# Cancellation latency: The good, the bad, and the ugly.

This paper provides several statistics concerning cancellation latency that would be helpful to regulators as they consider policies to establish a minimal quote life. We find that cancellation latency is related to market quality and is not constant. Rather, it varies depending upon the time of day, order price and size, market congestion, trader type, firm size, order imbalance, and technology used for submitting an order.The ability to quickly cancel trades is an integral aspect of active trading. Additionally, there has been recent regulatory interest in establishing minimum cancellation times. While regulators in the United States and Europe try to search for the best cutoff value for minimal quote life, we have not seen simple summary statistics for the time a cancellation order takes from being placed to execution. Many markets post the average time to cancel on their exchanges. However, it is not clear whether the average cancellation time is a dependable estimate for various markets or at various times throughout the day. Given that cancellations account for over 96% of all orders and cancellation latency is becoming the focus of various market participants, there appears to be a gap in the literature. (1) Simple descriptive statistics are hard to compute in the high-frequency trading world making in-depth analysis difficult (Gai, Yao, and Ye, 2012). This paper attempts to provide some initial documentation regarding cancellation latency.

One reason for the lack of research concerning the characteristics of cancellation latency is the lack of data. Few exchanges publish intraday data detailed enough to allow for orders entered on the limit order book to be connected to a subsequent cancellation order. However, this detailed data is available for stocks listed on the Korean Stock Exchange prior to 2007. Thus, we utilize the Korean intraday data in order to study cancellation latency and document its characteristics. In addition, we examine the relationship of cancellation latency to market characteristics and to various trade type characteristics.

Using the intraday data from the Korean Stock Exchange (KRX), we provide the first (to our knowledge) summary statistics on cancellation latency or time-to-cancel (TTC), defined as the difference between a cancel order submission time and its execution time. We also analyze the factors influencing TTC. Unlike the vastly fragmented US equities markets, the KRX is a consolidated market. As such, we capture the true cancellation volume for any given stock. (2) In addition, unlike the NYSE TAQ (Trades and Quote) data that do not report any trades or quotes for odd-lots, data from the KRX report the entire order flow.

In this paper, we find that cancellation latency matters to market quality in that lagged TTC predicts future market spreads. The cancellation latency of the market can vary depending upon various market characteristics. We find that cancellation latency depends on market load (total trading activity in terms of the total number of trades, quote placement, revisions, and cancellations) and individual stock-specific trade characteristics, such as the stock-specific cancellation-to-quotes ratio, trade-to-quotes ratio, average trade size, volatility, and liquidity.

We also determine that cancellation latency varies with how far the order is placed from the best quotes. We find that the canceled orders at or close to the best quotes suffer the worst cancellation latency. Prior research that focuses only on the top of the limit order book quotes may actually miss an arena where it is strategically advantageous for quote stuffers to participate. Use of the full order book is important as a quote stuffer's goal is to slow the latency of the trading system, not to trade. Thus, strategically, they may enter "safe" orders away from the best bid and ask. Our data include cancellations at all quote levels and, as such, capture this strategy. We find that orders placed away from the best quotes have the lowest cancellation latency. (3)

Next, we find that cancellation latency has a U-shaped intraday pattern. However, cancellation latency during the first 10 minutes of trading is orders of magnitude larger than that for the remainder of the trading day. In addition, odd-lots (orders with order sizes that are not divisible by 10) have significantly lower cancellation latency than round lots. We also show that small-cap stocks have significantly larger cancellation latency than large-cap stocks, suggesting that large cap stocks are more prone to "quote-stuffing."

Finally, we document that canceled orders from foreign investors, institutional investors, merchants, and program traders have the lowest cancellation latency. Likewise, canceled orders submitted from outside of Korea have lower cancellation latency than those inside Korea. Canceled orders entered with wired terminals (WTs) have lower cancellation latency than unwired terminals.

Gomber et al. (2011) argue that high-frequency traders attempt to profit from inefficiencies in data transfers between exchanges or other market centers. Brogaard (2010) suggests that by submitting large numbers of orders that are canceled very quickly, HFTs may create exploitable latency arbitrage opportunities.4 Biais and Woolley (2011) term such a trading strategy as "[quote] stuffing." This involves submitting an unwieldy number of orders to the market to generate congestion. Although our data are pre-HFT, our results are consistent with the findings in these papers. When market activity increases or when order imbalance becomes more severe, cancellation latency increases and the increase can be quite large.

I. Data and Summary Statistics

In this section, we describe the KRX institutional details, the unique features of the Korean trade-and-quote data set (including the variables used in our tests), and the methodology employed.

A. KRX Institutional Details

The KRX has one continuous electronic quote trading session and two simultaneous auctions each trading day. There is a 10-minute open auction from 8:50-9:00 followed by a continuous trading session from 9:00-14:50. (5,6) This is followed by a 10-minute closing single price batch auction from 14:50 to 15:00. All market participants who enter a batch order receive the same price at the end of the auction. We exclude the auction periods from our data. There are no market makers or designated liquidity providers on the KRX (i.e., the KRX is a purely order-driven market). Traders can enter limit orders, market orders, fill-or-kill orders, fill-and-kill orders, and auction orders. The KRX automated trading system prioritizes each order first by price and then by time. Orders can be entered via a broker's branch terminal, by a specialized home trading system (HTS), via wireless connection, or via a wired connection. Short sales were allowed in Korea during our data sample and are identified in our data. (7) Margin trades are also identified. Foreign ownership limits were eliminated in May 1998, so there are no limits on foreign ownership during our sample period. (8)

Online trading is widely available on the KRX and has been in existence for several years. Chung, Choe, and Kho (2009) find that in December 2000, online trading accounted for 61.5% of the total stock trading value. Korea has traditionally been a low-cost trading environment for online trading. Chung et al. (2009, p. 242) state that over 1999 and 2000 "... typical brokerage firms charged from 0.1% to 0.15% commissions for online trading, while they charged 0.5% commissions for offline trading." Trading in Korea is incentivized as the capital gains tax rate is zero for trading exchange-listed stocks.

The KRX has a 15% daily price limit system. If a special event occurs that alters the number shares outstanding, the KRX adjusts the price limits accordingly. (9) The KRX is a transparent market. Since January 2, 2002, the KRX instantaneously disseminates price and quantities for the 10 best bids and offers. (10) Most traders on the KRX use online trading and have real-time level three limit order information. Thus, online traders have fast access to market pricing and volume.

B. Data Description and Summary

We employ the full set of cancellation orders for the Korean stock market for 2006. (11) The data are collected from the Institute of Finance and Banking at Seoul National University and the Korea Stock Exchange order and trade database. Our data set includes every cancellation order. We have, for each minute, the number of trades and the number of quotes, where the quote includes revisions, cancellations, trades, and new quotes. For each cancellation, we have the order time and the post time. Every cancellation is provided with an identifier that marks it as a buy cancellation or a sell cancellation. Our data include indicators that identify a trade by a foreigner, the foreigner's country of residence, an institution (and, if an institution, what type of institution), a program trade identifier, and a mode of entry identifier. In addition, we collect market capitalization for each firm from Datastream and merge it with our cancellation order data set. There are 12 firms in our cancellation data that are not covered by Datastream. Thus, our final sample includes 838 firms. To make the analysis computationally manageable, we analyze the trading data for the first month in each of the four quarters of 2006.

Table I provides summary statistics of our variables. Columns 2-5 provide minute-by-minute information for the full trading day. The average TTC is 3.67 seconds, but the variation is large ([sigma] = 3.86). The same pattern can be seen with most market characteristics, e.g., the percentage of orders that are cancellations (CTQ) has a mean of 0.30 and a standard deviation of 0.27. On average, trade size (ATS) on the Korean market is small ([mu] = 292 shares).

The last eight columns in Table I report summary statistics for the first half hour of trade (from 9:00 to 9:30) and for all trades after the first half hour (from 9:30 to 14:50). Note that most of the variables are larger in the first half hour of trade, reflecting a higher level of trading. The differences can be large, e.g., cancellation latency is, on average, 8.65 seconds in the first half hour of trading compared with only 3.07 seconds for the rest of the day. The average trade size does not differ substantially (318 shares vs. 288 shares), but volume is much higher in the first half hour (8,159 vs. 4,443 shares). Somewhat surprisingly, on average, the variation in price is lower in the first half hour of trade than it is for the rest of the day, although the skew to variance is larger in the first half hour of trade with a 75th percentile of 0.009 compared to that of 0.006 for the remainder of the day.

Our cancellation data provide the receipt time and post time for each order. Trading in the first half hour increases the exposure to cancellation latency risk. This is apparent when TTC is compared for the two subperiods. The time to cancel is more than double (8.65 seconds) in the first half hour than it is for the rest of the day (3.07 seconds). Thus, we find an increase in the cancellation latency risk during the first half hour if a trader decides to cancel a trade. This is an important result from our cancellation data that has not been previously documented.

C. Data Characteristics by Size Deciles

We calculate the cancellation latency as the time it takes for a cancel order to be executed on the KRX. There are several interesting variables in order to subset the cancellations. Summary statistics for these subsets of data are provided in Table II. We compare cancellation latency across size deciles for various subsets of the data. One interesting comparison is the mean cancellation-to-quote ratio in Panel A to the mean number of cancellations in Panel B. The first half hour experiences a higher number of cancellations (4.48 for the largest decile 1) compared to the full day (3.42). This would be expected given the higher volume during this period. (12) However, Panel A indicates that there is a smaller percentage of cancellation orders in the first half hour of trade (14%) compared to the full day (19%). Although the number of trades increases in the first half hour (see Panel D), the trades-to-quotes ratio (TRTQ) remains constant (see Panel C). Since cancellations decrease as a percentage of quotes, revisions, the only remaining order category, must increase. This implies that in the first half hour, investors want to trade and will revise a quote rather than cancel. Thus, utility to trade is higher in the first half hour of trade. To our knowledge, we are the first to document this characteristic of trading. This utility to trade increases as the size of the stock decreases. This could reflect the market's knowledge that small stocks are more difficult to execute trades during regular hours due to low liquidity.

