Intraday Impact Of Price Limits On Mom

The Intraday Impact of Price Limits on Magnet and Momentum Effects Yan Du* Qianqiu Liu* and S. Ghon Rhee**

Current version: April 2006

*All at the College of Business University of Hawai’i at Manoa 2404 Maile Way, C-305 Honolulu, HI 96822-2282, USA **Contact Author Tel No.: (808) 956 2535 Fax No.: (808) 956 2532 e-mail: [email protected]

The Intraday Impact of Price Limits on Magnet and Momentum Effects

Abstract This paper unfolds the intraday impact of price limits on the magnet effect and the momentum effect. Using Korea Stock Exchange’s high frequency trading data and limit order book, we confirm the presence of the magnet effect by demonstrating accelerated trading activities during the 30-minute period prior to limit hits. We introduce quasi limit hits in the Korea Stock Exchange and pseudo limit hits in NASDAQ to distinguish the magnet effect from intraday momentum effect. This paper concludes that the magnet effect is led by the existence of price limits; dictated by the width of price limit band; and is not confined to a particular group of stocks. JEL Classification: G10; G14; G15; G18 Keywords:

Price Limits; Magnet Effect; Momentum Effect; Acceleration; Magnitude; Persistence

The Intraday Impact of Price Limits on Magnet and Momentum Effects 1.

Introduction Price limits set daily ceiling and floor prices of individual stocks, usually stated as a

percentage change from the previous day’s closing price. Market regulators use price limits as a means to curb excessive price movement. Price limits are used in a majority of the Asian and European stock markets, including France, Italy, Australia, China, Japan, Taiwan, etc. Many stock exchanges have adopted multiple price limit rules in search of their benefits. For instance, the Taiwan Stock Exchange used eleven different daily price limits since 1962 with its most recent change from 5% to 7% in 1989; the Stock Exchange of Thailand raised the price limit from 10% to 30% at the end of 1997; the stock markets in China initiated the 10% daily price limit at the end of 1996; the Korea Stock Exchange (KRX) raised its daily price limit from 4.6% to 15% in four phases from 1995 to 1999, and its most recent change was from 12% to 15% on December 7, 1998. The implications of price limits on market liquidity, volatility, and price discovery have drawn much attention from market participants, regulators and academia. Three hypotheses are proposed and documented in earlier studies: delayed price discovery, volatility spillover, and interfered trading [Kim and Rhee (1997), Lee et al. (1994), Kuhn et al. (1991), Fama (1989), Lehmann (1989), and Telser (1989)]. However, most of the early studies on price limits are limited to the analysis of days before and/or after limit hits due to the unavailability of intraday data. As a result, the intraday impact of price limits remains largely unexplored, i.e., the magnet effect, that is also known as the gravitational effect. The concept of the magnet effect is not new to the academia. In fact, it has been quoted many times in earlier research but the discussions remain conjectural due to the lack of empirical evidence. Miller (1991) proposes that circuit breakers could be self-fulfilling if traders rush to avoid

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being locked into their positions when prices come in the range of the trigger point.1 Greenwald and Stein (1991) note that the magnet effect makes circuit breakers vulnerable to criticism in that the very existence of a circuit breaker might cause large declines to feed on themselves and cause the market to crash. Gerety and Mulherin (1992) further point out that the possibility of a trading halt after a price change of a fixed percent would make investors generally nervous and prone to leave the market more quickly compared to a situation where a circuit breaker did not exist. Subrahmanyam (1994) is the first who provides concrete predictions of the magnet effect based on an inter-temporal model of circuit breakers. He proposes that price variability, market liquidity, trading volume, and the probability of the price crossing circuit breaker bounds will increase in the period before the limit hit due to suboptimal order submissions. The same notion is reflected in Subrahmanyam (1995), in which it is noted that discretionary closures, such as trading halts can bring more information into the closure decision. Therefore discretionary trading halts can be less susceptible to the magnet effect than rule-based halts, such as price limits. The implications of price limits may also be related to the literature on market closure because price limits effectively interrupt continuous trading. Slezak (1994) uses a multi-period model on market closure and predicts that market closures increase pre-closure trading volume because closures delay the resolution of information uncertainty and impose more risk on informed and uninformed traders. Theoretical studies on circuit breakers and price limits predict the existence of the magnet effect but relevant empirical evidence is limited. Previous studies on price limits primarily use futures contracts because price limits exist only in U.S futures markets, and their results are mixed. McMillan (1990) examines market breaks in S&P500 futures market on October 13th and 16th of 1987 and finds strong patterns of runs in prices prior to the triggering of the circuit breakers, in support of the magnet effect. Kuserk et al. (1989) and Arak and Cook (1997) both examine

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Circuit breakers in U.S. stock markets function similarly to price limits. Circuit breakers set the lower bound of major stock indices and the transaction of the entire market ceases once the bound is triggered. In comparison, price limits set both upper and lower price bounds for individual stocks and trading quickly dries up once price limits are triggered. However, the transaction may continue as long as execution prices are within the upper and lower bounds. 2

Treasury bond futures contracts and do not find the magnet effect. Berkman and Steenbeek (1998) investigate Nikkei 225 futures contracts traded in the Osaka Securities Exchange (OSE) and the Singapore International Monetary Exchange (SIMEX) and attribute the lack of the magnet effect to strong arbitrage links between OSE and SIMEX 2 Hall and Korfman (2001) examine five agricultural futures contracts and find that price limits in the futures markets has neither the stabilization nor the magnet effect. Studies on the magnet effect of price limits in equities markets spawned only recently. Ackert et al. (2001) find that market participants accelerate their transactions if a trading interruption is imminent in an experimental setting. Cho et al. (2003), using high-frequency data from the Taiwan Stock Exchange, document a distinct tendency for stock prices to accelerate toward the upper bound and weak evidence of acceleration toward the lower bound. Chan et al. (2005) find that price limits, albeit as wide as 30% in the Kuala Lumpur Stock Exchange, do not improve information asymmetry, delay the arrival of informed traders, and exacerbate order imbalance prior to limit hits. Nath (2003) finds that trading activity accelerates when stock prices approach the neighborhood of lower price limits, but not upper price limits using tick data from the National Stock Exchange of India. Abad and Pascual (2005) find that prices reverse or decelerate as they approach price limits in the Spanish Stock Exchange, rejecting the magnet effect. But their results are confounded by a five-minute post limit-hit call auction, which makes it hard to isolate the impact of price limits per se. Seasholes and Wu (2004) examine the profitability of exploiting price limit hits. They report that smart traders in the Chinese stock market make profit by accumulating shares on days of upper limit hits and selling them out to unsophisticated traders the following day. They find that those smart traders concentrate their orders within five minutes following its first time price limit hit, opposite to the implication of the magnet effect on heavier trading activities prior to limit hits.

2

The SIMEX is now a part of the Singapore Exchange. 3

Overall, previous studies on the magnet effect of price limits in equity markets are limited in their scope and the reported findings are inconclusive. We believe that three major limitations are observed in earlier studies. First, past studies have stopped short of highlighting the intraday accelerating nature of the magnet effect. Distinct from delayed price discovery, volatility spillover and interfered trading hypotheses, the magnet effect applies to the period immediately prior to limit hits. Many studies use days surrounding price limits to infer the magnet effect, which is ineffective in investigating intraday trading irregularities, not to say capturing the gravitational feature of the magnet effect. Second, the intraday momentum effect has not been controlled for when identifying the magnet effect. Behavioral finance has provided multiple theories that explain positive short-term price momentum: conservatism in Barberis et al. (1998), over-confidence and biased selfattribution in Daniel et al. (1998) and momentum traders’ reliance on past returns in Hong and Stein (1999). All three theories predict that investors underreact to news announcement in the short term and prices exhibit positive autocorrelation. Although these theories do not intentionally address intraday investor sentiment, it is reasonable to conjecture that intraday trend chasing may be pronounced on days with large price movements usually associated with news announcements. Cho et al. (2003) differentiate the intraday momentum and the magnet effect. They introduce the changes from opening prices as a momentum proxy but admit that their distinction might not be effective because the momentum and magnet variables are highly correlated. Third, previous studies do not provide conclusive evidence on the magnet effect for upper and lower limit hits. Some studies find that the magnet effect manifests differently on upper and lower limit hit days [Cho et al. (2003) and Nath (2004)]. We expand the scope of previous studies on the magnet effect by addressing all three limitations discussed above. We make contributions in the following four areas. First, we use a quadratic function to fathom the accelerating pattern of market activities. We focus on the 30minute period prior to limit hits to examine the behavior of five market microstructure variables; 4

namely, rates of return, trading volume, volatility, order flow, and order types. Our approach highlights the much-needed characterization of the magnet effect in a functional form and presents the analyses in three dimensions: acceleration rates, the magnitude and the persistence of acceleration of each variable under consideration. Our findings indicate that all five market microstructure variables exhibit abnormal behavior and significant acceleration rates prior to limit hits, signifying the presence of the magnet effect. Second, we identify the magnet effect after controlling for intraday momentum effect. We find that a narrow price limit features higher acceleration than a wide price limit, consistent with the predictions of the magnet effect, but not of the momentum effect. In addition, we introduce quasi limit hits on actual limit hit days to control for the intraday momentum effect. Quasi limit hits represent large price movements but they are not large enough to hit price limits. The difference between acceleration rates of actual and quasi limit hits is attributed to price limits after the intraday momentum effect is controlled for. We further provide evidence that no magnet effect exists in a market where no price limits exist. Using price movements of NASDAQ securities, we demonstrate the presence of a strong momentum effect only. Third, we compare the magnet effect between upper and lower limit hits. We find that the magnet effect is significant for both upper and lower limit hits. Upper limit hits draw heavier trading volume, greater order flow, and make more use of market orders than lower limit hits. In contrast, lower limit hits are associated with higher acceleration in volatility and rates of return than upper limit hits. Fourth, we examine the impact of firm characteristics on the magnet effect. Although small-cap stocks trigger price limits more frequently than medium- and large-cap stocks, no consistent differences in acceleration rates are observed. Therefore, we conclude that the magnet effect is not confined to stocks with certain characteristics. The remainder of this paper is organized as follows. In Section 2, we present the institutional background of the KRX and summary statistics of limit hits. In Section 3, detailed 5

discussions are presented on our research methodology. In Section 4, we characterize the magnet effect using five market microstructure variables in three dimensions of magnitude, acceleration rates, and persistence. In Section 5, we make distinction between the magnet effect and the momentum effect. In Section 6, we report the impact of firm characteristics on the magnet effect. In Section 7, we present conclusive remarks. 2.

