“The Impact of Stock Splits on Trading Activity”
By:
Wilco Groen
University of Groningen
MSc Finance
2
“The Impact of Stock Splits on Trading Activity”
University of Groningen
MSc Finance
By:
Wilco Groen - S2808552
w.groen.2@student.rug.nl
Under the guidance of:
Dr. Adri De Ridder
May 2016
Abstract
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Contents
1. Introduction ... 4 2. Literature review ... 7 3. Hypotheses development ... 11 3.1 Sample ... 11 3.2 Volatility ... 13 3.3 Liquidity ... 14 4. Results ... 16 4.1 Price-change ... 16 4.2 Volatility ... 184.3 Liquidity (expand it) ... 20
5. Conclusion ... 23
References ... 25
Appendix A ... 28
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1.
Introduction
The stock price of Alliance Fiber Optic Products Inc. (AFOB) increases 20 percent in two trading days, while in the past few days, the only event was a stock split. This happened to the stock price, listed on the NASDAQ on September the 17th in 2013. Since they announced a 2-for-1 stock split on August the 15th, the price of the stock increased significantly. The volatility of the returns increased with almost 100 percent, while the trading volume of the stock increased as well. What happened with the stock and the underlying company that caused this increase, is it the impact of a stock split1?
Baker and Powell (1993) examine the most important reasons given by the managers for undertaking a stock split. The results clearly show that manager believe the most important reason for undertaking a split is to move the stock price into a optimal trading range. The second most important reason for undertaking a stock split is to improve the stock’s liquidity. This phenomenon is called the ‘trading range hypothesis’ in the literature.
Copeland (1979) suggests that stock splits are used to improve the liquidity of trading by realigning stock prices to an ‘optimal’ trading range. Stocks which trade in this range are presumed to be more liquid. This ‘optimal’ trading range is considered to be a compromise between the desires of wealthy investors and institutions who will minimize brokerage cost if securities are high-priced, and the desires of small investors who will minimize odd-lot brokerage cost if securities are low-priced. Implicitly there is a trade-off between diversification benefits and the lower transaction cost of round-lot trading.
Another important reason, documented by Baker and Powell (1993), for undertaking a stock split is signaling optimistic managerial expectations about the future. This is known as the ‘signaling hypothesis’.
Klein and Peterson (1989) find that companies, when announcing splits, experience greater earnings forecast revisions than similar non-splitting matched controlled companies. The difference in forecast revision between split and control companies is significantly positive related to abnormal returns at the split announcement. Lakonishok and Lev (1987) support the signaling hypothesis, they suggest that split announcements convey information about future earnings and that this information may cause abnormal returns at the announcement.
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5 Stock splits seem to be a cosmetic event, since they appear to only change the number of outstanding shares. These events have no impact on the cash flow or ownership of the company. However, prior studies show that a significant price reaction is attributable directly to splits. Grinblatt et al. (1984) have found that a split in the ‘purest’ way, where no other firm specific event took place at the same time, generates a positive abnormal return of 3 percent after the announcement. Ikenberry and Ramnath (2002) document that stock splits outperformed the benchmark on average over a one year period after the announcement.
Many researchers focus their attention on stock returns for measuring the impact of stock splits. We use other elements of trading activity for measuring the impact of stock splits. Specifically, this study put the emphasis on stock return volatility and liquidity for measuring the impact of stock splits.
However, the empirical evidence regarding the effects of stock splits is contradictory. Anshuman and Kalay (2002) present a model that shows that firms split their stocks to create liquidity. Their model implies that because of price discreteness related commissions, liquidity traders will time their trades based on stock price levels. Specifically, liquidity traders may defer their trades until stock prices drop to lower base levels in order to minimize transaction costs. Under this framework, a firm can enhance its stock’s trading liquidity by moving the stock price to an optimal level with a stock split.
While Easley et al. (2001) and Anshuman and Kalay (2002) find evidence for an increase in trading activities after a split, Copeland, (1979) and Conroy et al., (1990) report that liquidity decreases after the split. While some researchers report changes around the split day, Lakonishok and Lev, (1987) and Huang et al. (2013) find evidence for an increase in the liquidity around the announcement. These studies measure liquidity as proportional trading volume and bid-ask spread.
6 In this paper, we evaluate the alternative hypotheses2 about stock splits by examining the impact of stock splits on volatility and liquidity. For measuring volatility, we use the same method as Ohlson and Penman (1985) and Koski (1998). In addition to the t-test, they use a binomial proportionality test for comparing the pre- and post-split volatility. For measuring the liquidity, we use the same method as Lakonishok and Lev (1987) and Huang et al. (2013). Unlike prior studies, which mostly use the bid-ask spread, Lakonishok and Lev (1987) and Huang et al. (2013) use the turnover ratio for measuring liquidity. Additionally, we report all the results in the following multiple subsamples: price ranges, magnitude of the split and the event window (length of the period between the announcement and the ex-day).
Prior studies tend to fix their event window around the announcement or ex-date for all observations. The period between the announcement date and the ex-date3 has not been examined that much in literature. In this paper, we use different periods for each observation, where the period between the announcement and the ex-day is leading and different for each observation. This method is necessary for examining the alternative hypotheses.
In summary, we find evidence for trading range hypothesis in the change of volatility, the liquidity shows evidence for the signaling and/or attention grabbing hypothesis. This liquidity effect is not permanently, after the ex-date the turnover ratio decreases significant, which is against the trading range hypothesis. Yet it might be that splits affect other aspects of volatility and liquidity, hence the effect of splits on volatility and liquidity is still an open issue.
The article is organized as follows. Section 2 reviews the literature on stock splits and considers multiple hypothesis around the stock split. Section 3 presents the sample and methodology of the paper. Section 4 shows the results. The last, section 5 concludes.