Panel E of Table II reports the TTC by size quintile. In the panel for the whole trading day, TTC increases 14.37% from the largest to the smallest size decile, while it increases 18.86% for the first half hour. Thus, small stocks take more time to execute a cancel order. However, it should be noted that the cancellation latency differential between the large and small caps is only 9.23% outside the first half hour of trade. One may expect that all cancellation orders are treated equally. However, we find here that cancellations in large stocks are executed more quickly. This important theme will repeat throughout our results.

Finally, in Panel F, relative spreads are reported across size deciles. Liquidity has different dimensions (i.e., depth, resiliency, and tightness). Relative spread most closely captures tightness. Interestingly, relative spread is about constant in both subperiods (first half hour and the rest of the day) for our data sample. Although intuition may deem liquidity higher during the first half hour of trade, this may not necessarily be true for all components of liquidity.

D. Cancellation Latency by Classification Types

In this section, we utilize several unique variables in our cancellation data in order to explore the variation of cancellation latency. Our data identify whether a trade was entered via a program trade or if it was a normal or nonprogram trade (NPT). If a trade is flagged as a program trade, it is then further identified as either an index arbitrage (IA) or a nonindex arbitrage trade (NIA). In Table III, Panel A, we calculate cancellation latency by trade type: NPT, IA, and NIA. Interestingly, in the first half hour, trades from both IA and NIA are cancelled faster than trades from NPT. The size differential can be large, i.e., from 5.18 seconds for an IA trade to 11.61 seconds for a NPT trade. Just as interesting, the cancellation latency is longest for IA trades during the rest of the trading day; however, the differential is very small (2.99 and 2.56 seconds for IA and NPT trades, respectively).

Panel C provides cancellation latency by time of day Note in the first entry (9:00), the first subset of columns (Full Trading Day) reports results for 9:00-10:00, the second subset (First Half Hour) reports results for 9:00-9:30, and the third subset (Ex First Half Hour) reports results for 9:30-10:00. For all other entries, the Full Trading Day sample provides results for the full hour period. Prior research indicates that the first half hour is different across various trade characteristics, e.g., it has higher volatility, greater liquidity, and higher trading volume (Mclnish and Wood, 1992). These characteristics tend to have a U-shaped pattern across the trading day. This U-shaped pattern is also apparent in our new variable, cancellation latency. Thus, our results confirm prior time-of-day trade characteristic patterns. However, it should be noted that our cancellation latency U-shaped pattern is asymmetric with a higher tail in the first half hour compared to the end-of-day trading. Figure 1 demonstrates the U-shape pattern for cancellation latency.

The next two variables categorize trades as either (1) trades by Korean nationals or trades by non-Koreans (Panel D) and (2) trades originating in Korea or trades originating outside of Korea (Panel E). On average, foreigner cancellation latency is lower in the first half hour of trade than those of Korean nationals (7.34 compared to 11.72 seconds, respectively). After the first half hour of trade, trades by foreigners experience slightly higher cancellation latency. At first, this may seem counterintuitive, but many foreign trades are from institutions, which typically experience lower cancellation latency. Institutions have been found to trade more actively in the first half hour of trading due to their need for higher volume (Wood, McInish, and Ord, 1985). Interestingly, orders originating outside of Korea have lower average cancellation latency than orders placed inside Korea. This may be due to foreign-based traders entering orders via brokers, while most locally based traders utilize the HTS system. Another possibility is that trades originating outside Korea engage in a higher percentage of program trading than locally based trades.

[FIGURE 1 OMITTED]

Finally, Table III, Panel F, provides the cancellation latency broken down by investor type. Our data identify the trader type of each cancellation order. We identify securities companies (Sec), insurance companies (Ins), investments companies (Inv), banks (Bank), merchants (Mer), mutual funds (Fund), country funds (Nat), individuals (Ind), and foreigners (For). Other investor types are lumped into a general category (Other). Surprisingly, banks have extremely high cancellation latency when compared to other trade types and this is particularly so during the first half hour of trading (33.10 seconds). Either banks are not sophisticated or they do not trade in a manner where cancellation latency is important. This is an interesting anomaly that needs explanation. Unfortunately, our data do not provide the details to explore this further. Merchants have the lowest cancellation latency across all time subperiods. The cancellation latency of all other trader types is within reasonable bounds, e.g., the middle six firm types have a cancellation ratio between 5.82 and 7.44 seconds in the first half hour of trade and between 2.51 and 2.95 seconds the remainder of the day.

II. Does Cancellation Latency Matter?

In this paper, we document and characterize cancellation orders. This is an important exercise as canceled orders are the largest trade category, yet little has been documented to date concerning cancellations. However, if canceled orders do not affect the market in a significant way, then one might ask why we should care about them? In this section, we address this question.

Hendershott and Riordan (2013) argue that the ability to continuously monitor market conditions and cancel the limit orders to avoid adverse selection is an important component in the supply of liquidity. Furthermore, Goettler, Parlour, and Rajan (2005) contend that immediate cancellation reduces pick-off risk. When immediate cancellation is available, the low level of pick-off risk encourages aggressive order submission. Traders can submit orders closer to their own valuation with little risk of suffering a loss. Thus, limit order submitters are willing to compete more aggressively for execution with immediate cancellation thereby reducing the cost of trading. We test the following hypothesis:

H1: Lower cancellation latency leads to higher liquidity.

Market quality has many dimensions. One important dimension is relative spread, which is a measure of market liquidity. In this section, we find that the TTC is predictive of market liquidity. Thus, a trader should pay close attention to TTC if liquidity is important to his trading strategy. Stoll (2000) demonstrates that the following variables are almost always important in explaining the cross section of liquidity: log share volume, return variance, log price, log number of trades, and log market value. Stoll (2000) proxies liquidity using various measures of spread. We design our test in line with these results. We run the following regression to determine whether TTC is predictive of liquidity.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

RSPRD, our measure of spread and our proxy for liquidity, is the dependent variable. The independent variable of interest is the lagged TTC (LagTTC). We use Stall's (2000) variables as control variables. These include volume (LogVOL), number of trades for every minute of trading (LogNTRDS), stock's market value (LogMV), stock price at the end of every minute (LogPRICE), and price volatility during the one-minute trading period (PRIVAR). [epsilon] is the error term. We control for time of day with six hourly dummy variables (HR). We run the regression with and without hourly time dummies.

The results are presented in Table IV. Our results confirm the findings in Stoll (2000). All of the control variables are highly significant. As one would expect, higher volume, larger number of trades, and higher market value imply lower spreads or more liquidity (i.e., the coefficient is negative on these variables). Alternatively, higher volatility suggests higher spreads or less liquidity (a positive coefficient), which is also very intuitive.

Of primary interest to our study is the coefficient on LagTTC. This coefficient is highly significant and positive. Thus, Hypothesis 1 is supported by the data. The results are robust to the inclusion of Stall's (2000) control variables or hourly time dummies. The positive coefficient on TTC implies that the longer it takes to cancel an order, the higher the next minute's spread (i.e., on average, liquidity will decrease over the next minute). It follows that if the TTC increases, a trader should expect that the liquidity of the market is going to deteriorate. Thus, cancellation latency is important as it contains information about important future market characteristics, like liquidity.

III. Determinants of Cancellation Latency

The results thus far establish that cancellation latency is not constant (or equivalent to the one set by an exchange). Rather, it varies depending on the market's condition. To provide greater insights we conduct a formal regression analysis.

A. Base Regressions

Our first testable hypothesis concerns the relationship of quote volume and cancellation latency. It has been proposed that one possible strategy of HFT is to engage in market latency arbitrage. For this to be practical, HFT should be able to reduce market latency by increasing the quote volume. Exchanges are sophisticated users of technology as well. Particularly, after the 1987 crash, many exchanges realized that technology bottlenecks can create market failure and invested significantly in technology upgrades. Thus, exchanges may be prepared for significantly higher volume than the average volume that the markets experience. As such, increasing quotes may have little effect. To distinguish between these possibilities, we examine whether cancellation latency increases with an increase in quote volume.

H2: We predict that cancellation latency increases as the aggregate market quote volume increases. Thus, the coefficient should be positive on overall market load (LOAD).

H3: We predict that cancellation latency increases as the stock specific trading activity increases. Thus, the coefficient should be positive on the cancellation-to-quote ratio (CTQ) and the trades-to-quote ratio (TRTQ).

Rosu (2009) conjectures that impatient traders submit market orders, while patient traders submit limit orders except when the markets are highly liquid. When the market is not liquid, new limit orders are primarily placed inside the bid-ask spread. When the market is very liquid, the nonexecution risk of limit orders is higher making traders impatient resulting in more frequent revisions of quotes to improve the execution probability (Jain, 2015; Jain, Jain, and McInish, 2016) or the cancellation of partially filled quotes (Goldstein et al., 2008). Thus, we should observe an increase in latency during liquid markets due to a significant increase in trading activity in the form of quote revisions. We test the following hypothesis:

H4: Higher liquidity results in higher cancellation latency. Our liquidity variable is relative spread. A decrease in relative spread implies an increase in liquidity. Thus, we predict a negative coefficient for relative spread (RSPRD) with respect to cancellation latency.

