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Working Paper Series
Changes in Trading Activity Following
Stock Splits and Their Impact on Volatility
and the Adverse Information Component
of the Bid-Ask Spread
A.S. Desai, M. Nimalendran and
S. Venkataraman
Working Papers Series
Issues in Financial Regulation
Research Department
Federal Reserve Bank of Chicago
December 1996 (WP-96-21)
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C h a n g e s in T r a d i n g Activity Following Stock Splits a n d Their I m p a c t o n
Volatility a n d the A d v e r s e Information C o m p o n e n t of the B i d - A s k S p r e a d
A. S. Desal
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C o lle g e o f B u s in e s s A d m in is t r a t io n
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(9 1 3 ) 5 3 2 -6 8 2 0
M. Nimalendran
D e p a rtm e n t o f F in a n c e , I n s u ra n c e , a n d R e a l E s ta te
C o lle g e o f B u s in e s s A d m in is t r a t io n
U n iv e r s it y o f F lo r id a
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S. Venkataraman
E c o n o m ic R e s e a r c h
F e d e r a l R e s e rv e B a n k o f C h ic a g o
2 3 0 , S o u th L a S a lle S tre e t
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W e would liketothank Jim Angel, David Brown, David Ellis,Mark Flannery, Joel Hasbrouck, Joel Houston, Chris
James, Gautam Kaul, and theparticipants at the Rutgers University conference on Recent Developments in Asset
Pricing and Optimal Trading Strategies, the 1994 Financial Management Association Meetings and the
Northwestem/JFI Conference on Market Microstructure and the Design o f Financial Systems fortheiruseful
comments. The views expressed in thispaper are not necessarily those of the Federal Reserve Bank ofChicago, or
the Federal Reserve system. All errors, ofcourse, are our own.
C h a n g e s in T r a d i n g Activity Following Stock Splits a n d Their I m p a c t o n
Volatility a n d the A d v e r s e Information C o m p o n e n t of the B i d - A s k S p r e a d
ABSTRACT
This paper examines the changes in trading activity around stock splits, and its impact on
both the volatility and the bid-ask spread. After a stock split, there is a significant increase in the
volatility and the spread, even after controlling for the effects of microstructure biases like price
discreteness and bid-ask bounce. The change in the number of trades is positively related to the
change in total volatility, as well as to the temporary and permanent components of volatility.
This suggests that the change in trading activity is associated with both informed and noise
traders. The change in the number of trades is also negatively related to the change in the total
spread, as well as the adverse information content of the spread. Firms that are successful in
attracting a large number of additional trades to their stock experience a smaller increase in
spreads. These results suggest that a crucial determinant of the liquidity changes experienced by a
firm after a stock splitisthe success of the split in attracting new trades to the security.
C h a n g e s in T r a d in g A c tiv ity F o llo w in g S to c k S p lits a n d th e ir I m p a c t
o n V o la tility a n d th e A d v e r s e I n fo r m a tio n C o m p o n e n t o f th e B id -A s k S p r e a d .
1. Introduction
W e examine the impact of trading activity and market microstructure on the volatility and
the adverse information component of the bid-ask spread around stock splits. Previous studies of
stock splits document an increase in both the volatility and the proportional bid-ask spread aftera
split However, they do not provide a satisfactory explanation for changes in these characteristics.
In this study, we firstexamine the relationship between changes in volatility and changes in
trading activity. This analysis is motivated by Jones, Kaul and Lipson (1994), who find that
volatility isprimarily and positively related to the number of trades. W e also examine the
relationship between changes in trading activity and the components of the bid-ask spread.
Our analyses also provides insights about the managerial objective of enhancing the
liquidity of the stock by splitting it.Splits per se do not altereither the cash flows of the firm or
the claims of the security holders. Yet, in any given year, about 10% of the firms splittheir stock.
Surveys of corporate managers by Baker and Gallagher (1980) and Baker and Powell (1993)
reveal that the two most important reasons given by managers for undertaking a split are to bring
the stock price into a better trading range and to improve itsliquidity. Managers believe that the
lower stock price makes itpossible for wealth constrained “small” traders to purchase round lots.
Baker and Powell argue that the managerial view of enhanced liquidity isthis increase in the
diversity and number of shareholders. Lamoureux and Poon (1987) and Maloney and Mulherin
(1992) document an increase in the number of shareholders after the stock split, and their
evidence is therefore consistent with the managerial motivations for stock splits.
On the other hand, studies have also found that after a split, there isalso an increase in the
proportional bid ask spread (Copeland (1979) and Conroy, Harris, and Benet (1990)), a decrease
in the split-adjusted trading volume (Copeland and Lamoureux and Poon), an increase in
brokerage fees (Copeland), and an increase in the volatility of the stock’s returns (Ohlson and
Penman (1985) and Dubofsky (1991)). Based on these measures, liquidity appears to decrease.
Taken together, the evidence suggests that by splitting the stock, managers achieve the objective
of increasing shareholder diversity but the splitdoes not, on average, lead to an improvement in
traditional measures of liquidity. However, these studies do not examine the implications of the
change in shareholder diversity for trading activity, and the consequent changes in volatility and
the bid-ask spread.
W e investigate two potential explanations for the increase in volatility following a split
First Ohlson and Penman (1985), Dravid (1988), and Dubofsky (1991) argue that part of the
increase in volatility could be attributed to microstructure biases. Particularly, both bid-ask
bounce and price discreteness induce an upward bias in volatility estimates based on transaction
prices, and this bias is exacerbated after the splitdue to the lower share prices. W e avoid die bias
due to bid-ask bounce by using returns based on bid-bid prices (see Kaul and Nimalendran
(1990)). The correction for price discreteness follows the model in Ball (1988). W e document
that while bid-ask bounce and price discreteness do inflate volatility estimates, the stock’s
volatility increases afterthe spliteven after we correct for these biases.
The second explanation for the increase in volatility is an increase in trading activity.
Jones, Kaul, and Upson (1994) find that volatility isprimarily and positively related to the number
2
of trades. Thus, ifthe number of trades increases after the split,then this would increase the
volatility. There are several theoretical reasons why the number of trades might increase after a
split. Black (1986) argues that noise traders prefer low priced stocks to high priced stocks. Ifthey
do, then the lower per share price after a split would attract noise traders and the resulting
increase in the number of trades would increase the volatility. The increase in noise trading would
be consistent with the managerial objective of increasing shareholder diversity. Brennan and
Hughes (1991) argue that the lower per share price afterthe splitmight give analysts the incentive
to collect more information on firms. They provide evidence that the number of analysts following
a firm increases after the firm announces a stock split. This suggests the presence of a larger
number of informed traders in the security afterthe split, and again, the resulting increase in the
number of trades would lead to an increase in the volatility. Itisalso possible that the levels of
both noise and informed traders increase after a split. In Admati and Pfleiderer’s (1988) model of
strategic trading with costly information acquisition, the number of informed traders isdetermined
endogenously. A higher number of noise traders would result in a higher number of informed
traders as well. Thus, iflower share prices aftera splitattract noise traders, the level of informed
traders would increase endogenously.
Note that all three models above imply an increase in the number of trades but differ in
theirimplications about the mix of traders (noise versus informed). Our analysis shows that the
number of trades does increase afterthe split. Further, we find a significant positive relationship
between the change in the number of trades and the change in the volatility. However, since we
cannot directly observe the mix of traders, we have to rely on indirect methods to provide relative
3
impacts of noise and information on volatility changes. W e employ two approaches. The first
approach uses multi-period volatility and variance ratios (the ratio of multi-period to single-period
volatilities). In the second approach, we use insider trading intensity as a proxy for informed
trading in a cross-sectional regression model. Our analysis of multi-day volatility and variance
ratios indicates that a significant part of the increase in the volatility isin the component that is
due to pricing errors, and that there is also an increase in the permanent component of the
volatility. In the cross-sectional regression framework, we find that changes in the total volatility,
as well as changes in the transient and permanent components of the volatility are positively
related to changes in the number of trades. This relationship isconsistent with an increase in both
noise and informed trading after the split.
The models of Black (1986), Brennan and Hughes (1991), and Admati and Pfleiderer
(1988) have implications for the adverse information component of the bid-ask spread as well. An
increase in noise trading after a split(as in Black) will decrease the adverse information
component, while an increase in informed trading (as in Brennan and Hughes) will increase this
component of the spread. Admati and Pfleiderer argue that an increase in the number of noise
traders would also endogenously increase the number of informed traders. The impact of this
change in trading activity would depend on whether the signals received by the informed traders
are close substitutes or complements.1When informed traders get identical signals, Admati and
Pfleiderer show that competition among traders would decrease the adverse information in the
1 Evidence to support the hypothesis thatsplitsconvey private information to the market ispresented in
Brennan and Copeland (1988) and in McNichols and Dravid (1990).
4
market However, ifinformed traders get diverse signals, then the effect on the adverse
information depends on the precision of the signal. Ifthe signal issufficiently imprecise, then
adverse information would decrease due to competition between informed traders, even ifthe
number of informed traders increases. Thus, by relating the change in the adverse information
component of the spread to measures of trading activity, we can draw inferences about the impact
of splits on liquidity. While we find that, on average, both the proportional spread and the adverse
information component of the spread increase after the stock split,these changes are less
pronounced the larger the increase in the number of trades. This negative relationship implies that
spread changes are either driven by noise traders or by informed traders with substantially similar
signals (or some combination thereof).
