J. Japanese Int. Economies 22 (2008) 417–438
www.elsevier.com/locate/jjie
Stock splits, liquidity, and information asymmetry—
An empirical study on Tokyo Stock Exchange
Fang Guo a , Kaiguo Zhou b,∗ , Jinghan Cai c
a Department of Marketing Operation, Top Glory International Holdings Limited, Top Glory Tower,
262 Gloucester Road, Causeway Bay, Hong Kong, China
b Department of Finance, Lingnan College, Sun Yat-sen University, Guangzhou 510275, China
c Research Institute, Shenzhen Stock Exchange, Futian District, Hongli (west) Road, Shangbu Industrial Zone, Bldg. 10,
Shenzhen 518028, China
Received 27 June 2007; revised 20 January 2008
Available online 12 February 2008
Guo, Fang, Zhou, Kaiguo, and Cai, Jinghan—Stock splits, liquidity, and information asymmetry—An
empirical study on Tokyo Stock Exchange
This paper comprehensively studies the effects of stock splits on the market characteristics of the stocks
and also tries to give an explanation for the results referring to the existing hypotheses and previous empirical results. We investigate the trading activity, liquidity, information asymmetry, and the investors’ behavior
changes around the stock splits. We find that the stock splits tend to increase the trading activity, to enhance the market liquidity, to reduce the information asymmetry, and to lower the probability of informed
trading. Several main existing explanations—signaling hypothesis, trading range hypothesis, and tick size
hypothesis—are largely supported by our empirical findings. J. Japanese Int. Economies 22 (3) (2008) 417–
438. Department of Marketing Operation, Top Glory International Holdings Limited, Top Glory Tower, 262
Gloucester Road, Causeway Bay, Hong Kong, China; Department of Finance, Lingnan College, Sun Yatsen University, Guangzhou 510275, China; Research Institute, Shenzhen Stock Exchange, Futian District,
Hongli (west) Road, Shangbu Industrial Zone, Bldg. 10, Shenzhen 518028, China.
© 2008 Elsevier Inc. All rights reserved.
JEL classification: G12; G14; G32
Keywords: Stock splits; Liquidity; Information asymmetry; Tokyo Stock Exchange
* Corresponding author. Fax: +86 20 84114823.
E-mail addresses: [email protected] (F. Guo), [email protected] (K. Zhou), [email protected] (J. Cai).
0889-1583/$ – see front matter © 2008 Elsevier Inc. All rights reserved.
doi:10.1016/j.jjie.2008.01.002
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F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
1. Introduction
The event of stock split is a very popular phenomenon in the equity market, yet it is also one of
the least understood corporate events. At first glance the split only changes the number of shares
outstanding of a firm, leaving the fundamentals unchanged. Since it will not affect the intrinsic
value, the cash flow, or the relative strength of any interested party of the firm, there should be no
motivation for the firm to split its shares. Even if the firm does split its stocks, there should be no
significant change to the firm’s value or trading characteristics. Why, then, does a rational firm
bother to take action to increase its outstanding shares when doing so will incur costs without
bringing any profit? The question needs further study to uncover more evidence on the effects of
stock splits.
Up to now, there are three main hypotheses proposed to explain the effects of stock splits: the
signaling hypothesis, the trading range hypothesis, and the tick size hypothesis. The signaling
hypothesis states that the management intends to transmit good information about the company’s future performance to the public. The trading range hypothesis argues that the management
would like to bring the stock price into a certain optimal range and hence the stability and liquidity of the stock will improve after a split due to an increase in the ownership base. The tick size
hypothesis regards stock split as a method for keeping the tick size relative to the stock price at
an optimal level.
Most of the previous studies on stock split are conducted in the US markets, while little evidence has been provided from Asian markets. The Tokyo Stock Exchange (TSE) is the biggest
stock market in Asia and attracts worldwide attention. Meanwhile, stock splits are very common
in this market. Therefore, it is necessary to conduct a study on TSE and to provide more evidence
on the effects of stock splits. The motivation of this study is to conduct a comprehensive empirical study on the trading characteristics and changes in traders’ behavior around stock splits by
investigating cases from the Tokyo Stock Exchange. This paper contributes to the literature by
providing non-US evidence. With the empirical results, we try to explain the effects with respect
to changes in investors’ behavior and to link the results to the existing hypotheses in order to
verify whether they are supported or not. The second, also the greatest, contribution of this paper
is to harmonize the three existing hypotheses with the empirical evidence from TSE.
We will focus on three aspects of effects induced by stock split: trading activity, liquidity, and
information asymmetry. Our empirical results are as follows.
First, the results show that both the number of quotations and the number of trades increase
significantly after stock splits, while the trade size decreases significantly and there is no significant change in the daily trading volume. Meanwhile, the quoted depth decreases significantly.
The findings imply that the stocks are traded more actively only on small trades after stock splits.
Second, the results about liquidity show that the absolute quoted spread, the absolute effective
spread, the relative quoted spread and the relative effective spread all decrease significantly after
stock splits, while the quoted depths at both sides decrease significantly. When the spread and
depth are combined into the quality index to measure the liquidity change, it is shown that the
liquidity is enhanced after stock splits.
Next, the information asymmetry is studied. The results show that the adverse-selection component decreases significantly after stock splits, which supports the trading range hypothesis,
which predicts that the reduction in price due to the splits attracts more small investors.
Finally, although both the informed and the uninformed traders increase significantly after
stock splits, the probability of informed trading (PIN) decreases, because compared with the informed traders, more uninformed traders join to trade after stock split. Therefore, the increase in
F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
419
the information asymmetry caused by the informed trades are offset or overwhelmed by the
decreasing effects caused by the uninformed trades. As the information asymmetry and the
probability to meet the informed traders are reduced after splits, the market makers or liquidity
providers are facing less risk. This decreased risk is reflected on the decrease in bid–ask spread.
So all the empirical results are consistent and can be explained soundly from the perspective of
the investors’ behavior change.
These empirical findings provide strong evidence for the effects of stock splits on Tokyo Stock
Exchange. The findings indicate that the events really affect the stocks’ quality. Moreover, it is
the change in the investors’ behaviors that causes the change in the market characteristics of the
stocks. These findings also prove that the firms may split their stocks due to multi-faceted reasons
because all existent hypotheses are supported by the empirical results in this study.
The rest of this paper is organized as follows. Section 2 is the literature review. Section 3
describes the data and methods adopted in this study. The empirical results and explanations are
presented in Section 4. Discussion and conclusions are given in Section 5.
2. Literature review
Fama et al. (1969) take advantage of the opportunity of stock split to study the market efficiency on the adjustment of stock price to new information. It is regarded as the first research to
study the effects of stock splits. Since then, a large number of researchers have contributed their
efforts to this study. There are two main schools of thought on this topic. One is the motivation of
the management to split the stocks. The other concentrates on the effects of stock split on market
characteristics.