To test these first three hypotheses, we run the following regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

The dependent variable is cancellation latency or the TTC. We pool across time and each cancellation order for stock j during the one-minute time interval t. The regression includes three sets of control variables for each stocky and minute t. The first set is market characteristic variables including total market activity (i.e., trade, quote, cancellation, and revision orders) aggregated across all stocks for the one-minute interval for which the cancellation order occurred (LOAD), the average trade size (ATS), the relative spread (RSPRD), and price volatility (VAR). The second set is the standard firm risk characteristic variables consisting of the size of the firm (MV) and the market-to-book value of the firm (MTBV). The third set is the quote-dependent variables including the percentage of cancellations to quotes (CTQ), the percentage of trades to quotes (TRTQ), the total number of quotes (NQ), and the order imbalance (OIM). These variables are calculated at one-minute intervals and standardized by subtracting the mean and dividing by the standard deviation. This allows us to compare the relative importance of each variable in describing cancellation latency. The coefficients can be interpreted as the number of standard deviation changes in the cancellation latency for a one standard deviation change in the independent variable.

For the market characteristic variables, Model 1 of Table V indicates a positive and statistically significant standardized coefficient of 0.0703 for LOAD, which indicates that a one standard deviation increase in LOAD increases TTC by 0.0703 standard deviations. This suggests that when the market is experiencing excessive trading, cancellation latency (TTC) increases. This finding supports Hypothesis 2. This result is robust across the different model specifications (Models 2-4). We also find a significant and negative coefficient on ATS and RSPRD. Thus, when the average trade size or the relative spread is larger, cancellation latency tends to be shorter. This result is consistent with the conjecture that liquid markets make investors impatient resulting in more quote revisions leading to higher TTC. The positive relationship between liquidity and cancellation latency supports Hypothesis 4.

Figure 2 graphically demonstrates that as the load on the market increases, the cancellation latency also increases. At first the increase is linear, but when LOAD approaches 7,000, there is a structural break and TTC jumps to a new trade congested regime. Recent literature on HFT argues that the HFTs "stuff" the various trading gateways to derive a comparative trading advantage (Gai et al., 2012; Egginton, Van Ness, and Van Ness, 2014). However, our results find that this market congestion phenomenon exists even in the absence of HFTs.

The negative relation between ATS and TTC in Table V documents the bias against small orders. Figure 3 graphically illustrates the unusually high TTC that occurs for very small order sizes. In a low HFT environment, most of the small orders are placed by retail investors. One possible explanation is that the typical input medium used by small trades is different than that used by large trades. In Korea, a high percentage of individual trades are entered employing the HTS. The HTS order input medium has the highest cancellation latency among all input medium options as reported in Table III, Panel B. On the other hand, large orders, which are generally initiated by institutional investors, are routed through WTs that have the lowest cancellation latency. An alternative explanation, consistent with our previous findings, is that there are many more small trades compared to large trades. This leads to cancellation order congestion given that search complexity increases exponentially with the number of orders to be searched. Again, our cancellation data are unique, but it does not allow us to differentiate between these two possible explanations. In Table V, we find a positive relation between the one-minute stock-specific variance ( VAR) and TTC. The positive coefficient on VAR suggests that when markets are volatile, traders revise their quotes more frequently resulting in higher TTC. (13)

Firm characteristics are also related to TTC. Both larger firms and higher market-to-book firms, on average, tend to have smaller cancellation latency when compared to their smaller and lower book-to-market counterparts.

The negative coefficient on MV indicates the existence of a cancellation latency bias against small-cap stocks. Cancellations in large-cap stocks are executed more quickly compared to cancellations in small-cap stocks. Given that the trade volume for large stocks is greater than that for small stocks, this size-bias against small stocks is an anomaly. One possibility could be due to a clientele effect. The KRX has a tiered listing fee structure. That is, the listing fee increases with the size of the firm (see the Appendix). As such, a large-cap firm that pays a higher listing fee is provided a higher level of technological service, which could lead to lower cancellation latency in spite of the larger volume. We cannot confirm this given the limitations of our data, but this is an interesting open anomaly concerning firm size and cancellation latency.

[FIGURE 2 OMITTED]

The quote-dependent variables are all statistically significant. In all cases, the coefficient is positive indicating that when cancellations or trades are a higher proportion of the total quotes, TTC increases. It is intuitive that the greater the number of quotes in the system, the longer the time to cancel. Finally, if order imbalance is larger, then cancellation latency is longer. This last result is also intuitive. Larger OIM implies that the market is more lopsided (i.e., either too many buy or sell orders). Thus, one side of orders will execute quickly eliminating the chance to cancel, while the other side builds up increasing the search costs. The positive coefficients on CTQ and TRTQ support Hypothesis 3. It should be noted that the coefficients for CTQ and TRTQ are smaller than the coefficient for LOAD, suggesting that while an increase in stock-specific trading activity can increase TTC, market-wide trading activity is a more important driver of market congestion.

B. Program Trade--Cancellation Latency Regressions

In this section, we carefully consider the effects of program trading on cancellation latency. Program traders hunt for temporary inefficiencies in the market and trade as quickly as possible to make money before the temporary mispricing disappears. The distinguishing characteristics of program trading strategies include a dependence on low latency trading platforms and the reliance on multiple asset classes and exchanges (Iati, 2009). The literature analyzing US markets has established that low latency of trading is very important to the mere survival of program traders as higher trading speed can create profit opportunities by enabling a prompt response to news or market activity (Hasbrouck and Saar, 2013). We extend this literature in a newer direction by presenting the first test of the following hypothesis:

H5: Program traders on KRX enjoy lower cancellation latency than nonprogram traders.

We define a new variable (PROG) as the proportion of orders that are from program trades calculated for each minute of trading. We then explore the effect of program trade orders on cancellation time and consider the potential interactive effects between PROG and the other explanatory variables. We run the following pooled regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Our results are presented in Table VI. In the following discussion, we will concentrate on the full model (Model 4). Overall, an increase in program trading is associated with lower cancellation latency in support of Hypothesis 5. This is evident by the negative and significant coefficient (-0.0507) on PROG. The overall signs and significance of the remaining variables agree with those reported in Table V. The main differences are that ATS and RSPRD have insignificant coefficients, while OIM has a significant coefficient.

The new results in Table VI are the cross-product terms. When there is a higher proportion of program trading in the market, we find that the negative impact on cancellation latency due to ATS, CTQ, and TTQ is reduced. Since we learned in Table III that program trades, on average, have a smaller TTC, then it is intuitive that if the average trade size increases due to a higher proportion of program trades, then TTC should decrease. The effect of higher cancellation orders per total quotes still has a negative overall effect (0.0142 = 0.0211-0.0069) on TTC; however, the effect is less severe when trades contain a higher percentage of program trades. Interestingly, higher LOAD, NQ, or OIM mitigates the lower latency advantage of program trades. That is, the coefficients on the associated cross products are positive. This cancellation latency advantage can even be reversed for large overall market loads as the cross term on LOAD is 0.1289, which is larger in magnitude than the coefficient on PROG (-0.0507).

C. Institutional Trade--Cancellation Latency Regressions

In the previous section, we explored the effects of program trading on cancellation latency. Program trading is likely dominated by institutions; however, program trades may not predominate institutional trades. Institutions are broadly defined to include banks (both national and commercial), insurance companies, funds, and investment firms. In this section, we consider the relationship between institutional trading and cancellation latency.

Institution traders are usually considered more astute than individual traders. Certainly, institutions have more resources and better contacts. They implement more sophisticated technology and do so more quickly than individuals. Better access and resources can give institutions a trading advantage. Therefore, we test the following hypotheses:

H6: Institutional traders on the KRX enjoy lower cancellation latency than individual traders.

We define a new variable (INST) as the proportion of orders that are from institutional trades. For every minute of trading, we explore the effect of institutional trade orders on cancellation time. We consider the potential interactive effects between INST and the other explanatory variables. We run the following pooled regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

Our results are presented in Table VII. In the following discussion, we again concentrate on the full model (Model 4). As one might expect, an increase in the proportion of institutional trading reduces the cancellation latency. This is evident by the negative and significant coefficient (-0.0107) on INST, which supports Hypothesis 6. Likely as intuitive, the effect for INST is considerably less than that for PROG, which was -0.0507. Given the broad definition for INST, this is intuitive as many institutions are not primarily trading institutions and, as such, will not heavily engage in program trading. The overall signs and significance of the explanatory variables mostly agree with those reported in Table V. The positive sign and significance of OIM are consistent with that reported in Table VI.

The results in Table VII indicate that few cross-product terms interact with the more broadly defined INST variable. Only three cross terms are significant: CTQ, NQ, and OIM. The coefficients on all three are positive. As CTQ, NQ, and OIM increase, the reduction on cancellation latency due to increased institutional trading is reduced. Thus, as markets become more active (increasing CTQ or NQ) or less balanced (increasing OIM), the advantage institutional trades have in cancellation is reduced.

D. Foreign Traders--Cancellation Latency Regressions

The effect on foreign traders on local emerging market characteristics, like cancellation latency, is not well documented. Thus, in this section, we consider the effects of foreign trading on cancellation latency.

