Pricing of Limit Orders. on the Xetra Electronic Trading System

Transcription

1 Pricing of Limit Orders on the Xetra Electronic Trading System Anna Schurba April 15, 2005 Preliminary and incomplete. Please do not quote or distribute without permission. Comments greatly appreciated. Abstract This paper analyzes empirically how the market activity and the state of an open limit order book affect traders choices of the limit order price. Large offered quantities on the same side of the market move the limit order price closer to the midquote; large offered quantities on the opposite side of the market lead to an increase in the relative limit order price. Large limit orders placed within the quotes gravitate towards the midquote, while large limit orders at a price beyond the quotes are pushed away from the midquote. The relative limit order price decreases in the number of trades. Sellers seem to monitor the market closely, and condition their choice on the information available publicly. In contrast, buyers probably have other sources of information than those considered in this study. JEL Classification: C29; G15; G29 Keywords: Limit order book; Limit orders; Microstructure; Traders behavior Graduate Program Finance and Monetary Economics, Goethe University of Frankfurt, Mertonstraße 17-21, Uni-PB 77, D Frankfurt/Main, Germany, to schurba@wiwi.uni-frankfurt.de. The research was supported by the Deutsche Forschungsgemeinschaft. I am grateful to Theofanis Archontakis, Uwe Hassler, Christian Schlag, seminar participants at the University of Frankfurt, and participants of the Augustin Cournot Doctoral Days for helpful comments and suggestions. Special thanks are due to the Deutsche Börse AG for providing the data set, to Micong Klimes for an introduction to limit order books, and to Burkart Mönch for invaluable advice in data processing and market microstructure issues. All errors are my responsibility. 1

2 Pricing of Limit Orders on the Xetra Electronic Trading System 2 1 Introduction Historically, market microstructure literature deals with dealer or quote-driven markets, where quotes are set by a single optimizing market maker, while traders arrive at the market, and either accept the price and trade, or do not trade at all. Nowadays, an increasing number of security exchanges function as a limit order book market, where traders transact with each other by submitting either market or limit orders. Traders have to choose between immediate execution against the best available price posted in the order book (market order), or a better execution price together with the non-execution risk (limit order). Limit orders can be picked off, that is executed not in favor of the limit order trader, either because of an execution against an informed trader, or if new information arrives, but mispriced limit orders are not cancelled promptly. Empirical studies of order choice include Biais, Hillion, and Spatt (1995), Griffiths, Smith, Turnbull, and White (1998), Ellul, Holden, Jain, and Jennings (2004), and others. The limit order price varies in its aggressiveness with respect to the current best bid-ask spread. The further is the limit order price from the midquote, the smaller is the probability of execution. Traders problem of choosing the optimal limit order price is hardly tractable in game theoretical framework due to its dependence on future actions of multiple traders that influence the probability of execution of all orders. Foucault (1999), Parlour (1998), Easley and O Hara (1992), and Handa and Schwartz (1996) derive theoretical predictions about the relationship between the choice of the order type and such parameters as the stock price volatility, the best bid-ask spread, the depth of the limit order book (offered quantities), trade and order intensity, and buy-sell imbalances on the market. This study analyzes empirically how the state of the open limit order book and market activity affect traders choice of the limit order price. Most studies to date present theoretical or empirical analysis of the choice between market and limit orders. In the data set under study, market and marketable limit orders constitute below 20% of the submitted order volume. Existing literature hardly differentiates between limit orders: if at all, they are classified as being at the best quote, inside the quote and beyond the quotes, for example up to the 5th best quote. This classification is sufficient for analysis of the market with a discrete tick size, or the market where traders can see the first five quotes only. However, in a market with a fully open limit order book

3 Pricing of Limit Orders on the Xetra Electronic Trading System 3 and a very fine tick size another form of assessment of the traders decisions is required. Why the choice of the limit order price is important? Because the limit order prices in the order book are the only prices at which liquidity is supplied. The main objective of this paper is an empirical analysis of limit order pricing in an open limit order book framework. We consider each single entered limit order from the point of view of the trader who already knows the direction of the trade, who wishes to trade via a limit order and has to choose the limit order price. Market activity parameters, such as volatility, the number of trades, and submitted order volume, along with the best bid-ask spread, the depth of the order book on both sides, and the shape of the order book are examined in order to determine their impact on traders decisions. The main findings are: The relative limit order price does not seem to depend either on the measure of the intraday volatility we use in this study, or on the short-term return. The increase of the relative limit order price in the relative spread is rather mechanical, since traders who undercut the best quotes have more room to move if the spread is wide. Large offered quantities on the same side of the market move the order limit price closer to the midquote to increase the probability of execution. Large offered quantities on the opposite side of the market lead to an increase in the relative limit order price, since they demonstrate an increase in demand on the other side, from which limit order traders may gain. Large limit orders placed within the quotes gravitate towards the midquote, while large limit orders at a price beyond the quotes are pushed away from the midquote. The relative limit order price decreases in the number of trades: traders might prefer a faster execution to bound the uncertainty during highly volatile periods. Sell order traders seem to monitor the market closely, and condition their actions on the information publicly available. In contrast, buy order traders probably have other sources of information than those considered in this study. The relative limit order price does not exhibit any prominent intraday patterns.

