Order Cancellations across Investors:
Evidence from an Emerging Order-Driven Market
Chaoshin Chiao
Department of Finance
National Dong Hwa University
Hualien, Taiwan
Zi-Mei Wang†
Department of Finance
Ming Chuan University
Taipei, Taiwan
Shiau-Yuan Tong
Department of Finance
Ming Chuan University
Taipei, Taiwan
This Draft: March 24, 2016
†
Corresponding author. Tel.: 886-228824564. Ext. 2834; Email: zimay@mail.mcu.edu.tw
Order Cancellations across Investors:
Evidence from an Emerging Order-Driven Market
Abstract
Employing comprehensive limit-order data which identify investor types, this paper
examines the determinants of order cancellations in the Taiwan Stock Exchange.
Evidence shows that, first, order cancellation is subject to a trade-off between the cost
of monitoring and the risks of limit orders, including the non-execution and the
free-trade-option risks. Second, significant differences exist in order cancellations
across investor groups. Foreign investors cancel their limit orders the most frequently,
while individual investors do the least. Finally, over the year of financial tsunami,
2008, the levels and the sensitivities to the selected variables of order cancellations
(particularly by institutional investors) rise.
Keywords: non-execution risk, free-trade-option risk, monitoring cost, order
cancellations
1. Introduction
The purpose of this paper is twofold. First, employing comprehensive order-level data for
years 2007 and 2008, this paper examines the determinants of order cancellations in the
Taiwan Stock Exchange (TSE), a pure order-driven market. Second, this paper analyzes the
motives to cancel limit orders, facing trade-offs between the costs of monitoring and the risks
of limit orders, including the non-execution (NE) risk and the free trade option (FTO) risk.
In a pure order-driven market, limit order traders are the only liquidity providers. Even in
a hybrid market like the NYSE, limit orders accounting for more than half of trading
activities still act as an essential source of liquidity (Chakrabarty et al., 2006). Chung et al.
(1999) observe that in the NYSE the number of quotes in which at least one side of the quote
originates exclusively from limit-order traders is about 75%. Given the importance, numerous
relevant studies investigate issues on intraday liquidity, but most of them (e.g., Lee et al.,
2004; Ranaldo, 2004, Menkhoff et al., 2010) focus on order submission behavior. Until
recently, research has been increasingly aware of the role of cancellations and revisions of
limit orders in liquidity provision. For example, Ellul et al. (2007) and Yeo (2005) observe
that in the NYSE more than one-third limit orders were canceled. Hasbrouck and Saar (2009)
state that 93% of limit orders submitted through Nasdaq INET are canceled, and 36.69% of
those are fleeting orders canceled in two seconds after submission.1
The placement of a limit buy (sell) offers other market participants the opportunity of
selling (buying) shares to the limit order liquidity supplier at that price. Hence, a limit buy
(sell) is analogous to writing a free put (call) option to the market (Copeland and Galai, 1983).
The exercise price of the call (put) is equivalent to the ask (bid) price of the limit order.
Adverse price changes may further make the order stale and the associated FTO
in-the-money. The uncertainty that the stale order may be picked off by other informed
traders is called the FTO risk.2 If not exercised, possibly either the option is
out-of-the-money or the order is canceled/revised (Liu and Sawyer, 2003). On the other hand,
1
Jain (2005) observes that, in 2001, 101 leading stock exchanges out of selected 120 countries have introduced
screen-based electronic trading within the last 25 years. Agreeing on the importance of improved technology,
Hasbrouck and Saar (2009) observe that 36.69% of limit orders are canceled within two seconds for
Nasdaq-listed stocks in order to explore latent liquidity. Other studies, e.g., Coppejans and Domowitz (2002)
and Foster and Liu (2008), find that investors frequently cancel limit orders in derivative markets as well.
2
Institutional investors (especially hedge funds), actively monitoring the orders for large-cap stocks, make
other large-cap stock traders face higher FTO risk (Duong et al. 2009).
1
when the prevailing bid-ask midpoint moves away from the submitted price, executions
become less possible, the uncertainty that is recognized as the NE risk.
Responding to variations in the FTO and the NE risks, traders can either price-protect
themselves by submitting limit orders at prices far from the best quotes, or closely monitor
the market and cancel/revise their stale limit orders, if necessary (Liu, 2009, Goldstein and
Kavajecz, 2000; Foucault, 1999). For example, Nasdaq dealers do the latter, when facing
professional day traders (Foucault et al., 2003).3 Since information randomly arrives,
although it is appealing to actively monitor the information flow and prevent limit orders
from being stale and picked off, the behavior inevitably incurs nontrivial search costs  the
monitoring cost (Foucault et al., 2003). Investors have to make efforts to find news sources,
to interpret information, and to justify its accurateness. Only if the monitoring cost is not
large, limit orders are actively canceled or revised in response to changes in the NE and the
FTO risks (Fong and Liu, 2010).
Thanks to technological advancements (e.g., on-line trading system and internet) that
effectively enhance information transmission and reduce the monitoring cost (Jain, 2005;
Stoll, 2006),4 order cancellations/revisions have substantially increased (Liu, 2009;
Hasbrouck and Saar, 2009). Even given the improvement, the monitoring cost still varies
different across investors. For example, unlike institutional investors, individual investors
cannot continuously monitor the market (Aitken et al., 2007). Especially for individual
investors with dedicated daytime jobs in non-securities-related industries, closely monitoring
the market during trading hours is costly and even jeopardizes their career.5
Moreover, institutional investors are perceived to be better informed than individual
investors (Chakravarty, 2001; Anand et al., 2005; Kaniel and Liu, 2006). Institutional
investors can effectively gather and interpret necessary information from closely monitoring
the market. As information arrives, their order behavior is expected to be more sensitive and
quickly respond to market changes than individual investors’ (Lee et al., 1991; Menkhoff et
3
Foucault et al. (2003) argue that the Nasdaq’s Small Order Execution System (SOES) bandits who closely
monitor the market and pick off the stale quotes posted by dealers who are slow to adjust.
4
To understand these risks, Hollifield et al. (2004) build a structural model of a pure limit order market which
captures the trade-offs among the order price, the order execution probability, and the winner’s curse risk.
5
Aitken et al. (2007) suggest that active traders, such as institutional investors, expend resources in monitoring
the market and the status of their orders whereas passive traders do not. Hence, the FTO risk is relevant to part
of the institutional investors and to all the individual investors.
2
al., 2010). This paper explores the differences in these costs and, more importantly, the
associated behavior on order cancellations across investor groups.
This paper contributes to the literature in three dimensions. Firstly, to investigate the
strategic roles in order cancellations among investor groups, we take advantage of the
richness of our data, named “the TSE Order and Quote Files” that unambiguously classify
each limit order into one of five groups: foreign investors, mutual funds, securities dealers,
individual investors, and corporate institutions. To our knowledge, this is the first study
applying such voluminous and comprehensive data to examine this issue. Secondly, we
improve the measures of the FTO and the NE risks originally proposed by Liu and Sawyer
(2003). Our results empirically support the improvement. Thirdly, unlike the FTO and the NE
risks, the monitoring cost is not only unobservable, but also conceptual. We explicitly apply
the proportion of limit orders submitted before the open as a proxy for the availability of
investors to monitor the market or, simply, the monitoring cost. Finally, we pay attention to
the levels and the sensitivities of order cancellations by institutional investors over the 2008,
known as the year of financial tsunami.
Our primary conclusions previously unexplored are as follows. First, there exist
significant differences in order cancellations across investor groups, regardless of firm size.
The intraday pattern of order cancellations, along with the proportion of limit orders
submitted before the open, supports that individual investors have the highest monitoring cost.
Second, foreign investors cancel their limit orders the most frequently and their order
cancellations are the most sensitive to the FTO and the NE risks, while individual investors
do the least. Third, the sensitivity by foreign investors and domestic institutions doubles from
2007 to 2008, known as the year of financial tsunami.
This remaining paper proceeds as follows. Section 2 briefly describes the institutional
background of the TSE and the data. Section 3 depicts the research design covering the
employed variables and methodology. In Section 4, we discuss their empirical results.
Finally, we conclude this paper in Section 5.
2. Institutional background and the data
2.1 Institutional background
All listed securities on the TSE are traded by auto-matching through a Fully Automated
Securities Trading (FAST) system maintained by the TSE. It is centralized, computerized,
and order-driven, and its trading mechanism is similar to the electronic limit-order system in
3
Hong Kong (e.g., Ahn, Bae and Chan, 2001), except that the FAST is purely a call market
system. Trading operates from 9:00 a.m. to 1:30 p.m., Monday through Friday. Orders can be
keyed in 30 minutes prior to the open during which neither are submitted orders executed nor
is the order information displayed. There are no designated market makers and liquidity is
solely provided by non-marketable limit order traders.
All orders must be priced at the submission. Neither market orders nor hidden orders are
allowed. Trades periodically take place for each stock about 15 seconds. Limit orders are
prioritized first by price and then by submission time. The execution price, determined by a
single-price auction, is the one maximizing trading volume. The orders not fully filled enter
the limit order book and wait for a subsequent call. Unfilled orders automatically expire at the
end of each trading day. Information regarding the limit order book (including the best five
bid and ask prices, and the number of shares demanded or offered at each of these five prices)
is disseminated to the public on a real-time basis.
Note that the FAST, unlike most systems worldwide, does not directly execute order
revisions. Instead, after an order revision is issued, it automatically executes an order
cancelation and an order resubmission with the revised quantity at the revised price, and
finally generates two separated records. Importantly, the resubmitted order has a different
cross-reference number from that of the canceled order. Given that no order revision is
officially recorded, we only study order cancellations in this paper.
2.2 The data and sample
This paper employs the Order and Quote Files obtained from the TSE, covering a period
from 1/2007 to 12/2008, totaling 496 trading days. The sample stocks of interest are the
largest 50% of common stocks, a total of 375 firms, based on the market capitalization at the
beginning of the sample period. The major concern is that part of small-cap stocks may not
be traded, at least frequently, by institutional investors, which creates difficulty to analyze
their order cancellation behavior. Other securities, such as debt securities, rights, warrants,
and preferred shares, are excluded.
The data contain the intraday information on all original limit orders and quotes. For each
order, the data include the time stamp (to the nearest one hundredth of a second), stock code,
investor type, a buy-sell indicator, order size, and limit price. The investor type precisely
classifies each limit order into the order submitted or canceled by foreign investors, mutual
funds, securities dealers, individual investors, and corporate institutions. Mutual funds are
4
solely composed of domestic mutual fund firms, while foreign investors cover a wide variety
of foreign institutions, including foreign (investment) banks, insurance companies, mutual
funds, pension funds and so on. Corporate institutions consist of all domestic institutional
investors other than mutual funds and securities dealers. For brevity and without loss of
generality, we aggregate mutual funds, securities dealers, and corporate institutions into the
group of domestic institutions.
The quote data provide snapshots of the limit order book for each listed stock. It shows
the time as well as bid (ask) information at 20-30 second intervals. The bid (ask) queue
information includes the number of shares waiting to be executed at the best bid (ask) and at
each of the four consecutive lower (higher) ticks. On each trading day, we take 18 snapshots
of the limit order book for each stock at 15-minute intervals from 09:00 am to 1:30 pm.
3. Research design
In this section, we shall specify order characteristics and models necessary to conduct this
research. As a first step, we define the order cancellation ratio, applied throughout this paper,
as the number of canceled orders by a given investor group (such as all investors, foreign
investors, domestic institutions, or individual investors) over a given 15-minute interval
relative to the number of submitted orders by the same investor group over the same trading
day.6 However, there are two exceptions with special purposes.
First, to distinguish the proportional intraday order cancelation patterns among investor
groups, Figure 2 employs an order cancelation ratio that replaces the denominator of the
order cancelation ratio above with the number of canceled orders. Second, to separately
compare the relative importance of submitted orders and canceled orders among investors,
Table 2 employs a measure calculated by the number of canceled orders by a given investor
group over a given 15-minute interval divided by the number of all cancelled orders.
3.1 Price aggressiveness of limit orders
Price aggressiveness of limit orders or order aggressiveness by investors reflects their
eagerness for order executions at the time of submission. Investor can submit very different
6
For conciseness, the results applying the 15-minute dollar volume of canceled buy and sell orders are not
reported and resemble the results in the context.
5
buy or sell orders, trading off probabilities of execution with transaction costs (Hasbrouck
and Saar, 2001). For all intents and purposes, a marketable limit order in a pure limit order
book is equivalent to a market order in floor or dealer markets. A trader who seeks immediate
execution will price the limit order to be marketable, e.g., a buy order priced at or above the
current ask price.
3.1.1
Limit orders submitted before the open
Biais et al. (1995), Ranaldo (2004), and Griffiths et al. (2000) define the price
aggressiveness of limit orders, embedding real-time order information such as bid and ask
prices and submitted prices. Recall that none of the real-time order information is
disseminated before the open in Taiwan. As such, it may not be appropriate to follow mostly
prior papers to apply the definition of the price aggressiveness of orders submitted after the
open to define that before the open. We follow Chiao et al. (2009) to define the price
aggressiveness of limit orders submitted before the open as follows:
the aggressiveness of buy order j for stock i = (Pi,jPi,C)/Pi,C,
(1)
the aggressiveness of sell order j for stock i = (Pi,jPi,C)/Pi,C,
where Pi,C is the closing price for stock i in the preceding trading day and Pi,j is the
submitted price of order j. Namely, the applied order aggressiveness measures the deviation
of the submitted price from the preceding day’s closing price. The higher (lower) the buy
(sell) order price, the greater the order aggressiveness.7
3.1.2
Limit orders submitted after the open
The price aggressiveness of limit orders after the open, measuring the distance of the
submitted buy (sell) price from the best ask (bid) at the submission, is defined as follows:
The aggressiveness of buy order j for stock i = (Pi,j Pi,j,ask,s)/Pi,j,ask,s,
The aggressiveness of sell order j for stock i = (Pi,j Pi,j,bid,s)/Pi,j,bid,s,
7
(2)
Note that the order size does not play a role in calculating the order aggressiveness, unlike that defined in
Ranaldo (2004) and Griffiths et al. (2000). We regard that order size may not be so important because an
informed trader may camouflage trades by splitting one large trade into several small trades.
6
where Pi,j,ask,s (Pi,j,bid,s) is the best (ask) ask price of stock i for buy (sell) order j at the
submission time and Pi,j,s is the submitted price of order j for stock i. All orders are sorted into
the following five groups: 0 ≤ the aggressiveness (the most aggressive), -0.5% ≤ the
aggressiveness < 0%, -1% ≤ the aggressiveness < -0.5%, -2% ≤ the aggressiveness < -1%, and
the aggressiveness < -2% (the least aggressive). Group 1 (the most aggressive) orders are
marketable limit orders expectedly consuming liquidity, while others (groups 2 to 5) are all
non-marketable limit orders providing liquidity. The higher the price aggressiveness of a limit
order, the more aggressively the trader tends to trade.
3.2 Order price priority
The price priority measures the distance from the submitted prices of a given buy (sell)
order to the concurrent best bid (ask). The specific definition is as follows:
The price priority of canceled buy order j for stock i = (Pi,jPi,j,ask,c)/Pi,j,ask,c,
The price priority of canceled sell order j for stock i = (Pi,j  Pi,j,bid,c)/Pi,j,bid,c,
(3)
where Pi,j,ask,c (Pi,j,bid,c) is the concurrent best (ask) bid of stock i for canceled buy (sell) order j
and Pi,j is the submitted price of canceled order j for stock i. All canceled buy and sell order
are separately grouped into six groups, based on price priority. An order is assigned to group
k, k = 1 to 5, if (-0.2%  (k  1)  price priority > -0.2%  k). For a given order in group 6, its
price priority  -1%. The higher the price priority of a limit order, the longer the order has to
wait to be filled.
3.3 Regression models
Mainly following Hasbrouck and Saar (2009) and Fong and Liu (2010), we propose
Tobit regressions of the cancellation ratio for each stock across investor groups on the
selected firm characteristics and market conditions as follows:
CANCELi ,t   i ,0   i ,1  PUTi ,t   i ,2  CALLi ,t   i ,3  RETURN i ,t 1   i ,4  RSPREADi ,t 1
  i ,5  VOLi ,t 1  i ,6  MARKETRETt 1   i ,7  MARKETVOLt 1
  i ,8  BIDDEPTH i , t 1  i ,9  ASKDEPTHi , t 1  i ,10  AVOLU i ,t , d , m
17
  i ,11  ORDERSIZE i ,t 1   i , n  INTERn  i ,t,
n 1
where:
7
(4)

