Limit order revisions

Journal of Banking & Finance 34 (2010) 1873–1885

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Journal of Banking & Finance journal homepage: www.elsevier.com/locate/jbf

Limit order revisions Kingsley Y.L. Fong a,*, Wai-Man Liu b a b

School of Banking and Finance, Australian School of Business, The University of New South Wales, Sydney NSW 2052, Australia School of Finance, Actuarial Studies and Applied Statistics, College of Business and Economics, Australian National University, ACT 0200, Australia

a r t i c l e

i n f o

Article history: Received 12 September 2008 Accepted 24 December 2009 Available online 4 January 2010 JEL classification: F10 G14

a b s t r a c t This paper empirically examines limit order revisions and cancellations which contribute to a significant portion of the order activity in many order-driven markets. We document that limit orders are more likely to be revised or cancelled if they are large and near the bid-ask quote. We show that order revisions generate net economic benefits to traders. Our evidence shows strong links between these activities and limit order submission risk using bid-ask spread, volatility and post-event return as proxies. We also find that these activities are less intense when the opportunity cost to monitor a stock is high, such as during lunch hours or when stock volume relative to the entire market is low. Ó 2010 Elsevier B.V. All rights reserved.

Keywords: Limit orders Free option risk Non-execution risk Limit order cancellation Limit order revision

1. Introduction Limit order revisions and cancellations1 contribute to a significant proportion of the order activity in many order-driven markets, but the reason for these decisions remains unclear. Ellul et al (2007) and Yeo (2005) document that traders on the NYSE cancelled almost half of all limit orders.2 Hasbrouck and Saar (2002) find that 93% of limit orders on INET3 are cancelled and 36.69% of limit orders are cancelled within two seconds of submission. On the Australian Securities Exchange where the data permits the distinction of order cancellation from order revision, Liu (2009) reports that orders are revised more often than cancelled.4 However, few studies investigate the reasons for limit order revision and cancellation. Thus, we con-

* Corresponding author. Tel.: +61 2 9385 4932; fax: +61 2 9385 6347. E-mail addresses: [email protected] (K.Y.L. Fong), [email protected] (W.-M. Liu). 1 Cancellations can be taken as a special case of revisions, with volume goes to zero. 2 Recent observation suggests that as high as 70% of limit orders on the NYSE are cancelled. We thank Li Wei from the NYSE for providing this information. 3 INET is an ECN found in 2002 as a result of merger of Island and Instinet. Nasdaq acquired INET in 2005 and it had integrated with SuperMontage and Brut system to become Nasdaq primary trading platform. 4 In equity warrants markets, Foster and Liu (2008) find that the about 95% of equity warrant’s order book activity is order revision. For instance, the price and the quantity of a limit sell order on a put warrant, on average, are revised, 69 and 119 times on a single day, and the corresponding average (median) time between consecutive revisions is 69 (8) s. 0378-4266/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2009.12.010

tribute to the literature by documenting the regularity of these activities and by examining their determinants. The two major reasons to revise or cancel a limit order are nonexecution (NE hereafter) risk and free option (FO hereafter) risk. NE risk arises from the possibility that a limit order will not be executed. FO risk arises because a limit order provides an option for other traders to transact. This differentiation is important because NE risk and FO risk lead to different order revisions. If traders are concerned about NE risk, they will revise orders to increase the price priority, and thus, increase the likelihood of execution. If traders are concerned about FO risk, they will revise orders to decrease the price priority, and thus, reduce the likelihood of execution.5 NE risk is one of the major reasons to revise or cancel limit orders. Hasbrouck and Saar (2002) and Liu (2009) argue that the execution probability and the expected payoff of a limit order decreases when the subsequent trading activity moves away from the original limit order price. This reduced payoff can induce a trader

5 While most datasets do not offer revision data, one might argue that the order sequence of (1) revision and (2) cancellation followed by a new submission should be observationally equivalent and hence we should not draw a different conclusion, at least from a theoretical standpoint. However, from an empirical standpoint, we cannot perfectly match the cancelled order with the new submitted order, especially when traders amend both price and quantity of the order and thus that leads to a series of problem in empirical implementation. As we will show later, the behaviors of cancellation and revision are quite different.

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When the release of public news changes: (i) the status of the limit order book;

Utility from trading is positive

Utility from trading is negative Don’t submit any order

Order Placement Decision

If E[FO cost] + E[NE cost] + MC > E[Spread]

Executed

Limit Order

If E[FO cost] + E[NE cost] + MC > E[Spread]

Adverse news

(ii) the short run movement of the stock prices

Utility is positive

Decrease the price priority of the order

Utility is negative

Cancel the order

FO risk increases

Not Executed Favorable news

Optimal order revision strategy:

NE risk increases Utility is positive

Market Order

Increase the price priority of the order

Fig. 1. Decision tree of order choice, revision and cancellation.

to revise or cancel the original order. Hasbrouck and Saar (2002) support this by investigating fleeting orders on the INET. A fleeting order involves placing a limit order within the bid-ask spread, and then canceling it within seconds. They find that investors place fleeting orders in order to execute hidden orders and to attract traders who are willing to execute any aggressively priced limit orders, but unwilling to place any limit orders themselves. Traders appear to fleet by canceling their orders upon non-execution in one market and move on to the next market in order to reduce NE risk and obtain better execution. FO risk may also induce an investor to revise or cancel a limit order. Placing a limit buy (sell) order is analogous to writing a free put (call) option.6 Thus, as market conditions change, traders may revise or cancel their limit orders in order to adjust their exposure to FO risk. Liu (2009) analyzes both FO risk and NE risk. He extends the monitoring game model of Foucault et al. (2003), and shows how monitoring and cancellation/revision strategies can reduce NE and FO risks. Foster and Liu (2009) demonstrate how appropriate order revision strategy can mitigate this free option problem in derivative markets. They find that traders frequently revise limit orders on equity warrants in response to changes in the price of the cash asset in an almost perfect delta-adjustment manner, and that the free option expires when the limit order price is revised. Limit orders are revised in response to NE risk and FO risk only if the cost of monitoring (MC hereafter) the flow of information and the order book status is sufficiently small. Since the arrival of information is random, traders monitoring their orders need to focus on the information flow specific to those stocks. This focused effort is an opportunity cost7 and it can be interpreted as the monetary value associated with the level of disutility caused by the effort exerted to

6 Copeland and Galai (1983) study free option risk in the context of private information and argue that free trading option risk is equivalent to adverse selection risk. Stoll (1992) distinguishes between the two and further argued that, in the presence of adverse selection risk, limit orders do not have a positive option value because they have an infinitesimally small maturity. An informed trader with private information will pick off limit orders immediately after they are entered. A much clearer distinction between the two is provided in Stoll (2003). He asserts that free trading option risk arises because of the arrival of adverse public information before the trade, while adverse selection risk arises because of the presence of private information before the trade, which is revealed some time after the trade. We focus on free option risk in this paper because (i) it is a risk that traders can reduce by monitoring news arrival and (ii) it is difficult to distinguish between the two types of risks empirically. 7 Boulatov et al (2009) and Kaul and Sapp (2009) provide evidence of a relationship between trader attention, trading profit and market efficiency, in stock and foreign exchange markets respectively.