4 Pricing of Limit Orders on the Xetra Electronic Trading System 4 The paper is organized as follows. The next section provides an overview of the related literature. Section 3 sketches out institutional details; Section 4 presents the data set and some descriptive statistics. Section 5 states the hypotheses and outlines the empirical methodology. Section 6 reports the results; and Section 7 concludes. 2 Related Literature Limit orders that enter the limit order book essentially represent the demand and supply schedules for the stock. Glosten (1994) models the equilibrium price schedule in an open limit order book market, where patient traders supply liquidity by submitting limit orders, while impatient (and probably informed) market order traders demand it. Limit order traders submit their orders only if the expected loss from transacting with an informed trader does not exceed the expected gain from transacting with an uninformed demander of liquidity. Sandås (2001) uses a data set from the Stockholm Stock Exchange to test a set of economic restrictions derived from Glosten (1994). For most stocks, the quantity offered on the market is lower than predicted by the model, but suggested extensions such as dependence of model parameters on market conditions improve the performance. Næs and Skjeltorp (2004) study empirically the link between the stock price volatility, the number of trades, and the demand and supply schedules in the limit order book of the Oslo Stock Exchange. The findings support the view that the distribution of prices and quantities in the order book is a proxy for heterogeneous beliefs among traders. Hollifield, Miller, and Sandås (2004) derive empirical restrictions from an order choice model. Traders determine the optimal submission strategy based on their valuation for the stock, and the trade-offs between different order prices, execution probabilities, and the risk of being picked off. The restrictions are rejected for the buy and sell orders considered jointly, but cannot be rejected for each side of the market considered separately. Parlour (1998) models the choice between limit and market orders within a one-tick dynamic limit order book market without asymmetric information. Traders condition their order submission on the state of the limit order book, and anticipate the impact their orders have on the strategies of incoming traders, whose actions in turn influence the execution probability of all orders. The dependence between the state of the limit

5 Pricing of Limit Orders on the Xetra Electronic Trading System 5 order book and the order flow generates systematic pattern in order submission strategies. For example, the probability of a limit order is smaller than the probability of a market order if the preceding order was a limit order on the same side of the market, since a preceding limit order increases the queue at the quote and thus decreases the probability of execution. Biais, Hillion, and Spatt (1995) define order aggressiveness in terms of the relation of the order price and quantity to the best quote and its quantity. The most aggressive orders are market orders of a larger quantity than the quantity available at the best quote. These orders are executed immediately and lead to a change in the best quote as they walk up the book. Less aggressive orders are limit orders with the limit order price within the best quotes, at the quote on the same side, or beyond the quote. The least aggressive trader actions are cancellations of the limit orders in the order book. Biais, Hillion, and Spatt (1995) find positive autocorrelation in the order type, and suggest it is a result of either strategic order splitting to reduce the price impact, or imitation of trading behavior, or a similar reaction to new information. Roll (1984) shows that the bid-ask bounce between transactions on both sides of the market generates negative autocorrelation in transaction returns. Biais, Hillion, and Spatt (1995) demonstrate that dynamics of liquidity supply results in negative autocorrelation in the quote changes and in the best bid-ask spread. When the spread is large, traders submit more limit orders inside the quotes to obtain price and time priority, and the bid-ask spread decreases. Positive cross-serial correlation between changes in the bid and ask quotes seems to be consistent with information effects. In particular, when a large market order consumes liquidity on one side of the market, the best quote on that side mechanically moves away from the midquote. If afterwards the best quote on the opposite side of the market moves in the same direction, i.e. closer to the midquote, it might indicate a revision in traders expectations. Bisière and Kamionka (2000) extend the analysis of Biais, Hillion, and Spatt (1995) by considering the durations between orders along with order aggressiveness, and obtain similar results, except for the absence of a strong autocorrelation for the orders inside the quote. Ellul, Holden, Jain, and Jennings (2004) perform a number of tests to analyze order choice decisions across various stocks on the New York Stock Exchange (NYSE), and find negative autocorrelation in order type for order flows computed over five minute intervals.

