cost of illiquidity evidence after hours trading

Electronic copy available at: http://ssrn.com/abstract=1473942

The Cost of Illiquidity:

Evidence from After-Hours Trading

Brian Walkup

University of Florida

September 9, 2009

Abstract

I use after-hours trading (post-close and pre-open) to examine the cost of finding liquidity in an

illiquid market. Using a large sample of after-hours trades from the three major U.S. stock

exchanges I determine the amount of price reversal that occurs when liquidity returns at the open

of normal trading hours. The size of the reversal is statistically and economically significant

with approximately 40%-65% of the after-hours price change reversing at the time of the

opening trade for the next trading day. However, during after-hours sessions with significantly

increased trading this reversal shrinks considerably, even becoming a momentum effect in

certain conditions. These days of heavy trading likely represent days in which an information

event has occurred outside of regular trading hours and therefore a price reversal would not be

expected as the price is reacting to the new information. This study suggests that those looking

for a large amount of liquidity in an illiquid market (such as the after-hours market) are forced to

pay a large premium for the liquidity.

Electronic copy available at: http://ssrn.com/abstract=1473942

The Cost of Illiquidity: Evidence from After-Hours Trading Walkup

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Introduction

The three major U.S. stock markets (New York Stock Exchange, Nasdaq, and American

Stock Exchange) all operate from 9:30am to 4:00pm on trading days. Outside of these normal

hours of operations information is still revealed and trades can still occur. However, the after-

hours market doesn’t come close to matching the liquidity available while the major exchanges

are open. Due to the lack of liquidity, those making trades during the after-hours sessions pay a

high liquidity premium to execute a trade.

This paper looks at the size of the price reversal/momentum when the market opens for

trading after there has been a price movement during the after-hours session. Due to the lack of

liquidity available after-hours, when liquidity is needed in one direction trades will have to be

executed at prices further and further away from the closing price of the prior day in order to be

able to find the liquidity to fulfill the orders. If the change in the price over the after-hours

session is mostly the result of a significantly larger liquidity premium outside of regular trading

hours, then we should expect to see a reversion back towards the original closing price from the

previous trading day when the market opens at 9:30am. However, if the change in price is the

result of new information (whether public or short-lived private information) being priced, then

we should not expect to see a price reversion.

I look at a large sample of stocks from all three U.S. exchanges and use trade-by-trade data

from the Trade and Quote database (TAQ). After-hours returns are calculated as well as the

stock’s price change from the last after-hours trade to the open price once the market opens for

trading. Multiple regressions are used to look at the impact of after-hours returns on the opening

price at the beginning of the next trading day as well as the price movement during the first hour


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of the trading day. Control variables include firm size, sign of the after-hours return, whether or

not there was a significant increase in after-hours trading during that session, whether or not

there was a single large trade that dominated the after-hours trading, and whether or not the after-

hours session took place over a weekend.

There are multiple hypothesis that can be formed regarding how the after-hours price change

of a stock could impact the opening price for the next trading day. Many of the trades made

outside of regular trading hours are likely to be liquidity based such as funds re-balancing. They

also could be based on new information being revealed publicly while the markets are closed,

such as an after-hours earnings announcement. It is also likely that many of the trades executed

after-hours are based on short-lived private information. If the prices are being shifted due to

liquidity demands, we should see a reversal due to the increased cost of finding liquidity after-

hours. However, if the trades are information based it is not likely that we will see this reversal

as there is information driving the price in a direction.

The results of this paper support the hypothesis that there is a significant increase in the cost

of trading associated with the illiquidity of the after-hours market. I show that returns that occur

outside of trading hours tend to reverse themselves at the open of trading the next trading day.

This is likely the effect of a high cost of demanding liquidity in the after-hours market.

However, if there is a high probability that new information was revealed (proxied by an increase

in after-hours trading of more than two standard deviations) then the reversal essentially

disappears.

The magnitude of the reversal is quite significant. If after-hours trading volume for a stock

during an after-hours session falls within the normal range (not more than a two standard


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deviation increase in trading volume) then approximately 40-65% of the after-hours price change

is reversed immediately upon the opening of regular trading hours. The reversal is statistically

stronger for small market capitalization stocks (approximately 7.7% larger reversal than large

market capitalization stocks), during after-hour sessions that occur over weekends

(approximately 6.6% larger reversal than non-weekend after-hours sessions), and during after-

hours session with negative after-hours returns (approximately 12.4% larger reversal than during

positive after-hours sessions).

The rest of the paper is organized as follows: In Section II I give an overview of the existing

literature on the microstructure of the after-hours market. Section III gives the details of the data

selection. Section IV discusses the findings of the paper. Finally, Section V concludes the paper

with a brief discussion of potential extensions of the paper.

I. Overview of Existing After-Hours Literature

Much of the early literature regarding after-hours trading dealt with stocks that were listed on

at least one stock market outside of the U.S. as well as being listed on one of the major U.S.

exchanges. For example, Neumark, Tinsley, and Tosini (1991) found that price changes on the

U.S. exchanges were adequately incorporated the next day in the international markets, but the

opposite wasn’t always the case. However, after-hours trading has come a long way since these

early articles and trading jointly listed stocks on an alternative exchange is no longer the only

manner of trading a stock after-hours. After-hours trading began in 1975 but was limited to only

institutional investors and large block trades. It wasn’t until 1999 that regular investors were

allowed to trade outside of the normal 9:30am – 4pm trading day. Due to this fundamental


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change, I will focus on the more modern strand of the literature which looks at the after-hours

market since the rule change in 1999.