monitoring activity. Liu (2009) shows that there is a trade-off between MC and limit order submission risks; if the cost of monitoring is low, traders actively monitor their orders and thus resulting more intense order revision and cancellation activities. Fig. 1 presents the order placement and revision problem as a decision tree. It proceeds as follows. First, the trader decides whether to trade or stay away from the market. The trader trades only if trading induces utility gains. Second, the trader decides whether to issue a market order or a limit order. The trader places a limit order if the limit order’s gain (the limit order spread) exceeds its cost (the sum of the expected cost of being picked off by the informed traders, the expected cost of non-execution and the cost of monitoring the limit order).8 Third, the limit order may execute or not execute. Fourth, if the limit order does not execute, then the trader faces NE risk and FO risk. Information releases influence the level of FO risk and NE risk. For example, if information is negative, then sell-side depth increases (buy-side depth decreases). If information is positive, then buyside depth increases (sell-side depth decreases). Thus, negative information increases FO risk for buy orders, and NE risk for sell-orders; but, positive information increases FO risk for sell orders and NE risk for buy orders. Fifth, the trader must respond to the information-changes. If there is no utility gain from staying in the market subsequent to the information release, the optimal response is to cancel the order. However, if the trader finds there is utility gain and stays in the market, then he/she will revise the order to reduce FO risk or NE risk, as applicable. For instance, the optimal response for a trader who chooses to stay in the market after negative information release is to decrease the price priority of the buy order to avoid being picked off, and to increase the price priority of the sell order to improve its chance of execution. In the existing literature, little attention is paid to outcomes when the limit order is not filled and the corresponding revision and cancellation activities. This paper contributes to the literature by investigating the link between limit order revisions and FO risk, NE risk and MC. The existing order decision literature does not fully investigate the impact of MC and changing NE and FO risks on order revision and cancellation. Extant literature focuses on the decision between placing a market order or a limit order; the second branch of the decision tree in Fig. 1. Extant literature also does not consider decisions after the investor places a limit order. Thus, the literature ignores the impact of changing NE and FO risks on order revision

8

We thank the referee who points this out.

K.Y.L. Fong, W.-M. Liu / Journal of Banking & Finance 34 (2010) 1873–1885

and cancellation and ignores the impact of MC.9 This omission is important. Liu (2009) shows that in a multi-period trading model, lower monitory costs (MC) induce lower spreads. Thus, one-period order choice models, such as Cohen et al (1981), Glosten (1994) and Foucault (1999), that ignore the impact of MC might understate the benefits of limit orders.10 The option to revise or cancel limit orders is particularly important following recent advances in information technology and the growing number of electronic trading venues11 that allow traders to manage orders directly from their computers. For leading exchanges like the NYSE, program trading amounted to about one-third of NYSE average trading volume and a significant amount of submitted orders are based on the use of an algorithm to save execution cost.12 This paper’s contribution proceeds in two steps. First, we use univariate analysis to examine the relationship between order characteristics and limit order revisions/cancellations. Second, our regression analysis examines if (1) proxies associated with FO risks influence priority-decreased price revisions and cancellations, and (2) proxies associated with NE risks influence priorityincreased price revisions and cancellations. We also examine if proxies associated with MC relate to order revision and cancellation activities. Our univariate analysis shows that investors monitor their limit orders and that limit order risk is an important factor in determining limit order revision and cancellation activities. We document that almost half of the limit orders are revised or cancelled, and the revision and cancellation activities decrease with the level of order aggressiveness. In addition, most revisions or cancellations are coming from limit orders placed at or near the bid-ask quote. This indicates that most revisions and cancellations are coming from traders who closely monitor the market because (1) these orders have the highest free option values and (2) these traders concern about getting their limit orders filled prior to some deadlines. Further, we find that traders revise large orders more often than they revise small orders. This is likely because the benefit of monitoring a large order is higher than the benefit of monitoring a small order. Finally, we find that order revisions result in statistically and economically significant reduction in NE and FO costs. The multivariate analysis further examines revision and cancelation activity. We examine the factors that influence priority-increased revisions/cancellations and priority-decreased revisions/ cancellations. Priority decreasing shows concern for FO risk. Priority increasing shows concern for NE risk. We examine data at 15 min intervals. For each interval we compute (1) the ratio of the number revisions/cancellations on the buy (sell) side of the book to the total number of shares on the buy (sell) side of the book; and (2) proxies for FO risk, NE risk, and the cost of monitoring. 9 Only recently have models of limit order trading began considering order revision and cancellation. Harris (1998) develops a dynamic limit order submission model that considers explicitly the option to revise the order strategy. Hollifield et al.’s (2004) empirical implementation does not allow for endogenous cancellation. Goettler et al.’s (2005) dynamic equilibrium model assumes orders are cancelled randomly with probabilities depending on the evolution of price path; cancellation probability for limit buy (sell) decreases (increases) with the change of common value. This formulation highlights the importance of cancellation strategy to avoid being picked off. 10 One might argue that the trading problem should be unchanged if unexecuted orders are assumed to be cancelled at the end of a period and are replaced with new orders. However, Harris (1998) shows that in a dynamic setting, the option to resubmit would have an impact on the original order choice decision. 11 Jain (2005) reports that in 2001, leading stock exchanges in 101 of 120 countries have implemented screen based electronic trading. However, there is evidence, e.g. Frino et al. (2008) that human intervention may improve upon a pure electronic system. 12 See www.nyse.com for the statistic of program trading. Stoll (2006) discusses how orders are managed through the use of algorithm. Bialkowski et al. (2008) and Humphèry (2009) analyze VWAP trading which often results in algorithmic trades.

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The regression results indicate that NE and FO risks influence revision/cancellation decisions. Both types of revisions and cancellations increase with the size of the bid-ask spread, and with volatility. High volatility leads to high NE risk because volatility increases the opportunity cost of unfilled orders and when bidask spread is wide, traders respond by revising their orders to gain execution priority. High volatility leads to high FO risk which implies positive relations between price uncertainty and priority-decreased revisions as well as cancellations as traders revise their orders away from the bid-ask quotes in order to reduce the risk that their orders will be executed by better informed traders. We also find a strong relation between revision/cancellation activities and post-interval midquote change; subsequent negative (positive) stock return associates with buyers (sellers) cancelling or reducing the price priority of their orders, and sellers (buyers) cancelling or increasing the price priority of their orders. Finally, we document evidence suggesting that MC matters. Order revisions/ cancellation activities are low during lunch hours or when the relative stock volume is low because the opportunity cost of closely monitoring the stock’s order book is high. The remainder of this paper is organized as follows. Section 2 presents the institutional background and the dataset that we use in this study. Section 3 presents and discusses the empirical patterns and behaviors of order revision and cancellation activities. Section 4 discusses the empirical hypotheses and the econometric method used before we present and discuss the empirical results in Section 5. Section 6 concludes.