Institutional background and sample statistics

2.1.

Institutional background This paper uses KRX tick-by-tick data of three months before and after December 7, 1998,

when the price limit was raised from 12% to 15%. The KRX is one of the most active stock exchanges in the world. At the end of 2005, the KRX had 702 listed companies and 858 listed issues and the total market capitalization is $648.6 billion.3 During the year of 2005, the average daily trading volume is 468 million shares and the average daily trading value is $3.1 billion in the KRX, compared to those of 1.6 billion shares and $56.1 billion in the NYSE. The annual share turnover is 504% in the KRX, much higher than 103% in the NYSE in 2005. The KRX opens from Monday to Friday and currently has four trading sessions in each trading day: a pre-hours session 7:30-8:30 A.M., a morning session 9:00 A.M.-12:00 Noon, an afternoon session 1:00-3:00 P.M., and an after-hours session 3:10-4:00 P.M.4 Like all other Asian stock markets, the KRX is an order-driven market, where buy and sell orders compete for the best prices. A call market auction is applied to the morning and afternoon session’s open and the market close. Orders are accumulated over a one-hour period prior to the opening call auction of each trading session. Orders are also accumulated over a 10-minute period before the closing call auction occurs at 3:00 P.M. During the rest of trading sessions, orders are continuously matched to satisfy

3

We use the exchange rate of US$1=KRW 1,010 as of December 31, 2005.

4

The pre-hours session was introduced to KRX on December 1, 2003. The after-hours session was extended by 20 minutes on October 14, 2002. It was from 3:10-3:40 P.M. in our sample period. The pre-hours and after-hours sessions are specially designed to facilitate basket trading where paired buy and sell orders are executed at the preceding closing prices. 6

both parties in terms of price and time priority. The KRX fully automated its securities trading on September 1, 1997. The KRX currently sets its daily price limit at 15%, which rules that stock prices can not move beyond 15% above or below their previous day’s closing prices. The most recent change on price limits took place on December 7, 1998, when it was raised from 12% to 15%. This event divides our sample period into two regimes: the pre-regime, from September 1 to December 6, 1998 and the post-regime, from December 8, 1998 to March 31, 1999.5 2.2.

Sample statistics We select common stocks that had over 100 daily transactions and traded on each trading

day in our study period. Our sample consists of 385 stocks, totaling $52.7 billion in capitalization and the average firm size is $137 million as of September 1, 1998. 354 out of these 385 stocks have at least one instance of limit hit during our study period. There are 80 trading days in the pre-regime and 73 trading days in the post-regime. Using the same sorting standards as the KRX fact book, there are 220 small firms, 77 medium firms, and 88 large firms in our sample and they are from 39 out of the 41 industries.6 Price limits are set at 12% in the pre-regime and 15% in the post-regime. However, we take into account tick size rules when limit hits are identified; prices do not need to reach actual limit prices to effectively trigger price limits for the purpose of our study.7 For example, if a stock closes at 4,900 won on day t and ruling price limits are 15%, its price range on day t+1 is 4,165 won 5,635 won. When its price reaches 5,630 won on day t+1, it will not be allowed to move up further 5

On the same day, the KRX closed Saturday trading and extended its morning session by one hour, from 9:30-11:30 A.M. to 9:00 A.M.-12:00 Noon. 6

Companies are defined as small-sized firms if their capitalization is less than 35 billion won, as mediumsized firms if their capitalization is between 35 billion won and 75 billion won, and as large-sized firms if their capitalization is above 75 billion won. 7

The tick size is the minimum price movement between two consecutive transactions. The tick size is 5 won if stocks price are below 5,000 won; 10 won if stock prices are between 5,000 won and 10,000 won; 50 won if stock prices are between 10,000 won and 50,000 won; 100 won if stock prices are between 50,000 won and 100,000 won; 500 won if stock prices are between 100,000 won and 500,000 won, and 1,000 won if stock prices are above 500,000 won. 7

because the tick size is 10 won. As a result, at the price of 5,630 won, we consider that this stock effectively triggers price limits. An upper limit hit is thus identified when Hk,t > (1+LIMIT)Pk,t-1 - TICKk,t, where Hk,t is stock k’s highest price on day t, Pk,t-1 is stock k’s closing price on day t-1, LIMIT is the prevailing daily price limit, which is 12% in the pre-regime and 15% in the post-regime, and TICKk,t is the tick size for stock k at Hk,t. A lower limit hit is identified when Lk,t < (1-LIMIT)Pk,t-1 + TICKk,t, where Lk,t is stock k’s lowest price on day t.8 We classify the sample of limit hits into four cases: the pre-up, the pre-down, the post-up; and the post-down limit hits with the prefix representing the regime and the suffix representing the direction of limit hits. Figure 1 plots the intraday distribution of limit hits for four price limit cases. [Insert Figure 1] We observe that the most limit hits occur in the first 30 minutes after market open in all four cases. The number of hits levels off during mid-day trading but rises prior to the market close. We use the Chi-squared goodness-of-fit test to compare the likelihood of limit hits during each half hour trading period. Our unreported results show that upper limit hits are most likely to occur during the first 30 minutes of the morning session and lower limit hits are most likely to occur during both the first and the last 30 minutes of the trading day. It is consistent with the belief that market open and market close feature higher volatility and heavier trading activities. [Insert Table 1] Table 1 presents detailed summary statistics of price limit hits. Panel A presents the counts of limit hits in various categories. We identify a total of 1,449, 300, 1,219, and 492 limit hits for the pre-up, pre-down, post-up and post-down cases, respectively. The average daily upper limit hits are 18.1 and 16.5 and lower limit hits are 3.8 and 6.6 under the pre- and the post- regimes, respectively. The fact that there are considerably more upper limit hits than lower limit hits is consistent with an 8

We exclude days when both upper and lower limit hits took place and days that prices moved beyond limit prices. The KRX may allow a wider daily price limit under two cases: (i) the market reopens after long holidays; and (ii) the exchange deems that the application of the daily price limit is extremely difficult due to drastic changes in market conditions. 8

upward market trend in the KRX during the study period. The Korea composite stock price index, KOSPI, increased 66% in the pre-regime and additional 20% in the post-regime. We also observe that limit hits spike at the market open, which accounts for 17% (12%) of upper limit hits and 14% (18%) of lower limit hits in the pre- (post-) regime. About 60% of upper limit hits and 48% of lower limit hits occur in the morning session. In addition, we find that around 65% of upper limit hits and 50% of lower limit hits close at limit prices, which are labeled as locked limit hits. Subsequent to locked limit hits, considerably more price continuations are observed than price reversals. For example, 78% of locked upper limit hits and 62% of locked lower limit hits are followed by price continuation, much higher than the equal probability of 50%. A high likelihood of price continuation is consistent with the delayed price discovery hypothesis [Kim and Rhee (1997)]. If the price discovery process is interrupted by limit hits, it will resume this process as the market reopens, thus continuing its earlier trend.9 In addition, there is an asymmetry between upper and lower limit hits in that lower limit hits are less likely followed by price continuation than upper limit hits. This may be explained by investors’ over-optimistic sentiment and the tendency of overreacting to positive news. De Bondt and Thaler (1990) and Butler and Lang (1991) report that financial analysts systematically produce over-optimistic forecasts on stock prices and earnings. Following these suggestions, investors are prone to chase upward trends more persistently than downward trends. Panel B of Table 1 provides intraday characteristics of limit hits: specifically, the number of intraday limit hits, the time duration of limit hits, and the count of limit hits by individual stocks. Most stocks trigger price limits repeatedly within a limit hit day: prices hit the limits; drift away; and hit limits again. The average number of intraday limit hits ranges from 5.1 of pre-down limit hits to 8.4 of post-up limit hits. Only the first time limit hit is considered an observation of limit hits in our study. The limit hit duration is the time period from the first time limit hit to the last moment that prices stay at limit prices. The average duration of limit hits varies from 50 minutes for pre9

Shen and Wang (1998) report that upper limit hits increase return autocorrelations much more than lower limit hits based on the Taiwan Stock Exchange-listed stocks. 9

down limit hits to 93 minutes for post-down limit hits, longer than those reported for the Taiwan market by Cho et al. (2003), 52 minutes for upper limit hits and 42 minutes for lower limit hits. The maximum number of limit hit days by an individual stock ranges from 7 of pre-down limit hits to 21 of pre-up limit hits. 3.

Research methodology

3.1.

Multiple market microstructure variables In this paper, we investigate the intraday behavior of five market microstructure variables

prior to limit hits. The five variables include: the rates of return, trading volume, volatility, order flow and the choice of order types. In order to explore the accelerating nature of the magnet effect, we focus on 30-minute period immediately preceding limit hits. It is reasonable to believe that the magnet effect becomes pronounced when prices reach a certain percentage of price limits and limit hits become imminent. A 30-minute period is considered long enough to capture the dynamics of the magnet effect and short enough to keep focused. Chordia et al. (2005) suggest that the adjustment to the weak form market efficiency is not instantaneous and it is well under way within no more than 30 minutes. Goldstein and Kavajecz (2004) find that investors change their trading behavior during nine minutes before the market breakdown on October 27-28, 1997, NYSE. We divide the half an hour pre-hit period to 10 three-minute intervals and measure the market microstructure variables in each interval. All the raw values are standardized by their means and standard deviations on non-limit hit days in respective regimes. To the best of our knowledge, it is the first study that provides a comprehensive view of the magnet effect using a multiple number of variables in the price limit literature. 3.2.

