Electronic copy available at: http://ssrn.com/abstract=2369470

Stock Repurchases and Liquidity∗

Alexander Hillert† Ernst Maug‡ Stefan Obernberger§

September 15, 2014

Abstract

We analyze the two-way relationship between share repurchases and liquidity basedon a newly available data set of realized share repurchases in the US, which covers50,204 repurchase months between 2004 and 2010. Repurchases unequivocally improveliquidity. Firms also adapt their buyback programs by reducing repurchase activitywhen the market for their stock is less liquid. Our findings suggest that endogenouscontrols have confounded results in earlier studies. Our results do not support thehypothesis that repurchases based on firms’ privileged information reduce liquiditybecause of adverse selection.

Keywords: Share repurchases, market microstructure, liquidity, limit order mar-

kets, informed trading

JEL classifications: G10, G30, G35

∗We are grateful to Manuel Adelino, Alon Brav, Casey Cheng, Darwin Choi, Philipp Geiler, John Graham,Jacob Oded, Ailsa Roell, and Florian Weigert for advice on this project and seminar participants at the 7thAnnual Meeting of the Swiss Finance Institute, University Carlos III, Erasmus Liquidity Conference, GermanFinance Association Conference, Hong Kong Polytechnic University, National University of Singapore, andSingapore Management University for fruitful discussions and feedback.†University of Mannheim, 68131 Mannheim, Germany. Email: hillert@bwl.uni-mannheim.de, Phone: +49

621 181 1462.‡Corresponding author. University of Mannheim, 68131 Mannheim, Germany. Email: maug@corporate-

finance-mannheim.de, Phone: +49 621 181 1952.§University of Mannheim, 68131 Mannheim, Germany. Email: obernberger@corporate-finance-

mannheim.de, Phone: +49 621 181 1948.

Electronic copy available at: http://ssrn.com/abstract=2369470

1 Introduction

This paper analyzes the two-way relationship between realized share repurchases and stock

market liquidity. Both directions of this relationship are of interest to financial economists.

Beginning with Barclay and Smith (1988), a large literature seeks to understand whether firms

act as liquidity providers or as consumers of liquidity in their own stock when they repurchase

their own shares. Conversely, stock liquidity influences repurchase decisions if managers try

to minimize the costs of executing buyback programs, but only few contributions address

the direction of the relationship.1 While there is a large literature on share repurchase

announcements, little is known about how managers execute stock repurchase programs.2

Research on this subject has not converged, because of limitations in the availability

of data as well as methodological differences across studies. Following Barclay and Smith

(1988), several authors have analyzed the impact of repurchases on stock liquidity and found

that repurchases reduce liquidity in France and Hong Kong, whereas their impact is positive

in Canada, Sweden, Switzerland, and Italy.3 The evidence for the US is ambiguous and

hampered by the fact that accurate data on realized share repurchases have become available

only recently.4 The challenge of analyzing this relationship is the fact that causality runs1To the best of our knowledge, Brockman, Howe, and Mortal (2008) were the first to address the causal

chain from liquidity to repurchase announcements. Brav, Graham, Harvey, and Michaely (2005) providesurvey evidence on CFOs motivations for repurchases, but find no evidence for liquidity concerns.

2Vermaelen (2010) surveys the large literature on repurchases, which is mostly concerned with announce-ments. A non-exhaustive list of more recent contributions includes Bonaimé, Hankins, and Harford (2013),Chen and Wang (2012), and Manconi, Peyer, and Vermaelen (2012). Further contributions are discussed be-low. Previous papers on the execution and completion of buyback programs include Babenko, Tserlukevich,and Vedrashko (2012), Stephens and Weisbach (1998), and Dittmar (2000), who establish drivers of actualrepurchases and the completion of share repurchase programs. These papers are not concerned with stockmarket liquidity.

3See Brockman and Chung (2001) for Hong Kong, De Cesari, Espenlaub, and Khurshed (2011) for Italy,Ginglinger and Hamon (2007) for France, Chung, Isakov, and Pérignon (2007) for Switzerland, McNally andSmith (2011) for Canada, and Rasbrant and De Ridder (2011) for Sweden.

4Barclay and Smith (1988) look at repurchase announcements and find a negative impact for the US,whereas Miller and McConnell (1995) find no evidence of a negative impact on liquidity. Wiggins (1994) andFranz, Rao, and Tripathy (1995) examine repurchase announcements and Nayar, Singh, and Zebedee (2008)analyze fixed price tender offers and dutch auctions. The latter three studies find a positive relationshipbetween repurchases and liquidity. Cook, Krigman, and Leach (2004) provide univariate analyses of a small,hand-collected sample of open market share repurchases and find a positive effect. Ben-Rephael, Oded, andWohl (2014) study recently disclosed, realized open market repurchases. The authors find ambiguous resultsand conclude from indirect evidence that “repurchasing firms consume liquidity rather than provide it” (page

1

both ways and repurchases, liquidity measures, and several commonly used control variables

such as stock volatility and trading volume are simultaneously determined and influenced

by factors that are difficult to observe. Hence, despite the importance and the considerable

interest in the subject, no coherent picture of the relationship between repurchases and

liquidity has emerged.

In this paper, we provide a fresh look at this topic. We collect a much larger and more

accurate data set than has been available so far for the U.S. and develop instruments for

repurchases as well as for liquidity in order to disentangle the causal connections between

the two variables. We formulate and test three hypotheses. (See Section 2 for a detailed

hypothesis development.) The liquidity-timing hypothesis adapts the argument of Brockman,

Howe, and Mortal (2008) and holds that managers attempt to time the liquidity of the

market for their stock and to minimize the costs of executing stock repurchase programs;

accordingly, they attempt to repurchase when liquidity is high and avoid repurchasing shares

when the market for their firms’ stock is illiquid. According to the competing market-maker

hypothesis of Barclay and Smith (1988), repurchasing firms act like market makers in their

own stock and supply additional liquidity to the market.5 Repurchases therefore increase

liquidity. By contrast, the adverse-selection hypothesis postulates that repurchasing firms

demand liquidity when they trade on non-public information and that more information-

based repurchases should be associated with less liquidity.

We collect monthly data on all repurchase programs and stock repurchases from all US

companies from 2004 to 2010 from SEC forms 10-Q and 10-K and compute three different

liquidity measures. Our data set covers 6,537 repurchase programs with an average (median)

size of 6.59% (5.27%) of the firm’s market capitalization. We collect data on 6,150 firms,

of which 2,930 firms conduct at least one repurchase during our sample period. Our data

1301).5The label “competing market-maker hypothesis” may be awkward in modern limit-order markets. We

maintain it for consistency with the literature to refer to the hypothesis that firms supply liquidity whenrepurchasing shares.

2

set is significantly larger and also more accurate than the ones used in previous research.6

In addition, we also collect the information on program characteristics, which allows us to

condition on them and develop new instruments.

Our methodology departs from previous research in three important ways. First, we avoid

contemporaneous control variables. Second, we use firm fixed effects and month fixed effects

to control for cross-sectional characteristics and macroeconomic factors. Hence, no part of

our identification comes from cross-sectional differences between firms. While simple, these

two steps together already account for most qualitative differences between our results and

those in the literature, and for differences between previous contributions themselves. Third,

we recognize that liquidity and repurchases are simultaneously determined and therefore

introduce instruments for both directions in this relationship. We use three instruments

for liquidity. The first instrument is the median monthly trading volume of all firms that

never undertake a repurchase. This instrument measures a factor of liquidity that is common

to all firms and cannot be influenced by the execution strategy of any particular firm’s

stock repurchase program. Alternatively, we use lagged trading volume instead. The third

instrument is the absolute difference between the stock price and $30, which has been used by

Choi, Getmansky, and Tookes (2009), and is motivated by the notion of an optimal trading

range centered around $30, so that stocks within this range are more liquid.

Our analysis focuses on repurchases under previously announced repurchase programs,

and our data allows us to use two characteristics of these programs as instruments for real-

ized repurchases, namely the size and the time that has elapsed since the inception of the

program.7 The time since program initiation increases each month by one month and the6Previous work on realized repurchases (Dittmar (2000), Stephens and Weisbach (1998)) is based on a

measure constructed from Compustat purchases of common stock. Banyi, Dyl, and Kahle (2008) documentthat this measure, which is only available on a quarterly basis, “deviates from the actual number of sharesrepurchased by more than 30% in about 16% of the cases.”

7Given our setup we need instruments for actual repurchases under previously announced programs.The only other paper that uses instruments for repurchases is Bonaimé, Hankins, and Harford (2013), whouse state-by-state transitions in regulation, which removed a preference for dividend for some institutionalinvestors. These transitions took place before our sample period and are not suitable to instrument for actualrepurchases.

3

size of the program is fixed at the beginning, when the program is announced. Thereby, we

ensure that predicted repurchases are not related to the level of liquidity during the execu-

tion of the program. All instruments are motivated in more detail below and validated using

several standard specification tests.

In a preliminary step, we analyze program initiations and the size of repurchase initiations

and find that there is a statistically significant, but economically negligible impact of firms’

past liquidity on the likelihood of program initiations and program size. Next, in our main

analysis we restrict ourselves to active programs and provide evidence for a strong impact

of liquidity on the way in which firms execute share repurchase programs. For each of three

liquidity measures we study, we find that firms significantly scale up their repurchase activity

when their stock is more liquid. Hence, our findings support the liquidity-timing hypothesis.

Next, we address the influence of repurchases on liquidity, which has been the focus of much

of the literature, and find that it is unequivocally positive. This finding provides support

for the competing market maker hypothesis, but is inconsistent with the adverse-selection

hypothesis.

We identify two sources of bias that account for differences between our results and

those in the previous literature. First, repurchases affect contemporaneous trading volume

and much of the impact of repurchases on liquidity seems to be through trading volume,

which therefore acts as a transmission channel. Controlling for contemporaneous trading

volume, or contemporaneous returns or volatility, therefore controls for the effect we wish

to measure. Once we remove contemporaneous controls we consistently obtain a positive

impact of repurchases on liquidity using OLS, even though this approach does not adequately

address endogeneity concerns. Second, comparing OLS results with instrumental variable

regressions indicates a significant negative bias, which suggests that unobserved variables

move repurchases and liquidity in opposite directions. Further univariate analyses reveal

that these omitted variables are also associated with higher short interest, lower returns, and

higher volatility, suggesting that liquidity and repurchases are both influenced by the same

4

investor perceptions.

We analyze a second prediction of the adverse-selection hypothesis, which implies that

more information-based repurchases should be associated with lower stock-market liquidity.

We test if liquidity-consuming repurchases reveal more information than liquidity-providing

repurchases, or whether informed repurchases are associated with higher spreads. We adapt

the methodology used in the insider trading literature and measure the information content of

repurchases by using abnormal stock returns. In our sample, liquidity-consuming repurchases

are on average followed by lower abnormal stock returns compared to liquidity-providing

repurchases. Analyzing filing-day returns leads to the same conclusion. This finding is

inconsistent with the adverse-selection hypothesis and the notion that information-based

repurchases reduce market liquidity. However, our results resonate well with recent findings

in the microstructure literature, which suggests that informed traders supply liquidity by

placing limit orders, at least when they exploit long-lived information. Our measurement of

abnormal returns extends over six months, which should be regarded as long term.8

We contribute to the literature in several ways. We are the first to analyze the liquidity-

timing hypothesis for actual repurchases. We add to the existing literature on the influence

of repurchases on liquidity by combining several methodological improvements, in particular,

a combination of fixed effects, exogenous control variables, and instruments for repurchases,

which helps us to avoid a number of biases that have confounded previous results. We also

use a broader set of liquidity measures than previous papers. Moreover, our analysis relies

on the largest data set for any of the questions we address. We also base the analysis on

the most accurate data that have been used in any study of repurchases in the US so far.

Previous papers rely either on repurchase announcements or manually collect smaller subsets

of the information available from SEC filings.9

8Bloomfield, O’Hara, and Saar (2005) and Kaniel and Liu (2006) both show in different contexts thatinformed traders use limit orders and supply liquidity when their information is sufficiently long-lived andtheir informational advantage is not too large. See also footnote 11.

9Cook, Krigman, and Leach (2003) collect data from companies and De Cesari, Espenlaub, and Khurshed(2011), Ben-Rephael, Oded, and Wohl (2014) collect data manually from filings.