6 Pricing of Limit Orders on the Xetra Electronic Trading System 6 This evidence supports the Parlour (1998) model, despite positive autocorrelation in order type typically found for individual orders. Hollifield, Miller, and Sandås (2004) show that the gradual adjustment of the limit order book to changes in the equilibrium stock price explains positive autocorrelation in order submissions. In line with the classification proposed by Biais, Hillion, and Spatt (1995), Griffiths, Smith, Turnbull, and White (1998), and Ranaldo (2004) study determinants of order aggressiveness on the Toronto Stock Exchange, and the Swiss Stock Exchange respectively. Aggressive orders are more likely after aggressive orders on the same side, more often posted when the spread is wider, and the depth on the same (opposite) side is larger (smaller). Griffiths, Smith, Turnbull, and White (1998) find buy orders more informative, since aggressive buy orders are followed by a price increase that offsets the immediate price impact. Ranaldo (2004) shows that sell orders are more likely to be motivated by liquidity reasons, since the average spread size is higher for an incoming sell order, and sell orders are less strongly autocorrelated. A larger average spread size suggests a higher risk of execution against an informed trader. A lower autocorrelation might indicate the absence of information motives, since information motives are typically related to a higher persistence in the order flow. Foucault (1999) examines price formation and choice between limit and market orders in a game theoretical framework. Market orders are executed immediately against given limit orders. Limit orders provide a better execution price at a cost of the non-execution risk and the risk of being picked off. The latter does not exist in the Parlour (1998) model. In case of high volatility, the risk of being picked off necessarily increases, and limit order traders require a higher compensation. Since market orders become more costly, traders avoid submitting market orders, and execution probabilities of limit orders decrease. Handa, Schwartz, and Tiwari (2002) model quote setting in a limit order book market as an extension of the Foucault (1999) model with adverse selection due to the presence of informed investors. The bid-ask spread increases in valuation differences among traders, and decreases in the buy-sell imbalance in the order flow. The data from the Paris Bourse provides supporting evidence to the model. Foucault, Kadan, and Kandel (2003) examine market resiliency, order submission strategies and the bid-ask spread in a dynamic model with liquidity traders. Traders vary in the degree of impatience and minimize the trading costs by trading off the cost of immediacy

7 Pricing of Limit Orders on the Xetra Electronic Trading System 7 against the risk of uncertain execution. Patient traders tend to supply liquidity, while impatient traders tend to demand it. The spread decreases in the proportion of patient traders and in the order arrival rate, since patient traders post limit orders. Handa and Schwartz (1996) study the rationality and profitability of limit order trading. Limit orders might either fail to execute because the market moves away, or might be executed due to unfavorable changes of the equilibrium price. Both outcomes are clearly undesirable for the limit order trader. However, a lack of limit orders can lead to temporary imbalances between the buy and sell sides of the market, and to short-term changes in transaction prices that increase transitory volatility. The transitory volatility encourages limit order submission, as limit orders are executed against short-term price fluctuations around the equilibrium level. Ahn, Bae, and Chan (2001) provide supporting evidence to the model, since buy-sell imbalances and higher volatility increase the proportion of limit orders in the order flow on the Stock Exchange of Hong Kong. Harris and Hasbrouck (1996) analyze performance of limit and market orders on the NYSE SuperDOT system and conclude that the most widely used limit order strategies are indeed the best in terms of the proposed performance measures, which compare the order execution price with the ex-post and ex-ante quotes. Harris (1998) derives numerically optimal order submission strategies for small order sizes that do not affect prices. Traders submit more aggressive orders if they face a deadline or try to exploit material information that becomes public quickly. Bloomfield, O Hara, and Saar (2004) study experimental asset markets to demonstrate that informed traders use market orders and thus consume liquidity when the value of their information is high, but use limit orders and provide liquidity otherwise. Kaniel and Liu (2004) present an equilibrium model, where limit orders might be more informative than market orders, since informed traders tend to use limit orders if the information is long-lived. Cao, Hansch, and Wang (2004) study the Australian Stock Exchange, and show that the content of an open limit order book is informative about future short-term price movements, and that traders condition their order submission choices on the state of the book beyond the best quotes. Hasbrouck and Saar (2002) report that over one quarter of limit orders submitted to the Island Electronic Communication Network are cancelled within two seconds. Therefore, limit order traders are not just patient providers of liquidity, but might have another rationale for order submission.

8 Pricing of Limit Orders on the Xetra Electronic Trading System 8 3 Institutional Details Xetra is the electronic trading system that was introduced in 1997 by the Deutsche Börse, the Frankfurt Stock Exchange. According to Deutsche Börse (2002a), securities trading shifts increasingly from quote-driven floor trading to order-driven electronic trading. Our data encompasses the first quarter of 2002, when Xetra s market share for DAX stocks amounted to 95.5% of total equities turnover as measured by order book volume. Trading in DAX stocks starts with an opening auction at 09:00 a.m., followed by continuous trading that is interrupted by two intraday auctions at 13:00 p.m. and 17:30 p.m. Trading ends with a closing auction, for the period under consideration at 20:00 p.m. During the auctions, only the indicative auction price is displayed to traders, the order book is closed. Price determination in auctions seeks to maximize the executable volume. During continuous trading, the limit order book is open, and traders can see all the limit order prices, the total order volume at each limit, as well as the number of orders at each limit. While all order sizes are considered in auctions, only round lots (order sizes that are multiples of 100 shares) can be traded during continuous trading. When a new order arrives, the system checks if it can be executed against the orders in the book. Orders that are not fully executed enter the book. Xetra supports market orders, limit orders, market-to-limit orders, and iceberg (hidden) orders. Market-to-limit orders are executed against the best quote in the book, and the remaining order size is converted to a limit order at the price of the executed part. Iceberg order traders must specify a limit price, an overall volume, and a peak size. The peak of an iceberg order is visible, but not marked as a part of a hidden order. As long as hidden volume is still available, a new peak enters the order book with a new time stamp as soon as the old peak is fully executed. Orders can be entered, modified, or cancelled even when the book is closed, i.e. during pre-trading or post-trading, or during auctions. Orders are executed according to price and time priority, that is the limit order with prices more favorable for an incoming market order and a smaller time stamp are executed first. Order modification alters time priority if either the limit order price changes, or the order size increases. Starting from the day of entry, order validity extends over a maximum of 90 calendar days; it might be restricted to the current trading day, or up to a specified day, or till cancellation.