Baseline model We use the following baseline model to examine the three dimensions of the magnet effect

for respective market microstructure variables: Market Microstructure Variable k ,t ,i = α + β INTk ,t ,i + γSQINTk ,t ,i + ε k ,t ,i

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The dependent variables are five market microstructure variables measured for stock k on day t at interval i. INT takes the value of 1 through 10 from the furthest to the closest interval to price limit hits, and SQINT is the squared INT. The baseline model allows us to examine the behavior of each variable in three dimensions: (i) magnitude; (ii) acceleration rates; and (iii) persistence of acceleration. Dummy variables will be introduced to the equation above to compare the estimated coefficients between pre- and post-regimes and between upper and lower limit hits, Under the magnitude dimension, we review the progression of each variable based on its magnitude in the ten 3-minute intervals prior to limit hits. This magnitude dimension is useful in three aspects: i) identify abnormal trading activities on limit hit days; ii) compare the association of upper and lower limit hits; and iii) contrast the pre- and post-regimes characterized by the narrow and wide price limit bands. The estimated coefficient of SQINT (γ) indicates the acceleration rate of each variable during the 30-minute pre-hit period. We believe that acceleration rates represent the core part of the magnet effect. It characterizes the trend of market activities when price limits are being approached. We will compare acceleration rates in the pre- and post-regimes to highlight the differential impacts of price limits depending on the narrow and wide limit bands. Acceleration rates should also be informative to contrast how the five market microstructure variables exhibit differential patterns prior to upper and lower limit hits. Lastly, estimated β and γ jointly determine the max/min point of a quadratic function. If γ is positive, the minimum point of the convex curve is positioned at INT being –β/2γ. Therefore, the persistence of acceleration is measured by 3(10+β/2γ), which is the length of the time period from the minimum point of a convex function to the limit hit moment. The persistence of acceleration will be estimated for the five market microstructure variable in each of four limit hit cases: pre-up, pre-down, post-up, and post-down. 3.3.

Magnet effect vs. intraday momentum effect

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One complication in identifying the magnet effect is that it is difficult to distinguish it from intraday momentum effect because both forces might lead to accelerating trading activities. Intraday momentum effect on the basis of high-frequency transaction data has not been welldefined in the literature while price momentum over intermediate-term investment horizons (ranging from three months to one-year) has been extensively researched.10 In this paper, we take the following three steps to make the distinction. First, we explore the different reactions of the magnet effect and the momentum effect to the width of price limit bands.11 We believe that a narrower price limit band is associated with higher acceleration rates because the likelihood of triggering price limits is greater than under a wider price limit band. In contrast, a narrower price limit band should be associated with lower acceleration rates as far as the momentum effect is concerned because larger price movements within a wider price limit band should trigger stronger speculation and more intense trend-chasing. Hence, we hypothesize that the momentum effect is prevailed by the magnet effect if the preregime features higher acceleration rates than the post-regime. Second, we construct quasi limit hits under both regimes and compare quasi limit hits with actual limit hits. Quasi limit hits in the pre- (post-) regime represent large price movements of 9% (12%). These price movements are large but not large enough to hit the predefined limits of 12% (15%) in the pre- (post-) regime.12 We expect that actual limit hits will exhibit higher acceleration rates than quasi limit hits and the differences would be attributed to the magnet effect.

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Refer to Jegadeesh and Titman (1993, 2001), Chan et al. (1996), Barberis et al. (1998), Daniel et al. (1998), Hong and Stein (1999), Conrad and Kaul (1998), Moskowitz and Grinblatt (1999), Grundy and Martin (2001), among others.

11

In the absence of precise definition of intraday momentum effect, Cho et al. (2003), for example, use an arbitrary 4% change from opening prices to capture the momentum effect on limit hit days. 12

The cutoff points of 9% in the pre-regime and 12% in the post-regime are arbitrarily chosen. We also used other cutoff points, such as 10%, 11% in the pre-regime and 13%, 14% in the post-regime. The results remain qualitatively the same. 12

Third, we impose hypothetical 12% and 15% price limits on NASDAQ securities. We refer to these cases pseudo limit hits since there is no price limits on the NASDAQ market. No differences in acceleration rates between the two hypothetical price limit regimes on the NASDAQ market confirm that the magnet effect is caused directly by the existence of price limits per se and it does not exist in markets without price limits. To summarize, our methodology goes beyond past studies in that we define the magnet effect in a functional form from a non-linear regression and review the behavior of five market microstructure variables in three dimensions: the magnitude, acceleration rates, and the persistence of acceleration. Moreover, we identify the magnet effect while controlling for intraday momentum effect and confirm that the magnet effect is driven by price limits per se. The empirical results are reported in Sections 4, 5, and 6. 4.

Empirical findings

4.1.

Magnitude We compute the cross-sectional average of five market microstructure variables in each 3-

minute interval during the 30-minute study period and Figure 2 plots their progression for four limit hit cases. The five variables are defined below and we use the rates of return as an example to demonstrate the computation. The rates of return at three-minute intervals (MSTRETi defined below) plotted in Figure 2A are measured as the percentage change between the last transaction prices from two consecutive intervals. Upper Limit Hits: RETk ,t ,i = ( Pk ,t ,i − Pk ,t ,i −1 ) / Pk ,t ,i −1 Lower Limit Hits: RETk ,t ,i = ( Pk ,t ,i −1 − Pk ,t ,i ) / Pk ,t ,i −1 13 STRETk ,t ,i = ( RETk ,t ,i − MRETk ,i ) / SDRETk ,i

MSTRETi = ∑ STRETk ,t ,i / N i

13

We take the additive inverse of negative rates of return to make it comparable to positive returns of upper limit hits. 13

where Pk,t,i is the last transaction price of stock k on day t at interval i. RET k,t,i is the three-minute rate of return from interval i-1 to interval i on day t for stock k. RETk,t,i is standardized by subtracting the mean (MRETk,i) and divided by the standard deviation (SDRETk,I) of stock k at interval i within respective regimes. Lastly, we compute the cross-sectional average of rates of return (MSTRETi ) for each interval i, where Ni is the number of limit hits in interval i.14 Trading volume, in Figure 2B, is measured by the share volume of transactions during each interval. We also measure the dollar amount of transactions and the frequency of transactions and their statistical results are qualitatively similar to those based on share volume. Following Lee et al. (1994), Corwin and Lipson (2000) and Christie et al. (2002), we use three intraday volatility measures, the absolute value of returns, high-low price differences and the number of quote revisions within each three-minute interval. To conserve space, we only report the results based on absolute returns, ABSRETURN, in Figure 2C.15 Figure 2D plots the share volume of regular order submissions for four limit hit cases. We focus on the side of the market that ultimately leads to limit hits, which are the buy side for upper limit hits and the sell side for lower limit hits. We measure order imbalances using the ratio of buy (sell) orders out of the total amount of submitted orders for upper (lower) limit hits and their results, not reported here, are qualitatively similar to those of order submissions. Figure 2E plots the share volume of market orders. Investors can place three types of orders: market orders, limit orders and limit-or-market-on-close-orders in the KRX, among which market and limit orders combined compose more than 99% of total orders. We, therefore focus on the choice between the market and the limit orders. We also investigate the ratio of market orders and their results, not reported here are qualitatively similar to the results based on the share volume of market orders.

14

We examined several other ways of standardization and the results remain qualitatively the same. Lee et al. (1994), Corwin and Lipson (2000), and Christie et al. (2002) standardize rates of return as a percentage of the mean return. Another alternative is to standardize the rate of return as a percentage of its standard deviation, used in Cho et al. (2003).

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The other two variables provide similar results. 14

[Insert Figure 2] At least three empirical regularities emerge from Figure 2. First, all five market microstructure variables are significantly positive during the 30-minute pre-hit period and their magnitude rises as prices approach price limits. Increasing positive values imply that investors intensify their trading activities when price limits are being approached, consistent with the predictions of the magnet effect. We characterize the rising pattern of respective variables formally in the next section. Second, upper limit hits draw heavier trading volume, greater order flow, and make use of a greater number of market orders than lower limit hits in the same regime, particularly during the intervals close to limit hits. The cross-sectional average of three minute trading volume is 1.91 for pre-up limit hits, compared to 1.23 for pre-down limit hits. It is 1.96 for post-up limit hits, compared to 0.77 for post-down limit hits. Mean differences of the trading volume, order flow, and market orders between upper and lower limit hits are statistically significant at 1% level. In contrast, lower limit hits are associated with higher volatility than upper limit hits in the same regime and the average three-minute rates of return do not significantly differ. The lack of short sale infrastructure in the KRX could contribute to heavier volumes of upper limit hits. Investors can capitalize their positive expectations by placing more buy orders, but the high costs associated with short sales inhibit the capitalization of negative expectations. As a result, investors are restricted from chasing a downward trend and fewer transactions take place prior to lower limit hits.16 Third, pre-regime limit hits do not show significantly heavier trading activities than postregime limit hits across the 30-minute pre-hit period. However, the trading activities for pre-regime

16

In the KRX, the proceeds from short sales are held by the securities companies as collateral in the margin account, which is again marked to market on a daily basis. Then the collateral has to be maintained up to a certain ratio of the extended credit to avoid the margin call. Moreover, securities companies raised the initial margin requirement and maintenance requirement after the Financial Supervisory Service relaxed relevant regulations to liberalize the market in March 1998. As a result, the short sales in 1998 and 1999 were materially none. 15

limit hits tend to become slightly higher than those of post-regime limit hits during the last six to nine minutes before limit hits. In summary, we conclude that investors intensify their transactions when limit hits become imminent. Price variations, trading volume, volatility, order flow and market orders rise substantially during the 30-minute period prior to limit hits. In addition, the direction of limit hits has a strong impact on the magnitude of market microstructure variables, while the width of price limits does not show such an impact. 4.2.

Acceleration rates Acceleration is the most important and direct measure of the magnet effect considering its

self-fulfilling nature. Table 2 reports acceleration rates (γ) of all market variables estimated from the quadratic function. A 2x2 matrix is created to contrast pre- with post- regimes and upper with lower limit hits in Panels A, B, and C. The bottom row reports the results of difference tests between pre- and post-regimes and the last column reports the results of difference tests between upper and lower limit hits. Panels D and E do not report the comparisons between upper and lower limit hits and they are not significantly different from each other for respective variables. One major finding on acceleration rates is that they are sensitive to the width of daily price limit bands. Acceleration rates estimated using five market microstructure variables are consistently higher in the pre-regime with a 12% limit band than in the post-regime with a 15% limit band. Higher acceleration in the pre-regime indicates that the intraday momentum effect is subsumed by the magnet effect during the 30-minute period prior to limit hits. Therefore, in this section, we can initially focus on the magnet effect without being concerned about the joint impact of magnet and momentum effects. In Section 5, however, we explore the possibility of controlling for the intraday momentum effect using quasi limit hits so that we can isolate a pure “magnet effect.” We report the results of five market microstructure variables individually in the following five sub-sections. 4.2.1.