The evidence sheds lighton several aspects puzzle regarding stock splits. First, we
establish that the observed increase in volatility and spreads cannot be attributed solely to
statisticalproblems (like price discreteness and bid-ask bounce). Consistent with the findings of
Jones, Kaul and Lipson, we also establish a positive relationship between the change in volatility
and the change in the number of trades. The fact that this relationship holds true for both the
transitory and permanent components of volatility suggests thatboth informed and noise traders
are contributing to the observed increase in the number of trades. Finally, we establish that while
spreads (total, as well as the adverse information component) increase from before to after a split,
firms thatexperience a substantial increase in the number of trades have a smaller increase in
spreads relative to other firms. This suggests that, all else kept the same, attracting additional
traders to the security enhances the liquidity of the stock. The puzzle that stillremains, of course,
5
is (i)what distinguishes firms in terms of their ability to attract additional traders to their stock,
and (ii)why a splitunconditionally worsens liquidity. These remain interesting areas for future
research.
The rest of the paper is organized as follows. In section 2, we describe the data and the
sample characteristics. In Section 3, we present our analysis of volatility changes afterstock splits.
Changes in the adverse information of the spread are discussed in Section 4. Our conclusions and
a summary are presented in the last section.
2.
2 .1
Data and Sample Characteristics
D a ta
The initial sample consists of N A S D A Q - N M S firms that announced stock splits and are
listed in the CRSP 1990 data base. W e confine our sample to N A S D A Q - N M S firms because
CRSP provides bid-ask spreads (inside quotes), daily trading volume, and number of trades
presently only for these firms. W e further restrictour sample to announcements of splitsduring
the period January, 1983 to December, 1990. This restriction isimposed because transaction
prices and bid-ask spreads for N M S securities are available in the CRSP data base on a regular
basis only afterNovember, 1982. There are 980 splits announced by 739 firms meeting the above
screens.
Pre-split microstructure variables for the sample (such as volatility, spreads, trading
intensity, etc.) are estimated over the 180 day period ending 21 days before the announcement of
the split. The post-split characteristics are estimated over the 180 day period beginning from 21
6
trading days after the stock firsttrades ex-split. W e exclude the period from 20 days before the
announcement to 20 days afterthe stock trades ex-split to avoid any contamination due to
information effects around the announcement day and the transient microstructure effects around
the ex-split date. W e require that allrelevant data items be available during the pre-split and the
post-split estimation periods. Finally, we exclude from our initial sample all observations that have
either a stock split or a stock dividend within 400 days of each other. This screen ensures that our
estimation period data are not contaminated by events similar to the ones examined in this study.
The final sample consists of 366 stock splits announced by 341 firms.
In our sample of 366 split announcements, 147 are 3-for-2 splits (a splitfactor of 0.5) and
138 are 2-for-l (a splitfactor of 1.0). Sixty three announcements involve a split factor of less than
3-for-2, while eighteen are splits greater than 2-for-l. Previous studies have suggested that there
is a difference between the motives of firms issuing small versus large stock splits.Elgers and
Murray (1985) document that small splits (with splitfactor < 25%) are associated with smaller
pre-splitprices and smaller market value firms than large splits. Further, they also suggest that
small splitfactors may be motivated by a desire to signal optimistic expectations, while larger split
factors are motivated by liquidity reasons. Baker and Powell (1992) find a significant difference
between the preferred trading ranges for the small (< 2-for-l) versus large (k 2-for-l) splits. Since
there appears to be differences between the motives for small versus large splits,we partition our
sample into two groups: a small splitfactor group of 3-for-2 splits and smaller, and a large split
factor group of 2-for-l splits and greater.
2.2
S a m p le C h a r a c t e r is t ic s
7
In Table 1A we report sample characteristics for some selected variables (market value,
number of shares, price, and number of market makers) for the entire sample, and for the two sub
samples based on the split-factor. W e find that there is a significant difference in the median presplitmarket values of the equities of the firms in the two sub-samples. The median value of equity
in the small splitfactor sub-sample is $85 million compared to $182 million for the large split
factor sub-sample. This difference in firm size isdriven by the higher pre-splitshare price for the
large splitfactor sub-sample ($37.7) compared to the small splitfactor sample ($21.8), because
the difference in the median pre-split outstanding shares isnot statistically significant. W e also
find that there isno statistical difference in the number of market makers between the two groups
in the pre- and post-splitperiods. Since we find significant differences in some firm characteristics
between the two groups, we analyze the market microstructure variables also by groups.
[Insert Tables 1A and IB here]
In Table IB, we report statistics for microstructure variables and measures of trading
activity. The table reports pre- and post-split means and medians for the proportional bid-ask
spread, the daily volatility based on transaction prices, the average daily number of trades, the
average volume turnover, the average volume turnover per trade, and the average number of
insider trades. The statistics are also presented for the ratio of post-splitto pre-split values for
these variables. Our objective isto confirm for our sample what existing studies have
documented. First, the median values of both the pre- and post-split proportional spreads are
higher for the small splitfactor sub-sample than for the large split factor sub-sample. This is
consistent with a smaller market value and lower pre-split share prices for the small split factor
8
sub-sample compared to the large splitfactor sub-sample. Next, we find a significant increase in
the total spread after the stock splitfor the total sample as well as for each sub-sample. This
increase in the post-split spreads isconsistent with the findings of Copeland (1979) and Conroy,
Harris, and Benet (1990). The median ratio of the post-split to the pre-split proportional spread is
1.08 for the small split factor sub-sample, and 1.45 for the large split factor sub-sample. While
both these values are significantly greater than 1.0 ,the median change in the spread isobviously
much greater for the large splitfactor sub-sample.
W e also document a significant increase in the post-split volatility relative to the pre-split
volatility for the total sample and also for each sub-sample. For the total sample the median
increase in volatility based on closing transaction prices is70%. For the small splitfactor sub
sample, the median increase in volatility is42%, while for the large splitfactor sub-sample, itis
119%. Ohlson and Penman (1985), who also use closing transaction prices for their volatility
estimates, report an increase of 63% to 83% in the volatility after the split, and their results are
comparable to ours.
In addition to spreads and volatility, we also examine changes in trading activity. W e find
a significant increase in the number of trades afterthe split for both groups. The median increase
for the small split factor sub-sample is 12% compared to 37% for the large splitfactor sub
sample. However, the median volume turnover (defined as the ratio of the transaction volume to
the number of outstanding shares) increases by only 7 % for the small split factor group and
decreases by 7% for the large split factor group, with the decrease for the latter group being
statistically insignificant. The increase in number of trades isconsistent with the findings by
9
Lamoureux and Poon (1987), and the effect on volume isconsistent with Murray (1985) and
Lakonishok and Lev (1987), who find that splits do not appear to exert a permanent effect on
volume. More interestingly, we find that the turnover volume per trade is significantly smaller in
the post-split period compared to the pre-split period for both groups. The median reduction in
the order size is 18% for the small split factor stocks and 35% for the large split factor stocks.
The smaller order size isconsistent with an increase in noise traders who are likely to trade
smaller quantities.
Finally, we report statistics on the average daily number of insider trades for our sample.
Seyhun (1988) finds evidence consistent with the argument that corporate insiders generally trade
on private information. This suggests that measures of trading activity by insiders can be used as a
reasonable proxy for informed trading. However, insiders may also trade for liquidity reasons. But
itis not obvious why their liquidity motivations for trading in theirfirms’stock would be altered
during the 180 day intervals before the announcement and after the ex-day of the split. Ifinsiders
withhold such trading prior to the splitin anticipation of the announcement, then such trades are
likely to be executed soon after the splitis announced. In our study, we measure the post-split
insider trading activity beginning twenty days after the ex-splitdate. Thus, itisunlikely that the
execution of any such backlog of trades will have a significanteffect on our measures of informed
trading activity by this group of investors.
For the sample of 366 firm events, we obtained insidertransactions from the Securities
and Exchange Commission’s Ownership Reporting System (ORS) cumulative file (which covers
the period 1980-1991). For this study, we classify allofficers and directors and others who have
10
substantial ownership in the firm as insiders. In addition, any transaction that was classified as an
open market purchase/sale, private purchase/sale, and exercise of options was considered as valid
transactions. The time period used for measuring insider trading activity in the pre-split and post
split is identical to that used for allother variables. In our sample, while the mean ratio of the
post-split insider transactions to the corresponding pre-split value issignificantly greater than 1.0 ,
the median is not. This difference arises due to skewness of the data.
The observed changes in the microstructure variables are consistent with previous
empirical findings. In the next section, we test the effect of microstructure biases and trading
activity on changes in the daily volatility.
3.
3 .1
Changes in Volatility Following Stock Splits
E ffe c t s o f M ic r o s t r u c t u r e B ia s e s o n V o la t ilit y E s tim a te s
Ohlson and Penman (1985), and Dravid (1988) suggest that the increased bid-ask spread
and the larger effect of price discreteness on lower priced stocks may account for part of the
increase in volatility that is observed afterthe split. Dubofsky (1991) finds that, for a sample of
A M E X listed stocks, there isno statistically significant increase in the weekly return volatility
afterthe split. Since volatility estimates based on weekly returns are less affected by bid-ask errors
and price discreteness, Dubofsky argues that measurement errors created by the bid-ask errors
and price discreteness could partially explain the increase in the return volatility of daily returns.