Since the liberalization of the Korean stock market in the 1990s, active participation by foreign investors has grown significantly on the KRX. In 2007, over one-third of the market capitalization on KRX was held by foreign investors (Kho, 2011). The increase in foreign investment flows to emerging markets is often considered beneficial as they provide additional capital and lower the cost of capital for emerging markets leading to the economic growth of the emerging market (Bekaert and Harvey, 1997, 2000; Henry, 2000). Seasholes (2000), Agudelo (2010), and Chan and Hameed (2006) argue that foreign institutions are better informed than locals concerning macrovariables and, as such, an increase in trading by foreign investors reduces the informational asymmetry resulting in more efficient capital markets. Finally, Huang and Shiu (2005) and Richards (2005) find that an increase in trading by foreign traders (more specifically foreign buying) is considered as a positive signal that attracts local uninformed investors and/or liquidity providers thereby improving the trading activity and liquidity of the stock markets. Thus, the presence of foreign investors on the KRX should be beneficial not only to the capital markets, but also to the broader economy. We argue that in order to attract foreign investors to the KRX, the exchange may provide better trading infrastructure to these traders that would reduce the cancellation latency for this group. Another possibility is that these more sophisticated foreign traders may have access to better technology. We are among the first to test the following hypotheses:

H7: Foreign traders on the KRX enjoy lower cancellation latency than domestic traders.

We define a new variable (FOR) as the proportion of orders that are from foreign trades. We explore the effect of the proportion of foreign trade orders on cancellation time and consider the potential interactive effects between FOR and the other explanatory variables. We run the following pooled regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Our analysis is presented in Table VIII. We will again concentrate on the full model (Model 4). In contradiction to Hypothesis 7, our results indicate that an increase in the proportion of foreign trading increases cancellation latency. This follows since there is a positive and significant coefficient (0.0240) on FOR. Evidently, foreign traders either suffer from a distance penalty or a large percentage of foreign trade is by individuals who do not have access to the fastest technology in Korea. The signs and significance of the explanatory variables agree with those reported in Table V.

Only three cross terms with FOR are significant: LOAD, MV, and NQ. The coefficients on all three are negative. As LOAD, MV, and NQ increase, the increase in cancellation latency due to increased foreign trading activity is reduced. Thus, as markets become more active (increasing LOAD or NQ) or the size of the firm increases (increasing MV), the disadvantage foreign traders have in cancellation is reduced.

E. First Half Hour of Trading--Cancellation Latency Regressions

In this section, we explore how cancellation latency may differ in the first half hour of trading compared to the rest of the trading day. This is an important consideration as it is well known that the first half hour of trading tends to be considerably more active than the rest of the trading day. We find that cancellation latency increases with trading activity (and several other variables). Thus, we control for both the level effects and the interaction effects of these variables to derive a pure first-half-hour effect. We test the following hypothesis:

H8: Cancellation latency is higher in the first half hour of trading.

We define a new dummy variable (FHH) that is equal to one if the trade occurs in the first half hour of trade, and zero otherwise. Again, we consider the potential interactive effects between FFH and the other explanatory variables. We run the following pooled regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

Our results are presented in Table IX. We once again concentrate on the full model (Model 4). Cancellation latency is higher in the first half hour of trading given the positive and significant coefficient (0.0867) on FFH. Thus, the data support Hypothesis 8. A positive and significant coefficient of 0.1186 for FHH(*)LOAD suggests that as trading activity (LOAD) increases, cancellation latency during first half hour of trading also increases. As market quality deceases, e.g., an increase in relative spread or market volatility (RSRD and VAR, respectively), the TTC in FFH increases correspondingly (i.e., cross-term coefficients are 0.0014 and 0.0125, respectively). The effect of FFH is less for larger firms and larger market-to book firms, i.e., the cross-term coefficients are -0.0033 and -0.0014, respectively. This is consistent with the exchange providing more resources for larger firms that pay higher exchange fees. In addition, the effect of FFH is less when there are a higher proportion of trades to quotes listed. This last result is intuitive as an outstanding quote would, on average, have less chance to cancel in an active market. As such, only the faster cancellations will be recorded.

IV. Qualitative Properties of Cancellation Latency

In this section, we graphically analyze cancellations and demonstrate some regularities in its distribution.

A. The Distribution for Cancellation Latency

It is interesting to examine the probability distribution of cancellation latency across various market characteristics. A particularly interesting variable to examine is the overall market load that includes the total trades, quotes, cancellations, and revisions aggregated over all stocks. There have been many recent research papers that explore the effects of HFT. However, to our knowledge, no paper establishes the base trading characteristics that a market may exhibit even in the absence of HFT. Our results in the next few sections can be seen as contributions along this line.

In Figure 4, we use the one-minute intervals with the highest and lowest 5% market load. We provide the probability distribution for the cancellation ratio for the whole trading day (Panels a and b). We find that there is a dramatic increase in cancellation latency when the market experiences a high market load (9.56 seconds) as compared to when it experiences a low market load (1.67 seconds). This is true for all time subperiods. Thus, we find that the overall market load is an important factor to control for when considering latency.

B. Proximity to Best Bid-Ask

In this section, we explore the relationship of cancellation latency to the distance the order is from the best bid or ask (i.e., to how far the order is from the best bid or best ask). Our main variable is tick defined as the difference in the order price and the best quote (either bid for a buy order or ask for a sell order). This allows us to visualize whether quotes close to the best bid or ask have higher or lower cancellation latency than quotes further out in the limit order book. This is an intrinsically interesting exercise as a cancellation order would have much higher urgency if it were close to being executed than if it were far from the trading activity. We explore whether the cancellation latency risk increases or decreases with respect to a trader's urgency to cancel. The answer is not immediately obvious and, to our knowledge, has yet to be documented in the literature. If an exchange is sensitive to traders' needs, the exchange may prioritize a cancellation according to its proximity to the best bid or ask. Alternatively, order congestion may increase latency near the best quotes due to high trading activity. Finally, there may be no difference if all of the orders are treated similarly regardless of trade location or activity.

Figure 5 demonstrates a high and severe cancellation latency risk for traders with the highest urgency to cancel. In high-load market conditions (Panels a, c, and e), we find that cancellation latency closer to the best bid-ask quote is systematically higher than cancellations far from the best quotes. In low-load market conditions (Panels b, d, and f), the tick effect is barely noticeable, although some effect is still visible in the first half hour of trading. The other noticeable point is seen by comparing the first half hour of trading with the rest of the day (Panels c and e). This load-tick effect is most prevalent during high-load open trading periods. Outside the first half hour, the load-tick effect still exists; however, it is mitigated in magnitude. Thus, cancellation latency risk is important and this importance increases precisely when a trader would be most anxious to trade (i.e., if his order is close to being executed).

C. Round-Lot Bias

Figure 6 presents the cancellation latency for different order sizes. Interestingly, we find that cancellation latency is much higher for round-lots than for odd-lots. This goes against common intuition. Panel a indicates that the orders with sizes in multiples of 10 have higher cancellation latency than the orders with sizes that are not divisible by 10. Panels c and d confirm that this odd-lot bias is even stronger for large order sizes. For example, in Panel d, an order size of 1,000 can take as much as 90 seconds to post, while an order size of 999 takes less than a few seconds. The role of odd-lots in modern markets has been of limited importance. Beginning in 1976, the NYSE formally allowed trading by specialists in odd-lots, but required that odd-lots be handled via a separate odd-lot trading system. The rationale for this separate system was to afford customers "... an inexpensive and efficient order execution system compatible with the traditional odd-lot investing practices of small, retail customers." (14) Traditionally, odd-lots have been used by academic researchers as a proxy for identifying uninformed traders (Rozeff, 1985; Francis, 1986; Ritter, 1988; Lakonishok and Maberly, 1990; Dyl and Maberly, 1992). According to this view, odd-lots are primarily used by unsophisticated investors. Thus, one might suggest that cancellation latency for these trades will be lower compared to round-lot trades. However, O'Hara, Yao, and Ye (2012) recently document the use of odd-lots by HFT. Since HFT firms are technologically sophisticated, we would expect the cancellation latency of odd-lot trades to be lower than that for round-lot trades. Our evidence suggests that a sophisticated trader could reduce cancellation latency risk by utilizing odd-lot trades.

V. Discussion and Conclusions

Cancellations are an integral part of the trading environment, but have received little attention by academics until recently. Additionally, high-frequency trading (HFT) has been blamed for a significant increase in superficial order flow. The speed with which the quotes are posted and cancelled has been criticized by market participants as it creates a false sense of deep liquidity supply for a stock. Regulators around the world are proposing regulations to curb HFT activities. (15) However, data are not readily obtainable, so that even simple summary statistics for the order cancellation latency are not available. Additionally, we do not know whether market congestion is truly an HFT phenomenon. Without these empirical facts on basic trading characteristics, such as cancellation latency, it is difficult to understand the potential impact of HFT or how to regulate it. This paper attempts to fill this gap in the literature and provide several statistics concerning cancellation latency.

[FIGURE 6 OMITTED]

Using high-frequency order cancellation data from the KRX, we demonstrate that cancellation latency is an important market characteristic that contains information regarding future market quality. Lagged cancellation latency changes contain useful information for future market spreads.

Additionally, we find that cancellation latency depends upon market load (total trading activity in terms of the total number of trades, quote placement, revisions, and cancellations). The more active the market, the larger is the cancellation latency. We present evidence of market congestion during the pre-HFT era. We also find that cancellation latency depends upon individual stockspecific trade characteristics, such as the stock specific cancellation ratio, the trade ratio, the average trade size, volatility, and liquidity. We confirm that foreign traders, when compared to domestic traders, experience larger cancellation latency, while institutional investors enjoy lower cancellation latency when compared to individual investors.

We also document that cancellation latency varies as to how far an order is placed from the best quotes. We find that the largest latencies occur for orders in the vicinity of the best quotes. This finding raises concern about the literature that suggests that HFTs are placing similar orders across different trading venues and, once an order is executed at one trading venue, all other parallel orders are canceled. However, we find that this may be difficult to execute as cancellation latency is highest near the best quotes, subjecting aggressive quotes to cancellation latency risk. That is, if the HFTs are placing aggressive limit orders, this increases the risk of execution due to higher cancellation latency for such orders. Additionally, our results that orders placed away from the tick have the lowest cancellation latency provide supporting evidence to the prediction that "quote-stuffing" can increase the market load by quickly submitting and canceling orders. However, this activity would strategically take place away from the best quote, as the cancellation latency (i.e., risk of execution) for these orders is the lowest.

