the effect of price limits on intraday volatility and information asymmetry

The effect of price limits on intraday volatility

and information asymmetry ☆

Yong H.Kim a,?,J.Jimmy Yang b

a

College of Business,University of Cincinnati,USA b College of Business,Oregon State University,USA

Received 24April 2007;accepted 12November 2007

Available online 19November 2007

Abstract

We investigate the effect of price limits on intra-day volatility and information asymmetry using transactions data from the Taiwan Stock Exchange.Proponents of price limits argue that they provide an opportunity for investors to reevaluate market information and make more rational trading decisions.We identify three different limit hits –closing,single,and consecutive –and hypothesize that only the consecutive limit hits are likely to provide such an opportunity,namely,to counter investor overreaction (volatility hypothesis)and to enhance information revelation (information asymmetry hypothesis).Our empirical evidence supports the volatility hypothesis.Our findings generate important policy implications for stock markets that have price limits.

?2007Elsevier B.V .All rights reserved.

JEL Classification:G14;G15;G18

Keywords:Price limits;Overreaction;V olatility;Information asymmetry;Transactions data

Available online at https://www.360docs.net/doc/235572376.html,

Pacific-Basin Finance Journal 16(2008)522–

https://www.360docs.net/doc/235572376.html,/locate/pacfin

☆

Earlier versions of this paper were titled “Price Limits and Overreaction ”or “Cooling-off Effects of Price Effects:Evidence from Transactions Data ”and presented at the meetings of Korea Money and Finance Association and Korea –America Economic Association,Seoul;Sociedade Brasileira de Finan?as,S?o Paulo;Financial Management Association,Denver;Theories and Practices of Securities and Financial Markets,Kaohsiung;and at University of Cincinnati.The authors are grateful for helpful comments from Marcelo Fernandes,Larry Harris,Brian Hatch,Steven Jones,Yi-tsung Lee,Marti Levy,Dave Manzler,anonymous referees,Ghon Rhee (the Editor),Jong-won Yoon and the participants at the presentations indicated above.Kim acknowledges financial support from the University of Cincinnati Foundation.The usual disclaimers apply.?Corresponding author.College of Business,PO BOX 210020,Cincinnati,OH 45221-0020,USA.Tel.:+15135567084;fax:+15135560979.

E-mail address:yong.kim@https://www.360docs.net/doc/235572376.html, (Y .H.Kim).

0927-538X/$-see front matter ?2007Elsevier B.V .All rights reserved.

doi:10.1016/j.pacfin.2007.11.002

1.Introduction

Research in behavioral finance has cast some doubt on the market efficiency hypothesis and provided both empirical evidence and theoretical models of market overreaction (e.g.,De Bondt and Thaler,1985;Daniel et al.,1998;Barberis and Thaler,2003;Shiller,2003).Although earlier evidence is from a relatively long-term perspective,recent studies have also found short-term investor overreaction (e.g.,Otchere and Chan,2003;Michayluk and Neuhauser,2006).Presumably,market overreaction creates unwanted excessive volatility,and thus,any market mechanisms that might reduce overreaction would benefit investors and security regulators if the gains outweigh the costs.Kim and Yang (2004)document in detail three such potential market mechanisms:market-wide circuit breakers,trading halts,and price limits.Although the New York Stock Exchange (NYSE)implemented circuit breakers after October 19,1988,because they are rarely activated,1we cannot be certain whether they are effective.Existing literature on trading halts consistently finds that both volatility and trading volume increase significantly after trading halts (e.g.,Lee et al.,1994;Corwin and Lipson,2000;Christie et al.,2002).However,unlike the NYSE,the U.S.futures markets and many stock exchanges around the world have adopted price limits.2The most popular rationale for imposing price limits is to reduce market overreaction,though no consistent evidence about the performance of price limits has been provided.We examine the effect of price limits using transactions data from the Taiwan Stock Exchange (TWSE),one of the major stock markets in Asia and also one of the most active stock markets in the world.

By definition,price limits regulate the magnitude of the change in price that can occur for a given asset during a single trading session.From their proponents'point of view,price limits provide an opportunity that allows investors to reevaluate market information and make more rational decisions during periods of extreme price changes,3thereby reducing traders'over-reaction and diminishing price volatility.However,opponents of price limits argue that they serve no purpose other than to slow or delay the price discovery process (e.g.,Fama,1989;Kim and Rhee,1997).Although price limits can stop the price of a share from falling or rising beyond the limit on a given trading day,opponents argue that the price will continue to move toward equilibrium when new trading limits are established on subsequent trading day(s).To resolve these two contrary arguments,we may have to rely on empirical evidence.However,empirical literature does not definitively answer whether price limits reduce overreaction or merely delay the price discovery process.Studies that test directly for the effect of price limits generally use relatively small data sets and reach different conclusions.In futures markets,Arak and Cook (1997)find that price limits act as stabilizers to “cool off ”the market,whereas Chen's (1998)investigation of 19futures contracts shows little evidence of such effect.In stock markets,Kim and Rhee (1997)and Bildik and Gulay (2006)find that price limits delay price discovery and interfere with trading in their respective examinations of Japanese and Turkish data.On the 1

Circuit breakers were triggered on the NYSE for the first and only time on October 27,1997,when the Dow Jones Industrial Average fell 350points at 2:35p.m.and 550points at 3:30p.m.Those declines reflected an approximate 7%overall decline,and the market was closed for the remainder of the day.See Goldstein and Kavajecz (2004)for more detail.