In this section, we firsttest this microstructure explanation for the observed increase in the
volatility using our sample of stock splits.
11
3. l . a
B ia s D u e to B id - A s k B o u n c e
Roll (1984) shows that in an efficient market, ifthe probability of the transaction price
being at the bid or the ask isequally likely, then, using transactions prices to estimate the true
volatility of the stock returns would induce spurious volatility equal to s2/2,where s is the
percentage bid-ask spread. Kaul and Nimalendran (1990) show that for a portfolio of small
market value N A 5 D A Q - N M S firms, this spurious volatility could be as high as 50% of the
underlying true volatility. Even for the largest firms, this proportion could, on average, be as high
as 23%. For our study, this bias could be particularly significant ifthe bid-ask spread increases
aftera split. However, given the availability of bid and ask prices for the N A S D A Q - N M S firms,
we can avoid the bid-ask spread bias by estimating volatilities based on returns computed using
bid-bid prices.2
In Table 2 we report statistics for sample variances estimated using daily returns in the
pre- and post-split periods. The estimate based on transaction price returns isdenoted by
,and
that based on bid-to-bid returns isdenoted by o \ .Since the sampling distribution of the estimated
variances are highly skewed and kurtotic, inferences based on the sample mean under the
assumption that the underlying distribution is normal could be misleading. Therefore, we report
only the sample medians before and after the split, and robust non-parametric test statistics for the
differences in the sample medians (note that sample means also give the same results).
[Insert Table 2 here]
2
The CRSP data base gives closing bid and closing ask prices in addition to the closing transactions
price.W e construct return series based on bid prices by adjusting fordividends and distributions on ex-days.
12
For the total sample, the median ratio of the post-split volatility to the pre-split volatility,
based on transaction price returns, is 1.70, indicating a 70% increase in the volatility. However,
there isan 80% increase in the volatility based on bid-to-bid returns. Both of these increases are
significant at the 1% level. Since the lattermeasure avoids the bias due to the bid-ask bounce, our
results suggest that bid-ask bounce alone cannot explain the increase in volatility. An increase in
the bid-ask bounce corrected volatility is also observed for the two sub-samples based on the split
factor. For the small split factor sub-sample, this volatility increases by 41%, while for the large
splitfactor sub-sample, the increase is 124%.
To estimate the bias in the transaction return volatility, we compare the median values of
C j
with those of
for each sample, in both the pre- and post-split periods. For the total sample,
the pre-split transaction return volatility is about 95% higher than the corresponding bid-bid
return volatility, indicating a significantly large bias due to the bid-ask bounce. Likewise, in the
post-splitperiod, the bias due to the bid-ask bounce is about 84%. These biases are also observed
for each sub-sample. For the small splitfactor sub-sample, the biases are 90% and 89% in the two
periods respectively, while those for the large splitfactor sub-sample are 91% and 71% in the preand post-splitperiods respectively.
Since previous studies have also documented an increase in the transaction return volatility
after stock splits, itwould be informative to estimate how much of this increase isdue to the bidask bounce. Note that the increase in the spread after the split will exacerbate the bias due to the
bid-ask bounce. For the total sample, the median o \ increases by 3.17x10"*. On the other hand, the
13
bid-bid return volatility increases by 1.91x10^, which is about 60% of the increase in
.
Therefore, about 40% of the increase in the transaction return volatility can be attributed to the
bid-ask bounce. Similarly, about 47% and 36% of the increase ina 2 for the small and large split
factor sub-samples respectively can be attributed to the bid-ask bounce.
3. l.b
B ia s D u e to P r ic e D is c r e te n e s s
Gottlieb and Kalay (1985) and Ball (1988) examine the effect of price discreteness on the
inflation in the volatility estimates. Ball shows that ifstock prices follow a Geometric Brownian
motion with an instantaneous true underlying variance o2,and price P, then the bias induced by
price discreteness can be approximated by dVbP2,where d isequal to the minimum price change
(typically, $0,125). W e apply this correction to the volatility measure to obtain an unbiased
estimator. The estimator,a \ D ,iscomputed using Equation A-l in Appendix A, and the results
are presented in the lastrow of Table 2.
The median ratio of the post-split volatility corrected for both the bid-ask bounce and
price discreteness is 1.81 in the total sample, and this estimate issignificantly greater than 1.0 at
the 1% level. Thus, even aftercorrecting for price discreteness, there isa significant increase in
the volatility afterthe split. A significant increase in the bias corrected volatility isalso observed
for each of tne two sub-samples, although we observe a much larger increase for the firms with a
large split factor (118% versus 42%).
To estimate the bias due to price discreteness, we compare the volatility corrected for
14
both the bid-ask bounce and price discreteness (
D) with the volatility corrected for the bid-ask
bounce alone ( ) . For the total sample, price discreteness inflates this volatilityestimate by
4.7% in the pre-split period, and by 3.9% in the post-splitperiod. This bias isrelatively small
compared to the bid-ask bias, and further, ithas a negligible effect on the change in volatility. For
the small splitfactor sub-sample, the biases in the pre- and post-split periods are 5.4% and 5.7%
respectively, while those for the large splitfactor sub-sample are 0.4% and 7.8% in the two
periods.
The preceding analysis suggests that the bid-ask bounce introduces a substantial bias in
estimates of volatility based on transaction prices, while the bias due to price discreteness is
negligible. More importantly, even aftercorrecting for these biases, we find a significant increase
in the volatility after the split. Thus, microstructure biases alone cannot account for the previously
documented increase in the volatility after stock splits. Further, firms that execute large splits
experience a much larger increase in the bias-corrected volatility than do firms that execute small
stock splits.
3 .2
E f fe c t o f C h a n g e s in T r a d in g A c t iv it y o n C h a n g e s in V o la t ilit y
As argued earlier, an increase in either noise traders or informed traders (or both) would
lead to an increase in the volatility of the stock. To examine the effect of the change in the trader
mix after the spliton the change in the volatility estimates, we need to estimate changes in trader
types after stock splits. Since itisnot possible to directly identify the type of traders, we use two
approaches. First, we analyze stock return dynamics and market microstructure variables to infer
15
the effect of changes in the types of traders. This allows us to decompose the change in the
volatility into changes in the permanent (information driven) component and the transient (noise
driven) component. In the second approach, we relate changes in volatility (and itscomponents)
to changes in trading activity using proxy variables for noise and informed trading.
3 .2 .a
C h a n g e s in P e r m a n e n t V o la t ilit y
French and Roll (1986) argue that, ifthe effects due to noise trading (i.e.pricing errors)
are subsequently corrected, then the volatility based on longer period returns would reflectthe
permanent component Thus we estimate the volatility based on multi-day returns. Due to the
limited number of observations in each estimation period, we use overlapping data and the
estimator in Lo and MacKinlay (1988). This estimator isgiven by Equation A-2 in Appendix A,
and corrects for the effects of both the bid-ask bounce and price-discreteness on volatility.
In Table 3, we report these multi-period volatility estimates for cumulating intervals up to
30 days for the total sample and for sub-samples based on the splitfactor. For the total sample,
we find that the median 30-day return volatility increases by 57% afterthe split,and the increase
isstatistically significant atthe 1% level. This indicates that a significant component of the
increase in volatility ispermanent The one day return volatility however, increases by 81% for
this sample (see Table 2). The larger increase in the one-day volatility relative to the increase in
the 30-day volatility suggests that there is also a large component of the increase in volatilitythat
istransient and attributable to noise. Similar results are obtained for the sub-samples based on the
split factor. However, for the small split factor group, the increase in the permanent component of
the volatility (based on 30-day returns) is only 32% compared to 81% for the large split factor
16
group.
[InsertTable 3 here]
These results indicate that for our sample, there is a substantial increase in volatilitythat is
permanent, in addition to a significant increase that istransient. Further, our finding that there is a
significant increase in the multi-day volatility are in contrast to those of Dubofsky (1991). He
finds that, for a sample of firms listed on A M E X that executed stock splits, there is no significant
change in the volatilitybased on weekly returns.
3 .2 .b
C h a n g e s in V o la t ilit y d u e to N o is e T r a d in g
An alternative metric to determine the relative contribution of noise trading to the total
volatility of a security’s returns isthe variance ratio, defined as the ratio of the variance based on
k-period returns to k times the variance based on one-period returns. The presence of noise
trading would induce negative autocorrelation in the returns, thereby reducing the variance based
on multi-period returns. The variance based on one period returns would be unaffected by this
negative autocorrelation ifittakes more than one period for the mis-pricing to be corrected.
Consequently, French and Roll (1986) argue that one minus the variance ratio reflects the fraction
of the one period volatility that can be attributed to noise.
Lo and MacKinlay (1988) show that the variance ratio can be written as a weighted sum
of the autocorrelations:
VR(k) = l
+
j=i
K
where Pj denotes the estimate of thej* order autocorrelation of daily returns. Ifall the
17
(1)
autocorrelations are due only to mis-pricing errors that are subsequently corrected, then, as
suggested by French and Roll, (1-VR) would estimate the effect of noise trading on volatility.