There are mainly three explanations on firms’ motivation for splitting stocks: signaling hypothesis, trading range hypothesis (or liquidity hypothesis), and tick size hypothesis. The signaling hypothesis is formed after observing the abnormal announcement returns following stock
split. It says that the management is sending a signal to the market that the firm is expected to
enjoy an income increase or that the firm’s value is underestimated. The trading range hypothesis
argues that the manager intends to bring the stock price to an optimal range by splitting stocks
and consequently to increase the stock’s market liquidity. The tick size hypothesis states that the
manager tends to split its stocks so that the minimum tick size is optimal relative to the stock
price.
The effects of stock split on market characteristics mainly focus on the abnormal return and
liquidity. Many studies have found that there are positive excess returns around announcement
day and effective day and that the trading volume increases significantly. These findings support
the signaling hypothesis. However, some studies have observed that the bid–ask spreads increase
significantly, which contradicts the liquidity enhancement hypothesis.
2.1. Signaling hypothesis
The empirical studies on stock splits by Fama et al. (1969), Bar-Yosef and Brown (1977), and
Charest (1978) find abnormal returns around the announcement day, which supports the signaling
hypothesis. According to the signaling model of Spence (1973), Ross (1977), Leland and Pyle
(1977) and Bhattacharya (1979), the financial decisions of the management convey information
about the firm value. This hypothesis assumes that the information between managers and investors are asymmetric and by splitting stocks the managers intend to convey good information
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to investors. This hypothesis also states that the managers are confident in their company’s future
earnings and will push the stock price upward.
Grinblatt et al. (1984) study the valuation effects of stock splits and stock dividends. They
conclude that some of the information content of stock split and stock dividend appears to be
associated with firms’ future cash flows or their future earnings or their equity values. Lamoureux
and Poon (1987) study the abnormal return and trading volume after the stock split. Their findings
of the positive cumulative abnormal return and the increase in raw trading volume after the
announcement also provide evidence to support the signaling hypothesis.
To support the signaling hypothesis, McNichols and Dravid (1990) test whether the stock
dividends and splits convey information about company’s future earnings and also test whether
the split factor acts as a signal. They use the analysts’ earnings forecast error, measured as the
percentage difference between the after-split annual earnings reported and the median analysts’
before-split earnings forecast, as a proxy for management’s private information. The result shows
that when pre-split stock price and market value of equity are controlled, the correlation between
split factors and earnings forecast errors is significant. This suggests that the choice of split factor
contains the management’s private information about future earnings. This result also supports
the signaling hypothesis.
Building their theory on the assumption that trading is costly, Brennan and Copeland (1988)
develop a two-period signaling model of stock splits to explain the abnormal return. They conclude that management can convey private information about the firm’s prospects to investors
through a stock split announcement because the cost of trading depends on the stock price.
Brennan and Hughes (1991), Ikenberry et al. (1996), and Conroy and Harris (1999) also find
evidences to support the signaling hypothesis.
Though the signaling hypothesis can be supported by empirical studies, it remains a puzzle
why companies split their stocks. There shall be no price limit on a stock, and other devices (such
as dividend) can also be adopted to issue the good signal. Furthermore, empirical research has
documented negative effects after splits, such as a larger relative bid–ask spread and a higher
level of information asymmetry. In addition, the signaling hypothesis cannot explain why excess
returns are also observed around the ex-split date since the ex-split date is predictable following
the split announcement and there should be no information content on the ex-date. So researchers
provide other explanations for stock split. Grinblatt et al. (1984), Maloney and Mulherin (1992)
explain the excess returns from the viewpoint of microstructure and suggest the liquidity-based
explanation for stock splits, and this induces the second hypothesis.
2.2. Trading range hypothesis
Copeland (1979) argues that firms prefer to keep the prices of their stocks within a certain
range. He explains that keeping a certain price range can attract a specific kind of clientele or
disperse the ownership of the company. The kind of clientele attracted by the lower prices brought
about after a stock split is usually considered to be uninformed or small investors. Baker and
Gallagher (1980) make a survey on managements’ views on stock split. The survey reveals that
the majority of a firm’s financial officers believe that the stock split is a good device to bring
the stock price to an optimal trading range. A lower stock price will attract investors and then
enhance the ownership base. Evidence has been found to support this hypothesis. Lamoureux
and Poon (1987) find that the daily number of transactions along with the raw trading volume of
shares increases following splits. Kryzanowski and Zhang (1996) make use of the trading value
to measure small and large traders and find that small traders trade more frequently after stock
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421
split and that the trade direction changes significantly from sell to buy. Angel et al. (1997), Desai
et al. (1998), and Schultz (2000) also find evidence of changes in trading behavior after stock
splits.
But why would a company want to attract small or uninformed traders to invest in its stocks?
One of the most popular explanations is that the enlarged investor base will increase the liquidity
of the stock and thereby reduce the trading cost for the investors. Therefore, the motivation of the
managers to split stocks is to enhance liquidity. From the viewpoint of liquidity, the trading range
hypothesis is also called “liquidity hypothesis.” Merton (1987) sets up a model of capital market
equilibrium with incomplete information. The model indicates that an increase in the relative size
of the firm’s investor base will reduce the firm’s cost of capital and increase the market value of
the firm. It is also stated that managers have incentives to expand the firm’s investor base. This
theory can explain the reaction of stock prices to stock splits. Because lower prices attract small
investors to take part in buying or selling stocks after a split, the liquidity of the stock increases.
Small traders are also considered as noise traders in contrast to informed traders. Black (1986)
states that noise trading is essential to the existence of liquid markets, and the more noise trades
there are, the more liquid the markets will be.
There are many kinds of measures of liquidity, but the most frequently used ones include trading volume, bid–ask spread, depth, and number of trades. The proxies can be classified into two
categories: indicators of friction and activity, which are the two dimensions of liquidity. Friction
is defined by Demsetz (1968), Grossman and Miller (1988), Stoll (2000) as the price continuity
for immediacy. Activity reflects the extent of trading. The bid–ask spread can be categorized as
a friction measure. In contrast, the depth, volume, number of trades and transaction value can
be classified as activity measures. Using different proxies for liquidity, the empirical results on
the impact of stock splits point to different conclusions. Some support the liquidity enhancing
hypothesis, while others contradict it.
Copeland (1979) takes both trading volume and bid–ask spread as measures of liquidity in
studying the 162 OTC firms for the period 1968–1976. The results show that the trading volume
is proportionately lower after split while the post-split bid–ask spread increases significantly as
a percentage of the stock price, meaning that the liquidity of the stock decreases after split. But
Murray (1985) finds no evidence of a change in percentage spread relative to a control group
by studying 100 OTC splitting firms during the period 1972–1976. Lakonishok and Lev (1987)
take the monthly shares traded relative to the shares outstanding as the measure of a stock’s
marketability and find that the result does not support a decrease in marketability. Lamoureux
and Poon (1987) study the stock’s factor-adjusted trading volume relative to the market’s trading volume after stock split, and the result shows that 87 sample stocks’ market-adjusted and
factor-adjusted trading volume decreased significantly while that of 27 sample stocks showed a
significant increase. They conclude that the value of shares traded fell following the ex-split day.
Conroy et al. (1990) also take absolute spreads and percentage spreads as measures of liquidity, but they employ high-quality inside quotes, which capture the lowest ask and highest
bid that would have been available to an investor. Their empirical results show that liquidity decreases after stock splits as measured by the percentage bid–ask spread. Although the
absolute spread decreases after split, the drop in price is sufficient to offset the decrease in absolute spread and leads to an increase in the percentage spread. The conflict in the results of
liquidity change after split mainly originates from the difference in measures adopted by the
researchers.