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The signaling hypothesis (Brennan et al., 1988), the attention grabbing hypothesis (Grinblatt et al., 1984), and the trading range hypothesis (Copeland, 1979).
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2.
Literature review
While stock splits do not affect a firm’s financial fundamentals, the market tends to react positively to them. Grinblatt et al. (1984) show that a split in the ‘purest’ way, where no other firm specific event took place at the same time, a positive abnormal return of 3 percent is generated after the announcement and a 1 percent increase on the ex-day. For the long run return, Ikenberry and Ramnath (2002), and Hwang et al. (2008) document that stock splits outperform the benchmark over a 12-month period after the announcement. Desai and Jain (1997), and Ikenberry et al. (1996) document a 7-8 percent excess return during one year after the announcement of the stock splits. Even 2 years prior to the announcement the companies demonstrate a strong operating performance, however the trend changes following the split (Lakonishok and Lev, 1987). Other studies find that after a period of significant price run-up, firms conduct splits to return stock prices to a normal range to improve liquidity. Schultz (2000) shows that the number of small orders increase significantly following the split.
Several explanations have been proposed to explain the positive market reaction, including the signaling hypothesis (Brennan et al., 1988), the attention grabbing hypothesis (Grinblatt et al., 1984), and the trading range hypothesis (Copeland, 1979).
The signaling hypothesis indicates that stock splits convey managers’ favourable private information about the firm’s future earnings and the payouts to investors. Ross (1977) suggests that managers possess more information than investors and have an incentive to convey favourable information to investors. Lakonishok and Lev (1987) document that firms that split their stocks have a higher short-term earnings growth than firms that do not. The signaling hypothesis implies an increase in demand of the stock shares of splitting firms around the announcement date. However, if the market is efficient, the increase in trading activity due to the positive split signal should not last long and should be limited to the announcement period.
8 hypothesis, firms use stock splits to attract more trading, especially from small investors. Baker and Gallagher (1980) suggest that a stock split may change the composition of the ownership structure as the number of small shareholders increase after the split. However, Mukherji et al. (1997) find no evidence of any change in the ownership structure after the stock split. Brennan and Hughes (1991) observe an inverse relationship between the stock price and the number of analysts following a firm, and conclude that managers carry out stock splits to attract the attention of analysts.
Similar to the signaling hypothesis, if stock splits are made to attract attention, any change in trading activity should last for only a short-term period around the announcement date. Copeland (1979) suggests that stock splits are used improve the liquidity of trading by realigning stock prices to an ‘optimal’ trading range. This hypothesis suggests that investors, particularly small investors, prefer to trade stocks with a price that is within a certain range. That range can differ among countries. For example the median U.S. stock sells for about 40 dollars while a typical London stock sells for about 7.50 dollars, whereas a typical Hong Kong stock sells for 2 dollars. Since the absolute tick size is fixed by regulation or tradition, the tick size relative to the stock size will be close to the optimal only within a certain price range. A company can maintain its price range through making stock splits (Angel, 1997). When the stock price is “too high”, small investors might be reluctant to trade the stock because of higher brokerage fees relative to the value traded. A stock split can minimize brokerage costs and thereby improving the trading liquidity (Muscarella and Vetsuypens, 1996). In addition, Powell and Baker (1993) suggest that the management prefers more small investors, investors who tend not to exercise too much control, hence bringing the firm into a more controllable ownership mix.
Unlike the other two hypotheses, the trading range hypothesis implies that the improvement in the trading liquidity will not occur before the ex-date. Furthermore, the effect of stock splits on trading activity should be a long-term phenomenon.
9 with it, a firm can enhance the stock’s trading liquidity by resetting the stock price to an optimal level with a stock split.
However, the empirical evidence for regarding the effects of stock splits on stock liquidity is mixed. While some studies report improvement in post-split liquidity (Baker and Phillips, 1994), others show a reduction, or no change in post split liquidity (Copeland, 1979). Easley et al. (2001), and Dhar et al. (2004) find evidence for an increase in the number of shareholders but a decrease in the split adjusted trading volume. Other studies find that shareholder’s liquidity, measured by the bid-ask spread, is actually higher after stock splits. The bid-ask spread as a percentage of the closing price increases after the ex-date, suggesting that stocks become less liquid after stock splits (Conroy et al. (1990) and Gray et al. (2003)).
10 correlated with the price level, suggesting that price discreteness is not responsible for the volatility increase (Koski, 1998).
While some papers couldn’t find evidence for price discreteness, Desai et al., (1998), French and Foster, (2002) report that the change in volatility depends on the magnitude of the split. Desai et al., (1998) obtain results for subsamples based on the split factor. They find an 32 percent increase in volatility for the small-split factor group versus 81 percent increase for the large-split factor group.
Table 1: Main findings of prior researchers
Toppic Authors Year
Grinblatt et al. 1984
Lakonishok & Lev 1987 A strong operating performance in the 2 year prior the announcement.
Ikenberry 1996
Ikenberry & Ramnath 2002 Outperform of the benchmark over a 1 year period after announcement.
Ohlson & Penman 1985
French & Dubofski 1986 Average increase of 10% in implied volatility after the ex-date. Kaul & Nimalendran 1990
Koski 1998
Lakonishok & Lev 1987
Gray et al. 2003 Dhar et al. 2004
This table shows shortly the main findings of prior researchers to who is referenced in the literature review. This, allocated to the main toppic of the paper.
Increase in relative bid-ask spread after the split, increase in investor's trading cost.
Change in trading volume is driven by two separate changes, an increase in the number of trades executed, and a decrease in the average number of shares per trade.
