an event study of price movements following realized jumps

8/6/2019 An Event Study of Price Movements Following Realized Jumps

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An event study of price movements following realized jumps

Hossein Asgharian, Mia Holmfeldt and Marcus Larson*

Department of Economics, Lund University

Abstract

Price jumps are mostly related to investor reactions to unexpected extreme news. We perform an

event study of price movements after jumps to analyze if investors reactions to news releases

are affected by psychological biases. We employ the recent non-parametric methods based on

intra-daily returns to identify price jumps. This approach enables us to separate large price

movements that are related to unexpected news from those merely caused by periods of high

volatility. To increase the likelihood of capturing news related price movements, we take also

into consideration the trade volumes around the jump events. To increase the robustness of the

results we analyze a set of different model specifications. In general, we find indications of

investor pessimism, as our results show a strong price reversal after negative jumps, except for

the bull market in 19972000 when investors tend to overreact to good news and underreact to

negative news.

Keywords: Behavioral finance; price jumps; event study; bi-power variation; high-frequency

data.

JEL classifications:.

* Department of Economics, Lund University, Box 7082 S-22007 Lund, [email protected] , [email protected] and [email protected] are very grateful toJan Wallanders och Tom Hedelius stiftelse for funding this research.


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1. Introduction

The volatility or total price variation can be divided in a smooth and systematic component and a

jump component. Recent developments provide strong econometric devices for measuring these

different components (see for example Barndorff-Nielsen and Shephard (2004, 2006)). The

ability to separate jumps from the continuous part of price variations makes it possible to

separate large price movements that are related to unexpected news from those merely caused by

periods of high volatility. This can help us to consistently analyze investor behavior around a

news release.

The traditional models in finance assume that investors behave rationally when they receive new

information, such that the prices in the financial market always reflect the true fundamental asset

values. However, investors overconfidence, optimism or pessimism may induce a deviation

between the observed market prices and what would be expected if the price setting were

rational. Investors trading psychology, such as overconfidence and optimism, or their anxiety

and pessimism may cause overreaction/underreactions to the news. The overreaction to the

information pushes prices up/down too far relative to the assets fundamental value. This

inefficient pricing may be temporary and subsequent trades pull the prices back to their correct

level. This possible scenario of reverting trend after the abnormal win/loss is usually denoted as

reversal. An inverse scenario is investors underreaction to the news. The underreaction can be

motivated as a result of the investors conservatism causing an insufficient initial jump and a

subsequent convergence toward the fundamental level. The overreaction and underreaction are

not necessarily similar for the good news and bad news. For example, pessimists may overreact

to the bad news and underreact to the good news.


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Investment strategies based on overreaction/underreaction, such as contrarian and momentum

strategies, have a long tradition in finance. It has been documented by a number of researches

that the contrarian effect is significant for long (5 years) and short (daily up to one month)

horizons, see e.g. De Bondt and Thaler (1985, 1987) and Fehle and Zdorovtsov (2003). The latter

authors find that US firms with a large price fall during a trading day usually experience an over-

night price adjustment. In contrast the momentum effect has been found on shorter horizons,

ranging from 3 month to 1 year (see e.g. Jagadeesh and Titman (1993, 2001). From an investors

perspective, it is important to understand the source of the success for such investment strategies.

Various explanations have been proposed about the profitability of the contrarian strategy. Short-

term reversals are often explained by bid-ask spreads or lead lag effects between stocks (e.g.

Jagadeesh and Titman (1995) and Lo and MacKinlay (1990)). The explanations for longer-term

reversals are often based on time-variation in expected returns (Ball and Kothari (1989)). The

momentum effect is, on the other hand, often traced back to a gradual response to new

information by the market. Chan et al. (1996) find that a substantial proportion of the momentum

effect is concentrated around earnings announcements.

Our study is related to the behavioral finance literature and analyses jumps from the viewpoint of

the investors psychology. The purpose is to perform an event study on the price movements

following jumps to investigate dominating behaviors in the market after news arrivals. To

increase the likelihood of capturing price movements that are related to unexpected extreme

news, we impose restriction in the trading volume, when defining the jump events. We use a

market model to control for the changes in the stock prices that are related to the general market

movements. We try to increase the reliability and robustness of the results by examining

different model specifications.


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We find strong evidence of investors overreaction to bad news and underreaction to good news

in the bear market examined. When market conditions are good we observe an overreaction to

good news while some negative jumps are likely to steam from underreaction. The significant

pessimism observed in the market from September 2000 to March 2003 was to some extent

carried over into the later part of our sample, although the market was upward trending. Our

results suggest that both contrarian and momentum effects might be attributed to investors

reacting differently to news depending on the current market conditions.

The remainder of the paper is organized as follow. Section 2 describes the identification of

realized jumps. Section 3 describes the data and outlines the event study methodology used.

Section 4 reports our empirical finding while section 5 concludes.

2. Non-parametric jump estimation

We assume the logarithmic price of a financial asset consists of two sources, one diffusive part

and one discontinuous part. To detect jump events, we use a non-parametric jump detection test

mainly developed in a number of papers by Andersen and Bollerslev and Barndorff-Nielsen and

Shephard.

The test relies on the quadratic variation of such a price process, which can be consistently

estimated by the sum of squared intra-daily returns,

.as1

2

, +===

MJCQVrRVpM

j

jtt (1)

This realized variance (RV) estimator encompasses both the variation due to the diffusive

component as well as the variation caused by the discontinuous price movements, the jumps.