However, Kaul and N imalendran (1990) document that for N A S D A Q - N M S firms, the average
autocorrelation of returns based on bid-bid prices at lag one is0 .IS, and this is much larger than
the negative autocorrelations athigher lags.
In Table 4 we report the median autocorrelations up to lag 10 for our sample. W e find
positive autocorrelations at lags one and two that are similar to the numbers reported by previous
researchers. These positive autocorrelations at low lags lead to variance ratios that are greater
than one, and gives infeasible estimates for the effects of noise trading. To mitigate the effects due
to large positive autocorrelations at short lags, we define one period of time as being three days.
Our long run measure of variance iscomputed over 30 days, i.e. 10 periods. Estimates of the
variance ratios based on these returns provide feasible estimates for the effects of noise.
[Insert Table 4 here]
Sample statistics for the variance ratios are reported in Table S. These variance ratios are
computed using the estimator given by Equation A -3 in Appendix A. The median differences in
the ratios (computed as the median of the matched difference in the post-split and pre-split
variance ratios) are significantly negative for the entire sample and also for the two sub-samples
based on the split factor. These ratios suggest that the fraction of volatility that can be attributed
to noise trading is higher after the splitrelative to the pre-split level for all three samples. Further,
since the total one-day volatility is also increasing for these groups, itsuggests that the volatility
due to noise trading afterthe splitis substantially higher relative to the pre-split level.
18
[InsertTable 5 here]
These estimates of the variance ratios, along with the bias-corrected estimates of the preand post-split one-day volatilities (reported in Table 2) can be used to estimate the fraction of the
increase in the volatility that is due to an increase in noise trading. Since both the variance ratio
estimates and the volatility estimates have been purged of microstructure biases, we can assume
that any remaining mis-pricing errors are caused by noise traders. For the total sample, the median
variance ratio is 0.94 before the split, and, from Table 2, the median pre-split one-day volatility is
2.75x1O'4.Thus, the volatility due to noise is0.165x1O'4 before the split. Similarly, after the split,
the median variance ratio is0.79, the total volatility is4.61xl0'4,and the volatility due to noise is
0.968X10"4.Thus, about 43% of the increase in the total volatility of 1.86x10"* is due to the
increase in noise volatility, with the remaining being attributable to an increase in the permanent
component Similar results are obtained for the sub-samples based on the splitfactor. For the
small splitfactor sub-sample, about 41% of the increase in the total volatility is due to noise, and
for the large split factor sub-sample, approximately about 40% of the increase in the total
volatility can be attributed as such.
The above results suggest thatthere is a significant increase in b o th the noise and the
permanent components of the volatility afterthe split. Further, as indicated in Table IB, the total
number of trades increases, on average, after the split. Note that the total number of trades
consists of trades executed by both noise and informed traders. Thus, an increase in both
components of the volatility, coupled with an increase in the total number of trades, is consistent
with the argument that after a stock split, there is an increase in the level of both noise and
19
informed trading. In the next section, we investigate this further using a cross-sectional regression
framework.
3 .2 .c
C r o s s - s e c t io n a l A n a ly s is o f V o la t ilit y C h a n g e s
Trading activity can be measured by either the number of transactions or the size of the
trade (i.e.the turnover volume). Earlier studies have documented a positive relationship between
volatility and trading volume (see Karpoff (1987) for a review). However, Jones, Kaul, and
Lipson (1994) conclude that itis the number of transactions per se, and not their size, that
generates volatility. That is,the effect of trade size is subsumed in the number of transactions.
Given their conclusions, we use changes in the number of trades as our measure of changes in
trading activity.3
Ifwe assume that insider transactions are information driven, then we can use the number
of trades executed by insiders as a proxy for informed trading. The change in the number of
insider transactions after the split (from the pre-splitvalues) would then proxy for the change in
informed trading activity. By netting out the insidertrades from the total number of trades, we can
use the change in the net number of trades as a proxy for the change in noise trading.4
Using these proxy variables, we investigate the relationship between changes in trading
3 Jones, Kaul, and Lipson include both the number of trades and volume in theircross-sectional
analysis of volatility. In our study, we are interested in the change in trading activity. W e find that inour sample,
the change in the number of trades ishighly correlated with the change in turnover volume: the correlation
coefficientbetween these two variables is0.79. Thus, including both measures of changes in trading activity results
in theusual problems associated with multi-collinearity in the independent variables.
4
However, ifinsider transactions are motivated by liquidity concerns, then thechange in trades would
not allow us to estimate the change in informed trading. Moreover, since the number of insider trades is a small
fractionof the total number of trades (see Table IB), the effectof theirtrades on volatility would be subsumed in
our proxy for noise trading.
20
activity and changes in the bias-corrected total volatility,the change in the long term volatility,
and the noise component of the volatility. In our firstmodel, the dependent variable is the change
in the bias-corrected total volatility of the stock. Specifically, the model is:
_2
>
° B ,D ,2
_2
i
f
n n t
2)
(
+ a.L In
= an
u + a.
1 In
In n t J i
w
NTT,"!
J
+ 0X3(1 + SFACj)+ cc4 ln(MVALj)+ e,
where Og Djisthe bias corrected volatility in periodj (jequals 1 for the pre-split period and 2 for
the post split period), NNTj is the number of trades in periodj,net of insider trades, NTT ,is the
number of insider trades in periodj,SFAC is the announced splitfactor, and M V A L isthe market
value of the splitting firm’s equity, measured two days before the announcement of the split.
The data presented in Table 2 indicates that the change in the bias-corrected volatility is
much higher for the sub-sample with the large split factors (SFAC k 1.0). To the extent that the
magnitude of the splitfactor conveys information to the market (see McNichols and Dravid
(1990)), this would affect the volatility as well, through itseffect on the permanent component of
the volatility. To control for the effect of this signal on volatility changes, we include the split
factor as an additional independent variable in our regressions. Finally, inclusion of M V A L allows
us to control for omitted variables which are correlated with the size of the firm.
The estimates of the model parameters in Equation (2) are presented in the firstrow of
Table 6.Our estimate of the coefficient on the change in the net number of trades (cti) is
significantly positive. Thus, an increase in the number of noise transactions increases the volatility
21
of the stock afterthe split. The coefficient on our measure ofinformed trading (a2)is
insignificantly different from zero at allconventional levels. There are two possible explanations
for this observation. First, this coefficient would be insignificant ifthere isno significant change in
the number of insider transactions after the split. The statisticsin Table IB indicate that the
median change isindeed zero. Alternatively, ifinsider transactions are a poor proxy for informed
trading, and in fact are motivated by liquidity concerns, then theireffect will be subsumed in the
measure of the change in net trades.
[Insert Table 6 here]
The coefficienton the splitfactor isalso significantly positive. Firms which employ a
larger splitfactorexperience a greater is the change in the total volatility. While this finding is
consistent with the statisticspresented in Table 2,additional insights about the role of the size of
the splitfactor can be obtained by examining the change in the components of the volatility. If
splits convey private information to the market, as suggested by the signaling hypothesis of splits,
then the change in the permanent component of the volatility would be positively related to the
magnitude of the splitfactor, and the change in the noise component of the volatility would be
unrelated to the split factor. W e further investigate this below.
Finally, the coefficient on M V A L issignificantly positive. Iflarge firms have low volatility
to begin with, even a small increase in the volatility would result in a large percentage change.
This would manifest in a positive relationship between firm size and volatility changes.5,65
5
When we partition our sample into two sub-samples based on thepre-splitfirm size (MVAL), we find
thatthe mean pre-splitbias-corrected volatilities for the small and large firm sub-samples are0.000461 and
0.000342 respectively. The mean ratios of the post-splitto pre-split volatilityforthese two sub-samples are 2.35
22
In our second model, the dependent variable is the change in the long term volatility of the
stock. Specifically, we estimate the following model:
{ NIT^
'n n t 2]
+ a,ln
= a„u+ a.1In
2,
iNrrJ
I n n t ;J
U 2Ji
+ oc3(1+ SFACj) + <x4 ln(MVALj) + e,
where Zj isthe volatility based on 30-day returns in periodj (jequals 1 for the pre-split period and
2 for the post splitperiod) and the other variables are as defined earlier. Estimates of the
parameters of this model are presented in the second row of Table 6.There is a significant
positive relationship between the change in the long term volatility and the change in the net
number of trades. The change in the long term volatility is again unrelated to the change in insider
trades. A possible reason for this is that the change in insider trades isa poor proxy for informed
trading.
Further, the coefficient on the splitfactor (a3) is significant and positive. Moreover, the
estimate of this coefficient (and the associated t-statistic) is greater than that in Equation 2. This is
consistent with the hypothesis that splits are signals of private information about the firm. The
effect of thisrelease of information on the total volatility isprimarily driven by itseffect on the
permanent component of the volatility. Further evidence to support this argument isprovided in
the model relating the change in the noise component of the volatility to trading activity.6
and 3.43 respectively.
6
We also estimate the model in Equation (2), as well as allsubsequent cross-sectional regression
models, without the term involving our measure of firm size (MVAL). In allcases, our parameter estimates are
virtually identical to those obtained with the inclusion of the M V A L term as an independent variable. Thus, our
conclusions do not depend on the inclusion or omission of this variable, and we report the results for the estimates
obtained by inclusion of this term.