CANCELi,t is the cancellation ratio for stock i over 15-minute interval t.

According to Liu and Sawyer (2003), PUTi,t (CALLi,t), the intrinsic FTO value of the
buy (sell) limit orders or the NE cost of sell (buy) limit orders, is defined as:
PUTi,t = max(ai,t  pi,t+1, 0), CALLi,t = max(pi,t+1  bi,t, 0),
(5)
where ai,t (bi,t) is the best ask (bid) for stock i at the end of interval t and pi,t+1 is the
quote midpoint at the end of interval t+1. CALLi,t and PUTi,t capture the
post-cancellation price movement. The FTO value of the limit buy (sell) becomes
effective only when the bid-ask midpoint falls (rises) by more than the half of spread
from the end of the previous interval. Due to the dual nature of the FTO and the NE
risks, the NE cost for limit buy (sell) is given by CALLi,t (PUTi,t) (Fong and Liu, 2010).
In other words, an effective CALLi,t for the FTO offered by a limit buy trader implies an
ineffective PUTi,t for the NE risk on that order, and vice versa.
This paper proposes another version by modifying (5) as follows:
PUTi,t = max(ai,t  min(pi,t+1), 0), CALLi,t = max(max(pi,t+1)  bi,t, 0),
(6)
where max(pi,t+1) and min(pi,t+1) are respectively the maximum and the minimum of pi,t+1
over 15-minute interval t+1. We regard that the end-of-period bid-ask midpoint is not as
sufficient as the maximum or the minimum to capture the possible price movement or
what the stock has really experienced over the interval. As a special case, the put values
in (5) and (6) are equivalent, only if the end-of-period midpoint is the lowest.
For instance, if the midpoint during interval t+1 falls below the end-of-period ask
price in interval t, the option associated with a limit buy becomes in-the-money and
opposite-side traders have a chance to exercise the option. However, suppose that the
midpoint at the end rebounds above the previous end-of-period ask, and the put value is
set to zero, according to equation (5). It follows that the FTO would not be exercised
over the entire interval, even thought it had been in-the-money for a while. Is the
argument right? The answer is clearly no. In this scenario, the end-of-period midpoint
fails to capture the true variation of the put option value over the interval. On the
contrary, as described by equation (6), the revised put value remains positive and well
captures the turning point of the FTO risk than that under equation (5) does. The revised
measures can better reflect the trade-off traders truly face over the 15-minute interval.

BIDDEPTHi,t-1 and ASKDEPTHi,t-1, the rates of changes in quoted depths on the bid
8
and ask sides, respectively, are given by:
BIDDEPTH i , t 1 

bi ,t 1  Bi ,t 2
Qib,t 1
Qib,t  2
 1, ASKDEPTHi , t 1 

a i ,t 1  Ai ,t 2
Qia,t  2
Qia,t 1
 1,
where Bi,t-2 (Ai,t-2) denotes the best bid (ask) price at the end of interval t-2. Qib,t 1 ( Qia,t 1 )
is the depth in thousand shares at a bid (ask) price of b (a) at the end of interval t-1.
Depths in the limit order book impact not only order submission but also order
cancellation behavior of investors. Cao et al. (2008) suggest that incremental
information is embedded in the limit orders behind the best bid and offer quotes.
Changes in depth are likely to induce variations in the FTO and the NE risks (Ranaldo,
2004; Duong et al., 2009). For example, when the buy-side depths become thin and/or
the sell-side depths become thick, the stock price faces downward sell pressure and
waiting limit buys are more likely to be filled (Parlour, 1998). Unfilled limit buys face
high FTO risk and limit sells face high NE risk. Responding to the changes, the order
cancellation behavior could change accordingly.
To capture the effect associated with changes in quoted depths, following Fong and
Liu (2010), BIDDEPTHi,t-1 and ASKDEPTHi,t-1 are calculated by using the best quotes
at the end of the previous interval, Bi,t-2 and Ai,t-2, as the benchmarks. When the best bid
(ask) rises (falls), all the orders with the submitted prices equal to or greater than the
benchmark are counted, BIDDEPTHi,t-1 (ASKDEPTHi,t-1) increases. When the best bid
(ask) falls (rises), the depth at the benchmark disappears, implying that BIDDEPTHi,t-1
(ASKDEPTHi,t-1) is -1.

ORDERSIZEi,t-1 is the average order size in thousand shares over interval t-1. The larger
the limit order, the longer the order takes to be filled, the more risk the order is exposed
to, the more likely the order is to be canceled. We expect a positive relationship between
order cancellation and order size.

RSPREADi,t-1, the average 15 minute-by-minute relative spreads over interval t-1, is the
bid-ask spread deflated by the midpoint of the best quotes. Bid-ask spreads could impact
the limit-order risks. A larger spread may reflect a change in expected value of the
associated asset, and increase the possibility of being picked off and, equivalently, the
FTO risk. On the other hand, a larger spread may not necessarily imply higher
information asymmetry, but be driven by liquidity shortage, which possibly increases
the NE risk and trigger order cancellations.
9

VOLi,t-1 is the standard deviation of 15 minute-by-minute midpoints.

RETURNi,t-1 is the log change in the quote midpoint of stock i, i.e. lnpi,t-1  lnpi,t-2. Stoll
(1992, 2003) argue that, when bad (good) news for a stock arrives, the stock price trends
downwards (upwards). This follows that the FTO (NE) risk of sell (buy) rises, the
change is likely to impact order cancellation behavior.

MARKETVOLt-1 is the standard deviation of 15 minute-by-minute market indices over
interval t-1. MARKETRETt-1 is the log index change of the market over interval t-1, i.e.,
ln(INDEXt-1)  ln(INDEXt-2). MARKETRETt-1 and MARKETVOLt-1 can measure the
impacts of market-wide information (Hollifield et al., 2004). They are expected to
change the order cancellation behavior, similar to the influences of RETURNi,t-1 and
VOLi,t-1.