In addition, we find that cancellation latency has a U-shaped intraday pattern. However, cancellation latency during the first 10 minutes of trading is orders of magnitude larger than those for the remainder of the trade day.

Our results also document that odd-lots (orders with order sizes that are not divisible by 10) have significantly lower cancellation latency than round-lots. This result supports the HFT behavior of submitting smaller, but frequent odd-lot orders. Finally, we also show that small-cap stocks have significantly larger cancellation latency than large-cap stocks suggesting that large-cap stocks are more prone to quote stuffing.

With the advancement of technology and the establishment of global trading venues, the market place is becoming much more complex. This study is a part of a growing literature that improves our understanding of these complex intertwined systems. Since cancellation orders are an important part of the trade environment, it is important to examine how cancellations are used and the characteristics of cancellation latency. As such, this paper is a first attempt at establishing some base empirical facts concerning cancellation latency.

Appendix: KRX Initial Listing Fees

In this appendix, we provide the listing fees for the different firm size categories for firms listed on the KRX. Stock listings include "... other types of stocks, but excluding collective investment securities." Foreign stock listings include "... foreign stocks, DRs of foreign stocks, and all other types of foreign stocks." This information was collected from: https://eng.krx.co.kr/m7/m7_1/m7_1_1/JHPENG07001_01.jsp

Capital Stocks to be listed (in billion KRW) Listing fees formula (KRW) [less than or equal to]20 KRW 1,200,000 >20and [less than or equal to]50 1,200,000 + 40,000 per 1 billion for the listing amount in excess of KRW 20 billion >50 and [less than or equal to]100 2,400,000 + 30,000 per 1 billion for the listing amount in excess of KRW 50 billion > 100 and [less than or equal to] 200 3,900,000 + 15,000 per 1 billion for the listing amount in excess of KRW 100 billion >200 and [less than or equal to]500 5,400,000 + 7,000 per 1 billion for the listing amount in excess of KRW 200 billion >500 and [less than or equal to]2,000 7,500,000 + 6,000 per 1 billion for the listing amount in excess of KRW 500 billion >2,000 and [less than or equal to] 16,500,000 + 4,000 per 1 billion 5,000 for the listing amount in excess of KRW 2,000 billion > 5,000 28,500,000 + 2,000 per 1 billion for the listing amount in excess of KRW 5,000 billion Max Fee KRW 80,000,000 shall be the maximum initial listing fee.

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Pawan Jain and Steven J. Jordan (*)

Pawan Jain would like to thank the College of Business Administration and the Office of Research and Graduate Studies at Central Michigan University for the financial support.

(*) Pawan Jain is an Assistant Professor in the College of Business at the University of Wyoming in Laramie, WY. Steven J. Jordan is an Associate Professor at Alfaisal University in Riyadh, Saudi Arabia.

(1) http://www.sec.gov/marketstructure/researchyhighlight-2013-01.html\#.VrDUaZeiiSq

(2) Van Kervel (2012) suggests that high-frequency trade submits duplicate limit orders on several trading venues and, after the execution of one limit order, they quickly cancel all of their outstanding orders on other venues. This high-frequency trade behavior may create selection bias for studies using the data from one market center (e.g., Nasdaq ITCH data).

(3) The literature argues that looking at the top of the book is not sufficient. Rosu (2009), Aitken et al. (2007), and theoretically Goettler, Parlour, and Rajan (2005) document that critical trading activity is occurring beyond the best quotes. We add to this literature by documenting that this is likely also true for quote sniffers.

(4) Market participants criticize the quick cancellation of limit orders as it creates a false sense of the true supply and demand for a stock and may adversely impact market quality (Egginton, Van Ness, and Van Ness, 2014). Regulators classify this stuffing activity as a type of market manipulation. The Dodd-Frank Act, Section 747 specifically prohibits "...bidding or offering with the intent to cancel the bid and offer before execution."

(5) Unfilled or partially filled orders during the open-price auction are posted to the continuous-trading session unless the order is canceled, revised, or a fill-or-kill.

(6) Prior to May 19, 2000, KRX held two trading sessions: a morning session (from 9:00-12:00) and an afternoon session (from 13:00-15:00).

(7) Short sales were banned in an experiment by KRX from October 1, 2008 to May 31, 2009.

(8) Another advantage of our Korean data is that the first hedge funds in Korea started in December 23, 2011. Thus, the existence of hedge funds cannot account for any of our findings.

(9) Examples of events that change the number of shares outstanding include stock dividends, splits, and right offerings.

(10) For the opening and closing single-price batch auctions, the three best bid and ask prices and quantities at each quote are disseminated.

(11) The last month of availability for the detailed Korean data is January 2007.

(12) McInish and Wood (1992) find that the first half hour is different in that it has higher volatility, higher liquidity, and higher trading volume. They document U-shapes in all of these variables intraday. Our results confirm their results, but we note that the U-shape is asymmetric with a higher tail in the first half hour when compared to the end-of-day trading.

(13) Goldstein and Kavajecz (2004) find that during extreme volatile market conditions, the number of cancellations increases.

(14) See NYSE (2007) "Odd-lot Order Requirements," Information Memo 07-60. In July 2010, the NYSE decommissioned its separate odd lot trading system, but the Security Exchange Commission reaffirmed its policy that odd-lot trades would not be reported to the consolidated tape. Since 25% of trades by HFT are odd-lots (O'Hara et al., 2012), drawing conclusions regarding any HFT research using the TAQ data is questionable.

(15) The US Securities and Exchange Commission is considering a cutoff value for minimal quote life, while Germany and France have already levied a tax on HFT.