9 Pricing of Limit Orders on the Xetra Electronic Trading System 9 Trading restrictions allow to restrict order validity to one specific auction or all auctions. Additional execution conditions include immediate execution restrictions, namely immediate-or-cancel orders and fill-or-kill orders. The former might be partially executed, the latter must be fully executed or not at all. If immediate full execution is not possible, non-executed parts of these orders are deleted without entry in the order book. Stop orders allow an automatical submission of an order when a predefined (stop) price is reached. 4 Data Set and Descriptive Statistics The data we analyze consist of order entries, modifications, cancellations and (partial) executions over a period of the 61 trading days from January 3 to March 28, We consider only the Xetra electronic trading without floor trading, and we do not account for possible links between Frankfurt and New York or London, where some of the DAX stocks are traded. The data set allows us to reconstruct the open limit order book at any point in time, and to compute flow variables such as the volume of incoming orders or traded volume. Based on the level of activity in the stock, we divide all 30 DAX stocks into three activity groups. LIN, BMW, and DBK stocks were randomly selected out of the group of the less liquid, more liquid, and most liquid DAX stocks respectively, as measured by the average daily traded volume. Table 1 reports daily market activity statistics averaged over the sample period for each of these three stocks. On average, limit orders represent over 80% of the submitted order volume. We restrict our attention to those limit orders that were entered during continuous trading, and did not have any trade or order restrictions. Orders that are reserved for trading in a call auction only, or require immediate execution without an entry in the order book are likely to be submitted because of other reasons than those we consider in this study. As our objective is to analyze limit orders that enter the order book, we disregard market and marketable limit orders, i.e. orders with the limit order price strictly better than the best quote on the opposite side, or with the limit order price at the best quote with a smaller order size than the quantity offered at the best quote.

10 Pricing of Limit Orders on the Xetra Electronic Trading System 10 We determine transaction prices and limit order book state variables such as the quotes and offered quantities that were valid immediately before each limit order submission. Flow variables are computed for 15 minutes before the order submission. We do not consider invisible parts of hidden orders in our analysis, as traders on the market cannot condition on hidden volume directly. We seek to capture prices and volume distribution in the book to be able to condition on most of the information traders see on the screen. Figure 1 shows a sample shape of the order book, and illustrates our procedure. We compute a shape measure similarly to Charoenwong, Ding, and Visaltanachoti (2004), but we have a finer price grid. The ask and bid shape of the book are equal to an average across all slope changes on the respective side, that is: Shape = 1 I 2 I 2 i=1 Slope i = 1 I 2 I 2 i=1 ( Q i+2 Q i+1 P i+2 P i+1 ( Q i+2 Q i+1 P i+2 P i+1 Q i+1 Q i P i+1 P i ) + Q i+1 Q i P i+1 P i ), where P i and Q i denote limit order prices and offered quantities at the ith quote from the midquote. If Shape is negative, the order book is concave, that is the spread between two adjacent quotes away from the market is wider, or the offered quantities at quotes away from the market is smaller. If Shape is positive, the order book is convex. A concave book implies concentration of liquidity (in terms of offered quantities) closer to the best quote. In our data, AskShape is negative on average (concave book); BidShape is positive on average (convex book). To measure the intraday volatility, we use the sum of squared returns on the midquote over 15 minutes preceding the submission of an order as an estimate of the current stock price volatility. A recent thorough treatment in Aït-Sahalia, Mykland, and Zhang (2004) illustrates biases, introduced by summing up all the squared returns to obtain an estimate for the cumulative volatility over a time period. Specifically, let S t be the price process of a stock. Assume that X t = ln S t follows dx t = µ t dt + σ t db t, where µ t is the time dependent drift component, σ 2 t is the instantaneous variance of the return process, and B t is a standard Brownian motion. The cumulative or integrated volatility from t 1 to t 2 is estimated by the sum of all squared returns over the period: t2 t1 σ 2 t dt t i (X ti+1 X ti ) 2.