AVOLUi,t,d,m, the abnormal trading volume, is defined as:
AVOLU i ,t , d , m 
VOLUMEi ,t , d , m
VOLUMEi ,t , m

,
MARKETVOLUMEt , d , m MARKETVOLUMEt , m
where VOLUMEi,t,d,m and MARKETVOLUMEt,d,m are respectively the trading volumes of
stock i and the market over interval t, date d, month m.
VOLUMEi ,t ,m
is the
MARKETVOLUMEt ,m
average of relative trading volume over the tth intervals in all trading days of month m.
Fong and Liu (2010) believe that investors closely monitor the market would
positively rely on the level of trading activities. The thicker the trading volume, for
instance, the richer the information, and the lower the monitoring cost.8 AVOLUi,t,d,m
measures the ratio of the trading volume of stock i to the market volume (the level of
trading activities, after controlling for the market trend and the seasonal effect) over
interval t, minus the stock’s average over all the tth intervals in month m. When
AVOLUi,t,d,m is positive, the trading volume of the stock is relatively thick, which implies
that the information on the stock is rich and encourages investors to closely monitor the
market, and vice versa.

INTERn, n = 1, …, 17, is a dummy variable and takes a value of one, if the cancellations
take place in the nth 15-minute interval in any trading day.
8
Additionally, high trading volume is likely to attract not only noise traders but also informed traders, which
raises the FTO values of limit orders, encouraging order cancellations by investors who closely monitor the
market (Liu and Sawyer, 2003).
10
Finally, Year 2008 is known as the year of financial tsunami. It is plausibly an
information-rich period and provides us a perfect opportunity to examine whether investors
would become extra prudent and substantially change their behavior on order cancellation.
Recall that Figures 1 and 2, as preliminary evidence, show the average cancellation ratios
separately by all investors and each investor group in 2008 are all higher than those in 2007.
Without loss of generality, we further conjecture that order cancellations may have different
sensitivities to the included variables in Equation (4) between 2007 and 2008. To verify our
conjecture, we highlight the increment of each coefficient in Equation (4) from years 2007 to
2008 by adding an interaction term for each independent variable as follows:
CANCELi ,t   i , 0   i ,1  PUTi ,t   i , 2  CALLi ,t   i ,3  RETURN i ,t 1   i , 4  RSPREAD i ,t 1   i ,5  VOLi ,t 1
  i , 6  MARKETRETt 1   i , 7  MARKETVOLt 1   i ,8  BIDDEPTH i ,t 1   i ,9  ASKDEPTH i ,t 1
17
  i ,10  AVOLU i ,t ,d ,m   i ,11  ORDERSIZE i ,t 1   i ,n  INTERn
m 1
  i  D   i ,1 ( D  PUTi ,t )   i , 2 ( D  CALLi ,t )   i ,3 ( D  RETURN i ,t 1 )
(7)
  i , 4 ( D  RSPREAD i ,t 1 )   i ,5 ( D  VOLi ,t 1 )   i , 6 ( D  MARKETRETt 1 )
  i , 7 ( D  MARKETVOLt 1 )   i ,8 ( D  BIDDEPTH i ,t 1 )   i ,9 ( D  ASKDEPTH i ,t 1 )
17
  i ,10 ( D  AVOLU t )   i ,11 ( D  ORDERSIZE i ,t 1 )    i ,n  ( D  INTERn )  i ,t ,
n 1
where D is a dummy variable and equal to one for year 2008, zero otherwise. Similarly, a
significantly positive (negative) δi,n implies that the sensitivity of order cancellation to the nth
variable for stock i rises (falls) in 2008.
4. Empirical results
4.1 Summary statistics
Table 1 documents the overall summary statistics of the sample. The quoted spread is the
difference between the best ask and bid at the close. The relative spread is the quoted spread
relative to the bid-ask midpoint. According to the reported statistics, the characteristics of the
selected stocks widely spread. For example, the sample covers firms with market
capitalization ranging from 1.6 trillion to 20 billion NT dollars. Applying the bid-ask spread
to measure liquidity, the most liquid (illiquid) stock has a relative spread of 0.04% (0.3%).
Stock prices and trading volumes demonstrate large spans as well.
Figure 1 chronologically plots the cancellation ratios, in terms of the dollar volume and
the number of canceled orders, over the sample period. Note that, no matter which measure is
11
applied, not only the mean but also the volatility of the cancellation ratio increases, starting
from the second half of 2007, about the time when the notorious financial tsunami broke out.
According to the annual reports published by the TSE
(http://www.twse.com.tw/en/statistics/statistics.php?tm=07), in year 2008, the Taiwan
composite stock index fell by 3,915.06 or 46%, while the average daily turnover fell by 15%.
A contagion of fear might discourage trading activities. If one still insisted on trading at the
market, he was likely to be extra cautious about the risks. He could submit less aggressive
limit orders and/or frequently canceled his orders.
In the following discussion, we partition the full sample into two sub-samples, large- and
small-cap firms, based on the market capitalization at the beginning of the sample period,
because investment preferences could make differences. For instance, institutions prefer to
large-cap stocks because investing in large-cap stocks alleviates liquidity concerns
(Falenstein, 1996; Gompers and Metrick, 2001; Frieder and Subrahmanyam, 2005). Large-cap
firms are often frequently traded and have a high degree of transparency, reducing the
monitoring cost for investors (Liu, 2009). Moreover, according to Hasbrouck and Saar (2001),
the execution rates for limit orders increase with market capitalization, implying that limit
orders for large-cap firms have smaller NE risks. Given the differences in investors’
preferences and the associated costs between large- and small-cap firms, in this paper we shall
examine the order cancellations conditional on firm size across investor groups.
Table 2, summarizing order submissions and cancellations across investor groups, reports
the average daily numbers of submitted (canceled) orders by each investor group to the
numbers of all submitted (canceled) orders and their order sizes. Focusing on submitted
orders, individual investors are clearly dominating traders. For large-cap stocks, their daily
submitted orders makes up about 80% of the orders of the market, while for small-cap stocks,
the share even soars beyond 90%. Between institutional investors, foreign investors
overwhelm domestic institutions. Foreign investors especially prefer large-cap stocks,
whereas the behavior of domestic institutions is similar but not as strong. Taking limit buy
orders as an example, the orders for large- (small-) cap stocks by foreign investors is about
16.1% (5.3%) of total buys, while that by domestic institutions is 3.9% (3.0%).
The above observation, in agreement with prior studies, supports that large-cap stocks
attract institutional investors. First, Ikenberry et al. (1995) and Kamara et al. (2008) believe
that large-cap firms are more diversified in their business lines and have less default risk,
generating less information asymmetry between investors and firms. According to Kang and
Stulz (1997), larger firms are better known internationally and more liquid, so foreign
12
investors find it cheaper to trade in those firms. Furthermore, foreign investors, investing
internationally and familiar with changes in the global business environment, can effectively
incorporate marketwide information into prices of large and leading firms with adequate
liquidity in related industries (Chiao, Chen, and Hu, 2010). Second, foreign investors
preferring large-cap stocks do not have an information advantage on small-cap stocks.
Taking a close look at the characteristics of submitted orders, the orders by domestic
institutions have the largest size, regardless of in terms of volume or dollar volume. Quite
interestingly, albeit the limit orders by foreign investors are more than four times larger than
those by domestic institutions, the foreign investors’ order size is only about a half of the
domestic institutions’. For example, for large-cap stocks, the order dollar volume by domestic
institutions is 1.251 million NT dollars, while that by foreign investors is 0.613 million NT
dollars. The observation is consistent with Chiao and Wang (2008) who observe that foreign
investors in Taiwan are more inclined to split their orders into smaller ones to camouflage
their intention and reduce unnecessary impact costs.
As for small-cap stocks, the order volumes by all groups of institutions are even smaller
those for large-cap stocks. However, the decreasing pattern is not as obvious for the orders by
individual investors. For example, the buy order volumes for large- and small-cap stocks by
foreign investors (domestics institutions) are respectively 13.524 and 7.504 (27.465 and
19.143) thousand shares, while those by individual investors are respectively 6.441 and 6.940.
Given that small-cap stocks are less liquid than large-cap stocks, the reductions in orders by
institutional investors possibly aim to decrease the transaction costs.
Regarding order cancellations, the patterns are similar to those of order submissions.
First, individual investors still play a dominant role. For example, for large-cap stocks, the
canceled buy orders by individual investors make up 74. 6% of total canceled buy orders,
while foreign investors (domestic institutions) make up 22.6% (2.8%). For small-cap stocks,
the ratio by individual investors is even higher and reaches up to 89.6%. Despite the
dominant roles shown above, foreign investors cancel their own orders more actively than
others do. Order cancelations by foreign investors are more noticeable than their own order
submissions, but the pattern does not exist for other investor groups. For example, for
large-cap stock the proportion of buy (sell) order cancelations by foreign investors is 0.226
(0.240) and larger than that of buy (sell) order cancelations, 0.161 (0.171).
Figure 2 draws the order cancellation ratios for large- and small-cap stocks among the
three investor groups over the sample period. It is visually apparently that, regardless of the
selected firm sizes, the cancellation ratios by foreign investors and domestic institutions are
13
obviously higher than those by individual investors, consistent with the impression that
institutional investors are mostly professional and informed investors and have lower
monitoring costs.9 Those with an informational advantage could face different levels of limit
order risks (Menkhoff et al., 2010). Moreover, institutional investors cancel their limit orders
more frequently in 2008 than 2007, but the pattern is not as evident for individual investors.
4.2 Conditional Analyses
4.2.1
Intraday pattern of order cancellations
The literature shows that trading activities are more intense right after the open and
before the close, making price volatility U-shaped (Forster and Viswanathan, 1990;
Brockman and Chung, 1999). Since uncertainty is plausibly high at the open, making high
either the FTO or the NE risk, those who have low monitor costs are prone to closely monitor
the market and cancel their orders, if necessary, to prevent themselves from exposing too
much to the risks. Afterwards, uncertainty falls and order cancellations reduce.
On the other hand, when the market is about to close, investors whose earlier limit orders
have not been filled may be under pressure to trade immediately. For example, day traders
usually do not hold positions overnight due to uncertainty. If the investors worry that the
previously submitted prices cannot clear their positions, they may revise their orders at the
prices more likely to make the orders successfully executed. In sum, if investors choose to
monitor the market the market, their order cancellations possibly have a U-shaped pattern
(Liu, 2009; Fong and Liu, 2010).
Figure 3 plots the average intraday 15-minute proportion of canceled orders for each
investors group. First, let us look at the proportion by all investors. Evidence shows that a
U-shaped pattern exists within a trading day, regardless of market capitalization. In words,
the first and the last 15-minute intervals have the most order cancellations (10% and 8% of
the order cancellations over the trading day, respectively), while the least order cancellations
take place in the middle of trading day.
Taking a second look at the intraday pattern by individual investors, order cancellations
rise right after 12 pm. This is possibly because individual investors have a higher monitoring
9
Foreign investors in Taiwan are mostly affiliated with famous international investment houses (e.g., UBS,
Goldman Sachs, Merrill Lynch, and so on), so they are possibly superior to domestic institutions in better
information-processing abilities in exploiting global business trends and stock fundamentals (Seasholes, 2004).
14
cost particularly during the morning hours. To defend our argument, let us a first look at
