Which is Limit Order Traders More Fearful Of: Non-Execution Risk or Adverse Selection Risk?

Transcription

1 Which is Limit Order Traders More Fearful Of: Non-Execution Risk or Adverse Selection Risk? Wee Yong, Yeo* Department of Finance and Accounting National University of Singapore September 14, 2007 Abstract Limit order traders can mitigate non-execution risk by canceling limit orders with low probability of execution and resubmitting them in front of their cancelled orders in the limit order book. Conversely, they can mitigate adverse selection risk by canceling limit orders at risk and resubmitting them further behind in the limit order book. The decision of limit order traders are tracked from limit order submission to cancellation and from cancellation to resubmission. The paper also performs both static and dynamic analyses of factors affecting the risks of limit order trading. The results show that limit order traders are generally more concerned with non-execution risk than adverse selection risk, except when trading in the least active stocks. The paper also shows that nearly 40 percent of all limit orders are cancelled and nearly 70 percent of these limit orders are never resubmitted into the market. In other words, liquidity leakage through order cancellations is rarely replenished by the same traders. JEL Classification: G19 Keywords: Limit order, Non-execution Risk, Adverse Selection Risk, Cancellation, Resubmission * Department of Finance and Accounting, NUS Business School, National University of Singapore, 1 Business Link, Singapore Tel: (65) , Fax: (65) bizyeowy@nus.edu.sg

2 Which is Limit Order Traders More Fearful Of: Non-Execution Risk or Adverse Selection Risk? Abstract Limit order traders can mitigate non-execution risk by canceling limit orders with low probability of execution and resubmitting them in front of their cancelled orders in the limit order book. Conversely, they can mitigate adverse selection risk by canceling limit orders at risk and resubmitting them further behind in the limit order book. The decision of limit order traders are tracked from limit order submission to cancellation and from cancellation to resubmission. The paper also performs both static and dynamic analyses of factors affecting the risks of limit order trading. The results show that limit order traders are generally more concerned with non-execution risk than adverse selection risk, except when trading in the least active stocks. The paper also shows that nearly 40 percent of all limit orders are cancelled and nearly 70 percent of these limit orders are never resubmitted into the market. In other words, liquidity leakage through order cancellations is rarely replenished by the same traders.

3 Introduction Limit order traders are a vital group of players in equity markets. In a quote driven market, limit order traders share the role of market making with the market makers. In an order driven market, limit order traders are the sole providers of liquidity to the market. As oppose to using market orders, limit orders allow traders to specify the price that they wish to trade. However, there are risks unique to the trading of limit orders that limit order traders have to bear, namely non-execution risk and adverse selection risk. This paper analyses the trading behavior of limit order traders to examine how they mitigate these two types of risks and to see which of these two types of risks they are more averse to. Limit order traders exchange the certainty of the execution of their orders for the certainty of the price they wish to trade. Their orders wait in the limit order book according to price and time priority rules and may not be executed before the traders desired time of execution. This is known as the non-execution risk. Uninformed limit order traders also face adverse selection risk from informed traders. In a quote driven market, limit order traders face a second-level adverse selection risk from the market makers, who can observe and derive information from the order flow as shown in Rock (1996). Many papers in the literature analyze order placement strategies in the light of the risks of limit order trading. For instance, papers such as Biais, Hillion, and Spatt (1995) and Parlour (1998) examine the pattern of limit order submission; Handa and Schwartz (1996) and Harris and Hasbrouck (1996) look at the submission of limit orders versus market orders; and Angel (1982), Foucault (1999), and Omura, Tanigawa, and Uno

4 (2000) study the factors affecting limit order submission. More recently, Hollifield, Miller, Sandas, and Slive (2004) and Goettler, Parlour, and Rajan (2004) discuss the optimal order submission in limit order markets by studying the trade off between nonexecution and adverse selection risks. However, not many studies have been conducted to see exactly how averse limit order traders are to these risks, nor has there been many studies to see which of these two types of risks limit order traders are more averse to. The cancellation and resubmission of limit orders contain a wealth of information yet to be explored. Few papers have focused on the cancellation of limit orders. Biais, Hillion, and Spatt (1995), Coppejans and Domowitz (2002), and Ellul, Holden, Jain, and Jennings (2005) look at the arrival rate of cancellation orders, among other types of orders (limit orders and market orders), and the factors affecting the arrival rate. So far, there has not been any study that extensively discusses the resubmission of limit orders after cancellation. This paper look at the cancellation and resubmission decisions of limit order traders to study how they mitigate the two types of risks associated with using limit orders. Limit orders that are further behind the best quotes have lower probability of execution. Limit order traders can reduce non-execution risk by canceling these orders and resubmitting them in front of the cancelled limit orders in the limit order book (i.e. with higher limit price for limit buy orders or lower limit price for limit sell orders). Informed traders can pick off limit orders that are priced too cheaply (i.e., limit buy orders with limit prices above the fair price or limit sell orders with limit prices below the fair price). To reduce adverse selection risk, traders can cancel their limit orders and