2Countries with price limits include Austria,Belgium,France,Greece,Italy,the Netherlands,Spain,Switzerland,and Turkey in Europe and China,India,Japan,Korea,Malaysia,Taiwan,and Thailand in Asia.

3Brennan (1986)also shows that price limits can act as partial substitutes for margin requirements,in that they ensure contract performance without the need for costly litigation.523

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524Y.H.Kim,J.J.Yang/Pacific-Basin Finance Journal16(2008)522–538

contrary,Bildik and Elekdag(2004)find evidence that price limits counter overreaction in the Istanbul Stock Exchange.

Prior studies have used daily data rather than trade-by-trade transaction data.However,to determine whether price limits reduce overreaction,transaction data should be used because the transitory volatility caused by overreaction is likely to be reflected in transaction data.For example,if a significant change in volatility occurs only during the first hour of trading before or after a limit hit,daily data would not reveal the real impact of price limits.Recently,transaction data have become available and been used to test the effects of price limits.However,again,the results are conflicting.Cho et al.(2003)use intraday data from the TWSE to test the magnet effect and find a statistically and economically significant tendency for stock prices to accelerate toward the upper bound and weak evidence of acceleration toward the lower bound as the price approaches the limits.However,Nath(2003)finds that trading activity accelerates as stock prices approach their lower,but not upper,price limits on the National Stock Exchange of India. Recently,Du et al.(2007)find evidence of the magnet effect from their study of transaction data from the Korea Stock Exchange.Chan et al.(2005)investigate transaction data and the limit order book from the Kuala Lumpur Stock Exchange and find no evidence that price limits improve information asymmetry.They conclude that price limits impose serious costs even in a market with a wide price limit band(30%for each of the two daily trading sessions).

We investigate the transaction data from the TWSE to study the effect of price limits on intraday volatility and information asymmetry.With trade-by-trade data,we are able to identify three different limit hits,namely,closing,single,and consecutive.A closing limit hit occurs when a price hits the limit and no other trades occur during the remainder of the day.A single limit hit occurs when non-limit-hit transactions follow a limit hit.Consecutive limit hits occur when additional trades at the same limit price take place after a limit hit.We hypothesize that only consecutive limit hits are likely to counter investor overreaction and thus reduce volatility and information asymmetry.

Specifically,we empirically test two hypotheses:the volatility hypothesis and the information asymmetry hypothesis.If price limits can provide traders with a time period during which they can obtain information,reassess the market price,and avoid or correct overreaction,the uncertainty and irrationality in the market will be less severe and thus the price volatility after a limit hit should be less than that before a limit hit.In contrast,if price limits delay the price discovery process and interfere with trading,the price volatility after a limit hit may be higher than that before(e.g.,Kim and Rhee,1997).Our empirical evidence supports the volatility hypothesis that only consecutive limit hits are likely to counter investor overreaction and reduce volatility.In addition,we find that the longer the duration of the consecutive limit hits,the more the volatility is reduced.

If price limits provide time for information dissemination and revelation,the degree of information asymmetry should be reduced after limit hits(e.g.,Chan et al.,2005;Chen et al., 2005).Thus,we hypothesize that,among the three types of limit hits,only consecutive limit hits would provide investors with time and incentive to obtain and reevaluate information to mitigate information asymmetry.Our empirical evidence does not support the information asymmetry hypothesis.None of the three types of limit hits can mitigate information asymmetry,consistent with Chan et al.(2005).

Our paper makes at least two significant contributions to the literature.First,we initiate a classification of three different types of limit hits.This classification may open new research avenues for further price limit studies with transactions data because the three limit-hit types have different informational characteristics.Second,to the extent that policymakers typically consider

curbing excessive volatility to be a justification for imposing price limits,our finding that volatility reduces only after consecutive limit hits has important regulatory implications.In terms of exploring the benefits of price limits associated only with consecutive limit hits,a hybrid or combination of price limits and trading halts might be considered as a policy alternative to pure price limits (or trading halts).That is,policymakers may combine a range of trading halt mechanisms with price limits so that the similar conditions associated with consecutive limit hits could be automatically induced.In other words,when the price hits the limit,a trading halt is automatically triggered,a situation similar to consecutive limit hits in the sense that investors have more time to obtain and reevaluate information and make rational trading decisions during the trading halt period.In fact,some stock exchanges (e.g.,Spain)have already introduced a form of hybrid policies,while existing literature is not providing any lead on this issue yet.4

It should be noted that our results only show that,if price limits are hit,the best scenario is the one where there are consecutive limit hits.That is,our results have no implications on whether a market is better off with consecutive limit hits as opposed to one that does not even have price limits.Nevertheless,our suggestion to mimic consecutive limit hits by combining price limits and trading halts are relevant to many markets that have price limits in place.In fact,the price limit system that triggers trading halts has been imposed in the U.S.Futures Markets.

We organize the remainder of this paper as follows:In the next section,we provide the institutional background of the TWSE.In Section 3,we describe our data and present the summary statistics.Then in Section 4,we discuss our hypothesis and establish the research design.Finally,we present the empirical findings in Section 5and conclude in Section 6.

2.Institutional background

According to the Monthly Bulletin of Statistics of the Republic of China (March 2001),531stocks were listed on the TWSE at the end of year 2000.The total market value is New Taiwanese Dollar (NT$)8,191,170million (or approximately US$248.5billion at the exchange rate of NT $32.96/US$1).The average daily trading volume is NT$112,640million (US$3.4billion).