11 Pricing of Limit Orders on the Xetra Electronic Trading System 11 The sum of squired returns is called realized volatility or realized variance, and is a widely used estimator for integrated volatility. In theory, the realized volatility computed at the highest possible sampling frequency yields the best estimate of the integrated volatility. But empirically, the robustness of the estimator at higher frequencies is reduced by the additional noise from microstructure effects, such as the existence of the bid-ask bounce between prices of transactions on the two different sides of the market. Aït-Sahalia, Mykland, and Zhang (2004) propose a method for bias correction, which involves subsampling at various frequencies. However, for our purposes the sum of squared returns on the midquote is an adequate stock price volatility proxy that mitigates the bid-ask bounce and uses all the available data. 5 Hypotheses and Empirical Methodology We compute the relative limit order price as (LimitOrderP rice Midquote) Midquote (Midquote LimitOrderP rice) Midquote for a buy order, and for a sell order. Figure 2 illustrates intraday dynamics of the limit order price, Table 2 provides descriptive statistics. A negative relative limit order price means that the limit order price is closer to the best quote on the opposite side than to the best quote on the own side of the market. Although the existing literature does not deal with the problem of the limit order price choice directly, hypotheses for the relative limit order price can be derived. We state them as alternative hypotheses. Volatility: Relative limit order price increases in volatility. Foucault (1999) shows that in a high volatility environment limit order traders require a greater compensation, as the risk of being picked off increases. Empirically, Næs and Skjeltorp (2004) find that the limit order book is more dispersed if the uncertainty is high. Spread: Relative limit order price increases in the relative spread. Both spread and volatility essentially represent a measure of uncertainty, thus the relative limit order price should increase in the relative spread in line with Foucault (1999).

12 Pricing of Limit Orders on the Xetra Electronic Trading System 12 Moreover, if the best bid-ask spread is wide, even those traders who wish to undercut the best quote can place their orders further from the midquote. Return: Relative limit order price increases (decreases) in return on the sell (buy) side. As a mechanical reaction to a price movement, buy orders might tend closer to the quote because otherwise the market may move away. In contrast, sell orders may move further away from the quote to capture the gain from the upward trend. Depth: Relative limit order price decreases in the depth on the same side, and increases in the depth on the opposite side. Parlour (1998) argues that a greater offered quantity implies a smaller execution probability on the same size, and more demand in orders on the opposite side. Hollifield, Miller, and Sandås (2004) demonstrate an increase in execution probability on one side of the market if the volume and thus competition on the other side increase. Cao, Hansch, and Wang (2004), and Handa and Schwartz (1996) report similar findings. Trade and Order Intensity: Relative limit order price increases in trade and order intensity. During periods of heavy trading Hollifield, Miller, and Sandås (2004) observe a higher probability of execution even far from the quote due to a higher stock price volatility. Easley and O Hara (1992) show that the best bid-ask spread decreases during no-trading periods, and increases in unexpected traded volume. If there is no trade, existence of new information is less likely, so the probability of transacting with an informed investor, and thus the risk of being picked off, is smaller. Symmetry: The behavior of the relative limit order price is not symmetric on both sides. Næs and Skjeltorp (2004) find that the bid side volume is concentrated closer to the inner quote than the volume on the ask side. Griffiths, Smith, Turnbull, and White (1998) find buy orders more informative, as aggressive buy orders are followed by a price increase that offsets the immediate price impact. Ranaldo (2004) shows that sell orders are more likely to be motivated by liquidity reasons, since the average spread size is higher for

13 Pricing of Limit Orders on the Xetra Electronic Trading System 13 an incoming seller, and sell orders are less strongly autocorrelated. A larger average spread size suggests a higher risk of execution against an informed investor. A lower autocorrelation might indicate the absence of information motives, as an opposite to a higher persistence in the order flow, typically linked to information motives. Time Dependence: Relative limit order price exhibits intraday and intraweek patterns. Bloomfield, O Hara, and Saar (2004) argue that time of day matters, since traders face a greater uncertainty about the equilibrium stock price at the beginning of the trading day. Moreover, traders might have to trade to meet a deadline at the end of the day; trading behavior changes as the deadline approaches. We estimate regressions for orders that were submitted from 09:15 a.m. to 17:30 p.m. since trading is less frequent after these hours: RelativeLimitOrderP rice = α 0 + α 1 RelativeSpread + α 2 MidquoteV olatility + α 3 Ln(Return) + α 4 NumberOfT rades + α 5 Ln(BuyOrderV olume) + α 6 Ln(SellOrderV olume) + α 7 BuyMarketT olimit + α 8 SellMarketT olimit + α 9 AskShape + α 10 AskConcentrationNearQuote + α 11 BidShape + α 12 BidConcentrationNearQuote + α 13 Ln(AskT otalv olume) + α 14 Ln(BidT otalv olume) + α 15 LargeOrderDummy + α 16 JanuaryDummy α 17,t HourDummy t + α 18,t W eekdaydummy t t=1 t=1 n 10 + α 19,n RelativeLimitOrderP rice n + ε. n 1 Table 2 reports descriptive statistics of the explanatory variables. RelativeSpread is computed relative to the midquote. M idquotev olatility is the sum of squared returns on the midquote (multiplied by 1,000) over 15 minutes preceding the order submission. Ln(Return) and flow variables are computed over 15 minutes before the order submission, logs are taken of volume in shares. We use NumberOfT rades as a measure of trading activity similarly to Ahn, Bae, and Chan (2001). BuyM arkett olimit