Table I. Summary Statistics In this table, we provide summary statistics for various characteristics of our data for January 2006. TTC is time to cancel (order placement time minus order post time), CTQ is the cancellations-to-quotes ratio, NC is the number of cancellations, TRTQ is the trades-to-quote ratio, NT is the number of trades, ATS is the average trade size, NQ is the number of quotes, RET is return, VAR is the volatility, RSPRD is the relative spread, and MV is the market capitalization. All of the variables are given on a per stock basis. Mean is the one minute mean over the sample period and SD is the one minute standard deviation. P25 and P75 are the 25th and 75th percentiles for each one minute observation. We report the summary statistics for the full sample and for two subperiods: for the first half hour (9:00-9:30) and the ex first half hour (9:30-14:50) of the trading day, respectively. Full Trading Day Variable Mean SD P25 P75 TTC 3.67 3.86 2.08 4.17 CTQ 0.30 0.27 0.12 0.39 NC 2.78 5.25 1.00 3.00 TRTQ 0.39 0.55 0.00 0.58 NT 9.05 24.48 0.00 9.00 ATS 292.00 1,132.00 0.00 283.00 NQ 17.82 34.95 4.00 19.00 RET 0.00 0.02 0.00 0.00 ATV 4,842.00 32,215.00 0.00 2,260.00 MV 2,000.00 7,114.00 63.00 1,361.00 VAR 0.00 0.00 0.00 0.00 RSPRD 0.01 0.08 0.00 0.01 First Half Hour Trades Variable Mean SD P25 P75 TTC 8.65 9.10 4.55 8.39 CTQ 0.24 0.23 0.09 0.29 NC 3.52 8.55 1.00 3.00 TRTQ 14.16 41.55 0.00 13.00 NT 0.41 0.97 0.00 0.54 ATS 318.00 1784.00 0.00 313.00 NQ 28.24 56.29 5.00 28.00 RET 0.00 0.02 0.00 0.00 ATV 8,159.00 50,894.00 0.00 3,620.00 MV 1,805.00 6,655.00 57.00 1,154.00 VAR 0.00 0.00 0.00 0.00 RSPRD 0.01 0.05 0.00 0.01 Ex First Half Hour Trades Variable Mean SD P25 P75 TTC 3.07 1.84 2.00 3.73 CTQ 0.31 0.27 0.13 0.40 NC 2.69 4.69 1.00 3.00 TRTQ 8.44 21.45 0.00 9.00 NT 0.39 0.48 0.00 0.58 ATS 288.00 1,025.00 0.00 280.00 NQ 16.56 31.19 4.00 18.00 RET 0.00 0.02 0.00 0.00 ATV 4,443.00 29,149.00 0.00 2,140.00 MV 2,024.00 7,167.00 63.00 1,451.00 VAR 0.00 0.00 0.00 0.00 RSPRD 0.01 0.08 0.00 0.01 Table II. Summary Statistics by Characteristics by Size Quintiles In this table, we provide summary statistics for various characteristics of our data for January 2006 for five size-based portfolios. Each panel describes a variable defined in the panel heading. All of the variables are given on a per stock basis. Mean is the one minute average over the sample period and SD is the one minute standard deviation. P25 and P75 are the 25th and 75th percentiles for each one minute observation. The full trading day columns provide summary statistics for the full sample. The columns under first half hour provide the summary statistics for 9:00-9:30 and those under ex first half hour present the summary statistics for 9:30-14:50, respectively. Full Trading Day First Half Hour Mean SD P25 P75 Mean SD P25 P75 Panel A. Cancellation-to-Quotes Ratio 1 0.19 0.17 0.09 0.22 0.14 0.14 0.07 0.17 2 0.34 0.27 0.15 0.50 0.27 0.23 0.12 0.33 3 0.41 0.30 0.18 0.50 0.31 0.26 0.13 0.40 4 0.43 0.30 0.20 0.50 0.32 0.25 0.14 0.40 5 0.59 0.33 0.33 1.00 0.47 0.31 0.20 0.67 Panel B. Number of Cancellations 1 3.42 5.74 1.00 4.00 4.48 7.89 1.00 5.00 2 2.79 5.83 1.00 2.00 3.46 8.39 1.00 3.00 3 1.89 5.17 1.00 2.00 2.48 14.08 1.00 2.00 4 1.91 2.88 1.00 2.00 2.34 4.92 1.00 2.00 5 1.57 1.60 1.00 2.00 1.82 2.47 1.00 2.00 Panel C. Trades-to-Quotes Ratio 1 0.48 0.53 0.20 0.66 0.49 0.94 0.19 0.59 2 0.36 0.62 0.00 0.53 0.40 1.26 0.00 0.50 3 0.32 0.54 0.00 0.50 0.35 0.76 0.00 0.50 4 0.29 0.50 0.00 0.50 0.34 0.77 0.00 0.50 5 0.17 0.46 0.00 0.21 0.23 0.87 0.00 0.29 Panel D. Number of Trades 1 14.07 29.79 2.00 15.00 22.69 50.92 3.00 23.00 2 7.18 24.47 0.00 6.00 10.81 39.58 0.00 8.00 3 3.58 11.89 0.00 4.00 6.04 26.58 0.00 6.00 4 3.24 10.97 0.00 3.00 5.65 23.52 0.00 5.00 5 1.37 4.67 0.00 1.00 2.41 7.73 0.00 2.00 Panel E. Cancellation Latency (TTC) 1 3.48 3.62 2.03 3.95 8.11 8.78 4.31 7.67 2 3.76 3.97 2.11 4.26 8.91 9.32 4.71 8.67 3 3.86 4.05 2.13 4.41 9.04 9.26 4.76 8.98 4 3.86 4.05 2.12 4.42 9.13 9.24 4.85 9.03 5 3.98 4.26 2.15 4.56 9.64 9.67 5.11 9.66 Panel F. Relative Spreads 1 0.00 0.04 0.00 0.00 0.00 0.01 0.00 0.00 2 0.01 0.10 0.00 0.01 0.01 0.06 0.00 0.01 3 0.02 0.12 0.00 0.01 0.02 0.07 0.00 0.02 4 0.01 0.09 0.00 0.01 0.01 0.02 0.01 0.02 5 0.03 0.13 0.01 0.03 0.04 0.13 0.01 0.04 Ex First Half Hour Mean SD P25 P75 1 0.19 0.17 0.09 0.23 2 0.35 0.27 0.16 0.50 3 0.43 0.30 0.20 0.50 4 0.45 0.30 0.20 0.50 5 0.61 0.33 0.33 1.00 1 3.30 5.43 1.00 3.00 2 2.71 5.43 1.00 2.00 3 1.82 2.13 1.00 2.00 4 1.85 2.50 1.00 2.00 5 1.54 1.45 1.00 2.00 1 0.48 0.46 0.20 0.67 2 0.36 0.48 0.00 0.54 3 0.31 0.50 0.00 0.50 4 0.29 0.46 0.00 0.50 5 0.16 0.38 0.00 0.20 1 13.09 26.16 2.00 14.00 2 6.74 21.87 0.00 6.00 3 3.27 8.23 0.00 4.00 4 2.93 8.01 0.00 3.00 5 1.24 4.10 0.00 1.00 1 2.95 1.78 1.96 3.58 2 3.12 1.85 2.03 3.79 3 3.19 1.89 2.05 3.90 4 3.19 1.90 2.03 3.91 5 3.25 1.94 2.06 4.01 1 0.00 0.04 0.00 0.00 2 0.01 0.10 0.00 0.01 3 0.02 0.12 0.00 0.01 4 0.01 0.09 0.00 0.01 5 0.03 0.13 0.01 0.03 Table III. Cancellation Latency by Category In this table, we provide summary statistics for cancellation latency (TTC) for January 2006 across various order characteristics. Panel A summarizes TTC based on a "Program Trade Indicator," which is divided into three subcategories of orders: (1) normal or nonprogram trade (NPT), (2) index arbitrage (IA), or (3) nonindex arbitrage (NIA). Panel B summarizes TTC based on "Order Input Media," which is divided into five subcategories: (1) orders entered via broker branch terminal (BT), (2) wired terminal (WT), (3) wireless terminal (WLT), (4) home trading system (HTS), or (5) other, etc. Panel C summarizes TTC based on "Time of Day." Panel D summarizes TTC based on "Trader Nationality," which is divided into two subcategories: (1) Korean (KOR) and (2) not Korean (NOT). Panel E summarizes TTC based on "Location of Trader," which is divided into two subcategories: (1) inside Korea (InK) and (2) outside Korea (OutK). Panel F summarizes TTC based on "Investor Type," which is divided into 10 subcategories: (1) securities companies (Sec), (2) insurance companies (Ins), (3) investments companies (Inv), (4) banks (Bank), (5) merchants (Mer), (6) mutual funds (Fund), (7) country funds (Nat), (8) individuals (Ind), (9) foreigners (For), and (10) other (other). All of the variables are given on a per stock basis. Mean is the one minute average over the sample period and SD is the one minute standard deviation. P25 and P75 are the 25th and 75th percentiles for each one minute observation. The first set of columns provides summary statistics for the full sample, while the second and third sets provide summary statistics for first half hour and ex first half hour of the trading day, respectively. Full Trading Day First Half Hour Mean SD P25 P75 Mean SD P25 P75 Panel A. Program Trade Indicator NPT 4.03 7.55 1.66 3.76 11.61 16.29 3.83 10.03 IA 3.56 1.73 2.22 4.38 5.18 2.04 3.56 6.31 NIA 3.69 5.74 1.62 3.93 10.04 13.59 3.61 8.94 Panel B. Order Input Medium BT 3.57 4.77 1.58 3.88 8.19 9.99 3.77 8.22 WT 2.98 3.83 1.56 3.21 7.15 8.62 3.06 7.79 WLT 3.50 5.15 1.68 3.69 9.12 11.37 3.89 8.36 HTS 4.12 8.05 1.67 3.71 12.19 17.10 3.82 10.48 etc 4.77 3.51 2.42 6.04 8.42 3.98 5.62 10.56 Panel C. Time of Day 9:00 8.61 13.52 2.99 7.27 11.58 16.25 3.83 10.00 10:00 3.30 2.17 1.95 4.09 - - - - 11:00 1.93 1.06 1.27 2.40 - - - - 12:00 1.68 0.85 1.11 2.09 - - - - 13:00 1.93 1.02 1.29 2.41 - - - - 14:00 2.85 1.97 1.92 3.35 - - - - Panel D. Trader Nationality KOR 4.03 7.67 1.65 3.73 11.72 16.45 3.82 10.07 NOT 3.96 3.81 1.93 4.46 7.34 6.88 3.84 8.70 Panel E. Location of Trader (Trade Entered from Korea or Not) InK 4.04 7.54 1.66 3.77 11.59 16.25 3.83 10.01 OutK 2.27 2.36 1.40 2.65 5.89 7.88 2.56 6.00 Panel F. Investor Type Sec 3.02 3.29 1.32 3.75 7.18 6.35 4.13 7.97 Ins 2.63 1.89 1.20 3.23 4.63 3.13 2.53 7.84 Inv 2.98 1.89 1.97 3.58 5.82 4.35 3.51 6.76 Bank 4.96 9.60 1.85 4.15 33.10 22.56 12.12 50.62 Mer 2.27 1.36 1.14 3.36 3.27 0.86 2.30 3.96 Fund 2.92 2.85 1.26 3.54 7.06 8.17 1.79 9.86 Nat 3.11 3.05 1.90 3.41 6.24 7.10 3.27 6.03 Ind 4.11 7.90 1.67 3.72 11.98 16.81 3.81 10.31 For 4.02 4.25 1.93 4.47 7.41 7.17 3.84 8.74 Other 3.75 3.88 1.99 