The TWSE is an order-driven market with no market makers or specialists in which investors can submit either market or limit orders.The automated central limit order book accumulates and matches orders against one another.Because there are no official market makers,the bid and ask quotations represent the best prices,provided by various traders,in the limit order book.According to the Taiwan Stock Exchange Corporation (TWSEC),since August 1985,the open outcry system gradually has been replaced by a computer-aided trading system and was upgraded to a fully automated securities trading system in 1993.The trading session of the centralized market lasts from 9:00a.m.to 12:00p.m.,Monday through Friday.On the first,third,and fifth (if there is one)Saturdays of each month,trading also takes place from 9:00a.m.to 12:00p.m.Thirty minutes before the market opens,orders can be submitted through security firms and are ranked on the basis of their price-time priority.The opening price is the one that maximizes the trading volume.Following the opening,the system matches orders on a periodic basis until the closing;each round of clearing takes approximately one minute.The actual time interval of each round of clearing may vary slightly according to the trading intensity.

4

In a recent comparative study of price limits and trading halts,Kim et al.(in press)find that trading halts perform better than price limits in curbing excess volatility and increasing market liquidity.Much remains to be done,however,in providing information on relative merits among the alternative policy combinations,e.g.,pure price limits versus trading halts triggered by price limit hits.525

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526Y.H.Kim,J.J.Yang/Pacific-Basin Finance Journal16(2008)522–538 The TWSE has imposed daily price limits since its inception in1962.According to the TWSEC,the purpose of price limits is to avoid excessive volatility and protect investors by limiting their potential daily losses.The TWSE sets both its upward and its downward daily price limits at a predetermined rate on the basis of the previous day's closing price.The price limit rate has been adjusted up or down several times in accordance with the market conditions.For example,Panel A of Table1provides the price limit rates during different periods of year2000. For stocks listed on the TWSE,tick sizes(i.e.,the minimum allowable unit that a stock price may change)vary with the market prices,as we illustrate in Panel B of Table1for each price range. Stocks that hit their price limits can be traded as long as the transaction prices are within the limits. Thus,the TWSE price limits are simply boundaries,not triggers for trading halts.

3.Data and summary statistics

3.1.Data description

We obtained transaction data for all TWSE-listed stocks in2000from the Taiwan Economic Journal Data Bank.The data contain time-stamped records of all transactions on the TWSE.In 2000,only439out of541stocks were traded during the entire year;the remainders were either delisted or initial public offerings.The data record the trading volume,trading price,and time for each transaction,as well as the prevailing bid and ask prices from the limit order book.

The year2000is an ideal period for examining price limit effects for several reasons.First,the stock market was relatively volatile in2000;the index rose from8756.55at the beginning of the year to10,202.20on February17,and then dropped to4743.94at the end of the year.Because of Table1

Price limit rates and tick sizes

Panel A:price limits in year2000

Periods Price limit rates

01/01/2000to03/19/20007%upward and7%downward 03/20/2000to03/26/20007%upward and3.5%downward 03/27/2000to10/03/20007%upward and7%downward 10/04/2000to10/11/20007%upward and3.5%downward 10/12/2000to10/19/20007%upward and7%downward 10/20/2000to11/07/20007%upward and3.5%downward 11/08/2000to11/20/20007%upward and7%downward 11/21/2000to12/31/20007%upward and3.5%downward Panel B:tick sizes

Price range Tick size

P b NT$5.00NT$0.01 NT$5.00≤P b NT$15.00NT$0.05 NT$15.00≤P b NT$50.00NT$0.10 NT$50.00≤P b NT$150.00NT$0.50 NT$150.00≤P b NT$1,000.00NT$1.00 NT$1000.00≤P NT$5.00 Panel A reports the price limit rates during different periods of year2000.Panel B reports the tick sizes for different price ranges on the Taiwan Stock Exchange.NT$is the Taiwanese https://www.360docs.net/doc/235572376.html,rmation from both panels was obtained from the Taiwan Stock Exchange Corporation.

this high volatility,the chance for stocks to hit their limits is high,and we probably can obtain more observations of limit hits.Thus,our data alleviate the concern of small sample sizes,as has been noted in previous studies.Second,some important events,such as a presidential election and the resignation of the prime minister,occurred in 2000,so the lower limit rate was adjusted down from 7%to 3.5%four times during the year,though the upper limit rate remained unchanged at 7%(see Panel A of Table 1).Therefore,we are able to test our hypothesis using two time periods with different price limit rates,providing insights to the impact of varying price limit rates.

3.2.Summary statistics

For limit hits,we identify three different cases.The first case,a closing limit hit ,occurs when a price hits the limit and no other trades occur during the remainder of the day.The second case is called a single limit hit ,which occurs when a limit hit is followed by non-limit-hit transactions.The last case is a consecutive limit hit and occurs when a limit hit is followed by additional trade (s)at the limit price.