2. Institutional details and data 2.1. Institutional details The Australian Securities Exchange (ASX hereafter) is a centralized electronic limit order book market with no designated market makers. The Stock Exchange Automated Trading System (SEATS) operated from 1987 and the Integrated Trading System (ITS) replaced it from 2 October 2006. While the ITS provides several operational improvements over SEATS, it does not change the ASX’s market structure or trading rules. Traders on the ASX may enter, revise or cancel orders in the trading system from the pre-open phase commencing at 7:00; however, the trading system does not match orders until the market opens. The opening call auction algorithm starts at 10:00 and completes the opening procedure of all stocks by around 10:10. Normal continuous trading follows the opening call auction and ends at 16:00. The closing call auction algorithm operates at 16:10 to establish the closing price of the day. Traders usually submit orders through brokers. However, some institutional investors can directly access the ASX’s trading system via the Trader Workstation software or a device connected to the Open Interface. The Open Interface allows market participants to enter, revise and cancel orders. Further, some online brokers provide ‘straight-through’ order entry software to retail investors such that they can electronically submit, revise and cancel orders via the broker. All entered limit orders have ‘‘expiry dates”. A ‘‘day-only” limit order is cancelled automatically at the end of the trading day, while a ‘‘fill-or-kill” limit order is cancelled automatically after about nine weeks. In addition, at 19:00, any order with a limit price that is too far from the market price is cancelled automatically by the system, unless it is the only order left in the queue for that stock. This study examines order revision and cancellation activities during the trading hours and thus, any automatic cancellation occurred after normal trading hours will not affect our analysis.

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The trading system matches and executes orders according to price-time priority. One exception to this rule is a crossing trade which occurs when a broker by-passes the time priority rule by matching a buy order to a sell order from his client order book. A crossing trade can occur only if first, the broker has an existing quote at the price (best bid or best ask) where the crossing trade is to occur; and second, the best bid and best ask prices are one tick apart. Brokers typically enter a single share order at the crossing price and create a one-tick market if one does not already exist. After the crossing trade is completed, the broker deletes the single share order. Crossing trades inflate the incidence of order submission and cancellation; and thus, we remove all single share order events from our dataset. 2.2. Dataset Our dataset comprises SEATS order flow data from the Securities Industry Research Centre of Asia-Pacific (SIRCA). The dataset records each order and trade including details such as the date, time to the nearest second, stock code, price, order volume, order type, order reference number and transaction reference number. Using the order reference number and time we track subsequent execution, revision and cancellation. Several aspects of our sample are notable: First, our sample contains the order flow of 50 large (top 50) and 50 small (101st–150th) capitalization stocks13 since firm size is related to the amount of information events and liquidity conditions. Second, the sample period spans from 1st January 2000 to 31st December 2001 and we compute market capitalization ranking at the beginning of each year. Third, we consider only orders activities during trading hours because it is only during this period that limit order traders are constantly exposed to FO risk. The sample contains 23,077,824 order events including submissions, revisions, and cancellations and 13,513,919 trades. Buy and sell order events account for equal share of the total sample and large stocks account for approximately 85% of all order events. 3. Univariate analysis of limit order revision/cancellation activity We conduct univariate analyses to test whether traders monitor their limit orders and whether FO and NE risks relate to order revision/cancellation activity. We make the following predictions. First, if MC is important, then revisions/cancellations should decrease with MC. And thus, revisions/cancellations should occur during the intraday time period that has the greatest risk and lowest MC. Second, if FO risk and NE risk induce revisions/cancellations, then revisions/cancellations should increase with factors that increase FO risk and NE risk. Thus, order-aggressiveness should influence revisions/cancellations due to its influence on FO/NE risk exposure. Third, revisions/cancellations should increase with order size since the opportunity cost of FO and NE risks increase with order size, while MC is unrelated to order size. Fourth, price priority-increased order revisions are associated with reduced NE costs and price priority-decreased order revisions are associated with reduced FO costs. 3.1. Frequencies and intraday distribution of order events The intraday distribution of order events indicates that revisions/cancellations increase during high FO/NE risk periods. Panel A of Fig. 2 plots the intraday distribution of order events and trades 13 The 50 large stocks account for more than 50% of the trading volume on the ASX. We avoid the micro-capitalization stocks that are infrequently traded in order to avoid excessively zero observations in high frequency analysis.

within their own group where the percentages sum to 1 over a trading day. Panel B plots a similar intraday distribution where the percentages sum to 1 over each interval. The figures indicate that order-event frequencies have a U-shaped pattern. The bottom of the U-shape corresponds to the time when MC is high (fewer public information releases and most traders go to lunch). Further, there is a disproportionate increase in order revision and cancellation events in the last interval relative to the earlier intervals. Compared with cancellations, revisions have the greatest intraday spike in the last 15 min of the normal trading hours. This is because at least the aggressively priced order revisions are commitments to trade while cancellations are not. Therefore, order revisions are more responsive to heightened NE risk than cancellation when the market is about to close. 3.2. Order aggressiveness We define six levels of limit order aggressiveness based on the information at the time of an order event. Our classification scheme is similar to Griffiths et al. (2000) and it is as follows. 1. Aggressive: An order submitted or revised that results in a limit buy (sell) order with the buy (sell) price greater (smaller) than the prevailing best ask (bid) quote. The order size exceeds those at the prevailing best ask (bid) quoted depth. The whole or part of this order is immediately executed upon submission during trading hours. 2. Large market: An order submitted or revised that (1) results in a limit buy (sell) order with the buy (sell) price equal to the prevailing best ask (bid) quote; and (2) has an order size greater than the prevailing ask (bid) quoted depth. Only part of this order is immediately executed upon submission during trading hours. The residual quantity remains in the limit order book as a limit order. 3. Small market: An order submitted or revised that (1) results in a limit buy (sell) order with the buy (sell) price equal to the prevailing best ask (bid) quote; and (2) has an order size equal to or less than the prevailing ask (bid) quoted depth. This order is fully executed upon submission during trading hours. 4. Price improve: An order submitted or revised that results in a limit order with a price inside the best bid and ask price. This order would not be executed immediately. 5. At quote: An order submitted or revised or cancelled that is a limit buy (sell) order at a limit price that is equal to the best bid (ask) price. This order is queued behind the existing orders at the best bid (ask) price due to time-priority. This order would not be executed immediately. 6. Outside quote: An order submitted, revised, or cancelled that is a limit buy (sell) order at a limit price that is lower (higher) than the prevailing best bid (ask) price. This order would not be executed immediately. Order aggressiveness is negatively related to the frequency of order revision. Table 1 reports the distribution of order revision and cancellation frequencies across order aggressiveness. The first column lists the number of unique limit orders submitted across order aggressiveness. The second column expresses the frequency of order revisions and cancellations as a percentage of the number of unique limit orders. Since an order can experience multiple revisions and a cancellation, the third column computes the percentage of submitted orders that experience at least one revision or cancellation. Columns four, five and six report the percentage of orders that have one revision, more than one revision, and cancelled, respectively. We ignore small market orders, which by definition are fully executed. We find a negative, near-monotonic, relationship between order aggressiveness and the frequency of order revi-

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(A) Percentage distribution of each order event of 50 large and 50 small stocks across 24 15-minutes intervals where the percentages sum to 1 over a trading day

(B) Percentage distribution of each order event of 50 large and 50 small stocks across 24 15-minutes intervals where the percentages sum to 1 over each interval

Fig. 2. Intraday Pattern of the frequency of order event.

sions and cancellations. Only 7–9% of aggressive orders are revised or cancelled,14 whereas over 47% of orders submitted outside the best quote are revised or cancelled. This finding is consistent with dynamic strategic behavior as traders adapt to time varying NE and FO risks by changing their limit orders. Table 2 shows the distribution of revised and cancelled orders across price steps just before the revision and cancellation, where 14 Some aggressive and large market orders are only partially executed upon submission, leaving a residual limit order in the book.

the 1st price step is the best bid or ask price.15 It also lists the percentage of one-tick revisions as a reference of the extent of price revisions. The results indicate a positive relation between order price priority and order revision. The first two price steps account for around 90% of revisions and cancellations across the entire limit or15 A price step grid is chosen because we are interested in the location of orders. A tick grid, in cents, would be descriptive but also too fragmented for patterns to emerge because there could be one or many ticks between price steps. This is particularly true outside the two best price steps.