Tables 3 and 4, describing order submissions based on price aggressiveness before and the
open, as defined in Equation (1) and (2), respectively. It is obvious that individual investors
obvious play a more dominant role before the open than after. They submit more than 90% of
orders before the open, possibly reflecting different monitoring costs borne by individual
investors and institutional investors.
Unlike institutional investors, most of individual investors neither work fulltime in
security-related industries nor are available to monitor the market all the time, but can still
submit orders before the open while not at work yet. After 12 pm, about the lunchtime,
individual investors are temporarily free from work. They can monitor the market and cancel
stale limit orders. The market is close at 1:30 pm when part of individual investors do not
back to work yet. By contrast, foreign investors seems to be conservative about submitting
limit orders before the open, since submitting limit orders before the open may expose
themselves to unnecessary overnight uncertainty. With a low monitoring cost, foreign
investors can effectively monitor the market and fast react to news after the open. Thus, the
observed pattern is consistent with the daily working schedule of regular workers.
4.2.2
Order cancellations with different submitted price aggressiveness
Fong and Liu (2010), observing a negative relation between price aggressiveness and
order revisions/cancellations, believe that order aggressiveness should influence order
revisions/cancellations due to its influence on the FTO and the NE risk exposures. The closer
the distance of a limit order, the more aggressive the limit order, the shorter the order waits
for execution, and the more likely the order is to be canceled. If the monitoring cost is
sufficiently low, traders are expected to cancel patient limit orders more often than aggressive
ones to manage their FTO and NE risks (Liu, 2009).
Table 4 reports the distributions of buy and sell order cancellations based on order
aggressiveness during regular trading hours, measured as the distance from the submitted
price to the best bid or ask price at the submission, as defined in Equation (2). Basically, all
canceled limit orders are grouped into five groups. Group 1, the most aggressive one,
contains all marketable limit orders expected to be filled immediately after the submission, if
the order size is not too large; otherwise, after walking up the limit order book, the part of
orders not filled will enter the limit order book. Groups 2 to 5 include non-marketable limit
orders at the submission, and group 5 is the least aggressive.
15
Overall, the canceled orders by all investors or any investor group demonstrate an
inverted U-shaped pattern, regardless of limit buys or sells by any investor group for large- or
small-cap stocks. Most of the cancellation ratios reach their peaks in aggressiveness group
3.10 The first half of the inverted U-shaped pattern is understandable and consistent with the
literature that order aggressiveness is negatively related to order cancellations. Intuitively, the
more aggressive the order, the less time to execute, the less frequently traders cancel the
order. More interestingly, the second half reflects the behavior of traders with a high
monitoring cost. We believe that there are traders who are unavailable to closely monitor the
market, but still want to trade. Given the traders’ high monitoring cost, they are even unable
to cancel their orders. To protect themselves from the FTO risk, they can submit patient limit
orders and ask for a larger compensation at the cost of non-execution (Liu, 2009).
To understand the argument, we compare the relations between price aggressiveness and
order cancellation across investor groups, and additionally calculate two ratios in Table 4,
RG1 and RG2. The RG1 is defined as the ratio of the number of group-1 (marketable) limit
orders to that of all limit orders by a given investor group, while the RG2 is the ratio of the
number of group-2 limit orders to that of all non-marketable limit orders from groups 2 to 5.
Intuitively, the RG1 of the investor group describes their relative preference for marketable
limit orders, while the RG2, focusing on non-marketable limit orders, describes the order
aggressiveness or the nearness of the submitted prices to the best quotes. The higher the RG2,
the higher the order aggressiveness, and the closer the submitted prices are to the best quotes.
First, the RG2’s for small-cap stocks are all lower than those for large-cap stocks. It is
not surprising because small-cap stocks have higher volatility. Traders, to protect themselves
from the FTO risk, demand a larger compensation by submitting non-marketable limit orders
at the prices farther away from the best quotes (Liu, 2009, Foucault, 1999). Second, it is clear
that individual investors with the lowest RG1 and RG2 (for example, 0.450 and 0.383 in
Panel A, respectively) act as liquidity providers, consistent with Lee et al. (2004). They not
only prefer non-marketable to marketable limit orders, but also submit orders at less
aggressive prices than other investor groups do. On the contrary, institutional investors
overall consume liquidity. They submit marketable limit orders more often than individual
investors. If placing non-marketable limit orders, their submitted prices are likely to be more
10
Fong and Liu (2010) partition non-marketable limit orders into “price improve”, “at quote”, and “outside
quote”, based on order aggressiveness. Clearly, their order groups are coarser than those in this paper, and it is
not surprising that the inverted U-shaped pattern is absent in their paper.
16
aggressive and closer to the best quotes.
Let us take the buy orders for large-cap stocks reported in Panel A of Table 4 as an
example. The RG2’s by foreign investors and domestic institutions are respectively 0.795 and
0.598, whereas that by individual investors is 0.383. It is plausible that individual investors
submit proportionately more limit orders at the least aggressive prices, because they are less
informed and have a higher monitoring cost, in line with the results in Table 3. Moreover,
regarding the reported numbers of submitted orders in group 5, individual investors have an
overwhelming role and submit more than 97% (57414/59212) of total group-5 limit orders.
As a conclusion, we observe an inverted U-shaped pattern between order aggressiveness and
order cancellations and believe that the pattern results from a high monitoring cost on traders
who submit the least aggressive limit orders. Finally, individual investors are, in aggregate,
these traders who submit mostly the least aggressive limit orders.11
In this sub-section, we have learned how limit order cancellations are affected by order
aggressiveness. However, from the standpoint of the timing of order cancellations, order
aggressiveness has been determined at the submission time and unrelated to subsequent
price movement, so the derived intuitions between order cancellations and order
aggressiveness cannot describe the dynamic development between risks. In the following,
we will pay attention to the relation between order cancellations and the distance from the
submitted prices to the prevailing best quotes, called the price priority that accommodates
the trade-off in a more dynamic sense.
4.2.3
Order cancellations with different concurrent price priorities
Goldstein and Kavajecz (2000) and Foucault (1999) suggest that traders can submit their
limit orders at prices far away from the best quotes, to reduce their exposure to the FTO risk.
Alternatively, Fong and Liu (2010) argue that, if closely monitoring the market, traders are
prone to cancel their orders, once adverse news hit. The submitted prices of those orders are
often near the prevailing best quotes or have higher price priorities, implying that these orders
have the higher expected FTO values.
In fact, when the concurrent best quotes move toward the submitted prices, the expected
FTO values of limit orders increase. Given the existence of monitoring cost, traders may not
be certain whether the movement is information-driven. To prevent their orders from being
11
For robustness, we use different price ranges to define the levels of aggressiveness. The results are
qualitatively equivalent to what we report in the context.
17
picked off, the traders can cancel the original orders and resubmit new orders with lower
price priorities as well as the likelihood of execution. Different from prior studies, we
additionally argue that if traders concern about the NE risk or are eager to get their limit
orders filled prior to certain deadlines, when the prevailing best quotes move away from the
submitted prices, they cancel and resubmit the orders to increase the price priorities, and,
thus, increase the likelihood of being filled. Thus, we expect that the relation between order
cancellation and price priority should look like a U-shaped curve.
Table 5 reports the distributions of buy and sell order cancellations across order price
priority groups. We calculate the ratio of the number of canceled limit orders to the number
of all limit orders in each priority group by each investor group. Firstly, as expected, the
canceled orders by all investors or any investor group demonstrate a U-shaped pattern. There
is a monotonically decreasing pattern from group 1 (with the highest price priority) to group
5, but a sudden jump for group 6 (with the lowest price priority), reflecting the trade-off
facing investors between the FTO and the NE risks mentioned above. That is, for groups 1 to
5, the higher the price priority, the higher the FTO value, the higher tendency investors have
to cancel their limit orders, if the investors’ monitoring cost is not too higher. Take the buy
orders for small-cap stocks as an example. From groups 1 to 5, the order cancellation ratios
by all investors are decreasing and respectively 0.276, 0.132, 0.101, 0.071, and 0.061.
Differently, for those group-6 limit orders with the lowest price priority, the NE risk
emerges and induces traders who have limit orders unfilled to cancel the orders and resubmit
orders at more aggressiveness prices, when they expect stock prices to trend away from the
orders’ prices. In other words, traders replace limit orders having low likelihood of execution
with those having higher likelihood. The order cancellation ratio for small-cap stocks by all
investors in group 6 is 0.308 and even higher than that in group 1 (0.276).
Secondly, market capitalizations make differences in order cancellation behavior.
According to Table 5, taking the sell orders as an example, the difference of the order
cancellation ratios in group 1 (the group with the highest price priority) by all investors
between the large-cap and the small-cap stocks is 0.052 (=0.290  0.238), while that in group
6 (the group with the lowest price priority) is -0.070 (=0.360  0.430). Obviously, the order
cancellations for large-cap stocks are likely to take place at the prices closer to the best quotes
than those for small-cap stocks. The observed pattern can be either attributable to the
trade-off of limit order risks or linked to the order submission tendency.
From the angle of order submission tendency, given greater volatility and illiquidity of
18
small-cap stocks, limit order traders tend to submit orders at the prices farther from the best
quotes or market makers tend to post a larger spread for them than for large-cap stocks to
maintain a compensation for higher risks (Goldstein and Kavajecz, 2000; Foucault, 1999). By
contrast, large-cap stocks are relatively transparent and liquid, which reduces the associated
monitoring cost and encourages traders or market makers to closely monitor those stocks (Liu,
2009) and sustain narrower spreads for those stocks.
On the other hand, from the angle of limit order risks, limit orders for large-cap stocks
submitted near the best quotes are exposed more to the FTO risk. Aitken et al.(2007) state
that aggressive institutional investors (e.g., hedge funds) actively monitor the market and
particularly large-cap stocks’ trading activities, which equivalently raises the possibility for
limit orders of being picked off around the best quotes. By contrast, the NE risk for small-cap
stocks is more pronounced. As reported in Table 4, the RG1 (ratio of the number of group-1
limit orders to the number of all limit orders) for small-cap stocks is smaller than that for
large-cap stocks, implying that the picked-off (FTO) risk for small cap-stocks is not as
serious as that for large-cap stocks. Furthermore, small-cap stocks are generally less liquid,
implying their demand curves are steeper (Campbell, Grossman and Wang, 1993). It follows