Rates of return

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The rates of return measure price progression. Earlier studies by Gerety and Mulherin (1992), Subrahmanyam (1994) and Cho et al. (2003) demonstrate that investors will rush onto the bandwagon when they observe that price limits are being approached. Therefore, we expect to observe that the rates of return accelerate prior to limit hits if price limits act as magnets. [Insert Table 2] We observe from Panel A of Table 2 that all four limit hit cases (pre-up, pre-down, post-up, and post-down) have significantly positive coefficients and the goodness of fit is fairly strong. To illustrate, γs are 0.06 for pre-up limit hits, 0.09 for pre-down limit hits, 0.04 for post-up limit hits, and 0.06 for post-down limit hits, respectively. Positive coefficients of SQINT delineate a convex function of price variation and support the prediction of the magnet effect. In addition, we make the comparisons between two regimes and between upper and lower limit hits. The last row and the last column of Panel A report the F-statistics of the coefficient comparisons.17 Pre-regime limit hits have significantly higher acceleration rates than post-regime limit hits for both upper and lower limit hits. Higher acceleration rates in the pre-regime confirm our hypothesis that the magnet effect prevails over the intraday momentum effect. The narrower price limits during the pre-regime gives investors less room for continuous trading and implies a higher likelihood of crossing price limits. Consequently, the cost of non-execution imposed by limit hits becomes more prominent and investors respond to price limits more frenetically than under a wider price limit regime. We also observe that lower limit hits have stronger acceleration than upper limit hits in respective regimes, which could be explained by investors’ over-optimistic sentiment in connection with the discussion of the acceleration persistence in the next section. 4.2.2.

Trading volume

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Lindley (1957), Leamer (1978) and Connolly (1995) point out the problem related to large sample size in classical test statistics. Hence, the size-adjusted F-test critical value is [(T-k1)/P][TP/T-1], where T is the sample size, k1 is the number of parameters estimated under the alternative hypothesis, and P is the number of restrictions being tested. The size-adjusted critical t-value is (T-k)0.5(T1/T-1). We use the 1% level of significance as the rejection criterion and our results are robust to the adjustment. 17

Another important market microstructure variable is liquidity as measured by share trading volume. Theoretical studies on the magnet effect have predicted heavier trading prior to limit hits. Subrahmanyam (1994) suggests that investors may sub-optimally advance trades to assure their ability to trade. According to Gerety and Mulherin (1992), skittish investors overreact and leave the market in anticipation of the market close. Empirically, Lee et al. (1994) and Kim and Rhee (1997) document higher trading activities on days subsequent to trading halts and limit hits but their analyses rely on daily observations. We expect to observe accelerated trading volume during the pre-hit period. Panel B of Table 2 reports that all four limit-hit cases demonstrate significantly positive acceleration patterns, which indicate that increasingly more transactions are drawn to the market as prices approach price limits. The acceleration rates are 0.10, 0.08, 0.10, and 0.06 for pre-up, post-up, pre-down, and postdown limit hits. Additionally, pre-regime limit hits feature significantly higher acceleration rates than post-regime limit hits for both upper and lower cases. Higher acceleration in the pre-regime confirms that a narrower price limit causes more frenetic transactions in anticipation of price limit hits as a result of a higher likelihood of crossing price boundaries. It supports our statement that the magnet effect dominates the intraday momentum effect. The comparisons of acceleration rates between upper and lower limit hits are insignificant even though upper limit hits attract heavier trading volume than lower limit hits. 4.2.3.

Volatility Proponents of price limits cite the cooling-off effect as a primary benefit of price limits. For

example, Ma et al. (1989) document attenuated volatility during the post-hit period. Berkman and Lee (2002) report that the widening of price limits increased long-term volatility and reduced overall trading volume in the KRX market. However, Gerety and Mulherin (1992) and Subrahmanyam (1994) suggest the opposite. Lee et al. (1994) and Corwin and Lipson (2000) state that volatility increases significantly subsequent to trading halts. Kim and Rhee (1997) also conclude that price limits lead to higher volatility levels on days subsequent to price limit hits. Kim 18

(2001) finds that narrower price limits do not usually lead to lower volatility using daily data of Taiwan Stock Exchange. But the above studies are confined to daily observations. More recently, Cho et al. (2003) conclude that the conditional volatility increases prior to upper limit hits but not prior to lower limit hits. However, it is hard to attribute higher conditional volatility solely to the magnet effect since they do not effectively isolate the magnet effect from the momentum effect. In this sub-section, we examine the variation of volatility and expect to observe rising volatility prior to limit hits. All four limit-hit cases exhibit significantly positive acceleration rates in volatility as reported in Panel C of Table 2. The acceleration rates are 0.07, 0.04, 0.13, and 0.10 for pre-up, postup, pre-down, and post-down cases, respectively. Rising volatility prior to both upper and lower limit hits refute the cooling-off effect. What is more notable is that the pre-regime exhibits significantly higher acceleration rates than the post-regime for both upper and lower limit hits, consistent with our predictions of the magnet effect, not the cooling-off effect. A narrower price limit imposes more pronounced non-execution costs to investors, therefore, leads to higher price variation. In addition, we observe that lower limit hits have significantly higher acceleration rates than upper limit hits, in line with our earlier findings on the rate of return. 4.2.4.

Order flow The predictions on trading volume can be naturally extended to order flow. If investors

become nervous and sub-optimally submit orders to avoid non-execution, we expect to observe increasingly high order submissions and high order imbalances during the pre-hit period. In section 4.1, we have observed unusually high order flows during the 30-minute pre-hit period. Panel D of Table 2 reports the regression results when the dependent variables are buy order volume, buy order ratio for upper limit hits and sell order volume and sell order ratio for lower limit hits.18

18

We also investigate revised orders during the pre-hit period. In the KRX, only limit orders can be later revised to better positions, which means that limit buy orders can only be revised to higher prices and/or higher volumes and limit sell orders can only be revised to lower prices and/or higher volumes. In unreported results, we find that investors revise their buy orders more often prior to upper limit hits, and revise their sell orders more often prior to lower limit hits. Their results are qualitatively similar to those of regular orders. 19

We observe that all the estimated coefficients of SQINT are significantly positive. It implies that investors place increasingly more orders on one side of the market, which causes larger order imbalances and ultimately leads to limit hits. The bottom row of Panel D reports the differences test between two regimes. The pre-regime has significantly higher acceleration rates than the post-regime for both order flow and order imbalances. For example, the acceleration rate of pre-up limit hits buy order volume is 0.04, relative to 0.02 for post-up limit hits. Similarly, the acceleration rate for pre-up limit hits buy order ratio is 0.006, relative to 0.002 for post-up limit hits. The same relation between the pre- and the post-regime holds true for lower limit hits as well. Higher acceleration rates in the pre-regime once again support the prevalence of the magnet effect. In addition, we compare acceleration rates between upper and lower limit hits within the same regime and do not find significant differences. 4.2.5.

Order types We have observed in section 4.1 that investors choose more market buy (sell) orders prior

to upper (lower) limit hits. The choice between limit and market orders is contingent on their costs and benefits. Greenwald and Stein (1991) point out that limit orders have two limitations. First, limit orders carry a risk of non-execution. Second, limit orders leave traders exposed to innovations in fundamentals that could occur between the time an order is placed and the time it is executed. Bae et al. (2003) provide additional evidence of the impact of non-execution on order types. They state that the proportion of limit orders monotonically decreases throughout the trading day because traders are less likely to submit limit orders when there is little time left until the market closes. A similar point is made by Goldstein and Kavajecz (2004). They note that the extreme uncertainty concerning the ability to trade continuously causes market participants to alter their behavior in that sellers use more market orders and less limit orders during the nine minutes before the trading halt. Based on Australian stock market experience, Verhoeven et al. (2004) report that the probability of traders submitting a limit order increases with (i) an increase in the spread; (ii) a decrease in the

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depth at the best price on the same side; and (iii) an increase in the depth at the best price at the opposing position. Price limits virtually close continuous trading and the non-execution cost becomes increasingly prominent as prices approach price limits. Therefore, we expect that investors will use more and more market orders to put their orders in the front of the order queue and to avoid the non-execution costs imposed by price limits. In this sub-section, we report the regression results of market order share volume and the ratio of market orders out of total orders from the buy side of upper limit hits and the sell side of lower limit hits.19 From Panel E of Table 2, we find that the acceleration rates (γ) are uniformly positive and significant for four limit hit cases, demonstrating that investors use increasingly more market orders in both absolute and relative terms. The pre-regime features significantly higher acceleration than the post-regime for both upper and lower limit hits. For instance, the acceleration rate for market sell orders is 0.05 of pre-down limit hits, significantly higher than 0.03 of post-down limit hits. The acceleration rate of market sell ratio is 0.03 of pre-down limit hits, relative to 0.02 of post-down limit hits. The same relation between two regimes holds true for upper limit hits, with the only difference being the statistical significance at 5% level. There are, however, no significant differences in acceleration rates between upper and lower limit hits within the same regime. Higher acceleration observed for the use of market orders in the pre-regime reinforces our prediction of the magnet effect. 4.3.