5 resubmit them behind the cancelled limit orders in the limit order book (i.e. with lower limit price for limit buy orders or higher limit price for limit sell orders). Liu (2005), using a sample of 23 of the most highly capitalized stocks from the Australian Stock Exchange (a pure limit order market), shows how monitoring for news arrival can mitigate the risks limit order traders bear. The rate of the arrival of limit order cancellations and revisions acts as proxies for the intensity of monitoring. He shows that when the cost of monitoring is high, traders do not monitor (periods of low rates of cancellations and revisions), and in order to reduce the risks involved in limit order trading, traders submit orders further away from the current price of the stock, resulting in large spreads, and vice versa. This paper, on the other hand, uses data from the NYSE, which is a hybrid market. The sample comprises 148 stocks from a wide spectrum of market capitalization. The data set records order cancellations but not revisions. Instead, this paper is able to infer orders that are cancelled and resubmitted. Instead of looking at the arrival rates of cancellation, the decision of limit order traders is tracked from submission to cancellation and from cancellation to resubmission. This enables distinguishing between resubmission of limit orders in front of and behind the cancelled orders. This is essential in differentiating between the mitigation of non-execution risk from the avoidance of adverse selection risk. This paper finds that traders are more likely to resubmit their limit orders in front of their cancelled limit orders, which implies that they are more concerned with non-execution risk than adverse selection risk. The exceptions are traders trading the least actively

6 traded stocks. These traders are more concerned with adverse selection risk than nonexecution risk. This paper also conducts analyses on static and dynamic factors affecting the risks of limit order trading. The results affirm that limit order traders are indeed more wary of non-execution risk than adverse selection risk. Amihud and Mendelson (1986), Brennan and Subrahmanyam (1996), and Pastor and Stambaugh (2003) show how liquidity can influence the expected return on risky assets, while Chordia, Roll, and Subrahmanyam (2005, 2006) show how liquidity can influence the efficiency of the stock market. In pure limit order markets, the limit orders are the sole providers of liquidity. Even in hybrid markets, such as the NYSE, limit orders are an important source of liquidity. Chung, Van Ness, and Van Ness (1999) show that 75 percent of all the quotes in the NYSE have at least one side of the quotes posted by limit orders. The cancellation and resubmission of limit order affects the liquidity provided by the limit order book. A closer examination of the cancellation and resubmission data reveals that about 37 percent of all limit orders are cancelled after their submission, with 95 percent of these cancellation orders submitted within 10 minutes of the submission of the original limit orders. Most of these cancelled orders are not resubmitted to replenish the liquidity in the limit order book. The organization of the paper is as follows. The data description is presented in Section I. Section II shows the descriptive statistics of the cancellations and resubmissions of limit orders. Section III studies how limit order traders use cancellation and resubmission to mitigate the different types of risks associated with limit order trading. A series of static

7 and dynamic logistic analyses of the cancellation and resubmission decisions of limit order traders is presented in Section IV. Section V concludes the paper. I. Data Description The data set used in this paper is similar to the 1990 NYSE trade, order, and quote (TORQ) limit order data compiled by Joel Hasbrouck (Hasbrouck (1992)). It consists of the System Order Database (SOD) and its companion quote file (SODQ) for 148 securities [1] drawn from a wide spectrum of securities. Henceforth, this new data set will be collectively referred to as the SOD (2001). There are two fields (not present in the TORQ data) in the SOD (2001) that are instrumental to the inference of limit order resubmissions. One field gives a unique code to each brokerage firm, and the other field gives a unique code to each branch of each brokerage firm that posts an order in the SuperDot system. The sample period in this study is the first trading week of April Only pure market and limit orders during the NYSE official market opening time are considered [2]. Table I shows the distribution of the different types of orders. Of the 4,002,030 orders submitted in the sample, percent and percent of them are market buy and market sell orders, respectively. Limit buy and limit sell orders constitute percent and percent of the total number of orders, respectively. There are 801,604 cancellation orders constituting percent of all the orders submitted. [Insert Table I]

8 II. The Nature of the Cancellation and Resubmission of Limit Orders A. Summary Statistics of the Cancellation of Limit Orders The descriptive statistics of the cancellation orders is recorded in Table II. From the figures in Table I, it is worth noting that cancellation orders are more common than either market buy orders or market sell orders in the order flow. As shown in Panel A of Table II, almost all of these cancellation orders (97.87 percent) are for limit orders. Furthermore, 37 percent (or 784,501) of all the (2,119,800) limit orders submitted are cancelled. Hence, it is clear that cancellations play a vital role in the trading of limit orders. In order to analyze these cancellation orders, they have to be first matched to their originating orders. For a cancellation order to be matched to its originating order, it must be for the same stock, be submitted by the same branch of the same firm, have the same turnaround number, be of the same type of order (market or limit), and have the same order size. This process manages to match percent of all the limit order cancellations. The analysis of this paper will be based on these 707,829 matched limit order cancellations. [Insert Table II] Panel B of Table II shows the breakdown of these matched cancellations, from which it can be seen that percent of them are for limit buy orders, while percent of them are for limit sell orders. Panel C further breaks down the cancellations into whether there is a positive, negative, or no change in the respective best quotes between the submission time of the original orders and their cancellations. Slightly more than half of