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2.3. Tick size hypothesis
This hypothesis suggests that stock splits will create an optimal tick size for stocks, and that
this optimal tick size will attract liquidity providers to take part in transactions. The liquidity
providers are regarded as uninformed traders who can gain from supplying liquidity via limit
orders.
Angel (1997) uses the minimum price variation to explain the price change around the stock
split. He states that the management tends to keep the tick size relative to the stock price at an
optimal level. If the relative tick size is larger than optimal, the company will allow the long-term
upward trend of stock prices to reduce it to the desired level. When the relative tick size is too
small, the stock split can be adopted to increase it back to the optimal level. As Harris (1991)
notes, tick size cannot be zero for the reason that the tick simplifies traders’ information sets
and reduces time spent on bargaining and the potential for costly errors. Also. the nonzero tick
enforces time and price priority in a limit order book, and provides an incentive for investors to
provide liquidity with limit orders. Furthermore, the tick also provides an incentive for dealers
to make market. However, the enlarged tick also increases the trading cost and offsets the liquidity gains from dealers’ perspective. The optimal tick is the trade-off between the benefits of a
nonzero tick and the cost that a tick imposes.
By combining the Merton’s (1987) model of an incomplete information capital market with
Amihud and Mendelson’s (1986) finding that higher bid–ask spreads are associated with higher
rates of return, Angel (1997) constructs a model in which the increase in the number of investors
who know about a stock tends to increase the stock price while a higher transaction cost due to
the increase of tick size depresses the stock price. The solution to this model is that the optimal
relative tick size can balance these effects. The result shows that the tick size can explain partially
why stock price levels differ across countries. Since the rule on tick size varies across countries,
the optimal trading range varies accordingly. However, the relative tick size is comparable from
country to country.
After Angel (1997), the results of some other researchers directly or indirectly support Angel’s (1997) conclusion that the wider percentage bid–ask spread stimulates brokers to promote
the stock. Schultz (2000) provides evidence that according to measures of percentage effective
spreads market making is more profitable following splits. Moreover, the increase in the number
of small buy orders following splits proves the traditional explanation that the shareholder base
of stock increases after splits. Some other studies such as Lamoureux and Poon (1987), Maloney
and Mulherin (1992), and Angel et al. (1997) show evidence that the number of shareholders
increases after splits, which supports Angel’s (1997) argument that a large relative tick size gives
brokers more incentives to promote the stock.
2.4. Information asymmetry argument
One of the arguments for the reason that companies split their stocks, though it may not be
regarded as a hypothesis, is the reduction of information asymmetry. Grinblatt et al. (1984) argue
that managers use stock splits or stock dividends to convey good information to the market or
just call attention to the firm to trigger reassessments of the firm’s future cash flows by market
analysts. The consequence of the information-leakage or attention-attraction will be the reduction
of the information asymmetry existing between the managers and investors.
But does more information-leakage result in the reduction of information asymmetry? Desai et
al. (1998) argue that the change in trading activity would affect the adverse-selection component
F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
423
of the bid–ask spread. The increase in noise trading will reduce the adverse-selection component,
while an increase in informed trading will increase this component. If both types of traders
increase, the effects on the adverse-selection component will be complex and unpredictable. They
adopt the method proposed by George et al. (1991) to decompose the total spread into the orderprocessing and adverse-selection components. They find that the adverse-selection component
increased by 0.17 or 22% following splits and thus conclude that the information asymmetry is
not reduced after splits. Actually, their finding implies that informed trading increases. Thus, it
is not clear whether the information environment of the firm following a split is characterized by
higher or lower information asymmetry before the behavior of uninformed traders is investigated.
But at least the technique of decomposing the spread is a method to test whether the information
asymmetry does change or not.
The decomposition of the bid–ask spread can only give information on the change of adverseselection component after splits. As to the change in composition of the trading population, it is
not so easy to give a conclusion. With this intention of trying to discover trading activity, but not
for the event of splits, researchers developed a microstructure model used to calculate the rates
of informed and uninformed trading, and the probability of information events. This method is
commonly called PIN value calculation.
Easley et al. (1996) develop an approach using the trading flow information to infer the
difference in information content between trading locales. This approach is used to test the
cream-skimming versus competition issue. Easley et al. (2001) use this method to test alternative hypotheses concerning the stock splits. Their model is an extension of the model of Easley
et al. (1996) and is used to estimate the underlying parameters that define trading activity. The
main parameters are the rates of informed and uninformed trading, the probability of information events, and the propensity to execute trading strategies using limit orders. As they state,
when analyzing stock splits using the trading data will sacrifice some of the non-trade related
implications of the explaining hypotheses, because any signaling-related effects of splits may be
immediately reflected in prices, and thus would not be reflected in trades. They find that both
uninformed and informed trading activities increase after the split and there is a small decrease
in the percentage of informed trades or PIN.
The model proposed by Easley et al. (2001) is based on the quote-driven market in which
there are more than one market-makers participating in competition. But this model can also
be adopted in the order-driven market in which liquidity is provided by the traders who submit
the limit-orders and the trader plays the role of market-maker, as in the quote-driven market.
Moreover, the competition on price also exists between traders. Empirical research has been
conducted on the latter market. Ahn et al. (2005) adopt this method in studying the event of
minimum trading unit (MTU) change on the Tokyo Stock Exchange which is an order-driven
market.
3. Data and methodology
3.1. Data
The basic sample is comprised of all Tokyo Stock Exchange (TSE) common stocks that have
split with a factor greater than 1.5 from January 1996 to December 2005 and that have a price
less than JP Yen 30,000 before split. We do not include the stocks with split factor of less than
1.5 because such cases are similar to stock dividends, which are not our study object. Besides,
we exclude the stocks with price over JP Yen 30,000 because the extremely high price would
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distort our later results, especially on relative spreads. The split sample is provided by the TSE
and we confirm the event by checking with the corresponding splits data from the Bloomberg
News Service and eliminate 10 firms due to the discrepancy in announcement date, effective date
or split factor. In order to avoid the effects of the previous split on the consequent split of the
same stocks, 3 more stocks are deleted from the sample because the interval between the stock’s
two splits is less than 8 calendar months. There remain 138 stock splits in our final sample.
The corresponding tick data are obtained from the Nikkei Economic Electronic Database System
(NEEDs).
3.2. Estimation windows
In a typical event study the pre-event period is usually set prior to the announcement day,
while post-event period begins on some spot after the effective day. In our case, the pre-split
window is [−69, −10] trading days prior to the split announcement (see Conroy et al., 1990) in
order to avoid other events such as stock dividends and mergers contaminating the effects of the
stock splits. Correspondingly, the post-split period is [10, 69] trading days after the effective day.
However, we adopt a 120-day window in PIN estimation.