that, once a demand shock hits, the prices will change substantially. Thus, order cancellations
for small-cap stocks are expected to happen in the groups with low price priorities.
Thirdly, across investor groups, foreign investors proportionally cancel the most limit
orders in the best price priority group, while domestic institutions and individual investors do
in the least price priority group. For example, for small-cap stocks, the cancellation ratio of
limit buy orders in the best and the least price priority groups are respectively 0.486 and
0.122, while domestic institutions (individual investors) are 0.266 and 0.358 (0.259 and
0.382), respectively. This sharp difference reflects distinct monitoring costs and order
submission behavior of investors. First, as shown in Table 4, the RG2’s by foreign investors
are the highest, implying that they tend to submit non-marketable limit orders near the best
quotes. Second, according to Table 3, foreign investors submit disproportionately few orders
before the open. The evidence collectively shows that foreign investors having the lowest
monitoring cost closely monitor the market to reduce their exposure to the FTO risk, which
explains why they cancel proportionally more limit orders near the best quotes.12
12
As a robustness test, we divide the sample into price-priority groups with different ranges from those in the
context, and the qualitative changes do not essentially change our conclusions.
19
4.2.4
Order cancellations with different order sizes
According to the literature, order cancellations increase with respect to order size (Fong
and Liu, 2010; Yeo, 2005; Chakrabarty et al., 2006). Fong and Liu (2010) argue that the
opportunity costs of the FO and the NE risks increase with order size, implying that order
cancellations should increase with order size, while the monitoring cost has nothing to do
with order size. Yeo (2005) suggests that the larger the order size, the longer the order takes
to be filled; hence, larger orders are exposed to higher risk and more likely to be canceled.
However, Biais et al. (1995), Bertsimas and Lo (1998), Chakravarty (2001), Aitken et
al. (2007), and Chan and Lakonishok (1995) suggest that large (institutional) traders tend to
split their large orders into a sequence of small orders, in order to hide their intentions and
avoid unnecessary price impacts. Moreover, Aitken et al. (2007) observe that institutional
investors not only split their orders but also adopt multi-price order submission strategies,13
which may blur the link from order size to order cancellation. Although not having the data
of traders’ exact identifications and the relation, especially for institutional investors who
often split their orders, turns into an empirical question, we still can learn the variations of the
relation across investor groups.
Table 6 reports the statistics, including the order cancelation ratios and the average
canceled order size conditional on order size across investors. For each stock, all limit orders
are equally partitioned into quartiles, based on their dollar order volume, from low to high.
Roughly speaking, for all investors, there exists an increasing pattern of order cancellations
with order size, consistent with the literature that order size is positively related to
opportunity costs with which traders are prone to closely monitor the market and to avoid
from being picked off by informed traders. For example, the order cancellation ratio of the
smallest limit sell orders is 0.166, whereas that of the largest is 0.201. If looking across
investor groups, interestingly, foreign investors are the only exception for which the positive
relation does not exist, albeit the average order size of canceled limit orders exhibits an
increasing pattern. The observation seems to be contradictory to what we have learned above;
that is, as professional institutional investors, foreign investors actively monitor the market
and frequently cancel their non-marketable limit orders.
13
Biais et al. (2000) propose that a multi-price schedule of offers will emerge as an optimal execution strategy
in order-driven markets with an asymmetrically informed and risk-averse liquidity demander facing competing
liquidity suppliers.
20
To explain the contradiction, first, as reported in Table 6, the average order sizes of
canceled limit orders by foreign investors are much smaller than those by domestic
institutions. Second, let us take another look at Table 2, the proportions of submitted and
canceled orders (particularly for large-cap stocks) by foreign investors are far larger than
those by domestic institutions, but the average order sizes are far smaller. Moreover, the
proportion of submitted orders by foreign investors to that by domestic institutions is smaller
than the proportion of canceled orders. For instance, in the Buy case of Panel A, the ratio for
submitted orders (4.13 = 0.161/0.039) is much smaller than that for canceled orders (8.07 =
0.226/0.028). This implies that foreign investors actively split their limit orders, which
obscures the relation between order size and order cancellation documented in the literature.
Up to now, we have shown that, to minimize the exposures to the FTO and the NE risks,
traders can closely monitoring the market and cancel their orders, which nevertheless incurs
the monitoring cost. Besides the evidence consistent with the literature, in regards to
differences across investor groups, our results indicate that, first, individual investors, bearing
a larger monitoring cost, submit and cancel limit orders not only less frequently but also
farther from the best quotes. Foreign investors demonstrate an exactly opposite behavior to
individual investors. Second, there exists a positive relation between order size and order
cancellation, except for foreign investors who often split their limit orders.
4.3 Regression analyses
In this sub-section, taking advantage of the richness of data, we attempt to apply
multivariate regressions to explore the determinants of order cancellations across investor
groups. We employ the Tobit regressions, because the dependent variable (CANCELi,t) is
continuous between 0 and 1. Recall that we revise the definition of PUTi,t (CALLi,t) in
Equation (5) proposed by Liu and Sawyer (2003)  the intrinsic FTO value of the buy (sell)
limit orders or the NE cost of the sell (buy) limit orders. The end-of-the-period bid-ask
midpoint is replaced with the minimum (maximum) midpoint over interval t+1, as described
in Equation (6). For conciseness, we do not report the full regression results applying the
original PUTi,t and CALLi,t but mention the differences between two the sets of coefficients in
the context. Table 7 reports the regression results applying the revised PUTi,t and CALLi,t.14
As expected, the coefficients on PUTi,t and CALLi,t in Table 7 are mostly significantly
positive, consistent with Fong and Liu (2010). It follows that the FTO and the NE risks
14
For brevity, we do not report the coefficients on the interval dummies but are available upon request.
21
unambiguously play a positive role in order cancellations. When stock prices move closer to
(away from) the best quotes, the rising FTO (NE) risk raises the possibility of order
cancellations. Taking a closer look, the coefficients for institutional investors are all positive
and larger than those for individual investors. The observation is plausible, given that
institutional investors have lower monitoring costs, as explained in Sections 4.2.1 and 4.2.2.
The unreported coefficients across investor groups on (the original) PUTi,t and CALLi,t
measured by Equation (5) are very different from those reported in Table 7. For instance, in
Panel A, the coefficients on PUTi,t/100 for limit buys (sells) by foreign investors, domestic
institutions, and individual investors are respectively 0.289, 0.148, and 0.036 (0.254, 0.214,
and 0.168), while the unreported coefficients on the original PUTi,t/100 are 0.335, 0.116, and
0.029 (0.118, 0.246, and 0.173). Only half of these coefficients on the original PUTi,t/100 are
significant at the 10% level, while those reported in Panel A are all significant at the 1% level.
Furthermore, the coefficient on the original PUTi,t/100 for limit sells by individual investors
(0.173) is counter-intuitively greater than that by foreign investors (0.118). Instead, those
reported in Table 7 are more convincing, supporting the improvement of the revised measures
of limit order risks.
According to Table 7, regardless of limit buys or sells, the impacts of the FTO and the
NE costs on order cancellations are greatest for foreign investors, followed by domestic
institutions, and those on individual investors are the least. In Panel B, three out of four
coefficients of the order cancellation ratio by individual investors are even negative. Recall
that we have demonstrated earlier that individual investors have a higher monitoring cost, and
they can neither closely monitor the market nor be as keen as institutional investors to
respond to changes in the FTO and the NE risks, as information arrives. It is quite reasonable
that the sensitivity of individual investors’ order cancellations is the lowest to PUTi,t and
CALLi,t among the three groups of investors.
As for the coefficients on other (control) variables, those on VOLi,t-1 are all significantly
positive, regardless of investor groups, implying that the option-like feature makes placing a
limit order more costly when price volatility is higher. This is because the FTO associated
with the order becomes more valuable and has a higher likelihood of turning into
in-the-money (Foucault, 1999; Stoll, 1992). To deal with rising volatility, limit order traders
ask for a larger compensation for the rising FTO risk, by cancelling the current limit orders
and resubmitting new orders with lower price priorities or farther away from the best quotes.
Proxying for the arrival of public information, the market index volatility (MARKETVOLt1)
22
similarly impacts the order cancellation ratios, indicating that high market index volatility
implies high uncertainty. As for the impacts of RETURNi,t1 and MARKETRETt1 on order
cancellations, they are not as strong as those of VOLi,t-1 and MARKETVOLt1, although most
of them are significantly positive. This is actually not surprising because part of the impacts
of price movement on order cancellations have been absorbed by the FTO and the NE costs,
denoted by PUTi,t and CALLi,t in (6).
Changes in the FTO and the NE risks could be induced by changes in depths as well
(Ranaldo, 2004; Duong et al., 2009). Recall that BIDDEPTHi,t-1 (ASKDEPTHi,t-1) employed
in Equation (4) measures the cumulated depth in period t1 above the best bid (ask) at the
end of period t2, relative to the depth at the best bid (ask) at the end of period t2. If the
period t1’s bid (ask) falls below (rises above) the period t2’s best bid (ask), the measure is
equal to -1. If certain news hits the stock, it could face abnormal buy (sell) pressure, driving
its BIDDEPTHi,t-1 (ASKDEPTHi,t-1) upwards.
The coefficients of buy (sell) order cancellations on BIDDEPTHi,t-1 are mostly positive
(negative), while those on ASKDEPTHi,t-1 are mostly negative (positive), particularly for
institutional investors. It implies that for a given stock, when the depth on the buy (sell) side
increases, investors who have unfilled limit orders on the same side may feel the rising NE
risk and possibly cancel the originally submitted orders and resubmit new orders at higher
(lower) prices. Interestingly, compared to the coefficients for institutional investors, those for
individual investors are not straightforward, and even part of them demonstrate a wrong sign.
Suppose that individual investors have a higher monitoring cost and tend to submit limit
orders at less aggressive prices. It is not surprising that they are insensitive to changes in
depth, especially when the concurrent best quotes are still far from the submitted prices.
The coefficients on the relative spread (RSPREADi,t-1) are mostly significantly positive,
consistent with the literature. The larger the relative spread, the greater uncertainty. Investors
can either ask for a larger compensation by placing orders farther from the best quotes or
closely monitor the market and cancel orders, if necessary (Liu, 2009). Regarding trading
volume, the coefficients are all significantly positive for each investor group. Recall that
AVOLUi,t,d,m measures the abnormal trading volume of stock i and proxies for the level of
trading activities. Trading volume is negatively correlated to the monitoring cost and
positively correlated to order cancelations.
Overall, individual stock returns and price volatility, market returns and index volatility,