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A similar estimator, although robust to the variation due to jumps, is the realised bipower

variation (BV) estimator. The jump robustness characteristic is achieved by the sum of adjacent

multiplied absolute intra-daily returns,

.as2

2,

3

,2

1

=

=

MCrrMMBV

p

jt

M

j

jtt (2)

where 1 is equal to [ ]ZE with )1,0(~ NZ . Following this framework, an estimator of the

variation due to the jumps is easily obtained by the difference between the RVt and the BVt

estimators,

.JBVRVJp

ttt = (3)

This estimator consists of the sum of all squared intra-daily jumps in the price and must hence be

non-negative. Due to sampling errors, the empirically estimatedJtmight be non zero even in the

absence of jumps during time period t. As a consequence, a number of jump test statistics have

been developed by e.g. Barndorff-Nielsen and Shephard (2004a), Andersen et al. (2007) and

Huang and Tauchen (2005). For a given significance level the test statistic helps to separate the

jumps from the continuous variation otherwise mistakenly incorporated into the jump

component.1 We chose to rely on the ratio statistic due to its finite sample properties,

( ) { }( ) ,as1,0

,1max52 2214

1

+

=

MNBVTQ

RVJMZ

p

tt

ttt

(4)

where TQtis called the tripower quarticity and is measuring the variance of the variance2. Hence

the realized jump component is obtained by,

( ) { },1, >=

tZtttt IBVRVJ (5)

1 This might be due to market frictions such as price discreteness, bid-ask bounce or non-synchronous trading etc.2 The TQ estimator is robust to jumps in the price process and was defined in Barndorff-Nielsen and Shephard(2004b).


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where is the cumulative density function of a standard normal distribution, is the

significance level and tI indicates the event of a jump occurrence during time period t. The final

continuous price variation is obtained by

{ } { }11 ,, += tt ZttZtttIRVIBVC . (6)

This framework allow for a non-parametric decomposition of total price variation, one due to

normal changes (smooth variation) and one due to non-normal changes (jumps). In the next

section we use this information to implement an event study of the price movements after such

non-normal change.

3. Data and methodology

The data used is high frequency transaction prices for the individual stocks included in the S&P

100 index3. The sample ranges from April 4, 1997 or company inception to Mars 16, 2007.

To check the reliability of the high frequency data we carefully compare all the computed daily

returns with data collected from Datastream. Eight assets are excluded due to an overall

suspicion of poor data accuracy. The resulting sample consists therefore of 92 individual assets.

In addition we found insufficient accuracy for some of the remaining assets in the beginning of

the sample. As a result we exclude days with insufficient trading and erroneous price quotes.

Index return data are obtained from Datastream.

Daily returns are calculated using the log closing prices and intra daily returns are based on the

log price nearest every 5-minute time stamp. Our estimate of returns relies on equidistant prices.

This is achieved by interpolating the high frequency prices using a previous tick method. We

choose the 5-minute sampling frequency in order to strike a balance between information and

3 Data is obtained from www.price-data.com


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bias when identifying the jumps. A too high sampling frequency will induce spurious jumps due

to market frictions while a too low sampling frequency will lead to poor properties of the test

statistic. To further limit ourselves to jumps that are information driven we impose the following

set of restrictions.

Inactive trading restriction: The estimators that constitute the test statistic are vulnerable to long

time periods with no price changes. To circumvent this in the event study we only consider jump

days where there are sufficient amount of trading activities. We only accept an identified jump as

an event if more than 2/3 of the returns on that day are different from zero.

Volume restriction: To increase the possibility of capturing price movements that are related to

unexpected extreme news and hence to a great extent information driven price movements, we

impose a volume restriction in the event study. We identify a jump date as an event day if the

trade volume on that date is above an expected normal volume. The expected normal volume is

estimated as the average volume in a window surrounding the jump date. To decrease the risk

that the expected normal volume is affected by the jump event we use the average over a 22-day

window including days -13 to -3 and +3 to +13.

Filtering outlier returns: To insure that a few number of observations cannot dominate the

results, we exclude outlier returns (values approximately outside 1% confidence interval) when

estimating the abnormal returns for the event window. A comparison between the result before

and after this restriction shows a small outlier effect. Hence, we choose to exclude the outliers in

our estimations.4

In our event study we investigate ex post realized returns following, positive or negative, realized

jumps using the identification scheme outlined in section 2. In order to detect the return

associated with jumps we first classify the direction of the jump of assetj on jump day tas,

4 The result of the outlier analysis is not reported but is available on request.


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{ } }1||max||.{)( 1,,,},,1{,,,=== > jtiii ZjtjtMijtjtjt

IandrrtsrSJdirK

(7)

where S is a sign function indicating +1 if jtir , is positive and -1 if it is negative. Then we

identify a positive and a negative jump return as,

{ }

{ }0)(.

0)(.

,,,

,,,

=

+

jtjtjt

jtjtjt

Jdirtsrr

Jdirtsrr

(8)

The abnormal returns are calculated by subtracting the expected normal returns from the actual

returns in days following a jump event,

)( ,,, jtjtjt rErAR = (9)

E(rt,j) is the expected normal return of asset j at time t conditioned on information that is

unrelated to the jump days. We use the market model to calculate the expected normal returns,

mtjjjt rrE )( , += (10)

We choose two different proxies for the market return, rmt, one equally weighted index consisting

of the individual assets in the sample and the S&P 100 index5. Estimates of j and j are

obtained from the following ordinary least squares regression.

tmtjjjt rr , ++= (11)

We exclude the trading week after the jump day in our estimation of and . We divide ARt,j

into positive and negative abnormal returns associated with the sign of the related jump.

Cumulative abnormal returns ( hjtCAR , ) are then calculated for each assetj as,

5 The S&P 100 index is obtained from Datastream. We also considered high frequency index futures of the S&P 500with similar results in our analysis.


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=

=h

tjt

hjt ARCAR

1,, (12)

We choose an event window, h, up to 100 days after the jump event (h={1,,100}). On each

day we define a N1 vector of weights, ws, including only those assets that have a significant

jump.6

We use the indexs for event days where we observe a jump and tfor all calendar days.

The aggregate cumulative abnormal returns across securities are then calculated as,

)( ,,,1, =h

Jt

h

ts

h

s CARCARwCAR K (13)

Aggregation through time is achieved by summing the hsCAR over the Snumber of jump events.

The test statistic of the null hypothesis of no abnormal return is defined as,

)( hs

h

s

hCARse

CARt = (14)

whereh

sCAR is the mean of thes number ofCARs.