3.3. Definition of measures
3.3.1. Bid–ask spread
In this study we adopt four types of bid–ask spreads: absolute quoted spread, absolute effective
spread, relative quoted spread and relative effective spread. Absolute quoted spread is defined as
the dollar difference between the ask and bid. Absolute effective spread is defined as twice the
absolute difference between the trade price (Pt ) and the quote midpoint (Mt ).1 The relative
quoted spread is the absolute quoted spread scaled by the quote midpoint. The relative effective
spread is the absolute effective spread scaled by the transaction price.
Absolute Quoted Spread = Ask − Bid
(1)
Absolute Effective Spread = |Pt − Mt | ∗ 2
(2)
Relative Quoted Spread = (Absolute Quoted Spread)/Mt
(3)
Relative Effective Spread = (Absolute Effective Spread)/Pt
(4)
3.3.2. Quality index
The quoted depth is also adopted in this study as a measure of liquidity. The spread and depth
are two dimensions of liquidity. The spread measures the price dimension of liquidity, while the
depth measures the quantity dimension of liquidity. In order to integrate the two dimensions into
one, we adopt the quality index (QI), proposed by Gray et al. (2003), to measure the market
quality. A larger quality index means higher liquidity. The quality index is calculated as follows:
QI t =
(depth_at_bidt + depth_at_askt )/2
relative_quoted_spreadt × split_adjustment
(5)
1 In a pure order matching system in which trades should always go off at the bid or the ask price. However, on the
TSE, market orders are allowed to cross each other. Therefore, it is possible that a market order is executed inside the
spread. That is why we introduce both absolute quoted spread and absolute effective spread. See also Ahn et al. (2007).
F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
425
3.3.3. Decomposition of the bid–ask spread
In this paper we adopt Glosten and Harris (1988) model to decompose the spread into two
components.2 The first one is the transitory component which is to cover the inventory costs,
clearing fees, and/or monopoly profits that are required of the market-makers. The second one is
called adverse-selection component which is an additional widening of the spread to compensate
the loss aroused from the market-makers’ trading with informed traders. Although the model
is based on the market-makers, their methodology can also be adopted in a pure order-driven
market. In fact, each limit-order trader in an order-driven market plays the role of market maker
as in a quote-driven market.
Here we briefly describe the two-component asymmetric information spread model. The
change in transaction price at time t is denoted as Dt = Pt − Pt−1 , where Pt indicates the
transaction price at time t , and Pt−1 indicates the previous transaction’s price. Qt is defined
as the buy–sell indicator variable for the transaction. We let Qt = +1 if the transaction is
buyer initiated and −1 if the trade is seller initiated. The share volume of trade at time t is
denoted as Vt . α is the transitory spread component, β is the adverse-selection component, and
μt is the error term. With the trading data mentioned above, the following equation is used to
estimate the transitory component or order-processing component and adverse-selection component.
Dt = α(Qt − Qt−1 ) + βQt Vt + μt
(6)
We use Generalized Method of Moments (GMM) to estimate the parameters of Eq. (6) because it imposes very weak distribution assumptions. This is especially important when the error
term includes rounding errors due to discreteness of stock prices (see Ahn et al., 2002).
To facilitate the estimation, we adopt the stocks that have trading data for at least 20 valid
trading days. A valid trading day must have no less than five valid transactions. When counting
the valid transactions, we exclude the opening and closing trades for the morning and afternoon
sessions, and the transactions against special quotes as well.
3.3.4. Probability of informed trading
Easley et al. (1996) develop a method for estimating the probability of informed trading (PIN).
In this model, the informed and uninformed investors trade a single risky asset with the risk
neutral market maker, and the price of the asset is set as equal to the expected value of the asset.
The information events happen prior to the beginning of any trading day and they are thought to
be independently distributed and to occur with probability α. This information event is bad news
with probability δ, and good news with probability of 1 − δ. Trades arrive according to a Poisson
process, with uninformed trades arriving at the rate of ε, and informed trades arriving at the rate
of μ. All of these arrival processes are assumed to be independent.
According to the results of Easley et al. (1996), the PIN is defined as:
PIN(t) =
μ(1 − Pn (t))
μ(1 − Pn (t)) + 2ε
(7)
2 There are two classes of statistical models. The first one relies on the serial covariance properties of the observed
transaction prices (see Roll, 1984; Lin et al., 1995; and Huang and Stoll, 1997). And the second class is based on the
trade initiation indicator variables (see Glosten and Harris, 1988; Madhavan and Smidt, 1991). As the trade direction is
clearly indicated in the dataset from the NEEDs, the trade indicator model is more appropriate in this study.
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Where Pn (t) represents the probability of no information event happening at time t . If the
parameters of θ = (α, δ, ε, μ) are known, the PIN can be easily calculated.
The parameters can be estimated using the MLE method from the structural model, which
extracts information on the parameters from the observable number of buys and sells. Though
the Poisson processes followed by the buys and sells are not known, the trading data reflect the
information structure: more buy orders on the days with good news; more sell orders on the days
with bad news; and fewer orders on the days with no news. Thus, the data on buys and sells (B, S)
will be enough to estimate the order arrival rates. Weighting the likelihood of the observed orders
with the probabilities of each type of day occurring (1 − α, αδ, α(1 − δ)), we get the likelihood
function as follows:
(εT )B −εT (εT )S
e
L (B, S) | θ = (1 − α)e−εT
B!
S!
B
(εT
)
[(μ + ε)T ]S
+ αδe−εT
e−(μ+ε)T
B!
S!
B
(εT )S
−(μ+ε)T [(μ + ε)T ]
+ α(1 − δ)e
(8)
e−εT
B!
S!
Where T is the number of time intervals in each day. With the data of buys and sells (B, S),
the estimation of the arrival rates of informed and uninformed traders can be found.
Trade data are taken from the NEEDs Daily Summary data. We take the 120 trading days as
the observation window. Again, we adopt the stocks that have trading data for at least 20 valid
trading days, and have no less than five valid transactions in each trading day. Two out of the 138
samples are dropped out because the results are not convergent.
4. Empirical results and explanations
4.1. Sample description
The distribution of the 138 samples across different years from 1996 to 2005 with different
factors is listed in Table 1. The split occurred only once in 1996, and the number increased to 13
in 1999. In the following 6 years it fluctuated from 13 times to 23 times. It reached its highest
value of 41 times in 2004.
The factors adopted by the companies range from 1.5 to 10. We can find the most frequently
adopted factor by the companies is 2 and the number of samples reaches 85. Factors of 1.5 and 3
are also what companies prefer to choose, and the total number of events is 47. These three
factors account for 95.7% of the total splits. There are 4 samples that split their stocks with a
factor equal to or larger than 10.
Fig. 1 plots the time interval between the announcement day (AD) and effective day (ED) for
the 138 samples. The time intervals are classified into 7 groups: no more than 10 days, greater
than 10 days but no more than 20 days, and so on. The longest interval is greater than 60 days.
Most of the samples take splits in effect in less than 40 days after announcing them. The mean
of the time interval is 32 days, and the median is 26 days. The minimum value is 7 days and the
maximum is 117 days.
The Tokyo Stock Exchange classifies the listed companies into 9 industries. The frequency
distribution of stock splits by industry is presented in Table 2. It can be seen that splits happen in
seven of the nine industries but concentrate on three industries (Manufacturing, Wholesale and
Retail, and Service). It shows that the sample is basically representative for the firms on TSE.