the relative bid-ask spread, and the abnormal trading volume have positive impacts on order
23
cancellations. The buy (sell) depth has a positive effect on buy (sell) order cancellation, and a
negative effect on sell (buy) order cancellations. Regarding the differences in order
cancellations across investor groups, individual investors, who have a higher monitoring cost,
may not respond as sharply as institutional investors on cancelling limit orders. Similarly,
individual investors behave differently in responding to changes in depth. Their order
cancellations are less sensitive than those by institutional investors as well.
4.4 Order cancellations during the year of financial tsunami, 2008
Recall that Figure 2 shows that the cancellation ratio is higher during year 2008, known
as the year of financial tsunami. Additionally, the intraday patterns of order cancellations are
also slightly different between years 2007 and 2008, as plotted in Figure 4. It is actually
reasonable that rising uncertainty made investors extra conservative during this crisis, as
conglomerate breakups quickly spread out and economies worldwide suffered. Investors
might face the increasing FTO and NE costs, relative to the monitoring cost, motivating them
to closely monitor the market and cancel their orders, if necessary. Because of different
monitoring costs among investor groups, as mentioned earlier, changes in order cancellations
might be different. In this sub-section, taking advantage of the richness of our data, we shall
pay attention to the differences among investor groups in detail.
Most academics agree that institutional investors are informed traders with professional
expertise in processing information, while individual investors are noise traders and their
behavior is easily influenced by market sentiment (e.g., Lee et al., 1991; Menkhoff et al.,
2010). Chiao, Chen, and Hu (2010) posit that foreign investors (mutual funds) trading in the
Taiwan stock market process global (local) expertise in interpreting new information about
the economy (fundamentals of individual firms). In practice, institutional investors, with not
only a lower monitoring cost, but also a better capability of collecting and interpreting
information about market and individual firms, have a strong incentive to closely monitor the
market and manage the FTO and the NE risks. Hence, we expect institutional investors to be
even increasingly sensitive more than individual investors in order cancellations during year
2008. Equation (7) estimates the increments of the sensitivities (δi,n , n = 1, …, 11) from 2007
to 2008. The results are reported in Table 8.
Evidence shows, first, most of the reported coefficients on the interaction terms are
significantly positive, except those on the bid and the ask depths (D×BIDDEPTHi,t-1 and D×
ASKDEPTHi,t-1). In addition, the coefficients for foreign investors are mostly the highest,
24
while those for individual investors are the lowest. It follows that, first, order cancellations
are indeed more frequent in 2008 than in 2007. Investors are increasingly insensitive to most
of included variables. Second, compared to the coefficients on PUTi,t and CALLi,t reported in
Table 7, the coefficients for foreign investors and domestic institutional investors are even
larger, implying that these two investor groups are increasingly prudent in year 2008. The
sensitivity of their order cancellations to the FTO and NE risks in year 2008 is more than
double that in year 2007. Regarding individual investors, their order cancellations do increase
but are not as strong.
5. Concluding remarks
Albeit a trader can submit a limit order to buy/sell a pre-specified quantity at a
pre-specified price considered optimal, but neither the transaction is guaranteed nor time to
execution is certain. When adverse information arrives, the limit order possibly becomes stale,
making the trader face the limit-order risks, such as the FTO and the NE risks. To mitigate
these risks, the trader can either submit orders at prices far from the best quotes or closely
monitor the market and cancel his orders, if necessary, which unavoidably incurs another
costs – the monitoring cost. Employing intraday data, this paper studies order cancellation
behavior among different investor groups. Noteworthy is that this paper proposes a revision
of the FTO and the NE risks initially developed by Liu and Sawyer (2003). The revision is
empirically confirmed in this paper as a contribution to the literature. To further differentiate
this paper from prior studies, the derived conclusions are separated into two major categories:
the ones consistent with the literature and the others previously unexplored.
In the first category, firstly, the limit order risks, including the FTO and the NE risks, are
crucial determinants for investors to cancel their limit orders. Secondly, order cancellations
exhibit a U-shaped intraday pattern; that is, investors cancel their orders more frequently at
the market open and close. Thirdly, the relation between order cancellation and concurrent
price priority is U-shaped. Namely, when the concurrent quotes move closer to (farther from)
the submitted prices, investors confront rising FTO (NE) risk, they are more likely to cancel
these orders. Fourthly, the larger the limit orders, the more frequently they are canceled.
Fourthly, firm size matters for order cancellations. Traders who submit limit order for
large-cap (small-cap) stocks face higher FTO (NE) risk, so they cancel their limit orders
when the prevailing quotes move closer to (farther from) the submitted prices. Finally, the
returns and the volatilities of a given stock price and the market index, the depths, the relative
25
bid-ask spread, and the abnormal trading volume affect order cancellations.
The second category includes the following. Firstly, institutional investors, especially
foreign investors, closely monitor the market and actively cancel their orders. Individual
investors with a higher monitoring cost do not frequently cancel their orders until noon,
reflecting their unavailability (high monitoring cost) during regular working hours. Secondly,
foreign investors and domestic institutions, having lower monitoring costs and submitting
limit orders around the best quotes, are highly aware of the FTO risk and tend to cancel limit
orders with high price priorities. Thirdly, order cancellations are tightly related to trading
strategies, e.g., order splits. Since foreign investors often split their orders into smaller ones
to camouflage their intention, the relation between their order cancellation and order size is
not obvious, while the relations for other investor groups are clearly positive. Fourthly,
applying a regression analysis, the sensitivities of order cancellations by foreign investors to
the FTO and the NE risks are the highest, while those by individual investors are the lowest.
Finally, in year 2008, known as the year of financial tsunami, order cancellations
proportionally rise, relatively to those in year 2007, possibly due to the growing uncertainty.
Especially, the sensitivities of order cancellation by foreign investors and domestic
institutions to the FTO and the NE risks double from 2007 to 2008.
26
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30
0.3
0.25
0.2
0.15
0.1
In dollar volume
In number of of orders
0.05
01/02/07
01/24/07
02/26/07
03/20/07
04/13/07
05/07/07
05/29/07
06/22/07
07/13/07
08/06/07
08/28/07
09/20/07
10/16/07
11/07/07
11/29/07
12/21/07
01/15/08
02/14/08
03/10/08
04/01/08
04/24/08
05/19/08
06/09/08
07/01/08
07/23/08
08/15/08
09/08/08
10/01/08
10/24/08
11/17/08
12/09/08
12/31/08
0
Figure 1. The daily proportions of canceled orders to all submitted orders
This figure plots the average daily proportions of canceled orders separately in dollar volume
and in number of canceled orders to total submitted limit orders over years 2007 and 2008. In
terms of dollar volume, the averages are 15.84% and 19.43% respectively over years 2007 and
2008, whereas in terms of number of canceled orders they are 19.52% and 21.75%.
31
Table 1. Summary statistics of selected stocks
This table reports the cross-sectional daily trading information of our sample firms from 1/2007 to
12/2008, totaling 496 trading days and 375 common stocks. The sample stocks are the largest 50
percent of firms, based on the market capitalization. The market value is calculated, using the closing
prices and the number of outstanding shares at the beginning of the sample period. The absolute
spread is the difference between the ask and the bid prices at the close. The relative spread is defined
as the ratio of the quoted spread to the midpoint of the best quotes. All reported statistics are
computed, using the time-series average of each selected firm. The reported statistics are
cross-sectional means over the time-series averages of individual stocks.
Market Cap.
Trading Volume
(in trillion NT$) (in million shares)
Mean
Median
Max
Min
50.766
15.199
158.6321
3.740
Stock price
(in NT$)
7.958
4.502
72.966
0.112
47.690
30.521
562.825
5.338
32
Absolute spread Relative spread
(in NT$)
(%)
0.170
0.094
2.839
0.016
0.092
0.085
0.297
0.042
Table 2. Submitted orders and canceled orders by three investor groups
This table reports the average daily numbers of submitted (canceled) orders by each investor group
relative to the numbers of all submitted (canceled) orders and their order sizes. The three investor
groups include FIs, DIs, and IIs, standing for foreign investors, domestic institutions, and individual
investors, respectively.
FIs
Sells
DIs
IIs
Panel A. For large-cap stocks
The proportion of submitted orders
0.161
0.039
0.800
1,000 shares
13.524 27.465
6.441
Order size in
1,000,000 NT dollars
0.613
1.251
0.252
0.177
14.326
0.636
0.038
27.314
1.244
0.785
6.343
0.249
The proportion of canceled orders
1,000 shares
Order size in
1,000,000 NT dollars
0.746
9.692
0.381
0.240
13.068
0.609
0.028
28.289
1.374
0.733
7.522
0.317
Panel B. For small-cap stocks
The proportion of submitted orders
0.053
0.030
0.917
1,000 shares
7.504
19.143
6.940
Order size in
1,000,000 NT dollars
0.232
0.633
0.180
0.068
7.144
0.212
0.031
18.206
0.599
0.901
6.500
0.167
The proportion of canceled orders
1,000 shares
Order size in
1,000,000 NT dollars
0.108
5.777
0.178
0.024
17.590
0.620
0.869
7.635
0.207
Order characteristics
Buys
DIs
FIs
0.226
11.971
0.562
0.082
6.269
0.204
0.028
28.645
1.372
0.023
19.855
0.691
33
IIs
0.896
10.983
0.286
Panel A. For large-cap stocks
0.6
0.5
FIs
DIs
IIs
0.4
0.3
0.2
0.1
01/02/07
01/17/07
02/01/07
02/27/07
03/14/07
03/29/07
04/16/07
05/02/07
05/17/07
06/01/07
06/20/07
07/04/07
07/19/07
08/03/07
08/20/07
09/04/07
09/20/07
10/08/07
10/24/07
11/08/07
11/23/07
12/10/07
12/25/07
01/10/08
01/25/08
02/19/08
03/06/08
03/21/08
04/08/08
04/23/08
05/09/08
05/26/08
06/10/08
06/25/08
07/10/08
07/25/08
08/12/08
08/27/08
09/11/08
09/26/08
10/15/08
10/30/08
11/14/08
12/01/08
12/16/08
12/31/08
0
Panel B. For small-cap stocks
0.7
FIs
DIs
IIs
0.6
0.5
0.4
0.3
0.2
0.1
01/02/07
01/17/07
02/01/07
02/27/07
03/14/07
03/29/07
04/16/07
05/02/07
05/17/07
06/01/07
06/20/07
07/04/07
07/19/07
08/03/07
08/20/07
09/04/07
09/20/07
10/08/07
10/24/07
11/08/07
11/23/07
12/10/07
12/25/07
01/10/08
01/25/08
02/19/08
03/06/08
03/21/08
04/08/08
04/23/08
05/09/08
05/26/08
06/10/08
06/25/08
07/10/08
07/25/08
08/12/08
08/27/08
09/11/08
09/26/08
10/15/08
10/30/08
11/14/08
12/01/08
12/16/08
12/31/08
0
Figure 2. The proportions of canceled orders by investor groups
This figure chronologically plots the average order cancellation ratios among investor groups for
large-cap (small-cap) stocks in Panel A (B). The order cancellation ratio is defined as the number of
canceled orders by a given investor group relative to the number of all submitted orders by the same
investor group. The three investor groups include FIs, DIs, and IIs standing for foreign investors,
domestic institutions, and individual investors, respectively. Their averages for large (small) stocks are
0.290, 0.165, and 0.143 (0.326, 0.174, and 0.150), respectively.
34
Panel A. Buy orders for large-cap stocks
Panel B. Sell orders for large-cap stocks
0.24
0.2
0.16
0.24
FIs
IIs
DIs
All
0.2
0.16
0.12
0.08
0.08
0.04
0.04
0
0
9:00-9:15
9:15-9:30
9:30-9:45
9:45-10:00
10:00-10:15
10:15-10:30
10:30-10:45
10:45-11:00
11:00-11:15
11:15-11:30
11:30-11:45
11:45-12:00
12:00-12:15
12:15-12:30
12:30-12:45
12:45-13:00
13:00-13:15
13:15-13:30
Panel C. Buy orders for small-cap stocks
Panel D. Sell orders for small-cap stocks
0.24
0.2
0.16
DIs
All
9:00-9:15
9:15-9:30
9:30-9:45
9:45-10:00
10:00-10:15
10:15-10:30
10:30-10:45
10:45-11:00
11:00-11:15
11:15-11:30
11:30-11:45
11:45-12:00
12:00-12:15
12:15-12:30
12:30-12:45
12:45-13:00
13:00-13:15
13:15-13:30