9 all the cancellations occur when the quotes are moving away, that is, a positive change in the bid for limit buy orders and a negative change in the offer for limit sell orders. Such movements of the quotes will reduce the probability of execution of the limit orders, which may explain their cancellations. However, there are still a substantial number of cancellations where there is either no change in the respective quotes or when the quotes are moving toward their limit prices. These limit orders may be cancelled to avoid being picked off by informed traders. These preliminary figures seem to suggest that limit order traders are more concerned with non-execution risk than adverse selection risk. Panel D shows the distribution of the time interval between the submission of the limit orders and their cancellations. It is worth noting that percent of the cancellations are submitted within 10 seconds of the submission of the original limit orders. Furthermore, percent of the cancellations are submitted within a minute of the original order submission, and percent of the cancellations are submitted within 10 minutes of the original order submission. B. Summary Statistics of the Resubmission of Limit Orders There have not been many studies that look into what takes place after a cancellation. Harris and Hasbrouck (1996) and Handa and Schwartz (1996), impute the cost of nonexecution of limit orders by considering the price which traders have to pay if they were to replace the cancelled limit orders with market orders. Harris and Hasbrouck (1996) qualify that this will exaggerate the penalty associated with limit order execution failure. Indeed, only urgent traders who stand to bear high opportunity costs of non-execution

10 will replace their limit orders with market orders. Traders may resubmit their orders as limit orders. The new limit price they set relative to the limit price of the original limit orders will depend on whether they are more wary of the risk of being picked off or the risk of non-execution. If it is the former, they will move their limit orders backward in the limit order book (i.e., lowering the limit price for limit buy orders or increasing the limit price for limit sell orders). If it is the latter, they will move their limit orders forward in the limit order book (i.e., increasing the limit price for limit buy orders or lowering the limit price for limit sell orders). Traders who are more patient may even withdraw from trading for the rest of the trading period (for example, for the rest of the day). This section traces the resubmission of cancelled limit orders. Limit orders for the same stock, in the same direction (buy or sell), and of the same order size as the cancelled limit orders, submitted by the same branch of the same member firm within a short time interval after the cancellation of the limit orders are considered to be resubmitted orders. [Table III] Table III shows the descriptive statistics for these resubmissions. There are a total of 224,161 resubmitted limit orders. This amounts to a resubmission rate of percent. Earlier, Table II shows that percent of limit order cancellations take place within ten minutes (600 seconds) of order submission. Here it shows that, percent of the resubmission take place within ten minutes of order cancellation. Once again, it shows

11 that limit order traders are actively using order cancellation and resubmission as a vital part of their trading strategy. There is an advantage of setting a short time interval between cancellation and resubmission when inferring order resubmission. First, it is likely that a trader would want to replace his cancelled orders (if he wants to replace them) as soon as possible. Second, the shorter the time interval is, the higher the probability that the resubmitted order would belong to the same trader. Hence, for this paper, only the orders resubmitted within ten minutes of order cancellation are consider as limit order resubmission. According to this criterion, 31.67% of cancelled limit orders are resubmitted. This method to infer order resubmission, although not perfect, is sufficiently robust. For example, in the first trading day of the sample, 11,121 unique firm-branch combinations submitted a total of 754,450 orders. This averages out to approximately 68 orders per firm-branch combination. These 68 orders can be any of the five different types of orders (market buy, market sell, limit buy, limit sell, and cancellation order) and be for any of the 148 stocks. With the additional conditions that the resubmitted orders are of the same order size as the cancelled orders and resubmitted within ten minutes of order cancellation, the chances of capturing order resubmission is high. A robustness check is conducted to show that these resubmitted orders are indeed distinct from newly submitted orders. All the limit orders are categorized as either resubmitted orders or newly submitted limit orders. Resubmission and newly submitted limit buy

12 orders and limit sell orders are each regressed against variables that are known in the literature to have an impact on limit order flow. The corresponding results are shown in Table IV. [Insert Table IV] As can be clearly seen in the table, new limit order submissions are distinct from limit order resubmissions. New limit buy (sell) orders are more probable when the depth at the best offer (bid) price is lower, the order size is larger, it is later during the trading day, the return for the stock is lower (higher) for that trading day, and the stock is less volatile. However, limit buy (sell) order resubmissions are more probable when the depth at the best offer (bid) price is higher, the order size is smaller, it is earlier during the trading day, the return for the stock is higher (lower) for that trading day, and the stock is more volatile. III. Cancellation, Resubmission, and the Risk of Limit Order Trading A. Cancellation and Non-Execution Risk When the respective best quotes move away from the limit orders in the limit order book (i.e., an increase in the bid for limit buy orders or a decrease in the ask for limit sell orders), the probability of execution of these limit orders is reduced. Table II shows that more than half of the cancellations of limit orders take place under such movements of the best quotes. One way of demonstrating the relationship between quotes movements

