Do Stock Splits Improve Liquidity?

Ruslan Y. Goyenko Indiana University

Craig W. Holden Indiana University

Andrey D. Ukhov Indiana University

May 2006

Abstract The prior literature finds that stock splits worsen liquidity, as measured by percent effective spread, over a short horizon (60 to 180 days) after the split. We innovate by examining a long-horizon window after the split and by using new proxies for percent spread constructed from daily data. This allows us to track the liquidity of thousands of stock splits taking place from 1963 through 2003. We find that both the percent spread of NASDAQ split firms and the spread proxies of NYSE/AMEX split firms temporarily increase, but return to even with the control firms in 5 to 12 months. This provides a missing link supporting the signaling theory of splits. We also find that split firms are experiencing gains in liquidity at loner horizons. The percent spread of NASDAQ split firms becomes significantly lower than that of the control firms in 12 to 39 months. The spreads for NYSE/AMEX split firms become lower than the spreads for the control firms in 12 to 24 months. The NYSE/AMEX results are robust to three different liquidity proxies. This suggests a net benefit of splitting, which provides a missing link supporting both the trading range theory and the optimal tick size theory. All three theories could be true at the same time and our findings provide new evidence supporting all three theories.

Keywords: Stock splits; Liquidity; Long-run effects. JEL Codes: G30; G32; G14.

_________________________________ We thank Darius Miller, Matthew Spiegel, Charles Trzcinka, Xiaoyun Yu, and seminar participants at Indiana University and McMaster University. The authors can be reached at Kelley School of Business, Indiana University, 1309 East 10-th Street, Bloomington, IN 47401. E-mail addresses are: Ruslan Goyenko (rgoyenko@indiana.edu), Craig Holden (cholden@indiana.edu), Andrey Ukhov (aukhov@indiana.edu).

2

Do Stock Splits Improve Liquidity?

Abstract The prior literature finds that stock splits worsen liquidity, as measured by percent effective spread, over a short horizon (60 to 180 days) after the split. We innovate by examining a long-horizon window after the split and by using new proxies for percent spread constructed from daily data. This allows us to track the liquidity of thousands of stock splits taking place from 1963 through 2003. We find that both the percent spread of NASDAQ split firms and the spread proxies of NYSE/AMEX split firms temporarily increase, but return to even with the control firms in 5 to 12 months. This provides a missing link supporting the signaling theory of splits. We also find that split firms are experiencing gains in liquidity at loner horizons. The percent spread of NASDAQ split firms becomes significantly lower than that of the control firms in 12 to 39 months. The spreads for NYSE/AMEX split firms become lower than the spreads for the control firms in 12 to 24 months. The NYSE/AMEX results are robust to three different liquidity proxies. This suggests a net benefit of splitting, which provides a missing link supporting both the trading range theory and the optimal tick size theory. All three theories could be true at the same time and our findings provide new evidence supporting all three theories.

Keywords: Stock splits; Liquidity; Long-run effects. JEL Codes: G30; G32; G14.

3

Introduction Why do companies split their stocks? This question has attracted a lot of attention in the

finance literature but the answer remains unclear. In perfect capital markets, splits would

neither create nor destroy value. But in the real world, splits have an impact. Firms do

split their stocks, which they would not make an effort to do if it was completely

irrelevant. On a split announcement, there is a significantly positive abnormal return.1 On

the split ex date, there is a variety of negative effects such as larger percent spreads,

increased volatility, and larger commission costs.

The research question we address is do stock splits improve liquidity? By liquidity,

we mean the average cost of trading as measured by percent effective spread.2 The prior

literature finds that stock splits cause the percent effective spread to increase immediately

and stay up over short horizons. The horizons that prior studies have examined range

from 60 to 180 days. Specifically, Conroy, Harris and Benet (1990) use a two month

window, Schultz (2000) uses a three month window, and Desai, Nimalendran and

Venkataraman (1998) uses a six month window.3 We innovate by examining a longer,

72-months, window after the split. For NASDAQ, the dependent variable is percent

quoted spread from the CRSP NASDAQ supplement. For NYSE/AMEX, we use new

spread proxies constructed from daily CRSP prices. This allows us to study liquidity

effects for time periods in which intraday microstructure data are not available.

Specifically, we analyze the liquidity effects of thousands of stock splits from 1963

through 2003. 1 Fama, Fisher, Jensen, and Roll (1969) suggest that splits may be interpreted by investors as a favorable signal that the firm is able to maintain a new, higher level of earnings. Grinblatt, Masulis and Titman (1984), Lamourex and Poon (1987) document a positive abnornal return accompanying the announcement of a split. 2 Liquidity is a multi-dimensional concept. One dimension is the average cost of trading as measured by the percent quoted (or effective) spread. Another dimension is the quantity that can be traded at a given cost as measured by the depth of the market. A third dimension is the speed as measured by the time from order submission to order execution. Other dimensions have been suggested as well. The percent effective spread of a trade is defined as (2 * | trade price - quote midpoint | ) / (quote midpoint) for that trade. The percent effective spread over a month is defined as the volume-weighted average of the percent effective spread for all trades in the month. 3 Maloney and Mulherin (1992) come close to analyzing the long-run pattern by graphing the percent quoted spread of 446 splitting NASDAQ firms for 500 days (16.4 months) before and after the split. The text interpreting the graph analyzes the pre-split period and the immediate impact of the split, but is silent about the long-run pattern. They do not qualitatively analyze nor formally test the long-run pattern and don’t have a control group. Kadapakkam, Krishnamurthy, and Tse (2005) study relative spreads and abnormal returns in a 10-day window around a split.

4

In the finance literature, we are accustomed to event study effects that happen

immediately. In particular, we are used to the idea that financial markets decipher

complex information very quickly and so prices react in minutes. However, with stock

splits we are not only concerned with the immediate price effect, but with the long-run

trading behavior of investors and/or the long-run revelation of private information. We

conjecture that there are long-run liquidity effects, in addition to short-run liquidity

effects. This makes sense because the leading split theories all propose mechanisms that

take time to work. The arguments in the prior literature suggest that a long-run study of

post-split liquidity is in order. Ikenberry, Rankine and Stice (1996) examine stock

performance three years after a split. They find abnormal returns and attribute them to

market under-reaction. If it takes financial markets three years to incorporate split

information into prices, then it may not be possible to fully understand the impact of

splits on liquidity by examining only short-term after-event windows. Brennan and

Hughes (1991) argue that the adjustment of analyst coverage is complete only five years

after a split. All arguments considered, a longer horizon study of post-split liquidity is

needed.

Our after-event window extends to 6 years (72 months), although we observe the first

set of interesting results less than a year after a split. Our main findings are that split

firms initially experience worse liquidity than control firms, but return to even in 9 to 12

months and then cross-over into better liquidity. First, we present new evidence that the

worsening of liquidity of split firms is temporary. Specifically, we find that for split firms

both their percent effective spread and their proxies for percent effective spread return to

even in 9 to 12 months, becoming indistinguishable from control firms. Second, we find

that split firms are experiencing gains in liquidity at loner horizons. We demonstrate that

for split firms their percent effective spread and proxies for percent effective spread

cross-over in 39 months, becoming significantly lower than control firms. Often the

improvement in liquidity is observed 24 months after the split. These results hold for

NASDAQ stocks, where liquidity is measured using percent quoted spread. The results

also hold for NYSE/AMEX stocks where liquidity is measured using three different

proxies.