5

2 Hypothesis development

Our conceptual framework departs from the prior work of Barclay and Smith (1988), who

formulate two hypotheses on the relationship between repurchases and liquidity. We adopt

their competing market-maker hypothesis, which builds on the notion that firms purchase

shares as a form of disbursing cash to shareholders and act as a market maker in their own

stock. By conducting transactions in their own stock they supply liquidity to the market for

their own stock.10

Hypothesis (Competing Market Maker): Repurchasing firms supply liquidity in their own

stock and improve liquidity.

Barclay and Smith (1988) develop a different perspective based on adverse selection.

Their hypothesis combines two arguments: First, firms use their privileged access to infor-

mation when executing share repurchases; second, such informed trading causes an increase

in spreads because of adverse selection. The first implication is closely related to the notion

of market timing, which is outside the scope of our analysis. The empirical literature has so

far mostly tested the second implication, which relies on the earlier microstructure literature

and postulates a close connection between informed trading, market orders, and liquidity

demand (e.g., Kyle (1985); Glosten and Milgrom (1985)).

The argument based on informed trading has therefore two parts. The first part focuses

on the trading strategy of firms if they trade on non-public information. According to this

hypothesis, they place market orders and consume liquidity. The second part is based on the

adverse-selection argument that market makers increase the spread if traders are more likely

to be informed.

Hypothesis (Adverse Selection): (i) Repurchasing firms act as informed traders and consume

liquidity in their own stock. (ii) Repurchases based on more non-public information are

also associated with lower levels of liquidity.10The argument in Barclay and Smith (1988) is based on the notion that firms provide competition to

existing market makers, which does not apply in a limit-order market. We maintain the label for consistencywith the literature to the hypothesis that firms supply liquidity as formulated in the text.

6

Hence, if the traditional microstructure argument for a connection between informed

trading and liquidity demand applies to repurchases, then we should observe such a negative

relationship. However, this argument may no longer hold in electronic limit order markets.

A number of recent papers conclude that informed traders may use limit orders and supply

liquidity. Kaniel and Liu (2006) develop a model in which traders prefer limit orders if they

trade on long-lived information, because patient informed investors can benefit from earning

the spread on their transactions. Limit orders may then reveal more information than market

orders.11 Kaniel and Liu (2006) also provide empirical evidence to support these claims (see

also Anand, Chakravarty, and Martell (2005)). Bloomfield, O’Hara, and Saar (2005) show in

an experimental asset market that traders with long-lived information may use limit orders,

whereas uninformed traders seem to avoid limit orders, which expose them to the risk of

trading against informed traders. Hence, informed trading by repurchasing firms may not be

inconsistent with liquidity demand.

Finally, we are interested in the reverse relationship between stock market liquidity and

repurchases. Here we follow Brockman, Howe, and Mortal (2008), who argue that managers

try to minimize the costs of executing stock repurchase programs and avoid repurchasing

shares when the market for their firms’ stock is illiquid.

Hypothesis (Liquidity Timing): Firms repurchase more (fewer) shares when the market is

more (less) liquid.

Managers can observe the liquidity of their own stock as well as that of other stocks and

they can adapt their repurchase strategies to the current observed liquidity, e.g., by placing

market orders. Firms using limit orders will also engage in liquidity timing as more limit

orders will be executed when the market is more liquid.11See Parlour and Seppi (2008) for a survey of recent research on limit order markets. See Chakravarty and

Holden (1995), Harris (1998) provide earlier theoretical analyses of informed trading in limit-order markets.Goettler, Parlour, and Rajan (2009) develop a dynamic model of a limit-order market with heterogeneousinvestors and show that investors with the highest inclination to become informed (“speculators”) use limitorders.

7

3 Data and methodology

Sample construction. New disclosure requirements in the US mandate the publication

of monthly share repurchases under the new Item 2(e) of Form 10–Q and under the new

Item 5(c) of Form 10–K. The requirement applies to all periods ending on or after March

15, 2004. Under these rules firms have to report the total number of shares purchased, the

average price paid per share, the number of shares purchased under repurchase programs,

and either the maximum dollar amount or the maximum number of shares that may still

be purchased under these programs. We are interested in the shares repurchased under a

program, which often differs from the total number of shares repurchased (see Appendix A.1

for further details).

To collect data on realized repurchases, we use CRSP to identify all ordinary shares (share

codes 10 and 11) that are traded on the NYSE, AMEX, and NASDAQ (exchange codes 1,

2, and 3), which gives us 6,504 firms over the period from January 2004 to December 2010.

We are left with 6,315 firms after matching these data with CRSP and Compustat. For all

firms we use a computer script to download all 10-Q and 10-K filings that were filed between

January 1, 2004 and March 31, 2011. Since many firms do not adhere to the proposed

disclosure format, we manually check and correct all observations.

We identify 9,100 repurchase programs and apply several screens to assure completeness

and integrity of our data (see Appendix A.1 for further details). After these screening pro-

cedures we are left with 6,537 repurchase programs, half of which have no fixed expiration

date, i.e. they remain active until they have been completed.12 This aspect may indicate

some desire on the part of firms to retain more flexibility in their future execution strategy12The regulation does not limit the length of a repurchase program. Stephens and Weisbach (1998) report

average program completion rates of 54.10%, 68.70%, and 73.80% one, two, and three years after the programannouncement. Oded (2009) reports unconditional completion rates of 56.1% and 92.3% four, respectively,eight quarters after the announcement. Bonaimé (2012) finds an average completion rate of 72.57% eightquarters after the quarter of the program announcement. The average completion rates in our sample are45.53%, 53.17%, and 59.31%, one, two, and three years after the beginning of the program. The loweraverage completion rates in our sample are partly attributable to the decline in repurchase activity duringthe financial crisis. Pre-crisis completion rates are four to eight percentage points higher.

8

and poses a potential concern for one of our instruments. In Table A-4 of the Internet Ap-

pendix, we restrict the sample to those observations with a definite program length and find

no differences. We therefore ignore this aspect of the data.

Usually, repurchase programs specify a maximal number of shares or a maximal dollar

amount that may be purchased. If a program is specified in shares (dollar) we compute

Program Size as the maximal number of shares (maximal dollar amount) that may be pur-

chased divided by the number of shares outstanding (market capitalization) at the time of

the announcement. In the last step we merge the data with I/B/E/S and TAQ.

The final sample contains 6,150 firms. Of these, 2,930 firms have repurchase programs. We

have 106,898 firm-months with an active program; firms conduct share repurchases in 50,204

of these firm-months. Table A-1 of the Internet Appendix shows the number of observations,

the number of firms, the number of repurchasing firms, and the number of repurchase months

for each year and for the entire sample period for the baseline sample. The large number of

observations allows us to overcome the limitations of monthly data. The monthly frequency

of the data makes our measurements more noisy if there are relationships within months.

This problem is no different from measurements at the daily level if relationships are also

intra-day, which is most likely the case with liquidity variables and repurchases. The lower

the data frequency, the harder it is to detect such relationships, which is why having a large

sample is useful here.13

Methodology and variables. Our generic specifications regress Repurchase Intensity on

a measure of stock market liquidity, respectively, a liquidity measure on Repurchase Intensity,13Brockman and Chung (2001) use daily data, but even within a single day liquidity can vary and we would

need instruments since we could not be sure whether repurchases happened before or after our measurementsof liquidity.

9

and a range of controls:

RIi,t = αR + δRIi,t−1 + βRLIQi,t +j=N∑j=1

γR,jControli,j,t + µRi + ηRt + uR,i,t,

LIQi,t = αL + δLIQi,t−1 + βLRIi,t +l=K∑l=1

γL,lControli,l,t + µLi + ηLt + uL,i,t.

(1)

Here, RI is Repurchase Intensity, defined as the number of shares repurchased under a

program during the month, divided by the number of shares outstanding at the beginning

of the month; LIQ is a liquidity measure. When testing the adverse selection hypothesis we

replace Repurchase Intensity with Repurchase Dummy, which assumes a value of one in a

month where the respective firm repurchased shares. Control refers to the control variables,

µRi and µLi are time-invariant firm fixed effects, µRt and ηLt are month fixed effects. The

month fixed effects account for changes in the macroeconomic environment not otherwise

captured by the control variables.

We sometimes omit monthly fixed effects in the repurchase regression, because one of

our instruments for liquidity has no cross-sectional variation and would then be absorbed

by the month fixed effects; then we use year fixed effects and controls for macroeconomic

conditions instead. We use GMM-IV to account for reverse causality and for unobserved

common effects, which might create a correlation between the error terms uL,i,t and uR,i,t.

The fixed-effects methodology significantly raises the hurdle for finding significant re-

lationships between repurchases and liquidity. Our approach relies only on the within-firm

variation in liquidity and repurchases that is firm-specific and not driven by common macroe-

conomic effects, whereas all time-invariant cross-sectional differences among firms and all

time-varying factors that are common to all firms are absorbed into the fixed effects.

Liquidity. We use three different measures of stock market liquidity. The precise details

of how these measures are calculated are provided in Appendix A.2 and we only summarize

them here. For all measures we first calculate a daily average and then the mean over all

10

trading days within a particular month. Spread is based on all relative spreads for a given

stock, weighted by the time the quote is valid. We calculate Price Impact as the absolute

value of the change in quotes over a five-minute interval and the Amihud measure as the

absolute daily return, divided by the daily trading volume in dollars.

Instrumental variables. The instruments for Repurchase Intensity are Program Size and

Program Month. We calculate Program Size as the maximal number of shares that may

be purchased under a particular program, divided by the number of shares outstanding

at the time of the announcement if the program volume is reported in shares.14 If the

program volume is reported in US Dollars we use the maximal Dollar volume that may be

repurchased under the program divided by the firm’s market capitalization at the time of the

announcement. The size of the program is fixed before the execution begins. It predicts future

repurchases and is therefore exogenous with respect to future variations in liquidity. Note that

we can use neither the realized size of the program nor the unutilized portion of the program

as instruments, because both depend on firms’ actual repurchase behavior and may be related

to the within-firm variation in liquidity. All our regressions include firm fixed effects, hence

unobserved factors that drive the design of repurchase programs and also influence subsequent

expected liquidity would be absorbed into these fixed effects. For example, a firm with a more

liquid stock may (and typically does) have larger repurchase programs and also a more liquid

market during the execution of the program. Such an relationship is absorbed into firm

fixed effects and does not bias our results. For our instruments it is only important that

unobserved factors do not influence the within-firm variation in liquidity after the start of

the program. Naturally, we expect Program Size to have a positive impact on repurchases.

Average (median) program size in our sample is 6.59% (5.27%) of the shares outstanding.

Program Month is the number of calendar months since the announcement of the repur-

chase program. The motivation is that the period for which the program has been active is14If there are multiple active programs, Program Size and Program Month are both calculated from the

most recently announced program.

11

Figure 1: Repurchase Intensity and Program Month. The figure plots RepurchaseIntensity, calculated as the median number of shares repurchased scaled by the number ofshares outstanding in the respective month after program inception, against Program Month,expressed as the number of calendar months since the inception of the program. In totalthere are 6,537 repurchase programs.

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also an ex ante feature of the program that is not influenced by the subsequent within-firm

variation of liquidity. However, we do not include observations of the program beyond one

year if the program has been active for more than one year, because a disappointing devel-

opment in a firm’s liquidity may lead managers to extend the length of the program beyond

one year, which would render Program Month endogenous. Hence, Program Month is simply

a number between one and 12. Figure 1 plots the median of Repurchase Intensity in each

month against Program Month. Firms front-load the execution of their programs, hence Pro-

gram Month has a negative impact on realized repurchases. The correlation of Repurchase

Intensity and Program Month is -0.0929. Effectively, Program Month predicts repurchases

based on the stage in the execution of the repurchase program. If actual repurchases deviate

from predicted repurchases, then these deviations are not used for identifying our effects

and therefore do not bias our estimates, even if the firm does not repurchase any shares in

a certain month. Both, Program Size and Program Month may reflect liquidity conditions

at the time of the program announcement. However, to the extent that these conditions

are firm-specific and predict liquidity during the later stages of the program, they would be

12

absorbed into firm fixed effects.

We use two instruments for liquidity in our baseline analysis. Exogenous Trading Volume

is calculated as the median trading volume of all firms that never conduct any repurchase

during the period from 2004 to 2010. The motivation for this instrument is that liquidity

depends on numerous unobservable factors that are common to many firms. We require

that the instrument incorporates these factors, but is not influenced by the specific factors

that would influence the liquidity of a particular firm, because these factors might then also

influence the firm’s repurchase behavior directly. It seems highly implausible that the specific

circumstances of the repurchase programs of some individual firm affect the stock market

liquidity of sufficiently many non-repurchasing firms to affect Exogenous Trading Volume.