One of the most important papers in the current after-hours literature is Barclay and

Hendershott (2003). This paper is not only important because of its overall findings, but also

because it has the most comprehensive summary statistics concerning after-hours trading. They

show a clear picture of after-hours trading relative to regular trading hours. The data used by

Barclay and Hendershott contains all after-hours trades and quotes for Nasdaq-listed stocks for

212 trading days during 2000. They show that these stocks average around 25,000 after-hours

trades per day. This represents almost 4% of the daily total trading volume on average.

Throughout their study they focus on the 250 highest-volume stocks from their sample, which

they show represents about 75% of all after-hours trading. Barclay and Hendershott show in

Figure 1 of their paper that after-hours trading is strongest directly before the open and after the

close of regular trading hours. It also shows that volatility follows the same pattern, but with a

much less severe drop-off during after-hours trading. The main finding of Barclay and

Hendershott (2003) is that the amount of information on a per-trade basis during after-hours

trading is significantly higher than during regular trading hours. Therefore, even though the

volume of trading is significantly lower, there is still strong price discovery outside of regular

trading hours.

Barclay and Hendershott also make some other interesting observations about after-hours

trading. First, they argue that the lack of popularity of after-hours trading likely stems from their

finding that there is a higher probability of information-based trades on a per-trade basis outside

of regular hours. Smaller liquidity traders prefer to try and trade together to minimize the

likelihood of trading against informed traders and are therefore better off pooling together during


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regular trading hours when the per trade likelihood of informed trading is lower and trading costs

are smaller. They also touch on how the different characteristics of after-hours trading could

affect whether or not a firm releases earnings announcement during regular trading hours or

after-hours. In their paper they claim, “The noisier stock prices and less efficient price discovery

after hours could affect firms’ decisions about the timing of their public announcements, such as

earning announcements. Announcements made after hours are likely to generate greater

volatility and larger price reversals than are announcements made during the trading day.”

(Barclay and Hendershott, 2003, p. 1070) The idea of after-hours trading affecting firms’

decisions on public announcements has generated some interest in recent years including Greene

and Watts (1996), Bagnoli et al (2006), and others.

In Barclay and Hendershott (2004) the authors look at after-hours trading and its effect on

market microstructure characteristics. They look specifically at how the lack of trading outside

of normal trading hours affects trading costs through bid-ask spreads. Their results are

consistent with what should be expected. The lack of liquidity in the after-hours market results

in higher trading costs. Both quoted and effective spreads increase significantly outside of

normal trading hours. The percentage effective half spread moves from an average of

approximately 0.17% during the trading day to approximately 0.6% after-hours. They also find

that spreads become significantly larger for stocks with lower trading volume. Barclay and

Hendershott then break the bid-ask spread down into its three fundamental components:

inventory holding costs, order processing costs, and adverse selection costs (as found in Stoll,

1989). They find that the adverse selection component of the spread is 15 times larger during the

pre-open than during normal trading hours and 7 times larger during the post-close than during


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normal trading hours. They sum up why they feel after-hours trading will never grow much

beyond its current low level of trading with the following thoughts:

“The magnitude of the liquidity externalities suggest that exchanges have little

incentive to expand their trading hours due to competitive pressure. Despite the

wide spreads, profit opportunities for dealers to provide liquidity appear limited

and the high adverse selection and low trading activity make monitoring the

market costly. The wide spreads should discourage investors from trading after

hours unless they have very high liquidity demands or short-lived private

information. Finally, the investor protections, for example, warnings of high

trading costs and volatility, currently employed by brokers and regulators should

be continued.” (Barclay and Hendershott, 2004, p. 709)

There are relatively few other papers that look at the current after-hours trading market. One

such paper that does is Zdorovtsov (2003). Zdorovtsov looks mostly at the volatility over the

after-hours period and considers the private information hypothesis and the public information

hypothesis. One of the main findings of the paper is that a large amount of trading volume in the

pre-open period coincides with more volatility in overnight returns and less volatility during

regular trading hours. According to the author this represents a shift in the price discovery

toward the pre-open hours. Another important finding of the paper is that the greater the flow of

public information after hours the greater the after-hours volatility (and the same is true for

during normal trading hours). Finally, Zdorovstov finds evidence (as in prior studies) that

information releases outside of trading hours are of greater economic significance than

information releases during trading hours.


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II. Data Selection and Variable Definition

I use transaction level TAQ data for all three U.S. exchanges from January 1, 2006 to

December 31, 2006. All of the stocks traded on all three exchanges are sorted by exchange and

then placed into deciles based on annual trading volume. Standard screens are used to eliminate

REITs, trusts and holding groups. A random sample of 50 stocks is selected from deciles four

through ten for each exchange, leaving a sample of just over 1,000 firms. Deciles one through

three are eliminated due to their very low frequency of after-hours trades (similar to Barclay and

Hendershot, 2003). All penny stocks (stocks traded at any point during the year for less than $5)

are eliminated from the sample. This step is taken to ensure that the after-hour returns are not

being caused in large part by the bid-ask bounce and the fact that there is almost no liquidity for

these stocks in the after-hours market. This is more likely to be the case for stocks with low

prices. The remaining sample consists of 617 firms. Prior to calculating after-hours returns all

prices are adjusted for splits and dividends.

I calculate the after-hours return as:

/

represents the after-hours return for firm i on day t, represents the

price of the last after-hours trade prior to the market opening for firm i on day t, and is

the closing price for firm i on day t-1. Out of a potential 155,484 after-hours returns (617 firms *

252 trading days) there are 140,997 days that I am able to calculate an after-hours return (not all

firms have non-zero after-hours trading every-day and one day per firm is lost in order to be able

to calculate an overnight return). Summary statistics for the complete sample of after-hours

returns are shown in Table 1.