5

We study the effect of splits on liquidity using two methods. The first methodology is

the matched-sample approach. For each firm with a split we find a matching firm and

study the liquidity of the two groups of stocks. This methodology has been widely used in

the literature on stock splits. We do not solely rely on the matched-sample methodology,

however. We introduce cross-sectional Fama-MacBeth (1973) regressions to the studies

of the impact of splits on liquidity. The regressions relate transaction costs for a stock to

variables that capture past stock splits and control variables. We find that splits have

long-run impact on transaction costs. Stocks that had a split in the past have lower

transaction costs, controlling for other transaction costs determinants. The results from

the matched sample methodology and cross-sectional regressions framework are

consistent with each other.

The regression framework enables us to establish another important result. It has been

shown that liquidity of individual stocks co-moves with aggregate liquidity.4 In the

regressions we confirm a positive relation between firm liquidity and aggregate liquidity.

The regression results also show that when we control for the aggregate liquidity, the

effect of stock splits on firm liquidity survives. This implies that at the times when

market liquidity worsens, companies that have split their shares remain more liquid than

those that have not.

How do these findings contribute to the literature? Three major theories have been

proposed for why firms split. We discuss each theory in turn by explaining what it is,

what empirical evidence currently supports it, and what empirical challenges it still faces.

After presenting the three theories we discuss how our findings contribute to overcoming

those challenges.

One major theory of splits is the signaling theory of Brennan and Copeland (1988).5

They assume that managers have private information about the future prospects of their

own firm. If a firm with good prospects splits, then its percent spread will increase

temporarily. Eventually the market will come to perceive the same good information that

the managers knew causing the firm price to rise and the percent spread to return to even. 4 Chordia, Roll, and Subrahmanyam (2000), Hasbrouck and Seppi (2001), and Huberman and Halka (2001). See also Pastor Stambaugh (2003) for a discussion of liquidity risk. 5 There are several variations of the signaling / attention-getting theory. See Grinblatt, Masulis, and Titman (1984), Brennan and Hughes (1991), and Ikenberry, Rankine, and Stice (1996).

6

If a firm with average or bad prospects splits, then its percent spread will increase

permanently. This cost differential allows good firms to signal by splitting and prevents

average or bad firms from mimicking. Signaling theory predicts that splitting firms

should receive positive abnormal returns on announcement. The empirical evidence finds

a positive abnormal return on split announcement. An empirical challenge for signaling is

that there is no evidence that split firms actually experience a temporary increase in

percent effective spread as compared to non-split firms.

Another major theory of splits is the trading range theory of Copeland (1979). The

idea is that a split lowers the price, which makes trading more affordable especially by

avoiding odd lot trading costs. Eventually this leads to an increase in the base of traders

in the firm. In turn, this eventually increases the volume of trade, which eventually

lowers the percent spread. The empirical evidence finds that split firms experience an

increase in the base of traders and an increase in volume. Baker and Gallagher (1980)

survey top executives and find that the dominant executive belief is that splits keep stock

prices within an optimal trading range, make it easier for small investors to buy round

lots, and result in an increase in the number of shareholders. An empirical challenge for

the trading range hypothesis is that there is no evidence that split firms eventually

experience a lower percent spread. In other words, there is no evidence that splitting

firms receive the predicted long-run liquidity improvement from splitting.

The third major theory of splits is the optimal tick size theory of Angel (1997). The

idea is that a split causes an increase in percent spread. This eventually causes more limit

orders to be submitted for two reasons. First, some traders will switch from using market

orders (which are now more costly) to using limit orders (which are now more

profitable). Second, some people will be enticed to become pseudo market makers who

profit by submitting limit order on both sides and gaining the spread. The increase in

limit orders will eventually cause the percent spread to cross-over and drop below where

it would be without the split. The empirical evidence finds that after a split the number of

limit orders does increase and the limit order to market order ratio does go up. An

empirical challenge for the optimal tick size is that there is no evidence that split firms

eventually experience a lower percent spread. Again, there is no evidence that splitting

firms receive the predicted long-run liquidity improvement from splitting.

7

Let us consider how our findings contribute to overcoming the empirical challenges

faced by the three theories of splits. We find that both the percent spread of NASDAQ

split firms and the spread proxies of NYSE/AMEX split firms temporarily increase, but

return to even with the control firms in 5 to 12 months. This provides a key missing link

that overcomes a major challenge facing the signaling theory of Brennan and Copeland.

We also find that the percent spread of NASDAQ split firms crosses-over the control

firms in 12 to 39 months. The proxies for effective spread for NYSE/AMEX split firms

cross-over the control firms in 12 to 24 months. This provides empirical support for a net

benefit of splitting. This provides a key missing link that overcomes a major challenge

facing both the trading range theory and the optimal tick size theory. There is nothing

inconsistent between the three theories and all three could be true at the same time. Our

findings end up providing support for all three theories.

The paper is organized as follows. Section 2 presents methodology and data. Section

3 describes our results. Section 4 concludes.

II. Methodology and Data

A. Liquidity measures

The focus of our paper is on the percent spread variation over long horizons after

stock splits. Our study covers the splits that took place between 1963 and 2003 for

NYSE/AMEX firms and between 1984 and 2003 for NASDAQ firms. We use quoted

percentage spreads to measure liquidity of NASDAQ stocks. The percentage spread is

defined as

( )BABAQS+

−=

5.0,

where A and B are daily closing quoted Ask and Bid prices available from CRSP daily

files. The high frequency microstructure data for NYSE/AMEX firms are limited by the

availability of ISSM/TAQ data. We therefore use spread proxies. This allows us to

capture a larger number of stock splits and extend after-split event time. It also allows us

to introduce cross-sectional regression framework to the literature that studies the effect

of stock splits.

8

Our choice of spread proxies is based on performance comparison in Goyenko,

Holden, Lundblad and Trzcinka (2005) (hereafter, GHLT). GHLT analyze multiple

effective spread proxies computed from low-frequency (daily) data. They determine how

closely these low-frequency proxies match effective spread as computed from high

frequency data (TAQ) over monthly and annual intervals. They use multiple performance

measures, including correlation, bias, and mean-squared error. The central idea of that

study is to determine which liquidity measures computed from daily data are good

proxies for liquidity computed from high frequency data.

We select three effective spread proxies that consistently do well in GHLT.

Specifically, we use Effective Tick introduced by Holden (2006), LOT Y-split,

introduced by GHLT, and LOT-Mixed, introduced by Lesmond, Ogden, and Trzcinka

(1999). Below we provide a description of each measure.

Effective Tick

Holden (2006) develops a proxy of the percent spread based on observable price

clustering. He assumes that the realization of the percent spread on the closing trade of

day is randomly drawn from a set of possible percent spreads , 1, 2, ,js j J= K with

corresponding probabilities , 1, 2, , .j j Jγ = K Based on the negotiation cost theory of

Harris (1991), he assumes that trade prices are clustered in order to minimize negotiation

costs between potential traders. Following the intuition of Christie and Schultz (1994), he

assumes that price clustering is completely determined by the percent spread size. He

then shows that the simple frequency with which closing prices occur in special clusters

can be used to estimate the percent spread probabilities ˆ , 1, 2, , .j j Jγ = K For example on

a 18$ fractional price grid, the frequency with which trades occur on 1

8odd s, 14odd s,

12odd s, and whole dollars can be used to estimate the probability of a 1

8$ spread, 14$

spread, 12$ spread, and a $1 spread. Similarly for a decimal price grid, the frequency of

off pennies, off nickels, off dimes, off half dollars and whole dollars can be used to

estimate the probability of a penny spread, nickel spread, dime spread, quarter spread,

and a whole dollar spread. Finally, the effective tick measure ET is simply a probability-

weighted average of each percent spread size

9

1

ˆJ

j jj

ET sγ=

=∑

A more detailed explanation of the effective tick computation is presented in the

Appendix.