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Table 1 Order revision and cancellation frequencies across order aggressiveness. This table reports the frequency of limit order across six level of order aggressiveness. For each level of order aggressiveness, we report the distribution across order revision frequencies. The last column reports the fraction of orders that are revised and cancelled. Aggressive refers to a submitted or revised order resulting in a limit buy (sell) order with the buy (sell) price and quantity that exceeds those at the prevailing best ask (bid) quote. The whole or part of this order may be immediately executed upon submission during trading hours. Large market refers to a submitted or revised order resulting in a limit buy (sell) order with the buy (sell) price at the prevailing ask (bid) price and quantity that exceeds the prevailing ask (bid) quote. Only part of this order would be immediately executed upon submission during trading hours. The residual quantity would remain in the limit order book as a limit order. Small market refers to a submitted or revised order resulting in a limit buy (sell) order with the buy (sell) price at the prevailing ask (bid) price and with quantity that is equal to or less than the prevailing ask (bid) quote. This order would be fully executed upon submission during trading hours. Price improve refers to a submitted or revised order resulting in a limit order with a price inside the best bid and ask price. This order would not be immediately executed. At quote refers to a submitted or revised order resulting in, or a cancelled order being, a limit buy (sell) order at a limit price that is equal to the best bid (ask) price. This order would not be immediately executed. Outside quote refers to a submitted or revised order resulting in, or a cancelled order being, a limit buy (sell) order at a limit price that is lower (higher) than the prevailing best bid (ask) price. This order would not be immediately executed. No. of orders submitted

No. of revisions and cancellations/ No. of orders entered

% of orders with at least 1 revision or cancellation

% of orders with 1 revision

% of orders with >1 revision

% of orders cancelled

Panel A: Large stock buy orders Aggressive 61,325 Large Market 783,475 Price Improve 476,866 At quote 1,640,516 Outside Quote 1,167,631

9.1 26.9 45.2 41.3 58.5

8.3 25.0 41.8 38.5 54.5

3.3 12.2 19.6 18.3 16.4

1.5 4.4 7.5 6.4 7.6

4.3 10.3 18.1 16.6 34.5

Panel B: Large stock sell orders Aggressive 64,676 Large Market 791,059 Price Improve 439,205 At Quote 1,312,223 Outside Quote 1,102,540

9.0 26.2 42.6 47.4 57.0

8.2 24.4 39.6 44.2 53.5

3.6 12.3 19.0 20.5 17.7

1.4 4.3 7.1 7.3 8.6

4.0 9.6 16.5 19.6 30.7

Panel C: Small stock buy orders Aggressive 12,488 Large market 103,068 Price improve 94,037 At quote 321,443 Outside quote 227,268

8.4 32.0 50.2 45.6 52.4

7.7 29.7 46.2 42.1 47.3

3.8 17.0 20.6 19.2 17.4

1.9 6.6 8.4 6.0 7.6

2.7 8.4 21.2 20.4 27.3

Panel D: Small stock sell orders Aggressive 13,501 Large market 106,925 Price improve 84,262 At quote 257,328 Outside quote 196,795

9.5 34.5 52.9 54.9 54.7

8.8 32.3 49.3 51.1 50.6

4.5 19.0 21.6 21.8 21.0

2.2 7.4 9.3 7.5 12.1

2.8 8.0 22.0 25.6 21.6

Table 2 Order price location immediately prior to revision and cancellation. This table presents the distribution of order price location immediately prior to revision and cancellation. The values are, respectively, the percentage of order revisions, the percentage of order revisions with the minimum price change, and the percentage of orders cancelled. Price Step refers to position of limit orders in the queue. ‘‘1st” refers to the number of orders revised or cancelled if the original limit buy (sell) price is the best bid (ask) of buy (sell) order. ‘‘2nd”refers to the number of orders revised or cancelled if the original limit buy (sell) price is at the next price step to the best bid (ask). Note that the difference between consecutive price steps can be more than the minimum tick size as it depends on how well the order book is filled. Percentage of one tick revisions is the ratio of the number of one tick price revisions to the total number of price revisions. Price step

Limit buy orders % of revisions

Limit sell orders % of 1 tick revisions

% of cancellations

% of revisions

% of 1 tick revisions

% of cancellations

Panel A: Large stocks >6th 3.7 6th 0.6 5th 1.2 4th 1.8 3rd 3.8 2nd 12.3 1st 76.6

19.9 21.8 28.0 26.1 28.2 40.3 54.0

4.9 1.0 1.4 2.1 6.1 17.5 67.1

3.8 0.6 1.1 2.0 3.9 12.4 76.2

16.5 16.7 19.7 27.9 27.2 39.3 51.5

2.1 0.5 0.7 1.3 4.2 16.2 75.0

Panel B: Small stocks >6th 1.4 6th 0.4 5th 0.6 4th 1.3 3rd 2.7 2nd 10.5 1st 83.1

13.0 7.7 20.4 38.9 36.9 41.5 42.2

6.6 2.3 2.5 3.8 3.9 8.3 72.6

2.1 0.6 1.1 2.2 3.8 11.1 79.2

7.3 31.3 11.4 18.8 26.8 30.6 38.6

2.1 0.5 0.9 2.1 3.2 6.7 84.5

der book. This high concentration of activity at the top end of the limit order queue suggests that limit order traders submit orders at the top of the queue and monitor the market closely in order to gain better execution. They stand ready to revise their limit orders

to market orders. This interpretation is consistent with Yeo’s (2005) observations that 62% of cancellations on the NYSE SuperDOT system occurred within 60 s of submission of the limit order. In addition, a majority of minimum price revisions take place at the best

K.Y.L. Fong, W.-M. Liu / Journal of Banking & Finance 34 (2010) 1873–1885 Table 3 Percentage of order cancellations and revisions across order size. This table presents the percentage frequency of order revision and cancellation across four order size quartile. We assign revised and cancelled orders into ascending size quartiles where the cutoffs are determined by ranking the dollar value of submitted orders on a stockby-stock basis. A revised or cancelled order with an order size within the first (fourth) quartile is designated a small (large) order. Limit buy orders

Limit sell orders

Revisions

Cancellations

Revisions

Cancellations

Panel A: Large stocks Q1 (small orders) Q2 Q3 Q4 (large orders)

18.3 22.0 27.1 32.6

13.3 22.5 31.2 33.0

16.0 21.7 27.1 35.2

10.8 22.6 31.8 34.8

Panel B: Small stocks Q1 (small orders) Q2 Q3 Q4 (large orders)