In Panel A of Table 2,we report the number of observations and ratios for limit hits during two periods for 439stocks traded on the TWSE in 2000.Period 1represents all times during which 7%upward and 7%downward price limits were applied,whereas Period 2represents all times with 7%Table 2

Summary statistics

Panel A:observations and ratios

Period 1

Period 2Ratio 2–Ratio 1Z-value #of observations

Ratios #of observations Ratios Upper limit hits

399,8900.0233104,1240.02940.006268.46Single

12,4555528Consecutive

26,8269156Closing

53432114Lower limit hits

305,4660.0178251,7570.07110.0534565.21Single

15,24614,973Consecutive

28,97825,285Closing

44714359Total limit hits 705,3560.0410355,8810.10060.0595462.62Panel B:daily market return

Period

N Mean S.D.Min Max Median 1

213?0.003750.01990?0.067740.04483?0.002922570.003250.02518?0.027570.06172?0.00125There were 439stocks traded during the whole year 2000on the Taiwan Stock Exchange.Panel A reports the number of observations and ratios for both upper and lower limit hits during Periods 1and 2.Upper (lower)limit hits occur when the transaction prices hit the upward (downward)price limits.Period 1represents all times with 7%upward and 7%downward price limits;Period 2represents all times with 7%upward and 3.5%downward price limits.There are 17,188,194transactions during Period 1and 3,539,160transactions during Period 2for all 439stocks.A single limit hit occurs when a limit hit is followed by non-limit-hit transactions.Consecutive limit hits occur when a limit hit is followed by additional trades at the limit price.Closing limit hits occur when a price hits the limit and no other trades occur during the remainder of the day.Ratios each are defined as the number of observations divided by the number of transactions in each period.Ratio 2–Ratio 1is the ratio of Period 2minus the ratio of Period 1.The Z-value of Ratio 2–Ratio 1is based on the standard binomial test.Panel B reports the summary statistics of the daily market return during Periods 1and 2from the TWSE Capitalization Weighted Price Index (TAIEX).S.D.represents the standard deviation.

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upward and3.5%downward price limits.During Period1,17,188,194transactions occurred,and 3,539,160transactions took place during Period2.We define upper(lower)limit hits as those that occur when the transaction prices hit the upward(downward)price limits.Ratios,as we display in Panel A of Table2,represent the number of observations divided by the number of transactions in each period.The tick size,set by the TWSE,effectively limits the number of stocks that can hit the exact7%price limit.For example,at a closing price of NT$80,the price of a stock on the next trading day may go up to NT$85.6or down to NT$74.4.However,the tick size for the price range NT$50–$150is NT$0.5;therefore,a limit hit occurs when the price rises to NT$85.5or declines to NT$74.5,even though the return is only6.875%or?6.875%,respectively.

During Period1,there are more upper limit hits than lower limit hits,and the overall limit-hit ratio is approximately4%.That is,for every100transactions,4hit the price limits.The sum of the numbers of observations for single,consecutive,and closing limit hits is much less than the total number of limit-hit observations;thus,many limit hits are categorized as consecutive.On average,each consecutive limit-hit observation consists of12limit-hit transactions.

In contrast,there are more lower limit hits than upper limit hits during Period2,largely because of the3.5%downward price limits.Furthermore,Period2is more volatile than Period1, probably because of several important events that occurred then,such as the presidential election and the resignation of the prime minister.In Period2,the overall limit-hit ratio is approximately 10%,and7%are lower limit hits.

In Panel B of Table2,we report the summary statistics of the daily market returns during Periods1and2,which are based on the TWSE Capitalization Weighted Price Index(TAIEX),the most frequently quoted index of the many stock indices published by TWSE.Period2is apparently more volatile than Period1because the standard deviation(SD)of daily market returns in Period2is higher than that in Period1.We perform the Wilcoxon rank sum test to determine if the median in Period1is significantly different from that in Period2,but we find no significant difference between them with a p-value of0.4104.Because the stock market is more volatile in Period2,we expect to find higher limit-hit ratios in Period2.Furthermore,given the asymmetric price limit rates during Period2,we also expect to find more lower limit hits than upper limit hits.The results we report in Panel A of Table2are consistent with our conjecture.

4.Hypotheses and methodology

4.1.Volatility hypothesis

If price limits can provide traders with a time period during which they can obtain information, reassess the market price,and avoid or correct overreaction,the uncertainty and irrationality in the market will be less severe and thus the price volatility after a limit hit should be less than that before a limit hit.In contrast,if price limits delay the price discovery process and interfere with trading,the price volatility after a limit hit may be higher than that before(e.g.,Kim and Rhee, 1997).

We hypothesize that,among the three types of limit hits,only consecutive limit hits are likely to reduce volatility.Because the single limit hit is just a one-time shot,it does not provide a time period for investors to obtain and reevaluate information to avoid potential overreaction.On the other hand,closing limit hits provide an overnight period,from the time price limits are hit till the next opening,during which investors have plenty of time if needed.However,we believe that closing limit hits are more likely related to delayed price discovery and less associated with investor overreaction.For example,Kim and Rhee(1997)find more price continuations

following closing limit hits,suggesting that prices continue to move in the same direction toward the equilibrium levels once new price limits are established on the following day.5That is,closing limit hits would occur because the equilibrium price is outside the daily allowable range,not because of the investor overreaction.In this case,the volatility spillover is likely to occur on the following day.

As to the consecutive limit hits,there are at least two reasons to believe that the volatility reduction is likely to happen.First,unlike the single limit hits,consecutive limit hits provide investors a time period necessary to obtain and reevaluate information.This period spans from the first limit hit till the last hit for a consecutive limit hit.During the period,prices are not moving because investors are trading at the same limit price.Second,unlike the closing limit hits where equilibrium prices are often outside the price limits,consecutive limit hits could be the outcome of three plausible cases —overreaction,equilibrium,and order imbalance.If limit hits are due to investor overreaction,the price will eventually move back to its equilibrium level,which is within the price-limit range.On the other hand,if the equilibrium price is exactly at the limit,investors will keep trading at the limit price.However,if there is order imbalance (only limit buy orders exist at the upper limit or only limit sell orders exist at the lower limit)and consecutive limit hits are simply the result of the arrival of liquidity traders,the equilibrium price is outside the price limits and thus will not be reached till the next day(s),a case similar to the closing limit hit.Because of these three possibilities,investors have incentive to reevaluate information once consecutive limit hits occur to develop their trading strategy.Thus,consecutive limit hits are more likely to cause volatility reduction than the single and closing limit hits.