LOT

Lesmond, Ogden, and Trzcinka (1999) develop a proxy of the percent spread (LOT

Mixed in the terminology of GHLT (2005)) based on the idea of informed trading on

non-zero return days and the absence of informed trading on zero return days. A standard

“market model” relationship holds on non-zero return days, but a flat horizontal segment

applies on zero return days.

The LOT model assumes that the unobserved “true return” *jdR on a stock j on day d

is given by *jd j md jdR Rβ ε= + ,

where jβ is the sensitivity of stock j to the market return mdR on day d and jdε is a public

information shock on day d. They assume that jdε is normally distributed with a mean of

zero and a variance of 2jσ . Let 1 jα be the transaction cost of selling stock j and let 2 jα

be the transaction cost of buying stock j. Then, the observed return jdR on a stock j is

given by * *

1 1* *

1 2* *

2 2

when when

when .

jd jd j jd j

jd jd j jd j

jd jd j j jd

R R RR R RR R R

α αα α

α α

= − <= < <= − <

The model is estimated via MLE. The computational details of LOT Mixed and LOT

Y-split are described in the Appendix. LOT Mixed has been used in Lesmond, Schill and

Zhou (2002), Lesmond (2002). LOT Y-split is used by GHLT (2005). These two

measures share the same origin, but they are capturing different aspects of liquidity.

GHLT (2005) find that LOT Y-split has one of the highest correlation with percent

spreads obtained from high frequency data (TAQ). Further, Goyenko (2005) presents

evidence that LOT Y-split represents percent spread better than LOT Mixed over long

10

time series, but LOT Mixed also captures some costs of price discovery. Lesmond,

Ogden, and Trzcinka (1999) argue that LOT Mixed captures effective spread and other

transaction costs, as well.

B. Data and Matching Methodology.

The split sample consists of all stock splits during the period from 1963 to 2003

recorded on CRSP NYSE/AMEX file and all stock splits from 1984 to 2003 recorded on

CRSP NASDAQ file. We consider NASDAQ and NYSE/AMEX stocks separately since

trading costs of NASDAQ-listed stocks are higher compared to NYSE/AMEX-listed

stocks (Bessembinder and Kaufman, 1997; Bessembinder, 1999; Bessembinder, 2003).

Split dates are the implementation dates obtained from CRSP. The splitting shares are

ordinary common shares (we omit ADRs, SBIs, REITs, and closed-end funds). Since our

goal is to look at long horizon after-split window and our sample spreads over four

decades we need a control non-split sample to account for non-event driven changes in

liquidity. There is no convention on what criteria the matching should be done for long-

run study of percent spreads. When the variable of interest is liquidity, the match should

be performed on the determinants of liquidity. Butler, Grullon and Weston (2005), who

compare investment banking fee across liquid and illiquid firms, use the match

conditioned on size, price and volatility (standard deviation of stock returns). The choice

of these variables is explained by the fact that firm liquidity is correlated with firm size,

share price and volatility.

While the importance of the above variables is undisputable, there is well established

empirical evidence that past liquidity is significant determinant of future liquidity (see,

for example, Chordia, Roll and Subrahmanyam, 2001; Amihud, 2002; Chordia, Sarkar

and Subrahmanyam, 2005). Therefore, as in Koski (1998) and Kamara and Koski (2001),

who study after-split trading liquidity, we use percentage spreads as one of the matching

criteria.

Previous literature also documents that an important characteristic of splitting firms is

that they typically experience a price run-up before the announcement of the split, i.e.

splitting firms load exceedingly high on momentum (Ikenberry and Ramnath, 2002). We

are interested in testing hypothesis about percentage spread fluctuations after splits. Since

11

spreads can be affected by past returns (Chordia, Roll and Subrahmanyam, 2001;

Chordia, Sarkar and Subrahmanyam, 2005), we also consider alternative control group

matched on momentum.

We thus consider two alternative matches. First, we match on size, 12-month

cumulative return and liquidity. Second, we match on size, price and volatility. This

allows us to test the robustness of our results. We use NASDAQ stocks to evaluate

performance of each matching technique. The choice of NASDAQ stocks is justified by

the availability of quoted spreads, the direct measure of liquidity.

Although, the focus of the study is a long-horizon after-event window (72 months),

we include all splits, even those with a shorter after-event window. For example, if the

stock A has a split at month t and then another split at month t+24, they are treated as two

separate events. The after-event window for the first split is 24 months and the after-

event window of the second split is 72 months. Therefore, in the short and medium

horizon we consider all splits reported at CRSP, and in the long-horizon we have only

those split-stocks which have 72 months of observations after the last split. As a

robustness check, we track splits over the full 72-month window irrespective of

subsequent splits and obtain the same results.

We use two matching criteria. The first criteria, which we call the base match, is

marched on market capitalization, 12 months cumulative return prior to the split, and

percent spread at the end of month t-1, where month t is the month when the split

occurred. The second criterion—which we call the alternative match—is the match on

size, price and volatility at the end of month t-1. By definition, non-split firms that we

pick from are those which do not have splits during the event window of split-firms.

Therefore, our control sample does include firms which have splits outside of the event

window. For NASDAQ split-stocks we are looking for non-split counterparts only among

NASDAQ universe. We follow the analogous procedure for NYSE/AMEX firms. Thus,

we are controlling for the exchange as well.

For a match based on size, price and volatility we include all splits without any

restrictions for before-and after event observations availability. For a match based on

size, 12 month cumulative return and liquidity, we require our split and control firms to

have at least 12 months of observations before the split-date. Table 1 presents summary

12

statistics of split occurrence by year given the availability of at least 12 month of data

before the split date. Our sample consists of 6, 928 splits of NYSE/AMEX firms (Panel

A), and 2,588 splits of NASDAQ firms (Panel B).

III. Results

A. Evidence from Matched Sample Technique

We begin the discussion of results with NASDAQ firms. Figure 1a depicts t-statistics

of the difference between quoted spreads of split and non-split firms. Figure 1b shows the

difference in spreads. The dark line shows the base match and the light line shows the

alternative match. Immediately after a split quoted percentage spread increases. This

result is consistent with the previous studies. Over a short horizon, spreads of split firms

are significantly higher than non-split firms for the first four-to-six month after the split.

As soon as nine month after the event, however, the spread for split and non-split firms is

the same. For both matches, the difference switches from being statistically significantly

positive at the 5% level in the early months to being statistically indistinguishable from

zero. This is the first result: The increase in transaction costs after a split is temporary.

Looking further out after the split in Figure 1a, the difference becomes negative. In

month 12 for the alternative match, and in month 39 for the more conservative base

match, the difference becomes statistically significant and negative. In other words, the

percent quoted spread of NASDAQ split stocks becomes significantly lower than their

control firm counterparts in the long-run.