19.1 20.8 26.6 33.5

20.4 24.3 26.2 29.1

13.7 19.0 27.9 39.4

20.4 23.7 25.6 30.3

quotes. Since the majority of price revisions are to increase price priority, this might indicate a significant amount of undercutting activity at the top of the limit order queue. 3.3. Order size and limit order revision/cancellation activity A trader who contemplates revising an order needs to monitor market conditions. Monitoring is costly. However, not monitoring has an opportunity cost: the possibility that the trader might be exposed to greater FO risk or NE risk. This cost increases with the size of the order. Thus, we expect larger orders are more likely to be revised. Table 3 compares the distribution of revised and cancelled orders across order size quartiles where we determine the cutoffs by ranking the dollar value of submitted orders on a stock-by-stock basis.16 If revising and cancelling orders are size independent decisions, we should observe 25% of activities in each quartile. We find in all cases of order revisions and cancellations, the proportion increase monotonically in order size. This finding supports our conjecture. 3.4. Effect of order revision on execution rate, non-execution and free option costs Relative to the case of no revision, we expect on average price priority-increased order revisions would increase execution rate and lower NE costs while price priority-decreased revisions would lower execution rate and FO costs. To test these conjectures we compute, for each revised order, the difference in execution rate, NE and FO costs based on the actual revised order and the hypothetical scenario where the order is not revised. In the hypothetical scenario, we consider the order to be ‘‘executed” if its pre-revision limit buy (sell) price is less (more) than the subsequent lowest (highest) trade price on the same day. For priority-increased buy order revisions, we define the NE cost as: NE cost = (closing price  revised limit buy price)/closing price  h, and for priority-decreased buy order revisions, FO cost = (revised limit buy price  closing price)/closing price  h, where h = 1 if not executed and 0 otherwise. We compute the corresponding NE and FO costs for the hypothetical un-revision case using the pre-revision order price instead of the revised price. Finally, we define these variables analogously for sell orders. Table 4 reports the differences in the percentage of revised and un-revised order executed and the mean of cost differences, i.e., for 16

The percentages here sum to 100 down the column.

1879

each order we compute value of the NE (FO) cost of the revised orders minus the NE (FO) cost of the ‘‘un-revised” orders. A positive cost difference indicates that order revision reduces NE and FO costs. This table also reports the dollar value of the reduction in NE and FO costs (in millions) and the percentage of order revisions resulted in lower (gains) and higher (losses) NE and FO cost. We calculate the dollar value by summing up the product of the difference in dollar saving per share and the order size across all revised orders. The result shows that order revisions generate statistically and economically significant net benefits. Priority-increased order revisions are associated with percentage NE cost reduction over 0.41%, with economic value of up to 15.55 million AUD. These savings are larger in sell orders and small stocks, with the largest percentage NE cost savings observed in small stock sell orders. FO cost differences associated with priority-decreased revisions are also positive as predicted and statistically significant. However their values are economically smaller than NE cost differences, particularly at the dollar values level. We also report the percentage of revised order that have made the trader better or worse off. We have strong evidence of FO cost saving associated with priority-decreased revisions as more than 63% of them have led to positive FO cost saving. This suggests that a lot of priority-decreased revisions have led to an immediate reduction in the risk of being picked off as the option value of the order reduces. Similar to priority-decreased revisions, there are far more priority-increased revisions that have made the trader better off than worse off; 24–38% of priority-increased revisions have led to a better outcome while only about 2% have led to a worse outcome. However, we also observe that there is a large fraction (between 60% and 75%) of priority-increased revisions that generate zero benefit. 4. Multivariate methodology The univariate analysis indicates that MC, FO and NE risks influence the decision to revise or cancel limit orders. We extend the analysis using multivariate regression to identify variables that best capture this relationship. This section outlines our methodology including the hypothesis, variable construction, and the econometric model. 4.1. Hypothesis and proxies Our primary hypothesis is that limit order revisions and cancellations are driven by changes in FO and NE risks. FO risk is the risk that a limit order became in-the-money as a result of changes in the expected value of the security. Priority-decreased revisions and cancellations can reduce the probability of such pricing error; and thus, reduce FO risk. Increasing spreads may connote increasing FO risk. A widening spread may indicate changes in the market’s expected value of the security. And, the cost of an unfavorable execution increases with the size of the spread. Thus, FO risk should increase with the size of the spread. High volatility may also indicate high FO risk. The literature suggests that high price volatility increases the execution probability of a limit order; and thus, causes higher FO risk (Copeland and Galai (1983), Stoll (1992), Harris (1998), Foucault (1999), and Wald and Horrigan (2005)). Because of the trade-off between MC and the cost associated with FO and NE risks, we hypothesize revision and cancellation activities are less intense when the opportunity cost to exert labor effort to closely monitor the order book is high. Price trend and news announcements are events that indicate potential shift in security value and should induce priority-decreased revisions and cancellations that reduce FO risk. Stoll (1992, 2003) observes that if a trader has an limit buy (sell) order when bad (good) news is announced, or when the trader expects

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Table 4 Effect of order revision on execution rate, non-execution and free option costs. We track the performance of revised orders based on their execution rate, the non-execution (NE) cost and the free option (FO) cost. For each revised order, we compute differences in execution rate, non-execution (NE) cost and free option (FO) cost based on the actual revised order and the hypothetical scenario where the order is not revised. In the hypothetical scenario, the order is considered to be ‘‘executed” if its pre-revision limit buy (sell) price is less (more) than the subsequent lowest (highest) trade price on the same day. We report the difference in the percentage of revised and ‘‘un-revised” order executed. For priorityincreased buy order revisions: NE Cost = (closing price  revised limit buy price)/closing price  h, where h = 1 if not executed and 0 otherwise. For priority-decreased buy order revisions: FO Cost = (revised limit buy price  closing price)/closing price  h, where h = 1 if not executed and 0 otherwise. The corresponding NE cost and FO cost for the hypothetical non-revision case are computed using the pre-revision order price instead of the revised price. We report the mean and the corresponding t-statistic (in parentheses) cost differences, i.e., for each order we compute value of the NE (FO) cost of the revised orders minus the NE (FO) cost of the ‘‘un-revised” orders. Positive value reflects order revision that reduces NE cost and FO cost. This table also reports the dollar value of the reduction in NEC and FOC (in millions) where we sum up across all revised orders the product of the difference in dollar saving per share and the number of shares. We also report% of revised order that made the trader better or worse than, or indifferent from, the hypothetical scenario where the order is not revised. These variables are defined analogously for buy and sell orders as well as price priority increased and decreased orders. Computations are performed separately for large and small stocks. Price Priority

**

Limit buy orders Difference in% executed

Limit sell orders

Difference in%

Difference in dollar value ($million)

% of revised orders that are better/worse than, or indifferent from not revising

NE Cost

FO Cost

NE Cost

FO Cost

Better

Worse

Indiff.

Panel A: Large stocks Increased 14.56 (t-stat.) Decreased 18.29 (t-stat.)

0.41** (26.95) – –

– – 0.21** (9.00)

15.55

–

24.78

1.42

73.80

16.95

–

1.07

76.29

12.84

10.87

27.07

Panel B: Small stocks Increased 16.95 (t-stat.) Decreased 27.07 (t-stat.)

0.65** (31.70) – –

– – 0.40** (14.85)

2.50

–

36.24

2.53

61.23

24.86

–

0.17

63.93

15.28

20.79

18.58

Difference in% executed

Difference in%

Difference in dollar value ($million)

% of revised orders that are better/worse than, or indifferent from not revising

NE Cost

FO Cost

NE Cost

FO Cost

Better

Worse

Indiff.