Main findings Panel A: Return
Panel B: Volatility
Panel C: Liquidity
A positive abnormal return of 3% after announcement, a 1% increase follows the ex-day.
Splitting firms generate a significant excess returns of 7.93% in the first year and 12.15% in the three years following the split.
Standard deviation of daily stock returns increases from 28% to 35% on average after the split.
Significant increase in volatility after the split. However eliminating the bid-ask effect, doesn't eliminate the volatility increase.
The bid-ask error component of transaction returns can explain over 50% of daily return variances.
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3.
Hypotheses development
3.1 Sample
The initial sample consists of NASDAQ listed firms with stock splits during the period 2007-2015. The daily closing price and trading volume for a period of 1 year before and after the split is collected from Yahoo finance. Data of stock splits are collected from investmenthouse.com, which reports all the information about North American stock splits, including announcements and ex-dates.
As can be seen in Table 1, the sample size consists of 984 stock splits ranging from a 3-for-1, 2-for-1 and 3-for-2 split. We started this study with a total sample of 206 observations, however more than 50 percent (108 stock splits) of the observations does not meet the requirements of the paper. As later discussed in this paper, we require a period of 20 trading days between the announcement and ex-day. However 108 observations does not meet this requirement or were outliers.
Table 2 shows that there were only 4 and 3 stock splits in the year 2008 and 2009 respectively. The main reason for this phenomenon is the financial crisis, stock prices decreased dramatically during these years. Further, in these years, the management most
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See appendix B for the list of firms.
Table 2: Stock splits
3-for-1 2-for-1 3-for-2
2007 17 6% 59% 35% 2008 4 25% 50% 25% 2009 3 0% 67% 33% 2010 10 20% 20% 60% 2011 18 11% 72% 17% 2012 11 18% 64% 18% 2013 16 6% 50% 44% 2014 11 18% 64% 18% 2015 8 0% 75% 25% all 98 11% 58% 31% Allocation Number of splits Year
12 important reason for undertaking a stock split, would not be satisfied (Baker and powell, 1993).
In this study, we divided the sample into multiple subsamples for comparing the pre-split and post-split volatility. Since previous researchers find that the volatility varies for splits with different factors (Desai, et al., (1998), French and Foster, (2002)), we separate the sample into three subsamples each with a different split factor. The most common split factor for this sample is the 2-for-1 split.
Blume and Stambaugh (1983) claims that price discreteness affect the volatility, generated by the relative higher bid-ask spread. Controlling for price discreteness, we sorted the sample by the after split-price, where each subsample has an increment of 10 US-dollars. As Table 3 shows, most firms convert their stock price into the “10≤ P <15” range. Before the split, 70 percent of the stocks have a price above 20 US-dollars while more than 70 percent of the stocks denote a price below 20 US-dollars after the split. The sample lowest and highest stock price is 2.48 and 37.31 US-dollars respectively after the stock split. The sample contains 6 ‘penny’ stocks after the split, ‘penny’ stocks are traded below the 5 US-dollars. We didn’t exclude these stocks, because they don’t have an impact on the results of the subsample.
Table 3: Stock price shift
P <5 1 6 5≤ P <10 5 17 10≤ P <15 7 27 15≤ P <20 17 22 20≤ P <25 15 15 25≤ P <30 7 8 30≤ P <35 14 1 35≤ P <40 10 2 40≤ P <45 5 -45≤ P <50 6 -50≤ P <55 4 -55≤ P 7 -Number of stocks Before split After split
Thi s ta bl e s hows the number of s tock wi thi n the gi ven pri ce ra nge, a s wel l before a s a fter the s pl i t.
13 The last and third group is sorted by the magnitude of the event window N, where N is the time period between the announcement day and the ex-day. These subsamples remain controls for the length of the event window effect. Following Koski (1998), this study requires an event window of at least 20 trading days for measure the variance. The largest event window is 91 days while an event window of 20 days is the most common event window in this sample.
3.2 Volatility
For examining the impact of a split we follow Koski (1998) and Ohlson and Penman (1985). They put the emphasis on the trading range hypothesis. This implies that the effect of stock splits on the trading activity occurs during the ex-date, when the prices moved into the target range. This should be a long-term effect on the volatility.
We use three statistical tests to examine the impact of stock splits on volatility. First, the F-test examines the equality of variances between the pre- and post-split period, assuming that the pooled pre and post-split returns are respectively drawn from two different normal distributions. The second test is the paired t-test, which compares the mean of the pre- and post-split variance of the stock returns, assuming that the differences between the pre- and post-split sample for each firm is independent and normally distributed. The hypothesis based on existing literature concerning volatility is as follow, where σ2 is the variance of the stock return.
H0: σ2Pre-Split = σ2Post-Split HA: σ2Pre-Split ≠ σ2Post-Split
Where the test hypothesis implies no change in variance versus the alternative hypothesis, which implies a change in the post-split variance compared with the pre-split.
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p = Pr( ₂) (1)
here 2 and 1 denote pre- and post-split returns respectively. The test hypothesis (H0 : p = 0.5) implies no change in volatility post-split, compared with the pre-split. The alternative hypothesis (HA : p ≠ 0.5) implies a change in volatility post-split, compared with the pre-split. In order to control for day of the week variations in volatility, Ohlson and Penman (1985) compared the pre- and post-split returns by matching the first trading day following the announcement with the first same trading day of the week after the ex-date, the second day after the announcement with the same day of the week following the ex-date, and so on. Assuming independence across M observations, the related binominal statistic (see equation 2) is asymptotically distributed. We use the same matching method in this paper to compute the binomial statistic.
Z = 2(p – 0,5)(√M) (2)
For all statistics about volatility, we use an N pre-split and post-split event window. Where N is the period between the announcement and ex-date, which is at least 20 trading days, starting at the first trading day after the announcement (Koski, 1998). Additionally, for all statistics about volatility, this paper uses the daily closing price.