Table 2 shows the results that correspond to Figure 1. Panel A reports percent spread

for split and non-split firms, the difference in spreads, and t-statistics for the test of the

significance of the difference for the first match. Panel B shows the same items results for

the alternative match. The difference returns to zero both for the base match and for the

alternative match by month 6. The difference becomes negative and significant at a

longer horizon for both matches.

Next, we consider all splits for NYSE/AMEX firms using the base match. Table 3

reports the spread proxy point estimates, a difference between spreads of split and non-

split firms and t-statistics for the test of the difference in spreads. We report these results

for Effective Tick, LOT Y-split and LOT mixed in Panels A through C respectively.

13

For all three spread proxies we observe an increase in transaction costs for split firms

immediately after the split. The increase in transaction costs is temporary. For Effective

Tick and for LOT Y-split the difference goes away by month 6. For LOT-mixed the

difference returns to zero by month 12. This effect can be seen in Figure 2A that shows t-

statistics for the difference in three spread proxies following a split. Figure 2B shows the

corresponding differences in the three spread proxies. We also establish that

approximately one-to-two years after the split the spreads of split firms become

significantly lower then the spreads of control sample. For Effective Tick and for LOT Y-

split, the difference between split and non-split firms becomes negative and significant at

the 5% level in month 19 after a split.

To summarize, controlling for the exchange, firm size, 12-month cumulative return,

and liquidity we find that split firms become more liquid compared to non-split

counterparts in no more than three years for NASDAQ firms and in one-and-a-half to two

years for NYSE/AMEX firms.

B. Evidence from Cross-Sectional Regressions

Matched sample technique establishes two new results. First, the increase in

transaction costs after a split is temporary. After the initial increase in transaction costs,

less than a year after the split, liquidity of split firms improves and becomes the same as

liquidity of the firms in the control group. The second result is that in the long run firms

that split their stocks experience improvement in liquidity. To investigate robustness of

these results we estimate the effect of splits on liquidity using cross-sectional regressions.

We focus on the robustness of the long-run improvement in liquidity because this result is

new. We perform Fama-MacBeth (1973) regressions with a measure of liquidity as the

dependent variable. We are the first to study the effect of splits on liquidity in the cross-

sectional Fama-MacBeth (1973) regression framework. Previous authors studying splits

could not use this approach because it requires a measure of liquidity for all

NYSE/AMEX stocks at monthly frequency for a long time span. Three liquidity

measures—Effective Tick, LOT Y-split, and LOT mixed—allow us to do this. Our

sample is all stocks on CRSP. As before, we study NASDAQ and NYSE/AMEX stocks

separately.

14

Each month we perform a cross-sectional regression of the NASDAQ quoted spread

of firm i , iQS , on a set of dummy variables that capture past split events and a vector of

control variables. In a given month, for every firm we construct seven dummy variables

that reflect past split events. The dummy variable 0D is set to 1 if the firm had a split

during preceding 6 months, and is set to zero otherwise. The dummy 1D is set to 1 if

there was a split in the months -7 to -12 before the month of the quoted spread (month -1

is the month immediately preceding the month for which the regression is estimated). The

dummy 2D is one if there was a split in year -2 (months -13 to -24). The dummies 3D ,

4D , 5D , and 6D are constructed in a similar way. Each month a set of dummies for all

firms is created. By construction, the dummy variables take into account all past split

events. Our dependent variable is quoted spread. If a split results in lower transaction

costs then we expect regression coefficients on the dummy variables to be negative. To

test this hypothesis we perform the following regression:

εγβββββββα +++++++++= ∑=

n

iiiiiiiiiii CDDDDDDDQS

16,65,54,43,32,21,10,0 .

We include several control variables,C , in the regression. We control for variables that

affect liquidity. The first control variable is TURNOVER, defined as trading volume in

the company shares over the month divided by the total number of shares outstanding.

We also include monthly return on the stock, RETURN, as a control variable. Previous

studies have found commonality in liquidity.6 Liquidity of individual stocks, therefore,

may depend on market-wide liquidity conditions. To account for this effect, we include

AGGREGATE LIQUIDITY variable in our regressions. Aggregate liquidity is equally

weighted quoted spread of all NASDAQ stocks computed each month.

The results from the matched sample method show that liquidity improves over 12

months after a split. To establish a stronger link between liquidity improvement and the

split we would like to show that splits have long-lasting effects. The regression

specification is designed to do this.

6 Chordia, Roll, and Subrahmanyam (2000), Hasbrouck and Seppi (2001), and Huberman and Halka (2001). See also Pastor Stambaugh (2003) for a discussion of liquidity risk.

15

Supporting the results from the matched sample technique, the regression results for

NASDAQ stocks reported in Table 4 indicate that stock splits are strongly related to

quoted spreads, even after controlling for other factors. As our hypothesis states, the

transaction costs are lower for stocks that had a split in the past. Regression coefficients

are negative for all dummy variables. The signs, magnitudes, and statistical significance

of the coefficients are consistent across all the specifications. The results hold when we

control for market-wide (aggregate) liquidity.

Our results suggest that a stock split has long-lasting impact on liquidity. Splits that

have taken place over four years ago result in a lower quoted spread. This is fully

consistent with the results we obtain using the matched sample technique.

The results also hold for the sample of NYSE/AMEX stocks. The regression

specification is the same as for NASDAQ stocks. The dependent variable is liquidity of a

stock, measured using one of the three liquidity measures. The control variable, aggregate

liquidity, matches the type of liquidity measure used for individual stocks. When the

dependent variable is effective tick, then aggregate liquidity is equally weighted effective

tick of all NYSE/AMEX stocks, computed each month. When the dependent variable is

LOT Y-split, then aggregate liquidity is equally weighted LOT Y-split, too.

Table 5 Panel A displays the results for effective tick as the liquidity measure. The

results indicate that past stock splits improve liquidity. Coefficients on all dummy

variables are negative. Again, a stock split has long-lasting impact on liquidity. The

results are the same for the other two measures of liquidity, LOT Y-split (Panel B), and

LOT mixed (Panel C).

The evidence from regression tests corroborates the results obtained in the matching

sample framework. By employing cross-sectional regression framework, not only we

verify that the results are not sensitive to the matching sample methodology, but we also

establish that the long-run effect of splits is robust to changes in the systematic liquidity

environment. It has been established in the liquidity literature that liquidity of individual

stocks co-moves with aggregate liquidity. Our cross-sectional regressions confirm

positive relation between aggregate liquidity and firm liquidity. The regression results

also show that the effects of stock splits survive when controlling for aggregate liquidity.

16

This implies that in the times when market liquidity worsens, companies that have split

their shares remain more liquid than those that have not.

C. A Discussion of Economic Significance

A firm may have several reasons to take active steps to improve market liquidity of

its securities. One incentive is that stock market liquidity is an important determinant of

the cost of raising external equity capital (Butler, Grullon, and Weston 2005; BGW

thereafter). In a study of a large sample of seasoned equity offerings they find that

investment bank fees are significantly lower for firms with more liquid stock. The

findings are robust. The authors conclude that firms can reduce the cost of raising capital

by improving the market liquidity of their stock.

Economic effect established by Butler, Grullon, and Weston (2005) helps assess the

economic significance of our findings. To establish their results, the authors split the

firms into liquidity quintiles. They then show that the difference in the investment

banking fee for firms in the most liquid vs. the least liquid quintile is about 101 basis

points or 21% of the average investment banking fee in the sample.