0.65** (31.70) – –

– – 0.40** (14.85)

2.50

–

24.09

1.09

74.82

–

0.17

76.29

12.84

10.87

4.96** (3.34) – –

– – 0.64** (10.54)

12.31

–

38.36

1.62

60.02

–

0.26

63.15

12.78

24.07

Represent significance levels of 1%.

the price to trend downward (upward), then the limit order may become in-the-money.17 The literature also suggests a link between the depth of the order book and FO risk. Cao et al. (2008) find that orders behind the best quotes contribute to 22% of price discovery. If the sell side of the limit order book thickens and the buy side thins out, it indicates a selling pressure from both the liquidity suppliers and the informed traders. This implies a greater FO risk for limit buy order. The converse holds for limit sell order. We summarize our predictions in relation to FO risk as: H1 (FO risk): Buy (sell) order cancellation and priority-decreased revision activity increases when (1) the spread is wide, (2) the stock price volatility is high, (3) midquote price exhibits a downward (upward) trend, (4) the opposite side of the book thickens, (5) the same side of the book thins out, and (6) after a bad (good) news announcement. NE risk is the risk that an order will not be executed. Traders can reduce NE risk through priority-increased revisions or cancellations and resubmit at a more aggressive price. NE risk increases with the size of the bid-ask spread. In the absence of adverse information risk, spread may widen due to a temporary lack of liquidity. Competitive limit order traders would take advantage of this by repositioning their orders inside the spread to increase the chance of execution. Ranaldo (2004) and Ellul et al (2007) document strong empirical evidence of this spread effect. Volatility in security value affects the NE risk in two ways. While a higher volatility reduces the probability of the non-execution of limit orders (Cho and Nelling (2000), Ahn et al. (2001) Lo et 17 Hollifield et al. (2004) use market index as proxy for a public information event and they show that that free option risk arises when the market index moves against the limit order of individual stocks. Liu and Sawyer (2003) examine free option costs conditional on 163 earnings announcements with ex post stock prices that are adverse to various hypothetical limit order strategies. They find that free option cost increases when the adversity of news increases because it is positively related to the intrinsic value of the free option.

al. (2002), Ellul et al. (2007)), a higher volatility also increases the opportunity cost of unfilled orders (Wald and Horrigan (2005)). This implies that the net relationship between volatility and cancellations/priority-increased revisions depends on the strength of these opposing factors. Thus, Smith (2000) finds that the impact of volatility on the order choice decision is mixed. Parlour’s (1998) limit order model demonstrates that when the opposite side of the book thins out, execution probability of limit orders is low. Thus, investors try to reduce non-execution risk by first cancelling their orders and then resubmitting at more aggressive prices. Conversely, when the same side of the book thickens, traders cancel their limit orders because their orders receive lower execution probability, their orders being ‘‘crowded out” by competing limit orders on the same side of the book. Ranaldo (2004) presents empirical evidence that supports Parlour’s (1998) theoretical prediction. Price trend and news should affect NE risk. If a trader expects stock price to trend downward (upward), or if the firm releases bad (good) news, then there is a risk that the market will move away from the order, and the limit sell (buy) order will not be executed. Therefore, if traders monitor the market closely, and observe an adverse trend or adverse news, then limit buy (sell) order cancellation/revision activities intensify. When the market is about to close, traders may revise their limit orders more aggressively to get them filled because they are facing a high risk of incurring the cost of non-execution. Hence we should expect cancellation and priority-increased revision activities intensify near the end of the trading hours. We summarize our predictions in relation to NE risk as: H2 (NE risk): Buy (sell) order cancellation and priority-increased revision activities increase when (1) the spread is wide, (2) volatility is higher, (3) the opposite side of the book thins out, (4) the same side of the book thickens, (5) the midpoint price exhibits an upward (downward) trend, (6) after a good (bad) news announcement and (7) the market is about to close.

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Note that H1 and H2 are not symmetric because existing theory does not predict FO risk to increase or to decrease when the market approaches the end of the trading hours. Finally, we conjecture that the opportunity cost to monitor the order in a stock is higher during lunch hours or when the relative stock to market trading volume is low. The opportunity cost is high during lunch hours because the arrival rate of public information is relatively low. Even when the arrival rate is uniform throughout the day, the opportunity cost remains relatively high since everyone expects other traders to put less effort into monitoring (as they go to lunch). If we view the monitoring game as a Nash game like Liu (2009), we would expect the revision and cancellation activity to be lowest during lunch hours. We also argue that the opportunity cost is high when the trading volume of the entire market relative to the stock is abnormally high. Traders will divert more of their labor effort to monitor other stocks if they are more active.18 This gives us the third hypothesis: H3 (Monitoring cost): Cancellation and revision activities decrease (1) during lunch hours and (2) the stock volume relative to the overall market is abnormally low.

P BIDDEPTHDt ¼

b bt1 PBt2 Q t1 Q bt2

P ASKDEPTHDt ¼

a at1 6At2 Q t1 a Q t2

 1;

 1:

Bt2 and At2 are the best bid and ask quote at the end of the interval t  2. Qb and Qa are the quantity outstanding of buy order price b and sell order price a. 4. Midquote return in the previous interval (RETURNt1). We compute the midquote return based on the logarithm of the midquote change recorded at the end of each interval. 5. Good news and bad news announcement dummies (GOODNEWSt; BADNEWSt).

GOODNEWS t ¼ signðRETURN t Þ  NEWS if RETURN t > 1:64rt ; and 0 otherwise

In order to test H1 and H2, we use the total volume revised/cancelled scaled by the volume on the same side of the book as proxies for order revision/cancellation activity. The use of volume ratio rather than the ratio of order count can incorporate the positive relationship between order revision and order size observed in Table 3. We use scaled values due to heterogeneity across stocks and intraday patterns. There are six dependent variables computed over 15-min intervals19; for buy and sell limit orders separately we have price priority-increasing revisions, price priority-decreased revisions and cancellations. We also construct the following explanatory variables: 1. Average bid-ask spread in the previous interval (SPREADt1). The bid-ask spread value is the average of the 15 minuteby-minute snapshots over the 15-min interval. 2. Price volatility in the previous interval (VOLATILITYt1). Stock price volatility is defined as the standard deviation of minute-by-minute snapshots of the midquote over the 15-min interval. 3. Changes in buy-side quoted depth. (BIDDEPTHDt1) and sellside quoted depth (ASKDEPTHDt1) in the previous interval. To derive the percentage change of quoted depth, we use the best quote at the beginning of the interval as the benchmark. If the best bid (ask) increases (decreases), we cumulate all the order quantity outstanding that equals or exceeds the best quote at the beginning of the interval. If best bid (ask) decreases (increases), all depth at the original price level disappeared and thus, the change of quoted depth is 100%. The mathematical expression of the variable, in interval t  1, 18 As a pilot test of our monitoring hypothesis we examine lunchtime/market volume impact on revision and cancellation. Future research can more rigorously investigate the monitoring issue with variables that capture monitoring costs more directly. For example, some traders may have better access to the trading platform or superior telecommunication technology which reduces the labor cost of monitoring. 19 We choose to aggregate the order data at 15-min interval because we want to focus on the intensity of order revision and cancellation activities across the limit order book, whether they take place at the quote or not, and using the common technique in the literature, such as Ranaldo’s (2004) ordered probit model would be problematic. 15-min level of aggregation is chosen after considering the trade-off between biases caused by the large proportion of zeros with finer interval and the lack of statistical lagged relation when longer interval is used. As robustness checks, we repeat the analysis based on 5-min interval. Results are qualitatively similar and they are available on request.