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The dependent variable in my regressions represents the change in price from the last

after-hours return to the opening price when regular trading resumes at 9:30am the next trading

day. It is calculated as follows:

/

Where is the dependent variable representing the change in price for firm i on

day t from the last after-hours trade executed to the opening price at 9:30am when the exchange

opens for trading. represents the price of the stock for firm i when the market opens for

trading on day t and is the price of the last after-hours trade for firm i on day t.

Control variables used in regressions include:

SmallMarketCap: Dummy variable that equals 1 if the stock is in MarketCap deciles 1, 2,

or 3; and 0 otherwise

o MarketCap: Average shares outstanding for January 2006 times average share

price for January 2006

SmallMarketCapInteraction: SmallMarketCap * AHreturn

AHnegativeDum: Dummy variable that is 1 if AHreturn < 0; and 0 otherwise

AHnegativeInteraction: AHnegativeDum * AHreturn

LargeNumberOfTradesDum: Dummy variable that equals 1 if there was more than a 2

standard deviation increase in the number of trades during that after-hours trading session

relative to the mean number of trades during all after-hours trading sessions for that stock

during the year 2006; and 0 otherwise

LargeNumberOfTradesInteraction: LargeNumberOfTradesDum * AHreturn

OneLargeTradeDum: dummy variable which equals 1 if there is a single trade during that

after-hours session larger than the mean after-hours trade size for that stock plus 2

standard deviations; and 0 otherwise

OneLargeTradeInteraction: OneLargeTradeDum * AHreturn

WeekendDum: dummy variable which equals 1 if the after-hours session is from Friday

after 4pm to Monday at 9:30am; and 0 otherwise

WeekendInteraction: WeekendDum * AHreturn


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One distinct way I look at the data for a robustness check is by eliminating trades with

after-hours price movement close to 0%. It is likely that in many of these cases there is very

little need for liquidity after-hours. There may be only a few trades executed while the

exchanges are closed and therefore the price remains relatively close to the closing price from

the prior day. In these cases a price reversal wouldn’t necessarily be expected. This could affect

the model. Therefore I remove these observations from the sample to see if the results of the

model are affected.

Another robustness check that I utilize is to re-run the regressions looking at longer

period returns. The dependant variable is changed from the very short time interval of

ReturnOpen to time intervals of 5 minutes, 15 minutes, 30 minutes, and 1 hour from the opening

of trade. This allows me to see whether or not the reversal is maintained as regular trading

continues through the early morning trading. These returns are calculated as follows:

Return5Min = /

Return15Min = /

Return30Min = /

Return1Hour = /

I start by eliminating any days in which the after-hours return is less than . The

remaining dataset consists of 54,445 days with after-hours returns greater than 0.25% or less than

-0.25%. I do the same procedure again cutting the dataset into after-hours returns greater than

0.5% or less than -0.5% which consists of 33,666 observations. This is once again done using


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1% as the cutoff (16,015 observations) and 2% as the cutoff (5,678 observations). Summary

statistics for each of these cuts are shown in Table 2.

III. Results

A. Full Sample Results

For the initial set of results I utilized my entire sample of 142,371 after-hours sessions from

617 firms. OLS regressions are run with ReturnOpen as the dependent variable. First I use only

AHreturn as the explanatory variable. From there other explanatory variables are added. The

initial assumptions on signs would be as follows (No prediction will be made on dummy

variables since the effect is likely to be opposite on positive AHreturns and negative AHreturns.

Therefore, the sign is ambiguous.):

AHreturn : Negative

o The illiquidity of the after-hours market is expected to cause a reversal of

prices for the open of trading. Since a reversal is expected the sign should be

negative.

SmallMarketCapInteraction: Negative

o If the company associated with the stock has a small market cap then it is

likely that the after-hours market for the shares of the company’s stock would

be even more illiquid causing a larger reversal. Therefore the coefficient is

expected to be negative.

AHnegativeDumInteraction : No prediction

o No prediction is made on the interaction term between AHnegativeDum and

AHreturn. This simply allows the slope of the reversal relative to the after-


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hours return to be different for negative after-hours returns than positive after-

hours returns. No prediction is going to be made about the direction of this

difference in slope.

LargeNumberOfTradesInteraction : Positive

o If there is a significant increase in the number of trades being executed during

the after-hours trading session then it is more likely that an information event

has occurred. In the event of information being released outside of trading

hours, then the price is being adjusted for the new information and we

therefore should not expect as large of a reversal (and possibly even some

momentum rather than reversal). Any reversal that would normally be found

(which would have a negative sign) would need to be offset, therefore making

the expectation on LargeNumberOfTradesDum positive assuming a net

reversal is found in the regression outside of the LargeNumberOfTradesDum

variable.

OneLargeTradeInteraction : No prediction

o In the case that there is a single large trade during an after-hours session the

prediction could go either way. A claim could be made that there is a high

probability that a single large trade during an after-hours session could be

inside information based. In this case the prediction would depend on how

short-lived the information is. If it is extremely short-lived and therefore

becomes public by the opening of trading then we should see no reversal and

therefore a positive sign on OneLargeTradeInteraction. However, if it is not

revealed until after the opening than it can be treated as a liquidity trade and


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should result in more reversal, therefore giving it a negative sign. The

argument could also be made that if there is only one single large trade then it

is likely liquidity based. The argument could be that if it was based on public

information there would likely be other large trades, while if it was inside

information it would likely be split into a series of small trades. Therefore a

single large trade would be liquidity based and result in increased reversal

giving OneLargeTradeInteraction a negative sign.

WeekendInteraction : No prediction

o No prediction is being made about the impact of the after-hours trading

session falling on a weekend (Friday close of regular trading to Monday open

of regular trading).