Consider the liquidity of the firms in BGW (2005). According to their Table 1, the

difference in percent bid-ask spread for the 75th percentile and for the 25th percentile

equals 0.009. This is the difference in liquidity between the most liquid and the least

liquid firms in their sample. We show that 38 month after the split, the difference in

spreads between split and control firms is -0.004, or more than a third of the difference

between liquid and illiquid firms in Butler, Grullon, and Weston (2005).7 In

approximately 60 months after a split, the difference in spread between split and non split

firms is -0.0063, or two-thirds of the difference in BGW (our Table 2, Panel B). The

magnitude is significant for a liquidity study. Thus, by a seemingly cosmetic change—a

split—a firm can improve the long-run liquidity of its stock by the same order of

magnitude that has been demonstrated to have an economically meaningful impact for the

direct cost of raising capital.

7 Our result is illustrated in Figure 1b.

17

D. Robustness: Matched Sample Technique

In our previous matching exercise we considered all split-firms, without requiring that

the firm has observations for the 72 months after the event. To make sure that our results

are not driven by firms that have less than 72 months of post-split observations, we

conduct an additional robustness check. In this section, we perform a match where we

keep the universe of firms fixed for the larger sample of NYSE/AMEX stocks.

We require that the stock splits meet the following criteria: (i) Market capitalization

data, liquidity estimate and cumulative 12 month return are available at the end of month

t-1, where month t is the month the split takes an effect; (ii) the splitting shares are

ordinary common shares (we omit ADRs, SBIs, REITs, and closed-end funds); (iii) at

least 72(12) months of data is available at the period subsequent (preceding) to the split;

(iv) stock splits which occur during 72 months after the first split are ignored.

As before, we compare the liquidity of our split sample with liquidity of non-split

peers. For each firm which had a split over our sample period we find non-split firm

which has the closest value of market capitalization, 12 month cumulative return and

liquidity estimate (effective tick) at the end of month t-1. We also require non-split peers

to have at least 72(12) months of data available at the period subsequent (preceding) to

the appropriate split. Our final sample consists of 2,293 stock splits and the same number

of non-split peers. Table A1 in the Appendix reports number of stock splits by year. Our

final split sample is now smaller in comparison to the previous section because we

impose additional requirement of 72 months of post-split data.

Table A2 analyzes the liquidity patterns for the sample. The table reports the spread

proxy point estimates, a difference between spreads of split and control firms and t-

statistics for the test of the difference in spreads. The table shows results for three

different liquidity measures. Panel A is based on the effective tick proxy. The difference

between split and non-split firms is positive and significant in the first month after a split:

The difference in effective tick is 0.07% (t-statistic equals 2.09). This is consistent with

previously reported results. The increase is temporary. Twelve month after a split,

however, there is no difference in effective tick (the difference equals -0.01%, t-statistics

is -0.14). The split stocks converge to their non-split peers and the post-split increase in

18

trading costs is no longer observed. Five years after the event, split firms have lower

effective tick (the difference equals -0.13%, t-statistic of -1.72).

Panel B presents results for LOT Y-split. The results follow a similar pattern. The

difference in LOT-Y is 0.25% in the first month (t-statistic is 2.50). Twelve months after

the event the difference in the LOT-Y measure is -0.01% (t-statistic -0.18) indicating that

there is no difference in transaction costs between the two groups. Five years after the

split transactions costs are lower for the split firms (the difference of -0.18%, t-statistics: -

2.05).

Panel C presents the results for LOT Mixed. In this case, too, the difference

between split and non-split stocks is 0.52% (t-statistics of 5.01). By the end of the year,

however, the difference in liquidity is not statistically different from zero. Liquidity of

split stocks continues to improve and by the end of year five they are more liquid than

non-split group (the difference of -0.24%, t-statistics of -1.96).

Based on this evidence we conclude that our finding that liquidity of split firms

improves over time is robust to the use of liquidity measures and to our universe of split

firms selected. It is also robust to the matching procedure.

IV. Conclusion

In this paper we study the effect of stock splits on liquidity in the long run. The

literature so far has presented evidence that splits worsen liquidity, but the focus of this

conclusion is primarily on a short after-event window. We use new proxies for percent

spread constructed from daily data for NYSE/AMEX stocks, and quoted spreads for

NASDAQ. This allows us to track the liquidity of thousands of stock splits taking place

from 1963 through 2003 for NYSE/AMEX and 1984 through 2003 for NASDAQ.

We confirm the increase in transaction costs found in the previous studies, but show

that the increase is temporary. We find that for split firms both their percent spread and

their proxies for percent spread return to even in 5 to 12 months, becoming statistically

indistinguishable from control firms. This provides a missing link supporting the

signaling theory of splits. We also find that for split firms their proxies for percent

effective spread cross-over in 12 to 39 months (often in less than 2 years), becoming

19

significantly lower than control firms. These results are robust to three different liquidity

proxies and hold for NASDAQ and NYSE/AMEX firms.

We use two methodological approaches to establish this result. First, we use the

matched sample approach. We do not, however, rely on matching alone. As a second

approach we introduce cross-sectional Fama-MacBeth (1973) regressions to the studies

of splits and liquidity. Both methods support the same set of conclusions.

In sum, our analysis suggests a net benefit of splitting, which provides a missing link

supporting both the trading range theory, signaling theory, and the optimal tick size

theory. All three theories could be true at the same time and our findings provide new

evidence supporting all three.

20

Appendix

Effective Tick

Let tS be the realization of the effective spread on the closing trade of day t . Assume

that tS is randomly drawn from a set of possible effective spreads , 1, 2, ,js j J= K with

corresponding probabilities , 1, 2, , .j j Jγ = K By convention, the possible effective spreads 1,s

2 , ,s K Js are ordered from smallest to largest. For example on a 18$ price grid, tS is modeled

as having a probability 1γ of 11 8$s = spread, 2γ of 1

2 4$s = spread, 3γ of 13 2$s = spread, and

4γ of 4 $1s = spread.

Let jN be the empirical number of special trade prices corresponding to the jth spread

( )1, 2, ,j J= K from positive-trade days. In the 18$ price grid example (where 4J = ), 1N

through 4N are the empirical number of 18odd prices, the number of 1

4odd prices, the number

of 12odd prices, and the number of whole dollar prices, respectively.

Let J jN + be the empirical number of no-trade midpoints corresponding to the jth

spread ( )1, 2, ,j J= K from no-trade days. In the 18$ price grid example (where 4J = ), 5N

through 8N are the number of 116odd midpoints, the number of 1

8odd midpoints, the number

of 14odd midpoints, and the number of 1

2odd midpoints, respectively. Thus, the complete

frequency distribution spans 2J events, with 1N through JN representing special trade prices

and 1JN + through 2JN representing no-trade midpoints.

Let jF and J jF + be the empirical probabilities of special trade prices and no-trade

midpoints, respectively, corresponding to the jth spread ( )1, 2, ,j J= K . These empirical

probabilities are computed as

21

2

1

jj J

jj

NF

N=

=

∑ for 1, 2, , 2j J= K .

Let jU be the unconstrained probability of the jth spread ( )1, 2, ,j J= K . The

unconstrained probability of the effective spread is

1

1

2 12 2,3, , 1 .

j J j

j j j J j

j j J j

F F jU F F F j J

F F F j J

+

− +

− +

⎧ + =⎪= − + = −⎨⎪ − + =⎩

K .