https://www.360docs.net/doc/235572376.html,rmation asymmetry hypothesis

If price limits provide time for information dissemination and revelation,the degree of information asymmetry should be reduced after limit hits (e.g.,Chan et al.,2005;Chen et al.,2005).According to Easley and O'Hara (1987)and Stoll (1989),when liquidity providers perceive an increase in the degree of information asymmetry,they tend to widen the bid-ask spread to compensate for the expected losses to informed traders.Whereas these studies are based on quote-driven markets,Biais et al.(1995),Hamao and Hasbrouck (1995),and Ahn et al.(2001)investigate major order-driven markets in the world and find similar results.In an order-driven market,such as the Tokyo Stock Exchange and the Paris Bourse,liquidity is provided by the traders who submit limit orders.The difference between the price of the lowest sell limit order and that of the highest buy limit order determines the effective bid-ask spread,which represents the compensation they expect in return for supplying immediacy.Because limit order prices are fixed,investors face adverse selection risk from the arrival of informed traders.Glosten (1994)shows that adverse selection costs generate positive bid-ask spreads in an order-driven trading environment.If price limits mitigate information asymmetry,liquidity providers will face fewer adverse selection risks from informed traders after limit hits and,accordingly,will narrow the bid-ask spreads.

We hypothesize that,among the three types of limit hits,only consecutive limit hits are likely to mitigate information asymmetry.The argument is similar to that of our volatility hypothesis —only consecutive limit hits provide investors with time and incentive to obtain and reevaluate 5

We perform a similar analysis to Kim and Rhee (1997)and find results consistent to theirs.Results are available upon request.529

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information.If this hypothesis holds,we expect to observe lower bid-ask spreads after con-secutive limit hits than before.

4.3.Methodology

To test our hypotheses,we examine the price volatility and bid-ask spreads before and after our three types of limit hits.On the basis of our preceding discussion,if price limits provide traders with a time period to obtain information,reassess the market price,and avoid unnecessary overreaction,the degree of price volatility after a limit hit should be less than that before a limit hit.6

We calculate the average3-and5-minute price volatility in either30or15min before and after the limit hits by obtaining the3-minute returns(R t3),5-minute returns(R t5),and mean return(Rˉ) from the following calculations:

R3t?S n

P t

P tà3

;e1T

R5t?S n

P t

P tà5

;ande2T

P R?1X

R t;e3T

where?n is the natural logarithm,P t is the transaction price at t,P t?3is the transaction price 3min prior to t,P t?5is the transaction price5min prior to t,and R t is either R t3or R t5.To achieve robust results,we use three different volatility measures:V1is the standard deviation of returns, V2is the mean of absolute returns,and V3is the log of high price to low price.7We calculate these measures as follows:

V1?

????????????????????????????????????????

1

nà1

X

R tàP R

àá2

;

r

e4T

V2?1

n

X

j R t j;ande5T

V3?S n

HP T

LP T

e6T

where n is the number of observations,R t is equal to R t3(R t5)for3-minute(5-minute)price volatility,Rˉis the mean of R t,and HP T(LP T)is the high(low)price during the T(either30or15)

6We do not form a comparison sample such as pseudo limit hits because of two reasons.First,stocks whose prices are in the neighborhood of price limits may also be affected by price limits and thus do not represent useful benchmarks to test price limit effects for the limit-hit sample.A good example is the magnet effect observed by Cho et al.(2003)and Du et al.(2007).Second,our purpose is to compare three different kinds of limit hits and thus a comparison sample does not necessarily reinforce our analytical results.

7See Grossman(1988)for merits of this volatility measurement.

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minutes before or after price limits.The volatility hypothesis holds if we observe lower volatility after consecutive limit hits than before.

As suggested by Roll (1984),to mitigate the distortion from the bid-ask bounce,we use the bid-ask midpoint instead of the transaction price to calculate the returns and volatilities.We define the bid-ask midpoint (M t )as follows:

M t ?P bt tP at eT2;e7Twhere P bt is the bid price at time t ,and P at is the ask price at time t .For bid-ask spreads,we calculate the relative spread (RS t )and the mean of relative spreads (R ˉS ˉ)with the following formula:

RS t ?P at tP bt eTM t

;and e8TP RS ?1n X RS t e9TThe information asymmetry hypothesis holds if we observe lower R ˉS ˉafter consecutive limit hits than before.

In summary,we hypothesize that,among the three types of limit hits,only consecutive limit hits are likely to reduce volatility and mitigate information asymmetry.The volatility hypothesis leads to the following testable proposition:the price volatility after limit hits will be lower than that before limit hits for consecutive limit hits,but not for closing and single limit hits.The information asymmetry hypothesis leads to the following testable proposition:the relative spread after limit hits will be lower than that before limit hits for consecutive limit hits,but not for closing and single limit hits.

5.Results

5.1.Volatility hypothesis

In Table 3,we report the average return R

ˉand average volatilities,V 1,V 2and V 3,from the 3-minute return analysis based on bid-ask midpoints.Pre-Hits refer to the period 15min prior to limit hits.For closing limit hits,Post-Hits refer to the time 15min after the opening on the next trading day.For single and consecutive limit hits,Post-Hits refer to the 15min after limit hits.8If no trading occurs during the 3-minute interval,we use the previous trading price to determine the return (zero in this case).