The results for the regressions on the full sample are shown in Table 3. All of the

independent variables theoretically signed have the predicted signs and are statistically

significant at the 99% significance level. Figure 1 shows the expected amount of reversal given

differing after-hour returns. It is quite evident from Figure 1, as well as from Table 3, that the

most important determinant in deciding if a large reversal will take place is whether or not there

is large number of trades (greater than 2 standard deviation increase from the mean number of

trades). Given that the variable representing a large number of trades should be a good signal of

some form of public information event these results are quite consistent with the lack of liquidity

and high cost of finding liquidity during after-hours trading story. If the trading levels are

normal, a very significant portion of the price change during the after-hours session is

immediately reversed upon the opening of regular trading hours at 9:30am the next morning.

Approximately 40-65% (depending upon factors such as whether or not the firm is a small


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market cap firm, whether or not the after-hours return was negative, etc) of the after-hours price

movement can be explained as simply an additional cost of liquidity during an illiquid market

given that it is immediately reversed once normal liquidity resumes. If there is an information

event then liquidity becomes less of an issue and the reversal effect becomes much less

significant as the price is being moved closer to the true value given the new information.

The after-hours return variable alone is extremely statistically significant and shows that

approximately 44% of after-hours price movement is reversed if there is positive price

movement with approximately an additional 12% reversal if the after-hours return is negative

(giving a reversal of 56%). A potential explanation for negative after-hours returns experiencing

a larger reversal is that those being forced to sell for liquidity during the after-hours sessions are

likely in more of a “must-sell” mode than those buying are in a “must-buy” mode and therefore

are willing to pay higher premiums to find the liquidity. The other key variables (the interaction

terms) also come through as statistically significant. As predicted, small market capitalization

firms tend to experience larger reversals as liquidity is harder to find. The coefficient on the

SmallMarketCapInteraction shows an expected 7.7% larger reversal for small market cap firms.

A stock having a single large trade during the after-hours session results in approximately a 9.5%

smaller reversal. The reversal effect is approximately 6.6% stronger following a weekend.

B. Restricted Sample Results – After-Hour Return Cutoffs

A large portion of the observations have very little after-hours price movement. In fact, over

60% of the observations have price changes of less than 0.25% during the after-hours session. In

these cases it is likely that there wasn’t much need for liquidity outside of the regular trading

hours. If there are only a few trades made and the price has very little movement, it becomes


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less likely that we will see a significant reversal when the market opens at 9:30am and regular

liquidity resumes. These observations could affect the model. Therefore, I rerun the regressions

after making restrictions on the size of the after-hours price movement to determine if the results

are significantly affected.

The first step taken is to eliminate all observations during which the after-hours return is less

than the absolute value of 0.25%. The results of these regressions can be found in the first

column of Table 4 (also shown in Figure 2). After removing approximately 60% of the

observations which were clustered around an after-hours price change of 0% the results of the

regressions have not changed much. The magnitude of the price reversal is still around 40%-

65% of the after-hours price change. The explanatory variables all remain of the same sign and

nearly the same magnitude. The t-statistics fall due to the significantly decreased number of

observations. However, the explanatory variables all remain extremely significant statistically.

The adjusted R2 of the model increases as it is now able to explain a larger amount of the

variation in the reversal.

I then continue to reduce the observations clustered near an after-hours price movement of

0% from the model by eliminating all observations for which the after-hours return is less than

the absolute value of 0.5%. The results for these regressions are shown in the second column of

Table 4 and can be seen in Figure 3. Once again the magnitude of the results is relatively

unchanged while the statistical significance of the model and the independent variables stay very

high. This same procedure is repeated again using the absolute value of 1% as the cutoff for

AHreturn (results in the third column of Table 4 and shown in Figure 4) and once more for 2%

as the cutoff for AHreturn (results in the fourth column of Table 4 and shown in Figure 5). The

magnitude continues to be relatively unchanged as the sample size is reduced and the clustered


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observations with very little movement are peeled away. Despite the shrinking sample size the

statistical and economic significance remain large. From comparing all of the models utilizing

different cutoffs, it appears that the clustering around an after-hours price change of 0% does not

significantly affect the results of running the regression on the whole sample. Regardless of

whether the regression is run on the full sample or a restricted sample, it still remains evident that

there is a large price reversal of around 40-65% conditional on there not being abnormally high

trading.

C. Longer Time-Length Returns: Return5Min, Return15Min, Return30Min, Return1Hour

As another robustness check, the time-length of the return is expanded from simply the

change between the last after-hours trade and the opening trade of the next trading day. I look at

5-minute returns and 1-hour returns (15 and 30 minute returns also used with similar results but

excluded from the paper to avoid overkill). The 5-minute return regression results are available

in Table 5 and the 1-hour returns regression results are available in Table 6. The expected

amount of reversal given differing after-hours returns are available in Figures 6 and 7 for the 5-

minute returns and 1-hour returns, respectively. The results from these regressions show that the

magnitude of the reversal remains relatively unchanged as the regular trading hours take place

the morning after the after-hours price change. As was the case with the earlier regressions, even

after 5 minutes or 1 hour the magnitude of reversal is still approximately unchanged with

approximately 40-60% of the after-hours price change being reversed if there is not a large

amount of trading. It is also still the case that a significant increase in the amount of trading

results in this reversal decreasing significantly, and even becoming a slight momentum effect

depending on other factors. These results show that is not simply the opening trade that


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experiences this reversal. Instead, the reversal is more permanent and continues as trading picks

up throughout the morning.

IV. Conclusion

This paper demonstrates the importance and magnitude of the costs associated with trading in

an illiquid market. When traders are forced to find liquidity when there isn’t much available,

they can tend to have a strong impact on the price until the liquidity returns to normal levels.

The after-hours market is a perfect testing ground for this impact. The liquidity found in the

after-hours market is substantially less than the liquidity found during regular trading hours.