0.12
FIs
IIs
0.24
FIs
IIs
DIs
All
0.2
FIs
IIs
DIs
All
0.16
0.12
0.08
0.08
0.04
0.04
0
0
9:00-9:15
9:15-9:30
9:30-9:45
9:45-10:00
10:00-10:15
10:15-10:30
10:30-10:45
10:45-11:00
11:00-11:15
11:15-11:30
11:30-11:45
11:45-12:00
12:00-12:15
12:15-12:30
12:30-12:45
12:45-13:00
13:00-13:15
13:15-13:30
9:00-9:15
9:15-9:30
9:30-9:45
9:45-10:00
10:00-10:15
10:15-10:30
10:30-10:45
10:45-11:00
11:00-11:15
11:15-11:30
11:30-11:45
11:45-12:00
12:00-12:15
12:15-12:30
12:30-12:45
12:45-13:00
13:00-13:15
13:15-13:30
0.12
Figure 3. The proportions of canceled orders by each investor group over 15-minute intervals
This figure plots the 15-minute order cancelation ratio for each investors group, defined as the number
of canceled buy and sell orders over a given 15-minute interval to that by the investor group over the
entire trading day, separately for large- and small-cap stocks. The three investor groups include FIs,
DIs, and IIs standing for foreign investors, domestic institutions, and individual investors,
respectively.
35
2007
2008
9:00-9:15
9:15-9:30
9:30-9:45
9:45-10:00
10:00-10:15
10:15-10:30
10:30-10:45
10:45-11:00
11:00-11:15
11:15-11:30
11:30-11:45
11:45-12:00
12:00-12:15
12:15-12:30
12:30-12:45
12:45-13:00
13:00-13:15
13:15-13:30
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
Panel B. Sell orders for large-cap stocks
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
2007
2008
9:00-9:15
9:15-9:30
9:30-9:45
9:45-10:00
10:00-10:15
10:15-10:30
10:30-10:45
10:45-11:00
11:00-11:15
11:15-11:30
11:30-11:45
11:45-12:00
12:00-12:15
12:15-12:30
12:30-12:45
12:45-13:00
13:00-13:15
13:15-13:30
Panel A. Buy orders for large-cap stocks
Figure 4. The proportions of canceled orders for large-cap stocks in years 2007 and 2008
This figure plots the average 15-minute proportions of the number of canceled buy and sell orders for
large-cap stocks in years 2007 and 2008, separately.
36
Table 3. Aggressiveness of limit orders submitted before the open
This table reports the proportions of canceled orders based on price aggressiveness, measured as the
relative distance from the submitted prices to the previous closing prices. The order aggressiveness of
limit orders submitted before the open in this paper as follows:
The aggressiveness of buy order j for stock i = (Pi,jPi,C)/Pi,C,
The aggressiveness of sell order j for stock i = (Pi,jPi,C)/Pi,C,
where Pi,C is the closing price for stock i for the preceding trading day and Pi,j is the submitted price of
order j for stock i. For a given stock, the applied order aggressiveness measures the deviation of the
submitted price from the preceding day’s closing price. All orders are sorted into the following five
groups: 0 ≤ the aggressiveness (the most aggressive), -0.5% ≤ the aggressiveness < 0%, -1% ≤ the
aggressiveness < -0.5%, -2% ≤ the aggressiveness < -1%, and the aggressiveness < -2% (the least
aggressive). FIs, DIs, and IIs stand for foreign investors, domestic institutions, and individual
investors, respectively.
Order
aggressiveness
Number of submitted buy orders
ALL
FIs
DIs
IIs
1 (Most)
2
3
4
5 (Least)
13871
1305
2591
6601
30814
159
49
64
126
382
RG1
0.251
0.204
1 (Most)
2
3
4
5 (Least)
5652
515
961
2366
10835
43
12
17
33
98
RG1
0.278
0.212
Number of submitted sell orders
ALL
FIs
DIs
IIs
Panel A. For large-cap stocks
720
12992
8147
296
43
1212
907
42
47
2480
2162
69
65
6411
7216
159
188
30244
50534
673
0.677
0.244
0.118
0.239
Panel B. For small-cap stocks
73
5535
3219
102
8
495
304
13
6
939
754
21
7
2327
2592
49
19
10718
20723
206
0.646
0.277
37
0.117
0.261
712
49
56
76
248
7140
815
2038
6981
49613
0.624
0.107
63
6
7
11
40
3055
285
727
2531
20477
0.496
0.113
Table 4. Aggressiveness of limit orders submitted after the open
This table reports the numbers of submitted orders and the order cancelation ratios based on price
aggressiveness. The order cancellation ratio is defined as the number of canceled limit orders by a
given investor group in each aggressiveness group to the number of submitted limit orders by the
same investor group. Price aggressiveness measures the relative distance from the submitted prices to
the best quotes when the orders are submitted during regular trading hours and is defined as follows:
The aggressiveness of buy order j for stock i = (Pi,jPi,j,ask)/Pi,j,ask,
The aggressiveness of sell order j for stock i = (Pi,jPi,j,bid)/Pi,j,bid,
where Pi,j,ask (Pi,j,bid) is the best (ask) ask price of stock i for buy (sell) order j and Pi,j is the order price
of order j for stock i. All orders are sorted into the following five groups: 0 ≤ the aggressiveness (the
most aggressive), -0.5% ≤ the aggressiveness < 0%, -1% ≤ the aggressiveness < -0.5%, -2% ≤ the
aggressiveness < -1%, and the aggressiveness < -2% (the least aggressive). The most aggressive or the
first-group orders are marketable limit orders, while those in other groups are all non-marketable limit
orders. For the investor groups including FIs, DIs, and IIs standing for foreign investors, domestic
institutions, and individual investors, respectively, the aggressiveness of their canceled orders with
difference price priorities is separately reported. The RG1 is defined as the ratio of the number of
group-1 (marketable) limit orders to that of all limit orders, while the RG2 is defined as the ratio of
the number of group-2 limit orders to that of all non-marketable limit orders from groups 2 to 5.
38
Order
aggressiveness
Number of submitted orders
ALL
FIs
DIs
IIs
ALL
Order cancellation ratio
FIs
DIs
IIs
Panel A. Buy orders for large-cap stocks
Marketable
1 (Most)
207667
32791
9089
165787
0.060
0.080
0.044
0.057
Non-marketable
2
3
4
5 (Least)
107191
39902
35197
59212
25531
3974
1601
1012
4092
1227
736
786
77568
34701
32860
57414
0.282
0.341
0.308
0.216
0.448
0.663
0.588
0.402
0.253
0.309
0.287
0.235
0.227
0.301
0.291
0.211
RG1
RG2
0.462
0.444
0.505
0.795
0.571
0.598
0.450
0.383
Panel B. Sell orders for large-cap stocks
Marketable
1 (Most)
199023
33661
8690
156672
0.051
0.082
0.046
0.044
Non-marketable
2
3
4
5 (Least)
88822
33373
35087
83160
24959
4005
1710
1132
3438
1051
721
1106
60425
28317
32656
80922
0.318
0.370
0.325
0.215
0.465
0.679
0.610
0.423
0.280
0.331
0.288
0.194
0.255
0.321
0.304
0.211
RG1
RG2
0.453
0.369
0.514
0.785
0.579
0.544
0.436
0.299
Panel C. Buy orders for small-cap stocks
Marketable
1 (Most)
73367
3489
2239
67639
0.066
0.099
0.069
0.065
Non-marketable
2
3
4
5 (Least)
33583
17190
15056
22066
2661
719
337
152
1015
472
309
224
29907
15999
14410
21690
0.238
0.307
0.322
0.236
0.435
0.596
0.613
0.508
0.235
0.258
0.244
0.260
0.219
0.293
0.314
0.233
RG1
RG2
0.455
0.382
0.474
0.688
0.526
0.502
0.452
0.365
Panel D. Sell orders for small-cap stocks
Marketable
1 (Most)
72511
3951
2444
66116
0.051
0.103
0.058
0.048
Non-marketable
2
3
4
5 (Least)
27576
13783
14673
35488
2801
833
517
238
937
401
299
342
23838
12549
13857
34908
0.283
0.340
0.334
0.236
0.476
0.627
0.621
0.475
0.277
0.295
0.254
0.206
0.254
0.314
0.315
0.232
RG1
RG2
0.442
0.301
0.474
0.638
0.553
0.474
0.437
0.280
39
Table 5. Canceled orders with different price priorities
This table reports the ratios of canceled orders with different price priorities by the three groups of
investors. The order cancellation ratio is defined as the number of canceled limit orders by a given
investor group in each priority group to the number of submitted limit orders by the same investor
group in the same priority group. The price priority measures the relative distance from the concurrent
stock price associated with a given buy (sell) order to the concurrent best bid (ask). The specific
definitions are as follows:
the price priority of canceled buy order j for stock i = (Pi,jPi,j,bid,c)/Pi,j,bid,c,
the price priority of canceled sell order j for stock i = (Pi,j,ask,cPi,j)/Pi,j,ask,c,
where Pi,j,ask,c (Pi,j,bid,c) is the concurrent best (ask) ask price of stock i for canceled buy (sell) order j
and Pi,j is the order price of canceled order j for stock i. All canceled buy and sell order are separately
grouped into six groups, based on price priority. For orders in groups 1 to 6, respectively,
0  price priority > -0.2%,
-0.2%  price priority > -0.4%,
-0.4%  price priority > -0.6%,
-0.6%  price priority > -0.8%,
-0.8%  price priority > -1%,
-1%  price priority,
Then, the average cancellation ratios are calculated separately for buy and sell orders for all limit
orders in each priority group by each group of investors over all stocks. FIs, DIs, and IIs stand for
foreign investors, domestic institutions, and individual investors, respectively.
Price priority
ALL
Buy order cancellation ratio
FIs
DIs
IIs
Sell order cancellation ratio
ALL
FIs
DIs
IIs
High
2
3
4
5
Low
0.318
0.150
0.102
0.068
0.054
0.308
0.513
0.194
0.110
0.054
0.035
0.094
Panel A. Large-cap stocks
0.298
0.263
0.290
0.148
0.137
0.137
0.105
0.098
0.095
0.078
0.070
0.065
0.063
0.059
0.053
0.309
0.372
0.360
High
2
3
4
5
Low
0.276
0.132
0.101
0.071
0.061
0.360
0.486
0.179
0.112
0.061
0.040
0.122
0.266
0.132
0.101
0.077
0.066
0.358
0.508
0.188
0.108
0.056
0.037
0.103
0.277
0.140
0.102
0.077
0.064
0.340
0.225
0.120
0.089
0.066
0.057
0.443
Panel B. Small-cap stocks
0.259
0.238
0.128
0.116
0.099
0.091
0.071
0.067
0.062
0.059
0.382
0.430
0.476
0.174
0.109
0.062
0.045
0.136
0.243
0.126
0.099
0.076
0.069
0.387
0.214
0.110
0.087
0.065
0.059
0.465
40
Table 6. Canceled orders in different size groups
This table reports the statistics of canceled limit orders conditional on order size. The statistics include
the ratios of the numbers of canceled limit orders in the left panels and the average order sizes in the
right panels. For each selected stock, all limit orders are equally sorted into quartiles, from low to high,
based on their dollar order volume. The order cancellation ratio is defined as the number of canceled
limit orders by a given investor group in each size group to the number of submitted limit orders by
the same investor group. The average cancellation ratios and order sizes are calculated separately for
buy and sell orders for all limit orders for all stocks in each order-size quartile by each group of
investors. FIs, DIs, and IIs stand for foreign investors, domestic institutions, and individual investors,
respectively.
Order
size
ALL
Cancellation ratio
FIs
DIs
Small
2
3
Large
0.185
0.176
0.175
0.200
0.294
0.270
0.288
0.290
Panel A. Buy orders for large-cap stocks
0.107
0.170
4.975
8.208
0.133
0.159
5.459
8.881
0.164
0.154
7.181
10.643
0.176
0.184
23.078
19.683
11.738
17.195
26.062
52.535
4.025
4.228
5.500
22.891
Small
2
3
Large
0.166
0.180
0.184
0.201
0.290
0.275
0.291
0.296
Panel B. Sell orders for large-cap stocks
0.101
0.146
3.278
5.724
0.138
0.161
3.813
6.320
0.169
0.162
5.973
9.279
0.177
0.183
22.031
28.431
6.933
13.182
23.302
58.882
2.478
2.794
4.265
18.637
7.009
10.771
16.167
38.664
3.183
3.940
6.315
27.466
3.869
7.777
13.926
37.400
1.912
2.654
4.841
19.202
IIs
Canceled order size (in thousand shares)
ALL
FIs
DIs
IIs
Small
2
3
Large
0.179
0.167
0.171
0.213
0.325
0.298
0.305
0.296
Panel C. Buy orders for small-cap stocks
0.112
0.173
3.137
2.488
0.149
0.160
3.960
2.726
0.166
0.164
6.344
4.343
0.168
0.210
26.850
15.364
Small
2
3
Large
0.161
0.175
0.177
0.209
0.321
0.329
0.319
0.310
Panel D. Sell orders for small-cap stocks
0.108
0.151
1.887
1.870
0.155
0.164
2.669
1.959
0.176
0.168
4.933
3.656
0.173
0.203
19.309
14.773
41
Table 7. Tobit regressions
This table presents the cross-sectional regression results of the Tobit model for each of the three
investor groups as follows:
CANCELi ,t   i , 0   i ,1  PUTi ,t   i , 2  CALLi ,t   i ,3  RETURN i ,t 1   i , 4  RSPREADi ,t 1   i ,5  VOLi ,t 1
  i , 6  MARKETRETt 1   i , 7  MARKETVOLt 1   i ,8  BIDDEPTH i ,t 1
17
  i ,9  ASKDEPTH i ,t 1   i ,10  AVOLU i ,t ,d ,m   i ,11  ORDERSIZE i ,t 1    i ,n  INTERn  i ,t ,
n 1
where CANCELi,t is the cancellation ratio defined as the number of canceled orders for stock i by the
given investor group over 15-minute interval t to the number of submitted limit orders by the same
investor group over that trading day. PUT i,t (CALL i,t) is the free option value of the buy (sell) limit
orders or the cost of non-execution of the sell (buy) limit orders defined as:
PUTi,t = max(ai,t  min(pi,t+1), 0), CALLi,t = max(max(pi,t+1)  bi,t, 0),
where ai,t (bi,t) are the best ask (bid) for stock i at the end of interval t and pi,t+1 is the quote midpoint at
the end of interval t+1. RSPREADi,t-1 is the average one-minute relative spread over interval t-1.
VOLi,t-1 is the standard deviation of the one-minute quote midpoints and MARKETVOLt-1 is the
standard deviation of the one-minute market index over interval t-1. RETURNi,t-1 is the log price
change of stock i and MARKETRETt-1 is the log index change of the market over interval t-1. The
rates of changes in depths on bid and ask sides are defined as follows:
BIDDEPTH i ,t 1 