The sample sizes reported in Table 3are smaller than those in Table 2for closing limit hits because we delete observations whose bid and/or ask prices are unavailable.The sample sizes for single and consecutive limit hits are much smaller than those reported in Table 2because we eliminate many observations in the process of selecting a qualified sample.We delete observations that occur during the first and last 15min of each trading day to ensure the availability of trading data both 15min prior to and after each selected observation.Fur-thermore,we delete an observation if another limit hit occurs during the time 15min prior to or 8

The results from the 30min before and after limit hits are similar,but the sample sizes are smaller.Although not reported,the medians of volatilities also show similar results.These results are available on request.531

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Table3

V olatility hypothesis:return and volatility

Panel A:closing limit hits

Period1Period2

Pre-Hits Post-Hits Pre-Hits Post-Hits Upper limit hits(N=3416)(N=1531)

Rˉ 1.040? 1.622 1.063? 2.165

V1 3.419? 6.754 3.089?7.647

V2 2.247? 4.672 1.977? 5.078

V311.005?18.70010.348?21.699 Lower limit hits(N=3141)(N=2162)

Rˉ?0.902??2.040?0.292??0.996 V1 3.330?7.599 1.907? 4.569

V2 2.157? 5.107 1.145? 3.000

V310.002?21.373 6.246?12.771 Panel B:single limit hits

Period1Period2

Pre-Hits Post-Hits Pre-Hits Post-Hits Upper limit hits(N=133)(N=79)

Rˉ 1.663??1.190 2.208??1.210 V1 4.735< 6.2667.335 6.554

V2 3.298< 4.143 5.170 4.280

V310.36411.09215.128>11.576 Lower limit hits(N=212)(N=234)

Rˉ?1.880? 1.380?0.960?0.839

V1 6.7347.265 4.221? 6.369

V2 4.689 4.817 2.741? 3.963

V313.90412.7897.956?10.007 Panel C:consecutive limit hits

Period1Period2

Pre-Hits Post-Hits Pre-Hits Post-Hits Upper limit hits(N=188)(N=127)

Rˉ 2.811??1.280 3.546??1.780 V1 6.104> 5.3258.022> 6.812

V2 4.687? 3.524 5.918? 4.682

V317.894?10.39923.140?12.311 Lower limit hits(N=323)(N=332)

Rˉ?2.840? 1.418?0.990?0.615

V1 5.883 6.067 3.125 3.162

V2 4.523> 3.996 2.011 1.947

V316.502?11.186 6.404> 5.468

after the trading took place.These strict selection criteria enable us to obtain a clean sample to test our hypotheses.

Results from closing limit hits,as shown in Panel A,support the volatility hypothesis.For upper limit hits,R

ˉis significantly higher during Post-Hits than during Pre-Hits,whereas R ˉis significantly lower during Post-Hits than during Pre-Hits for lower limit hits.These results are consistent with the price continuation observed in the literature (e.g.,Kim and Rhee,1997).Our argument that closing limit hits occur because the equilibrium price is outside the daily allowable range is supported.All three volatility measures show that the volatility is significantly higher during Post-Hits than during Pre-Hits.Results are the same for upper and lower limit hits and for both Periods 1and 2.Since we find no evidence of volatility reduction from closing limit hits,our volatility hypothesis is supported.

Results from single limit hits,as shown in Panel B,also support the volatility hypothesis.For upper limit hits,R ˉis significantly higher during Pre-Hits than during Post-Hits;it also is positive for Pre-Hits but negative for Post-Hits.For lower limit hits,R

ˉis significantly lower during Pre-Hits than during Post-Hits.These results intuitively make sense because prices must keep going up to hit the upper price limits and then recede away from the limits.For lower limit hits,the same intuitive explanation applies.V olatilities either increase after single limit hits or do not show significant differences between Pre-Hits and Post-Hits.The only exception is the V 3measure for upper limit hits during Period 2.These results suggest that there is no evidence of volatility reduction following single limit hits,supporting our volatility hypothesis.

Results from consecutive limit hits provide further support for the volatility hypothesis.The results for returns are similar to those for single limit hits.However,unlike the results for single limit hits,volatilities decrease from Pre-Hits to Post-Hits for both upper and lower limit hits (see Panel C).Although results for the lower limit hits are not as strong as those for the upper limit hits,when we examine 30min before and after consecutive limit hits,the results are very strong that volatility reduces significantly after consecutive limit hits for all measures,for both upper and lower limit hits,and for both Periods 1and 2.

Overall,our volatility hypothesis is supported -the volatility after limit hits is lower than that before limit hits for consecutive limit hits,but not for closing and single limit hits.This finding on volatility changes is important to the extent that policymakers typically consider curbing excessive volatility to be a justification for imposing price limits.Our results indicate that only consecutive limit hits are able to achieve what price limits are designed to accomplish.