Over a short period of time the liquidity is restored (at 9:30am when the markets open) and we

would expect to see a reversal of the price changes that occurred after-hours if the prices were

being mostly driven by liquidity demands. However, in the cases where the price is being moved

by information rather than liquidity demands, we would expect this reversal to become much less

significant and potentially go all the way to zero or become a momentum effect.

I look at a large sample of after-hours trading and calculate the return from the close of

trading the previous trading day until the last after-hours trade. I then calculate the change in

price from the last after-hours trade to the opening price when trading resumes the next trading

day. Using this data, as well as other explanatory variables, I find that there is a significant

reversal of the magnitude of 40%-65% when the regular trading hours begin and high liquidity

returns. This reversal becomes much smaller and, depending on other variables, can even

become a slight momentum effect when there is a significant increase in the amount of after-

hours trading. This increase in trading has a high probability of signaling an information event.

Therefore the significant lessening of the reversal effect, and even potential momentum effect, is


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expected given that the price is moving during the after-hours session in response to the new

information. The price is becoming more efficient and a reversal would not be needed when

regular trading hours resume the next trading day.

My results would tend to imply that there are abnormal potential profits to be made by being

one of the traders providing liquidity during the after-hours sessions. This is in contrast to the

results of Barclay and Hendershott (2004) where they claim that the dollar profit per share is the

same after-hours as it is during the day. They look at the bid/ask spread and break it down into

its fundamental components and find that the profit from the spread is approximately the same

after-hours as it is during the trading day. I believe that it would be worthwhile to look into this

further with my results to identify whether there are excess profits to be made by providing

liquidity after-hours relative to providing liquidity during the trading day.

Another possible extension to my paper would be to identify which observations are linked to

the release of new information being revealed outside of regular trading hours. By identifying

instances linked to information events, such as quarterly earnings announcements, being made

outside of regular trading hours, I could more efficiently test the exact reversal for non-

information event after-hours sessions verse information event after-hours sessions. However,

given that it is impossible to precisely identify private information events, I would not be able to

determine the impact that private information events have on the reversal/momentum of after-

hours returns once regular trading hours resume.


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References

Bagnoli, Mark, Michael Clement, and Susan Watts. May 2006 version. McCombs Research

Paper Series. “Around-the-Clock Media Coverage and the Timing of Earnings

Announcements.”

Barclay, Michael and Terrence Hendershott. 2003. “Price Discovery and Trading After Hours.”

The Review of Financial Studies. Vol 16 No 4. pp 1041-1073.

Barclay, Michael and Terrence Hendershott. 2004. “Liquidity Externalities and Adverse

Selection: Evidence from Trading After Hours.” The Journal of Finance. Vol 59 No 2.

pp 681-709.

Damodaran, Aswath. 1989. “The Weekend Effect in Information Releases: A Study of Earnings

and Dividend Announcements.” The Review of Financial Studies. Vol 2 No 4. pp 607-

623.

Easley, David, Nicholas Kiefer, Maureen O’Hara and Joseph Paperman. 1996. Liquidity,

Information and Infrequently Traded stocks. The Journal of Finance. Vol 51 No 4.

pp 1405-1436.

Francis, Jennifer, Donald Pagach, and Jens Stephan. 1992. “The Stock Market Response to

Earnings Announcements Released During Trading versus Nontrading Periods.” Journal

of Accounting Research. Vol 30 No 2. pp 165-184.

Greene, Jason and Susan Watts. 1996. “Price Discovery on the NYSE and the NASDAQ: The

Case of Overnight and Daytime News Releases.” Financial Management. Vol 25 No 1.

pp 19-42.

Neumark, David, P.A. Tinsley, and Suzanne Tosini. 1991. “After-Hours Stock Prices and Post-

Crash Hangovers.” The Journal of Finance. Vol 46 No 1. pp 159-178.

Patell, James and Mark Wolfson. 1982. “Good News, Bad News, and the Intraday Timing of

Corporate Disclosures.” The Accounting Review. Vol 57 No 3. pp 509-527.


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Penman, Stephen. 1987. “The Distribution of Earnings News Over Time and Seasonalities in

Aggregate Stock Returns.” Journal of Financial Economics. Vol 18 No 2. pp 199-228.

Stoll, Hans R. 1989. “Inferring the Components of the Bid-Ask Spread: Theory and Empirical

Tests.” Journal of Finance. Vol. 44 No 1. pp 115-134.

Zdorovtsov, Vladimir. Dec 2003 version. University of South Carolina Working Paper. “Firm-

Specific News, Extended-Hours Trading and Variances over Trading and Nontrading

Periods.”


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Table 1. Summary Statistics for Whole Sample

This table shows summary statistics for the entire sample of after-hours sessions.

ReturnOpen is calculated as / . AHreturn is calculated

as / where represents the price of the last after-hours trade prior to the

market opening for firm i on day t, and is the closing price for firm i on day t-1. SmallMarketCap is a dummy

variable which equals 1 if the stock is in MarketCap deciles 4, 5, or 6 and 0; otherwise. AHnegativeDum is a

dummy variable that equals 1 if AHreturn < 0; and 0 otherise. LargeNumberOfTradesDum is a dummy variable

which equals 1 if there was more than a 2 standard deviation increase in the number of trades during that after-hours

trading session relative to the mean number of trades during all after-hours trading sessions for that stock during the

year 2006; and 0 otherwise. OneLargeTradeDum is a dummy variable which equals 1 if there is a single trade

during that after-hours session larger than the mean after-hours trade size for that stock plus 2 standard deviations;

and 0 otherwise. WeekendDum is a dummy variable which equals 1 if the after-hours session is from Friday after

4pm to Monday at 9:30am; and 0 otherwise.