The effective tick model directly assumes price clustering (i.e., a higher frequency on

rounder increments). However, in small samples it is possible that reverse price clustering may be

realized (i.e., a lower frequency on rounder increments). Reverse price clustering unintentionally

causes the unconstrained probability of one or more effective spread sizes to go above 1 or below

0. Thus, constraints are added to generate proper probabilities. Let ˆ jγ be the constrained

probability of the jth spread ( )1, 2, ,j J= K . It is computed in order from smallest to largest as

follows

{ }

{ }1

1

,0 ,1 1ˆ

ˆ,0 ,1 2,3, , .

j

jj

j kk

Min Max U j

Min Max U j Jγ

γ−

=

⎧ ⎡ ⎤ =⎣ ⎦⎪⎪= ⎨ ⎡ ⎤− =⎪ ⎢ ⎥

⎪ ⎣ ⎦⎩∑ K

Finally, the effective tick measure ET is simply a probability-weighted average of each

effective spread size

1

ˆJ

j jj

ET sγ=

=∑ .

Additional explanation and intuition for the effective tick model can be found in

Holden (2006). The appendix of Holden (2006) presents the more complicated general formula

of the effective tick model, which works on any decimal or fractional price grid.

22

LOT

Lesmond, Ogden, and Trzcinka develop the following maximum likelihood

estimator of the model’s parameters

( )1 2

1

1

2 1

0

2

2

, , , | ,

1

1 ,

j j j j jd md

jd j j md

j j

j j md j j md

j j

jd j j md

j j

L R R

R Rn

R RN N

R Rn

α α β σ

α βσ σ

α β α βσ σ

α βσ σ

⎡ ⎤+ −= ⎢ ⎥

⎢ ⎥⎣ ⎦⎡ ⎤⎛ ⎞ ⎛ ⎞− −

× −⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦⎡ ⎤+ −

× ⎢ ⎥⎢ ⎥⎣ ⎦

∏

∏

∏

where ( )N is the cumulative normal distribution.

A very important issue of the LOT measure is the definition of the three regions over

which the estimation is done. One way, which GHLT (2004) call LOT Y-split, is to break

out the three regions based on the Y-variable. That is, region 0 is 0jdR = , region 1 is

0jdR > , and region 2 is 0jdR < . An alternative way to do it, which GHLT (2004) call

LOT Mixed, is to break out the three regions based on both the X-variable and Y-

variable. That is, region 0 is 0jdR = , region 1 is 0jdR ≠ and 0mdR > , and region 2 is

0jdR ≠ and 0jdR < .

23

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Table 1. Stock Splits by Year: NYSE/AMEX and NASDAQ Stocks

The table presents the number of splits by year. The split sample consists of all stock splits during the period from 1963 to 2003 recorded in CRSP NYSE/AMEX database and from 1984 to 2003 recorded in NASDAQ database. Split announcement dates are the declaration dates obtained from CRSP. The stock splits are required to meet the following criteria: (i) Market capitalization data, liquidity estimate and cumulative 12 month return are available at the end of month t-1, where month t is the month the split takes effect; (ii) the splitting shares are ordinary common shares (we omit ADRs, SBIs, REITs, and closed-end funds).

Panel A:

NYSE/AMEX firms Panel B:

NASDAQ firms Year Splits Year Splits Year Splits 1963 22 1984 197 1984 10 1964 102 1985 247 1985 60 1965 125 1986 379 1986 31 1966 160 1987 290 1987 104 1967 103 1988 123 1988 61 1968 202 1989 174 1989 82 1969 175 1990 119 1990 51 1970 32 1991 139 1991 78 1971 75 1992 204 1992 130 1972 110 1993 220 1993 204 1973 88 1994 154 1994 166 1974 51 1995 193 1995 205 1975 72 1996 232 1996 240 1976 165 1997 239 1997 219 1977 184 1998 196 1998 231 1978 244 1999 144 1999 207 1979 201 2000 99 2000 195 1980 331 2001 74 2001 92 1981 333 2002 83 2002 100 1982 149 2003 70 2003 122 1983 428 Total 6,928 Total 2,588

Table 2. Analysis of Liquidity Before and After a Split: NASDAQ Stocks

The table reports transactions costs for firms that had a stock split and for a matched sample of control firms. Month 0 is the month in which the split occurred and one is the month immediately following the event. Our sample consists of all firms listed on NASDAQ that had a stock split during the period 1984 through 2003, and had a one year of observations on CRSP before a split. Relative quoted spread is defined as a quoted ask price minus quoted bid price divided by the midpoint of the bid and ask prices. For each firm with a split we find a matching firm which has the closest transaction cost (percentage quoted spread), market capitalization, and 12 month cumulative return, all measured at the end of month -1. These results are reported in Panel A. As a robustness check, we conduct a second match. In Panel B, for each firm with a split we find a matching firm with the closest price, market capitalization, and volatility of daily returns, all measured for the month -1. Volatility is computed as standard deviation of daily returns over the month. The difference equals the value of the spread of split firms minus the value of the spread for control firms. The t-statistics test the hypothesis that the difference in transaction costs of split and control firms is different from zero.

Panel A: Relative Quoted Spread

Event Month

Split Firms

Control Firms

Difference Split - Control

t-stat For Difference

-1 0.0260 0.0245 0.0015 1.60 0 0.0296 0.0253 0.0043 4.11 1 0.0315 0.0257 0.0058 5.58 3 0.0300 0.0269 0.0031 3.07 6 0.0286 0.0279 0.0007 0.69

12 0.0287 0.0287 0.0000 -0.03 18 0.0295 0.0293 0.0002 0.15 24 0.0285 0.0291 -0.0006 -0.48 36 0.0298 0.0313 -0.0014 -0.93 48 0.0278 0.0301 -0.0023 -1.43 60 0.0266 0.0314 -0.0048 -2.80 72 0.0259 0.0307 -0.0047 -2.53

Panel B: Robustness Check

Event Month

Split Firms

Control Firms

Difference Split - Control

t-stat For Difference

-1 0.0283 0.0303 -0.0019 -2.17 0 0.0318 0.0301 0.0017 1.84 1 0.0342 0.0307 0.0035 3.52 3 0.0329 0.0315 0.0015 1.56 6 0.0318 0.0318 0.0000 -0.07

12 0.0319 0.0341 -0.0021 -1.98 18 0.0332 0.0356 -0.0023 -1.91 24 0.0324 0.0348 -0.0024 -2.07 36 0.0337 0.0362 -0.0025 -1.80 48 0.0340 0.0373 -0.0033 -2.07 60 0.0345 0.0407 -0.0062 -3.61 72 0.0341 0.0404 -0.0063 -3.09

Table 3 Analysis of Liquidity Before and After a Split: NYSE and AMEX Stocks

The table reports transactions costs for firms that had a stock split and for a matched sample of control firms. Month 0 is the month in which the split occurred and one is the month immediately following the event. Our sample consists of all firms listed on NYSE and AMEX that had a stock split during the period 1963 through 2003, and had a one year of observations on CRSP before a split. As a proxy for a relative effective spread we use Effective Tick, LOT Y-split and LOT mixed. For each firm with a split we find a matching firm which has the closest transaction cost (percentage effective spread), market capitalization, and 12 month cumulative return, all measured at the end of month -1. These results are reported in Panel A through Panel C for each measure of transaction costs. The difference equals the value of the spread of split firms minus the value of the spread for control firms. The t-statistics test the hypothesis that the difference in transaction costs of split and control firms is different from zero.