14 Pricing of Limit Orders on the Xetra Electronic Trading System 14 and SellM arkett olimit relate the volume of incoming market and marketable limit orders to the incoming limit order volume for each side of the market. AskShape and BidShape are computed as illustrated in Figure 1 immediately before the order submission. AskConcentrationN earquote and BidConcentrationN earquote denote the fraction of the volume offered up to the median quote to the total volume offered on the respective side. We add a dummy for order sizes greater than the median order size, since traders might treat large orders differently. A dummy for January should capture any abnormal pattern in January. We use hour and weekday dummies to account for intraday and intraweek patterns typically found in intraday data. Separate regressions are run for each side of the market and for the limit prices that improve the current best quote. The latter distinction stems from the order type choice literature, where these orders form separate groups. Traders who undercut the best quotes might have different objectives than those who place their orders beyond the best quotes. We do not aim to analyze the order type choice, but rather the choice of the limit order price given the order type. We compute heteroscedasticity and autocorrelation-consistent standard errors using the Newey-West estimator with ten lags to account for autocorrelation in the order flow. Multicollinearity does not represent a problem with our specification, since the variance inflation factor V IF values do not indicate problems: V IF = 1, where r 2 is the 1 r 2 multiple correlation between an explanatory variable and the other explanatory variables. 6 Empirical Results Since large sample sizes decrease standard errors of the estimates and thus increase t- statistics, the statistical significance of the results may be spurious if based on t-statistics only. Following Griffiths, Smith, Turnbull, and White (1998), we use a posterior odds ratio test to determine critical t-values. The posterior odds ratio evaluates the odds against the null hypothesis of the coefficient being zero given the data. For instance, a t-statistic of over 4 is required to obtain a posterior odds ratio of 20:1 for our numbers of observations. The large sample posterior odds ratio r can be approximated by r = exp ( t 2 /2) (π df)/2,

15 Pricing of Limit Orders on the Xetra Electronic Trading System 15 where t is the t-statistic, and df is the degrees of freedom. Regression results for limit orders with the limit order price behind the best quote are presented in Table 3, while regression results for limit orders with the limit order price at or inside the best quotes are presented in Table 4. Volatility. The relative limit order price does not seem to depend on the measure of volatility we use in this study, namely the sum of squared returns on the midquote (multiplied by 1,000) over 15 minutes before the order submission. Spread. The increase of the relative limit order price in the relative spread is rather mechanical in nature, as we observe strongly statistically significant coefficients of the relative spread in case of limit orders with the limit order price at or inside the best quotes. When the spread is wide, traders who undercut the best quotes have clearly more room to move. Return. There is no statistically significant dependence between the relative limit order price and the return over last 15 minutes before the limit order submission. Depth. The influence of depth on the relative limit order price in mostly in line with theoretical predictions. Large offered quantities on the same side of the market move the relative order limit price closer to the midquote to increase the probability of execution. Large offered quantities on the opposite side of the market lead to an increase in the relative limit order price, since they demonstrate an increase in demand on the other side, and limit order traders attempt to gain from it. Trade and Order Intensity. The relative limit order price decreases in the number of trades. Hasbrouck and Saar (2002) argue that risk-averse traders might have a greater fear of being picked off during volatile periods, and thus might prefer the certain execution of a market order. This line of reasoning may be extended to the case of limit order pricing, where traders might prefer a faster execution to bound the uncertainty, and thus choose a limit order price closer to the midquote. Symmetry. In general, the sell side of the market seem to have more statistically significant coefficients that the buy side. This is consistent with the view that sell order traders either trade for liquidity reasons or provide liquidity, and therefore monitor the market to obtain the best possible execution. In contrast, buy order traders seem to condition

16 Pricing of Limit Orders on the Xetra Electronic Trading System 16 their decision on other variables than publicly available. Time Dependence. Coefficients of time dummies (not reported) are almost never statistically significant, not even separately, so there is no statistically significant time dependence of the relative limit order price. The coefficient of the large order dummy that marks the limit orders with the order size greater than the median size is always statistically significant. It is negative for the limit orders that improve the best quote, and mostly positive for the orders that are placed beyond the best quote. Therefore, large limit orders placed within the quotes gravitate towards the midquote, while large limit orders at the price beyond the quotes are pushed away from the midquote. Robustness Checks. The close-to-close log return of LIN, BMW, and DBK was positive for 33, 31, and 29 days out of 61 trading days under consideration. Splitting the sample into bull and bear subsamples provides qualitatively similar results (not reported). In the previous analysis, time period from 09:15 a.m. to 17:30 p.m. was considered, due to infrequent trading after these hours. Including the previously omitted orders from the end of the day does not change the results materially. 7 Conclusion This study analyzes empirically how the market activity and the state of the open limit order book affect traders choice of the limit order price. The relative limit order price does not seem to depend either on the measure of the intraday volatility we use in this study, or on the short-term return. The increase of the relative limit order price in the relative spread is rather understandable, as traders who undercut the best quotes have more attainable prices if the spread is wide. Large offered quantities on the same side of the market move the order limit price closer to the midquote to increase the probability of execution. Large offered quantities on the opposite side of the market lead to an increase in the relative limit order price, since they demonstrate an increase in demand. Large limit orders placed within the quotes gravitate towards the midquote, while large limit orders at a price beyond the quotes are pushed

17 Pricing of Limit Orders on the Xetra Electronic Trading System 17 away from the midquote. The relative limit order price decreases in the number of trades: traders might prefer a faster execution to bound the uncertainty during highly volatile periods. Sell order traders seem to monitor the market closely, and condition their actions on the information publicly available. In contrast, buy order traders probably have other sources of information than those considered in this study. Finally, the relative limit order price does not exhibit any prominent intraday patterns. Theoretical or empirical investigations into the nature of the order size effect on the choice of the order type and the limit order price are fruitful directions for future research. In addition, the determinants of the limit order pricing on the buy side deserve further attention.