Since the parameters of expected returns are estimated with errors we mainly use the prediction

error variance to estimate the t-values. We start by calculating the portfolio variance on each

event day by

s

st

mmt

st

mmts

h

s

mms

s

s V

RRRRw

RR

Lw

hhV

Jj

+

+=

=

22

1

2

2

)(,,)(

)(~

K

(15)

sss wwV

=

6 We use an equally weighted portfolio in this study. We find similar result for at portfolio where the weights aredependent of the jump size.


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wheresjdenotes the jump days plus an additional trading week after the jump event for asset j. L

is a N1 vector with the sum of all the remaining days. mR is the mean market return, sw is

defined as before and finally is the variance-covariance matrix of the residuals from the OLS

regression in equation (11).

The standard error for the cumulative abnormal return aggregated over all the events is then

calculated as,

=

=S

s

sh

s VSCARse1

1 ~)( (16)

An alternative way to estimate the variance is to calculate the cross-sectional variance, which

assumes the same variance for all the abnormal returns and also ignores the fact that the

estimated parameters of the market model contain error. The cross-sectional variance is defined

as,

=

=S

s

h

sh

s

h

s CARCARSCARse1

2 )()( (17)

The test for cumulative abnormal returns after a jump event is implemented for three different

sub-periods in addition to the entire sample. The OLS regression in equation (11) is then

estimated separately for the corresponding sample while the residual covariance matrix is

assumed to be constant for the entire period. The above test procedure is adopted for positive as

well as negative event days.


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4. Analyses

A. Analysis of jump

Figure 1 illustrates S&P100 index under the period 199704-200703. We divide the entire sample

into three sub periods. The first period covers the bull market from 1997 to the end of August

2000. The second period is characterized by falling stock prices, ranging from September 2000

to March 2003. Finally, the third period is also an upmarket period, although a much more

moderate, starting March 2003 and ending March 2007.

Table 1 shows a summary of return statistics. The cross-sectional average of the daily mean

stock returns over the entire sample is equal to 0.03%. Both the first and the third sub-periods

have an average daily mean return of about 0.06% while the value for the second subsample is

-0.05%. The stock prices have on average been less volatile during the third period; the average

standard deviation in the third period is about half of that in the two other periods. This is also

supported by the estimated average realized variance and bipower variance. It is worth noting

that the daily return volatility of the S&P100 in the third period is around 0.62%, which is much

lower than the index return volatility in the first and second period (1.31% and 1.58%

respectively). The skewness on average is not considerably large, however it is slightly more

negative in the second period (the bear market). The relatively large average kurtosis in all the

periods signals for a possible outlier problem. It is interesting to note that the variation induced

by jumps in the first period is about four times that of the third period, characterizing the fourth

period as an upmarket period with low variance and few unexpected extreme news. The trade

volume is also larger in the third period comparing to the rest of the sample.

Table 2 shows some cross sectional descriptive statistics of the estimated jumps for the different

sub-periods examined. In the top panel it shows the number of observations across assets and


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time periods. It is evident that some, or exactly 7, stocks are not contained in the first sub-period.

During the second and third sub-periods, all stocks are traded although not all from the start. The

following two panels show some descriptive statistics about the cross-sectional jump frequency,

both with and without the volume restriction imposed. The first row, in each section, displays the

total number of jumps for all traded stocks during the specific sample period. However, as the

length of the sample periods is different it is more interesting to look at the jump frequency,

which is displayed on the remaining rows both for the cross-sectional average as well as the

minimum and maximum values. It is interesting to note the strong time variation in the jump

frequency across the three sub-periods. The first period is the most jump-intensive time period

and moving forward in time the jump intensity declines. Imposing the volume restriction will by

definition reduce the number of jumps, and from the last part it is evident that the volume

restriction reduces the jump frequency by roughly a third.

Figure 2 illustrates the jump frequency for different firms before and after imposing the volume

restriction for all stocks. From the figure we can see that the positive and negative jump

intensities are almost the same. For an overview of the impact of our restriction on the number of

observations for each stock, see the appendix.

From Table 2 it is evident that the jump frequency not only varies a lot over time but also exhibit

a large cross-sectional spread. An interesting question is whether there are any common factors

influencing the individual jump intensities. Do some types of assets jump more frequently than

the others? In other words, we want to see if some stocks are more exposed to under- or

overreactions than the other stocks. In Table 3 we report the correlation matrix between the

cross-sectional jump frequencies and some potentially important factors. One obvious issue is

whether stocks with higher market risk, i.e. higher market beta, are more likely to jump.

However, a negative and small correlation coefficient of -0.19 does not support this conjecture.


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We then investigate if high volatility stocks tend to jump more frequently. We use the bipower

variation as the measure of price volatility in order to filter out the variation that is caused by

jumps. The small and insignificant correlation coefficient suggests no such a relation. The same

goes for the idiosyncratic price variations, for which we obtain an insignificant, negative

correlation with the jump frequency. What is more interesting is that conditioned on the size of

the firms, we find that smaller firms tend to jump more frequently. One possible explanation

might be that large firms tend to be more closely monitored by market participants who hence

might have better information and expectations about future developments compared to smaller

firms. On the other hand, if we condition the jump frequency of the firms book-to-market ratio

(b/m) we find that those with high b/m tend to have higher jump frequency.

In Figure 3 we show the number of days with simultaneous jumps, i.e. when different firms jump

in the same day. On the majority of the jump days we observe between 1 or 5 simultaneous

jumps, after imposing the volume restriction. The result is stable over all three sub-periods as

well as the entire sample. At most we find 15 individual stocks experiencing a jump during the

same trading day, during end of April 1997. Table 4 shows the number of days with

simultaneous jumps as a percentage of the total number of trading days in each sample. The

results indicate during which time-period we observe most simultaneous jumps among the

stocks. The results are similar both with and without the volume restriction. The highest

concentration of simultaneous jumps is found in the first and the last sub-periods.