Persistence of acceleration Sections 4.1 and 4.2 report two dimensions of the magnet effect, the magnitude and

acceleration rates. In this section, we focus on the persistence of acceleration process, the third dimension of the magnet effect. The persistence is the time period from the minimum point of the convex function to the moment of limit hit, which is derived from the quadratic functions estimated. 19

We also examined the dollar amount of market orders and the frequency of market orders. The results remain qualitatively similar. 21

Table 3 reports persistence measurements and the comparisons between two regimes and between upper and lower limit hits. [Insert Table 3] We observe from Table 3 that the acceleration persistence ranges from 17 minutes to 24 minutes for various market microstructure variables. The range of persistence falls into our study period of 30 minutes, indicating that the acceleration behavior does not occur until price limits have become in sight and it is unique to a short time period preceding limit hits. When we compare the persistence between the pre- and the post-regime limit hits of the same direction and between upper and lower limit hits within the same regime, two empirical regularities emerge. First, the postregime has significantly longer persistence than the pre-regime in many cases, and there is not a single case that the pre-regime has longer persistence than the post-regime. Second, upper limit hits have longer persistence than lower limit hits in many cases. The only exception is that post-down limit hits have longer persistence than post-up limit hits when the dependent variable is the market order ratio. Using the rates of return as an example, the persistence of 21 minutes observed for post-up limit hits, is longer than 19.75 minutes of pre-up limit hits. The persistence of 20 minutes observed for post-down limit hits is also longer than 17.67 minutes of pre-down limit hits. At the same time, upper limit hits have longer persistence than lower limit hits within the pre- and the post-regime respectively. Persistence measures for other variables are similar in scale. For example, the persistence of trading volume is 18.75, 18.45, 21.81, and 19 minutes for pre-up, pre-down, post-up and post-down limit hit cases, respectively. Longer persistence in the post-regime could be explained from two reasons that may not be mutually exclusive. First, the intensity of acceleration is less with wider price limits. In previous sections, we have documented that all market microstructure variables have significantly lower acceleration rates in the post-regime than the pre-regime. Second, it takes longer for prices to attain wider price movements in the post-regime. 22

The difference between upper and lower limit hits could be explained by investors’ overoptimistic sentiment. If investors believe that an upward trend tends to persist, liquidity buyers will hurry to fulfill their liquidity needs in anticipation of a limit hit and speculators will bid up prices upfront with the expectation of realizing their profits at higher prices. However, when prices are going down, investors tend to believe it is transitory. Liquidity sellers are likely to wait for the price reversal until the last chance of execution and speculators will defer locking in their losses as long as possible. As a result, investors jump onto an upward trend at an earlier stage with relatively mild acceleration and investors respond to a downward trend at a later stage but in a more concentrated fashion, resulting to shorter persistence and higher acceleration. In summary, we conclude that the magnet effect, featured by accelerated trading activities lasts for about 20 minutes before ultimately triggering price limits. There is some evidence that the pre-regime has shorter persistence than the post-regime and upper limit hits exhibit longer persistence than lower limit hits, both with some exceptions. 5.

A closer look at the intraday momentum effect In section 4, we provide consistent evidence of higher acceleration rates in the pre-regime

than in the post-regime. This finding is consistent with the predictions of the magnet effect but not with those of the momentum effect. The underlying rationale is that the magnet effect implies stronger acceleration under narrower price limits and the momentum effect implies the opposite because the momentum effect rises along with the extent of price movements. Hence, we conclude that the magnet effect is more dominant than the momentum effect during the 30-minute period before daily limits are hit. However, one caveat of the regime comparison is that we are comparing two different time periods and their information sets may differ. To address this empirical difficulty, we rely on quasi limit hits in the KRX to compare with actual limit hits in the same regime. Quasi limit hits are large price movements but they are not large enough to hit daily limits. More importantly, the

23

introduction of quasi limit hits allows us to isolate the pure magnet effect after controlling for the intraday momentum effect. 5.1.

Quasi limit hits in KRX We define quasi limit hits in the pre-regime as 9% price movements before 12% price

limits are triggered. Quasi limit hits in the post-regime are defined as 12% price movements prior to hitting 15% price limits. In total, we identify 281 quasi upper limit hits and 75 quasi lower limit hits in the pre-regime; 247 quasi upper limit hits and 114 quasi lower limit hits in the post-regime. All of our selected quasi limit hits have at least half an hour trading prior to the cutoff moments. Table 4 reports the mean statistics and the regression results. To conserve space, we only report the results of the rates of return and trading volume. Other variables exhibit similar results. [Insert Table 4] From Panel A of Table 4, we observe that the average 3-minute rate of return and trading volume are significantly positive during the period prior to both types of limit hits in two regimes. The last three rows of Panel A reports the results of mean difference tests between paired groups. It is clear that quasi limit hits have significantly lower rates of return and trading volume than actual limit hits in the same regime. For example, the average 3-minute rate of return for quasi upper limit hits is 0.65, which compares with 0.85 of actual upper limit hits in the pre-regime. The average 3minute trading volume for quasi upper limit hits is 1.18, which is significantly lower than 1.91 of actual upper limit hits in the pre-regime. The same relation remains valid for all eight paired comparisons between quasi and actual limit hits. In contrast, only one out of four comparisons between actual limit hits in two regimes is significant: pre-down limit hits have heavier trading volume than post-down limit hits. Lower trading activities prior to quasi limit hits support our hypothesis that binding price limits have the magnet effect for actual limit hits. We therefore attribute the differences between quasi limit hits and actual limit hits to the magnet effect in the latter group. For the purpose of completeness, we compare upper and lower quasi (actual) limit hits within the same regime and 24

find that an upward-trending market attracts more trading volume than a downward-trending market. The differences in the rate of return are not significant except that quasi lower limit hits have stronger rates of return than quasi upper limit hits in the post-regime. Panel B of Table 4 reports the regression results from the quadratic function for quasi limit hits. Both upper and lower quasi limit hits exhibit significant acceleration in rates of return and trading volume. At the bottom of Panel B, we reiterate the coefficient estimates of γ for various limit hit cases and compare the acceleration rates between quasi limit hits and actual limit hits. Quasi limit hits have significantly lower acceleration rates than actual limit hits in the same regime for all eight comparisons. For example, the acceleration rate estimated using rates of return is 0.04 for quasi upper limit hits in the pre-regime, significantly lower than 0.06 for pre-up limit hits. Trading volume accelerates at 0.03 for quasi lower limit hits in the pre-regime, compared with 0.10 for pre-down limit hits. The observed differences in acceleration rates between actual and quasi limit hits may be considered as the impact of the pure magnet effect after the intraday momentum effect is controlled for. Hence, we conclude that the magnet effect becomes pronounced when price limits are imminent. Another useful comparison can be made between post-regime quasi limit hits and preregime limit hits. Because both groups have the same amount of price movements, their differences could be attributed to binding price limits in the latter group. We observe from Panel A that postregime quasi limit hits have lower trading activities than pre-regime limit hits, and Panel B indicates that the acceleration rate of post-regime quasi limit hits is lower than those of pre-regime limit hits. Lower acceleration rates of quasi limit hits in the post-regime than those of actual limit hits in the pre-regime suggest that the magnet effect is taking effect for the later group. In addition, we compare the acceleration rates between quasi upper and lower limit hits and find that quasi lower limit hit have higher acceleration in rates of return but not in trading volume. It is consistent with our earlier findings on actual limit hits.

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In summary, quasi limit hits have smaller rates of return, lower trading volume, and weaker acceleration of both variables than actual limit hits in respective regimes. We attribute less intensive trading activities prior to quasi limit hits than actual limit hits to the lack of the magnet effect because price limits are not binding for quasi limit hits. In addition, the extent of price movement can not explain the fact that pre-regime limit hits have consistently higher acceleration than both post-regime quasi limit hits and post-regime actual limit hits. We conclude that the magnet effect becomes pronounced when prices get close to price limits and the extent of the magnet effect is governed by the width of price limit band. We use the NASDAQ as an example below to illustrate that there is no magnet effect in a market without price limits. 5.2.

Pseudo limit hits in NASDAQ The identification of the magnet effect has been based on the differences between limit hits

in two regimes and between quasi and actual limit hits. We find significant differences in these comparisons and attribute them to the existence of the magnet effect and the width of price limits. These comparisons are meaningful in a market with the daily price limit system in place, but another interesting test can be conducted for a market without price limits. We choose the NASDAQ for our experiment because it does not have price limits and it has more similarities with the KRX-listed stocks in terms of firm size, price level, and investor profiles than the NYSE. To construct a scenario identical to the two price limit regimes in KRX, we impose hypothetical price limits of 12% and 15% on price movements of the NASDAQ securities respectively and label them as pseudo limit hits. The underlying idea for a test using the market without the price limit system is intuitive. In the absence of price limits, any trading behavior we could observe in the NASDAQ should be attributed to intraday momentum and, as a result, we expect no significant differences between pseudo limit hits, in contrast to significant differences in acceleration rates between the pre- and the post-regime in the KRX. Pseudo limit hit based approach allows us to avoid making cross-country comparisons which are virtually impossible unless fundamental differences between the KRX and the NASDAQ are adequately controlled. 26

The study period of the NASDAQ securities is from September 1 to December 31, 1998. Our sample consists of 587 common stocks with the average number of daily transactions of 100 or greater and the average price is greater than $5 to avoid any distortion caused by penny stocks.20 The intraday transaction data are retrieved from the Trade and Quote (TAQ) database and the filters in Bessembinder (2003) are adopted to eliminate the errors in the dataset. Then we identify pseudo upper and lower limit hits in the 12% and 15% regimes respectively.21 In total, we come up with 540 upper limit hits and 367 lower limit hits under the 12% price limits and 276 upper limit hits and 143 lower limit hits under the 15% price limits. Table 5 reports the results based on rates of return and trading volume during the 30-minute period prior to pseudo limit hits. [Insert Table 5] Panel A of Table 5 reports average three-minute rate of return and trading volume prior to pseudo limit hits. We observe that price variations and trading volume increase prior to pseudo limit hits, consistent with the notion that large price movements are associated with heavier trading volume. We also observe that pseudo limit hits in the 15% price limit regime have greater price variations than those in the 12% price limit regime and trading volume between two regimes does not show significant differences. These results are different from what we observe from the preand the post- regimes in KRX, where the rates of return do not show significant differences. There is also evidence that an upward market draws more trading volume than a downward market and pseudo lower limit hits have more price variation than pseudo upper limit hits in respective regimes, consistent with the results in the KRX.

20

The U.S. Securities and Exchange Commission defines penny stocks trading at prices below $5.00. Ball et al. (1995) report that the problem in measuring contrarian portfolio returns is most severe because i) contrarian portfolios invest in extremely low-priced ‘loser” stocks; and (ii) microstructure-related biases in measured returns are most pronounced at the calendar year-end, which is usually when contrarian portfolios are formed.