18 Pricing of Limit Orders on the Xetra Electronic Trading System 18 References Ahn, H.-J., K.-H. Bae, and K. Chan, 2001, Limit Orders, Depth, and Volatility: Evidence from the Stock Exchange of Hong Kong, Journal of Finance, 56, Aït-Sahalia, Y., P. Mykland, and L. Zhang, 2004, A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High-Frequency Data, Working Paper. Biais, B., P. Hillion, and C. Spatt, 1995, An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse, Journal of Finance, 50, Bisière, C., and T. Kamionka, 2000, Timing of Orders, Orders Aggressiveness and the Order Book at the Paris Bourse, Annales d Économie et de Statistique, 60, Bloomfield, R., M. O Hara, and G. Saar, 2004, The Make or Take Decision in an Electronic Market: Evidence on the Evolution of Liquidity, Forthcoming in the Journal of Financial Economics. Cao, C., O. Hansch, and X. Wang, 2004, The Informational Content of an Open Limit Order Book, Working Paper. Charoenwong, C., D. Ding, and N. Visaltanachoti, 2004, Liquidity Distribution in Limit Order Books, Working Paper. Deutsche Börse, 2002a, Interim Report: Quarter 1/2002, Quarterly Report. Deutsche Börse, 2002b, Xetra Market Model Stock Trading, Technical Report. Easley, D., and M. O Hara, 1992, Time and the Process of Security Price Adjustment, Journal of Finance, 47, Ellul, A., C. Holden, P. Jain, and R. Jennings, 2004, Order Dynamics: Recent Evidence from the NYSE, Working Paper. Foucault, T., 1999, Order Flow Composition and Trading Costs in a Dynamic Limit Order Market, Journal of Financial Markets, 2, Foucault, T., O. Kadan, and E. Kandel, 2003, Limit Order Book as a Market for Liquidity, Working Paper. Glosten, L., 1994, Is the Electronic Open Limit Order Book Inevitable?, Journal of Finance, 49, Greene, W., 1993, Econometric analysis, Macmillan, New York. Griffiths, M., B. Smith, A. Turnbull, and R. White, 1998, The Costs and Determinants of Order Aggressiveness, Journal of Financial Economics, 56, Handa, P., and R. Schwartz, 1996, Limit Order Trading, Journal of Finance, 51, Handa, P., R. Schwartz, and A. Tiwari, 2002, Quote Setting and Price Formation in an Order Driven Market, Forthcoming in the Journal of Financial Markets.

19 Pricing of Limit Orders on the Xetra Electronic Trading System 19 Harris, L., 1998, Optimal Dynamic Order Submission Strategies in Some Stylized Trading Problems, Financial Markets, Institutions & Intruments, 7, Harris, L., and J. Hasbrouck, 1996, Market vs. Limit Orders: The SuperDOT Evidence on Order Submission Strategy, Journal of Financial and Quantitative Analysis, 31, Hasbrouck, J., and G. Saar, 2002, Limit Orders and Volatility in a Hybrid Market: The Island ECN, Working Paper. Hollifield, B., R. Miller, and P. Sandås, 2004, Empirical Analysis of Limit Order Markets, Review of Financial Studies, 71, Kaniel, R., and H. Liu, 2004, So What Orders Do Informed Traders Use?, Working Paper. Næs, R., and J. Skjeltorp, 2004, Order Book Characteristics and the Volume-Volatility Relation: Empirical Evidence from a Limit Order Market, Working Paper. Parlour, C., 1998, Price Dynamics in Limit Order Markets, Review of Financial Studies, 11, Ranaldo, A., 2004, Order Aggressiveness in Limit Order Book Markets, Journal of Financial Markets, 7, Roll, R., 1984, A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market, Journal of Finance, 39, Sandås, P., 2001, Adverse Selection and Competitive Market Making: Empirical Evidence from a Limit Order Market, Review of Financial Studies, 14,