Notes to Table 3:

This table reports returns and volatilities before and after three types of limit hits.A closing limit hit occurs when a price hits the limit and no other trades occur during the remainder of the day.A single limit hit occurs when non-limit-hit transactions follow a limit hit.Consecutive limit hits occur when additional trades at the same limit price take place after a limit hit.Upper (lower)limit hits occur when prices hit the upward (downward)price limits.Period 1represents all times with 7%upward and 7%downward price limits;Period 2represents all times with 7%upward and 3.5%downward price limits in year 2000.Pre-Hits refer to the 15min prior to the limit hits.For closing limit hits,Post-Hits refer to the 15min after the opening on the next trading day.For single and consecutive limit hits,Post-Hits refer to the 15min after limit hits.R ˉis the mean of 3-minute returns,V 1is the standard deviation of returns,V 2is the mean of absolute returns,V 3is the log of high price to low price,and N is the sample size.Panel A reports the return and volatility before and after closing limit hits.Panel B reports the return and volatility before and after single limit hits and Panel C reports the return and volatility before and after consecutive limit hits.All figures reported are multiplied by 1000.?(?)indicates that the left-side figure is higher (lower)than the right-side figure at the 1%level of significance.>(<)indicates that the left-side figure is higher (lower)than the right-side figure at the 5%level of significance.The t-test is used to determine the level of significance.

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534Y.H.Kim,J.J.Yang/Pacific-Basin Finance Journal16(2008)522–538

https://www.360docs.net/doc/235572376.html,rmation asymmetry hypothesis

Results from the spread analysis show no support for the information asymmetry hypothesis.To support this hypothesis,the relative spread after limit hits should be lower than that before limit hits for consecutive limit hits,but not for closing and single limit hits.Table4reports the means of the relative spreads before and after closing limit hits(Panel A),single limit hits(Panel B),and consecutive limit hits(Panel C).For closing limit hits,spreads increase significantly from Pre-Hits to Post-Hits,consistent with our hypothesis.Closing limit hits delay price discovery process,leading to higher information asymmetry after limit hits.The results from single limit hits show no significant differences between Pre-Hits and Post-Hits,supporting our information asymmetry hypothesis.Our explanation is that single limit hits are a one-shot deal and,by nature,do not offer investors sufficient time to obtain and digest information.This explanation implies that consecutive limit hits are more likely to mitigate information asymmetry because they provide more time for information Table4

Information asymmetry hypothesis:bid-ask spread

Panel A:closing limit hits

Period1Period2

Pre-Hits Post-Hits Pre-Hits Post-Hits Relative spread

Upper limit hits 5.615 5.923 6.255< 6.501 Lower limit hits 6.606? 6.696 6.788?7.226 Panel B:single limit hits

Period1Period2

Pre-Hits Post-Hits Pre-Hits Post-Hits Relative spread

Upper limit hits 5.626 5.753 6.091 6.372 Lower limit hits 6.630 6.6197.6977.907 Panel C:consecutive limit hits

Period1Period2

Pre-Hits Post-Hits Pre-Hits Post-Hits Relative spread

Upper limit hits 5.335? 6.540 5.551? 6.186 Lower limit hits 6.665 6.4177.3957.680 This table reports the mean of the relative spreads before and after three types of limit hits.The relative spread is defined as the bid-ask spread divided by the bid-ask midpoint.A closing limit hit occurs when a price hits the limit and no other trades occur during the remainder of the day.A single limit hit occurs when non-limit-hit transactions follow a limit hit.Consecutive limit hits occur when additional trades at the same limit price take place after a limit hit.Upper(lower)limit hits occur when prices hit the upward(downward)price limits.Period1represents all times with7%upward and7%downward price limits;Period2 represents all times with7%upward and3.5%downward price limits in year2000.Pre-Hits refer to the15min prior to the limit hits.For closing limit hits,Post-Hits refer to the15min after the opening on the next trading day.For single and consecutive limit hits,Post-Hits refer to the15min after limit hits.Panel A reports the relative spread before and after closing limit hits. Panel B reports the relative spread before and after single limit hits and Panel C reports the relative spread before and after consecutive limit hits.All figures reported are multiplied by1000.?(?)indicates that the left-side figure is higher(lower) than the right-side figure at the1%level of significance.>(<)indicates that the left-side figure is higher(lower)than the right-side figure at the5%level of significance.The t-test is used to determine the level of significance.

dissemination and revelation.However,we find that spreads increase significantly from Pre-Hits to Post-Hits for upper consecutive limit hits and do not change for lower consecutive limit hits,contradicting with our information asymmetry hypothesis.

The fact that we observe lower volatility and higher spreads after consecutive limit hits seems puzzling.Under normal circumstances,we would expect to see positive relation between volatility and spread (e.g.,periods with high volatility be associated with high spread).However,the inverse relation between volatility and spread is not unique to our study.For example,Wahal (1997)documents a negative correlation between spread and volatility measured by squared returns on the NASDAQ.Also,Cai et al.(2004)summarize intra-day patterns of spread and volatility across markets from various papers.They show that there are some periods of time during which spread and volatility are moving in different directions,especially for order-driven markets.In addition,there is no apparent explanation for the different results of relative spreads from upper and lower consecutive limit hits,but the asymmetric properties of upper and lower price limits have been documented by many studies (e.g.,Cho et al.,2003).

In sum,although the volatility hypothesis is supported,the information asymmetry hypothesis is not.Consecutive limit hits appear to be the best scenario among the three types of limit hits.Closing limit hits cause higher volatility and spreads after limit hits.Single limit hits cause higher volatility after limit hits but they do not seem to impact spreads significantly.Consecutive limit hits are the only type of limit hits that are able to reduce price volatility.However,none of the three types of limit hits can mitigate information asymmetry.