21

We use more flexible cutoff points, (11.5%, 12.5%) and (14.5%, 15.5%) for pseudo upper limit hits, and (12.5%, -11.5%), (-15.5%, -14.5%) for pseudo lower limit hits in two regimes respectively. We do not use the exact cutoff at 12% and 15% because the number of pseudo limit hits based on exact cutoffs is fairly small. The results based on exact cutoffs are qualitatively similar to our reported results. 27

Panel B reports the estimated coefficients of SQINT for respective pseudo limit hits cases. We observe that all the coefficients are significantly positive except for trading volume of 15% pseudo upper limit hits. Even though positive coefficients support the momentum effect, the most important finding is that the two pseudo limit hit regimes do not exhibit significant differences in estimated acceleration rates as indicated in the bottom row of Panel B. In comparison, the preregime features significantly higher acceleration rates in all market variables than the post-regime in the KRX with the price limit system in place. Therefore, we conclude that the lack of price limits in the NASDAQ explains the insignificant differences between the two pseudo limit hit regimes. It supports our argument that the magnet effect is led by price limits per se, not by large price movements. And the magnet effect is unique to markets with price limits. Hence, positive acceleration rates on the NASDAQ market reflect the intraday momentum effect. 6.

Firm size effect We have documented the existence of the magnet effect from various aspects in earlier

sections of the paper. In this section, we demonstrate that the magnet effect is robust to firm specific characteristics. We categorize our sample of limit hits that occurred before 2:50 P.M. into three capitalization groups: small-, medium-, and large-cap. There are 973, 172, 253 upper limit hits and 208, 37, 34 lower limit hits for the small-, medium-, and large-cap groups in the pre-regime. There are 839, 169, 201 upper limit hits and 340, 80, 50 lower limit hits in the post-regime for the small- to the large-cap groups. As summarized in Panel A of Table 6, small-cap stocks have the highest average limit hits per stock among three capitalization groups. High probability of limit hits for small-cap stocks is consistent with the findings reported by earlier studies. Kim and Limpaphayom (2000) report that volatile stocks and small-cap stocks hit price limits more often than other stocks. Chen et al. (2005) report that illiquid stocks with wide bid-ask spreads hit price limits more often than liquid stocks. [Insert Table 6] 28

Panel A of Table 6 reports standardized rates of return and trading volume for capitalization stratified limit hits during the pre-hit period. We observe that the cross sectional average is significantly positive for all limit hits. In addition, we compare mean differences among capitalization groups and find that small-cap stocks have significantly lower trading volume than large-cap stocks for both upper and down limit hits. However, there is no consistent pattern in rates of return among capitalization stratified groups. Panel B of Table 6 reports estimated coefficients of SQINT where dummy variables are introduced to identify three size groups. All the estimated coefficients are significantly positive, indicating that the acceleration pattern is not subject to stock capitalization. No significant differences in acceleration rates of trading volume are observed between small- and large-cap stocks for four limit hit cases. There is no consistent relation for the acceleration rates estimated using the rates of return either. For instance, small-cap stocks show a lower acceleration rate in rates of return than large-cap stocks for pre-up limit hits. However, small-cap stocks exhibit a higher acceleration rate in rates of return than large-cap stocks for post-down limit hits. We therefore, conclude that the magnet effect is not driven by firm characteristics. The magnet effect stands out significantly across stocks of various market capitalizations and the magnet effect is not confined to a particular group of stocks. 7.

Conclusion In this paper, we use KRX tick-by-tick data and limit order book to examine the presence

of the magnet effect. We introduce five market microstructure variables (rates of return, trading volume, volatility, order flow and order types) to define the magnet effect in a time-series quadratic function over the 30-minute period prior to limit hits. While so doing, we provide strong evidence of the intraday accelerating nature of the magnet effect in three dimensions: magnitude; acceleration rates; and persistence of acceleration. We find that investors alter their trading behavior as security prices approach either upper ceiling or lower floor price limit. Approximately twenty minutes prior to limit hits represent a 29

critical period when investors exhibit an unusual trading behavior to assure order executions. Specifically, they place an increasing number of buy (sell) orders when prices approach upper (lower) limit. Investors also choose disproportionately more market buy (sell) orders when an upper (lower) limit hit becomes imminent. As a result, the rates of return, trading volume and volatility accelerate prior to limit hits. In addition, we distinguish the magnet effect from the intraday momentum effect by making two sets of comparisons. First, we find that the pre-regime with 12% price limits has greater acceleration rates than the post-regime with 15% price limits. Since the magnet effect predicts higher acceleration in the pre-regime, while the momentum effect predicts the opposite, our empirical evidence indicates that the momentum effect is subsumed by the magnet effect in the 30minute period prior to limit hits. Second, we introduce quasi limit hits on actual limit hit days in two regimes and compare quasi limit hits and actual limit hits. Lower acceleration rates and weaker market activities of quasi limit hits support that the magnet effect is led by the existence of price limits, not by large price movements. To strengthen our results, we impose pseudo price limits on the NASDAQ market where no price limit system is in place. We demonstrate that no differences in acceleration rates exist between the 12% and 15% pseudo limit hits on the NASDAQ market. The lack of difference between the two regimes in the NASDAQ reinforces our belief that the magnet effect is driven by price limits per se and is therefore unique to markets with price limits, while the acceleration rates observed on the NASDAQ market are simply an indication of the intraday momentum effect. Moreover, this paper examines the reactions to price limits under different market conditions. We conclude that the direction of limit hits has a significant impact on the trading intensity. Upper limit hits often feature heavier trading volume, more order submissions, and more use of market orders than lower limit hits, while lower limits hits are associated with greater changes in prices and volatility. Upper limit hits also exhibit slightly longer persistence than lower limit hits. Investor psychology and the limited availability of short sales in the KRX may explain 30

these differences between upper and lower limit hits. In the end, this paper presents that the magnet effect is robust to firm characteristics. Stocks with small, medium and large market capitalization uniformly exhibit significant magnet effect.

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Christie, William G., Shane A. Corwin, and Jeffrey H. Harris, 2002, NASDAQ trading halts: the impact of market mechanisms on prices, trading activity, and execution costs, Journal of Finance 3, 1443-1478. Connolly, Robert A., 1995, An examination of the robustness of the weekend effect, Journal of Financial and Quantitative Analysis 24, 133-169. Conrad, Jennifer and Gautam Kaul, 1993, Long-term overreaction or biases in computed returns? Journal of Finance 48, 39-63. Corwin, Shane A. and Marc L. Lipson, 2000, Order flow and liquidity around NYSE trading halts, Journal of Finance 4, 1771-1801. Daniel, Kent, David Hirshleifer, and Avanidhar Subrahmanyam, 1998, Investor psychology and security market under- and overreactions, Journal of Finance 53, 1839-1885. De Bondt, Werner F. and Richard H. Thaler, 1990, Do security analysts overreact?’ American Economic Review 80, 52-57. Factbook, 2005 Facts & Figures, Korea Stock Exchange. Fama, Eugene F., 1989, Perspectives on October 1987, or What did we learn from the crash? In: Kamphuis Jr., R.W., Kormendi, R.C., Henry Watson, J.W. (Eds.), Black Monday and the future of the financial markets. Irwin, Homewood, IL. Gerety, Mason S. and J. Harold Mulherin, 1992, Trading halts and market activity: an analysis of volume at the open and the close, Journal of Finance 5, 1765-1784. Goldstein, Michael and Kenneth Kavajecz, 2004, Trading strategies during circuit breakers and extreme market movements, Journal of Financial Markets 7, 301-333. Greenwald, Bruce C. and Jeremy C. Stein, 1991, Transactional risk, market crashes, and the role of circuit breakers, Journal of Business 64, 443-462. Grundy, Bruce and S. Martin, 2001, Understanding the nature of the risks and the source of the rewards to momentum investing, Review of Financial Studies 14, 29-78. Hall, Anthony D. and Paul Korfman, 2001, Limits to linear price behavior: futures prices regulated by limits, Journal of Futures Markets 21, 463-488. Hong, Harrison and Jeremy C. Stein, 1999, A unified theory of underreaction, momentum trading and overreaction in asset markets, Journal of Finance 54, 2143-2184. Jegadeesh, Narasimhan and Sheridan Titman, 1993, Returns to buying winners and selling losers: implications for stock market efficiency, Journal of Finance 48, 65-91 Jegadeesh, Narasimhan and Sheridan Titman, 2001, Profitability of momentum strategies: An evaluation of alternative explanations, Journal of Finance 56, 699-720. Kim, Kenneth A., 2001, Price limits and stock market volatility, Economics Letters 71, 131-136.

33

Kim, Kenneth A. and Piman Limpaphayom, 2000, Characteristics of stocks that frequently hit price limits: empirical evidence from Taiwan and Thailand, Journal of Financial Markets 3, 315332. Kim, Kenneth A. and S. Ghon Rhee, 1997, Price limit performance: evidence from the Tokyo Stock Exchange, Journal of Finance 32, 885- 901. Kuhn, Betsy A., Gregory. J. Kuserk, and Peter Locke, 1991, Do circuit breakers moderate volatility? Evidence from October 1989, Review of Futures Markets 10, 136-175. Kuserk, Gregory J., Eugene Moriarty, Betsey Kuhn, and J. Douglas Gordon, 1989, An analysis of the effect of price limits on price movements in selected commodity futures markets, CFTC Division of Economic Analysis Research Report. Leamer, Edward E., 1978, Specification searches: ad-hoc inference with non-experimental data, New York: John Wiley & Sons. Lee, Charles M.C., Mark J. Ready, and Paul J. Seguin, 1994, Volume, volatility, and New York Stock Exchange trading halts, Journal of Finance 49, 183-214. Lehmann, Bruce N. 1989, Commentary: volatility, price resolution, and the effectiveness of price limits, Journal of Financial Services Research 3, 205-209. Lindley, Dennis V., 1957, A statistical paradox, Biometrika 44, 187-192. Ma, Christopher K., Ramesh P. Rao, and R. Stephan Sears, 1989, Volatility, price resolution, and the effectiveness of price limits, Journal of Financial Services Research 3, 165-199. McMillan, Henry, 1990, The effects of the S&P 500 futures market circuit breakers on liquidity and price discovery, Office of Economic Analysis, U.S. Securities and Exchange Commission, June. Miller, Merton H., 1991, Volatility, episodic volatility and coordinated circuit-breakers, in S. Ghon Rhee and Rosita P. Chang ed.: Pacific-Basin Capital Markets Research Volume II, 23-47. Moskowitz, Tobias J. and Mark Grinblatt, 1999, Do industries explain momentum, Journal of Finance 54, 1249-1290. Nath, Purnendu, 2003, Do price limits behave like magnets? London Business School WP. Seasholes, Mark and Guojun Wu, 2004, Profiting from predictability: smart investors, daily price limits, and investor attention, University of California Berkeley Working Paper. Shen, Chung-Hua and Lee-Rong Wang, 1998, Daily serial correlation, trading volume and price limits: Evidence from the Taiwan stock market, Pacific-Basin Finance Journal 6, 251-273. Slezak, Steve, 1994, A theory of the dynamics of security returns around market closures, Journal of Finance 49, 1163-1211. Subrahmanyam, Avanidhar, 1994, Circuit breakers and market volatility: a theoretical perspective, Journal of Finance 49, 237-254. 34

Subrahmanyam, Avanidhar, 1995, On rules versus discretion in procedures to halt trade, Journal of Economics and Business 47, 1-16. Telser, Lester G., 1989, October 1987 and the structure of financial markets: an exorcism of demons. In: Kamphuis Jr., R.W., Kormendi, R.C., Henry Watson, J.W. (Eds.), Black Monday and the future of the financial markets. Irwin, Homewood, IL. Verhoevena, Peter, Simon Ching, and Hock Guan Ng, 2004, Determinants of the decision to submit market or limit orders on the ASX, Pacific-Basin Finance Journal 12, 1-18.