20 Pricing of Limit Orders on the Xetra Electronic Trading System 20 Table 1. Daily Summary Statistics. The table reports Xetra daily market activity statistics averaged over the sample period of the 61 trading days from January 3 to March 28, LIN, BMW, and DBK stocks were randomly selected out of the group of the less liquid, more liquid, and most liquid DAX stocks respectively, as measured by the average daily traded volume. For each characteristic, the minimum, mean (bold, in the middle), maximum values, and standard deviation (in brackets) are reported; volume is in thousand shares. LIN BMW DBK Traded volume ,930 5,130 1,782 3,880 9,267 (156) (796) (1,325) Number of trades , ,614 3,122 1,738 3,450 6,256 (176) (463) (898) Daily high in euro (3.71) (2.71) (4.46) Daily low in euro (3.75) (2.66) (4.52) Close-to-close log return in % (1.27) (1.79) (2.06) Buy order volume 709 1,529 2,680 1,468 5,427 11,347 4,625 9,636 16,890 entered (406) (1,689) (2,152) Sell order volume 948 1,519 2,562 1,457 5,403 10,034 4,440 9,572 16,274 entered (350) (1,588) (2,195) Limit buy order volume 636 1,318 2,144 1,173 4,405 10,207 3,793 7,629 11,966 entered (325) (1,428) (1,665) Limit sell order volume 825 1,356 2,381 1,226 4,431 8,692 3,278 7,489 11,173 entered (327) (1,362) (1,614) Limit buy order volume to all order volume (5.62) (5.73) (4.01) Limit sell order volume to all order volume (3.79) (4.66) (4.46)

21 Pricing of Limit Orders on the Xetra Electronic Trading System 21 Table 2. Dependent and Explanatory Variables. The upper panel summarizes descriptive statistics of the dependent variable the limit order price relative to the midquote over the 61 trading days from January 3 to March 28, The mean, minimum, and maximum values are reported, together with the standard deviation and the number of observations. The lower panel provides descriptive statistics of explanatory variables used in the regressions. In addition to the RelativeSpread (relative to the midquote), the best bid-ask spread is reported for comparison. M idquotev olatility is the sum of squared returns on the midquote (multiplied by 1,000) over 15 minutes before the order submission. Ln(Return) and flow variables are computed over 15 minutes before the order submission, logs are taken of volume in shares. BuyM arkett olimit and SellM arkett olimit relate the volume of incoming market and marketable limit orders to the incoming limit order volume for each side of the market. AskShape and BidShape are computed as illustrated in Figure 1 immediately before the order submission. AskConcentrationN earquote and BidConcentrationN earquote denote the fraction of the volume offered up to the median quote to the total volume offered on the respective side. Relative Limit Order Price Mean Std. Dev. Min Max Nr. of Obs. LIN Buy Limit Orders ,108 Sell Limit Orders ,530 BMW Buy Limit Orders ,013 Sell Limit Orders ,934 DBK Buy Limit Orders ,492 Sell Limit Orders ,696 LIN BMW DBK Explanatory Variable Mean Std. Dev. Mean Std. Dev. Mean Std. Dev. RelativeSpread Best Bid-Ask Spread MidquoteV olatility Ln(Return) NumberOfT rades Ln(BuyOrderV olume) Ln(SellOrderV olume) BuyMarketT olimit SellMarketT olimit AskShape BidShape AskConcentrationNearQuote BidConcentrationNearQuote Ln(AskT otalv olume) Ln(BidT otalv olume) Number of observations 291, , ,188

22 Pricing of Limit Orders on the Xetra Electronic Trading System 22 Table 3. Regression Results for Orders beyond the Best Quote. The table reports regression results for orders with the limit order price behind the best quote that were submitted from 09:15 a.m. to 17:30 p.m. The explanatory variable are those from Table 2, along with hour and weekday dummies, a dummy for order sizes greater than the median order size, and a dummy for January: RelativeLimitOrderP rice = α 0 + α 1 RelativeSpread + α 2 MidquoteV olatility + α 3 Ln(Return) + α 4 NumberOfT rades + α 5 Ln(BuyOrderV olume) + α 6 Ln(SellOrderV olume) + α 7 BuyMarketT olimit + α 8 SellMarketT olimit + α 9 AskShape + α 10 AskConcentrationNearQuote + α 11 BidShape + α 12 BidConcentrationNearQuote + α 13 Ln(AskT otalv olume) + α 14 Ln(BidT otalv olume) + α 15 LargeOrderDummy + α 16 JanuaryDummy + 8 α 17,t HourDummy t + t=1 n α 18,t W eekdaydummy t t=1 α 19,n RelativeLimitOrderP rice n + ε n 1 Heteroscedasticity and autocorrelation-consistent standard errors are computed using the Newey-West estimator with ten lags. For coefficients in bold the posterior odds against the null hypothesis of the coefficient being zero exceed 20:1. LIN BMW DBK Coefficient Std. Err. t-stat. Coefficient Std. Err. t-stat. Coefficient Std. Err. t-stat. Buy Orders RelativeSpread MidquoteV olatility Ln(Return) NumberOfT rades e e e Ln(BuyOrderV olume) Ln(SellOrderV olume) BuyMarketT olimit SellMarketT olimit AskShape AskConcentrationNearQuote e BidShape BidConcentrationNearQuote Ln(AskT otalv olume) e Ln(BidT otalv olume) LargeOrderDummy JanuaryDummy Constant Number of obs. 79, , ,456 Adjusted R F -stat