Panel A: Effective Tick

Event Month

Split Firms

Control Firms

Difference Split – Control

t-stat For Difference

-1 0.0068 0.0071 -0.0003 -1.35 0 0.0074 0.0083 -0.0008 -4.08 1 0.0089 0.0083 0.0007 3.08 3 0.0087 0.0084 0.0003 1.28 6 0.0088 0.0089 -0.0001 -0.50

12 0.0090 0.0094 -0.0004 -1.78 18 0.0095 0.0104 -0.0009 -2.47 24 0.0096 0.0102 -0.0005 -1.68 36 0.0104 0.0109 -0.0005 -1.09 48 0.0111 0.0113 -0.0002 -0.46 60 0.0120 0.0122 -0.0002 -0.26 72 0.0120 0.0130 -0.0010 -1.68

Table 3—Continued Analysis of Liquidity Before and After a Split: NYSE and AMEX Stocks

Panel B: LOT Y-split

Event Month

Split Firms

Control Firms

Difference Split – Control

t-stat For Difference

-1 0.0134 0.0135 -0.0001 -0.11 0 0.0126 0.0133 -0.0007 -1.25 1 0.0149 0.0138 0.0011 1.65 3 0.0142 0.0134 0.0009 1.31 6 0.0142 0.0146 -0.0004 -0.45

12 0.0134 0.0146 -0.0012 -1.82 18 0.0141 0.0158 -0.0017 -2.43 24 0.0140 0.0152 -0.0012 -1.67 36 0.0150 0.0160 -0.0011 -1.24 48 0.0161 0.0157 0.0004 0.43 60 0.0152 0.0169 -0.0017 -1.97 72 0.0160 0.0180 -0.0019 -2.11

Panel C: LOT mixed Event Month

Split Firms

Control Firms

Difference Split – Control

t-stat For Difference

-1 0.0256 0.0265 -0.0010 -1.17 0 0.0281 0.0262 0.0019 2.69 1 0.0307 0.0264 0.0044 5.56 3 0.0288 0.0261 0.0027 4.10 6 0.0290 0.0274 0.0016 1.76

12 0.0279 0.0282 -0.0004 -0.52 18 0.0293 0.0295 -0.0002 -0.30 24 0.0291 0.0291 0.0000 0.03 36 0.0303 0.0309 -0.0006 -0.57 48 0.0314 0.0306 0.0008 0.87 60 0.0311 0.0316 -0.0004 -0.42 72 0.0335 0.0368 -0.0033 -2.00

Table 4 The Effect of Stock Splits on Liquidity: Regression Analysis for NASDAQ

The table reports the results of Fama-MacBeth (1973) regressions relating transaction costs for a stock to dummy variables that capture past stock splits and control variables. Transaction costs (QS) are measured by relative quoted spread which is defined as a quoted ask price minus quoted bid price divided by the midpoint of the bid and ask prices. The quoted ask and bid prices are from CRSP NASDAQ files. Cross-sectional regression is estimated monthly for the period from January 1988 through December 2003 for all NASDAQ stocks. The regression specification is

εγβββββββα +++++++++= ∑=

n

iiiiiiiiiii CDDDDDDDQS

16,65,54,43,32,21,10,0 ,

where 0D is equal to 1 if a particular stock had a split within 6 months prior to the month for which regression is estimated and zero otherwise, 1D is equal to 1 if the stock had a split between 6 to 12 months ago and zero otherwise, 2D is equal to 1 if the stock had a split between 13 to 24 months ago and zero otherwise, 3D is equal to 1 if the stock had a split between 25 to 36 months ago and zero otherwise,

4D , 5D and 6D are dummy variables which indicate that split occurred between 37 and 48, 49 and 60,

61 and 72 months ago accordingly. The set of control variables, C, includes turnover, stock return and aggregate liquidity. Turnover is defined as trading volume divided by number of shares outstanding. Aggregate Liquidity is equally weighted average of firm-specific relative quoted spreads for each month across all NASDAQ common stocks. Return states for firm-specific return. All data are from CRSP NASDAQ file. t-statistics are reported in parentheses below coefficient estimates.

Specification

Variables (1) (2) (3) 0D : 6 months -0.021

(-1.664) -0.015

(-1.537) -0.015

(-1.537)

1D : 1 year -0.021 (-1.762)

-0.016 (-1.754)

-0.016 (-1.754)

2D : 2 years -0.018 (-2.023)

-0.016 (-2.044)

-0.016 (-2.044)

3D : 3 years -0.015 (-1.977)

-0.014 (-1.999)

-0.014 (-1.999)

4D : 4 year -0.013 (-1.965)

-0.013 (-2.031)

-0.013 (-2.031)

5D : 5 years -0.013 (-1.678)

-0.014 (-1.682)

-0.014 (-1.682)

6D : 6 years -0.017 (-1.612)

-0.016 (-1.709)

-0.016 (-1.709)

Turnover -0.002 (-1.303)

-0.002 (-1.303)

Return -0.022 (-0.592)

-0.022 (-0.592)

Aggregate Liquidity

1.233 (19.386)

Table 5 The Effect of Stock Splits on Liquidity: Regression Analysis for NYSE/AMEX

The table reports the results of Fama-MacBeth (1973) regressions relating transaction costs for a stock to dummy variables that capture past stock splits and control variables. Transaction costs (QS) are measured by effective spread proxies – Effective Tick, LOT Y-split, LOT mixed in Panels A through C accordingly. Cross-sectional regression is estimated monthly for the period from August 1967 through December 2003 for all NYSE/AMEX stocks. The regression specification is

εγβββββββα +++++++++= ∑=

n

iiiiiiiiiii CDDDDDDDQS

16,65,54,43,32,21,10,0 ,

where 0D is equal to 1 if a particular stock had a split within 6 months prior to the month for which regression is estimated and zero otherwise, 1D is equal to 1 if the stock had a split between 6 to 12 months ago and zero otherwise, 2D is equal to 1 if the stock had a split between 13 to 24 months ago and zero otherwise, 3D is equal to 1 if the stock had a split between 25 to 36 months ago and zero otherwise,

4D , 5D and 6D are dummy variables which indicate that a split occurred between 37 and 48, 49 and 60, 61 and 72 months ago accordingly. The set of control variables, C, includes turnover, stock return and aggregate liquidity. Turnover is defined as trading volume divided by number of shares outstanding. Aggregate Liquidity is equally weighted average of firm-specific liquidity estimates for each month across all NYSE/AMEX common stocks computed with Effective Tick, LOT Y split and LOT mixed in Panels A, B and C respectively. Return states for firm-specific return. All data are from CRSP NYSE/AMEX files. t-statistics are reported in parentheses below coefficient estimates.