35

Table 1 Descriptive statistics Price limit hits are identified as instances when prices reach the floor or ceiling prices governed by daily price limits. The study period is from September 1, 1998 to March 31, 1999 in Korea Stock Exchange. The pre-regime is from September 1 to December 6, 1998 when price limit is 12% and the rest of the period is the post-regime when the price limit is 15%. The sample of limits hits are groups in four categories: the pre-up, the pre-down, the post-up, and the post-down limit hits, with the prefix representing the regime and the suffix representing the direction of limit hits. Panel A of Table 1 presents the distribution of limit hits. It lists the counts of total limit hits; average daily limit hits; limits hits that occurred in the morning and the afternoon sessions respectively; limit hits that occurred at market open; limit hits that lock at limit prices until the market closes; and cases of price continuation and reversal. If a limit hit locks at the upper (lower) limit price and the subsequent first nonlimit-hit day opens at a higher (lower) price, we define it as a price continuation. A price reversal is identified if the market reopens at a lower (higher) price subsequent to a locked upper (lower) limit hit day. We also report the percentage of each item out of the total number of limit hits. The percentage of price continuation and reversals are based on the counts of locked limit hits. Percentages are reported in parentheses. Panel B of Table 1 presents intraday statistics of limit hits. We present the mean, the median and the maximum of three variables: 1) number of limit hits per day; 2) duration of limit hits, defined as the time period from the first moment of limit hits to the last moment that prices stay at limit prices; 3) number of limit hits by an individual stock that has at least one limit hit in the study period. The medians are reported in parentheses and the maximums are reported in brackets.

Panel A Limit hits distribution

Total Limit Hits Daily Limit Hits

PRE-UP

PRE-DOWN

POST-UP

POST-DOWN

1449

300

1219

492

18.1

3.8

16.5

6.6

Morning Limit Hits

870

(60%)

140

(47%)

744

(61%)

234

(48%)

Afternoon Limit Hits

579

(40%)

160

(53%)

475

(39%)

258

(52%)

Limit Hits at Market Open

244

(17%)

42

(14%)

148

(12%)

91

(18%)

975

(67%)

139

(46%)

794

(65%)

267

(54%)

Price Continuation

776

(80%)

73

(53%)

610

(77%)

177

(66%)

Price Reversal

118

(12%)

46

(33%)

115

(14%)

73

(27%)

Locked Limit Hits

Panel B Intraday statistics PRE-UP

PRE-DOWN

POST-UP

POST-DOWN

Multiple Limit Hits Per Day

5.4 (4) [94]

5.1 (2) [90]

8.4 (5) [288]

5.2 (3) [75]

Duration of Limit Hits (Minutes)

82 (57) [242]

50 (11) [240]

62 (30 [300]

93 (32) [302]

5.2 (4) [21]

2.4 (2) [7]

4.1 (3) [14]

2.3 (2) [11]

Limit Hits by Individual Stocks

36

Table 2 Acceleration rates of market microstructure variables Panels A through E of Table 2 report the estimated acceleration rates of five market microstructure variables from the quadratic function in the main text. The dependent variables of the quadratic function are the rate of return in Panel A, trading volume in Panel B, market volatility in Panel C, order flow [the share volume and the ratio of buy (sell) orders on upper (lower) limit hit days] in Panel D, and market orders [the share volume and the ratio of market buy (sell) orders on upper (lower) limit hit days] in Panel E. The independent variables are INT and SQINT. INT takes the value of 1 to 10, from the furthest to the closest 3-minute interval prior to limit hits. SQINT is the squared INT. The acceleration rate is defined as the coefficient of SQINT in the quadratic function. In each table, we report the estimated coefficients of SQINT (γ), its standard errors, and adjusted R2. We select limit hits that occur before 2:50PM to avoid the last 10 minute call auction period. All dependent variables are standardized by their mean and standard deviation of non-limit-hit days. F-tests report the coefficient comparison between the pre- and the post-regimes for all five market microstructure variables and between upper and lower limit hits for rates of return, trading volume and volatility. Standard errors are reported in parentheses. P-values of F-tests are reported in brackets. All coefficient estimations are significant at 1% level.

Panel A Rates of return γ

UPPER LIMIT HITS

LOWER LIMIT HITS

F-TEST (Upper vs. Lower)

PRE REGIME

0.06

(0.002)

0.09

(0.01)

32.95

[<0.0001]

POST REGIME Adjusted R2

0.04

(0.002)

0.06

(0.004)

17.44

[<0.0001]

0.34

0.32

F-TEST Pre-regime vs. Post-regime

32.22

[<0.0001]

17.43

[<0.0001]

Panel B Trading volume γ

UPPER LIMIT HITS

LOWER LIMIT HITS

F-TEST (Upper vs. Lower)

PRE REGIME

0.10

(0.01)

0.10

(0.01)

0.09

[0.76]

POST REGIME Adjusted R2

0.08 0.13

(0.01)

0.06 0.15

(0.01)

1.39

[0.24]

4.58

[0.03]

9.16

[0.003]

F-TEST Pre-regime vs. Post-regime

37

Panel C Volatility γ

UPPER LIMIT HITS

LOWER LIMIT HITS

F-TEST (Upper vs. Lower)

PRE REGIME

0.07

(0.002)

0.13

(0.01)

103.46

[<0.0001]

POST REGIME Adjusted R2

0.04 0.26

(0.002)

0.10 0.28

(0.01)

200.05

[<0.0001]

F-TEST Pre-regime vs. Post-regime

57.49

[<0.0001]

12.82

[0.0003]

Panel D Order flow UPPER LIMIT HITS γ

BUY VOLUME

LOWER LIMIT HITS

BUY RATIO

SELL VOLUME

SELL RATIO

PRE REGIME

0.04

(0.002)

0.006

(0.001)

0.04

(0.01)

0.01

(0.002)

POST REGIME

0.02

(0.002)

0.002

(0.001)

0.02

(0.004)

0.006

(0.003)

2

Adjusted R

F-TEST Pre-regime vs. Post-regime

0.38

15.26

0.29

[<0.0001]

32.28

0.22

[<0.0001]

21.27

0.24

[<0.0001]

16.93

[<0.0001]

Panel E Market order UPPER LIMIT HITS γ

MK BUY VOLUME

LOWER LIMIT HITS

MK BUY RATIO

MK SELL VOLUME

MK SELL RATIO

PRE REGIME

0.05

(0.003)

0.03

(0.002)

0.05

(0.006)

0.03

(0.004)

POST REGIME Adjusted R2

0.04 0.29

(0.003)

0.02 0.18

(0.002)

0.03 0.25

(0.005)

0.02 0.16

(0.003)

3.81

[0.05]

3.91

[0.05]

6.63

[0.01]

8.16

[0.004]

F-TEST Pre-regime vs. Post-regime

38

Table 3 Persistence of acceleration Table 3 reports the persistence measurements of market microstructure variables during the process of acceleration. Persistence is measured as the time period from the minimum point of the convex function onward to the moment of limit hit, stated in number of minutes. Numerically, it is calculated as 3(10+β/(2γ)), where β is the coefficient of INT and γ is the coefficient of SQINT from the quadratic function. In addition, we compare persistence measurements between the pre- and the post-regimes and between upper and lower limit hits. Delta method is used to compute the approximate standard errors for the comparisons. > and < shows the direction of the comparisons that are significant at 5% level. = indicates that the comparisons of two paired groups are insignificant at 5% level. Upper vs. Lower Variables

Pre-Up

Post-Up

Pre-Down

Post-Down

Preregime

Postregime

Rate of Return

19.75

<

21.00

17.67

<

20.00

>

=

Trading Volume

18.75

<

20.81

18.45

=

19.00

=

>

Market Volatility

18.00

=

19.13

17.19

<

19.35

=

=

Order Flow Share

22.88

=

22.50

19.88

<

24.00

>

=

Order Flow Ratio

22.50

=

22.50

19.50

=

20.00

>

>

Market Order Share

20.10

=

20.63

18.90

=

19.50

>

>

Market Order Ratio

21.00

=

21.00

18.00

<

23.25

>

<

39

Table 4 Quasi limit hits in Korea Stock Exchange Quasi limit hits are defined as large price movements that occur before triggering price limits on limit hit days. In the pre-regime, quasi limit hits are cases that prices move 9% from the previous day’s closing price before actually triggering 12% price limit. We identify 281 quasi upper limit hits and 75 quasi lower limit hits during the pre-regime. Likewise, we define post-regime quasi limit hits as cases that prices move 12% before hitting 15% price limits. 257 quasi upper limit hits and 114 quasi lower limit hits are identified in the post-regime. Table 4 presents the statistics for quasi limit hits in respective groups. All values are standardized by their mean and standard deviation of non-limit-hit days. Panel A reports the cross-sectional average of 3-minute rate of return and trading volume during half hour period before quasi limit hits and actual limit hits. The bottom three rows of Panel A report the mean differences between quasi limit hits and actual limit hits within the same regime and between actual limit hits of two regimes. We also compare quasi (actual) upper and lower limit hits within the same regime. Values in brackets are the P-values of T-tests between paired groups. Panel B reports the estimated coefficients of SQINT for respective quasi limit hit groups. The bottom two rows in Panel B reiterate the acceleration rates of respective limit hits and report the comparison between quasi limit hits and actual limit hits within each regime. Standard errors are reported in parentheses. Values in brackets are the P-values of the F-tests. The mean values in Panel A and estimations in Panel B are all significant at 1% level.