23
The lastrow of Table 6 reports our estimates of the following model:
(4)
+ a 4 ln(MVAL-,)+ a 5In -§•
+ £,
V2 i )\
In this model, since we control for the change in the permanent component of the volatility on the
right hand side, the dependent variable then measures the change in the noise component of the
volatility. Once again, the estimate of a \ issignificantly positive, while the estimate of a 2 is
insignificantly different from zero. Thus, the change in the noise component of the volatility is
significantly positively related to the change in the net number of trades, but not to the change in
insider trades. Interestingly, the coefficient on the splitfactor variable (a3)isalso insignificant and
provides supporting evidence for the argument presented earlier, that splits convey private
information to the market. Since the noise component of the volatility would be unrelated to
private information released through the split, the change in this component of the volatility would
be unrelated to the size of the announced split factor.
Taken together, our results suggest the following. Stock splits, on average, result in an
increase in trading activity, and this in turn leads to an increase in the volatility even after we
control for microstructure biases in the estimated volatility. There is an increase in both the
permanent as well as the transient component of the volatility, and the increase in trading activity
positively affects both of these components. These results allow us to extend the conclusions
drawn by Jones, Kaul, and Lipson (1994) about the relationship between the level of the volatility
and the level of the number of transactions. Changes in these variables are also positively
24
correlated in the case of stock splits. Finally, the change in the permanent component of volatility
ispositively related to the split factor, but the change in the noise component is not. This is
consistent with the signaling hypothesis for stock splits.
4.
Changes in Bid-Ask Spreads Following Stock Splits
In this section, we investigate changes in bid-ask spreads following stock splits. The
descriptive statisticspresented in Table IB indicate that for the total sample, the proportional
spread increases after the splitby an average of 32% and thatthis increase iseven higher for firms
that employ a large split factor. W e examine two possible reasons for this increase. First, an
upward bias in post-split absolute spreads, caused by price discreteness, could result in an increase
in the post-split proportional spread. Discreteness in stock prices leads to minimum absolute
spreads of 12.5 cents, and increments in the spreads are also forced to be in steps of 12.5 cents.7
Second, the increase in the proportional spread could be due to an increase in one or more
components of the bid-ask spread. Specifically, an increase in the information asymmetry in the
market would lead to an increase in the adverse information component of the spread, thereby
leading to an increase in both the absolute spread as well as the proportional spread.
4 .1
E f fe c t o f P r ic e D is c r e te n e s s o n S p re a d s
Suppose a stock has a pre-split share price of $50 and a pre-split bid-ask spread of $1,375
7
Unlike the NYSE, NASD does not have a minimum spread policy. However, N A S D A Q isdesigned to
process spreads of l/32ndfor stocks priced under $10 and l/8thfor stocks priced above $10. On the consolidated
tapes (CTA), trades in N A S D A Q stocks under $10 are rounded to l/16th(Source: Market 2000 Study by the SEC).
25
(i.e. a proportional spread of 2.75%). After a 2:1 stock split,the share price would drop to $25.
In order to keep the proportional spread constant, the absolute spread after the split would have
to be $0.6875. Ifthe spread isconstrained to be in multiple of eighths, the post-split spread would
be adjusted upwards to the nearest eighths. This results in a ‘target’post-split absolute spread of
$0.75. Ifthe post-split spread is indeed $0.75, the proportional spread would be $0.75/$25 or 3%
after the split,indicating a 9.1% increase in the proportional spread. In this case, all of the
increase in the proportional spread can be attributed to price discreteness. Ifthe post-split spread
is set at $0,875 (i.e. a proportional spread of 3.5%), the observed increase in the proportional
spread would be 27.27%. Ifwe control for price discreteness, the spread increases from the target
spread of $0.75 to the actual spread of $0,875, representing a 16.67% increase.
The preceding example illustrates how discreteness in absolute spreads can inflatethe
observed increase in proportional spreads. W e employ the adjustment procedure illustrated in this
example to our sample of stock splits. Specifically, letABSj represent the absolute spread in
period j (j= 1 for the pre-split period and j=2 for the post split period). Let AS represent the ratio
of A B S 2 to [ABSi/(l + SFAC)], where SFAC isthe announced split factor. Thus, AS measures
the uncorrected change in the spread. The target post-split spread, TS2,is computed as [ABSi/(l
+ SFAC)] rounded up (ifnecessary) to the next highest multiple of $0,125. Then the ratio
[ABS2/TS2],denoted by AS* represents the change in the absolute spread after correcting for
price discreteness. Ifprice discreteness is the only reason for the observed increase in spreads,
then AS* should equal 1.0. On the other hand, ifAS* is greater than 1,then price discreteness
alone cannot explain the observed increase in spreads.
26
To estimate AS*, we use the median absolute spread in the pre and post-splitperiods for
each stock. In Table 7, we report the cross-sectional mean and median values of AS and AS* for
the total sample as well as for the sub-samples grouped by the splitfactor. For the total sample,
we find that the median increase in the absolute spread isa significant 50% before correcting for
price discreteness, and 33% afterthe correction. Thus, price discreteness alone cannot account for
the observed increase in spreads following stock splits.The statistics for the sub-samples based on
the splitfactor lead to similar conclusions for each sub-sample. W e also note that the increase in
spreads is greater for the large split factor sub-sample, both before and aftercorrecting for price
discreteness.
[InsertTable 7 here]
4 .2
C h a n g e s in th e A d v e r s e S e le c tio n C o m p o n e n t o f th e S p r e a d
Since price discreteness alone cannot account for the observed increase in spreads,
we focus on the components of the proportional spread to gain insights about the reasons for the
observed increase. In particular, we decompose the proportional spread into itsorder processing
and adverse information components, using the methodology in George, Kaul, and Nimalendran
(1991). The total spread in general consists of three components: order processing, adverse
information, and inventory cost. In George, Kaul, and Nimalendran, the part of the inventory cost
component that decays within a day across a number of transactions is included in the order
processing component, while that which does not decay within a day is included in the adverse
selection component [see Jegadeesh and Subrahmanyam (1993)]. However, Stoll (1989) has
27
found that the inventory cost component is a small fraction of the total spread (less than 10%).
Madhavan and Smidt (1991) also find that inventory effects are economically and statistically
insignificant. Given these results, we focus only on the order processing and adverse information
components in our study.
The methodology in George, Kaul, and Nimalendran depends on using the difference in
returns based on transaction prices and returns based on bid-to-bid prices to purge the bias due to
changing expected returns and partial adjustment. In addition, by taking the difference between
the two returns, the effects due to the unanticipated component of returns (which are a large
fraction of the error) are eliminated. This substantially increases the efficiency of the estimates.
Let R*tand R® represent the returns based on the closing transaction price and the closing
bid price of firm iat time trespectively. Define R?t= R?t- R®, as the difference in these returns.
George, Kaul, and Nimalendran show that ifSj isthe quoted spread, and jq is the fraction of the
quoted spread due to order processing costs (and 1-7tjis the fraction due to adverse selection
costs, then
Cj = 2^-[Cov(RPt,RPt_,)] = jtjSj
(5)
Ifwe assume that for a group of stocks the fraction of the quoted spread that isdue to
order processing costs (JtO is constant and equal to it , then we can use the following crosssectional model to estimate k
:
Q = ito+ JcSj + Ei,i= 1,.... N
(6)
W e firstestimate Equation (6)separately for the pre-split and the post-split periods for the
28
total sample, as well as for the sub-samples based on the splitfactor. In thisestimation, Si is the
average proportional spread. For each sample, this procedure provides us with estimates of it in
the pre-split and the post-split periods. These estimates of n are then used to compute the order
processing costs as a percentage of the share price (= itSj) and the adverse information costs (=
(l-7t)S0.
Table 8 reports the average values of the proportional spread, as well as of the order
processing and adverse information components of the spread. These values are reported for the
pre- and the post-split periods, and for the total sample as well as for the sub-samples based on
the magnitude of the split factor. The last column in Table 8 reports the difference between the
pre- and post-split values.
[InsertTable 8 here]
In the total sample, the proportional spread increase by 0.513, and this increase is roughly
evenly divided into the increases in the order processing and the adverse information component
of the spread. For the small splitfactor sub-sample, virtually allof the increase in the proportional
spread isdue to the increase in the adverse information component, with the order processing
component remaining statistically unchanged from the pre-split level. By contrast, there isa
relatively large increase in the proportional spread, and about 69% of this increase is due to an
increase in the order processing component.
The increase in both the total proportional spread and the adverse information component
of the spread suggest that unconditionally, liquidity worsens after a stock split. Moreover, the
increase in the adverse information component also suggests an increase in the information
29
asymmetry in the market. This isconsistent with an increase in informed trading activity (as in
Brennan and Hughes (1991)). However, Admati and Pfleiderer (1988) argue that an increase in
noise trading would endogenously increase the number of informed traders, and the net impact of
this change in trading activity would depend on whether the signals received by the informed
traders are close substitutes or complements. Ifthe signals received are diverse and sufficiently
precise, information asymmetry would increase even ifthe number of noise traders in the market
increases. Thus, a net increase in the adverse information component isnot inconsistent with an
increase in the level of noise trading afterthe split. W e examine below the relationship between
changes in trading activity and changes in both the total proportional spread and the adverse
information component.