Entire Sample of After-Hour Returns

Variable Observations Mean

Percent of Variable

Equal to 1

Standard

Deviation

Ahreturn 140997 0.043% 1.20%

ReturnOpen 140997 0.003% 1.00%

Return5Min 127550 0.007% 1.14%

Return1Hour 140997 -0.018% 1.54%

SmallMarketCapDum 140997 2.105%

AHnegativeDum 140997 41.732%

LargeNumberOfTradesDum 140997 2.394%

OneLargeTradeDum 140997 11.444%

WeekendDum 140997 21.505%

Trade Size (in shares) 2372080 4742.6


- 21 -

Table 2. Summary Statistics for Restricted Samples

This table shows summary statistics for the restricted samples of after-hours sessions.

ReturnOpen is calculated as / . AHreturn is calculated

as / where represents the price of the last after-hours trade prior to the

market opening for firm i on day t, and is the closing price for firm i on day t-1. SmallMarketCap is a dummy

variable which equals 1 if the stock is in MarketCap deciles 4, 5, or 6and 0 otherwise. AHnegativeDum is a dummy

variable that equals 1 if AHreturn < 0 and 0 otherise. LargeNumberOfTradesDum is a dummy variable which

equals 1 if there was more than a 2 standard deviation increase in the number of trades during that after-hours

trading session relative to the mean number of trades during all after-hours trading sessions for that stock during the

year 2006; and 0 otherwise. OneLargeTradeDum is a dummy variable which equals 1 if there is a single trade

during that after-hours session larger than the mean after-hours trade size for that stock plus 2 standard deviations;

and 0 otherwise. WeekendDum is a dummy variable which equals 1 if the after-hours session is from Friday after

4pm to Monday at 9:30am; and 0 otherwise.

Panel A : AbsValue(Ahreturn) > 0.25%


Percent of Variable

Equal to 1

Standard

Deviation

Ahreturn 54445 0.100% 1.93%

ReturnOpen 54445 -0.005% 1.34%

Return5Min 49265 0.006% 1.53%

Return1Hour 54445 -0.040% 1.93%






Panel B : AbsValue(Ahreturn) > 0.5%


Percent of Variable

Equal to 1

Standard

Deviation

Ahreturn 33666 0.158% 2.44%

ReturnOpen 33666 -0.020% 1.58%

Return5Min 30530 0.013% 1.17%

Return1Hour 33666 -0.035% 1.66%







- 22 -

Panel C : AbsValue(Ahreturn) > 1%


Percent of Variable

Equal to 1

Standard

Deviation

Ahreturn 16015 0.295% 3.44%

ReturnOpen 16015 -0.051% 2.08%

Return5Min 14489 0.013% 1.17%

Return1Hour 16015 -0.049% 1.96%






Panel D : AbsValue(Ahreturn) > 2%


Percent of Variable

Equal to 1

Standard

Deviation

Ahreturn 5678 0.547% 5.46%

ReturnOpen 5678 -0.079% 3.02%

Return5Min 5065 0.027% 1.53%

Return1Hour 5678 -0.059% 2.51%







- 23 -

Table 3. Regression Results for Whole Sample

This table shows regression results for the entire sample of after-hours sessions.

The dependent variable in each regression is ReturnOpen calculated as:

/

AHreturn is calculated as / .where represents the price of the last after-

hours trade prior to the market opening for firm i on day t, and is the closing price for firm i on day t-1.

SmallMarketCap is a dummy variable which equals 1 if the stock is in MarketCap deciles 4, 5, or 6 and 0 otherwise.

SmallMarketCapInteraction is calculated as SmallMarketCap times AHreturn.AHnegativeDum is a dummy variable

that equals 1 if AHreturn < 0 and 0 otherise. AHnegativeInteraction is calculated as AHnegativeDum times

AHreturn. LargeNumberOfTradesDum is a dummy variable which equals 1 if there was more than a 2 standard

deviation increase in the number of trades during that after-hours trading session relative to the mean number of

trades during all after-hours trading sessions for that stock during the year 2006; and 0 otherwise.

LargeNumberOfTradesInteraction is calculated as LargeNumberOfTrades * Ahreturn. OneLargeTradeDum is a

dummy variable which equals 1 if there is a single trade during that after-hours session larger than the mean after-

hours trade size for that stock plus 2 standard deviations; and 0 otherwise.. OneLargeTradeInteraction is calculated

as OneLargeTradeDum * Ahreturn. WeekendDum is a dummy variable which equals 1 if the after-hours session is

from Friday after 4pm to Monday at 9:30am; and 0 otherwise. WeekendInteraction is calculated as WeekendDummy

* Ahreturn.

T-statistics are given in parenthesis. * represents statistical significance at the 90% confidence level. ** represents

statistical significance at the 95% confidence level. *** represents statistical significance at the 99% confidence

level.


- 24 -

Observations : Full Sample

Dependent Variable: ReturnOpen

Indep. Variable Expected

Sign

Intercept N/A 0.00244

(0.65)

AHreturn Negative -0.44156***

(-107.98)

SmallMarketCapDum N/A 0.01538***

(2.81)

SmallMarketCapInteraction Negative -0.07706***

(-19.97)

AHnegativeDum N/A 0.00714

(1.39)

AHnegativeInteraction N/A -0.12381***

(-29.03)

LargeNumberOfTradesDum N/A -0.12227***

(-7.81)

LargeNumberOfTradesInteraction Positive 0.49613***

(123.94)

OneLargeTradeDum N/A -0.00578

(-0.82)

OneLargeTradeInteraction N/A 0.09533***

(11.91)

WeekendDum N/A -0.04388***

(-7.96)

WeekendInteraction N/A -0.06584***

(-14.48)

N 140997

Adjusted R2 0.2572


- 25 -

Table 4. Regression Results for Restricted Samples

This table shows regression results for the restricted samples of after-hours sessions.