Panel A. Effective Tick

Variables (1) (2) (3)

0D : 6 months -0.009 (-1.847)

-0.008 (-1.802)

-0.007 (-1.845)

1D : 1 year -0.009 (-1.844)

-0.008 (-1.782)

-0.007 (-1.828)

2D : 2 years -0.008 (-1.750)

-0.007 (-1.701)

-0.007 (-1.736)

3D : 3 years -0.006 (-1.682)

-0.006 (-1.650)

-0.005 (-1.668)

4D : 4 year -0.005 (-1.507)

-0.005 (-1.551)

-0.004 (-1.527)

5D : 5 years -0.005 (-1.651)

-0.005 (-1.652)

-0.004 (-1.581)

6D : 6 years -0.004 (-1.419)

-0.004 (-1.398)

-0.004 (-1.212)

Turnover -0.001 (-0.869)

-0.001 (-0.868)

Return -0.012 (-0.421)

-0.012 (-0.416)

Aggregate Liquidity

1.109 (9.109)

Panel B. LOT Y-split Variables (1) (2) (3)

0D : 6 months -0.011 (-1.797)

-0.010 (-1.768)

-0.010 (-1.768)

1D : 1 year -0.010 (-1.881)

-0.010 (-1.792)

-0.010 (-1.792)

2D : 2 years -0.009 (-1.731)

-0.009 (-1.701)

-0.009 (-1.701)

3D : 3 years -0.007 (-1.721)

-0.007 (-1.683)

-0.007 (-1.683)

4D : 4 year -0.006 (-1.385)

-0.006 (-1.400)

-0.006 (-1.400)

5D : 5 years -0.005 (-1.345)

-0.005 (-1.338)

-0.005 (-1.338)

6D : 6 years -0.005 (-1.082)

-0.005 (-1.040)

-0.005 (-1.040)

Turnover -0.001 (-0.684)

-0.001 (-0.684)

Return -0.001 (-0.029)

-0.001 (-0.029)

Aggregate Liquidity

1.089 (3.911)

Panel C. LOT mixed

Variables (1) (2) (3) 0D : 6 months -0.014

(-1.653) -0.013

(-1.686) -0.013

(-1.686)

1D : 1 year -0.014 (-1.897)

-0.013 (-1.815)

-0.013 (-1.815)

2D : 2 years -0.013 (-1.768)

-0.012 (-1.754)

-0.012 (-1.754)

3D : 3 years -0.010 (-1.669)

-0.010 (-1.668)

-0.010 (-1.668)

4D : 4 year -0.008 (-1.374)

-0.008 (-1.415)

-0.008 (-1.415)

5D : 5 years -0.008 (-1.420)

-0.007 (-1.400)

-0.007 (-1.400)

6D : 6 years -0.007 (-1.188)

0.007 (-1.128)

-0.007 (-1.128)

Turnover -0.0003 (-0.165)

-0.0003 (-0.165)

Return 0.010 (0.145)

0.010 (0.145)

Aggregate Liquidity

1.034 (6.726)

Figure 1.a T-statistics for a difference in quoted percentage spreads between split and non-split NASDAQ firms

-4

-2

0

2

4

6

-3 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72

t-st

atis

tics

t-statistics 10% Confidence 5% Confidence t-stats (robustness)

Figure 1.b A difference in quoted percentage spreads between split and non-split NASDAQ firms

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

-3 3 9 15 21 27 33 39 45 51 57 63 69

diff diff (robustness)

Figure 2.a T-statistics for a difference in effective percentage spreads between split and non-split NYSE/AMEX firms

-4.1

-2.1

-0.1

1.9

3.9

5.9

-3 3 9 15 21 27 33 39 45 51 57 63 69

t-sta

tistic

s

T-stat-Effective Tick T-stat-LOT Y-split T-stat-LOT-mixed 10% Confidence 5% Confidence

Figure 2.b A difference in effective percentage spreads between split and non-split NYSE/AMEX firms

-0.004

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

-3 3 9 15 21 27 33 39 45 51 57 63 69

Diff-Effective Tick Diff-LOT Y-split Diff-LOT-mixed

Appendix - Table A1. Stock Splits by Year: NYSE and AMEX Stocks

The table presents the number of splits by year. The split sample consists of all stock splits during the period from 1964 to 1998 recorded in CRSP NYSE/AMEX database. Split announcement dates are the declaration dates obtained from CRSP. The stock splits are required to meet the following criteria: (i) Market capitalization data, liquidity estimate and cumulative 12 month return are available at the end of month t-1, where month t is the month the split takes effect; (ii) the splitting shares are ordinary common shares (we omit ADRs, SBIs, REITs, and closed-end funds); (iii) at least 72(12) months of data is available at the period subsequent (preceding) to the split; (iv) stock splits which occur during 72 months after the first split are not included.

Year Splits Year Splits

1964 71 1981 89 1965 81 1982 35 1966 116 1983 99 1967 67 1984 77 1968 124 1985 58 1969 99 1986 106 1970 19 1987 101 1971 42 1988 46 1972 51 1989 52 1973 44 1990 40 1974 31 1991 31 1975 37 1992 59 1976 79 1993 62 1977 74 1994 46 1978 91 1995 75 1979 55 1996 71 1980 84 1997 81

Appendix - Table A2. Analysis of Liquidity Before and After a Split: NYSE and AMEX Stocks

The table shows effective spread proxies for the split firms and firms in the non-split control sample by event month. The results are reported in Panel A through Panel C for Effective Tick, LOT Y-split and LOT mixed measures respectively. Zero is the event month, minus one is the month preceding the event, and one is the month immediately following the event. The difference (Diff) equals the value of the effective spread proxy of split firms minus the value for control firms. Our sample consists of all firms listed on NYSE and AMEX that had a stock split during the period 1964 through 1997. Split firms that had less then one year of observations before the split month and less then 72 months of observations after the split month on CRSP NYSE/AMEX files are filtered out. The splits occurred during after-event window (during 72 months after the first split) are ignored. For each firm with a split we find a matching firm which has the closest transaction cost (percentage effective spread), market capitalization, and 12 month cumulative return, all measured at the end of month -1. The t-statistics test the hypothesis that the difference in transaction costs of split and control firms is different from zero.

Panel A: Effective Tick Event Month

Split Firms

Control Firms

Difference

t-stat For Difference

-1 0.0067 0.0071 -0.0003 -0.87 0 0.0074 0.0083 -0.0009 -2.94 1 0.0089 0.0082 0.0007 2.09

12 0.0091 0.0092 -0.0001 -0.14 24 0.0098 0.0094 0.0004 1.16 36 0.0104 0.0108 -0.0004 -0.72 48 0.0113 0.0114 -0.0001 -0.26 60 0.0122 0.0135 -0.0013 -1.72 72 0.0120 0.0130 -0.0010 -1.68

Panel B: LOT Y-split Panel C: LOT Mixed

Event Month

Split Firms

Control Firms

Difference

t-stat For Difference

Event Month

Split Firms

Control Firms

Difference

t-stat For Difference

-1 0.0133 0.0122 0.0011 0.94 -1 0.0250 0.0259 -0.0009 -0.76 0 0.0122 0.0131 -0.0009 -1.07 0 0.0275 0.0263 0.0012 1.10 1 0.0153 0.0128 0.0025 2.50 1 0.0310 0.0258 0.0052 5.01

12 0.0132 0.0134 -0.0001 -0.18 12 0.0282 0.0273 0.0009 0.97 24 0.0138 0.0135 0.0003 0.43 24 0.0290 0.0276 0.0015 1.67 36 0.0149 0.0153 -0.0003 -0.42 36 0.0302 0.0302 0.0000 0.01 48 0.0161 0.0160 0.0002 0.19 48 0.0316 0.0308 0.0008 0.72 60 0.0154 0.0172 -0.0018 -2.05 60 0.0314 0.0338 -0.0024 -1.96 72 0.0160 0.0180 -0.0019 -2.11 72 0.0335 0.0368 -0.0033 -2.00