3.3 Liquidity
Following Huang et al. (2013), we examine the impact of a stock splits on trading volume for two different events, the announcement day and the ex-day. If stock splits convey positive information on a firm’s future profitability, then trading volume of the stock should increase after the announcement. This is the signaling hypothesis (Brennan et al., 1988) or the attention grabbing hypothesis (Grinblatt et al., 1984). On the other hand, if returning the stock price into the target range is the main purpose of stock splits, the trading volume is likely to increase after the ex-day, which is the trading range hypothesis effect (Copeland, 1979). To investigate which hypothesis better explains the stock split decision, this study examines the change in trading volume surrounding the announcement day and the ex-day with the following hypothesis.
15 Following Lakonishok and Lev (1987) and Huang et al. (2013), we use the turnover ratio as the metric of liquidity. The turnover ratio is defined as daily trading volume divided by the number of total shares outstanding. We use two statistical tests to examine the impact of stock splits on liquidity. The first statistical test is the paired t-test. The paired t-test compares the pre- and post-period turnover ratio, assuming that the differences in turnover ratio between the periods for each firm are independent and normally distributed. The test and alternative hypothesis is as follow: (where TR represents the average turnover ratio for each period)
H0: TR Pre-ann/ex-day = TR Post-ann/ex-day HA: TR Pre-ann/ex-day ≠ TR Post-ann/ex-day
Since Ajinkya and Jain (1989) find that the prediction errors for raw trading volume measures are significantly positive skewed5, we use additionally a non-parametric test for the liquidity examining. The most appropriate non-parametric test for liquidity is the Wilcoxon signed rank test. The test is based on difference scores, but in addition to analyzing the signs of the differences, it also takes into account the magnitude of the observed differences.
The test statistics for the Wilcoxon signed rank test is W, where W(+) is the sum of positive ranks and W(-)the sum of negative ranks. The Wilcoxon singed rank test, tests the following hypothesis
H0 : W+ = W -HA : W+ ≠ W
-As explained before, we examine the impact of stock splits on trading volume for the announcement day and the ex-day event (Similar to Huang et al., 2013).
The first event, the announcement day, compares pre-announcement period with the post-announcement period (in this paper similar to the pre-split period). The pre-post-announcement period starts 200 trading days before the ex-date and ends the last trading day before the announcement. Post-announcement period (pre-split period) starts at the first trading day
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16 after the announcement and ends one trading day before ex-day (Koski (1998) and Huang et al. (2013)). The second event is the ex-day event, which compares the pre-split with the post-split period. The pre-split period is the same as the post-announcement period. The post-split period is N days long and starts at the ex-day, where N is the number of days between the announcement and the ex-date (pre-split period), see Figure 1 for illustration.
4.
Results
4.1 Price-change
Typically for stock split, the total outstanding shares increase and the stock price decreases proportionally after a split. Table 4 shows the average price change around the split. For the overall sample the stock price decreases from 29,74 US-dollars before to 15,54 after the split. This change in price is almost proportional with the split factor. Similar to the findings of Lakonishok and Lev (1987) and Ikenberry and Ramnath (2002), we find an price run-up prior the announcement. Table 4 compares the stock’s price 1 year prior to the announcement with the announcement price.
Figure 2 shows the cumulative price for all observations starting at 220 trading days before the ex-day and ending 90 days after the ex-day. Following the results of Lakonishok and Lev (1987), we find a change in the run-up price during the ex-day, where the price increases significantly before ex-day, it stays constant after.
Figure 1: Event window time line
(200 - N-days) (N-days) (N-days)
Where the fi rs t peri od s ta rts a t 200 tra di ng da ys , before the ex-da y a nd end 1 da y before the
a nnouncement da y. The s econd peri od s ta rts 1 da y a fter the a nnouncement a nd ends the tra di ng da y before ex-da y. The l a s t en thi rd peri od s ta rts a t the ex-da y a nd ends N da ys a fter ex-da y, where N i s the number of da ys between the a nnouncement a nd ex-da y.
(200 days)
Ann-day Ex-day
17 The splitting sample observations outperformed the NASDAQ index on average. While the compounded annual growth rate of the NASDAQ index was roughly 8,4 percent during the period 2007 – 20156, our sample increase roughly with 44 percent within 220 trading days.
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NASDAQ index 1-1-2007: 2415,3 – 31-12-2015: 5007,4 CACG =((ti+1 /ti )^(1/n) )-1 = 0,084
Table 4: Price before and after split
Sample
Number of firms
1 yr prior
ann Pre-split Post-split Overall 98 19,78 29,74 15,54 Panel A 3:1 split 11 19,13 25,08 8,37 2:1 split 57 22,05 33,76 16,89 3:2 split 30 15,71 23,80 15,61 Panel B P <10 23 10,27 14,31 6,51 10≤ P <20 48 18,39 27,41 14,28 20≤ P <30 23 29,14 46,24 24,68 30≤ P 4 43,62 59,46 35,40 Panel C N ≤20 23 18,66 28,26 15,20 20˂ N ≤25 30 17,10 27,49 14,71 25˂ N ≤30 17 21,79 29,42 16,00 30˂ N 28 22,35 33,55 16,43
Compa ri s on of the a vera ge 1 yea r pri or the a nnouncement, pre-s pl i t a nd pos t-s pl i t s tock pri ce di vi ded i nto groups , s ca l ed by the ma gni tude of the s pl i t fa ctor, pri ce l evel a nd event wi ndow.