Panel A Summary statistics RETURN UPPER

VOLUME

LOWER

T-TEST

UPPER

LOWER

T-TEST

PRE QUASI LIMIT HITS

0.65

0.64

[0.43]

1.18

0.64

[<0.0001]

POST QUASI LIMIT HITS PRE LIMIT HITS POST LIMIT HITS

0.32 0.85 0.82

0.78 0.85 0.91

[<0.0001] [0.82] [0.25]

1.36 1.91 1.96

0.43 1.23 0.77

[<0.0001] [<0.0001] [<0.0001]

PRE QUASI vs. PRE HIT

[<0.0001]

[<0.0001]

[<0.0001]

[<0.0001]

POST QUASI vs. POST HIT

[<0.0001]

[<0.0001]

[<0.0001]

[<0.0001]

[0.14]

[0.21]

[0.28]

[<0.0001]

T-TEST

PRE HIT vs. POST- HIT

Panel B Regression results RETURN γ

VOLUME

UPPER

LOWER

UPPER

LOWER

0.04 (0.004)

0.06 (0.01)

0.03 (0.005)

0.03 (0.01)

0.13

0.12

0.12

0.05

0.02 (0.002) 0.05

0.04 (0.01) 0.11

0.04 (0.004) 0.11

0.01 (0.01) 0.04

PRE QUASI vs. PRE HIT

0.06 [<0.0001]

0.09 [<0.0001]

0.10 [<0.0001]

0.10 [<0.0001]

POST QUASI vs. POST HIT

0.04 [<0.0001]

0.06 [0.03]

0.08 [<0.0001]

0.06 [<0.0001]

PRE QUASI LIMIT HITS Adjusted R2 POST QUASI LIMIT HITS Adjusted R2 F-TEST

40

Table 5 Pseudo limit hits in NASDAQ We impose hypothetical 12% and 15% price limits to the NASDAQ securities and identify the days that trigger these price limits, which are defined as pseudo limit hits. There are 540 upper limit hits and 367 lower limit hits under the hypothetical 12% price limit and 276 upper limit hits and 143 lower limit hits under the hypothetical 15% price limit. Table 5 reports the statistics of rates of return and trading volume for pseudo limit hits in respective groups. All values are standardized by their mean and standard deviation of non-limit-hit days. Panel A reports the cross-sectional average of 3-minute rate of return and trading volume during the half hour pre-hit period. We report T-test of the mean comparison between pseudo limit hits in two hypothetical regimes and between upper and lower pseudo limit hits. Panel B reports the estimated coefficients of SQINT from the quadratic regression, where the dependent variables are the rate of return and trading volume respectively. We compare the acceleration rates between 12% pseudo limit hits and 15% pseudo limit hits. F-statistics and P-values are reported at the bottom of Panel B. P-values are reported in brackets. Standard errors are reported in parentheses. All the mean values in Panel A and coefficient estimates in Panel B are significant at 1% level unless marked by +.

Panel A Summary statistics RETURN

VOLUME

UPPER

LOWER

t-TEST

UPPER

LOWER

t-TEST

PSEUDO 12% LIMIT HITS

2.41

2.75

[0.06]

4.55

3.36

[0.03]

PSEUDO 15% LIMIT HITS

2.8

3.66

[0.02]

5.17

3.62

[0.001]

[0.05]

[0.01]

[0.31]

[0.53]

T-TEST Pseudo 12% vs. Pseudo 15%

Panel B Regression results RETURN

VOLUME

γ

UPPER

LOWER

UPPER

LOWER

PSEUDO 12% LIMIT HITS

0.22 (0.02)

0.29 (0.02)

0.16 (0.06)

0.11 (0.03)

PSEUDO 15% LIMIT HITS

0.24 (0.02)

0.35 (0.03)

0.11 (0.09)

0.15 (0.05)

Adjusted R2

0.18

0.19

0.02

0.08

0.62 [0.43]

2.10 [0.15]

0.25 [0.62]

0.70 [0.40]

+

F-TEST Pseudo 12% vs. Pseudo 15%

41

Table 6 Firm size effect The sample stocks are divided into the small-, the medium-, and the large-cap stocks based on the standards in the Korea Stock Exchange fact book. Small-cap stocks have market capitalization less than 35 billion won on September 1, 1998. Medium-cap stocks have market capitalization between 35 billion won and 75 billion won. Large-cap stocks have market capitalization above 75 billion won. There are 220 smallsized stocks, 77 medium-sized stocks and 88 large-sized stocks. Table 6 reports the statistics of price limit hits stratified by capitalizations. Panel A reports the number of limit hits, cross-sectional average of 3-minute rate of return and trading volume during the half hour period prior to limit hits. The average number of limit hits per stock is reported in parentheses. T-tests report the mean comparison between the small- and the large-cap stocks. Panel B reports the estimated acceleration rates for respective groups. Standard errors are reported in parentheses. At the bottom of Panel B, we report the comparisons of estimated coefficients between the small- and the large-cap limit hits. Pvalues are reported in brackets. All the mean values in Panel A and coefficient estimations in Panel B are significant at 1% level.

Panel A Summary statistics NO. OF OBSERVATIONS

RETURN

VOLUME

UPPER

LOWER

UPPER

LOWER

UPPER

LOWER

Small-Cap

973 (4.4)

208 (0.9)

0.80

0.89

1.49

0.75

Medium-Cap

172 (2.2)

37 (0.5)

0.93

0.76

2.06

1.16

Large-Cap

253 (2.9)

34 (0.4)

0.99

1.00

2.24

1.71

[0.0001]

[0.58]

[0.0001]

[0.04]

0.72

0.90

1.45

0.44

PRE-REGIME

T-Tests POST-REGIME Small-Cap

839 (3.8)

340 (1.5)

Medium-Cap

169 (2.2)

80 (1.0)

0.82

1.03

2.16

0.59

Large-Cap

201 (2.3)

50 (0.6)

0.80

1.20

1.88

0.84

[0.08]

[0.01]

[0.001])

[0.001]

T-Tests

Panel B Regression results RETURN γ

UPPER PRE POST

VOLUME

LOWER PRE POST

UPPER PRE POST

LOWER PRE POST

Small-Cap

0.05 (0.003)

0.03 (0.003)

0.10 (0.01)

0.07 (0.005)

0.10 (0.005)

0.08 (0.01)

0.10 (0.01)

0.07 (0.01

Medium-Cap

0.07 (0.01)

0.03 (0.01)

0.05 (0.02)

0.07 (0.01)

0.13 (0.01)

0.09 (0.03

0.09 (0.03)

0.05 (0.01)

Large-Cap

0.07 (0.005)

0.04 (0.005)

0.11 (0.02)

0.02 (0.01)

0.11 (0.01)

0.09 (0.03

0.16 (0.03)

0.07 (0.02

Adjusted R2

0.38

0.30

0.34

0.32

0.33

0.06

0.15

0.12

[0.006]

[0.11]

[0.18]

[0.003]

[0.33]

[0.55]

[0.09]

[0.95]

F-TEST Small- vs. Large-cap

42

Panel A. Pre-regime

Counts 450 400 350 300 250 200 150 100 50 0 9:30- 10:00- 10:30- 11:00- 1:0010:00 10:30 11:00 11:30 1:30

1:302:00

2:002:30

2:30Interval 3:00

Panel B. Post-regime Counts 450 400 350 300 250 200 150 100 50 0 9:00- 9:30- 10:00- 10:30- 11:00- 11:30- 1:00- 1:30- 2:00- 2:30-Interval 9:30 10:00 10:30 11:00 11:30 12:00 1:30 2:00 2:30 3:00

Fig. 1. Intraday distribution of price limit hits Price limit hits are identified as instances when prices reach the floor or ceiling prices governed by daily price limits. The study period is from September 1, 1998 to March 31, 1999 in Korea Stock Exchange. The pre-regime is from September 1 to December 6, 1998 when price limit is 12% and the rest of the period is the post-regime when the price limit is 15%. The sample of limits hits are groups in four categories: the pre-up, the pre-down, the post-up, and the post-down limit hits, with the prefix representing the regime and the suffix representing the direction of limit hits. Figure 1 A-B plots the distribution of price limit hits during each half hour period within a trading day. The morning trading session in the pre-regime is 9:30 A.M. - 11:30 A.M. and it is 9:00 A.M. - 12:00 Noon in the post-regime. The afternoon trading session is 1:00 P.M. - 3:00 P.M. in both regimes. The bars on the left represent upper limit hits and the bars on the right represent lower limit hits.

43

Panel A Rate of Return 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 1

2

3

4

5 6 Interval

7

8

9

10

Panel B Trading Volume 6 5 4 3 2 1 0 1

2

3

4

5

6

7

8

9

10

7

8

9

10

Interval

Panel C

Volatility 7 6 5 4 3 2 1 0 1

2

3

4

5 6 Interval

44

Panel D Order Flow 3 2.5 2 1.5 1 0.5 0 1

2

3

4

5 6 Interval

7

8

9

10

Panel E: Market Order 4 3.5 3 2.5 2 1.5 1 0.5 0 1

Pre-Up

2

3

4

Pre-Down

5 6 Interval

7

8

9

Post-Up

10

Post-Down

Fig. 2. Behavior of market microstructure variables prior to limit hits Price limit hits are identified as instances when prices reach the floor or ceiling prices governed by daily price limits. The study period is from September 1, 1998 to March 31, 1999 in Korea Stock Exchange. The pre-regime is from September 1 to December 6, 1998 when price limit is 12% and the rest of the period is the post-regime when the price limit is 15%. The sample of limits hits are groups in four categories: the pre-up, the pre-down, the post-up, and the post-down limit hits, with the prefix representing the regime and the suffix representing the direction of limit hits. Figure 2 A-E plots the cross sectional average of five market microstructure variables during each 3-minute interval prior to limit hits. The variables are rate of return, trading volume, volatility, order submission (buy orders on upper limit hit days and sell orders on lower limit hit days), and volumes of market orders (market buy orders on upper limit hit days and market sell orders on lower limit hit days). All the values are standardized by subtracting the mean and dividing by the standard deviation on non-limit-hit days.

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