4.42 7.44 6.82 4.49 8.13 Ex First Half Hour Mean SD P25 P75 NPT 2.56 1.77 1.54 3.12 IA 2.99 1.17 2.11 3.83 NIA 2.74 1.90 1.51 3.44 BT 2.89 2.80 1.47 3.37 WT 2.30 1.36 1.45 2.81 WLT 2.50 1.33 1.58 3.14 HTS 2.47 1.40 1.55 3.06 etc 4.16 3.02 2.26 5.11 9:00 3.53 1.85 2.39 4.27 10:00 - - - - 11:00 - - - - 12:00 - - - - 13:00 - - - - 14:00 - - - - KOR 2.50 1.65 1.53 3.08 NOT 3.58 3.06 1.84 4.03 InK 2.57 1.78 1.54 3.13 OutK 2.02 0.84 1.37 2.49 Sec 2.30 1.49 1.22 2.97 Ins 2.51 1.74 1.15 3.08 Inv 2.81 1.47 1.93 3.45 Bank 2.95 1.60 1.76 3.89 Mer 2.13 1.37 1.13 3.01 Fund 2.62 1.67 1.25 3.42 Nat 2.78 1.99 1.88 3.20 Ind 2.51 1.59 1.55 3.07 For 3.63 3.58 1.84 4.03 Other 3.02 2.42 1.87 3.66 Table IV. Liquidity and Cancellation Latency In this table, we provide the results from estimating the following regression model: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where the dependent variable is RSPRD or the relative spread. The independent variable of interest is the lagged time-to-cancel (LagTTC). We follow Stoll (2000) for the choice of the control variables. These include volume (LogVOL), number of trades for every minute of trading (LogNTRDS), stock's market value (LogMV), stock price at the end of every minute (LogPRICE), and price volatility during the one minute trading period (PRIVAR), [epsilon] is the error term. We run the regression with and without hourly time dummies (HR Dummies). The subscripts j and t represent stock j and minute t. This table summarizes the results for the full sample. We run the following models: (Model 1) No control variables, (Model 2) Stoll's control variables, and (Model 3) Stoll's control variables plus hourly time dummies. Adj [R.sup.2] is the adjusted [R.sup.2] for each regression model. Model 1 Model 2 Variable COEF SE COEF SE LagTTC 0.0010 (***) 0.0050 0.0011 (***) 0.0005 LogVOL -0.0103 (***) 0.0011 LogNTRD -0.0031 (***) 0.0001 LogMV -0.0083 (***) 0.0013 LogPRICE -0.0318 (***) 0.0015 PRIVAR 0.0352 (***) 0.0117 Hr Dum Adj [R.sup.2] 0.0041 0.0193 0.0210 Model 3 Variable COEF SE LagTTC 0.0013 (***) 0.0005 LogVOL -0.0542 (***) 0.0058 LogNTRD -0.0068 (***) 0.0013 LogMV -0.0574 (***) 0.0083 LogPRICE -0.0606 (***) 0.0040 PRIVAR 0.0351 (***) 0.0117 Hr Dum YES (***) Adj [R.sup.2] (***) Significant at the 0.01 level. (**) Significant at the 0.05 level. (*) Significant at the 0.10 level. Table V. Cancellation Latency Explanatory Regression--Full Sample In this table, we provide the results from estimating the following regression model: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where the dependent variable is TTC or the time to cancel (order placement time--order post time). The explanatory variables include the sum of the number of trades (LOAD), quotes, cancellations, and revisions, the average trade size (ATS), the relative spreads (RSPRD), the volatility (VAR), the market capitalization (MV), the market-to-book ratio (MTBV), the cancellations-to-quotes ratio (CTQ), the trades-to-quote ratio (TTQ), the number of quotes (NQ), and the net order imbalance (OIM = the bid order volume--the ask order volume, averaged at a one minute frequency). [epsilon] is the error term. The subscripts j and t represent stocky and minute t. This table summarizes the results for the full sample. We run the following models: (Model 1) Market characteristic variables including LOAD, RSPRD, VAR, and ATS; (Model 2) standard risk factor characteristic variables MV and MB; (Model 3) quote characteristics variables CTQ, TRTQ, NQ, and OIM; and (Model 4) the full model with all of the variables. The coefficient (COEF) and standard errors (SE) are provided for each model. Adj [R.sup.2] gives the adjusted [R.sup.2] for each regression model. Model 1 Model 2 Variable COEF SE COEF SE LOAD 0.0703 (***) 0.0015 ATS -0.0033 (***) 0.0006 RSPRD -0.0015 (***) 0.0004 VAR 0.0005 (*) 0.0003 MV -0.0009 (**) 0.0004 MTBV -0.0028 (***) 0.0002 CTQ TTQ NQ OIM Adj [R.sup.2] 0.2152 0.1774 Model 3 Model 4 Variable COEF SE COEF SE LOAD 0.0732 (***) 0.0017 ATS -0.0029 (***) 0.0005 RSPRD -0.0019 (***) 0.0005 VAR 0.0006 (*) 0.0003 MV -0.0019 (***) 0.0005 MTBV -0.0019 (***) 0.0003 CTQ 0.0055 (***) 0.0008 0.0097 (***) 0.0008 TTQ 0.0038 (***) 0.0006 0.0009 (*) 0.0005 NQ 0.0178 (***) 0.0014 0.0061 (***) 0.0015 OIM 0.0030 (***) 0.0005 -0.0003 0.0005 Adj [R.sup.2] 0.2466 0.2466 0.3491 (***) Significant at the 0.01 level. (**) Significant at the 0.05 level. (*) Significant at the 0.10 level. Table VI. Program Trade--Cancellation Latency Regressions In this table, we provide the results from estimating the following regression model: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where the dependent variable is TTC or the time to cancel (order placement time--order post time). PROG is the proportion of orders that are program trades calculated at one minute intervals. VAR represents the list of explanatory i = 1 to N variables that includes the level of total market activity (LOAD = the sum of the number of trades, quotes, cancellations, and revisions), the average trade size (ATS), the relative spreads (RSPRD), the volatility (VAR), the market capitalization (MV), the market-to-book ratio (MTBV), the cancellations-to-quotes ratio (CTQ), the trades-to-quote ratio (TTQ), the number of quotes (NQ), and the net order imbalance (OIM = the bid order volume--the ask order volume, averaged at a one minute frequency). [epsilon] is the error term. The subscripts j and t represent stock j and minute t. This table summarizes the results for the full sample. We run the following models: (Model 1) Market characteristic variables LOAD, RSPRD, VAR, and ATS; (Model 2) Standard risk factor characteristic variables MV and MB; (Model 3) Quote characteristics variables CTQ, TRTQ, NQ, and OIM; and (Model 4) Full model with all of the variables. The coefficient (COEF) and standard errors (SE) are provided for each model. Adj [R.sup.2] gives the adjusted [R.sup.2] for each regression model. Model 1 Model 2 Variable COEF SE COEF SE LOAD 0.0273 (*) 0.0030 ATS 0.0010 0.0014 RSPRD -0.0016 (*) 0.0004 VAR 0.0019 0.0016 MV -0.0063 (**) 0.0049 MTBV -0.0073 (*) 0.0008 CTQ TTQ NQ OIM PROG -0.0448 (*) 0.0039 -0.0546 (*) 0.0041 PROG(*)LOAD 0.0645 (*) 0.0062 PROG(*)ATS -0.0044 (*) 0.0016 PROG(*)RSPRD -0.0001 0.0008 PROG(*) VAR 0.0025 (*) 0.0014 PROG(*)MV -0.0051 (*) 0.0000 PROG(*) MTBV -0.0049 (*) 0.0009 PROG(*) CTQ PROG(*) TTQ PROG(*)NQ PROG(*)OIM Adj [R.sup.2] 0.2305 0.2305 0.1996 0.1996 Model 3 Model 4 Variable COEF SE COEF SE LOAD 0.0350 (*) 0.0086 ATS 0.0011 0.0016 RSPRD -0.0001 0.0015 VAR 0.0022 0.0019 MV -0.0126 (*) 0.0038 MTBV -0.0042 (*) 0.0014 CTQ 0.0296 (*) 0.0031 0.0211 (*) 0.0032 TTQ 0.0111 (*) 0.0031 0.0084 (*) 0.0031 NQ 0.0324 (*) 0.0096 0.0318 (*) 0.0102 OIM 0.0081 (*) 0.0022 0.0046 (**) 0.0023 PROG -0.0132 (*) 0.0021 -0.0507 (*) 0.0056 PROG(*)LOAD 0.1289 (*) 0.0120 PROG(*)ATS -0.0043 (*) 0.0017 PROG(*)RSPRD -0.0014 0.0019 PROG(*) VAR 0.0029 (*) 0.0017 PROG(*)MV -0.0104 (**) 0.0040 PROG(*) MTBV -0.0026 (*) 0.0015 PROG(*) CTQ -0.0183 (*) 0.0022 -0.0069 (*) 0.0023 PROG(*) TTQ -0.0163 (*) 0.0030 -0.0100 (*) 0.0029 PROG(*)NQ 0.0507 (*) 0.0113 0.0370 (*) 0.0120 PROG(*)OIM 0.0115 (*) 0.0021 0.0053 (**) 0.0022 Adj [R.sup.2] 0.2575 0.2575 0.3710 0.3710 (***) Significant at the 0.01 level. (**) Significant at the 0.05 level. (*) Significant at the 0.10 level. Table VII. Institutional Investors--Cancellation Latency Regressions In this table, we provide the results from estimating the following regression model: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where the dependent variable is TTC or the time to cancel (order placement time--order post time). INST is the proportion of orders submitted by institutional investors calculated at one minute intervals. V AR represents the list of explanatory i = 1 to N variables that includes the level of total market activity (LOAD = the sum of the number of trades, quotes, cancellations, and revisions), the average trade size (ATS), the relative spreads (RSPRD), the volatility (VAR), the market capitalization (MV), the market-to-book ratio (MTBV), the cancellations-to-quotes ratio (CTQ), the trades-to-quote ratio (TTQ), the number of quotes (NQ), and the net order