F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
427
Table 1
Summary of splits
Year
Factor
1.5
1996
1999
2000
2001
2002
2003
2004
2005
Total
6
7
8
4
3
8
4
40
2
7
6
9
9
10
29
15
85
3
4
2
2
3
7
1
1
2
10
Total
1
1
13
13
17
16
14
41
23
138
1
1
1
4
This table presents the distribution of stock splits by year and by factor. The sample includes 138 events of stock splits
that took place between March 1996 and December 2005 on Tokyo Stock Exchange. The factor ranges from 1.5 to larger
than 10.
This figure gives an illustration of the distribution of the time intervals between announcement day (AD) and effective
day (ED) of the total 138-split sample.
Fig. 1. Frequency distribution of splits by time interval.
The stocks at Tokyo Stock Exchange are well-known for their high prices. Table 3 gives a
basic description on the stock prices before and after the split. This description is based on the
average closing trading price of the last two trading days before announcement day and the
consequent two trading days after effective day. The mean of the stock price is 535,307 JP Yen
before the split announcement and 182,887 JP Yen after the split. The high stock price gives
some explanation on the high absolute spread in the coming section. Also, we can observe from
Table 3 a large price drop around the stock split.
428
F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
Table 2
Industry distribution of the sample stocks
Industry
No. of stocks
Construction
Manufacturing
Wholesale and retail
Financial and insurance
Real estate
Transportation and communication
Service
Total
1
46
39
6
10
1
35
138
This table presents the frequency distribution of the studied sample by the industry that they are classified into. The Tokyo Stock Exchange divides stocks into 9
main industries. The splits cover 7 of them.
Table 3
Stock price description
Number of observations
Mean
Median
Standard deviation
Maximum
Minimum
Upper quartile 75%
Lower quartile 25%
Pre-split
Post-split
138
535,307
15,160
1,485,538
10,300,000
462
493,000
4905
138
182,887
6850
370,169
2,300,000
16
264,000
2510
This table presents basic description on the stock prices of the pre-split period and post-split period. This description
includes the mean, median, maximum, minimum values of the stock price.
4.2. Announcement effects
We begin our empirical analysis with the transaction direction. As indicated in Fig. 1, there are
time intervals, large or small, between AD and ED, and the announcement effect will probably
disappear after the effective day, so we do not count the change after ED. Rather, we document
the announcement effect in the 10 trading days after AD. Moreover, in the semi-strong form of
market efficiency the impact of the release of private information (good news) from the firm’s
management to investors through a stock split should disappear quickly on the announcement
day. It is not likely that the effect of signaling lasts over the window of [10, 69] after AD. So the
signaling hypothesis makes no judgment in the long window.
As the signaling hypothesis states, the management uses splits to convey good information
to the public. If this assumption is right, we can expect that more buying orders would appear
because investors are motivated by good news. Different from other researchers’ methods that
adopt the abnormal return (AR) or cumulative abnormal return (CAR) as proof to support the
signaling hypothesis, we use the change in the ratio between transactions at bid and transactions
at ask to test this hypothesis. The result is presented in Table 4. The estimation period is 60 trading
days before AD and the observation period is 10 trading days after AD. The ratio decreases
significantly in the following 10 trading days after AD. This indicates a significant increase in
the number of transactions at ask compared to that of transactions at bid. Investors are more likely
F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
429
Table 4
Transaction direction change after AD
Relative day
AD
Change (Log-diff.)
Statistic
p-value
+1
Mean
Median
−0.58
−0.56
−12.88
−3066
0.00
0.00
+2
Mean
Median
−0.36
−0.33
−8.4
−2792
0.00
0.00
+3
Mean
Median
−0.33
−0.32
−7.11
−2778
0.00
0.00
+4
Mean
Median
−0.36
−0.33
−7.48
−3030
0.00
0.00
+5
Mean
Median
−0.29
−0.27
−5.8
−2497
0.00
0.00
+6
Mean
Median
−0.36
−0.28
−6.87
−2820
0.00
0.00
+7
Mean
Median
−0.33
−0.32
−7.15
−2814
0.00
0.00
+8
Mean
Median
−0.31
−0.31
−6.48
−2735
0.00
0.00
+9
Mean
Median
−0.33
−0.31
−6.82
−2774
0.00
0.00
+10
Mean
Median
−0.32
−0.38
−5.57
−2497
0.00
0.00
This table presents the change on the ratio between the number of transaction at bid and the number of transaction at ask
during 10 trading days after the announcement day (AD). The estimation window is [−69, −10] relative to AD, and the
studied period is [+1, +10] relative to AD. The percentage change of the ratio, the test statistic on mean or median, and
the p-value of corresponding test are given in the corresponding columns.
to buy stocks instead of selling them in the short run. Our empirical result gives direct support to
the signaling hypothesis.
4.3. Trading activity effects
To examine the trading activity effects of stock split, we use three measures on trades: the
number of trades, trade size, and daily trading volume, as well as three measures on quotations:
the number of quotations, the numbers of quotations at ask and at bid.
It is considered that the lower price of the stock after split will attract small traders to participate in trading this stock and that small traders buy or sell at small amount in measure of shares
or values. Thus, there should be an increase in the number of trades and also in the number of
quotations while the trading size may not increase proportionally.
The results can be found in Tables 5 and 6. For each measure of the trading activities, the
mean and median during pre-split period and post-split period are presented in the second and
third column, respectively. As to the trade size and daily volume measures, the post-split numbers
are based on the factor-adjustment.
Table 5 presents the quotation change. The mean of the daily number of quotes increases
significantly from 655 during the pre-split period to 925 during the post-split period. There is a
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F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
Table 5
The number of quotes
Full sample (N = 138)
Pre
Post
t-value
A. Daily number of quotes
Mean
Median
654.87
430.43
925.05
685.73
8.55
B. Bid quotations
Mean
Median
327.44
215.22
462.52
342.87
8.55
C. Ask quotations
Mean
Median
327.43
215.22
462.43
342.87
8.54
Sign-rank
Log-diff.
(p-value)
3416
0.388 (0.00)
0.384 (0.00)
3416
0.388 (0.00)
0.384 (0.00)
3415
0.388 (0.00)
0.384 (0.00)
This table presents the cross-sectional means and medians of the average daily number of quotes, bids and asks. The
pre-split period (‘Pre’) is the [−69, −10] window relative to the announcement day (AD). The post-split period (‘Post’)
is the [+10, +69] window relative to the effective day (ED). The opening and closing trades and the quotes before the
opening trade or after the closing trade are excluded. The log-difference (percentage change) and p-value from t -tests
(for mean) or sign-rank tests (for median) are reported in the last column.
38.8% increase in the daily quotation after stock splits on average. This increase is statistically
significant at 1% confidence level. The median changes from 430 to 686 and there is an increase
of 38.4%. The median test also shows this increase is significant at 1% level. The results show
that there are significant increases on both ask quotations and bid quotations after stock split.