Split-factor
Price (after split) US-dollar
N-days Stock price 60 70 80 90 100 110 120 130 140 150 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 Ex -d ay 20 40 60 80
Figure 2: Cumulative price index around the ex-day
18 4.2 Volatility
Table 5 reports the results of the statistical test, comparing the pre-split with the post-split variance. We find a significant increase in the post-split variance. The average variance increases from 5.45 percent before the split to 8.47 percent after the split7, representing an increase by 55 percent. This is similar to comparable studies of Ohlson and Penman (1985) and Koski (1998) which find an increase of the post-split variance of 55 percent and 67 percent respectively. For the binomial proportionality test, Koski (1998) finds that Pr( ₂) is 0.556, where we find that Pr( ₂) is 0.568 for the overall sample. This implies that the probability of an increase in daily variances after the split is slightly higher for our sample. However, both statistics shows an increase in the after split daily variance.
As Panel A of Table 5 shows, the increase in variance is higher for the small-split factor group. The small-split factor group, ‘3-for-2’, has an increase of more than 100 percent versus a 20 percent increase for the large-split factor group. This is interesting as other researchers (Desai, et al., (1998), French and Foster, (2002)) find opposite results. They find a larger increase in variance for the large-split factor group and a lower increase in variance for the small-split factor group. The increase in variance, sorted by the split-factor, is almost significant for all statistical tests. However the ‘3-for-1’ is only significant for the F-test.
Controlling for price discreteness, Panel B separate the sample by price ranges with an increments of 10 US-dollars. Where Blume and Stambaugh (1983) found evidence for price discreteness, relative higher variance in the lower price ranges, we find the highest variance in higher price ranges and the lowest variance (relative) in the lower price ranges. Even the binomial proportionality test shows that the variance is positive correlated with the stock price. This contradicts the results of prior studies. For example, Kaul and Nimalendran (1990) show that the bid-ask spread introduces an upward bias in measuring return variances and means that the variance increases at lower price levels are caused by a relatively higher bid-ask spread. The only evidence for this effect in this paper is the F-test, which is higher at the lower price range, but only significant for the ‘10≤ P <20’ subsample.
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19 The last panel, Panel C, is separated by the duration of the event window. The binomial proportionality test shows an increase in the variance for all subsamples. However, the paired t-test does not show an increase for ‘25˂ N ≤30’ subsample, where the t-test shows an increase for the other subsamples. While Chakravaty et al. (2004) suggest that volatility decline or revert to ‘normal’ pre-split level, we could not find strong evidence for this phenomenon. Furthermore we find a slightly decline in variance in the last three subsamples for the binomial proportionality test.
To summarize, the binomial proportionality test shows a significant increase in the volatility for all types of splits independently of the split factor, ex-split price range or duration of the event window. Table 5: Volatility Sample Pr (R̄ >R̄ ₂) Overall 5,45% 8,47% 1,6029 ** 3,12 *** 7,21 *** 0,569 Panel A 3:1 split 5,05% 6,04% 1,8937 *** 0,94 1,34 0,533 2:1 split 6,24% 8,92% 1,2911 2,16 ** 5,96 *** 0,575 3:2 split 3,71% 8,10% 1,8723 *** 2,28 ** 4,00 *** 0,574 Panel B P <10 4,19% 3,57% 1,4069 -0,51 2,94 *** 0,558 10≤ P <20 4,01% 8,49% 1,5633 ** 2,93 *** 4,84 *** 0,567 20≤ P <30 7,17% 9,77% 0,5855 1,46 3,49 *** 0,570 30≤ P 7,96% 9,60% 0,4743 0,77 2,02 ** 0,582 Panel C N ≤20 5,00% 9,03% 1,31 2,08 ** 2,45 ** 0,559 20˂ N ≤25 4,84% 8,30% 2,67 *** 1,34 4,82 *** 0,594 25˂ N ≤30 4,42% 4,40% 0,46 -0,02 2,75 *** 0,565 30˂ N 6,85% 10,35% 1,52 ** 2,34 ** 4,23 *** 0,561
* denotes s tatis tics s i gni fi ca nt a t 10%, ** denotes s tatis tics s i gni fi ca nt a t 5%, a nd *** denotes s i gni fi ca nce a t 1%.
F-test
Paired t
-test Z-test
Split-factor
Compa ri s on of pre - a nd pos ts pl i t va ri a nce by ma gni tudl e of s pl i t fa ctor, pri ce l evel a nd event wi ndow N. Where N i s the peri od between the a nnouncement da y a nd the ex-da y. F-s tat i F-s the reF-s ul t of the pool ed F-teF-s t of cha nge i n va ri a nceF-s . Pa i red t-F-s tat reportF-s reF-s ul t of compa ri ng the mea n pres pl i t s a mpl e va ri a nce to the mea n pos ts pl i t s a mpl e va ri a nce . The pre-s pl i t a nd pos t-s pl i t va ri a nce i s ba s ed on a peri od of 29 da ys . Z-s tat i s the res ul t of the bi nomi a l Z-s tatis tic for Pr ( ̄ > ̄ ₂). Pr (σ̄ >σ̄ ₂) repres ents the proportion of obs erva tions for whi ch (σ̄ >σ̄ ₂) a nd Pr ( ̄ > ̄ ₂) repres ents the proportion of obs ervations for whi ch ( ̄ > ̄ ₂).
Price (after split) US-dollar
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4.3 Liquidity
Similar to prior studies (Lakonishok and Lev, (1987) and Huang et al. (2013)), we find evidence for an increase in trading volume after the announcement. However, around the ex-day the trading volume, expressed as a turnover ratio8, seems to decline. In spite of that, the trading volume expressed in absolute traded shares is constant for the overall sample. The decline in the after split turnover ratio is mainly caused by an increase in the total outstanding shares. Comparable to the previous study by Copeland (1979), the volume increase less than proportionately after stock splits. As Table 6 shows, the turnover ratio increase from 0.62 percent in the pre-announcement period, to 0.77 percent in the post announcement. This implies that the trading volume increase with 0.15 percent of the total outstanding shares. However the increase is significant for the overall sample, for the subsamples the increase seem to be less significant. Panel B shows even a slightly decrease in liquidity during the announcement day for the ‘20< P ≤30’ range.