The average volume around jump dates is illustrated in Figure 4. The values are computed before

imposing the volume restriction to avoid an overestimation of the average volume in event date.7

The figure shows a clear increase in the average volume around the jump events. The maximum

volume is reached at day 0 which is the jump day. This shows that the identified jumps are

7 We have also computed the values without imposing the transaction restriction when identifying jumps. Theestimated average volume around the event date is robust to this restriction and exhibits almost the same pattern.


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associated with the arrival of unexpected news to the market. The increase in the volume before

the jump days may show that the jump occurrences are mostly related to the expected release

dates. The increase in volume may hence be due to speculations of market participants before

news release.

One might wonder if it is necessary to identify jumps to examine investors response to the

extreme news, when we can simply look at the extreme returns in the market. Our conjecture is

that the extreme returns may sometimes be a result of large market volatilities instead of the

reactions to unexpected or extreme news. In figure 5 we compare the identified jumps, the

extreme returns and the cross-sectional average of the estimated bipower volatilities (the smooth

part of price variation). As extreme returns we define the returns in the upper/lower quantiles,

such that the number of extreme positive/negative returns is equal to the number of identified

positive/negative realized jumps. As Figure 5 shows the distribution of the jump events over time

is much smoother compared to the extreme events. A comparison with the bipower volatility

shows that the extreme returns are mostly gathered in the periods when the systematic volatility

of the market is very large. The average correlation between the bipower volatility and the

positive and negative jumps is 0.08, while the average correlation between extreme returns and

the positive and negative extreme returns is slightly above 0.50. These results confirm our

conjecture that extreme returns are not sufficient to capture market reactions to unexpected news.

B. Event study

Table 5 presents the average return and average abnormal return on jump days and one day after.

The mean of the event day returns are around 1% in absolute value. The mean returns of the

positive jumps are in absolute value larger than that of the negative jumps in the first and the

third sample whereas the result is reversed for the second sample. This is not surprising as the


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first and the third periods both are characterized by a positive market trend. Both mean returns

and mean abnormal returns of the jump days are highly significant. However, these values are

insignificant for the day following a jump, except after the positive jumps in the second sample

(down market). For the latter case, this might be interpreted as an indication of a conservative

reaction to positive news in the down market in day 0, which is corrected by a positive price

movement in the subsequent day.

Since our purpose is to investigate a long run price movement after a jump, we choose to use an

event window of 100 days. We believe that this window is sufficiently long to capture long run

price corrections after a possible underreaction/overreaction.

Before analyzing the final results of the event study in details we use the entire sample to

examine the impact of our different choices of model restrictions on the final results. For

simplicity we only report the t-values of the estimated CAAR in the robustness analysis.

We first look at the impact of the volume restriction on the results in the event study. Figure 6

plots the t-values of the estimated CAAR with and without volume restriction when identifying

jumps. For the positive jumps, there is a considerable difference between the t-values of the two

alternatives; the volume restriction results in more conservative t-values in the long run and are

almost insignificant throughout the entire window, while restricted CAAR become significant

after about 80 days. For the negative jumps are more or less robust to the imposed restriction.

Next we examine how our results are affected by using extreme returns instead of jumps as

events. Figure 7 shows that the two alternatives result in the same conclusion for the positive

jumps, i.e. insignificant CAARs through the entire event window. For the negative jumps the

CAARs calculated from the extreme returns are not significant while those following jump

events are significant at a 5% level. The insignificance of the CAARs following extreme returns

might indicate that extreme returns are partially due to large market volatility and partially to the


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arrival of the unexpected news. The subsequent price movements may therefore vary by events

and do not show any systematic pattern.

The stock included in the S&P100 index may vary over time. However, the high frequency

database employed in this study consists of firms included in the S&P100 at the end of the

sample period. Consequently, we cannot observe jumps occurred for de-listed firms, while these

firms affect the returns of our benchmark index, S&P100. Since the de-listed firms are supposed

to perform worse than the survived firms it may induce an upward bias in our estimated CAAR.

To control for this possibility, we also use an equally weighted index, constructed based on the

existing firms, as benchmark index. Figure 8 shows that our results are not affected by the choice

of the benchmark index.

Finally, in Figure 9, we compare the t-values estimated by the two alternative variance

estimations, i.e. either the prediction error variance or the cross-sectional variance. As the figure

shows the two alternatives give almost the same results for both the negative and positive jumps.

We employ the following model in the rest of the event study: the model with volume restriction,

the S&P100 index as a proxy for the market portfolio and the t-values are calculated using the

prediction error variance. The analysis is conducted for the entire sample as well as the three

sub-periods. Figure 10 illustrates the estimated CAAR and the related 95% confidence interval

for positive and negative jumps for these different time periods. The estimations are based on the

value weighted market index and the prediction error variance.

For the first sub-period, characterized by an equity bull market, the estimated CAARs after

positive jumps are negative and become significant after about 20 days. This may show an

overreaction to positive news, which is corrected in the subsequent trades. The estimated CAARs

for negative jumps are close to zero in the beginning and become significantly negative only in

the end of the event window (approximately day 80 and onward). The negative CAARs


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following the negative jumps indicate a possible underreaction to the bad news. The overreaction

to the positive news and underreaction to the negative news may reflect the known optimism

dominating in the up market between in 1997-2000.

The estimated CAARs of the second sample, characterized by a bear market, are positive and

strongly significant throughout the event window for both negative and positive jumps. This

finding indicates a strong underreaction to the good news and overreaction to the bad news.

Regarding the economic depression and the serious worldwide political crises in the major part

of the second period, this scenario is in accordance with the deep pessimism prevailed in that

period.

Despite the fact that the third period experienced a positive market trend, it still shows an

overreaction to negative news, i.e. significant negative CAARs following negative jumps, but the

CAARs after positive jumps are insignificant.