Exogenous Trading Volume has no cross-sectional variation, we can therefore not use it and

also estimate month fixed effects and we estimate only year fixed effects instead in those

regressions that use this instrument. In order to make sure that Exogenous Trading Volume

does not capture within-year macroeconomic fluctuations that might also have direct impact

on repurchases, we use four controls for macroeconomic factors suggested by Baker and

Wurgler (2006) to remove within-year macroeconomic fluctuations: growth in the industrial

production index, growth in consumer durables, non-durables, and services. Alternatively, we

use Lagged Trading Volume, which is the previous month’s trading volume of the same firm

and therefore has cross-sectional variation and allows us to also include month fixed effects.

Here the identifying assumption is that the last month’s trading volume has no impact on

repurchases other than through its ability to predict current liquidity. We are not aware of

theoretical arguments that would identify a variable which simultaneously affects liquidity,

and also affects repurchases through channels other than the liquidity of the market itself.

The second instrument for liquidity is Deviation from $30, which is defined as the absolute

value of the difference between the stock price and $30. This instrument has been used

successfully by Choi, Getmansky, and Tookes (2009) and is calculated as the log of the

absolute price deviation from $30, where Price is the monthly average of the daily closing

13

prices from CRSP. The motivation of this instrument, as in Choi, Getmansky, and Tookes

(2009), is the notion of an optimal trading range around $30. The further a stock trades

away from this assumed center of the trading range, in either direction, the less it is traded.

Note that some stocks trade far away from $30 and yet are very liquid. Since we always

include firm fixed effects, such cross-sectional variations can be ignored. The instrument is

only related to the within-firm variation of liquidity and relies on the assumption that We

liquidity improves for sufficiently many stocks as firms move closer to the optimal trading

range.

We always conduct several tests to validate our instruments. We always report the

Hansen-J statistic on the overidentifying restrictions. We test for underidentification by

using the statistic proposed by Kleibergen and Paap (2006). Their test is for the rank of a

matrix; in our case it checks the rank of the matrix of reduced-form coefficients and tests

whether the instruments are sufficient to identify the endogenous variables. Finally, we test

for weak instruments by using the weak-identification test of Stock and Yogo (2005), which

tests the hypothesis that the maximal bias of the IV estimator does not exceed a certain

threshold, expressed as a percentage of the corresponding OLS estimator. In all of our spec-

ifications, the test statistic is above the critical value and the test rejects the hypothesis

that the maximal bias according to this test is above 5% of the OLS estimator. Given the

uniformity of the results, we do not report this test in the tables. However, we do report the

t-statistics from the first-stage regression to provide further information on the strengths of

the instruments.

Table A-2 of the Internet Appendix provides descriptive statistics for all variables of

the entire sample, which covers 346,978 firm-months and which is used for the event-study

analysis in Section 4.3.15 Table 2 describes the sample restricted to active programs, which

we use for testing our main hypotheses in Sections 4.1 and 4.2. This sample covers 106,898

firm-months except for the repurchase volume and Repurchase Intensity, which are reported15The number of observations for cumulative abnormal returns is lower because it requires more data. The

number of observations on Filing CAR depends on the number of filings.

14

only for the months in which repurchases are positive (50,204 firm-months).

The Spread is on average (median) 1.05% (0.27%). The average Repurchase Volume over

50,204 repurchase months is $49.4 million, which is equivalent to buying back 0.66% of shares

outstanding or 6.74% of monthly trading volume.16 The median repurchase volume is 0.35%

of shares outstanding or 3.29% of trading volume.

To be protected by the Safe Harbor Rule 10b-18, firms’ daily repurchases must not exceed

25% of the average daily trading volume of the preceding four calendar weeks (ADTV).

However, once a week firms may purchase shares in a block trade that is not subject to the

25%-restriction. Since repurchases are only reported monthly we are not able to assess in

detail whether repurchasing firm comply with the volume condition of the Safe Harbor Rule.

Instead, we approximate ADTV from last month’s trading volume. In 3,019 of the 50,204

repurchase-months firms purchase more than 25% of last month’s trading volume. Since

we cannot observe block repurchases, which do not count towards the 25%-limit, the true

number of months in which firms exceed the safe-harbor limit will be lower than 3,019.

4 Analysis

We begin the analysis with a discussion of the empirical results on how liquidity influences

repurchases (Section 4.1) and continue with the reverse relationship between repurchases and

liquidity (Section 4.2). Section 4.3 tests the adverse-selection hypothesis.

4.1 The influence of liquidity on repurchases

In this section we test the liquidity-timing hypothesis, which implies that increases in liquidity

induce increases in share repurchases. We hypothesize that companies wish to minimize the

costs from repurchasing their own stock and therefore prefer to repurchase when the market

for their shares is more liquid. This hypothesis is about the timing and the execution of16Ben-Rephael, Oded, and Wohl (2014) study a sample of CRSP firms randomly drawn from all NYSE

size deciles and their descriptive statistics are similar to ours (see their Table 1).

15

repurchase programs that have already been announced, i.e., at some point in the past,

companies have already made a decision to repurchase shares. It is plausible that firms with

more liquid stocks are also more likely to announce a repurchase program, in line with the

liquidity-timing hypothesis (see Brockman, Howe, and Mortal (2008)). We therefore proceed

in two steps. In the first step we briefly analyze program initiations and in the second step

we analyze program execution, which is the focus of our analysis.

4.1.1 Program initiations

Table 3 analyzes how the probability of program initiations and the size of repurchase pro-

grams depends on market liquidity and a range of other control variables suggested by the

literature. Panel A presents linear probability models, in which the dependent variable is

Program Initiation, a dummy variable, which equals one in a month when a firm announces

and begins a new program, and zero otherwise. (We use the month of the board meeting

date from the filings.) In Panel B the dependent variable is Program Size, as defined above.

The variable of interest is Average Spread, which is calculated as the previous six-months

average of the Spread. The control variables include variables related to past returns, total

assets, cash holdings, leverage, market-to-book ratio, and acquiror and target status in ac-

quisitions. These are suppressed in Panel B, because the results are very similar to those

obtained in Panel A. We present six specifications. Specifications (4) to (6) include firm fixed

effects, whereas specifications (1) to (3) do not included fixed effects. We successively restrict

the sample from including all observations (specifications (1) and (4)), to firm-months with

no active program in the previous month ((2) and (5)), and finally to those with no active

program in the previous six months ((3) and (6)).

The impact of Average Spread is mostly insignificant for Program Initiation without

fixed effects, showing that there is no additional cross-sectional information in the liquidity

variable that is not already reflected in the control variables. If we include fixed effects, then a

higher spread reduces program initiations and the effect is statistically significant. The effect

16

of liquidity on Program Size is statistically much stronger, suggesting that in more liquid

markets firms announce larger programs. The economic significance is negligible though.

For example, the coefficient of -0.0036 (Panel A, specification (4)) implies that an increase

in the spread by 1% reduces the probability of a program initiation by 0.36%. A similar

comment applies to the results for Program Size in Panel B. The qualitative effects of the

control variables are similar to those we find in our analysis of program executions below, and

mainly confirm findings from the prior literature. We defer the discussion of these variables

to the next section.

We conclude that our subsequent analysis of program executions can safely neglect the

impact of lagged liquidity on program initiations, because the combination of firm fixed effects

and a saturated set of control variables already absorbs all effects that might plausibly lead

to selection bias.

4.1.2 Program execution

Next, we analyze the impact of liquidity on program execution. Table 4 reports the results

for the baseline specification with one regression for each liquidity measuring as the inde-

pendent variable to proxy for liquidity. The dependent variable is Repurchase Intensity, as

defined above and all regressions are estimated using GMM-IV. Columns (1) – (3) use the

specification as in equation (1) with Exogenous Trading Volume and Deviation from $30 as

instruments (see Section 3). This specification uses year fixed effects instead of month fixed

effects and controls for within-year fluctuations in the macroeconomic environment by using

the four continuous macroeconomic control variables suggested by Baker and Wurgler (2006).

Columns (4) – (6) use Lagged Trading Volume and Deviation from $30 as instruments and

control for the macroeconomic environment with month fixed effects.

Both regressions are correctly specified and yield similar results. The Hansen J-statistic

for the test of overidentifying restrictions cannot reject the null that the model is correctly

specified for any specification in Table 4. The Kleibergen-Paap test for underidentification

17

always rejects the null of underidentification at all conventional significance levels. First-

stage t-statistics indicate that none of our instruments is weak: In most cases, instruments

are significant at the 1% level while only once significance is at the margin (1.87 for Deviation

from $30 in specification (5)). The sign of the instruments is also intuitive (see the signs of the

t-statistics in Table 4): Higher Exogenous Trading Volume and Lagged Trading Volume both

reduce Spread, Price Impact, and Amihud, whereas a higher Deviation from $30 increases

spreads, consistent with the hypothesis that trading further outside the typical trading range

reduces liquidity. As mentioned above, the Stock-Yogo test on the weak-instrument bias

always rejects the hypothesis that the bias exceeds 5% of the bias from OLS (not tabulated).

We find that for all liquidity measures, lower liquidity leads to lower repurchases. Esti-

mates for the coefficient of interest are virtually identical across the two alternative specifi-

cations for Spread (compare (1) with (4)) and Amihud (compare (3) with (6)) and somewhat

different in magnitude for Price Impact (compare (2) with (5)). In Table A-3 of the Internet

Appendix we show the within-firm standard deviation for the main independent variables,

which is 0.46 for the logarithm of the spread. Hence, increasing the Spread by one within-

firm standard deviation leads on average to a reduction in Repurchase Intensity of 0.13%

(= 0.46 × 0.0028; 0.0028 is the coefficient from Table 4). The same calculation gives 0.12%

for Amihud and 0.21% for Price Impact. From Table 2, the median of Repurchase Intensity is

0.35%. Hence, increasing Spread by one within-firm standard deviation leads to a reduction

in Repurchase Intensity equal to about one-third of its median value and is therefore eco-

nomically significant.Thus, repurchase volumes respond strongly to changes in the liquidity

of the stock and we conclude that firms engage in liquidity timing.

Controls. The regressions include a range of control variables. We include lagged stock

returns for the past three months. Based on the prior literature we expect a negative sign,

because firms tend to repurchase more shares after their stock has declined.17 We find that

repurchases respond strongly to past stock returns and all lags have the predicted negative17See Brav, Graham, Harvey, and Michaely (2005), and Stephens and Weisbach (1998)

18

signs. The program characteristics Program Month and Program Size, which we will later

use as instruments for repurchases, are both highly significant with t-statistics around 20

(Program Month) and seven (Program Size). Both variables have the sign we predicted

above (see Section 3), i.e., positive for Program Size, and negative for Program Month.

Jensen (1986) and Stephens and Weisbach (1998) find that firms tend to repurchase more

shares if they have stronger cash flows. We measure operating cash flows as the ratio of

EBITDA to total assets and corroborate the findings of the previous literature, but results

are significant only if Spread and Amihud are used as liquidity measures. Dividends seem

to have no impact on repurchases, consistent with the notion that firms view repurchases

as complementary to dividend payments rather than as substitutes. Dittmar (2000) shows

that firms use repurchases to increase leverage, which is consistent with our finding that

firms with a higher leverage conduct fewer repurchases. Value firms with a higher book-

to-market ratio consistently conduct more repurchases, probably because they have fewer

growth opportunities to reinvest their free cash flow. Options Exercised is the scaled number

of shares obtained by employees through stock-option exercises and has a positive impact on

repurchases, most likely because firms want to hold the number of shares outstanding constant

and avoid dilution from option exercises, confirming earlier results (Dittmar (2000)).18 The

dummy variable Acquiror indicates acquiror status in a takeover and has a negative, but

economically negligible impact on repurchases. The dummy variable Target indicates target

status in a takeover attempt and equals one from the time of the announcement until the

completion or cancellation of the takeover. Bagwell (1991) develops a theoretical model to

show that repurchases may serve as a takeover defense and Dittmar (2000) finds supporting

evidence for this hypothesis by showing that there is a positive relationship between takeover

attempts or takeover rumors and share repurchases. We find a negative coefficient on Target,18Babenko (2009) argues that there may be a reverse effect, because repurchases may trigger lower incentive

grants if repurchases and grants are substitutes. The coefficients of interest remain unchanged if we removethis control, hence, this potential endogeneity of Options Exercised is not a concern here.

19

which is never significant.19

Note that the R-squared provided for the GMM-models is statistically meaningless be-

cause the residuals are computed using the actual values whereas the parameter estimates

are obtained using estimated values. Therefore, even negative R-squareds are not unusual in

GMM-models. The R-squareds of our OLS-specifications presented in Table 5 are all close

to 8% and refer to the explanatory power of the right-hand-side variables in addition to the

fixed effects.