bi ,t 1  Bi ,t  2
Qib,t 1
Qib,t 2
 1, ASKDEPTHi ,t 1 

ai ,t 1 Ai ,t  2
Qia,t 1
Qia,t 2
 1,
where Bi,t-2 (Ai,t-2) denotes the best bid (ask) price at the end of interval t. Qib,t 1 ( Qia,t 1 ) denotes the
depths in thousand shares at price b (a) in the bid (ask) side at the end of interval t-1. The abnormal
trading volume (AVOLUi,t,d,m) is calculated as:
AVOLU i ,t ,d ,m 
VOLUMEi ,t ,d ,m
MARKETVOLUMEt ,d ,m

VOLUMEi ,t ,m
MARKETVOLUMEt ,m
where VOLUMEi,t,d,m and MARKETVOLUMEt,d,m are respectively the trading volumes of stock i and
the market over interval t, date d, month m.
VOLUMEi ,t ,m
is the average trading volume over
MARKETVOLUMEt ,m
intervals t in all trading days of month m. ORDERSIZEi,t-1 is the order size in thousand shares. INTERn,
n = 1,.., 17, is a dummy variable and takes a value of one, if the cancellation requests are submitted in
the nth interval of a given trading day. For brevity, the coefficients on the interval dummies are not
reported. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively. FIs, DIs, and
IIs stand for foreign investors, domestic institutions, and individual investors, respectively.
42
Independent variable
FIs
Buys
DIs
IIs
FIs
Sells
DIs
IIs
Constant
PUTi,t/100
CALLi,t/100
RETRUNi,t-1
RSPREADi,t-1
VOLi,t-1
MARKETRETt-1
MARKETVOLt-1/100
BIDDEPTHi,Δt-1/10000
ASKDEPTHi,Δt-1/10000
AVOLUi,t,d,m
ORDERSIZEi,t-1/10000
0.014***
0.289***
0.276***
0.073***
0.827***
0.006***
0.221***
0.163***
0.188***
-0.115***
2.441***
0.020 **
Panel A. Large-cap stocks
0.028***
0.013***
0.148
0.036
0.121*
0.083***
0.189***
0.067***
***
0.242
0.250***
***
0.011
0.013***
***
0.039
-0.066***
***
0.048
0.063***
***
0.157
0.044
-0.099***
0.012
2.217***
2.188***
0.008***
0.009***
0.014***
0.254***
0.427***
0.021
0.845***
0.008***
-0.057***
0.206***
-0.130***
0.120
2.072***
0.025***
0.023***
0.214***
0.335***
-0.072***
0.230***
0.012***
0.139***
0.068***
-0.081***
0.069
2.600***
0.011***
0.019***
0.168***
-0.158***
0.051***
0.317***
0.013***
-0.001
0.089***
0.041***
0.039
2.335***
-0.002*
Constant
PUTi,t/100
CALLi,t/100
RETRUNi,t-1
RSPREADi,t-1
VOLi,t-1
MARKETRETt-1
MARKETVOLt-1/100
BIDDEPTHi,Δt-1/10000
ASKDEPTHi,Δt-1/10000
AVOLUi,t,d,m
ORDERSIZEi,t-1/10000
0.012***
0.341***
0.445***
0.045***
0.413***
0.021***
0.370***
0.168***
0.168***
-0.132**
2.749***
0.149***
Panel B. Small-cap stocks
0.015***
0.012***
***
0.269
-0.008
0.300***
-0.002
0.121***
0.066***
0.107*
0.279***
***
0.011
0.012***
***
0.055
-0.072***
***
0.054
0.073***
***
0.114
0.203***
***
-0.084
-0.009
3.587***
2.905***
0.031***
0.007***
0.010***
0.510***
0.461***
0.079***
0.570***
0.022***
-0.090***
0.188***
-0.045
0.233***
2.895***
0.202***
0.012***
0.287***
0.449***
-0.042***
0.058
0.014***
0.122***
0.055***
-0.067**
0.242***
3.664***
0.032***
0.018***
0.175***
-0.159***
0.032***
0.249***
0.015***
-0.016***
0.088***
0.075***
0.147***
3.218***
0.000
43
Table 8. Tobit regressions with an additional dummy of year 2008
This table presents the cross-sectional regression results of the Tobit model for each of the three
investor groups as follows:
CANCELi ,t   i , 0   i ,1  PUTi ,t   i , 2  CALLi ,t   i ,3  RETURN i ,t 1   i , 4  RSPREAD i ,t 1   i ,5  VOLi ,t 1
  i , 6  MARKETRETt 1   i , 7  MARKETVOLt 1   i ,8  BIDDEPTH i ,t 1   i ,9  ASKDEPTH i ,t 1
17
  i ,10  AVOLU i ,t ,d ,m   i ,11  ORDERSIZE i ,t 1   i ,n  INTERn
m 1
  i  D   i ,1 ( D  PUTi ,t )   i , 2 ( D  CALLi ,t )   i ,3 ( D  RETURN i ,t 1 )
  i , 4 ( D  RSPREAD i ,t 1 )   i ,5 ( D  VOLi ,t 1 )   i , 6 ( D  MARKETRETt 1 )
  i , 7 ( D  MARKETVOLt 1 )   i ,8 ( D  BIDDEPTH i ,t 1 )   i ,9 ( D  ASKDEPTH i ,t 1 )
17
  i ,10 ( D  AVOLU t )   i ,11 ( D  ORDERSIZE i ,t 1 )    i ,n  ( D  INTERn )  i ,t ,
n 1
where D is a dummy variable and takes a value of one, if interval t is in year 2008, and zero otherwise.
Other variables’ definitions are identical to those described in Table 7. For brevity, only the
coefficients on the interaction terms (δi,n , n = 1, …, 11) are reported. *, **, and *** indicate significance
at the 10%, 5%, and 1% levels, respectively. FIs, DIs, and IIs stand for foreign investors, domestic
institutions, and individual investors, respectively.
Independent variable
FIs
Buys
DIs
IIs
FIs
Sells
DIs
IIs
DPUTi,t/100
DCALL i,t/100
DRETRUN i,t-1
DRSPREAD i,t-1
DVOL i,t-1
DMARKETRETt-1
DMARKETVOLt-1/100
DBIDDEPTH i,Δ t-1/10000
DASKDEPTH i,Δt-1/10000
DAVOLUi,t,d,m
DORDERSIZE i,t-1/10000
0.441***
0.532***
0.053***
0.705***
0.018***
0.178***
0.058***
-0.055
0.007
0.829*
0.066*
Panel A. Large-cap stocks
0.596***
0.087***
***
0.479
0.158***
***
0.066
0.000
0.775***
0.224***
0.017***
0.007***
***
0.173
0.077***
***
0.097
-0.007
0.030
-0.027
-0.006
-0.117
1.246***
0.478*
0.004**
-0.006***
0.361***
0.354***
0.145***
0.905***
0.021***
0.228***
0.021*
0.070
0.279
0.583
0.035
0.477***
0.800***
0.151***
0.839***
0.021***
0.274***
0.095***
-0.023
0.308*
1.194***
0.005***
0.026
0.021
0.049***
0.096
0.007***
0.094***
-0.026***
0.011
-0.019
0.735***
-0.019***
DPUTi,t/100
DCALL i,t/100
DRETRUN i,t-1
DRSPREAD i,t-1
DVOL i,t-1
DMARKETRETt-1
DMARKETVOLt-1/100
DBIDDEPTH i,Δt-1/10000
DASKDEPTH i,Δt-1/10000
D AVOLUi,t,d,m
DORDERSIZE i,t-1/10000
0.771***
0.724***
0.245***
0.327***
0.018***
0.148***
0.098***
0.151*
0.042
2.892***
0.361***
Panel B. Small-cap stocks
0.523***
0.064**
***
0.617
0.089***
***
0.049
0.006
0.340***
0.117***
0.018***
0.006***
0.196***
0.077***
0.059***
-0.001
**
0.138
0.030
0.044
-0.007
1.929***
1.676***
***
0.019
-0.013***
0.785***
0.571***
0.072***
0.824***
0.010***
0.265***
0.027*
-0.151
0.094
4.488***
0.171***
0.478***
0.508***
0.151***
0.466***
0.018***
0.162***
0.078***
-0.054
0.033
3.399***
0.024***
0.120***
0.081**
0.050***
0.107***
0.006***
0.095***
-0.015***
0.003
0.083**
2.631***
-0.020***
44