4 .3
E f f e c t o f C h a n g e s in T r a d in g A c t iv it y o n C h a n g e s in S p re a d s
To examine the relationship between changes in the proportional spread and changes in
trading activity, we estimate the following cross-sectional model using ordinary least squares
regression:
= a 0 + a,ln
"n n t 2"
+ a 2ln
I nnt.1
where Sj isthe proportional spread in period j (j= 1 for the pre-split period and 2 for the post
splitperiod) and the other variables are as defined earlier. Estimates of the parameters of this
model are presented in Table 9. In the firstrow of Table 9, we present our estimates using both
measures of changes in trading activity. In the second and third rows, we use the change in the net
30
number of trades and the change in insidertrades as the measure of change in trading activity,
respectively.
[Insert Table 9 here]
The results presented in Table 9 indicate that changes in proportional spreads are inversely
related to changes in the net number of trades, regardless of whether we control for the change in
insidertrades. Our estimates of at are significantly less than zero in the firsttwo rows of Table 9.
Thus, while unconditionally, the proportional spread increases after the split, thiseffect is less
pronounced the larger the increase in the net number of trades.
Curiously, the change in the proportional spread is unrelated to the change in insider
trades when the change in net trades is also used as an explanatory variable, but inversely related
to itwhen the change in insider trades isthe only measure of the change in trading activity. The
estimate of eta isinsignificant in the firstrow of Table 9, but significantly less than zero in the last
row. This suggests that the effect of the change in insider trades on proportional spreads is
subsumed in the effect of the change in non-insider trades. There are two possible reasons why
this might be the case. First,insider trades are relatively small in number when compared to non
insider trades (see Table IB). Second, changes in insider trades may be motivated by liquidity
reasons rather than being information driven. Ifso, an increase in insider trades afterthe split
would tend to attenuate the increase in spreads. This inverse relationship is observed in the
negative estimate of <Xa in the last row of Table 9. Ifchanges in insider trades were information
driven, then we would expect this estimate to be positive. W e investigate this furtherby
examining the relationship between changes in the adverse information component of the spread
31
and our measures of changes in trading activity.
Finally, we note that the estimates of the coefficients on the splitfactor, as well as those
on the firm size variable are significantly positive in all three versions of Equation (7) in Table 9.
Firms that employ a larger split factorexperience a greater increase in the proportional spread, as
do large firms.
Changes in trading activity would also have an impact on the adverse selection component
of the spread. An increase in noise trading would reduce this component of the spread, while an
increase in informed trading would tend to increase this component. To examine the relationship
between the change in the adverse information component of the spread and our measures of
trading activity, we estimate the following model:
(8)
where COVj isdefined as the auto-covariance of R® in periodj, and the other variables are as
defined earlier. From Equation (6),this allows us to control for the change in the order processing
component of the spread. Since the dependent variable in Equation (8) isthe change in the total
proportional spread, and we control for the change in the order processing costs on the right hand
side, Equation (8) allows us to estimate the change in the adverse information component of the
spread.
Table 10 reports our estimates of the parameters of Equation (8).As in Table 9, we
estimate three versions of the model. The change in the adverse information component of the
32
spread isinversely related to the change in the net number of trades (the estimate of cti is
significantly negative in the firsttwo rows of Table 9). This isconsistent with an increase in noise
trading after the split. Interestingly, allof our estimates of the coefficient on the change in insider
trades (ai) are significantly negative. Ifchanges in insider trades are motivated by information, a
large increase in these trades would result in a proportionately large increase in the adverse
information component of the spread. Consequently, we would expect these coefficients to be
positive. Our results suggest that this is not the case.
[Insert Table 10 here]
Taken together, our analysis of the changes in spreads following stock splits suggest the
following. The observed increase in the proportional spread isnot solely due to price discreteness.
Rather, we observe an increase in both the order processing as and the adverse information
component of the spread. While this indicates that liquidity worsens after the split,the increase in
spreads isinversely related to changes in trades. Since we find that on average, the number of
trades increases afterthe split, the decline in liquidity isless pronounced the larger the increase in
the number of trades.
5. Conclusion
This paper has examined the impact of the change in trading activity surrounding a stock
spliton the liquidity of the stock. The results establish that the increase in volatility and spreads
cannot be attributed solely to microstructure biases like price discreteness and bid-ask bounce.
There isan increase in the number of trades around the split, and the larger the increase in the
33
number of trades, the larger isthe change in volatility and the smaller isthe change in spreads
(total, as well as adverse information component). Since the change in the number of trades
affects both the transient and permanent components of volatility, the increased trading activity
cannot be attributed solely to either an increase in informed trading or an increase in noise trading.
The finding that increased trades lead to lower spreads isconsistent either with these trades being
predominantly noise motivated, or with the informed traders having very similar information (so
thatcompetition between them reduces spreads).
These findings suggest that any analysis of the impact of stock splits on traditional
measures of liquidity (like volatility and spreads) must firstexamine why differentfirms seem to
be more or less successful in attracting additional trades to their security. The subsequent
consequences for liquidity then seem to be consistent with existing theories on the way in which a
change in trading activity affects liquidity. An analysis of these causes for a change in the number
of trades represents an interesting direction for future research.
34
APPENDIX A
A.1
E s t im a t o r o f th e v o la t ilit y c o r r e c t e d f o r p r ic e d is c re te n e s s
Ball (1988) shows that ifstock prices follow a Geometric Brownian motion with an
instantaneous true underlying variance o2 and price P, then the bias induced by price discreteness
can be approximated as dVbP2,where d isequal to 1/8. This approximation is valid for values of
d/aP less than 2.50 (see Ball (1988), Table HI). To correct for this bias, we need to estimate 1/P2.
Since there is a price trend in the pre-split period, we use the average of I/P3 from the estimation
periods instead of one over the average of price squared. From Jensen’s inequality, since E(l/P2)
> l/EtP2),the estimated bias would bias ittowards an upper value.
For the sample of firms in this study, the average value of d/aP is 0.34 and 99.9% of the
estimates are less than 2.50 (based on an estimate of s using bid-to-bid prices and an estimate of P
using the average bid price in the estimation period). Hence, Ball’s approximation should be valid
for our sample. W e correct for the bias due to price discreteness by deflating the volatility
estimate using bid-to-bid prices as follows:
2
^B.D =
a5
**B ~
Y-
6(T2 -T,)t
^ P B2t
where a BD is the volatility corrected for price discreteness,
(A.1)
isthe volatility estimated using bid-
to-bid prices, (T2 - TO is the range of the estimation period, and PB,tis the bid price at time t(Ti^
t £ T 2).
35
B.
2
E s t im a t o r o f m u lt i- p e r io d v o la t ilit y
W e use the following estimator of the k-period volatility,based on Lo and MacKinlay
(1988):
-k+l
(A.2)
° ‘*k)
S
^R , J
^
6r|;p,2,
where d*(k) = estimate of k-period volatility based on bid-to-bid prices and with correction for
price discreteness (the second term corrects for discreteness),
m = actual number of overlapping k-period observations,
n = number of one-period (daily) observations,
Rg = k-period return using overlapping one period returns based on bid-bid prices,
jj.k= the sample mean of overlapping k-period returns,
T = number of daily observations (= 180), and
PB,,= bid price on day t.
B .3
E s t im a t o r o f th e v a r ia n c e r a t io
The variance ratio isdefined as the ratio of the k-period volatility to k times the oneperiod volatility. The volatility estimates are corrected for the biases due to the bid-ask bounce
and price discreteness. For each firm i,the variance ratio isgiven by:
36
Var(R^) —
VR(k) = k*
GEt
Var(R'B)-
2 yfk-j^l
-lM
(A~3)
k J
6P2
where Var(Rg) is the k-period variance based on bid-to-bid returns. The quantity [d^P2] in the
RHS of the above equation isthe adjustment for the bias die to price discreteness. The final term
in the RHS of above corrects for the small sample bias in the expected value of the
autocorrelation. Even ifthe returns are uncorrelated, the expected value of the autocorrelation is
biased by -1/(T-1) [See Kendall ar.d Stuart (1977)].
37
TA BLE1A
Sample Characteristics for 366 Stock Split Announcements made by N A S D A Q - N M S Firms
between January 1983 and December 1990, for the Total Sample, and for Sub-samples Classified
by the Split Factor.*
TotalSample
Variable
Mean
N
LargeSplitFactor
Sub-Sample
(SFAC £1.0)
Mean
Median
21L0
156
366
p-value'H’
SFAC
0.72
0.50
0.41
0.50
1.14
MVAL
259
123
176
85
371
182
NSHR
pAV
rl
P“
pAV
7.36
4.38
6.52
4.10
8.50
4.93
0.110
25.80
22.80
19.65
17.51
34.14
31.61
<0.001
30.50
27.50
23.30
21.80
40.30
37.70
<0.001
17.70
16.50
16.50
15.50
19.30
18.0
0.001
PB
r2
NMMKi
18.20
17.70
16.90
15.90
19.90
19.0
<0.001
7.80
6.00
7.30
6.00
8.40
7.0
0.12
nmmk2
7.00
6.00
6.70
6.00
7.50
6.0
0.32 I
r2
t
Median
SmallSplitFactor
Sub-Sample
(SFAC 2 0.5)
Mean
Median
1.00
<0.001
N isthenumberofobservationsineachsub-sample; SFAC istheannouncedsplitfactor; MVAL isthe
marketvalueofequity(in$ millions),measuredtwodaysbeforetheannouncementofthesplit; NSHR isthe
numberofoutstandingshares,inmillions,asoftwodaysbeforetheannouncementofthesplit;PAVand
PAVaretheaveragebidpricesinthepre-splitandthepost-splitestimationperiods,respectively;P*andP*are
theclosingbidpricestwodaysbeforetheannouncementofthesplitandtwodaysaftertheex-splitday,
respectively;andNMMKi andNMMK-i aretheaveragenumber ofmarketmakers inthepre-splitandpost
splitperiods.