GMM-IV vs. OLS. To better understand the impact of endogeneity, we compare the

GMM results from Table 4 with the same estimations using OLS, which we report in Table

5. The table has the same format and includes the same variables as Table 5, but we do not

report the results for the control variables to conserve space. All OLS regressions show a

negative sign on the coefficients of the liquidity measures, but the size of the OLS coefficients is

numerically much smaller. The OLS regressions predict that doubling the spread, respectively

the price impact measure, would result in reductions of Repurchase Intensity by 0.15% for the

Spread, by 0.04% for Price Impact, and by 0.09% for Amihud. Hence, the IV specifications

predict that the impact of a reduction in Repurchase Intensity from a less liquid market is

much larger compared to OLS.

In this case, the OLS bias does not result form reverse causality, because the impact of

repurchases on spreads is also negative, so that reverse causality reduces the OLS coefficient,

rendering the bias negative. We find a positive bias and attribute it to unobserved factors

that simultaneously move spreads and repurchases in the same direction. One possible ex-

planation may be that investors sometimes trade on private negative information they have

obtained, whereas firms react to negative information about their price by increasing Re-

purchase Intensity. This hypothesis is untestable with our data. We provide more evidence

on the likely characteristics of the omitted variables after discussing the reverse relationship19We do not include a control for convertible issues, which seem to be associated with repurchases (see

de Jong, Dutordoir, and Verwijmeren (2011)), because only 115 (0.2%) of the repurchase-months in oursample are associated with convertible bond issues.

20

between repurchases and liquidity.

4.2 The influence of repurchases on liquidity

In this section we turn to the impact repurchases have on liquidity. Based on the previous

literature and the discussion in the Introduction, the impact of repurchases on liquidity can

be positive or negative. Again, we restrict our baseline analysis to the sample of firm-months

with active repurchase programs. Our discussion of repurchase initiations in the previous

section reveals only a negligible impact of repurchase announcements on liquidity; any sig-

nificant impact of repurchases on liquidity therefore has to come from program execution.

Table 6 reports the results for our baseline specification. The dependent variables in

the regressions are the three liquidity measures introduced before. We include fixed effects

again, so we require instruments that vary within firms. As instruments we use the program

characteristics Program Month and Program Size. As before, we cannot reject the overiden-

tifying restrictions. However, we can reject the hypothesis of underidentification, that the

instruments are weak, and that the bias exceeds the OLS bias by more than 5% at all conven-

tional significance levels. The instruments also have the predicted signs: higher Program Size

implies higher Repurchase Intensity, and a higher Program Month implies lower Repurchase

Intensity. We therefore conclude that the model is correctly specified.

We find a negative coefficient on repurchases in all regressions, which is always statistically

significant at the 1%-level: A coefficient of -7.487 on Repurchase Intensity in the regression

for Spread implies that a change in Repurchase Intensity by 0.62% - its within-firm stan-

dard deviation - changes Spread by 4.64% (= 7.487 × 0.62%). Hence, there is a clear and

unequivocally positive impact of repurchases on stock market liquidity.

In Table A-4 in the Internet Appendix, we impose a stricter requirement and limit the

analysis to those repurchase programs with a definite expiry date to address the potential

concern that firms may not specify expiry dates when they want to have flexibility over

program duration. In Table A-5 in the Internet Appendix, we exclude all programs that are

21

completed within less than 12 months. Thereby, we exclude programs that complete faster,

potentially because the market for the stock was more liquid in the past. This should not

be a concern, because our instruments already address this problem: Repurchase Intensity

predicted by Program Month and Program Size can not be correlated with future shocks to

liquidity. The sample restrictions in Tables A-4 and A-5 have no consequences for our results,

which supports our baseline specification.

Controls. Our regressions control for size using the logarithms of market capitalization

and the book value of assets, and both measures imply that larger firms are more liquid,

which confirms earlier findings of Stoll (2000) and Chung, Elder, and Kim (2010). Firms in

the S&P 500 and with higher levels of the stock price also tend to be more liquid. In line with

Chung, Elder, and Kim (2010), we control for the number of analysts. In order to avoid a

high number of missing observations, we assume that a firm has no analyst coverage if there

is no information about the firm on I/B/E/S. We find that firms are more liquid if more

analysts follow the stock; Chung, Elder, and Kim (2010) conjecture the same relationship,

but find the opposite result.

Firms are consistently less liquid when their book-to-market ratio is high and when their

leverage is low. Leverage typically does not change significantly over a seven-year period, so

the impact of leverage has probably no meaningful interpretation.

We also control for transaction characteristics. Specifically, we include dummies for ac-

celerated share repurchases (ASRs), repurchases conducted as tender offers, and privately

targeted share repurchases.20 However, none of the transaction characteristics has any con-

sistent and significant effect on liquidity. The stock return over the previous month has a

highly significant and positive impact on stock liquidity.

We also control for three lagged variables. The autoregressive coefficient is highly signifi-

cant and large. We include the lags of stock volatility and trading volume, which have been20Accelerated share repurchases (ASRs) involve a contract with an intermediary who borrows the shares,

delivers them to the firm, and subsequently covers its short position through repurchases in the open market.See Bargeron, Kulchania, and Thomas (2011) for a more detailed discussion of ASRs.

22

used as controls for the spread in the previous literature.21 Trading Volume is scaled by the

number of shares outstanding and defined excluding share repurchases to avoid contaminat-

ing the repurchase variable itself with the influence from trading volume. The coefficients

on Volatility change signs across liquidity measures and are difficult to interpret. We at-

tribute these patterns to the fact that we use lagged volatility. We obtain the usual positive

coefficient if we control for contemporaneous volatility. The directions of causality between

volatility, liquidity, and trading volume are not clear. These variables are probably deter-

mined simultaneously and therefore omitted from the standard specifications.

OLS and contemporaneous controls. We compare our IV analysis again to the corre-

sponding OLS results, which we report in columns (1) - (3) of Table 7. The specification is

identical to that in Table 6 except that we do not use instrumental variables here. The bias

is positive. The coefficient estimates are all negative, but only about 30% in absolute value

of the corresponding GMM-IV coefficient. As such, the pattern of the findings is similar to

the one found in the comparison of Tables 4 and 5. Since reverse causality would result in

a negative bias, the only explanation is that OLS suffers from the presence of unobserved

factors that move spreads and repurchases in the same direction. We analyze these omitted

variables further below.

For better comparison with the literature, columns (4) - (6) of Table 7 also reproduce the

conventional specification in the literature with contemporaneous volatility and contempora-

neous trading volume as controls. We have several concerns about this specification, but it

helps us to illuminate why some previous papers have found a negative relationship between

repurchases and liquidity, whereas our results are unequivocally positive.22 Especially con-

trolling for trading volume is problematic, because trading volume also measures liquidity

and is correlated with the liquidity measures we use as dependent variables.23 With these21Cf. Stoll (2000) and also Brockman and Chung (2001), and Ginglinger and Hamon (2007)22See Barclay and Smith (1988), Brockman and Chung (2001), and Ginglinger and Hamon (2007) for

studies that find a harmful effect of repurchases on liquidity.23Our specification differs from that in the literature in more than one dimension. Specifically, we lag

trading volume, use a definition of trading volume net of the volume from share repurchases, and scale be the

23

controls, the coefficient of interest is always positive. Spread, Price Impact and Amihud all

increase with repurchases in this specification and the relationship is significant for Spread

and Amihud.

This finding is significant, because it may explain the inconsistent results found in the

literature on the liquidity-repurchase relationship. We suggest from comparing Tables 6

and 7 that trading volume acts as a transmission channel, i.e., repurchases affect liquidity

mainly through their impact on trading volume. Similar arguments apply to contempora-

neous volatility (contemporaneous returns), which is negatively (positively) associated with

liquidity. If repurchases increase returns, and returns increase liquidity, then contemporane-

ous returns act as a transmission channel for repurchases. If we control for trading volume

or other transmission channels, we ultimately control for the effect we want to measure and

bias our results. The main qualitative difference between our results and those in some of

the prior literature therefore do not result from endogeneity, but from using inappropriate

controls.

Omitted variables. Endogeneity is still important for the quantitative difference between

the OLS results and the GMM-IV results. In the next step we return to the omitted variables

that move spreads and repurchases in the same direction. These variables are most likely

unobservable, and we can therefore not identify or measure them directly. However, as

indicated above, we expect that they are related to information in the market. In order

to narrow down the likely set of omitted variables we therefore analyze some additional

contemporaneous variables that should change with repurchases and liquidity if both are

driven by information.

In Table 8 we provide univariate statistics on several variables and compare them across

two scenarios. In the “Low-Low” scenario, Repurchase Intensity and Spread are both below

their medians; in the “High-High” scenario, both variables are above their medians. If spreads

number of shares outstanding. In untabulated results we show that using lags of trading volume as defined inTable 7 also leads to negative coefficient estimates. Hence, we focus on the question whether trading volumeis contemporaneous or lagged.

24

and repurchases are both driven by negative perceptions of the firm by some investors, then

we expect higher short interest and lower stock returns in the High-High scenario compared

to the Low-Low scenario. In Table 8, we compare one-month returns, abnormal returns,

return volatility, trading volume, and short interest between the “High-High” and “Low-

Low” scenarios.

Univariate comparisons of means and medians show that short interest and volatility are

both significantly higher, whereas stock returns and trading volume are both significantly

lower when repurchases and spreads are both above their sample medians, compared to

situations in which both are below their sample medians. Results for abnormal returns

are significant only for medians, but not for means. These results are consistent with the

hypothesis that during high repurchase - low liquidity months, some investors take a negative

view of the stock, short sell it, and move returns downward, while firms provide some price

support by repurchasing the stock. These results are only indicative, and we cannot use

any of the contemporaneous variables from Table 8 in our regressions, because they are all

simultaneously determined with the repurchase and liquidity measures.

4.3 The adverse-selection hypothesis

In this section we analyze whether the information content of share repurchases explains

how repurchases affect liquidity. The second part of the adverse-selection hypothesis (see

Section 2) implies that repurchases associated with a larger information content should also

be associated with stronger negative impact on stock-market liquidity.

We use two different methods to analyze the relationship between information and liq-

uidity and to test the adverse-selection hypothesis. The first is an event-study analysis of

disclosure-date returns, the second method is an investigation into how liquidity in the re-

purchase month depends on information as measured by subsequent cumulative abnormal

stock returns.

25

Event studies around the filing date. The first method we employ for testing the

adverse-selection hypothesis builds on the premise that the information content of repurchases

should be revealed in stock price changes at the disclosure date. If the market interprets

repurchases as signals about insiders’ information, then the disclosure of actual repurchases

in 10-Q and 10-K filings should cause stock price reactions. We assume that the filing date

is also the date around which the information about actual repurchases becomes public and

perform a standard event study. Cumulative abnormal returns (CARs) around the filing

date are calculated from a market model using daily data with an estimation window of 200

days and a minimum of 100 days of stock return data. Disclosure day returns are calculated

around the filing date in which the repurchase is published by the company. We calculate

the CAR from one day before to one day after the filing. Filings are quarterly and filing

dates are typically about six weeks after the end of the quarter. For example, a firm may

disclose share repurchases executed in January by mid-May, when it files the 10-Q statement

for the first quarter. We then associate the CAR for the three days around the filing date in

May with the average liquidity of the stock on all trading days in January. The dependent

variables are the liquidity measures in the repurchase month and the independent variables

include Repurchase Dummy, Filing CAR, the interaction of Repurchase Dummy with Filing

CAR, and the controls from Table 6.

Table 9 presents the results. The coefficient of interest is the interaction between Filing

CAR and Repurchase Dummy. Under the adverse-selection hypothesis, the coefficient on

the interaction should be positive: A higher value of Filing CAR shows that repurchases are

more informative, and they should then reduce liquidity, i.e., increase the spread. Under

the alternative hypothesis that informed firms use limit orders to exploit their information,

the coefficient on the interaction should be negative. The results in Table 9 contradict

the adverse-selection hypothesis: For all liquidity measures, a higher abnormal filing day

return is associated with more liquidity in the month of the actual repurchase. Hence, those

repurchases that tend to reveal more positive information to the market at the filing date

26

tend to be associated with higher liquidity. This result lends support to the alternative

hypothesis that firms provide liquidity rather than consume liquidity when they repurchase

shares based on private information.