ð2aÞ

BADNEWS t ¼ signðRETURN t Þ  NEWS if RETURN t < 1:64rt ; and 0 otherwise;

4.2. Variable construction

ð1Þ

ð2bÞ

where NEWSt is a dummy variable that takes the value of 1 if there is any news announcement made by the company during the interval t. rt is the return volatility in the interval t. We only regard news as good news/bad news if the return exceeds 90% confidence interval. The exact timing of the announcement is recorded in the Signal G Database, which is provided by SIRCA. 6. FO cost based on post-revision midquote change (PUTt for limit buy and CALLt for limit sell). Similar to Liu (2009), we construct the intrinsic value of the option based on the next period change of the midquote. Since a limit buy (sell) order is analogous to writing a free put (call) option, the intrinsic value of this option is given by:

PUT t ¼ max½at  ptþ1 ; 0; CALLt ¼ max½ptþ1  bt ; 0;

7.

8. 9.

10.

ð3Þ

where pt+1 is the midquote at the end of interval t + 1, at and bt are the best ask and the best bid at the end of interval t, respectively. Notice that option values (3) are positive only when the midquote increases by more than the half of spread. Unlike Liu (2009), option values (3) do not suffer the problem of endogeneity since both at and bt are quotes recorded at the end of interval t. NE cost based on post-interval midquote change (CALLt for limit buy and PUTt for limit sell). Because of the dual nature of FO risk and NE risk, the NE cost for limit buy (sell) is given by CALLt (PUTt). Last interval dummy (ENDt). This dummy variable takes the value of 1 if interval t is the last interval: 15:45–16:00. Lunch hours dummy (LUNCHt). This dummy variable takes the value of 1 if interval t belongs to the lunch hours: 12:00–14:00. Abnormal change of the relative stock’s volume (VOLUMERATIODt). For each interval t, we compute a volume ratio, which is the trading volume in a stock over interval t divided by the trading volume of all stocks in the entire market in the same interval. To obtain the abnormal change of this volume ratio, first, for each stock and each interval, we compute the normal level based on its average over that month. This method allows us to clean out any seasonality of volume across intervals and trend effects of volume over time. We define the abnormal change of this ratio as the difference between the volume ratio of the interval on that day and the normal ratio.

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Table 5 A summary of the predicted sign of the estimated coefficient for each variable. This table summarizes the predicted sign of the estimated coefficient for each variable, which relates to free option risk (FO), non-execution risk (NE) and monitoring cost (MC). The dependent variable under investigation is the scaled volume of limit buy order priorityincreased revision (LBRUt), limit buy order priority-decreased revision (LBRDt) and limit buy order cancellations (LBCt), limit sell order priority-increased revision (LSRUt), limit sell order priority-decreased revision (LSRDt) and limit sell order cancellations (LSCt) in the 15-min interval t. BIDDEPTHDt1 and ASKDEPPTHDt1 are the percentage changes in buyside quoted depth and sell-side quoted depth, respectively, in the previous interval (t  1). SPREADt1 is the bid-ask spread based on an average value of a minute-by-minute snapshot of the spread in the previous interval. VOLATILITYt1 is the standard deviation of the stock price in the previous hour. The standard deviation is computed based on each 15-min snapshot of the stock price. RETURNt1 is average log return of the stock price in the previous interval. The news dummies: GOODNEWSt (BADNEWSt) is a dummy variable that takes the value of 1 if there is a news released during the interval t and the return is more (less) than 1.64rt for the respective interval. CALLt and PUTt are variables that capture post-revision/cancellation price movement, for CALLt = max[pt+1  bt, 0] and PUTt = max[at  pt+1, 0], where pt+1 is the midquote at the end of interval t + 1, at and bt are the best ask and the best bid at the end of interval t, respectively. ENDt is a dummy variable that takes the value of 1 if interval t is the last interval (15:45–16:00). LUNCHt is a dummy variable that takes the value of 1 if interval t belongs to the lunch hours: 12:00–14:00. VOLUMERATIODt is the abnormal change of the ratio: stock’s trading volume/ trading volume for the entire market over the interval t. Hypotheses/expected Sign Order type

Limit buy orders

Dependent variables

LBRDt

Explanatory variables for BIDDEPTHDt1 ASKDEPTHDt1 SPREADt1 VOLATILITYt1 RETURNt1 GOODNEWSt BADNEWSt CALLt PUTt ENDt Explanatory variables for VOLUMERATIODt LUNCHt

Limit sell orders LBCt

LBCt

FO risk  + + + 

+

+

+ 

LBRDt

NE risk

 + + + 

+

LBRUt +  + +/ + +

+  + + + +

+  + + + +

+

+

+

+

+

+

+ 

+ 

+

+ 

Monitoring cost (MC) + 

For each trading day, we subdivide the trading hours into 24 15min intervals from 10:00 to 16:00. Since we have a 2-year order flow sample of 100 stocks, our original sample comprises of 1,209,600 intervals. Approximately 6.7% of the sample intervals are discarded due to empty books, missing data, and data error. To avoid the potential problem of endogeneity, lagged values of quotedepth changes, spread and return volatility are used, which leaves us with 23 data point for each trading day and for each stock. Our regression analysis is based on two sets of panel data; each consists of 50 large stocks and 50 small stocks. Scaled values of total volume revised/cancelled in each interval is used as a proxy for order revision/cancellation activity because regressing total volume revised/cancelled against market variables might lead to spurious results. Since the scaled value is bounded by construction between 0 and 1, OLS regression is likely to produce highly biased estimates when there are many observations lying at the boundaries or near them (in our case, we have a large number of intervals containing zero revision and cancellation). The common approach to employ the log-odd transformation is inappropriate here because by construction, log-odds ratio is suitable only when the dependent variable is strictly within the (0, 1) bounds. A better alternative is the fractional logit model introduced by Papke and Wooldridge (1996). Papke and Wooldridge propose a non-linear function for estimating the expected value of fractional variables zit, conditional on a vector of covariates xit:

ð4Þ

In here, G(), the link function, is chosen to be a cumulative distribution function such that the predicted values of zit lie in the interval

LBRUt

+ 

 + + +/ 

 + + +/ 

+

+

+ +

+ +

+ 

+ 

(0, 1), thus 0 6 G() 6 1. In the GLM literature, G() is chosen to be a logit function:

Eðzit jxit Þ ¼ Gðb0 xit Þ  4.3. Econometric model

LBCt NE risk

+  + +/ + +

Table 5 summarizes the predicted coefficients of the regression models of order cancellation, priority-increased revision and priority-decreased revision.