The results for the entire sample period show no significant effect after positive jumps but a

significant positive effect after negative jumps. Since the CAARs following the positive jumps

have different signs in the first and the second periods, the combined effect over the entire

sample result in insignificant CAARs. The significantly positive CAARs of the entire period for

the negative jumps are most likely driven by the results of the second period. Altogether, it

seems as if investors react asymmetrically to positive and negative unexpected news, as they

tend to overreact to negative news but react normally to positive news. These results signal

some evidence of overall investor pessimism, although the results are dependent on the economic

state.


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5. Conclusion

In this paper we investigate the investor behavior around large price movements resulting in

discontinuities (jumps) in the prices of individual stocks. The jumps are estimated using recent

non-parametric methods based on intra-daily returns. We find a considerable time variation in

the contribution of jumps to total price variance during our different sub-samples. The later part

of the sample is characterized by relatively lower volatility and fewer jumps but more extensive

trading.

Volume and volatility theories (see for example Andersen (1992)) propose a close relation

between volume and price movement. We find new evidence of such relationship between the

jump component and volume. Volume is significantly higher on jump days suggesting that the

identified jumps are associated with the arrival of unexpected news to the market.

Previous studies on investor behavior and news announcements uses to a large extent extreme

returns defined by some threshold as a proxy for such events. A comparison of the extreme

returns with our measure of continuous volatility indicates that using extreme returns might not

be sufficient to capture market reactions to unexpected news.

The first sample period, between 1997 to August 2000, is characterized as a bull market. In such

market, positive jumps are followed by negative cumulative average abnormal returns (CAAR)

after about 20 days. This result suggests an overreaction to positive news, which is corrected in

the subsequent trading days. Part of the negative jumps on the other hand is likely to steam from

investors underreaction to bad news. Hence this period might reflect an overall optimism among

the investors.

In the second period from September 2000 to March 2003 which was characterized by a bear

market we find significant CAARs for both negative and positive jumps suggesting an


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overreaction to bad news and an underreaction to good news. Although the third period, between

April 2003 and March 2007, experienced a positive market trend we still report a significant

overreaction to negative news, suggesting that the deep pessimism during the second period is

carried over into the third. The results for the entire sample period show no significant effect

after positive jumps but a significant positive effect after negative jumps. Overall, it seems as if

investors tend to respond asymmetrically to positive and negative unexpected news although the

results depend on the current market conditions.


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Barndorff-Nielsen, O. and N. Shephard, 2004a, Power and Bipower Variation with StochasticVolatility and Jumps, Journal of Financial Econometrics 2, 137.

Barndorff-Nielsen, O., and N. Shephard, 2004b, Measuring the Impact of Jumps on Multivariate

Price Processes Using Bipower Variation, Discussion Paper, Nuffield College, OxfordUniversity.

Barndorff-Nielsen, O. and N. Shephard, 2006, Econometrics of Testing for Jumps in FinancialEconomics using Bipower Variation, Journal of Financial Econometrics 4, 130.

Chan, L., N. Jegadeesh, and J. Lakonishok, 1996, Momentum strategies, Journal of Finance 51,1681-1713.

De Bondt, W. and R. Thaler, 1985, Does the stock market overreact? Journal of Finance 40,793808.

De Bondt, W. and R. Thaler, 1987, Further evidence on investor overreaction and stock marketseasonality, Journal of Finance 42, 557581.

Fehle, F. and V. Zdorovtsov, 2003, Large Price Declines, News, Liquidity, and TradingStrategies: An Intraday Analysis, University of South Carolina Working Paper.

Huang, X., and G. Tauchen, 2005, The Relative Contributions of Jumps to Total Variance,Journal of Financial Econometrics, 3, 456499.


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Jegadeesh, N. and S., Titman, 1993, Returns to buying winners and selling losers: implicationsfor stock market efficiency. Journal of Finance 43, 6591.

Jegadeesh, N. and S., Titman, 1995, Overreaction, delayed reaction, and contrarian profits,Review of Financial Studies 8, 973993.

Jegadeesh, N. and S., Titman, 2001, Profitability of momentum strategies: an evaluation ofalternative explanations, Journal of Finance 56, 699720.

Lo, A., and A. MacKinlay, 1990, When are contrarian profits due to overreaction? Review ofFinancial Studies 2, 175205.


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Table 1. Summary of return statistics

The table shows the cross-sectional means and the related 90% confidence limits over followingstatistics for individual firms: average return, standard deviation of returns, skewness, kurtosis,average realized variance (RV), average bipower variance (BV), average trading volume, thepercentage of total variance induced by the systematic variation and finally, the percentage of

total variance induced by jumps.

Entire Sample 1 Sample 2 Sample 3

5% mean 95% 5% mean 95% 5% mean 95% 5% mean 95%

Average return % -0.02 0.03 0.07 -0.09 0.06 0.26 -0.28 -0.05 0.04 -0.01 0.06 0.13

Stdev 1.40 2.07 3.54 1.79 2.43 3.48 1.65 2.57 5.04 0.86 1.36 2.18

Skewness -1.92 -0.14 0.39 -1.12 0.05 0.58 -1.82 -0.13 0.55 -1.44 0.00 0.61

Kurtosis 5.48 8.81 35.24 4.01 5.50 19.02 3.99 6.12 22.25 3.89 6.77 22.22

Average RV 1.85 3.32 9.41 2.92 4.91 10.30 2.61 4.84 17.63 0.78 1.48 4.06

Average BV 1.81 3.21 9.12 2.82 4.66 9.63 2.59 4.72 17.43 0.76 1.45 3.91

Average volume (1000$) 875 3620 29068 489 2623 50288 715 3415 25512 970 3809 22757

Diffusion induced variance 0.93 0.98 0.99 0.85 0.96 0.99 0.95 0.98 0.99 0.97 0.99 0.99

Jump induced variance 0.07 0.02 0.01 0.15 0.04 0.01 0.05 0.02 0.01 0.03 0.01 0.01


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Table 2. Cross-sectional statistics of jump frequency

The table shows the cross-sectional statistics of the jump frequencies for the different sub-periods. In the top panel it shows the number of observations across assets and time periods. Thefollowing two panels show the descriptive statistics of the cross-sectional jump frequency, bothwith and without the volume restriction. The first row, in each section, displays the total number

of jumps for all traded stocks during the specific sample period.