Just as expected, the numbers of quotations on ask side (327.43) and bid side (327.44) are almost
equal during pre-split period. This situation does not change after stock split. The results from
median numbers are highly consistent with the mean results. They confirm that stock splits do
not affect the balance between the ask quotation and bid quotation. These results are consistent
with the trading range hypothesis because if a reduced price attracts more uninformed traders’
participation, it tends to proportionally appear on both buy and sell sides.
The changes in number of trades, trade size and trading volume are reported in Table 6. The
mean of the daily number of trades increases significantly from 132 during the pre-split period
to 182 during the post-split period. In percentage, the increase is 41%. The increase is statistically significant at 1% level. The median changes from 69 during the pre-split period to 121
during the post-split period with an increase by 42% and is also statistically significant at 1%
level.
Will the increase in the number of trades be accompanied by an increase in trading volume
proportionally? The results of trade size and trading volume are reported in part B and part C
respectively. The trade size decreases from the mean of 575 shares during pre-split period to
360 shares during post-split period, which is factor adjusted. The t -value is −21.28 and p-value
of the log-difference between pre-split and post-split values is less than 0.01, which shows that
the change is statistically significant. The result is confirmed by the median test. The p-value
of log-difference of the medians is less than 0.01 which also shows that the median change is
statistically significant.
The results show that the trade size decreases significantly while the number of trades increases significantly. Then we may consider the result of trading volume. Part C of Table 6
reports that there is no significant change in the daily trading volume after stock splits. The mean
decreases from 85,513 shares to 84,508 shares after stock splits and the median decreases from
F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
431
Table 6
Number of trades, trade size and trading volume
Full sample (N = 138)
Pre
Post
A. Number of trades
Mean
Median
132.44
69.62
182.18
121.67
7.48
B. Trade sizes (factor adjusted)
Mean
575.18
Median
343.91
360.30
204.21
−21.28
C. Daily volume (factor adjusted)
Mean
85,513
Median
23,733
84,508
22,665
−0.75
t-value
Sign-rank
Log-diff.
p-value
Log-diff.
3038
0.409
0.424
0.00
0.00
−4612
−0.464
−0.454
0.00
0.00
−179
−0.048
−0.004
0.45
0.70
This table presents the means and medians of average daily number of trades, trade size and trading volume. The presplit period (‘Pre’) is the [−69, −10] window relative to the announcement day (AD). The post-split period (‘Post’) is the
[+10, +69] window relative to the effective day (ED). The trade size and daily trading volume for the post-split period
are factor adjusted, i.e., divided by the split factor. The opening, post-closing and closing contracts are excluded. The
log-difference (percentage change) and p-value from t -tests (for mean) or sign-rank tests (for median) are reported in
the last two columns.
23,733 to 22,665. Neither the mean test nor the median test can reject the null hypothesis that
there is no significant change between the trading volumes during pre-split and post-split periods.
Some researchers examine the trade direction change around splits. Kryzanowski and Zhang
(1996) find that the trade direction switches significantly from sell to buy after the split ex-date
for all but large trades, where the change is in the opposite direction. We also investigate the
trade direction change after stock splits. The daily mean and median numbers of trades at ask
and at bid during the pre-split period and post-split period are presented in Table 7. The results
can reveal some information on the traders’ behavior change. It is found that there is a significant
increase in the number of trades both at ask and at bid. The average number of trades at ask
increases from 69 to 92, while the median changes from 35 to 59. The p-values of the mean and
median tests are both less than 0.01. The average number of trades at bid increases from 64 to 91,
while the median changes from 34 to 61. It seems that stock splits encourage small traders not
only to buy stocks but also to sell stocks, and it is possible that the sellers reduce the trade size.
The balance between the seller-initiated and buyer-initiated trades does not change after splits in
the long run.
According to the results of the trading activities, we discover the following findings. After
stock split, the transaction frequency increases significantly, the trade size decreases significantly,
while the daily trading volume in shares does not show any change. These results are largely
consistent with the trading range hypothesis, which states that the reduced stock price tends to
attract more small investors to participate in trading. The entrance of the small investors will
then cause increased trading frequency and decreased trade size. Also, since small investors are
mostly uninformed, we expect to see that the number of quotes and number of trades increase
proportionally on both bid and ask sides. These are exactly what our empirical results indicate.
In addition, the empirical results are also consistent with the tick size hypothesis, which states
that the adjustment of tick size will attract liquidity traders to take part in transactions. However,
neither the trading range hypothesis nor the tick size hypothesis can explain why the trading
volume stays almost unchanged after the split. One potential explanation is that the large traders
now use the lower price to break up their orders into even smaller chunks. Given that the market
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F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
Table 7
Number of trades at ask and at bid
Full sample (N = 138)
Pre
Post
t-value
A. Number of trades at ask
Mean
Median
68.94
35.32
91.73
58.59
6.18
B. Number of trades at bid
Mean
Median
64.27
33.85
90.53
61.08
8.26
Sign-rank
Log-diff.
p-value
Log-diff.
2719
0.346
0.333
0.00
0.00
3252
0.428
0.430
0.00
0.00
This table presents the mean and median of the average daily number of trades at ask and at bid. The pre-split period (‘Pre’) is the [−69, −10] window relative to the announcement day (AD). The post-split period (‘Post’) is the
[+10, +69] window relative to the effective day (ED). The opening, post-closing and closing contracts are excluded. The
log-difference (percentage change) and p-value from t -tests (for mean) or sign-rank tests (for median) are reported in
the last two columns.
is fully computerized, the smaller price may make it easier for algorithmic traders to break up
orders into smaller pieces. But existing theories are largely silent on these kinds of explanations.
4.4. Liquidity effects
The results of the quoted depths measured in shares are reported in Table 8. Part A describes
the results of depth at bid. The results at ask are reported in part B. The cross-sectional means
and medians of the daily average depths tell us that there is a significant decrease in the depth
after splits. The mean of the depths at bid decreases from 1599 shares before split to 1154 shares
after split and the p-value of the log-difference is less than 0.01, which is statistically significant.
This decrease in percentage is 28.7%. The median also decreases significantly, with the p-value
of the log-difference being less than 0.01. The depth at ask also shows the same tendency. The
decrease of the depth shows that one aspect of the stock’s liquidity becomes worse after split.
The results of the spreads are represented in Table 9. The mean and median of each type of
spread are given during the two periods. The p-values of the log-difference are given in the last
column to test whether the difference is significant or not. The four types of bid–ask spreads all
show a decrease after stock splits compared with those during pre-announcement periods. In Part
A, the mean of the absolute effective spread decreases from 44.55 JP Yen to 23.46 JP Yen with
the p-value being less than 0.01. The decrease in percentage is 83.3%. Part B indicates that the
mean of the absolute quoted spread decreases from 63.73 JP Yen to 35.39 JP Yen with the pvalue being less than 0.01. In percentage, the decrease is 83.2%. The mean of the relative quoted
spread decreases from 1% to 0.8%, with the p-value of the log-difference being less than 0.01.
The mean of the relative effective spread also decreases significantly, from 0.72% to 0.61%. The
median test on all spread measures gives consistent results. Here our findings are different from
those yielded by previous research, most of which find that the relative bid–ask spread increases
after split. However, our evidence on relative spread shows that the stock’s liquidity increases
after split.