** p-ValueisfortheWilcoxon SignRank Sum testofdifferencesinmediansbetweenthetwo sub-samples.
38
T A B L E IB
Changes in Samples Estimates of the Proportional Spread, Transaction Price Based Daily
Volatility, and Measures of Trading Activity for 366 Stock Split Announcements Made by
N A S D A Q - N M S firms between January 1983 and December 1990.
1
Variable,
Subscript 1= Pre-Split
Subscript2 = Post-Split
SampleSize(N)
Proportional
s,
Spread
s2
S2/S,
DailyReturn
Volatility
BasedonClosing
TransactionPrices
(x 104)
of
2
of'O?
AverageNumber
ofDailyTrades
AverageVolume
Turnover
(xlO3)
|
AverageVolume
Turnoverper
Trade(x 104)
AverageNumber
ofInsiderTrades
(x 101)
TotalSample
Mean
SFACS0.5
SFAC^l.O
Median
Mean
3.11
2.32
3.36
2.68
3.62
2.79
3.09
1.32**
1.23t+
3.64
♦*
1.20
7.73
5.63
12.42
8.80
366
**
2.25
Median
210
1.70n
Mean
Median 1
156
II
2.78
1.77 |
2.48
1.08"
3.60
♦*
1.49
8.29
5.95
6.97
4.56
11.38
8.37
13.83
9.67
**
1.98
1.42"
**
2.61
1.45"
2.19"
NT,
21.56
9.37
15.88
7.76
29.21
10.96
nt 2
32.33
12.00
20.77
9.95
47.90
**
1.71
17.56
nt 2/n t ,
1.53“
1.28"
1.39”
1.12"
1.37"
VT,
3.40
2.50
3.24
2.52
3.69
2.49
vt 2
3.80
2.30
2.41
3.90
2.13
v t 2/v t .
1.19“
1.00
3.81
**
1.24
1.07"
1.11
0.93 I
(VT/NT),
3.19
2.64
3.45
3.00
2.83
2.09
(VT/NT)2
2.53
1.92
2.81
2.44
1.89
1.41
I
|
(VT/NT)2
/(VT/NT),
**
0.83
0.77"
0.93*
0.82"
0.68“
0.65"
1
NIT,
11.98
6.11
10.21
5.56
14.37
6.67
nit2
11.76
**
6.67
10.26
5.83
13.77
7.22
nit2/nit1
2.12
1.00
2.21"
1.00
2.01"
1.00
+t(*) The median ratioissignificantlydifferentfrom 1atthe 1%(5%)levelbasedon theWilcoxonSignRank Test.
( ) Hie mean ratioisstatisticallydifferentfrom 1atthe 1% (5%) levelusingasimplet-test.
39
I
I
|
T A B LE2
Median Estimates of Daily Return Volatilities Before and After a Split, Based on Transaction Prices, Bid Prices, and Bid Prices
Adjusted for Price Discreteness for the Total Sample and for the Sub-Samples by Split Factor.
Foreachfirm,thepre-andpost-splitvolatilityestimatesarebasedon 180dailyreturnsinthetwoestimationperiodsrespectively. Medianestimatesreported
inthetablearebasedon thecross-sectionalestimatesforeachsample.Allreportedmedianvaluesarescaledby afactorof104.d* isthevolatilityestimate
basedon transactionpricereturns, d* isthevolatilityestimatebasedon bid-bidreturns,and d* Disthevolatilityestimatecorrectedforboththebid-ask
bounceandpricediscreteness. Itiscomputedasfollows:
d2
S.2
^B.D
a
i
(Ta-T,)£p2T
where(T2 -TO istherangeoftheestimationperiod,andPB,isthebidpriceondayt.
TotalSample,N = 366
SFAC £ 0.5,N = 210
SFAC £ 1.0,N= 156
PreSplit
PostSplit
Difference
(p-value/
Ratio
(p)tt
PreSplit
PostSplit
Difference
(p/
Ratio
(P)ft
PreSplit
PostSplit
Difference
(P)f
Ratio
(P)n
$
5.63
8.80
2.90
(<0.001)
1.70
(<0.001)
5.95
8.37
1.74
(<0.001)
1.42
(<0.001)
4.56
9.67
4.66
(<0.001)
2.19
(<0.001)
K
2.88
4.79
1.72
(<0.001)
1.80
(<0.001)
3 14
4.43
0.99
(<0.001)
1.41
(<0.001)
2.39
5.66
2.65
(<0.001)
2.24
(<0.001)
2.75
4.61
1.63
(<0.001)
1.81
(<0.001)
2.98
4.19
1.00
1.42
(<0.001)
2.38
5.25
2.61
(<0.001)
2.18
(<0.001)
(<.001)
t p-valuefortwo tailtestbasedon theWilcoxonmatchedpairsignranktestforHo:Median Difference= 0.
tt p-valuefortwo tailtestbasedontheWilcoxonmatchedpairsignranktestforHq:Median Ratio= 1.
40
T A B LE3
Median Estimates of Multi-Period Return Volatilities in the 180 Day Pre-Split and Post-Split
Periods, for the Total Sample and for Sub-Samples Classified by the Split Factor.
The estimatorusedis
n-k-4
Oc
2(k) =
d^
m(l-k/n) X W - A J
6T
where,m istheactualnumberofoverlappingk-periodobservations,nisthenumberofoneperiod(daily)
observations, R*is thek-periodreturnusingoverlappingoneperiodreturnsbasedonbid-bidprices,|ikisthe
samplemean oftheoverlappingk-periodreturns,andPBtisthebidpriceon day t.
1
Numberof
Days
Pre-Split
Volatility
(x 104)
Post-Split
Volatility
(x104)
Median
Difference
(x 104)
Median Post-Split
Volatility/Pre-Split
Volatility
TotalSample,N = 366
5
18.38
28.43
9.26”
1.62”
10
37.29
57.36
18.11”
1.58”
20
68.43
102.74
28.20”
1.54”
30
95.76
139.17
34.33”
1.57”
SFAC £ 0.5,N = 210
5
19.06
27.19
5.69”
1.37”
|
10
38.09
53.17
10.65”
1.32”
I
20
75.79
97.96
12.11”
1.29”
I
30
102.10
126.52
11.87”
1.32”
I
SFAC ^ 1.0,N = 156
* (**)
f (n)
I
5
16.76
32.33
12.85”
2.00”
10
36.29
64.71
25.04”
2.08”
20
61.51
111.56
47.74”
1.96”
30
77.24
146.57
55.65”
---- -- 1.81” — . ..n
1
Indicates a rejection of the null hypothesis that the median difference is zero based on the Wilcoxon Matched Pair
Sign Rank Test, at the 5 % (1 % ) level for a two-tail test.
Indicates a rejection of the null hypothesis that the median ratio is one based on the Wilcoxon Sign Rank Test, at the
5% (1%) level for a two-tail test.
41
TA BLE 4
Median Auto-Correlations ofReturns (xlO2)Based on Bid Prices fortheTotal Sample,
and forthe Sub-Samples Classifiedby the SplitFactor.
TotalSample,N=366
SI-AC £ 0.5, N= 210
SAFC 2:1.0,N=156
Lag
Pre-Split
Post-Split
Difference
(p-value)t
Pre-Split
Post-Split
Difference
(p-value)*
Pre-Split
Post-Split
Difference
(p-value)*
1
15.40
10.98
-3.19
(c.001)
14.57
11.45
-2.30
(0.094)
16.60
10.77
-4.85
(<0.001)
2
3.38
1.95
-1.16
(0.011)
2.46
3.81
0.60
(0.670)
4.52
0.24
-3.31
(<0.001)
3
1.21
-1.00
-1.89
(<0.001)
1.25
-0.45
-1.06
(0.111)
1.10
-1.31
-3.95
«0.001)
4
0.07
1.13
1.05
(0.12)
-0.33
1.19
1.28
(0.277)
0.45
1.11
1.01
(0.286)
5
0.30
0.72
0.55
(0.62)
0.65
0.15
0.189
(0.716)
-0.97
1.04
1.08
(0.239)
6
-0.30
0.05
0.56
(0.40)
-0.01
-0.11
-0.55
(0.552)
-1.21
0.77
2.23
(0.048)
7
-1.10
-0.97
-0.26
(0.62)
-1.08
-0.92
-0.18
(0.950)
-1.28
-1.12
-0.26
(0-410)
8
-1.15
-1.26
-0.21
(0.35)
-1.14
-0.62
0.11
-1.16
-2.54
-0.66
(0.407)
-0.73
(0.11)
-2.18
-1.56
0.24
(0.866)
-0.09
-2.24
-2.41
(0.008)
0.22
-1.10
-0.14
0.40
(0.394)
-0.48
-1.29
-0.53
(0.384)
9
-1.38
-2.08
10
-0.85
-0.51
(0.602)
(0.99)
t p-value based on the Wilcoxon matched pairs sign rank test. H o :Median difference = 0.