13 and non-execution risk leading to limit order cancellations is the study of undercutting behavior between limit order traders. Undercutting takes place when a trader submits a limit order with a limit price that is slightly better than the current best price for the sole purpose of gaining execution priority. By improving on the current best price, the trader reduces the economic rent that he may earn. Such a reduction in the economic rent is the cost of undercutting. This cost has been dramatically reduced due to decimalization. Limit order traders can undercut the best quotes by improving the quotes by as little as one penny. Hence, one would expect undercutting behavior among limit order traders to be common in the NYSE. Limit orders in the limit order book are exposed to such undercutting which increases their nonexecution risk. The trader whose order has been undercut may choose to cancel his order as the probability of execution of his order is now reduced. Subsequently, he may resubmit his order to engage in further undercutting, which may in turn cause the trader whose order he has undercut to cancel his orders. Traders may also undercut one another behind the best quotes. However, since the NYSE did not have an open limit order book system during the sample period of this paper, such undercutting behavior is unlikely. In this section, we shall see how many of the cancellations of limit orders are results of the increase in non-execution risk due to undercutting behavior among limit order traders. Submitting a limit order with a limit price better than the current best price, by itself, is not an undercutting activity, for the reason that the limit price the trader posts may be his private evaluation of the fair price of the stock. In order to reduce the possibility of

14 including such orders as undercutting orders, an undercutting order is defined as a limit order that improves on the current quote within a short time interval after it has just been improved. The originating orders of the cancelled limit orders are checked to see whether they were involved in undercutting activity. The maximum time interval is set to five minutes (300 seconds) as limit order traders competing for price priority are likely to do so with speed. The longer the time interval between two orders improving on the best quotes, the less likely they are intended for undercutting. Table V shows the results. [Insert Table V] Cancellations of limit orders as a result of undercutting activity constitute percent of all limit order cancellations when the time interval between two consecutive limit orders that improve on the best quotes is set to 10 seconds. This percentage increases to percent as the time interval increases to five minutes (300 seconds). Although, cancellations as a result of undercutting activity increase with the length of the time interval allowed between two undercutting orders, the increase is only marginal beyond the 60-second time frame. This demonstrates the urgency of limit order traders engaging in undercutting activity. Generally, undercutting behavior among limit order traders contributes more to the number of cancellation orders for more active stocks than less active ones. However, for the time interval of 120 seconds, undercutting contributes more to the number of cancellation orders for Quartile 2 than Quartile 1. Similarly, for the time interval of 300 seconds, undercutting contributes more to the number of cancellation orders for Quartile 3 than Quartile 1 and 2. Overall, the results demonstrate that limit

15 order traders are indeed wary of non-execution risk. They cancel their limit orders as non-execution risk increases as a result of the undercutting behavior of other limit order traders. B. Resubmission and the Mitigation of Risk Informed agents with negative (positive) news can pick off limit buy (sell) orders by selling (buying) against them. Hence, limit buy (sell) orders tend to be executed adversely when the asset price falls (increase). Limit orders also suffer on the opposite side of the coin. When good (bad) news enters the market, sending the asset price upward (downward), the probability of execution for limit buy (sell) orders will be greatly reduced. Even in the absence of new information, limit orders still bear the risk of nonexecution. Limit orders that are further away from the best quotes have a lower probability of execution, with or without news arrival. These orders may be intentionally placed behind the best quotes by patient traders hoping to reap a higher economic rent should prices move temporarily in their favor. They could also have been orders initially placed at, or even in front of, the best quotes but were subsequently undercut by other limit orders. The solution to the adverse selection problem is to cancel and resubmit the limit orders behind the cancelled orders in the limit order book (i.e., further behind the best quotes) when the risk is high. This is analogous to the widening of spreads by market makers in defense against informed trades. On the other hand, to reduce the risk of nonexecution, limit order traders can cancel and resubmit the limit orders in front of the cancelled orders in the limit order book (i.e., nearer to or in front of the best quotes).

16 In relation to Liu (2005), there are a couple of things that should be noted. First, limit order traders who monitor for news arrival may cancel and resubmit their orders whenever necessary to avoid risks. However, the reverse is not necessarily true. Cancellation and resubmission may be the result of micro-trading behaviors, such as undercutting as demonstrated in the above section, rather than of news monitoring. Second, the cancellation and resubmission of limit orders are necessary conditions for risk mitigation, but they alone are not sufficient to help in distinguishing the type of risks the limit order traders are trying to mitigate. The limit prices of the resubmitted orders relative to the cancelled orders are essential for such a distinction. For example, the resubmission of limit buy orders in front of the cancelled orders when the price of the security falls cannot be said to be intended for the mitigation of adverse selection risk. The relation between changes in asset prices and the direction of the change in limit prices will be further explored in the next section. [Insert Table VI] Table VI shows the number and percentage of cancelled limit orders that are resubmitted in front of [3] (Panel A) and behind (Panel B) the cancelled orders in the limit order book. For the full sample, the resubmission of limit orders in front of the cancelled limit orders ranges from 7.24 percent to percent (for time intervals ranging from ten seconds to ten minutes between order cancellations and resubmissions). The differences between the quartiles are marginal for the first three quartiles. Resubmission of limit orders in front of the cancelled limit orders is not common for the least active quartile.