During the ex-day, the turnover ratio decrease from 0.77 percent to 0.40 percent, which is significant for both statistics. For the overall sample the decrease in turnover ratio seem to be proportional to the increase of the total outstanding shares. This implies that the actual number of trades does not change significant around the ex-day. Figure 3 shows the movement of the turnover ratio and the indexed absolute trading volume, starting 200 trading days before ex-day. Where the turnover ratio is measured as the absolute trading (numerator) volume divided by the number of total outstanding shares (denominator) Following Table 6, Figure 3 shows an increase in trading volume around the post-announcement period (pre-split period), where the first post-announcement starts 90 trading days till 20 trading days before ex-day. After ex-day the absolute (indexed) trading volume increase for a short period. However, through an increase in the total outstanding shares, the turnover ratio decrease sharply for a long period after the split. While the absolute trading volume convert back to their normal ‘range’.
8
21 Since the trading range hypothesis (Copeland, 1979) suggests that stock splits are to improve the liquidity by realigning stock prices to an ‘optimal’ trading range, an increase in the turnover ratio is expected after ex-day, especially for the lower price ranges. Nevertheless, the findings of this report shows a decline in turnover ratio for all subsamples around the ex-day, which is mainly caused by an increase in the total number of outstanding shares through a split.
22 In summary, we find an increase in turnover ratio around the announcement, which is significant for the overall sample. After the announcement, during the ex-day, the turnover ratio decrease significant for the overall sample and all subsamples. This turnover decrease is mainly caused by an increase in the total outstanding shares. However the absolute trading volume doesn’t change significantly around the ex-day. This is against the managers’ main reason for undertaking a stock split. Baker and Gallagher (1980) find that 65 percent of managers stated that they split their stock to provide a better trading range and attract small investors. It is possible that the split does have this effect, but that it does not show up in the aggregate turnover statistics since the trading activity of small investors is overwhelmed by the trading activity of large investors.
Table 6: Volume Sample Pre-ann (1) Pre-split (2) Post-split (3) ∆ [1-2] ∆ [2-3] ∆ [1-2] ∆ [2-3] Overall 0,62% 0,77% 0,40% 2,38 ** -8,01 *** 2,21 ** -7,42 *** Panel A 3:1 split 0,68% 0,84% 0,23% 0,71 -3,00 *** 0,98 -2,93 *** 2:1 split 0,68% 0,85% 0,44% 1,89 * -6,72 *** 1,41 -5,89 *** 3:2 split 0,49% 0,59% 0,38% 1,48 -4,27 *** 1,49 -3,59 *** Panel B P <10 0,67% 0,93% 0,37% 1,96 ** -4,02 *** 1,55 * -4,20 *** 10≤ P <20 0,47% 0,64% 0,36% 1,70 * -5,58 *** 1,06 -4,59 *** 20≤ P <30 0,82% 0,79% 0,46% -0,46 -4,83 *** 0,94 -3,80 *** 30≤ P 1,04% 1,27% 0,66% 1,16 -2,18 ** 0,73 -1,83 * Panel C N ≤20 0,84% 1,03% 0,54% 0,80 -4,27 *** 0,64 -3,50 *** 20˂ N ≤25 0,52% 0,60% 0,33% 2,14 ** -6,69 *** 0,67 -4,78 *** 25˂ N ≤30 0,52% 0,63% 0,29% 1,34 -2,82 *** 1,49 -3,62 *** 30˂ N 0,61% 0,83% 0,41% 2,59 *** -4,14 *** 1,62 * -3,01 ***
* denotes statistics significant at 10%, ** denotes statistics significant at 5%, and *** denotes significance at 1%. Comparison of pre-announcement, pre-ex and post-ex average turnover ratio collected by magnitudle of
split factor, price level and event window N. Where N is the period between the announcement day and the ex-day. the turnover ratio is calculated as the average daily volume divided by the total shares outstanding. Paired t-test reports result of comparing the mean pre-announcement, pre-ex and post-ex turnover ratio, where ∆ is the difference between the two observations . The Wilcoxon signed rank sum test reports the result of the nonparametric test.
Wilcoxon Signed Rank Sum Test (z-value) Paired t -test
Average daily volume (as % of total outstanding)
Split-factor
Price (after split) US-dollar
23
5.
Conclusion
This study examines the impact of stock splits on trading activity, in particular the volatility of the stock returns and the liquidity of the shares. The volatility is measured by comparing the mean of the pre- and post-split variance, where only daily closing prices are required. The proportional volume of traded shares is the metric of liquidity.
Using a sample of 98 stock splits in the U.S. over a period of 2007-2015, we find a significant increase in volatility after the stock split for all the subsamples, which is similar to the results of Koski (1998). Even controlling for price discreteness, the change in variance is not significantly correlated with the price level, which implies that price discreteness is not responsible for the increase in volatility.
The findings of volatility support the trading range hypothesis of Copeland (1979), which should be a long term effect. Because this paper did not examine the announcement impact on volatility, we could not exclude the signaling or grabbing hypothesis of Brennan et al. (1988) and Grinblatt et al. (1984) for the volatility.