imbalance (OIM = the bid order volume - the ask order volume, averaged at a one minute frequency). [epsilon] is the error term. The subscripts j and t represent stock j and minute t. This table summarizes the results for the full sample. We run the following models: (Model 1) Market characteristic variables LOAD, RSPRD, VAR, and ATS; (Model 2) standard risk factor characteristic variables MV and MB; (Model 3) quote characteristics variables CTQ, TRTQ, NQ, and OIM; and (Model 4) full model with all of the variables. The coefficient (COEF) and standard errors (SE) are provided for each model. Adj [R.sup.2] gives the adjusted [R.sup.2] for each regression model. Model 1 Model 2 Variable COEF SE COEF SE LOAD 0.0693 (***) 0.0019 ATS -0.0019 (***) 0.0004 RSPRD -0.0011 (***) 0.0003 VAR 0.0004 (*) 0.0002 MV -0.0028 (***) 0.0000 MTBV -0.0008 (***) 0.0002 CTQ TTQ NQ OIM INST -0.0078 (**) 0.0036 -0.0169 (***) 0.0020 INST(*)LOAD 0.0099 (**) 0.0042 INST(*)ATS -0.0015 (***) 0.0005 INST(*)RSPRD -0.0009 0.0017 INST(*)VAR 0.0020 0.0015 INST(*)MV -0.0071 (***) 0.0000 INST(*)MTBV -0.0067 (***) 0.0015 INST(*)CTQ INST(*)TTQ INST(*)NQ INST(*)OIM Adj [R.sup.2] 0.2194 0.1807 Model 3 Model 4 Variable COEF SE COEF SE LOAD 0.0735 (***) 0.0023 ATS -0.0015 (***) 0.0003 RSPRD -0.0012 (***) 0.0004 VAR 0.0005 (*) 0.0003 MV -0.0013 (*) 0.0007 MTBV -0.0005 (**) 0.0002 CTQ 0.0046 (***) 0.0005 0.0026 (***) 0.0005 TTQ 0.0045 (***) 0.0006 0.0029 (***) 0.0005 NQ 0.0121 (***) 0.0009 0.0007 0.0009 OIM 0.0050 (***) 0.0004 0.0014 (***) 0.0004 INST -0.0210 (***) 0.0035 -0.0107 (**) 0.0059 INST(*)LOAD 0.0044 0.0046 INST(*)ATS -0.0001 0.0004 INST(*)RSPRD -0.0006 0.0021 INST(*)VAR 0.0022 0.0017 INST(*)MV 0.0002 0.0013 INST(*)MTBV -0.0006 0.0013 INST(*)CTQ 0.0301 (***) 0.0035 0.0251 (***) 0.0036 INST(*)TTQ 0.0014 0.0019 0.0023 0.0020 INST(*)NQ 0.0111 (***) 0.0040 0.0111 (***) 0.0042 INST(*)OIM 0.0043 (***) 0.0013 0.0027 (**) 0.0014 Adj [R.sup.2] 0.2684 0.3532 (***) Significant at the 0.01 level. (**) Significant at the 0.05 level. (*) Significant at the 0.10 level. Table VIII. Foreign Traders--Cancellation Latency Regressions In this table, we provide the results from estimating the following regression model: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where the dependent variable is TTC or the time to cancel (order placement time--order post time). FOR is the proportion of orders submitted by foreign traders (non-Korean) calculated for every minute. VAR represents the list of explanatory i = 1 to N variables that includes the level of total market activity (LOAD = the sum of number of trades, quotes, cancellations, and revisions), the average trade size (ATS), the relative spreads (RSPRD), the volatility (VAR), the market capitalization (MV), the market-to-book ratio (MTBV), the cancellations-to-quotes ratio (CTQ), the trades-to-quote ratio (TTQ), number of quotes (NQ), and the net order imbalance (OIM = the bid order volume - the ask order volume, averaged at a one minute frequency). [epsilon] is the error term. The subscripts j and t represent stock j and minute t. This table summarizes the results for the full sample. We run the following models: (Model 1) market characteristic variables LOAD, RSPRD, VAR, and ATS; (Model 2) standard risk factor characteristic variables MV and MB; (Model 3) quote characteristics variables CTQ, TRTQ, NQ, and OIM; and (Model 4) full model with all of the variables. The coefficient (COEF) and standard errors (SE) are provided for each model. Adj [R.sup.2] gives the adjusted [R.sup.2] for each regression model. Model 1 Model 2 Variable COEF SE COEF SE LOAD 0.0734 (***) 0.0018 ATS -0.0031 (***) 0.0006 RSPRD -0.0014 (***) 0.0003 VAR 0.0005 (*) 0.0003 MV -0.0024 (***) 0.0000 MTBV -0.0024 (***) 0.0002 CTQ TTQ NQ OIM FOR 0.0199 (***) 0.0018 0.0022 (**) 0.0009 FOR(*)LOAD -0.0152 (***) 0.0020 FOR(*)ATS 0.0000 0.0000 FOR(*)RSPRD 0.0008 0.0012 FOR(*)VAR 0.0009 0.0008 FOR(*)MV -0.0041 (***) 0.0000 FOR(*)MTBV -0.0022 (***) 0.0006 FOR(*)CTQ FOR(*)TTQ FOR(*)NQ FOR(*)OIM Adj [R.sup.2] 0.2211 0.1815 Model 3 Model 4 Variable COEF SE COEF SE LOAD 0.0770 (***) 0.0020 ATS -0.0026 (***) 0.0005 RSPRD -0.0019 (***) 0.0004 VAR 0.0006 (*) 0.0003 MV -0.0035 (***) 0.0009 MTBV -0.0017 (***) 0.0003 CTQ 0.0033 (***) 0.0008 0.0096 (***) 0.0008 TTQ 0.0041 (***) 0.0005 0.0015 (***) 0.0005 NQ 0.0185 (***) 0.0016 0.0069 (***) 0.0017 OIM 0.0039 (***) 0.0004 -0.0006 0.0004 FOR 0.0057 (***) 0.0013 0.0240 (***) 0.0028 FOR(*)LOAD -0.0176 (***) 0.0023 FOR(*)ATS 0.0003 0.0003 FOR(*)RSPRD 0.0014 0.0015 FOR(*)VAR 0.0009 0.0009 FOR(*)MV -0.0025 (***) 0.0008 FOR(*)MTBV -0.0003 0.0008 FOR(*)CTQ 0.0079 (***) 0.0011 0.0014 0.0011 FOR(*)TTQ 0.0011 (*) 0.0006 0.0012 (*) 0.0007 FOR(*)NQ -0.0035 (***) 0.0008 -0.0041 (***) 0.0009 FOR(*)OIM 0.0022 (***) 0.0007 0.0010 0.0007 Adj [R.sup.2] 0.2501 0.3620 (***) Significant at the 0.01 level. (**) Significant at the 0.05 level. (*) Significant at the 0.10 level. Table IX. First Half Hour of Trading--Cancellation Latency Regressions In this table, we provide the results from estimating the following regression model for the fist half hour of trading (9:30-14:50): [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where the dependent variable is TTC or the time to cancel (order placement time--order post time). FHH is a dummy variable that is equal to one if the trade occurs in the first half hour of trading (9:00-9:30) and zero otherwise. VAR represents the list of explanatory i = 1 to N variables that includes the level of total market activity (LOAD = the sum of the number of trades, quotes, cancellations, and revisions), the average trade size (ATS), the relative spreads (RSPRD), the volatility (VAR), the market capitalization (MV), the market-to-book ratio (MTBV), the cancellations-to-quotes ratio (CTQ), the trades-to-quote ratio (TTQ), the number of quotes (NQ), and the net order imbalance (OIM = the bid order volume - the ask order volume, averaged at a one minute frequency). [epsilon] is the error term. The subscripts j and t represent stocky and minute t. This table summarizes the results for the full sample. We run the following models: (Model 1) market characteristic variables LOAD, RSPRD, VAR, and ATS; (Model 2) standard risk factor characteristic variables MV and MB; (Model 3) quote characteristics variables CTQ, TRTQ, NQ, and OIM; and (Model 4) full model with all of the variables. The coefficient (COEF) and standard errors (SE) are provided for each model. Adj [R.sup.2] gives the adjusted [R.sup.2] for each regression model. Model 1 Model 2 Variable COEF SE COEF SE LOAD 0.0431 (***) 0.0007 ATS -0.0025 (***) 0.0005 RSPRD 0.0000 0.0000 VAR 0.0001 0.0001 MV -0.0006 (*) 0.0003 MTBV -0.0027 (***) 0.0002 CTQ TTQ NQ OIM FHH 0.0764 (***) 0.0089 0.0490 (***) 0.0005 FHH(*)LOAD 0.1070 (***) 0.0098 FHH(*)ATS 0.0024 (**) 0.0012 FHH(*)RSPRD 0.0019 (**) 0.0010 FHH(*)VAR 0.0022 0.0017 FHH(*)MV -0.0008 (**) 0.0000 FHH(*)MTBV -0.0005 0.0005 FHH(*)CTQ FHH(*)TTQ FHH(*)NQ FHH(*)OIM Adj [R.sup.2] 0.2368 0.1895 Model 3 Model 4 Variable COEF SE COEF SE LOAD 0.0426 (***) 0.0009 ATS -0.0017 (***) 0.0004 RSPRD -0.0001 0.0004 VAR 0.0001 (*) 0.0001 MV -0.0025 (***) 0.0004 MTBV -0.0013 (***) 0.0002 CTQ 0.0094 (***) 0.0008 0.0097 (***) 0.0009 TTQ 0.0017 (**) 0.0007 0.0005 0.0007 NQ 0.0050 (***) 0.0003 0.0010 0.0003 OIM -0.0005 0.0005 0.0002 0.0005 FHH 0.0497 (***) 0.0021 0.0867 (***) 0.0100 FHH(*)LOAD 0.1186 (***) 0.0110 FHH(*)ATS 0.0009 0.0010 FHH(*)RSPRD 0.0014 (**) 0.0006 FHH(*)VAR 0.0125 (***) 0.0030 FHH(*)MV -0.0033 (**) 0.0015 FHH(*)MTBV -0.0014 (***) 0.0004 FHH(*)CTQ -0.0041 (***) 0.0012 -0.0020 (*) 0.0011 FHH(*)TTQ -0.0014 (**) 0.0006 -0.0016 (***) 0.0006 FHH(*)NQ -0.0162 (***) 0.0029 -0.0020 (***) 0.0006 FHH(*)OIM 0.0030 (***) 0.0004 0.0025 (*) 0.0014 Adj [R.sup.2] 0.2958 0.4063 (***) Significant at the 0.01 level. (**) Significant at the 0.05 level. (*) Significant at the 0.10 level.

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Author: | Jain, Pawan; Jordan, Steven J. |
---|---|

Publication: | Financial Management |

Article Type: | Report |

Geographic Code: | 9SOUT |

Date: | Jun 22, 2017 |

Words: | 15043 |

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