17 Panel B shows the number and percentage of cancelled limit orders that are resubmitted to avoid adverse selection risk. Traders may cancel their limit orders in fear of being picked off. If they should later discover that their fear was unfounded or if the risk disappears, they may resubmit their orders with the same limit prices. Hence, this Panel includes both limit orders that are resubmitted with the same price as, and behind, the cancelled orders. For convenience, both types of resubmissions will collectively be referred to as resubmissions behind the cancelled limit orders. The results show that such resubmissions are common. For the full sample, depending on the length of the time interval between order cancellations and resubmissions, between 5.29 percent and percent of all limit order cancellations are resubmitted behind the cancelled limit orders. The inter-quartile differences between the first two quartiles are marginal. The rate of resubmission behind the cancelled orders for the third quartile is greater when considering time intervals of 60 seconds and longer. Resubmission of limit orders behind the cancelled limit orders is most common for the least active stocks (last quartile) for time intervals of 60 seconds and longer. A comparison between Panel A and B seems to suggest that limit order traders are more wary of non-execution risk than adverse selection risk. More limit orders are resubmitted in front of the cancelled limit orders than behind. However, the reverse is true for trading in the least active stocks. Resubmissions behind the cancelled orders are much more common than resubmissions in front of the cancelled orders for these stocks. This implies that adverse selection risk is higher for these least active stocks. Traders of these stocks

18 are more wary of adverse selection risk than non-execution risk. The result that resubmission behind cancelled orders are more common for the two less active quartiles, than the two more active ones, also shows that adverse selection risk increases with the decrease in trading activity. Furthermore, they tend to wait longer to resubmit their orders after cancellation. The large number of cancellations in the order flow is by itself of independent interest. This paper also contributes to the study of liquidity by looking at the relation between cancellations and resubmissions. For a pure limit order market, the limit order book is the sole provider of liquidity. Even for a hybrid market such as the NYSE, the limit order book is still an important source of liquidity, as documented by Chung, Van Ness, and Van Ness (1999) and Kang and Yeo (2006). As mentioned earlier in the paper, 37 percent of all limit orders are cancelled, with 95 percent of these cancellations taking place 10 minutes after submission. At the ten-minute interval, the total resubmission rate is slightly less than 32 percent [4]. This means that about 24 percent of the limit orders leave the market 10 minutes after their submission and never enter the market again [5]. Hence, looking at limit order submission without accounting for limit order cancellation and resubmission will grossly overestimate the liquidity provided by the limit order book. IV. Analysis of the Variables That Influence Cancellations and Resubmissions Different market conditions, stock, and order characteristics may affect the risks limit order traders face and hence influence the decision of limit order traders to cancel and resubmit their limit orders. These factors may be static or dynamic. Static variables such

19 as the time of submission (cancellation), the order size, the spread, and the bid and offer depth at the time of submission (cancellation) may influence the decision to cancel (resubmit) the limit orders. After the limit orders are submitted, the decision of whether to cancel the orders is an ongoing dynamic process, ending only when the orders are terminated either by execution or cancellation. At every instant in time, before the orders are terminated, traders make active decisions to either cancel the orders or to leave them in the limit order book according to their assessment of the risks they face. Similarly, the decision to resubmit and where in the book to resubmit the orders after cancellation is also an ongoing dynamic process, ending when the orders are resubmitted or when the current trading horizon expires. Dynamic factors such as changes in the spread, changes in the asset price, and changes in the bid and offer depth, from the time the limit orders are submitted (cancelled) may influence the decision of the traders to cancel (resubmit) the limit orders. Tables II shows that more than 95 percent of cancellations occur within 10 minutes from the time of limit order submission. Hence, this section will trace the decision of the traders at six different points in time (10, 30, 60, 120, 300, and 600 seconds) starting from the time they submit the limit orders. For each time point, for example at the 60- second time point, limit orders that are either executed or cancelled at or before the preceding time point (i.e., 30 seconds) are removed from the data. The remaining limit orders are analyzed to see how changes in variables, such as the spread and the bid and

20 offer depth, from the time of submission of the limit orders to the 60-second time point, may influence the decision of traders to either cancel these orders or to leave them in the limit order book. Tables III shows that more than 91 percent of resubmissions occur within 10 minutes from the time of cancellation. Hence, the same time points are also used for the analysis of the dynamic decision to resubmit the limit orders after their cancellation. Different variables influence different types of decisions in different directions. An increase in the asset price, for example, may increase the probability of limit sell orders execution but reduce the probability of limit buy orders execution. At the same time, an increase in the asset price may increase the adverse selection risk of limit sell orders but increase the non-execution risk for limit buy orders. If such differences are not taken into account, the result of the analysis may only reveal the net impact (of adverse selection risk and non-execution risk) of the variables. Hence, limit buy order cancellation and resubmission are modeled separately from limit sell order cancellation and resubmission. The decision to resubmit the limit orders in front of (to reduce non-execution risk) and behind (to reduce adverse selection risk) the cancelled limit orders are modeled together in a multinomial logistic framework. This section will present the results of eight logistic regression models as follows: i. Static analysis of the cancellation of limit buy orders ii. Static analysis of the cancellation of limit sell orders iii. Dynamic analysis of the cancellation of limit buy orders