Measuring cumulative abnormal returns after repurchase months. Our second

approach to testing the adverse-selection hypothesis is based on a standard procedure from

the insider trading literature and identifies the information content of repurchases by looking

at abnormal stock returns associated with repurchases after the repurchase month.24 The

insider trading literature uses abnormal announcement returns, typically beginning with the

disclosure of insider trades, whereas we include also the period before the filing, assuming that

information may become known to the market through other means, including repurchases

themselves. We use the market model with the CRSP equally-weighted index and estimate

the parameters based on 60 months of monthly data.

One difficulty is that we do not know at which point in the month a repurchase transaction

took place, hence CARs that include the repurchase month itself may measure price changes

before and after the repurchase. We exclude the repurchase month itself from the calculation

of CARs and therefore miss the abnormal stock returns between the repurchase transactions

and the last day of the repurchase month. Hence, we potentially underestimate the impact

of repurchases on CARs. This fact should at most create some noise in the CAR variable

and give rise to attenuation bias, i.e., the coefficients would be biased towards zero. Table

10 presents results for CARs measured over the six months subsequent to the repurchase

month.

We include CAR, Repurchase Dummy, and the interaction of CAR with Repurchase

Dummy. The coefficient on Repurchase Dummy has the same interpretation as before. The

coefficient on CAR reveals how market liquidity responds to abnormal stock returns inde-

pendently of whether these abnormal stock returns are related to repurchases or not. Our24E.g., see Lakonishok and Lee (2001) and Fidrmuc, Goergen, and Renneboog (2006). Babenko, Tserluke-

vich, and Vedrashko (2012) apply a similar method to repurchase announcements.

27

coefficient of interest is the one on the interaction term, which should be positive if firms

execute repurchases with a higher informational content with liquidity-consuming market or-

ders, and negative if firms provide more liquidity if the informational content of repurchases

is larger. The control variables are the same as in the previous regressions with the liquidity

measures as dependent variables. They are always included, but not displayed in the table.

Hence, the effect of repurchases that can be anticipated based on the control variables is

removed.

We observe that the coefficient on the interaction term Repurchase Dummy × CAR is

negative and the interaction is always significant at the 5%-level or better. Hence, for a

six-months horizon after the repurchase month, higher abnormal returns are significantly

associated with larger liquidity improvements during the repurchase month itself. This find-

ing contradicts the adverse-selection hypothesis, which predicts that repurchases with larger

information content reduce liquidity.

The coefficient on CAR itself is negative and significant at the 1%-level in all regressions.

Hence, even firms that do not undertake a repurchase in a particular month experience higher

CARs in subsequent months if the liquidity of their stock is higher today. Higher liquidity

therefore seems to predict higher abnormal stock returns in the subsequent six months and

the interaction term only reflects that this effect is stronger for repurchasing firms than for

non-repurchasing firms. A possible explanation may be that higher liquidity is associated

with traders with long-lived positive information placing limit orders. This effect is stronger

for repurchase months, but prevails also in non-repurchase months.

Conclusion. We conclude from the discussion in this section that the information content

of repurchases is not associated with a deterioration in liquidity, which could be attributed

to adverse selection. To the contrary, higher information content seems to be associated with

improvements and not with deteriorations in liquidity at the time repurchases were executed.

While theoretical models do not specify how the notions of “long-lived” information and

“short-lived” information should be operationalized, it seems fair to assume that the typical

28

three-months gap between repurchases and the subsequent filings as well as the six-months

period over which we calculate CARs count as longer periods. Under this interpretation, the

results support the predictions of the models of Harris (1998) and Kaniel and Liu (2006),

who see patient informed traders as suppliers of liquidity.

Unlike our previous analysis, the analysis in this section does not address concerns about

causality. Rather, our research strategy relies on the correlation between spreads and sub-

sequent abnormal returns. The adverse-selection hypothesis, which underlies much of the

literature, unequivocally implies that this correlation is positive, i.e., higher returns are re-

lated to lower liquidity. We reject this hypothesis by showing that the correlation is in fact

negative.

5 Discussion and Conclusion

In this paper we investigate both directions of the two-way relationship between share repur-

chases and stock market liquidity. We analyze how firms execute their active share repurchase

programs on a comprehensive sample of repurchases for the United States. We find that firms

adapt their repurchases to the liquidity of the market and avoid repurchases when the market

is illiquid, apparently in an attempt to reduce the costs from repurchasing shares. Similarly,

repurchases provide liquidity to the market, probably because firms mostly use limit orders

to buy back shares. Even though firms sometimes have privileged information, there is no

evidence that they withdraw liquidity from the market when they trade on their information.

To the contrary, repurchases based on more information improve liquidity.

Two methodological choices account for our results. First, we do not control for contem-

poraneous trading volume. Repurchases influence liquidity through their impact on trading

volume and we do not wish to control for this, because it is a transmission channel and

ultimately the effect we wish to measure. Second, OLS estimates seem to be severely biased,

and we attribute the bias to unobserved factors that move spreads as well as repurchases in

29

the same direction, leading to a positive bias of the coefficients of interest.

30

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A Appendix

A.1 Data collection

This appendix provides more detailed information on how we collected the information onshare repurchases and how we constructed the final sample.

Collection from filings. We collected and edited data on repurchase programs from theform 10-Q and 10-K filings. The difference between the total number of shares purchasedand the number of shares purchased under a program is important. The total number ofshares purchased includes, among other things:

• shares delivered back to the issuer for the payment of taxes resulting from the vestingof restricted stock units;

• shares delivered back to the issuer for the payment of taxes and the exercise price ofstock options exercised by employees and directors;

• the repurchase of unvested restricted stock units from employees whose employmentterminated before their shares vested.

In these cases the employee and not the company decides whether the company has topurchase shares while in a repurchase program the purchase decision is made by the company.Significantly, in transactions with employees the price can be different from the current stockmarket price, e.g., if companies use their own fundamental valuation instead of the marketprice when purchasing shares from their employees.25

Repurchases of unvested restricted stock units from employees whose employment termi-nated before their shares vested are typically executed at the nominal share value, which isoften just one cent. Therefore, repurchases of unvested restricted stock introduce a significantdownward bias of the average purchase price.26

In addition to the above mentioned more common repurchase activities outside of a pro-gram there are other, less common transactions, which also lead to repurchases outside ofactive repurchase programs. One example is the repurchase of shares that were issued as

25In October 2007 Morgan Stanley (CIK 895421) repurchased shares from employees at an average price of$66.34 while it purchased shares under the repurchase program at an average price of $63.32 (see form 10-Kfiled on January 29, 2008). In October 2008 the difference became even more pronounced, when shares fromemployees were purchased at $36.13, while shares under the repurchase program were purchased in the openmarket at $15.09.

26For example, in April 2006 Sun Microsystems Inc. (CIK 709519) purchased 188,675 shares at an averageprice of $0.09 although its stock price during that month was around $5.

35

acquisition currency when the target is later divested.27 Finally, some data corrections arenecessary if companies report transactions under a repurchase program that were repurchasedoutside the program, e.g., when shareholders held put options against the company.28. Insome cases, companies even report buybacks as repurchases under a program even though noprogram existed at the time.29 While misclassifications from put options, divestitures, andsimilar transactions are rare, the misclassification of repurchases from employees as repur-chases under a program is more common.

It is generally not possible to determine the transaction price of the shares purchasedunder a program when the total number of shares purchased differs from the number of sharepurchased under a program. Companies then provide the average purchase price, whichcorresponds to the total number of shares purchased, and therefore includes purchases outsidethe program that were conducted at different prices. We therefore correct for these errors bymanually checking the footnotes and remarks in the filings and setting the repurchases undera repurchase program to zero whenever such a misclassification took place.

Furthermore, we manually adjusted the number of shares and the purchase price for stocksplits and stock dividends when necessary. Usually, companies report the repurchase dataduring the period covered by the filing on a post stock split basis even if the stock split tookplace not before the second or the third month of the quarter. For example, if a companyrepurchases 100 shares at $10.00 in January and conducts a 2:1 stock split in February, thenthe company will report this transaction in its filings for the period from January to Marchas 200 shares purchase at $5.00. This means that the repurchases in the first and in thesecond month of a quarter can be reported post-split although they can take place pre-split.We always adjusted the repurchase data to match the stock market data from CRSP.

Details on sample selection. From our computerized download, we obtain 96,203 10-Qsand 34,589 10-Ks and extract the repurchase data from these filings. This procedure leavesus with 376,843 firm-month observations. Among these are more than 20,000 firm-months

27One example is The Interpublic Group of Companies Inc. (CIK 51644), which recorded a repurchaseof 15,325 shares in February 2010. The company writes in its 10-K that these shares consist “(...) of ourcommon stock that we received as consideration for the sale of our interest in a company that we previouslyhad acquired (the “Acquisition Shares”).”

28In the Form 10-Q filing for the period from April to June 2006 Refac Optical Group (CIK 82788) reportsrepurchases under a program when shareholders exercised their right to sell their shares to the company ata predetermined price pursuant to a merger agreement.

29Unit Corp (CIK 798949) records in its 10-Q filing for April to June 2008 all shares as purchased undera program although they were all related to the payment of taxes and to the payment of the exercise priceof stock options and Unit Corp did not have any repurchase program at this time.Versata Inc. (CIK 1034397) reports in its 10-Q filing for February to April 2005 purchases from sharehold-

ers, who received the right to sell their shares back to the company at a premium in a security class action,as repurchases under the program. At this time Versata Inc. did not have a repurchase program.

36

with missing CRSP data if the firms are no longer or not yet listed on AMEX, NASDAQ, orNYSE at the time of the repurchase.

From the 9,100 repurchase programs, we drop 167 programs with unknown announcementdate, 1,587 programs, which were started before 2004, and a further 50, which were announcedafter 2010. Furthermore, 144 programs are excluded, because they are not executed in theopen-market (e.g., as private transactions or tender offers). About 3% of the programs inour sample have an unlimited or variable volume. We exclude these because the programsize is one of our instruments and needs to be determined.

From CRSP we obtain closing prices, the number of shares outstanding, the number ofshares traded, and daily and monthly stock returns. From Compustat we obtain data ontotal assets, book value of equity, book value of debt, operating income before depreciation,and S&P 500 membership. Data on analyst coverage is from I/B/E/S. All liquidity measuresare obtained from TAQ and explained below. We eliminate all observations from the finalsample for which the variables used in the baseline analysis are not available; these variablesare listed in Table 2.

A.2 Liquidity measures30

For all high frequency measures, we use the NYSE TAQ database to extract the necessaryintraday transaction data. For each trade we assign the prevailing bid and ask quotes thatare valid at least one second before the trade took place. If there is more than one transactionin a given second, the same bid and ask quotes will be matched to all of these transactions.If there is more than one bid and ask quote in a given second, we assume that the last quotein the respective second is the prevailing quote.31

For measures that are not based on transactions we use the NBBO (National Best Bidand Offer) quotes. The NBBO offer size is computed by aggregating all offer sizes at the bestbid and best offer (=ask) over all U.S. exchanges (see WRDS website).32

The final data set contains the following items for each transaction:

1. Date and time stamp (up to seconds)

2. Transaction price (Pt)

3. Transaction volume in shares (wt)30The description of the calculation procedures for the liquidity measures overlaps partially with the one

in Lebedeva (2012).31Henker and Wang (2006) consider this procedure to be more appropriate compared to the classical Lee

and Ready (1991) five-second rule. Bessembinder (2003) tries zero to thirty-second delays in increments offive seconds and does not find any differences in the results.

32http://wrds-web.wharton.upenn.edu/wrds/research/applications/microstructure/NBBO%20derivation/

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4. Prevailing bid quote (Bt)

5. Prevailing ask quote (At)

We calculate the quote midpoint price (Qt) as the average of the prevailing bid and ask quotes(Qt = At+Bt

2 ). We further use the algorithm of Lee and Ready (1991) to classify trades intobuys and sells. We define trades with a transaction price above the quote midpoint (Pt > Qt)as buys and those with a transaction price below the quote midpoint (Pt < Qt) as sells. Ifa transaction price is equal to its quote midpoint, we compare the current transaction pricewith the previous transaction price. If Pt < Pt−1, we consider a trade to be seller-initiated;if Pt > Pt−1, we consider it to be buyer-initiated. Should the two prices be equal, we leavethe trade unclassified.

Spread

We calculate the relative spread for each transaction as RelativeSpreadt = At−Bt

Qt.We further

aggregate the relative spreads of all transactions within a day for a particular stock. Spreadrepresents the daily average of all NBBO spreads for a given stock weighted by the time thequote is valid.