# of observations 2501 860 632 1009

Min observations 1308 0 299 1009

Max observations 2499 858 632 1009

No volume restriction


# of jumps 14654 8089 3212 3353

Mean jump frequency 6,81 12,23 5,75 3,69Min jump frequency 1,84 2,56 0,79 1,29

Max jump frequency 19,26 33,68 35,92 8,42

With volume restriction


# of jumps 4963 2399 1210 1354

Mean jump frequency 2,32 3,67 2,17 1,49

Min jump frequency 0,60 0,75 0,16 0,40

Max jump frequency 6,59 11,11 11,39 4,06


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Table 3. Correlation matrix

The table reports the correlation matrix between the individual firms jump frequencies and somepotentially important firm specific factors, i.e. the market beta, the average of bipower variationover time, the residual variance of the estimated market model, firm size and firm book-to-market value. The correlations marked by an asterisk (*) are significant at the 5% level.

Jump freq Beta BV Residual Var. Size B/M

Jump freq 1.00

Beta -0.19* 1.00

BV 0.16 0.64* 1.00

Residual Var. -0.02 0.54* 0.89* 1.00

Size -0.54* 0.13 -0.30* -0.14 1.00

B/M 0.23* 0.11 0.11 -0.05 -0.18* 1.00


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Table 4. Percentage of simultaneous jump days of the total number of trading days

The table shows the number of days with simultaneous jumps as a percentage of the total numberof trading days in each sample. The upper limit of 25 represents the maximum number of co-jumps on one trading day.

No volume restriction With volume restriction

# of Jumps/Day Entire Sample 1 Sample 2 Sample 3 # of Jumps/Day Entire Sample 1 Sample 2 Sample1 7.40 0.35 7.12 13.58 1 25.31 18.37 25.79 30.922 11.04 1.28 13.13 18.04 2 21.03 21.74 22.31 19.623 12.99 3.02 13.77 21.01 3 14.67 18.84 15.03 10.904 10.44 4.07 12.03 14.87 4 8.92 13.72 8.54 5.055 10.16 5.70 10.44 13.78 5 4.20 7.79 3.64 1.496 7.68 6.86 9.49 7.23 6 1.96 4.19 1.27 0.507 6.80 9.53 9.65 2.68 7 1.08 2.56 0.63 0.108 6.72 10.81 9.02 1.78 8 0.44 0.93 0.47 0.009 5.68 11.63 4.75 1.19 9 0.48 0.93 0.63 0.00

10 4.36 10.35 2.85 0.20 10 0.16 0.47 0.00 0.0011 3.44 7.67 2.85 0.20 11 0.00 0.00 0.00 0.0012 2.36 6.40 0.63 0.00 12 0.00 0.00 0.00 0.00

13 2.16 5.81 0.63 0.00 13 0.08 0.12 0.16 0.0014 2.08 5.23 1.11 0.00 14 0.00 0.00 0.00 0.0015 0.92 2.67 0.00 0.00 15 0.04 0.12 0.00 0.0016 0.80 2.33 0.00 0.00 16 0.00 0.00 0.00 0.0017 0.44 1.16 0.16 0.00 17 0.00 0.00 0.00 0.0018 0.40 1.16 0.00 0.00 18 0.00 0.00 0.00 0.0019 0.40 1.16 0.00 0.00 19 0.00 0.00 0.00 0.0020 0.08 0.23 0.00 0.00 20 0.00 0.00 0.00 0.0021 0.08 0.23 0.00 0.00 21 0.00 0.00 0.00 0.0022 0.12 0.35 0.00 0.00 22 0.00 0.00 0.00 0.0023 0.04 0.12 0.00 0.00 23 0.00 0.00 0.00 0.0024 0.12 0.35 0.00 0.00 24 0.00 0.00 0.00 0.0025 0.04 0.12 0.00 0.00 25 0.00 0.00 0.00 0.00


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Table 5. One-day returns and abnormal returns

The table presents the average return and average abnormal return on jump days (t= 0)and oneday after the jumps (t= 1). We use the market model to estimate the expected normal returns,where S&P100 is used as the market index. The reported t-values are based on the predictionerror variances. In identifying event days we use the estimated jumps and impose the volume

restriction.

Positive Jumps


mean t-value mean t-value mean t-value mean t-value

t=0

Return % 1,13 18,77 1,23 13,78 1,16 8,29 0,91 9,99

Abnorm. Ret. % 0,94 17,40 1,05 13,23 1,04 8,11 0,78 9,29

t=1

Return % 0,06 1,17 0,08 1,04 0,06 0,58 -0,02 -0,39

Abnorm. Ret. %

0,03 0,75 -0,01 -0,20 0,25 2,49 -0,02 -0,47

Negative Jumps


mean t-value mean t-value mean t-value mean t-value

t=0

Return % -0,89 -13,97 -0,89 -9,16 -1,17 -7,27 -0,67 -8,51

Abnorm. Ret. % -0,86 -14,13 -0,94 -10,46 -1,00 -6,33 -0,62 -8,33

t=1

Return % 0,03 0,52 0,05 0,60 -0,08 -0,72 0,05 0,71

Abnorm. Ret. % -0,04 -0,94 -0,02 -0,27 0,01 0,10 -0,02 -0,36


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Figure 1. S&P 100 index

The figure illustrates S&P100 index under the period 199704-200703. We divide the entiresample into three sub periods. The first period covers the bull market from 1997 to the end of

August 2000. The second period is characterized by falling stock prices, ranging from September2000 to March 2003. The third period is also an upmarket period starting April 2003 and endingMarch 2007.