The dependent variable in each regression is ReturnOpen calculated as:

/

AHreturn is calculated as / where represents the price of the last after-hours trade prior to the market opening for firm i

on day t, and is the closing price for firm i on day t-1. SmallMarketCap is a dummy variable which equals 1 if the stock is in MarketCap deciles 4, 5, or 6

and 0 otherwise. SmallMarketCapInteraction is calculated as SmallMarketCap times AHreturn.AHnegativeDum is a dummy variable that equals 1 if AHreturn <

0 and 0 otherise. AHnegativeInteraction is calculated as AHnegativeDum times AHreturn. LargeNumberOfTradesDum is a dummy variable which equals 1 if

there was more than a 2 standard deviation increase in the number of trades during that after-hours trading session relative to the mean number of trades during

all after-hours trading sessions for that stock during the year 2006; and 0 otherwise. LargeNumberOfTradesInteraction is calculated as LargeNumberOfTrades

* Ahreturn. OneLargeTradeDum is a dummy variable which equals 1 if there is a single trade during that after-hours session larger than the mean after-hours

trade size for that stock plus 2 standard deviations; and 0 otherwise. OneLargeTradeInteraction is calculated as OneLargeTradeDum * Ahreturn.

WeekendDummy is a dummy variable which equals 1 if the after-hours session is from Friday after 4pm to Monday at 9:30am; and 0 otherwise.

WeekendInteraction is calculated as WeekendDummy * Ahreturn.

T-statistics are given in parenthesis. * represents statistical significance at the 90% confidence level. ** represents statistical significance at the 95% confidence

level. *** represents statistical significance at the 99% confidence level.


- 26 -


Sign 0.25% 0.5% 1% 2%

Intercept N/A -0.04514*** -0.08850*** -0.16078*** -0.20791***

(-4.92) (-6.20) (-5.63) (-2.72)

AHreturn Negative -0.41784*** -0.40157*** -0.38018*** -0.37570***

(-69.78) (-53.59) (-34.90) (-19.88)

SmallMarketCapDum N/A 0.02526** 0.03318** 0.06533** 0.15455**

(2.46) (2.23) (2.41) (2.33)

SmallMarketCapInteraction Negative -0.08104*** -0.08462*** -0.08972*** -0.08715***

(-16.40) (-14.68) (-11.81) (-7.41)

AHnegativeDum N/A 0.06392*** 0.11836*** 0.19927*** 0.10143

(5.20) (6.00) (4.84) (0.89)

AHnegativeInteraction N/A -0.14362*** -0.15390*** -0.16758*** -0.19125***

(-23.51) (-20.39) (-15.59) (-10.45)

LargeNumberOfTradesDum N/A -0.22817*** -0.26907*** -0.33419*** -0.47862***

(-9.17) (-8.58) (-7.25) (-5.66)

LargeNumberOfTradesInteraction Positive 0.48640*** 0.47908*** 0.47073*** 0.47662***

(89.47) (73.23) (52.73) (33.82)

OneLargeTradeDum N/A -0.01021 -0.01296 -0.01020 0.02573

(-0.71) (-0.61) (-0.25) (0.24)

OneLargeTradeInteraction N/A 0.09540*** 0.09422*** 0.09095*** 0.09620***

(9.32) (7.83) (5.59) (3.57)

WeekendDum N/A -0.05603*** -0.06172*** -0.07352** -0.05715

(-5.01) (-3.76) (-2.41) (0.76)

WeekendInteraction N/A -0.06486*** -0.06498*** -0.06873*** -0.08094***

(-11.18) (-9.60) (-7.70) (-5.84)

N 54445 33666 16015 5678

Adjusted R2 0.3556 0.3937 0.4286 0.4362

Cutoff: AbsValue(Ahreturn) >


- 27 -

Table 5. Regression Results for 5-Minute Returns


The dependent variable in each regression is Return5Min calculated as:

Return5Min = /














- 28 -


Sign Whole Sample 0.25% 0.5% 1% 2%

Intercept N/A 0.00189 -0.03578*** -0.06529*** -0.12026*** -0.14741*

(0.39) (2.94) (-3.44) (-3.50) (-1.69)

AHreturn Negative -0.41509*** -0.39637*** -0.38539*** -0.36899*** -0.37045***

(-78.00) (-50.00) (-38.66) (-28.15) (-17.14)

SmallMarketCapDum N/A 0.01751** 0.02862** 0.03703* 0.03015 0.09529

(2.46) (2.10) (1.87) (0.92) (1.25)

SmallMarketCapInteraction Negative -0.06194*** -0.06543*** -0.06764*** -0.07354*** -0.06674***

(-12.33) (-10.00) (-8.82) (-8.05) (-4.96)

AHnegativeDum N/A 0.00933 0.04671*** 0.07873*** 0.12044** -0.03033

(1.39) (2.87) (3.00) (2.43) (-0.23)

AHnegativeInteraction N/A -0.12538*** -0.14375*** -0.15241*** -0.16649*** -0.18704***

(-22.59) (-17.77) (-15.18) (-12.87) (-8.94)

LargeNumberOfTradesDum N/A -0.11061*** -0.20559*** -0.24934*** -0.29131*** -0.40400***

(-5.43) (-6.24) (-5.98) (-5.25) (-4.18)

LargeNumberOfTradesInteraction Positive 0.48391*** 0.47748*** 0.47362*** 0.46964*** 0.47738***

(92.89) (66.34) (54.41) (43.72) (29.62)

OneLargeTradeDum N/A -0.01355 -0.01709 -0.01966 -0.00934 0.01139

(-1.48) (-0.89) (-0.69) (-0.19) (0.09)

OneLargeTradeInteraction N/A 0.09762*** 0.09703*** 0.09565*** 0.09431*** 0.09981***