5.3.Regression analysis

We examine our sample further to determine what features associated with consecutive limit hits may contribute to our result,such as the number of transactions at the limit price or the time duration between the first limit hit and the last limit hit for each consecutive limit hit.Panel A of Table 5provides descriptive statistics of the duration and the number of limit hit transactions.The mean (median)duration is 442(129)s,with a maximum and minimum duration of 8391and 0s,respectively.There are 105consecutive limit hits whose durations are 0because two separate limit-hit transactions occurred at the same time.9The mean (median)number of transactions is 5

(3),with a maximum and minimum of 137and 2,respectively.The correlation between the duration and number of transactions is 0.5248.

To determine whether the duration or number of transactions can explain the magnitude of the volatility change,we run the following regressions:

V Pre eTàV Post eT?a tb 1Duration te ;

e10TV Pre eTàV Post eT?a tb 1Transaction te ;

e11TV Pre eTàV Post eT?a tb 1Duration tb 2UP tb 3SEVEN te ;and

e12TV Pre eTàV Post eT?a tb 1Transaction tb 2UP tb 3SEVEN te e13Twhere V (Pre)is the pre-hit volatility multiplied by 1000,V (Post)is the post-hit volatility multiplied by 1000,Duration is the total time (in seconds)from the first to the last limit hit,9Our results do not change when these 105observations are removed.

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Transaction refers to the number of limit hit transactions for each consecutive limit hit,UP takes a value of 1for upper limit hits and 0for lower limit hits,and SEVEN takes a value of 1for Period 1and 0for Period 2.

In Panel B of Table 5,we show that the coefficients of Duration are positive and significant,which indicates that there is positive relationship between duration and the magnitude of volatility change (i.e.,the longer the duration of consecutive limit hits,the more the volatility decreases).10If price limits provide a time period for market participants to obtain and evaluate information and make rational decisions,we should expect a positive relationship between duration and the magnitude of volatility reduction.In other words,the longer the duration,the more time investors have to discover the right price for the stock,which in turn lowers the volatility.Our regression results support this argument.

Table 5

Regression analysis Panel A:descriptive statistics

Duration (in seconds)

Transaction Mean

4425Median

1293Maximum

8391137Minimum

02Panel B:regressions

Independent variables

[1][2]Constant

0.24103a 1.09086(0.2654)(0.0007)Duration

a 0.00064a 0.00059(0.0032)(0.0062)UP

b ?0.90086(0.0312)SEVEN

a ?1.03584(0.0077)F value

a 8.75a 7.32Adjusted R 2

0.00790.0190N 976976In the regression equations,the dependent variable is the difference between Pre-Hit volatility and Post-Hit volatility for consecutive limit hits.A consecutive limit hit occurs when a limit hit is followed by additional trades at the limit price.Pre-Hit (Post-Hit)refers to the 15min prior to (after)each consecutive limit hit.Panel A provides descriptive statistics of the duration and number of transactions.Duration is the total time (in seconds)from the first to the last limit hit,and transaction refers to the number of limit hit transactions for each consecutive limit hit.Panel B reports the regression results of the regression:V (Pre)–V (Post)=α+β1Duration+β2UP+β3SEVEN+?,as well as its simplified specification.V (Pre)is the pre-hit volatility multiplied by 1000and V (Post)is the post-hit volatility multiplied by 1000,both from the 3-minute return analysis;UP takes a value of 1for upper limit hits and 0for lower limit hits.Upper (lower)limit hits occur when prices hit the upward (downward)price limits.SEVEN takes a value of 1for Period 1and 0for Period 2.The numbers in parentheses are p -values.

a Significant at the 1%level.

b Significant at the 5%level.

10

In addition to volatility,we perform a similar regression analysis for the relative spread.However,neither duration nor the number of transactions explains the change in relative spread.Results are available on request.536

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The regression of volatility reduction on the Transaction variable does not show any significant results.The number of transactions occur during consecutive limit hits does not have explanatory power over volatility reduction.That is,the duration,not the number of transactions,matters when it comes to the volatility reduction.

6.Conclusion

Given the recent development of behavioral finance and its empirical evidence about market overreaction,we attempt to answer the question,“Can price limits,one form of circuit breakers,reduce overreaction?”Although the most popular rationale for imposing price limits is to counter market overreaction,opponents of price limits argue that they serve no purpose other than to slow or delay the price discovery process.We develop the volatility hypothesis and the information asymmetry hypothesis and use transactions data from the TWSE to examine the effects of price limits.

We identify three different limit hits:closing,single,and consecutive.Among the three types of limit hits,we hypothesize that only consecutive limit hits are likely to reduce volatility and mitigate information asymmetry.In other words,only consecutive limit hits can reduce over-reaction by providing a time period during which investors reevaluate market information and form more rational trading decisions.We find that the price volatility drops significantly following consecutive limit hits,supporting the volatility hypothesis.We also find that the longer the duration of consecutive limit hits,the more the volatility is reduced.Our results indicate that price limits counter overreaction only when prices hit the limit consecutively.However,our empirical evidence does not support the information asymmetry hypothesis.Although con-secutive limit hits reduce volatility,they are unable to mitigate information asymmetry.

Our findings may have important regulatory implications.Because price limits can reduce overreaction after consecutive limit hits at an apparent cost of impeding trading,policymakers should evaluate the net effect of price limits and set rules to explore their benefits optimally.For example,because consecutive limit hits can potentially reduce volatility,a hybrid or combination of price limits and trading halts might be considered as an alternative mechanism to pure price limits (or trading halts)in exploring the benefits of consecutive limit hits.In line with the recognition of regulatory implications,some countries in the European Union (e.g.,Spain)have employed a price limit mechanism that also triggers trading halts.However,whether a hybrid system is better than pure price limits and trading halts must await for definitive answers until the findings of further empirical research.

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