Since the evidence from spread and depth gives inconsistent conclusions on the liquidity
change, it is necessary to adopt the quality index to combine the effects from these two dimensions in order to detect the liquidity change after stock splits. The result in Table 10 shows
that the mean of quality index increases from 41,560 to 160,784, with the p-value being less
than 0.01. The median also increases from 3118 to 4982 with the p-value being less than 0.01.
F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
433
Table 8
Quoted depth at bid and at ask
Full sample (N = 138)
Pre
Post
t-value
A. At bid (factor adjusted)
Mean
Median
1599.77
857.44
1154.26
574.91
−5.013
B. At ask (factor adjusted)
Mean
Median
1865.92
947.21
1139.00
648.33
−5.098
Sign-rank
Log-diff.
p-value
Log-diff.
−2691
−0.287
−0.237
0.00
0.00
−2986
−0.323
−0.344
0.00
0.00
This table presents the mean and median of quotation sizes at bid and ask in number of shares. The pre-split period
(‘Pre’) is the [−69, −10] window relative to the announcement day (AD). The post-split period (‘Post’) is the [+10, +69]
window relative to the effective day (ED). The depth of ‘Post’ is factor adjusted which means it is divided by the split
factor. The log-difference (percentage change) and p-value from t -tests (for mean) or sign-rank tests (for median) are
reported in the last two columns.
Table 9
The bid–ask spreads
Full sample (N = 138)
Pre
Post
t-value
A. Absolute effective spread
Mean
Median
44.55
15.30
23.46
7.35
−14.31
B. Absolute quoted spread
Mean
Median
63.73
23.78
35.39
10.96
−14.41
C. Relative quoted spread
Mean
Median
0.0100
0.0068
0.0080
0.0048
−5.05
D. Relative effective spread
Mean
Median
0.0072
0.0051
0.0061
0.0035
−2.63
Sign-rank
Log-diff.
p-value
Log-diff.
−4646
−0.833
−0.698
0.00
0.00
−4637
−0.832
−0.693
0.00
0.00
−3001
−0.002
−0.001
0.00
0.00
−1062
−0.0011
−0.0008
0.01
0.00
This table presents the mean and median of the effective spread, absolute spread and relative spread. The
pre-split period (‘Pre’) is the [−69, −10] window relative to the announcement day (AD). The post-split
period (‘Post’) is the [+10, +69] window relative to the effective day (ED). Absolute Quoted Spread =
Ask − Bid; Absolute Effective Spread = |Pt − Mt | ∗ 2; Relative Quoted Spread = (Absolute Quoted Spread)/Mt ;
Relative Effective Spread = (Absolute Effective Spread)/Pt . The last four columns report the t -value (mean test), Signrank (median test), percentage change, and the corresponding p-value from t -tests or sign-rank tests.
From the result of quality index, we can conclude that the stock’s liquidity is enhanced on the
whole after stock splits. Thus, our findings support the trading range hypothesis and the tick size
hypothesis, which state that the stock’s liquidity increases after split.
4.5. Information asymmetry effects
We adopt the model of Glosten and Harris (1988) to estimate the adverse-selection component
of bid–ask spread. The results are presented in Table 11. The results indicate that the decrease
occurs on the adverse selection cost but not on the order processing cost. Here, we examine the
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F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
Table 10
Quality index
Full sample (N = 138)
Pre
Post
t-value
Quality index
Mean
Median
41,560
3118
160,784
4982
3.76
Sign-rank
Log-diff.
p-value
Log-diff.
1893
0.333
0.342
0.00
0.00
This table presents the mean and median of the quality index. The quality index is adopted to combine the effects of bid–ask spread and depth on the liquidity and it is calculated by the equation: QI = [(depth at bidt +
depth at askt )]/(relative quoted spreadt ∗ split adjustment). The pre-split period (‘Pre’) is the [−69, −10] window relative to the announcement day (AD). The post-split period (‘Post’) is the [+10, +69] window relative to the effective
day (ED). The split-adjustment will be employed only on the ‘Post’. The log-difference (percentage change) and p-value
from t -tests (for mean) or sign-rank tests (for median) are reported in the last two columns.
Table 11
Components of the bid–ask spread
Full sample (N = 138)
Pre
Post
A. Percentage adverse selection cost
Mean
0.109
Median
0.087
0.087
0.072
B. Percentage order processing cost
Mean
0.102
Median
0.081
0.110
0.075
C. Adverse selection proportion
Mean
51.43
Median
52.42
46.28
48.53
t-value
−3.59
Sign-rank
Diff.
p-value
(Diff.)
−2628
−0.023
−0.017
0.00
0.00
−426
0.009
−0.002
0.44
0.36
−1679
−5.15
−3.61
0.02
0.00
0.773
−2.28
This table reports the results of the adverse selection component, the order-processing component, and the proportion of
the adverse selection component of the bid–ask spread. The pre-split period (‘Pre’) is the [−69, −10] window relative to
the announcement day (AD). The post-split period (‘Post’) is the [+10, +69] window relative to the effective day (ED).
The Glosten and Harris (1988) model is adopted to estimate components: Dt = α(Qt − Qt−1 ) + βQt Vt + μt , where α
is the order processing cost; β is the adverse selection cost. Opening and closing trades are excluded in the regression.
The selected stocks also must meet the requirement of at least 20 valid trading days where the valid trading day is defined
as a trading day with at least five valid transactions. The log-difference (percentage change) and p-value from t -tests (for
mean) or sign-rank tests (for median) are reported in the last two columns.
components in the percentage of stock price. The mean of the adverse selection cost is 0.109%
during the pre-split period and 0.087% during the post-split period. The mean difference is significant, with the p-value being less than 0.01. This result is confirmed by the median test. The
median declines from 0.087% during pre-split to 0.072% during post-split with the p-value being less than 0.01. From Part B of Table 11, we can find that the order processing cost does not
change significantly after stock splits. We also give the result on the proportion of adverse selection component among the spread. It can be seen that this proportion falls significantly after
stock splits.
Our empirical results show that the adverse-selection component decreases after stock splits. It
means that information asymmetry has been reduced after stock splits. At this point, our findings
support the trading range hypothesis, which states that information asymmetry will be reduced
because stock splits will attract small investors, most of whom are uninformed, and thus cause
the ratio of informed traders to decrease in comparison to that before split.
F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
435
Is this decrease attributed to decreased participation by informed traders or increased participation by uninformed traders, or the fact that both informed and uninformed traders trade more
in the market while the proportion of the informed traders decreases after stock splits? This question cannot be answered before we move on to the next part, which presents the results on the
uninformed and informed traders’ behavior changes. The next part also reports evidence on the
probability of informed trading before and after stock splits.
4.6. Probability of informed trading before and after stock splits
As we have discussed before, more uninformed traders will be attracted by the lower price
after split, so the arrival rate of the uninformed traders (ε) is expected to increase. More uninformed trader participation would, all else equal, lower the probability of informed trading (PIN).
The signaling hypothesis also foresees a decrease in information asymmetry due to a speeding
up of information discovery.