As to liquidity, we find an improvement in liquidity after the announcement. This improvement in liquidity is significant for the overall sample. While after the ex-date, the liquidity expressed as proportional volume decrease significantly for all subsamples. However most of the decline in ratio is caused by the increase of total outstanding shares (denominator), the absolute trading volume (numerator) doesn’t change significantly around the ex-day9. In short, concerning the liquidity, the improvements seem to be only short term phenomena, which occurs after the announcement and is limited till the ex-day. Given these results, liquidity seems to be more consistent with the signaling hypothesis and/ or the attention-grabbing hypothesis.
However, the results of this paper ca not exclude the presence of the signaling hypothesis (Brennan et al., 1988), the attention grabbing hypothesis (Grinblatt et al., 1984), or the trading range hypothesis (Copeland, 1979). While this paper found evidence for the trading range hypothesis in the change of volatility, we find a decline in the liquidity measured by the turnover ratio after the ex-day, which is in contrast of the trading range hypothesis. The liquidity shows evidence for the signaling hypothesis and/ or the attention-grabbing
9
25
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29
Appendix B
Company split factor announcement split-date
1 MDVN MEDIVATION INC. 2-for-1 jul-31 2015 sep-16 2015
2 EMCI EMC INSURANCE GROUP INC. 3-for-2 MAY 07 2015 jun-24 2015
3 IDXX IDEXX LABORATORIES, INC. 2-for-1 MAY 06 2015 jun-16 2015
4 ROST ROSS STORES INC. 2-for-1 MAR 24 2015 jun-12 2015
5 INSY INSYS THERAPEUTICS, INC. 2-for-1 MAY 07 2015 jun-08 2015
6 EXPO EXPONENT, INC. 2-for-1 apr-22 2015 jun-05 2015
7 PATK PATRICK INDUSTRIES, INC. 3-for-2 apr-30 2015 jun-01 2015
8 SGC SUPERIOR UNIFORM GROUP, INC. 2-for-1 dec-30 2015 feb-05 2015
9 HAIN THE HAIN CELESTIAL GROUP, INC. 2-for-1 nov-25 2014 dec-30 2014
10 FLIC THE FIRST OF LONG ISLAND CORPORATION 3-for-2 sep-17 2014 OCT 16 2014
11 COLM COLUMBIA SPORTSWEAR COMPANY 2-for-1 jul-24 2014 sep-29 2014
12 AAON AAON INC. 3-for-2 jun-05 2014 jul-17 2014
13 SFBS SERVISFIRST BANCSHARES, INC. 3-for-1 jun-17 2014 jul-17 2014
14 ACIW ACI WORLDWIDE, INC. 3-for-1 apr-10 2014 jul-11 2014
15 CORE CORE-MARK HOLDING COMPANY, INC. 2-for-1 MAY 21 2014 jun-27 2014
16 OZRK BANK OF THE OZARKS, INC. 2-for-1 MAY 19 2014 jun-24 2014
17 ARLP ALLIANCE RESOURCE PARTNERS, L.P. 2-for-1 apr-28 2014 jun-17 2014
18 FFIN FIRST FINANCIAL BANKSHARES, INC. 2-for-1 apr-22 2014 jun-03 2014
19 CTSH
COGNIZANT TECHNOLOGY SOLUTIONS
CORPORATION 2-for-1 feb-05 2014 MAR 10 2014
20 ANDE THE ANDERSONS INC. 3-for-2 dec-19 2013 feb-19 2014
21 MGEE MGE ENERGY, INC. 3-for-2 dec-20 2013 feb-10 2014
22 PZZA PAPA JOHN'S INTERNATIONAL, INC. 2-for-1 nov-05 2013 dec-30 2013
23 MDSO MEDIDATA SOLUTIONS, INC. 2-for-1 nov-11 2013 dec-17 2013
24 MDCA MDC PARTNERS INC. 3-for-2 OCT 28 2013 nov-29 2013
25 SHOO STEVE MADDEN, LTD. 3-for-2 aug-20 2013 OCT 02 2013
26 AFOP ALLIANCE FIBER OPTIC PRODUCTS INC. 2-for-1 aug-15 2013 sep-17 2013
27 CGNX COGNEX CORPORATION 2-for-1 jul-29 2013 sep-17 2013
28 PRAA PORTFOLIO RECOVERY ASSOCIATES, INC. 3-for-1 jun-10 2013 aug-02 2013
29 AAON AAON INC. 3-for-2 may-22 2013 jul-03 2013
30 CERN CERNER CORPORATION 2-for-1 MAY 28 2013 jul-01 2013
31 CRVL CORVEL CORPORATION 2-for-1 MAY 17 2013 jun-27 2013
32 INBK FIRST INTERNET BANCORP 3-for-2 MAY 21 2013 jun-24 2013
33 MRTN MARTEN TRANSPORT, LTD. 3-for-2 MAY 13 2013 jun-17 2013
34 HOMB HOME BANCSHARES, INC. 2-for-1 apr-18 2013 jun-13 2013
35 TRMB TRIMBLE 2-for-1 feb-11 2013 MAR 21 2013