Price Impact

We follow the approach of Riordan and Storkenmaier (2011) and define the price impact ofeach trade after 5 minutes as PrcImpt = 2 |Qt+5 −Qt| /Qt,where Qt+5 represents the quotemidpoint price of the stock after five minutes (300 seconds). In the analysis we use the dailyaverage of this measure for all stocks.

Amihud

The Amihud illiquidity measure is calculated by dividing the absolute daily return by tradingvolume denoted in dollars:

Amihudt = |rt|Pt � V olt

,

where

1. rt represents the daily holding period return,

2. Pt represents the daily closing transaction price,

3. V olt represents the daily transaction volume.

Data for these calculations are from CRSP.

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Tables

Table 1: Description of Variables. The table describes all control variables and somerepurchase variables. For each variable the table reports the definition, the data source, andthe unit of measurement. Variables denoted with (ln) are expressed as natural logarithms.

Name Definition Source UnitAcquiror 1 if firm is currently (time between announcement SDC binary

and end of the offer) bidding for another companyAmihud Monthly average of daily Amihud illiquidity ratio CRSP ratioAnalysts Number of analysts (ln) IBES UnitAccelerated Share Repurchase via accelerated share repurchase SEC binaryRepurchaseAverage Spread Average of Spread from t-6 to t-1 TAQ UnitBook to Market Book value equity / market cap, winsorized at 1% Comp. ratioBook Value Equity Common equity (Compustat item: ceqq) Comp. millionCAR (6 months) Cumulative abnormal return over six months following CRSP unit

repurchase monthConvertible Issue 1 if convertible issue takes place in respective SDC binary

monthDeviation from $30 Absolute difference between Price and $30 (ln) CRSP unit

before start of the repurchase program plus 1 (ln)EBITDA Operating income before depreciation (Compustat Comp. million

item: oibdpq)Exogenous Median Trading Volume in current month of all CRSP unitTrading Volume firms with no repurchase activity between 2004

and 2010 (ln)Filing Car Cumulative abnormal return over three days around the CRSP unit

day of the filing of the quarterly reportLeverage (Total asset - book value equity) / Comp. ratio

(total asset - book value equity + market cap) /CRSPMarket Cap Monthly average of daily market capitalization (ln) CRSP millionOptions Exercised Number of shares obtained by option exercises of TR ratio

coporate insiders in the respective month divided Insiderby shares outstanding Data

Price Monthly average of daily closing price (ln) CRSP unitPrice Impact Monthly average of intraday price impact, TAQ ratio

transaction based (ln)Private Repurchase Repurchase via private transaction SEC binaryProgram Month Difference between current month and month SEC unitProgram Size Size of the repurchase program scaled by shares SEC ratio(scaled) oustanding as of the beginning of the programRepurchase Volume Number of shares repurchased during the month SEC millionRepurchase Dummy 1 if repurchase transaction takes place SEC binary

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Table 1: Description of Variables. (continued)

Name Definition Source UnitRepurchase Intensity Number of shares repurchased during the month SEC ratio

divided by the number of shares outstanding at the /CRSPlast trading day of the previous month

Repurchase Intensity Number of shares repurchased during the month SEC ratio(TV) divided by the number of shares traded over the /CRSP

current monthReturn Monthly stock returnS&P 500 1 if firm is in the S&P 500 CRSP binarySEO 1 if SEO takes place in respective month SDC binaryShares Outstanding Number of shares outstanding at last trading CRSP million

day of monthShort Interest Shares sold short scaled by shares outstanding CRSP ratioSpread Monthly average of intraday relative spread, TAQ ratio

time-weighted (ln)Target 1 if firm is currently (time between announcement SDC binary

and end of the offer) a target of another companyTender Offer Repurchase via tender offer or Dutch auction SEC binaryTotal Assets Total assets (Compustat item: atq) (ln) Comp. millionTrading Volume Monthly total dollar trading volume (ln) CRSP millionTrading Volume (number of shares traded - number of shares CRSP ratio(scaled) repurchased)/number of shares outstanding /SECVolatility Standard deviation of daily returns over one CRSP unit

month (ln)

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Table 2: Descriptive Statistics - Active Programs. This table provides descriptivestatistics for the months with active repurchase programs. Appendix A.2 provides definitionsof the liquidity measures. The repurchase variables and the control variables are defined inTable 1. Filing CAR is the cumulative abnormal return of the respective stock from t=-1 tot=+1 relative to the filing day of the 10-Q or 10-K report. We report the arithmetic mean,the median, the standard deviation (S.D.), the 1st percentile, and the 99th percentile of thedistribution for each variable. None of the variables is expressed in natural logarithms unlessotherwise stated.

Mean Median S.D. 1st

Perc.99th

Perc.N

Liquidity measuresSpread 0.71% 0.14% 1.75% 0.02% 9.18% 106,898Price Impact 1.88% 0.73% 3.50% 0.18% 17.03% 106,898Amihud 3.60 0.00 95.94 0.00 40.85 106,898Repurchase measuresRepurchase Volume (million) 49.4 4.6 180.8 0.0 768.5 50,204Repurchase Intensity 0.66% 0.35% 0.98% 0.00% 4.51% 50,204Repurchase Intensity (TV) 6.74% 3.29% 9.91% 0.00% 52.13% 50,204Control variables & instrumentsAnalysts 7.66 6.00 7.11 0.00 29.00 106,898Accelerated Share Repurchase 0.01 0.00 0.25 0.00 0.00 106,898Book to Market 0.68 0.54 0.59 -0.10 3.50 106,898Deviation from $30 18.26 15.59 34.75 0.33 74.70 106,898Exog. Trading Volume 16.61 16.55 6.27 3.73 33.78 106,898Leverage 0.45 0.39 0.29 0.03 0.98 106,898Market Cap (million) 6,070 807 21,145 12 106,899 106,898Options Exercised 0.07% 0.00% 0.24% 0.00% 1.43% 106,898Price 27.57 21.41 39.18 0.86 104.70 106,898Private Repurchase 0.00 0.00 0.07 0.00 0.00 106,898S&P 500 0.21 0.00 0.41 0.00 1.00 106,898Tender Offer 0.00 0.00 0.12 0.00 0.00 106,898Total Assets (million) 14,447 1,171 96,099 21 220,005 106,898Trading Volume (million) 1,094 145 3,282 0 15,038 106,898Trading Volume (scaled) 19.04% 13.53% 23.30% 0.32% 98.06% 106,898Volatility 0.03 0.02 0.02 0.01 0.11 106,898Program descriptivesProgram Size (scaled) 6.59% 5.27% 4.86% 0.47% 25.11% 6,537Duration 16 12 14 1 67 6,537

41

Table 3: Panel A: Program Initiations. Panel A presents linear probability models,in which the dependent variable is Program Initiation, a dummy variable which equals onein a month when a firm begins a new program, and zero otherwise. Average Spread is theprevious six-months average of Spread. All specifications include year fixed effects. Spec-ifications (4) to (6) also include firm fixed effects, whereas specifications (1) to (3) do notincluded firm fixed effects. We successively restrict the sample from including all observations(specifications (1) and (4)), only firm-months with no active program in the previous month((2) and (5)), and no active program in the previous six months ((3) and (6)). In Panel B,the dependent variable is Program Size and has the same specifications as Panel A.

Dependent Variable: Program Initiation(1) (2) (3) (4) (5) (6)

Selection criteria: All excl. Follow- excl. Follow- All excl. Follow- excl. Follow-ups ups within ups ups within

6 months 6 monthsAverage Spreadt 0.0035∗∗∗ 0.0003 0.0001 –0.0036∗∗ –0.0017∗∗ –0.0021∗∗

(5.19) (0.72) (0.15) (–2.21) (–2.07) (–2.56)Returnt−1 –0.021∗∗∗ –0.012∗∗∗ –0.011∗∗∗ –0.013∗∗∗ –0.010∗∗∗ –0.009∗∗∗

(–12.70) (–10.76) (–10.13) (–8.92) (–9.15) (–8.64)Returnt−2 –0.009∗∗∗ –0.006∗∗∗ –0.006∗∗∗ –0.006∗∗∗ –0.006∗∗∗ –0.006∗∗∗

(–6.18) (–6.09) (–6.16) (–4.76) (–5.89) (–5.70)Returnt−3 –0.012∗∗∗ –0.006∗∗∗ –0.006∗∗∗ –0.009∗∗∗ –0.006∗∗∗ –0.006∗∗∗

(–8.41) (–6.37) (–5.99) (–7.28) (–6.83) (–6.16)Returnt−4 –0.011∗∗∗ –0.004∗∗∗ –0.003∗∗∗ –0.008∗∗∗ –0.004∗∗∗ –0.004∗∗∗

(–7.01) (–3.61) (–2.97) (–5.43) (–3.83) (–3.72)Returnt−5 –0.007∗∗∗ –0.002∗∗ –0.002∗∗ –0.005∗∗∗ –0.003∗∗∗ –0.003∗∗∗

(–4.50) (–2.27) (–1.97) (–4.30) (–2.84) (–3.11)Returnt−6 –0.004∗∗ –0.001 –0.001 –0.004∗∗∗ –0.002∗ –0.002∗∗

(–2.40) (–1.02) (–0.86) (–2.99) (–1.83) (–2.13)Total Assetst−3 0.017∗∗∗ 0.004∗∗∗ 0.003∗∗∗ 0.006∗∗∗ 0.004∗∗∗ 0.004∗∗∗

(27.25) (11.14) (9.22) (2.60) (3.88) (3.99)Cash to Assetst−3 0.003 0.007∗∗∗ 0.007∗∗∗ 0.006 0.013∗∗∗ 0.015∗∗∗

(1.27) (4.83) (5.02) (0.98) (4.00) (4.45)EBITDA to Assetst−3 0.090∗∗∗ 0.048∗∗∗ 0.044∗∗∗ 0.033∗∗∗ 0.013∗ 0.011

(12.98) (10.97) (10.11) (2.86) (1.86) (1.51)Dividends to Assetst−3 0.253∗∗∗ 0.021 0.010 –0.031 –0.044 –0.068∗∗

(8.79) (1.26) (0.67) (–0.55) (–1.35) (–2.13)Leveraget−3 –0.052∗∗∗ –0.012∗∗∗ –0.009∗∗∗ –0.028∗∗∗ –0.014∗∗∗ –0.010∗∗∗

(–17.30) (–6.39) (–5.14) (–4.10) (–4.07) (–3.05)Book to Markett−3 –0.003∗∗∗ –0.000 0.000 –0.004∗∗ 0.000 0.000

(–6.80) (–0.09) (0.87) (–2.54) (0.75) (0.72)

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Table 3: Panel A: Program Initiations (continued).

Dependent Variable: Program Initiation(1) (2) (3) (4) (5) (6)

Acquirort –0.0140∗∗∗ –0.0065∗∗∗ –0.0056∗∗∗ –0.0089∗∗∗ –0.0065∗∗∗ –0.0057∗∗∗

(–7.60) (–6.33) (–5.63) (–5.28) (–5.81) (–5.19)Targett –0.0310∗∗∗ –0.0096∗∗∗ –0.0073∗∗∗ –0.0127∗∗∗ –0.0058∗∗∗ –0.0040∗∗

(–10.18) (–4.57) (–3.10) (–4.70) (–2.82) (–2.02)Constant –0.0596∗∗∗ –0.0181∗∗∗ –0.0156∗∗∗ –0.0305∗∗∗ –0.0244∗∗∗ –0.0270∗∗∗

(–23.04) (–11.98) (–10.68) (–2.78) (–4.41) (–5.02)R2 0.029 0.007 0.006 0.012 0.005 0.005Observations 168,539 163,390 150,249 168,539 163,390 150,249Firm FE No No No Yes Yes YesTime FE Year Year Year Year Year YearNumber of initiations 6,918 2,413 1,829 6,918 2,413 1,829

Table 3: Panel B: Program Size.