S&P100

0.0

0.1

0.2

0.3

0.4

0.5

0.60.7

0.8

0.9

1.0

19

9704

19

9710

19

9804

19

9810

19

9904

19

9910

20

0004

20

0010

20

0104

20

0110

20

0204

20

0210

20

0304

20

0310

20

0404

20

0410

20

0504

20

0510

20

0604

20

0610


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Figure 2. Jump frequency

The figure illustrates the jump frequency for different firms before and after imposing thevolume restriction.

Jump frequency without volume restriction

All jumps

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

18.0%

20.0%

1 6 11 1 6 2 1 2 6 31 3 6 4 1 4 6 51 5 6 6 1 6 6 71 7 6 8 1 86 9 1

Stocks

Frequency

Jump frequency without volume restriction

Positive jumps

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91

Stocks

Frequency

Jump frequency without volume restrictionNegative jumps

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

1 6 1 1 16 2 1 26 3 1 3 6 41 4 6 51 5 6 6 1 66 7 1 76 8 1 8 6 91

Stocks

Frequency

Jump frequency with volume restriction

All jumps

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

18.0%

20.0%

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91

Stocks

Frequency

Jump frequency with volume restriction

Positive jumps

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91

Stocks

Frequency

Jump frequency with volume restrictionNegative jumps

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

1 6 1 1 16 2 1 2 6 31 3 6 4 1 46 5 1 5 6 61 6 6 7 1 76 81 8 6 91

Stocks

Frequency


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Figure 3. Number of days with simultaneous jumps

The figure shows the number of days with simultaneous jumps, i.e. when different firms jump inthe same day, before and after imposing the volume restriction.

# jumps / day

Entire

0

100

200

300

400

500

600

700

1 3 5 7 9 11 13 15 17 19 21 23 25

# of jumps

#

ofdays


# jumps / day

Sample 1

0

20

40

60

80

100

120

140

160

180

200

1 3 5 7 9 11 13 15 17 19 21 23 25

# of jumps

#

ofdays


# jumps / day

Sample 2

0

20

40

60

80

100

120

140

160

180

1 3 5 7 9 11 13 15 17 19 21 23 25

# of jumps

#

ofdays


# jumps / day

Sample 3

0

50

100

150

200

250

300

350

1 3 5 7 9 11 13 15 17 19 21 23 25

# of jumps

#

ofdays



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30

Figure 4. Average volume around the jump day

The figure shows the average volume around jump dates. The values are computed beforeimposing the volume restriction to avoid an overestimation of the average volume in event date.

Average volume (no restriction)

positive jumps

010000

20000

30000

40000

50000

60000

70000

80000

90000

100000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Event w indow

Average volume (no restriction)

negative jumps

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Event w indow


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Figure 5. Comparing jumps, extreme values and bi-power variation

The figure shows the identified jumps, the extreme returns and the cross-sectional average of theestimated bipower volatilities. As extreme returns we define the returns in the upper/lowerquantiles, such that the number of extreme positive/negative returns is equal to the number ofidentified positive/negative realized jumps. The first and the second figures in the left refer to the

positive jumps and positive extreme returns, while the first and the second figures in the right arefor the negative jumps and negative extreme returns. The third figure is the estimated bipowervolatilities and is placed in both right and left to make the comparison more convenient.

0

5

10

15

20

25

30

35

40

45

50

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007Year

Numberofjumps

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Index

# of po sitive Jumps

SP100 Index

0

5

10

15

20

25

30

35

40

45

50

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Year

Numberofjumps

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Index

# o f extreme returns

SP100 Index

0

5

10

15

20

25

30

35

40

45

50

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Year

Numberofjumps

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Index

# o f extreme returns

SP100 Index

0

5

10

15

20

25

30

35

40

45

50

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Year

AverageBV

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Index

Average BV

SP100 Index

0

5

10

15

20

25

30

35

40

45

50

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007Year

Numberofjumps

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Index

# o f negative Jumps

SP100 Index

0

5

10

15

20

25

30

35

40

45

50

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Year

AverageBV

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Index

Average BV

SP100 Index


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Figure 6. Effect of the volume restriction

The figure compares the t-values of the estimated CAAR with and without volume restrictionwhen identifying jumps. We use the market model to estimate the expected normal returns,where S&P100 is used as the market index. The reported t-values are based on the predictionerror variances.

Conditioning on volume

positive jumps

-4

-3

-2

-1

0

1

2

3

4

5

6

1 11 21 31 41 51 61 71 81 91 101

Holding period

t-valueCAAR

Restricted

Unrestricted

Conditioning on volume

negative jumps

-4

-3

-2

-1

0

1

2

3

4

5

6

1 11 21 31 41 51 61 71 81 91 101

Holding period

t-valueCAAR

Restricted

Unrestricted


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Figure 7. Jump versus extreme returns

The figure compares the t-values of the estimated CAAR when using jumps versus when usingextreme returns as events. We use the market model to estimate the expected normal returns,

where S&P100 is used as the market index. The reported t-values are based on the predictionerror variances.

Jump vs extreme values

positive jumps

-4

-3

-2

-1

0

1

2

3

4

5

6

1 11 21 31 41 51 61 71 81 91 101

Holding period

t-valueCAAR

Jumps

Extreme returns

Jump vs extreme values

negative jumps

-4

-3

-2

-1

0

1

2

3

4

5

6

1 11 21 31 41 51 61 71 81 91 101

Holding period

t-valueCAAR

Jumps

Extreme returns


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Figure 8. The choice of the index for estimating normal returns

The figure compares the t-values of the estimated CAAR for two alternative estimations of themarket model. In the first alternative we use the S&P100 as benchmark index and in the secondalternative we use an equally weighted index, constructed based on the existing firms. Thereported t-values are based on the prediction error variances.

Comparing indices

negative jumps

-4

-2

0

2

4

6

1 11 21 31 41 51 61 71 81 91 101

Holding period

t-valueCAAR

Value weighted index

Equally weighted index

Comparing indices

positive jumps

-4

-2

0

2

4

6

1 11 21 31 41 51 61 71 81 91 101

Holding period

t-valueCAA

R

Value weighted index

Equally weighted index

7


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Figure 9. Comparing different t-values

The figure compares the t-values estimated by the two alternative variance estimations, i.e. theprediction error variance and the cross-sectional variance. We use the market model to estimatethe expected normal returns, where S&P100 is used as the market index. In identifying eventdays we use the estimated jumps and impose the volume restriction.