36 GILD GILEAD SCIENCES, INC. 2-for-1 dec-10 2012 jan-28 2013
37 AIRM AIR METHODS CORPORATION 3-for-1 sep-28 2012 dec-31 2012
38 LKQ LKQ CORPORATION 2-for-1 aug-17 2012 sep-19 2012
39 RAVN RAVEN INDUSTRIES, INC. 2-for-1 MAY 23 2012 jul-26 2012
40 CME CME GROUP 3-for-1 MAY 24 2012 jul-23 2012
41 DLTR DOLLAR TREE, INC. 2-for-1 MAY 29 2012 jun-27 2012
42 ABCO THE ADVISORY BOARD COMPANY 2-for-1 MAY 02 2012 jun-19 2012
30
44 DGAS DELTA NATURAL GAS COMPANY, INC. 2-for-1 feb-21 2012 MAY 02 2012
45 ASUR ASURE SOFTWARE, INC. 3-for-2 MAR 29 2012 MAY 01 2012
46 SCVL SHOE CARNIVAL, INC. 3-for-2 MAR 23 2012 apr-30 2012
47 QSII QUALITY SYSTEMS, INC. 2-for-1 jul-28 2011 OCT 27 2011
48 RGCO RGC RESOURCES, INC. 2-for-1 jul-25 2011 sep-02 2011
49 HMSY HMS HOLDINGS CORP. 3-for-1 jul-11 2011 aug-17 2011
50 OZRK BANK OF THE OZARKS, INC. 2-for-1 jul-19 2011 aug-17 2011
51 SNHY SUN HYDRAULICS CORPORATION 3-for-2 jun-09 2011 jul-18 2011
52 LULU LULULEMON ATHLETICA INC. 2-for-1 MAR 28 2011 jul-12 2011
53 PLCM POLYCOM, INC. 2-for-1 jun-01 2011 jul-05 2011
54 IIVI II-VI INCORPORATED 2-for-1 MAY 17 2011 jun-27 2011
55 AAON AAON INC. 3-for-2 may-05 2011 jun-14 2011
56 FFIN FIRST FINANCIAL BANKSHARES, INC. 3-for-1 apr-26 2011 jun-02 2011
57 FTNT FORTINET 2-for-1 apr-27 2011 jun-02 2011
58 LECO LINCOLN ELECTRIC HOLDINGS, INC. 2-for-1 apr-29 2011 jun-01 2011
59 FAST FASTENAL COMPANY 2-for-1 apr-19 2011 MAY 23 2011
60 ALXN ALEXION PHARMACEUTICALS INC. 2-for-1 MAR 30 2011 MAY 23 2011
61 NDSN NORDSON CORPORATION 2-for-1 MAR 01 2011 apr-13 2011
62 DEST DESTINATION MATERNITY CORPORATION 2-for-1 jan-26 2011 MAR 02 2011
63 PRGS PROGRESS SOFTWARE CORPORATION 3-for-2 dec-21 2011 jan-31 2011
64 ADVS ADVENT SOFTWARE, INC. 2-for-1 dec-13 2011 jan-19 2011
65 MNRO MONRO MUFFLER BRAKE, INC. 3-for-2 nov-15 2010 dec-27 2010
66 HCSG HEALTHCARE SERVICES GROUP, INC. 3-for-2 OCT 12 2010 nov-15 2010
67 TSCO TRACTOR SUPPLY COMPANY 2-for-1 jul-29 2010 sep-02 2010
68 DLTR DOLLAR TREE, INC. 3-for-1 may-26 2010 jun-25 2010
69 IDSA INDUSTRIAL SERVICES OF AMERICA, INC. 3-for-2 MAY 03 2010 jun-02 2010
70 TESS TESSCO TECHNOLOGIES, INC. 3-for-2 apr-28 2010 MAY 27 2010
71 SLGN SILGAN HOLDINGS INC. 2-for-1 MAR 29 2010 MAY 04 2010
72 SHOO STEVE MADDEN, LTD. 3-for-2 mar-25 2010 may-03 2010
73 BCPC BALCHEM CORPORATION 3-for-2 dec-11 2010 jan-21 2010
74 EBIX EBIX, INC. 3-for-1 OCT 12 2010 jan-05 2010
75 NEOG NEOGEN CORPORATION 3-for-2 nov-16 2009 dec-16 2009
76 MYGN MYRIAD GENETICS, INC. 2-for-1 feb-24 2009 MAR 26 2009
77 VLGEA VILLAGE SUPER MARKET, INC. 2-for-1 dec-05 2009 jan-23 2009
78 EBIX EBIX, INC. 3-for-1 aug-01 2008 oct-09 2008
79 ATVI ACTIVISION BLIZZARD, INC. 2-for-1 jul-11 2008 sep-08 2008
80 SYNA SYNAPTICS INC. 3-for-2 jul-31 2008 sep-02 2008
81 HOLX HOLOGIC INC. 2-for-1 jan-30 2008 apr-03 2008
82 FLIR FLIR SYSTEMS, INC. 2-for-1 OCT 25 2007 dec-11 2007
83 IDXX IDEXX LABORATORIES, INC. 2-for-1 OCT 26 2007 nov-27 2007
84 CTSH
COGNIZANT TECHNOLOGY SOLUTIONS
CORPORATION 2-for-1 sep-17 2007 OCT 17 2007
85 PCAR PACCAR, INC. 3-for-2 sep-11 2007 OCT 10 2007
86 MNRO MONRO MUFFLER BRAKE, INC. 3-for-2 MAY 22 2007 OCT 02 2007
87 NEOG NEOGEN CORPORATION 3-for-2 jul-26 2007 sep-05 2007
88 AAON AAON INC. 3-for-2 jul-12 2007 aug-22 2007
31
90 IOSP INNOSPEC INC. 2-for-1 jun-18 2007 jul-23 2007
91 VSEC VSE CORPORATION 2-for-1 MAY 01 2007 jun-29 2007
92 GILD GILEAD SCIENCES, INC. 2-for-1 MAY 08 2007 jun-25 2007
93 SEIC SEI INVESTMENTS COMPANY 2-for-1 MAY 23 2007 jun-22 2007
94 MIDD THE MIDDLEBY CORPORATION 2-for-1 MAY 03 2007 jun-18 2007
95 PMFG PEERLESS MFG. CO. 2-for-1 MAY 04 2007 jun-08 2007
96 BCPC BALCHEM CORPORATION 3-for-2 dec-12 2007 jan-22 2007
97 SIAL SIGMA-ALDRICH 2-for-1 nov-14 2007 jan-03 2007