21 iv. Dynamic analysis of the cancellation of limit sell orders v. Multinomial static analysis of the resubmission of limit buy orders vi. Multinomial static analysis of the resubmission of limit sell orders vii. Multinomial dynamic analysis of the resubmission of limit buy orders viii. Multinomial dynamic analysis of the resubmission of limit sell orders A list of the independent variables for each model is shown in Table VII. [Insert Table VII] A. Analysis of the Cancellation of Limit Orders 1. Static Analysis of the Cancellation of Limit Orders Static analysis of the cancellation of limit orders analyzes the impact of static factors, at the time of order submission, on the cancellation of the limit orders. The models for limit buy order cancellation ( CXLLB i, s, t, D ) and limit sell order cancellation ( CXLLS i, s, t, D ) for limit order i, stock s, and at the time of submission t, on day D, are CXLLB b 1,5 i,s,t,d Time i = a 1,6 1 Ret 1,1 Spread 1,7 s,t,d MkCap 1,2 Bidsz 1,8 Vol s,t,d 1,3 1,9 Ofrsz s,t,d Volatility 1,4 Ordsz i + (1) CXLLS b 2,5 i,s,t,d Time i = a 2,6 2 Ret 2,1 Spread 2,7 s,t,d MkCap 2,2 Bidsz 2,8 s,t,d Vol 2,3 2,9 Ofrsz s,t,d Volatility 2,4 Ordsz i + (2)

22 where b l,k is the coefficient of independent variable k in equation l. Two different types of variables are used for Time i. The trading day is divided into seven trading periods. The first type is a discrete variable, running from 1 to 7 depending on the time period the limit orders are submitted. The second type uses seven different dummy variables to represent each trading period. The daily data for Ret, MkCap, Vol, and Volatility are taken from the CRSP database. [Insert Table VIII] The results are shown in Table VIII. For ease of interpretation, the tables for all the logistic analyses will show the marginal effects of one standard deviation change in the respective independent variables rather than the coefficients. For example, the marginal effects of 0.05 for Spread in the first column of Panel A means that an increase of one standard deviation of the log difference between the bid and offer price at the submission of the limit order increases the probability of cancellation of that limit order by 5 percent. Limit buy orders and limit sell orders submitted at a time when the spread is wide are more likely to be cancelled than when the spread is narrow. Papers written by Angel (1992) and Ellul, Holden, Jain, and Jennings (2005) have documented the positive relation between spread and limit order submission. When the spread is wide, new limit orders will be submitted inside the spread, pushing limit orders already in the limit order book backward in the queue. This reduces the probability of execution for the limit orders that are already in the book and hence increases their probability to be cancelled. A larger depth at the same (opposite) side of the quotes reduces the probability of execution of

23 limit orders and increases (reduces) the likelihood of cancellation of the limit orders. Large orders are less likely to be cancelled than small orders. Large orders are exposed to a higher risk as they have more price impact and take longer to be filled. It seems that traders who place large orders are more cautious in setting the limit prices, thereby reducing the need to cancel the orders [6]. Both the discrete time variable and the time dummies show that limit buy orders submitted earlier in the day are more likely to be cancelled than those submitted later. Orders submitted earlier are exposed to higher risk as there is more time for new information arrival (increasing adverse selection risk) and more time for other traders to undercut the orders (increasing non-execution risk). Although the relation between the time variables and the cancellation of limit sell orders is also negative, the decrease in the probability of cancellation over time is less smooth. The relation between time of the day and the probability of cancellation in this analysis is not directly comparable to studies such as those of Biais, Hillion, and Spatt (1995), Coppejans and Domowitz (2002), Ellul, Holden, Jain, and Jennings (2005), and Liu (2005) who find a U-shaped pattern for cancellations. These papers study the arrival rate of cancellations in the order flow regardless of when these orders are submitted. A U- shaped pattern means that more cancellations are submitted at the start and at the end of the trading day. This section, instead, looks at the probability of limit order cancellation given the time that they are submitted. Limit buy (sell) orders of stocks with positive (negative) return on the day of submission will more likely be cancelled as non-execution risk increases. Stocks with larger market capitalization are more likely to be cancelled. Liu (2005) explains that this is due to the fact that larger stocks are more information transparent, and traders can more easily monitor for new information and adjust their

24 trading strategies accordingly to reduce the risk they are exposed to. Limit orders of stocks that are more actively traded are less likely to be cancelled. Limit orders of more volatile stocks are more likely to be cancelled. As the volatility of the stock price increases, traders will have to reconsider their trading strategies more often and hence this will lead to more cancellations. 2. Dynamic Analysis of the Cancellation of Limit Order Dynamic analysis of the cancellation of limit orders analyzes the impact of changes in certain variables, from the time of submission of the limit orders, on the cancellation of these orders. The models for limit buy order cancellation ( CXLLB i, s, t, T, order cancellation ( CXLLS i, s, t, T, point T, on day D, are D ) and limit sell ) for limit order i, stock s, submitted at time t, at time D CXLLB b b 3,4 3,9 Ofrsz Vol i,s,t T,,D s,t T,,D = a 3,10 3 3,5 3,1 Ordsz Volatility Cngpx i s,t,t,d 3,6 i 3,2 Time Spread 3,7 Ret s,t,t,d 3,8 3,3 Bidsz MkCap s,t,t,d + + (3) CXLLS b b 4,4 4,9 Ofrsz Vol i,s,t T,,D s,t T,,D = a 4,10 4 4,5 4,1 Volatility Cngpx Ordsz i s,t T,,D 4,6 i 4,2 Time Spread 4,7 Ret s,t T,,D 4,8 4,3 Bidsz MkCap s,t T,,D + + (4) Note that some of the independent variables for the dynamic models, in contrast to those for the static models, are further indexed by T. For example, Spread s,t,t,d measures the change in the spread for stock s, on day D, from the time of submission t to time point T.

