 0.013 0.031 0.009 0.012 3 0.045 0.045 0.005 0.009 0.003 0.004 4 0.104 0.104 0.016 0.028 0.011 0.012 5 0.015 0.017 0.004 0.006 0.003 0.003 The table presents probabilities associated with different order types, calculated from the probit regression estimates presented in Table 6. Order aggressiveness is defined on a scale from (1) to (5), where (1) is for orders posted below the best buy price; (2) is for orders posted at the best buy price; (3) is for spread improving orders; (4) is for market order without price impact; and (5) is for market orders with price impact. Predicted is the probability of each order type based on regression estimates when each explanatory variable is equal to its unconditional mean. Actual is the frequency observed for each order type. Marginal effects show the impact (change in order type probabilities) of a one standard deviation shock to one of the explanatory variables, with the other explanatory variables kept at their unconditional mean. Results are given for regressions for each trader group (MM HFT, Opp HFT, and Non HFT) and each month. Panel A holds results for August 2011 and Panel B for February 2012. 49

Table A6: Ordered probit regressions on sell side orders Panel A: August 2011 MM HFT Opp HFT Non HFT Buy side depth 0.080 ( 15.4) 0.204 ( 23.8) 0.110 ( 17.4) Sell side depth 0.301 (53.6) 0.223 (23.5) 0.039 (5.8) Relative spread 0.035 (29.6) 0.019 (10.4) 0.008 (5.5) Realized volatility 0.002 ( 4.6) 0.004 ( 3.5) 0.005 ( 6.1) γ 2.923 (36.8) 1.010 (7.7) 0.226 (2.3) γ 4.212 (52.1) 2.153 (16.3) 0.722 (7.3) γ 5.402 (65.2) 2.395 (18.1) 0.989 (10.0) γ 5.798 (68.5) 2.648 (20.0) 1.485 (14.9) Observations 30602 13396 32219 Panel B: February 2012 MM HFT Opp HFT Non HFT Buy side depth 0.096 ( 18.6) 0.218 ( 20.1) 0.131 ( 20.1) Sell side depth 0.211 (39.1) 0.181 (14.3) 0.067 (10.3) Relative spread 0.010 (5.7) 0.008 ( 2.7) 0.013 (6.1) Realized volatility 0.015 ( 7.7) 0.005 ( 1.6) 0.003 ( 0.9) 1.143 (13.5) 0.062 ( 0.3) 0.577 ( 5.6) 3.238 (37.7) 0.803 (4.3) 0.295 (2.8) 3.749 (43.2) 0.977 (5.2) 0.534 (5.1) 4.273 (48.0) 1.231 (6.6) 1.398 (13.4) Observations 37234 7217 21182 The table presents the estimates of the ordered probit regressions. The dependent variable is sell order aggressiveness defined on a scale from (1) to (5), where (1) is for orders posted above the best sell price; (2) is for orders posted at the best sell price; (3) is for spread improving orders; (4) is for market order without price impact; and (5) is for market orders with price impact. The probit threshold above order type i is denoted. The explanatory variables include Buy side depth and Sell side depth (the SEK volume available at the best buy and sell prices); Relative spread (the basis point spread between the best sell and buy prices); and Realized volatility (squared basis point second by second returns averaged across the 10 whole seconds preceding the order). For each coefficient estimate, the t statistic is given in parentheses. We run one regression for each trader group (MM HFT, Opp HFT, and Non HFT) and each month. Panel A holds results for August 2011 and Panel B for February 2012. 50

Table A7: Cumulative and marginal probabilities of sell side orders Panel A: August 2011 Cumulative probability Order type Predicted Actual MM HFT Buy side depth Marginal effects Sell side Relative depth Spread Realized Volatility 1 0.429 0.435 0 0.042 0.147 0.084 0.016 2 0.438 0.409 0 0.020 0.042 0.031 0.007 3 0.123 0.139 0 0.019 0.087 0.045 0.007 4 0.007 0.011 0 0.002 0.011 0.005 0.001 5 0.004 0.006 0 0.001 0.007 0.003 0.000 Opp HFT 1 0.723 0.711 0 0.082 0.106 0.041 0.029 2 0.236 0.238 0 0.064 0.072 0.029 0.022 3 0.017 0.020 0 0.007 0.011 0.004 0.003 4 0.011 0.013 0 0.005 0.009 0.003 0.002 5 0.013 0.018 0 0.007 0.014 0.004 0.003 Non HFT 1 0.850 0.848 0 0.031 0.012 0.012 0.023 2 0.087 0.087 0 0.015 0.006 0.006 0.011 3 0.027 0.027 0 0.006 0.002 0.002 0.004 4 0.025 0.025 0 0.007 0.003 0.003 0.005 5 0.011 0.012 0 0.004 0.002 0.002 0.003 51

Panel B: February 2012 Cumulative probability Order type Predicted Actual MM HFT Buy side depth Marginal effects Sell side Relative depth Spread Realized Volatility 1 0.339 0.354 0 0.047 0.094 0.015 0.037 2 0.614 0.596 0 0.036 0.060 0.011 0.028 3 0.032 0.033 0 0.007 0.020 0.003 0.006 4 0.011 0.012 0 0.003 0.009 0.001 0.002 5 0.003 0.005 0 0.001 0.004 0.000 0.001 Opp HFT 1 0.690 0.684 0 0.092 0.088 0.012 0.011 2 0.223 0.217 0 0.055 0.044 0.007 0.006 3 0.024 0.025 0 0.009 0.009 0.001 0.001 4 0.026 0.026 0 0.010 0.011 0.001 0.001 5 0.037 0.048 0 0.018 0.023 0.003 0.002 Non HFT 1 0.557 0.557 0 0.065 0.035 0.021 0.007 2 0.288 0.283 0 0.029 0.013 0.008 0.003 3 0.050 0.050 0 0.009 0.005 0.003 0.001 4 0.088 0.087 0 0.021 0.013 0.007 0.003 5 0.017 0.019 0 0.006 0.004 0.002 0.001 The table presents probabilities associated with different order types, calculated from the probit regression estimates presented in Table 6. Order aggressiveness is defined on a scale from (1) to (5), where (1) is for orders posted above the best sell price; (2) is for orders posted at the best sell price; (3) is for spread improving orders; (4) is for market order without price impact; and (5) is for market orders with price impact. Predicted is the probability of each order type based on regression estimates when each explanatory variable is equal to its unconditional mean. Actual is the frequency observed for each order type. Marginal effects show the impact (change in order type probabilities) of a one standard deviation shock to one of the explanatory variables, with the other explanatory variables kept at their unconditional mean. Results are given for regressions for each trader group (MM HFT, Opp HFT, and Non HFT) and each month. Panel A holds results for August 2011 and Panel B for February 2012. 52