42
TA BLES
Median Estimates of Variance Ratios During the 180 Day Pre-Split Period
and the 180 Day Post-Split Period, For the Total Sample and for Sub-Samples Classified by the
Split Factor.
The estimatorforthevarianceratiois
VR =
where,Var(R‘
,)isthe 1-period(3-day)dayreturnvariancebasedonbid-to-bidreturns,andVar(R‘)isthek-period
(30-day)returnvariancebasedon bid-bidprices,andk isequalto 10.Thequantity[(1/6P2]istheadjustmentfor
thebiasduetopricediscreetness,whered isequalto1/8th.,andP '.sthepriceofthestock. The finalterminthe
equationcorrectsforthesmallsamplebiasintheexpectedvalueoftheautocorrelation,andT isthenumberof
one-periodreturnsused.
r
r
I
Pre-Split
Post-Split
Difference
™
(N = 366)
0.94
0.79
-0.13**
SFAC <i 0.5
(N=210)
0.95
0.88
-0.12**
SFAC £1.0
(N=156)
0.93
0.75
-0.15**
Indicatesarejectionofthenullhypothesisthatthemediandifferenceiszerobased on theWilcoxonMatched
PairSignRank Test,atthe 1percentlevel.
43
TA B LE6
Ordinary Least Squares Estim ates of Model of the Determinants of the Change in the B ias Corrected V olatility Follow ing Stock Sp lits/
1 Dependent
Variable
Intercept
,( nnt^
In n t J
-0.892
(-1.68)*
0.393
(4.62)
/V 2>
i.1 2
X 2J
V^l
-1.136
(-2.07)**
0.428
(4.25)***
'2
'
In °B,D,2
.CTB.D.l,
-0.196
(-0.53)
0.117
(1.73)*
(1+SFAC)
I nit J
ln(MVAL)
|
' i
'
B,D,2
In °_2
B.D.l,
|
lnf
(
0.028
(0.53)
-0.22
(-0.38)
0.042
(1.11)
y 2 "N
Adjusted R 2
0.173
(1.75)*
0.089
(2 .02)***
0.08
0.198
(1.66)***
0.086
(1.84)**
0.08
0.051
(0.65)
0.035
(1.11)
0.633
(18.25)***
0.52
o*D,isthedailyvolatilityinperiodj,correctedforthebiasduetoboththebid-askbounceandpricediscreteness(j= 1forthepre-splitperiodand 2forthe
post-splitperiod);E*isthevolatilitybasedon30-dayreturnsinperiodj;NNTj isthenumberoftradesinperiodj,netofinsidertrades;NITjisthenumberof
insidertradesinperiodj;SFAC istheannouncedsplitfactor;andMVAL isthemarketvalueofthesplittingfirm’sequity,measuredtwodaysbeforethe
announcementofthesplit.
t-statisticsareinparenthesis.*indicatessignificanceatthe10% level,** atthe5% leveland *** atthe 1% level.
44
T A B LE7
Effect of Price Discreteness on Absolute Spreads Around Stock Splits for the Total Sample and
for Sub-Samples Classified by the Split Factor.
The table reports the cross-sectional mean and median values for the ratio of the median post-split
spread to the median pre-split spread (AS), and also for the ratio of the median post-split spread
to the median target spread in the post-split period (AS*). For each firm i,
. ABS,.
and AS = •
''
TSW
ABSU
ABSW
where ABSjj isthe median absolute spread in periodj (j= 1 for the pre-splitperiod and 2 for the
post-split period), TS2,i= {ABSi,i/(l+SFAQ)} rounded up to the next highest eighths, and S F A Q
isthe splitfactor.
Total Sample
(N = 366)
r
AS
AS*
Mean
(p-value)f
Median
(p-value)n
Mean
(p-value)t
Median
(p-value)t+
1.55
(< 0.001)
1.50
« 0 .001)
1.53
(< 0.001)
1.33
(< 0.001)
SFAC < 0.5
(N = 210)
1.36
(< 0.001)
1.50
(< 0.001)
1.42
(< 0.001)
1.33
(< 0.001)
SFAC > 1.0
(N = 156)
|
1.80
(< 0 .001)
2.00
(< 0.001)
1.69
0 .001)
2.00
« 0.001)
1
[
I
I
(<
I
I
I
1
f p-values are for the t-test that the sample mean isequal to one.
t+p-values are for the Wilcoxon Signed Rank test that the sample median isequal to one.
45
TA B LE8
Changes in the Average Proportional Spread and its Order Processing and Adverse Information
Components Following Stock Splits.
1Total Sample
| Small Split
IFactor SubSample
(SFAC < 0.5)
Large Split
Factor SubSample
(SFAC >1.0)
Pre-Split
3.111
Post-Split
3.624
Difference
0.513*”
Order Processing
1.683
1.947
0.264*”
Adverse Information
1.428
1.677
0.249***
Spread
3.360
3.638
0.278***
Order Processing
1.783
1.765
Adverse Information
1.577
1.873
0.296***
Spread
2.777
3.605
0.828*”
Order Processing
1.498
2.067
0.569***
Adverse Information
1.279
1.538
0.259**’
Spread
46
-0.018
TA BLE 9
Ordinary Least Squares Estimates of M odels of the Determinants of the Change in the Proportional Spread Follow ing Stock Sp lits/
Dependent
Variable
Intercept
, f NNT,1
I
nnt J
Infs 0
kA j
-1.338***
(-7.49)
-0.429
(-13.06)***
Infs 0
j
-1.355
***
(-7.64)
-0.435***
(-13.57)
H Is , J
-0.923*♦*
(-4.59)
, f Nrr,^
I m J
-0.017
(-0.88)
-0.070***
(-2.82)
(1 + SFAC)
ln(MVAL)
Adjusted R2
0.239
(6.16)
0.105
(6.90)” *
0.39
0.240#**
(6.20)
0.107
***
(7.01)
0.:9
0.139
(2.19)**
0.076***
(4.03)
0.10
Sjistheproportionalspreadinperiodj(j= 1forthepre-splitperiodand2forthepost-splitperiod);NNTj isthenumberoftradesinperiodj,netofinsider
trades;NITjisthenumberofinsidertradesinperiodj;SFAC istheannouncedsplitfactor;andMVAL isthemarketvalueofthesplittingfirm’sequity,
measuredtwodaysbeforetheannouncementofthesplit
* t-statisticsareinparenthesis.*indicatessignificanceatthe10% level,**atthe5% leveland ***atthe1% level.
47
T A B L E 10
Ordinary Least Squares Estimates of Models of the Determinants o f the Change in the Adverse Information Component of the B id -A sk
Spread Follow ing Stock Splits.
Dependent
Variable
In
IsJ
In ( s 2 ]
j
Infs 0
^s t J
,
NNT.'i
Intercept
. fc o v ,^
Ico v J
-0.486***
(-5.26)
0.800
(33.21)*”
-0.171***
(-9.47)
-0.511***
(-5 53)
0.799
(32.92)*”
-0.180***
(-10.12)
-0.247***
(-2.49)
0.898
(36.99)*”
{
I
,
nnt J
f
Nrr,^
N J
-0.024***
(-2.49)
-0.042***
(-4.04)
Adjusted R2 I
(1 + SFAC)
ln(MVAL)
-0.015
(-0.73)
0.049
(6.32)
0.85
-0.013
(-0.62)
0.051
(6.54)***
0.85
-0.079
(-3.60)***
0.033
(3.84)***
0.81
Sjistheproportionalspreadinperiodj(j= 1forthepre-splitperiodand2 forthepost-splitperiod);COVj isthecovariancebetweenRf andR°,,whereRj5is
thedifferencebetweenthetransaction-pricebasedreturnandthereturnbasedonbid-to-bidprices; NNTj isthenumberoftradesinperiodj,netofinsider
trades;Nil)isthenumberofinsidertradesinperiodj;SFAC istheannouncedsplitfactor;andMVAL isthemarketvalueofthesplittingfirm’sequity,
measuredtwodaysbeforetheannouncementofthesplit.
f t-statisticsareinparenthesis.*indicatessignificanceatthe10% level,**atthe5% leveland *** atthe1% level.
48
R eferen ces
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Black, Fischer. "Presidential Address: Noise,"
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F in a n c ia l
J o u r n a l o f F in a n c e ,
1986, v41C3), 529-544.
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J o u r n a l o f F in a n c e ,
Copeland, Thomas E. and Dan Galai. "Information Effects of the Bid-Ask Spread,"
F in a n c e , 1983, v38(5), 1457-1469.
1979,
Jo u rn a l o f
Dravid, Ajay R., “A Note on the Behavior of Stock Returns around Ex-Dates of Stock
Distributions,” J o u r n a l o f F in a n c e , 1987, v42(l), 163-168.
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