25 [Insert Table IX] Table IX shows the results for the dynamic analysis of cancellation. Other than for the 10-second time point, an increase in the stock price after the submission of the limit buy (sell) orders increases (reduces) the probability of their cancellation. This may mean that traders are more concerned with the non-execution risk than with the adverse selection risk. This is consistent with the results in Section III. In the above static analysis, the limit orders submitted when the spread is wide are more likely to be cancelled. However, here it shows that increasing the spread after submission actually reduces the probability of cancellation. A widening spread increases the probability of execution for limit orders that are already in the book, but at the same time, it increases the adverse selection risk of these limit orders. Hence, the negative relation between the change in spread and the probability of cancellation implies that limit order traders are more averse to nonexecution risk than adverse selection risk. As shown above, a larger bid (offer) depth at the time of submission reduces the chance of execution of limit buy (sell) orders and increases the likelihood of cancellation. An increasing bid (offer) depth after submission, on the other hand, means an increase in limit buying (selling) interest. Since orders already submitted have the time priority of execution, the need to cancel these orders is reduced. An increasing offer (bid) depth discourages submission of limit sell (buy) orders. Sellers (buyers) with the urgency to trade will use market sell (buy) orders instead. This will increase the probability of execution of limit buy (sell) orders and hence reduce the probability of their cancellation. Order size and time of submission

26 remain negative in the dynamic analysis. Daily stock-specific control variables (Ret, MkCap, Vol, and Volatility) show similar patterns as the static models, with a few exceptions. The direction of influence of the daily return and trading volume for most of the time points for the limit sell order cancellation are different from those of the static models. B. Analysis of the Resubmission of Limit Orders Where in the limit order book, limit order traders choose to resubmit their limit orders after cancellation carries different implications with regard to how they perceive the trading environment. Resubmitting orders in front of the cancelled limit orders reduces the risk of non-execution, while resubmitting behind the cancelled limit orders reduces the risk of adverse selection. The resubmission of limit orders in front of and behind the cancelled limit orders is modeled using multinomial logistic regressions, with nonresubmitted cancelled limit orders as the base case. 1. Static Analysis of the Resubmission of Limit Order The static models for limit buy order resubmission ( resubmission ( on day D, are RSLS i,s,ct,d RSLB i,s,ct,d ) and limit sell order ) for limit order i, for stock s, and at the time of cancellation ct, RSLB b 5,5 i,s,ct,d i = a Time 5,6 5 Ret 5,1 Spread 5,7 s,ct,d MkCap 5,2 Bidsz 5,8 s,ct,d Vol 5,3 5,9 Ofrsz s,ct,d Volatility 5,4 Ordsz i + (5)

27 RSLS b 6,5 i,s,ct Time i = a 6 6,6 6,1 Ret Spread 6,7 s,ct,d MkCap 6,2 Bidsz 6,8 s,ct,d Vol 6,3 Ofrsz 6,9 s,ct,d Volatility 6,4 Ordsz i + (6) [Insert Table X] The results are shown in Table X. Panels A and B show the results for limit buy order resubmitted in front of and behind the cancelled limit orders, respectively, while Panel C and D show the results for limit sell orders resubmitted in front of and behind the cancelled limit orders, respectively. While a wide spread at the time of submission increases the probability of limit order cancellations, a wide spread at the time of cancellation reduces the probability of resubmission. The negative relation between spread and resubmission of limit orders is stronger for resubmissions in front of than behind the cancelled orders. Hence, a wide spread encourages cancellations and discourages resubmissions (especially in front of the cancelled orders). In other words, when the spread is wide, traders tend to cancel limit orders and shun away from the market in fear of adverse selection risk. A larger bid (offer) depth at the time of cancellation increases the probability of resubmission for limit buy (sell) orders in front of the cancelled limit orders but reduces the probability of resubmission behind the cancelled orders. Together with the results from the previous section (that a larger bid (offer) depth increases the probability of cancellation of limit buy (sell) orders), the results show that limit order traders re-position their limit orders to avoid non-execution risk. These results are also consistent with the undercutting behavior among limit order traders, as shown in Section III. A large offer (bid) depth discourages limit sell (buy)