Dependent Variable: Program Size(1) (2) (3) (4) (5) (6)

Selection criteria: All excl. Follow- excl. Follow- All excl. Follow- excl. Follow-ups ups within ups ups within

6 months 6 monthsAverage Spreadt –0.0001∗∗∗ –0.0001∗∗∗ –0.0001∗∗∗ –0.0005∗∗∗ –0.0002∗∗∗ –0.0002∗∗∗

(–2.64) (–4.11) (–3.61) (–3.95) (–3.10) (–3.11)R2 0.020 0.005 0.004 0.010 0.004 0.004Observations 168,268 163,331 150,203 168,268 163,331 150,203Firm FE No No No Yes Yes YesTime FE Year Year Year Year Year YearNumber of initiations 6,918 2,413 1,829 6,918 2,413 1,829

43

Table 4: The Influence of Liquidity on Repurchases - GMM. The table presentsGMM-regressions of Repurchase Intensity on three different liquidity measures as specifiedin the table heading and control variables. All variable definitions can be found in AppendixA.2 and Table 1. Columns (1) - (3) use Exogenous Trading Volume and Deviation from$30 as instruments for liquidity and control for year fixed effects. Columns (4) - (6) uselagged Trading Volume and Deviation from $30 as instruments for liquidity and control foryear month effects. The sample is restricted to the first 12 months of a repurchase program.Monthly returns are from CRSP. Standard errors are clustered at the firm level. t-statisticsare provided in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% levelrespectively. The Hansen-J statistic tests for the validity of the overidentifying restrictions.The Kleibergen-Paap test is for underidentification and tests for the full rank of the reduced-form coefficient matrix following Kleibergen and Paap (2006). The table reports the teststatistics and the p-values for both tests. The t-tests for the instruments are from the first-stage regressions. The test suggested by Stock and Yogo (2005) rejects the hypothesis thatthe bias exceeds the OLS bias by more than 5% in all cases.

44

Dependent Variable: Repurchase Intensity(1) (2) (3) (4) (5) (6)

Liquidity measure: Spread Price Amihud Spread Price AmihudImpact Impact

Liquidityt –0.0028∗∗∗ –0.0037∗∗∗ –0.0013∗∗∗ –0.0028∗∗∗ –0.0063∗∗∗ –0.0011∗∗∗

(–3.44) (–3.66) (–3.89) (–7.29) (–5.77) (–7.58)Repurchase Intensityt−1 0.1189∗∗∗ 0.1180∗∗∗ 0.1220∗∗∗ 0.1264∗∗∗ 0.1217∗∗∗ 0.1291∗∗∗

(10.56) (10.41) (11.05) (11.12) (10.29) (11.49)Returnt−1 –0.0063∗∗∗ –0.0066∗∗∗ –0.0066∗∗∗ –0.0054∗∗∗ –0.0061∗∗∗ –0.0055∗∗∗

(–10.62) (–10.36) (–10.74) (–11.13) (–10.55) (–11.20)Returnt−2 –0.0037∗∗∗ –0.0034∗∗∗ –0.0040∗∗∗ –0.0040∗∗∗ –0.0046∗∗∗ –0.0041∗∗∗

(–7.58) (–8.13) (–7.71) (–10.32) (–9.67) (–10.49)Returnt−3 –0.0010∗∗∗ –0.0007∗∗ –0.0012∗∗∗ –0.0012∗∗∗ –0.0013∗∗∗ –0.0013∗∗∗

(–3.09) (–2.38) (–3.54) (–3.71) (–3.75) (–4.09)Total Assetst−3 0.0005 0.0009∗ 0.0001 0.0004 0.0001 0.0004

(0.87) (1.84) (0.23) (0.97) (0.16) (1.03)Cash to Assetst−3 0.0034∗∗∗ 0.0032∗∗∗ 0.0035∗∗∗ 0.0035∗∗∗ 0.0029∗∗∗ 0.0036∗∗∗

(3.82) (3.51) (4.03) (3.92) (2.92) (4.15)EBITDA to Assetst−3 –0.0049∗∗ –0.0026 –0.0056∗∗ –0.0045∗∗ –0.0014 –0.0047∗∗

(–2.21) (–1.12) (–2.57) (–2.12) (–0.56) (–2.27)Dividends to Assetst−3 0.0035 0.0039 0.0042 0.0018 0.0019 0.0027

(0.76) (0.82) (0.94) (0.40) (0.36) (0.62)Leveraget−3 –0.0054∗∗∗ –0.0060∗∗∗ –0.0045∗∗∗ –0.0052∗∗∗ –0.0040∗∗∗ –0.0051∗∗∗

(–3.89) (–4.57) (–3.09) (–4.68) (–2.86) (–4.59)Options Exercisedt 0.0457∗∗ 0.0534∗∗∗ 0.0422∗∗ 0.0422∗∗ 0.0508∗∗∗ 0.0407∗∗

(2.52) (2.92) (2.31) (2.38) (2.74) (2.30)Book to markett−3 0.0021∗∗∗ 0.0021∗∗∗ 0.0021∗∗∗ 0.0021∗∗∗ 0.0029∗∗∗ 0.0019∗∗∗

(4.73) (4.92) (5.12) (6.68) (6.22) (6.51)Acquiror Dummyt –0.0003∗∗ –0.0004∗∗∗ –0.0003∗∗ –0.0003∗ –0.0005∗∗∗ –0.0003∗∗

(–2.09) (–2.92) (–2.21) (–1.91) (–3.40) (–1.99)Target Dummyt –0.0005 –0.0002 –0.0005 –0.0004 –0.0002 –0.0004

(–0.72) (–0.32) (–0.78) (–0.70) (–0.23) (–0.71)Program Montht –0.0016∗∗∗ –0.0017∗∗∗ –0.0016∗∗∗ –0.0015∗∗∗ –0.0015∗∗∗ –0.0015∗∗∗

(–20.08) (–20.06) (–20.11) (–19.24) (–17.51) (–19.49)Program Sizet 0.0153∗∗∗ 0.0147∗∗∗ 0.0160∗∗∗ 0.0146∗∗∗ 0.0127∗∗∗ 0.0155∗∗∗

(7.40) (6.94) (7.92) (7.20) (5.48) (7.76)R2 (adjusted) 0.0152 - 0.0363 0.0212 0.0376 - 0.1084 0.0426Observations 51,652 51,477 51,704 51,652 51,477 51,704Macro Variables Yes Yes Yes No No NoFirm FE Yes Yes Yes Yes Yes YesTime FE Year Year Year Month Month MonthHansen’s J (test) 1.1 0.1 0.0 0.6 0.5 0.1Hansen’s J (p-value) 28.57% 76.13% 88.89% 45.24% 47.21% 70.37%Kleibergen-Paap (test) 224.0 149.0 362.7 368.3 69.7 436.9Kleibergen-Paap (p-value) 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%First stage t-statistics of included instrumentsExogenous Trading Volume -15.32 -29.60 -21.63Lagged Trading Volume -12.74 -8.40 -45.5Deviation from $30 6.77 6.52 3.57 2.11 1.87 3.0645

Table 5: The Influence of Liquidity On Repurchases - OLS. The table presentsOLS-regressions of Repurchase Intensity on the liquidity measures as indicated and controlvariables. We include the same controls as in Table 4. Monthly returns are from CRSP.Appendix A.2 provides definitions of the liquidity measures. The repurchase variables andthe control variables are defined in Table 1. Standard errors are clustered at the firm level.t-statistics are provided in parentheses. *, **, *** indicate significance at the 10%, 5% and1% level respectively.

Dependent Variable: Repurchase Intensity(1) (2) (3)

Liquidity measure: Spread Price AmihudImpact

Liquidityt –0.0015∗∗∗ –0.0004∗∗∗ –0.0009∗∗∗

(–13.08) (–5.65) (–15.09)R2 0.0828 0.0796 0.0848Observations 51,683 51,508 51,735Firm FE Yes Yes YesTime FE Month Month Month

Table 6: The Influence of Repurchases on Liquidity - GMM. The table presentsGMM-regressions of liquidity on Repurchase Intensity and control variables. As instrumentsfor Repurchase Intensity we use Program Size and Program Month. The sample is restrictedto the first 12 months of a repurchase program. Monthly returns are from CRSP. AppendixA.2 provides definitions of the liquidity measures. The repurchase variables and the controlvariables are defined in Table 1. Standard errors are clustered at the firm level. t-statisticsare provided in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% levelrespectively. The Hansen-J statistic tests for the validity of the overidentifying restrictions.The Kleibergen-Paap test is for underidentification and tests for the full rank of the reduced-form coefficient matrix following Kleibergen and Paap (2006). The table reports the teststatistics and the p-values for both tests. The t-tests for the instruments are from the first-stage regressions. The test suggested by Stock and Yogo (2005) rejects the hypothesis thatthe bias exceeds the OLS bias by more than 5% in all cases.

46

(1) (2) (3)Spread Price Amihud

ImpactRepurchase Intensityt –7.4870∗∗∗ –3.4352∗∗ –17.1465∗∗∗

(–7.85) (–2.42) (–7.32)Returnt−1 –0.1155∗∗∗ –0.0965∗∗∗ –0.3371∗∗∗

(–9.44) (–5.79) (–9.76)Volatilityt−1 0.0187∗∗∗ –0.0009 –0.0413∗∗

(4.12) (–0.13) (–2.47)Trading Volumet−1 (scaled) –0.0800∗∗∗ –0.1125∗∗∗ –0.4403∗∗∗

(–4.26) (–4.44) (–4.95)Total Assetst –0.0900∗∗∗ –0.0327∗∗ –0.4403∗∗∗

(–8.13) (–2.03) (–11.87)S&P 500t –0.0749∗∗∗ –0.0730∗∗ –0.1391∗∗∗

(–3.87) (–2.03) (–3.17)Deviation from 30t 0.0160∗∗∗ 0.0068∗∗ 0.0204∗∗∗

(8.31) (2.18) (4.89)Pricet –0.1691∗∗∗ –0.1130∗∗∗ –0.6889∗∗∗

(–18.13) (–8.40) (–20.55)Analystst –0.0254∗∗∗ –0.0309∗∗∗ –0.0860∗∗∗

(–4.18) (–3.19) (–4.62)Book to markett−3 0.0496∗∗∗ 0.0605∗∗∗ 0.2074∗∗∗

(5.65) (4.91) (7.00)Leveraget−3 –0.0476 –0.0347 0.2817∗∗

(–1.32) (–0.65) (2.49)Accelerated share repurchaset –0.0091∗∗∗ –0.0079∗ –0.0224∗∗∗

(–2.99) (–1.76) (–4.82)Private repurchaset –0.0052 –0.0041 –0.0201

(–0.70) (–0.33) (–0.97)Tender offert –0.0068 –0.0162∗ –0.0589∗∗∗

(–0.99) (–1.90) (–5.30)Time-weighted spreadt−1 0.6520∗∗∗

(95.05)Price impactt−1 0.5900∗∗∗

(52.18)Amihudt−1 0.3809∗∗∗

(23.74)R2 0.6392 0.5161 0.5253Observations 59558 59255 59611Firm FE Yes Yes YesTime FE Month Month MonthHansen’s J (test) 0.9 2.1 0.2Hansen’s J (p-value) 28.57% 76.13% 88.89%Kleibergen-Paap (test) 405.0 407.2 404.3Kleibergen-Paap (p-value) 0.00% 0.00% 0.00%First stage t-statistics of included instrumentsProgram Month (ln) -23.01 -23.10 -23.00Program Size 7.15 7.21 7.24

47

Table 7: The Influence of Repurchases on Liquidity - alternative OLS specifica-tions. The table presents OLS-regressions of liquidity on Repurchase Intensity and controlvariables. In columns (1) to (3), we include the same controls as in Table 6. The sample isrestricted to the first 12 months of a repurchase program. Monthly returns are from CRSP.Appendix A.2 provides definitions of the liquidity measures. The repurchase variables andthe control variables are defined in Table 1. Standard errors are clustered at the firm level.t-statistics are provided in parentheses. *, **, *** indicate significance at the 10%, 5% and1% level respectively.

(1) (2) (3) (4) (5) (6)Spread Price Amihud Spread Price Amihud

Impact ImpactRepurchase Intensityt –2.4729∗∗∗ –1.5341∗∗∗ –6.0022∗∗∗ 0.5008∗∗ 0.3218 3.3895∗∗∗

(–16.43) (–7.80) (–17.25) (2.06) (1.12) (10.28)Returnst−1 –0.0995∗∗∗ –0.0859∗∗∗ –0.2966∗∗∗

(–8.68) (–5.46) (–8.99)Volatilityt−1 0.0166∗∗∗ 0.0019 –0.0560∗∗∗

(3.77) (0.27) (–3.37)Volatilityt 0.3826∗∗∗ 0.5957∗∗∗ 0.9228∗∗∗

(107.02) (122.43) (199.07)Trading Volumet−1 (scaled) –0.0889∗∗∗ –0.1195∗∗∗ –0.4441∗∗∗

(–4.38) (–4.56) (–4.99)Trading volumet (ln) –0.4852∗∗∗ –0.2512∗∗∗ –1.1343∗∗∗

(–477.21) (–174.68) (–711.40)Pricet –0.1610∗∗∗ –0.1125∗∗∗ –0.6688∗∗∗ 0.0767∗∗∗ 0.0370∗∗∗ 0.0419∗∗∗

(–18.35) (–8.51) (–20.47) (23.95) (8.77) (11.45)R2 0.6709 0.5386 0.5643 0.9154 0.6434 0.9758Observations 62,238 61,904 62,293 62,872 62,654 62,928Firm FE Yes Yes Yes No No NoTime FE Month Month Month No No No

48

Table 8: Comovement of Repurchases and Liquidity. In this table, we form twogroups according to whether an observation is above median Repurchase Intensity and abovethe median of Spread, (High - High) or below both median Repurchase Intensity and medianSpread (Low - Low). Differences in means are tested using a standard two-tailed t-test.Differences in medians are tested using the Wilcoxon-Mann-Whitney test (two-tailed). *, **,*** indicate significance at the 10%, 5% and 1% level respectively.