Eðzit jxit Þ ¼ Gðb0 xit Þ:

LBCt FO risk

expðb0 xit Þ : 1 þ expðb0 xit Þ

ð5Þ

Note that expression (5) is well defined even if zit takes on 0 or 1 with positive probability. The quasi-maximum likelihood estimator (QMLE) of b can be obtained by maximizing the following Bernoulli log-likelihood function:

max ^ b

M X T X t¼1

i¼1

^  lit ðbÞ

M X T X i¼1

^0 xit ÞÞ þ ð1  zit Þ zit lnðGðb

t¼1

^0 xit ÞÞ:  lnðGðb

ð6Þ

We obtain the asymptotically robust variance based on Papke and Wooldbridge (1996, pp. 622–623). Let g(z)  dG(z)/dz, ^ it  Gðb ^0 xit Þ  y ^0 xit Þ. Then the estimated information ^it and g^it  gðb G matrix is:

^ A

M X T X i¼1

t¼1

g^it x0it xit : ^ it ð1  G ^ it Þ ½G

ð7Þ

^ we need To obtain a valid estimate of the asymptotic variable of b, 0 ^ ^ the outer product of the score. Let uit  yit  Gðb xit Þ be the residuals and define:

^ B

M X T X i¼1

t¼1

^ 2it g^2it x0it xit u : ^ it ð1  G ^ it Þ2 ½G

ð8Þ

^ The following sandwich form produces the estimated variance of b:

^ 1 B ^ 1 : ^A A

ð9Þ

By taking the square root of the diagonal elements of matrix (9) we ^ When dealing with panel can generate the standard errors of b. data, it is likely that the observations are not truly independent because of correlation within the group. As a result, the standard errors of estimates may be downwardly biased. The robust

Table 6 Fractional logistic estimation of the scaled volume of limit order cancelled and revised based on 15-min intervals. This table reports the results of the fractional logistic regression model of the scaled volume of limit order revised/ cancelled on market variables. Robust z statistics are given in parentheses. We enclose the estimates with the predicted sign with borders and inside the enclosure, we use bold font for statistically significant estimates.

K.Y.L. Fong, W.-M. Liu / Journal of Banking & Finance 34 (2010) 1873–1885 1883

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asymptotic covariance matrix estimators that consider group effects are20:

^H ^ 1 G ^ 1 ; H

ð10Þ

^ ¼ PK ui u0 and ui ¼ PT @ ln Lit =@b. ui is the group score, where G i¼1 t¼1 i which computes the sums of the individual scores for firm i. In con^ in (9), ui yields the contribution from group i to trast to B ^ ¼ PK PT @ 2 ln Lit @b@b0 . This robust estimation ui ¼ @ ln Lit =@b. H i¼1 t¼1 relaxes the independence assumption within the group but requires that the observations be independent across groups. 5. Results Table 6 contains the regression results. For readability, we enclosed the estimates with the predicted sign with borders. Inside the enclosure, we use bold font for statistically significant estimates. The coefficient on lagged spread indicates that FO and NE risks drive revision and cancellation activity. Consistent with our prediction, a wide spread is positively associated with revision and cancellation of limit orders as almost all the coefficients of lagged spread are statistically significant at the 1% level. When the spread widens temporarily, traders improve the execution-likelihood of their orders by revising it inside the spread. When the spread widens because of heightened information risk, orders are cancelled or revised away to reduce the risk of being picked off. The statistically significant coefficient on lagged price volatility indicates that FO and NE risk influences order revision and cancellation. For priority-decreasing revisions and cancellations (LBRD, LSRD, LBC and LSC), the positive coefficient on price volatility shows that when traders observe a large price swing, they either withdraw their orders or relocate their orders away from the market price. This finding strongly supports the presence of FO risk. For priority-increased revisions and cancellations, the significant coefficient indicates that high price volatility increases the opportunity cost of unfilled orders; and thus, increases NE risk. The coefficients on book depth and price trend variables are relatively weak but their signs are mostly consistent with our predictions. The coefficient of end-of-the-day dummy (END) is significantly positive across all priority-increased and cancellation regressions, which suggests that traders concern about filling the order before the market closure. We also test to see if the effect of time is asymmetric across different types of order revision because FO risk should be orthogonal to time. When we include END in the priority-decreased regression (unreported), the estimated coefficients are insignificant for small stocks. For large stocks, the coefficients are two to four times smaller than that of the priority-increased revision regression. This suggests the FO risk is not affected by time. Contrary to our expectations, the relation between news announcement and order revision/cancellation activities is significantly negative for small stocks. There are two plausible reasons. First, the effect on the lagged order book variables (spread, depth and volatility) might have overshadowed the news announcement effect as the market gradually processes information prior to the news release. Second, limit order traders would be given more opportunity to revise when the market moves away from it than when the market moves against it. When company sensitive news is announced, mispriced limit orders are quickly picked off by news-watchers after the trading halt and thus cancellation/revision strategy is futile.21 20

See Petersen (2009) for the discussion of the clustered standard errors. We also check if market sensitive news announcement made by other firms within the same industry affect revision and cancellation activity. We do not find any evidence supporting this association (not reported). 21

We find strong evidence of post-revision/post-cancellation cost saving. For buy order, priority-increased (-decreased) revision activities associate with a subsequent increase (decrease) in midquote for more than the half of the spread and for sell order, priority-increased (-decreased) revision activities associate with a subsequent decrease (increase) in midquote. We find strong evidence of a negative relation between MC and order revision/cancellation activities. Consistent with the Ushaped pattern shown in Fig. 2, order revision and cancellation activities are less intense during lunch hours. This result holds even after we control for the spike in the early interval using a ‘‘first interval dummy” (FIRSTt). Also, we find evidence that when the relative stock volume is abnormally low, traders divert their attention to the rest of the market as the opportunity cost of not monitoring the rest of the market is high. 6. Conclusion In order-driven markets, limit order traders gain better terms of trade (higher sell price and lower buy price) but they expose their orders to non-execution (NE) risk where they do not know when and whether their orders will be executed. They also expose their orders to free-option (FO) risk where their orders may be picked off by better informed traders if the arrival of information causes their limit orders to be mispriced. Limit order traders employ order revision strategy to reduce these risk exposures if the cost of monitoring (MC) is sufficiently small. This paper contributes to the literature by providing evidence for the effects of MC, FO and NE risks on limit order revision and cancellation activities. We identify price priority-increased revisions, price priority-decreased revisions and cancellations at order event level and discover four significant findings. First, almost half of all revisions/cancellations occur within the two best prices in the limit order book indicating limit order traders are monitoring market conditions. This result indicates that revision and cancellation activities are not random and limit order traders monitor market conditions closely. Second, we find that traders revise large orders more than small orders because of the fixed cost of order monitoring. Third, we document statistically and economically significant NE and FO cost savings as a result of order revisions. Finally, we find strong evidence of the relationship between limit order revisions/cancelations and proxies of MC, FO risk and NE risk. The evidence in this paper indicates that traders pursue dynamic order placement strategies. Traders actively monitor limit orders after they place them. This finding suggests that theoretical order choice models that incorporate the decision to cancel and revise subsequent to the order submission would improve our understanding of limit orders. In terms of empirical research, one extension is to study the order level decisions by tracking and analyzing the revision history of limit orders. Another direction is to consider a special and recently popular (in some exchanges) type of limit orders: hidden orders. Bessembinder et al. (2009), for instance, find that the primary motive of using these orders is to lower FO risk but these orders face higher NE risk than the exposed limit orders. Studying the revision decisions of hidden orders in dealing with changing NE risk would add to our knowledge on dynamic order strategies. Acknowledgments The authors gratefully acknowledge the assistance and support of the Securities Industry Research Centre of Asia-Pacific (SIRCA) for provision of the data. We thank F. Douglas Foster, David Gallagher, Joel Hasbrouck, Stephen Brown, Mark Humphèry, Terry Walter, Jian-Xin Wang, Robert Wood, Onayev Zhan, conference and seminar participants at the University of New South Wales, Hong

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