28 orders and encourages market sell (buy) orders, thereby increasing the probability of limit buy (sell) order execution. In such a situation, limit buyers would rather resubmit behind the cancelled orders in the hope of reaping a higher economic rent. In both tables, the relation between limit order resubmission and order size, regardless of limit buy orders or limit sell orders, is negative. This is consistent with the results for the cancellation of limit orders: limit order traders are more cautious when pricing large limit orders, thereby reducing the need to cancel and resubmit the orders. Although the relation between resubmission and the time of cancellation is negative, the separate dummies for each trading period show that the decline in the probability of resubmission over time is not constant. In fact, there does not seem to be a defined pattern. Hence, while the decision to cancel the limit orders is influenced by the time the limit orders are submitted, the decision to resubmit the orders after cancellation is less affected by the time of the day that they are cancelled. The results for the daily stock-specific controls will be discussed in the following section. 2. Dynamic Analysis of the Resubmission of Limit Order The dynamic models for limit buy order resubmission ( RSLB i,s,ct,ct,d ) and limit sell order resubmission ( RSLS i,s,ct,ct,d ) for limit order i, for stock s, at the time of cancellation ct, at time point ct, on day D, are RSLB b b 7,4 7,9 i,s,ct,ct,d Ofrsz Vol s,ct,ct,d = a 7,10 7 7,5 7,1 Volatility Cngpx Ordsz i s,ct,ct,d 7,6 i 7,2 Time Spread 7,7 Ret s,ct,ct,d 7,8 7,3 Bidsz MkCap s,ct,ct,d + + (7)

29 RSLS b b 8,4 8,9 Vol i,s,ct,ct,d Ofrsz s,ct,ct,d = a 8,10 8 8,5 8,1 Volatility Cngpx Ordsz i s,ct,ct,d 8,6 i 8,2 Time Spread 8,7 Ret s,ct,ct,d 8,8 8,3 Bidsz MkCap s,ct,ct,d + + (8) [Insert Table XI] Table XI shows the results of the dynamic multinomial logistic regressions. Limit order traders are wary of both the non-execution risk and adverse selection risk. The change in asset price is positively related to the resubmission of limit buy orders in front of cancelled orders but is negatively related to the resubmission of limit buy orders behind the cancelled orders. In other words, increasing asset price after the cancellation of limit buy orders increases the probability of resubmission in front of the cancelled orders, while decreasing asset price after cancellation increases the probability of resubmission behind the cancelled orders. The same can be said for the resubmission of limit sell orders. The marginal effects for the case of resubmission in front of the cancelled orders, especially for limit buy orders, are generally stronger than those of resubmission behind. Hence, this may once again imply that limit order traders are, in general, more wary of non-execution risk than adverse selection risk. The static analysis in the above section shows that a wide spread at the time of cancellation reduces the probability of resubmission of limit orders. However, a widening spread after cancellation encourages resubmission both in front of and behind the cancelled orders. As the spread widens, limit order traders who are more averse to non-execution risk may be tempted to resubmit the orders closer to the best quotes, or even within the spread to increase execution

30 probability; meanwhile, those who are more averse to adverse selection risk may resubmit further behind in the book for fear of being picked off. An increasing bid depth increases (reduces) the probability of resubmission of limit buy (sell) orders, while an increasing offer depth decreases (increases) the probability. However, the relation is not strong. As in the static analysis, a larger order size decreases the probability of limit order resubmission, and the time of cancellation does not have a clear influence on the resubmission decision of limit order traders. The results for the daily stock-specific control variables are not always consistent for the static and dynamic analyses. However, certain weak, general patterns can still be identified. Resubmission seems to be more likely on days of positive returns. Larger capitalized stocks are less likely to be resubmitted once they are cancelled. A higher trading volume increases the probability of resubmission in front of but reduces the probability of resubmission behind the cancelled orders. In other words, resubmission behind the cancelled orders is more likely for less active stocks. This is consistent with the results in Table VI: traders are more concerned with adverse selection risk for less actively traded stocks. Resubmission in front of (behind) the cancelled limit orders is more (less) probable for more volatile stocks. C. Summary of the Results of the Logistic Analyses The results of the above analyses show that limit order traders are indeed aware of both non-execution risk and adverse selection risk. However, they are more concerned with the former than the latter. When stock price increases (decreases), limit buy (sell) orders

31 are more likely to be cancelled and resubmitted in front of the cancelled orders. This is also consistent with the undercutting behavior among limit order traders competing for price priority. In the event when limit buy (sell) orders are cancelled when stock price decreases (increases), they are more likely to be resubmitted behind the cancelled orders. A wide spread at the time of submission increases the probability of cancellation, but a widening spread after the time of submission reduces the probability of cancellation. This may help to explain why Liu (2005) finds a negative relation between spread and cancellation, while other papers such as Coppejans and Domowitz s (2002) and Ellul, Holden, Jain, and Jennings (2005) find a positive relation. On a separate note, it is clearly demonstrated here that a wide spread reduces liquidity in the limit order book in two ways: increasing limit orders cancellations and reducing limit order resubmissions. Bid and offer depth, and the change in bid and offer depth, influence the cancellation and resubmission of limit orders so as to avoid non-execution risk more than adverse selection risk. Larger limit orders are less likely to be cancelled, and if cancelled, are less likely to be resubmitted. This implies that traders are more careful when pricing their large limit orders. Limit orders submitted earlier in the day are more likely to be cancelled. Resubmission of limit orders, however, does not seem to exhibit any consistent time of the day effect. Consistent with the work of Liu (2005), large cap stocks are more likely to be cancelled. However, this paper shows that they are less likely to be resubmitted once cancelled.