Panel A. Comparison of MeansLow - Low High - High

N Mean N Mean Difference t-statShort Interest 11,568 3.89% 11,577 4.74% -0.85%*** -13.5Return 11,582 1.03% 11,576 -0.75% 1.77%*** 12.5Abnormal Return 11,233 -0.34% 10,023 -0.50% 0.16% 1.1Volatility 11,582 1.78% 11,580 2.81% -1.03%*** -48.1Trading Volume 11,582 3,196 11,580 120 3,076 *** 57.1

Panel B. Comparison of MediansLow - Low High - High

N Median N Median Difference ranksumShort Interest 13,719 2.43% 13,692 3.09% -0.66%** -2.3Return 13,715 1.08% 13,712 0.19% 0.89%*** 14.8Abnormal Return 12,246 -0.32% 13,115 -0.67% 0.35%*** 3.0Volatility 13,745 1.50% 13,712 1.58% -0.08%*** -53.4Trading Volume 13,745 1,221 13,712 1,094 127*** 120.7

49

Table 9: Measuring Information Using Filing-day Returns. The table presentsregressions of the liquidity measures on Repurchase Dummy, cumulative abnormal filing datereturns, their interaction, and controls. We include the same controls as in Table 6. AppendixA.2 provides definitions of the liquidity variables. Filing CAR is the cumulative abnormalreturn (CAR) of the respective stock from t=-1 to t=+1 relative to the filing day of the 10-Qor 10-K report. The CARs are subsequently matched to the months covered by the report.CARs are computed with the market model using the CRSP equally weighted index. Theestimation window ends 31 days prior to the event day. The estimation length is 200 dayswith a minimum of 100 days being required. All control variables are defined in Table 1.

(1) (2) (3)Spread Price Impact Amihud

Repurchase Dummyt –0.005∗∗ –0.006∗∗ 0.003(–2.57) (–2.00) (0.74)

Filing CAR 0.011∗ –0.007 0.074∗∗∗

(1.74) (–0.88) (4.59)Repurchase Dummyt –0.075∗∗∗ –0.065∗ –0.171∗∗∗

x Filing CAR (–3.24) (–1.95) (–2.82)R2 0.768 0.597 0.734Observations 334,143 332,371 334,392Firm FE Yes Yes YesYear FE Yes Yes Yes

50

Table 10: Measuring Information Using Abnormal Returns. The table presentsregressions of the liquidity measures on Repurchase Dummy, cumulative abnormal returns,their interaction, and control variables. We include the same controls as in Table 6. AppendixA.2 provides definitions of the liquidity variables. The repurchase variables and the controlvariables are defined in Table 1. CARs are computed with the market model using the CRSPequally weighted index. The estimation window ends 6 months prior to the event month. Theestimation length is 60 months with a minimum of 36 months. Standard errors are clusteredat the firm level. t-statistics are provided in parentheses. *, **, *** indicate significance atthe 10%, 5% and 1% level respectively.

(1) (2) (3)Spread Price Impact Amihud

Repurchase Dummyt –0.004∗ –0.006∗∗ 0.011∗∗

(–1.75) (–2.04) (2.41)CAR (6 months) –0.016∗∗∗ –0.023∗∗∗ –0.040∗∗∗

(–8.71) (–10.11) (–7.89)Repurchase Dummyt –0.013∗∗ –0.043∗∗∗ –0.050∗∗∗

x CAR (6 months) (–2.22) (–5.83) (–3.97)R2 0.762 0.598 0.732Observations 291,965 290,360 292,145Firm FE Yes Yes YesYear FE Yes Yes Yes

51

Internet Appendix for “Stock Repurchases and

Liquidity”

September 15, 2014

This Internet Appendix provides additional analyses and results that were omitted from our

paper “Stock Repurchases and Liquidity”. The discussion can be found in the main text of

the paper and the tables in the Internet Appendix are referred to as A-#, where # is the

table number in the appendix.

Tables

Table 1: Breakdown of Sample. The table provides a breakdown of the sample byyear. The columns display the total number of firms in the sample, the number of firmsthat repurchase shares in that particular year, the number of firm-months covered, and thenumber of months in which repurchases took place.

Firms Repurchasing Firms Firm Months Repurchase Months2004 4,558 1,233 51,287 6,2832005 4,578 1,424 51,271 7,7472006 4,547 1,508 51,102 8,2832007 4,571 1,690 50,414 9,1712008 4,488 1,766 50,427 8,4992009 4,212 974 47,178 4,5802010 4,040 1,084 45,299 5,641Total 6,150 2,930 346,978 50,204

A-1

Table 2: Descriptive Statistics - Total Sample. Panel A provides descriptive statisticsfor the repurchase variables used in the baseline specification, for the liquidity measures, andfor the control variables for the total sample. Appendix A.2 of our paper provides definitionsof the liquidity measures. The repurchase variables and the control variables are defined inTable 1 of our paper. Filing CAR is the cumulative abnormal return of the respective stockfrom t=-1 to t=+1 relative to the filing day of the 10-Q or 10-K report. We report thearithmetic mean, the median, the standard deviation (S.D.), the 1st percentile, and the 99thpercentile of the distribution for each variable. None of the variables is expressed in naturallogarithms unless otherwise stated.

Mean Median S.D. 1st

Perc.99th

Perc.N

Liquidity measuresSpread 1.05% 0.27% 2.09% 0.02% 10.71% 346,978Price Impact 2.30% 1.03% 3.55% 0.20% 17.03% 346,978Amihud 5.15 0.01 178.43 0.00 63.06 346,978Repurchase measuresRepurchase Volume (million) 49.4 4.6 180.8 0.0 768.5 50,204Repurchase Intensity 0.66% 0.35% 0.98% 0.00% 4.51% 50,204Repurchase Intensity (TV) 6.74% 3.29% 9.91% 0.00% 52.13% 50,204Control variables & instrumentsAnalysts 5.53 4.00 6.23 0.00 27.00 346,978Accelerated Share Repurchase 0.00 0.00 0.15 0.00 0.00 346,978Book to Market 0.64 0.51 0.63 -0.86 3.80 346,978Exog. Trading Volume (million) 16.63 16.55 5.85 3.73 33.78 346,978Leverage 0.42 0.36 0.29 0.02 0.97 346,978Market Cap (million) 3,229 345 15,142 6 54,887 346,978Price 38.64 14.77 1,346 0.42 92.68 346,978Private Repurchase 0.00 0.00 0.06 0.00 0.00 346,978S&P 500 0.11 0.00 0.32 0.00 1.00 346,978Tender Offer 0.00 0.00 0.09 0.00 0.00 346,978Total Assets (million) 7,307 516 64,166 7 108,585 346,978Trading Volume (million) 607 45 2772 0 9341 346,978Trading Volume (scaled) 17.62% 11.14% 32.49% 0.28% 103.03% 346,978Volatility 0.03 0.03 0.03 0.01 0.13 346,978Abnormal returnsCAR (6 months) -1.70% -2.65% 38.78% -97.66% 119.01% 291,527Filing CAR (-1,+1) -0.08% -0.10% 8.36% -23.63% 23.67% 111,940

A-2

Table 3: Descriptive Statistics - Within-firm Variation. This table reports thewithin-firm variation of our measures of liquidity and repurchase activity. Appendix A.2 ofour paper provides definitions of the liquidity measures.

Within-firm variation Within-firm variation Nof ln of variable

Spread 0.93% 0.46 106,898Price Impact 2.56% 0.58 106,898Amihud 93.36 0.95 106,898Repurchase Dummy 41.41% 106,898Repurchase Intensity 0.62% 106,898

Table 4: The Influence of Repurchases on Liquidity - programs with fixed expirydates only. The table presents GMM-regressions of liquidity on Repurchase Intensity andcontrol variables. As instruments for Repurchase Intensity we use Program Size and ProgramMonth. The sample is restricted to the first 12 months of a repurchase program of programswith fixed expiry dates. Monthly returns are from CRSP. Appendix A.2 of our providesdefinitions of the liquidity measures. The repurchase variables and the control variables aredefined in Table 1 of our paper. Standard errors are clustered at the firm level. t-statisticsare provided in parentheses. *, **, *** indicate significance at the 10%, 5% and 1% levelrespectively. The Hansen-J statistic tests for the validity of the overidentifying restrictions.The Kleibergen-Paap test is for underidentification and tests for the full rank of the reduced-form coefficient matrix following Kleibergen and Paap (2006). The table reports the teststatistics and the p-values for both tests. The t-tests for the instruments are from the first-stage regressions. The test suggested by Stock and Yogo (2005) rejects the hypothesis thatthe bias exceeds the OLS bias by more than 5% in all cases.

(1) (2) (3)Spread Price Amihud

ImpactRepurchase Intensityt –7.9342∗∗∗ –6.1333∗ –16.1205∗∗∗

(–3.63) (–1.88) (–3.17)R2 0.6519 0.5011 0.5188Observations 20369 20258 20383Firm FE Yes Yes YesTime FE Month Month MonthKleibergen-Paap (test) 125.3 124.7 125.2Kleibergen-Paap (p-value) 0.00% 0.00% 0.00%Hansen’s J (test) 0.4 0.2 0.0Hansen’s J (p-value) 54.52% 65.92% 92.40%First stage t-statistics of included instrumentsProgram Month (ln) -11.54 -11.55 -11.54Program Size 5.19 5.38 5.21

A-3

Table 5: The Influence of Repurchases on Liquidity - programs longer than 12months only. The table presents GMM-regressions of liquidity on Repurchase Intensity andcontrol variables. As instruments for Repurchase Intensity we use Program Size and ProgramMonth. The sample is restricted to both the first 12 months of a repurchase program andprograms which are not completed within the first 12 months. Monthly returns are fromCRSP. Appendix A.2 of our provides definitions of the liquidity measures. The repurchasevariables and the control variables are defined in Table 1 of our paper. Standard errorsare clustered at the firm level. t-statistics are provided in parentheses. *, **, *** indicatesignificance at the 10%, 5% and 1% level respectively. The Hansen-J statistic tests for thevalidity of the overidentifying restrictions. The Kleibergen-Paap test is for underidentificationand tests for the full rank of the reduced-form coefficient matrix following Kleibergen andPaap (2006). The table reports the test statistics and the p-values for both tests. The t-testsfor the instruments are from the first-stage regressions. The test suggested by Stock andYogo (2005) rejects the hypothesis that the bias exceeds the OLS bias by more than 5% inall cases.

(1) (2) (3)Spread Price Amihud

ImpactRepurchase Intensity –8.3399∗∗∗ –4.2959∗∗ –20.0170∗∗∗

(–6.30) (–2.07) (–6.10)R2 0.6078 0.4914 0.5062Observations 41753 41508 41772Firm FE Yes Yes YesTime FE Month Month MonthKleibergen-Paap (test) 321.4 322.9 320.1Kleibergen-Paap (p-value) 0.00% 0.00% 0.00%Hansen’s J (test) 1.0 3.4 0.3Hansen’s J (p-value) 32.15% 6.69% 57.66%First stage t-statistics of included instrumentsProgram Month (ln) -18.98 -19.02 -18.93Program Size 6.27 5.38 6.27

A-4

ReferencesKleibergen, F., and R. Paap, 2006, “Generalized reduced rank tests using the singular- valuedecomposition,” Journal of Econometrics, 127, 97–126.

Stock, J. H., and M. Yogo, 2005, Testing for Weak Instruments in Linear IV Regression. Iden-tification and Inference for Econometric Models, in: Donald W.K. Andrews and James H.Stock, eds: Essays in Honor of Thomas Rothenberg, Cambridge University Press, Cam-bridge.

A-5