Comparing alternative t-values

positive jumps

-4

-3

-2

-1

0

1

2

3

4

5

6

1 11 21 31 41 51 61 71 81 91

Holding period

t-valueCAAR

CS variance

PE variance

Comparing alternative t-values

negative jumps

-4

-3

-2

-1

0

1

2

3

4

5

6

1 11 21 31 41 51 61 71 81 91

Holding period

t-valueCAA

R

CS variance

PE variance


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36

Figure 10. Comparing different samples

The figure illustrates the estimated CAAR and the related 95% confidence interval for positiveand negative jumps for the different time periods. The left column shows the results for positivejumps and corresponding results for negative jumps are shown in the right column. We use themarket model to estimate the expected normal returns, where S&P100 is used as the market

index. In identifying event days we use the estimated jumps and impose the volume restriction.The reported t-values are based on the prediction error variances.

Sample 1

positive jumps

-5.0%

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

1 11 21 31 41 51 61 71 81 91

Holding period

CAAR

Sample 2

positive jumps

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

1 11 21 31 41 51 61 71 81 91

Holding period

CAAR

Sample 3

positive jumps

-2.0%

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

1 11 21 31 41 51 61 71 81 91

Holding period

CAAR

Entire

positive jumps

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

1 11 21 31 41 51 61 71 81 91

Holding period

CAAR

Sample 1

negative jumps

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

1 11 21 31 41 51 61 71 81 91

Holding period

CAAR

Sample 2

positive jum ps

-2.0%

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

1 11 21 31 41 51 61 71 81 91

Holding period

CAAR

Sample 3negative jumps

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

1 11 21 31 41 51 61 71 81 91

Holding period

CAAR

Entire

negative jumps

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

1 11 21 31 41 51 61 71 81 91

Holding period

CAAR


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37

Appendix

Table A1. Data Restrictions

Table XX shows the number of trading days and jump days pre and post imposing the tradingand volume restrictions respectively.

Stock # of trading days # of jump days# of trading daysafter trading restriction

# of jump days aftervolume restriction

AA 2499 2474 189 60

ABT 2498 2473 116 47

AEP 2491 2463 293 93

AES 2498 2400 315 105

AIG 2498 2472 87 33

ALL 2498 2472 176 67

AMGN 2495 2471 113 47

ATI 1776 1712 342 117

AVP 2498 2472 299 90

AXP 2498 2473 99 41

BA 2498 2471 132 57

BAC 2497 2470 100 31

BAX 2498 2472 217 75

BDK 2496 2466 384 115

BHI 2498 2471 173 70

BMY 2498 2471 131 52

BNI 2488 2451 318 92

BUD 2498 2471 164 61

C 2467 2401 67 24

CAT 2497 2472 135 38

CCU 2496 2391 236 59

CI 2497 2470 300 70

CL 2496 2470 138 43

CMCSA 2493 2159 313 106

COF 2485 2419 202 53

CPB 2487 2446 243 80

CSC 2496 2468 231 66CSCO 2304 2284 73 29

CVX 1364 1350 32 10

DD 2472 2415 104 43

DELL 2494 2469 81 40

DIS 2495 2470 132 52

DOW 2495 2469 199 70

EK 2496 2471 170 49


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38



EMC 2496 2471 130 37

EP 1308 1275 82 29

ETR 2496 2468 409 102

EXC 1601 1585 77 35

F 2463 2402 196 83

FDX 2496 2469 227 71

GD 2495 2425 332 102

GE 2495 2471 69 25

GM 2495 2469 147 49

GS 1977 1958 81 24

HAL 2495 2470 135 41

HD 2495 2470 124 43

HET 2495 2469 392 125

HIG 2495 2469 300 92HNZ 2495 2470 251 84

HON 1950 1931 87 31

HPQ 2495 2469 113 39

IBM 2495 2470 46 15

INTC 2345 2321 69 27

IP 2471 2418 149 54

JNJ 2495 2449 119 38

JPM 1600 1585 37 19

KO 2496 2470 112 36

LTD 2494 2468 369 122MCD 2493 2468 136 48

MDT 2493 2467 147 51

MEDI 2494 2278 206 76

MER 2493 2468 70 28

MMM 2498 2467 121 34

MO 2474 2416 131 44

MRK 2493 2468 93 34

MSFT 2358 2321 74 31

NSC 2493 2467 231 83

NSM 2493 2467 173 60ORCL 2494 2470 133 50

PEP 2493 2467 133 46

PFE 2493 2468 98 43

PG 2493 2468 66 24

ROK 2473 2428 363 126

RTN 1429 1392 83 31

SLB 2457 2399 96 37

SLE 2493 2466 229 84


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39



SO 2493 2468 242 93

TGT 1788 1771 74 29

TXN 2493 2469 100 36

TYC 2476 2443 169 49

UPS 1844 1823 109 40

USB 1516 1501 71 34

UTX 2493 2467 144 44

VZ 1680 1663 71 28

WB 1428 1414 68 26

WFC 2200 2179 90 26

WMB 2493 2467 218 71

WMT 2488 2457 98 41

XOM 1829 1812 41 24

XRX 2495 2469 219 84


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Figure A1. Fractions removed by restrictions

The figure shows the fraction of total trading days removed by the restriction on inactive trading(top graph) and on traded volume (bottom graph) for each individual stock.

Fraction Removed

Trading Restriction

0,00%

2,00%

4,00%

6,00%

8,00%

10,00%

12,00%

14,00%

16,00%

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 7 3 7 6 79 82 85 88

Fraction Removed

Volume Restriction

30,00%

35,00%

40,00%

45,00%

50,00%

55,00%

60,00%

65,00%

70,00%

75,00%

80,00%

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88

an event study of price movements following realized jumps

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