As Admati and Pfleiderer (1988) state, informed traders would take advantage of the uninformed traders’ trading activity. They think the informed traders will trade more actively in the
periods when liquidity trading is concentrated. Therefore, we expect that the informed traders
will take part in trades more aggressively if more uninformed traders are attracted to the market by the lower price after stock splits. The latter situation is predicted by the trading range
hypothesis, so the arrival rate of the informed traders (μ) is expected to increase.
The estimation results of all parameters are presented in Table 12. We find that the probability
of information event happening (α) increases significantly from the mean of 0.337 during the
pre-split period to 0.419 during the post-split period, and the difference is significant at the significance level of 1%. The median test is supportive of the post-pre change and it is significant
at the level of 1%. The increase in the number of information events is consistent with the result that the informed traders increase significantly after stock splits. Easley et al. (2001) use the
information events happening to test information asymmetry. Their findings of the statistically
insignificant increase in the probability of an information event cast doubt on the information
asymmetry explanation for splits. As stated before, we think the information events appearance
Table 12
Probability of informed trading (N = 136)
Pre
α
ε
μ
PIN
Mean
Median
0.337
0.284
Post
0.419
0.319
Post-Pre
t-value
0.083
0.056
2.82
Mean
Median
41.44
23.01
63.04
41.33
25.42
9.69
4.82
Mean
Median
58.86
39.52
65.52
44.60
8.10
5.13
1.72
Mean
Median
0.230
0.204
0.208
0.197
−0.023
−0.023
−2.41
Sign-rank
p-value
1499
0.00
0.00
2980
0.00
0.00
963
0.08
0.04
−1572
0.02
0.00
This table presents the cross-sectional means and medians of the probability of an information event (α), the arrival rate
of uninformed traders (ε), the arrival rate of informed traders (μ), and the probability of information based trade (PIN).
The pre-split period (‘Pre’) is the [−129, −10] window relative to the announcement day (AD). The post-split period
(‘Post’) is the [+10, +129] window relative to the effective day (ED). Estimation on these parameters is based on the
Easley et al. (1996) model. The analysis is carried out for the sample of 136 stock splits. The p-value from t -tests (for
mean) or sign tests (for median) are reported in the last column.
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is determined only by the appearance of the informed traders. Actually, the information environment should be measured by the adverse-selection component of spread that is not only caused
by the probability of the informed traders’ appearance but also related to the uninformed traders’
appearance. This will be discussed in more details after the PIN value is estimated in later part.
The uninformed traders’ arrival rate (ε) shows a significant increase after splits. The mean of
ε increases from 41.44 to 63.04, and the change is significant at the significance level of 1%. The
same result can be found in the median test, which is also significant at the significance level
of 1%. As to the informed traders’ arrival rate (μ), its mean increases from 58.86 to 65.52 and
median increases from 39.52 to 44.60. The mean test and median test are both significant at the
significance level of 10%. The increase in uninformed trades and informed trades is consistent
with the predictions of the trading range hypothesis and tick size hypothesis.
The probability of informed trading (PIN) gives the estimate for how many trades are dealt
by the informed traders among the total trades. The estimated result shows that the mean of PIN
decreases from 0.23 to 0.21, and this decrease is significant at the significance level of 5%. This
result is also confirmed by the median test. Desai et al. (1998) argue that the increase in noise
trading will reduce the adverse-selection component, while the increase in informed trading will
increase this component. The PIN value can show the combined effect when both types of traders
increase. The trading range hypothesis and the signaling hypothesis both predict the decrease in
the information asymmetry and the fall in PIN. The empirical results in this study support the
trading range hypothesis, which predicts the increase in the uninformed traders, and the signaling
hypothesis, which predicts the decrease in information asymmetry caused by the decrease in the
proportion of the informed trades to the total trades.
Specifically, after split, uninformed traders are attracted by the lower price compared to the
pre-split price. With more uninformed traders participating in trading the stock, the informed
traders are encouraged to trade more aggressively based on their judgment on the stock price.
They will sell the stock if they think it is overpriced and buy it if they think it is undervalued. The
uninformed traders are thought to bring about the increased liquidity of the stock due to the lower
price after split. Though both the uninformed and informed traders execute the transactions more
frequently after stock splits, the magnitude for each is different. The decrease in the PIN value
shows that the proportion of informed trades among the total trades decreases significantly. As a
result, the information asymmetry decreases, which would lower adverse selection cost and consequently narrow down the spread. Because the PIN value change gives a good explanation for
the previous results, including changes in the adverse selection component and bid–ask spread,
the relation between the traders’ behavior and the market characteristics of the stock is justified.
5. Discussion and conclusions
In this research we comprehensively investigate the effects of stock splits on the market characteristics of stocks on the Tokyo Stock Exchange. By comparing the trading activity, liquidity,
information asymmetry and probability of informed trading, we are able to identify whether the
predictions of existing theories are supported or not. We find that stock splits tend to increase
trading activity, enhance market liquidity, reduce information asymmetry, and lower the probability of informed trading.
Our results are mildly supportive of the signaling hypothesis, which predicts that the splits
convey good information to investors. In a semi-strong form of market efficiency, the impact of
the release of private information (good news) from the management to investors through stock
splits will affect the originally uninformed investors and push them to purchase the stock in the
F. Guo et al. / J. Japanese Int. Economies 22 (2008) 417–438
437
short run. Thus, the results of Table 4, which shows a significant increase in the number of trades
at ask compared to that at bid, indicating that investors are more likely to buy stocks instead
of selling them, are highly consistent with the signaling hypothesis. However, since the impact
of information release will soon disappear, the signaling hypothesis remains silent on the later
results that are based on the [10, 69] trading day window.
Our findings can be viewed as highly consistent with the trading range hypothesis. Under the
trading range context, lower stock prices attract more small investors, which are largely uninformed. If this hypothesis is true, we expect to observe an increase in both quotations and trades,
as well as in market liquidity. In addition, due to the influx of noise traders, the spread tends to
decrease and the adverse selection component of spread tends to shrink. In the case of probability
of informed trading, the uninformed traders’ arriving rate (ε) is expected to increase, and the PIN
value will decrease accordingly. These are exactly what we observe from this paper.
Our empirical evidence also supports the tick size hypothesis, which predicts more liquidity
traders (or uninformed traders) participating in trading stocks after splits. The results in this study
show that stock liquidity is enhanced after splits and that the arrival rate of uninformed traders
increases.
As one of the most studied phenomena, the stock split is also the least understood one. Existing theories try to explain the phenomenon from different aspects. Based on a comprehensive
investigation of the stock splits on the Tokyo Stock Exchange, our research provides sound
evidence that the firms may choose to split their stocks for multi-faceted reasons such as the
signaling consideration, the trading range consideration, and the information asymmetry consideration because the predictions of those hypotheses are largely supported by the empirical results
in this study.
Acknowledgments
We would like to thank Takeo Hoshi (the editor), Junbo Wang, Lifan Wu, Xianming Zhou,
and two anonymous referees for their valuable comments and suggestions. Part of the job was
completed when Guo was a PhD student in City University of Hong Kong. Various supports
from City University of Hong Kong (Guo, Zhou and Cai) and the “985 Project” of Sun Yat-sen
University (Zhou) are acknowledged. All errors remain our own, of course.
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