(9.37) (7.16) (5.98) (4.82) (3.24)

WeekendDum N/A -0.03982*** -0.05130*** -0.05245** -0.03740 0.05407

(-5.55) (-3.46 (-2.40) (-1.02) (0.5321)

WeekendInteraction N/A -0.07141*** -0.07073*** -0.07233*** -0.07703*** -0.09364***

(-12.07) (-9.21) (-8.03) (-7.17) (-5.91)

N 140997 54445 33666 16015 5678

Adjusted R2 0.1538 0.2184 0.2455 0.3154 0.3457

Restriction


- 29 -

Table 6. Regression Results for 1-Hour Returns


The dependent variable in each regression is Return5Min calculated as:

Return1Hour = /














- 30 -


Sign Whole Sample 0.25% 0.5% 1% 2%

Intercept N/A -0.03035*** -0.09640*** -0.13824*** -0.18056*** -0.11415

(-4.58) (-6.18) (-5.86) (-4.01) (-1.03)

AHreturn Negative -0.44718*** -0.41519*** -0.40280*** -0.39158*** -0.40652***

(-61.75) (-40.82) (-32.56) (-22.82) (-14.75)

SmallMarketCapDum N/A 0.00517 0.03441** 0.05382** 0.07530* 0.12433

(0.53) (1.97) (2.19) (1.76) (1.28)

SmallMarketCapInteraction Negative -0.03497*** -0.04036*** -0.04222*** -0.04474*** -0.03348*

(-5.12) (-4.81) (-4.44) (-3.74) (-1.95)

AHnegativeDum N/A 0.05829*** 0.12342*** 0.15544*** 0.13168** -0.25736

(6.39) (5.91) (4.78) (2.03) (-1.56)

AHnegativeInteraction N/A -0.10446*** -0.13492*** -0.14634*** -0.16340*** -0.19205***

(-13.83) (-13.00) (-11.74) (-9.65) (-7.20)

LargeNumberOfTradesDum N/A -0.05045* -0.20656*** -0.25922*** -0.30842*** -0.45649***

(-1.82) (-4.89) (-5.01) (-4.25) (-3.70)

LargeNumberOfTradesInteraction Positive 0.49766*** 0.48580*** 0.48185*** 0.48117*** 0.49676***

(70.21) (52.61) (44.61) (34.21) (24.18)

OneLargeTradeDum N/A -0.01329 -0.00617 -0.00838 -0.00331 0.06638

(-1.06) (-0.25) (-0.24) (-0.05) (0.42)

OneLargeTradeInteraction N/A 0.08334*** 0.08227*** 0.08277*** 0.07141*** 0.05542

(5.88) (4.73) (4.17) (2.79) (1.41)

WeekendDum N/A -0.05314*** -0.08677*** -0.07066*** -0.0481 0.01745

(-5.45) (-4.56) (-2.61) (-1.00) (0.16)

WeekendInteraction N/A -0.09320*** -0.09125*** -0.09319*** -0.10308*** -0.12413***

(-11.58) (-9.26) (-8.34) (-7.33) (-6.14)

N 140997 54445 33666 16015 5678

Adjusted R2 0.0990 0.1591 0.1889 0.2240 0.2545

Restriction


- 31 -

Figure 1. Opening Trade Return for the Whole Sample

This figure shows ReturnOpen relative to AHreturn for the observations such that AbsValue(AHreturn) > 2%. The blue lines are conditional on SmallMarketCap

being equal to 1. The dashed lines are conditional on LargeNumberOfTradesDum being equal to 1. OneLargeTradeDummy, OneLargeTradeInteraction,

WeekendDummy, and WeekendInteraction are all held constant at 0.

-6

-4

-2

0

2

4

6

8

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Retu

rn fr

om la

st A

H t

rade

to

Ope

ning

Tra

de (%

)

After-Hours Return (%)

Opening Trade Return:Small vs Large Market Caps

Normal Trading vs High Trading

Small Market Cap - high trading

Large Market Cap - high trading

Small Market Cap - normal trading

Large Market Cap - normal trading


- 32 -

Figure 2. Opening Trade Return for AbsValue(AHreturn) > 0.25%




-6

-4

-2

0

2

4

6

8

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

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turn

fro

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pe

nin

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ade

(%

)









- 33 -

Figure 3. Opening Trade Return for AbsValue(AHreturn) > 0.5%




-6

-4

-2

0

2

4

6

8

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

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turn

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nin

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(%

)









- 34 -

Figure 4. Opening Trade Return for AbsValue(AHreturn) > 1%




-6

-4

-2

0

2

4

6

8

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

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turn

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pe

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ade

(%

)









- 35 -

Figure 5. Opening Trade Return for AbsValue(AHreturn) > 2%




-6

-4

-2

0

2

4

6

8

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

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turn

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ade

(%

)









- 36 -

Figure 6. 5 Minute Return for the Whole Sample

This figure shows Return5Min relative to AHreturn for the observations such that AbsValue(AHreturn) > 2%. The blue lines are conditional on SmallMarketCap



-6

-4

-2

0

2

4

6

8

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

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(%

)


5-Minute Return:Small vs Large Market Caps







- 37 -

Figure 7. 1 Hour Return for the Whole Sample

This figure shows Return1Hour relative to AHreturn for the observations such that AbsValue(AHreturn) > 2%. The blue lines are conditional on

SmallMarketCap being equal to 1. The dashed lines are conditional on LargeNumberOfTradesDum being equal to 1. OneLargeTradeDummy,

OneLargeTradeInteraction, WeekendDummy, and WeekendInteraction are all held constant at 0.

-6

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1 Hour Return:Small vs Large Market Caps






cost of illiquidity evidence after hours trading

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