Stock Splits And Return Volatility
A stock split by itself is merely an accounting change with no change in firm value. It does not alter the total market value of shareholders' wealth; hence, there should be no effect on stock returns or return variances. In theory, stock returns and return volatility in the pre- and post-split proposal period should not be different. In an efficient market, prices fully and instantaneously reflect all available relevant information. However, in practice, the adjustment process cannot be completed instantaneously.
The purpose of this paper is to examine the adjustment of stock returns to stock split proposals. The adjustment process to the release of new information is examined using daily return data. The objective is first to determine the beginning and ending time of the adjustment process due to a stock split proposal. The difference between the ending time and the beginning time provides an estimate of the total time. In addition, the adjustment process is grouped by contaminated versus non-contaminated announcements, firm size, and change in dividends after the split announcement.
In general, larger firms are closely followed by a large number of investors, security analysts, and the financial press. Hence, publicly available information is more rapidly available about them, and this should result in a more rapid adjustment than for smaller firms . A stock split proposal effect may actually be the result of expected cash dividend increases after the split. Therefore, we divide our sample into three groups of dividend increase, dividend decrease, and no change in dividend. The dividend decrease group should react to the negative information quickly and the adjustment process for this group should be the fastest. We empirically examine these issues and provide some answers.
Previous studies, e.g., [1,3], on stock splits did not analyze the effect of potential contamination by other information releases on return at the split announcement dates. We find, for our sample, over 85% of the announcements had some other significant simultaneous announcement. In addition, some of the previous empirical techniques used in event studies have come under criticism. We employ daily return data and do not rely on these previous empirical models in our study. Using a different methodology, we are able to show how return and volatility of securities change around the announcement time of stock splits.
Studies examining the return adjustment process are very limited in number. Patell and Wolfson  examine the effects of earnings and dividend announcements on intraday stock price behavior. Two types of analysis are conducted to detect any systematic influences of the announcements on stock prices. First, the stochastic process tests compare the time series properties of consecutive price changes during disclosure and nondisclosure periods. Next, the increased variability of stock price changes was determined. Their results indicate that the major adjustment occurs within fifteen minutes of an earnings release. It takes essentially the entire trading day to "absorb" an earnings announcement. Large variance increases persist for up to four hours after the disclosure and smaller but significant variance increases continue into the following day. Dividend announcements did not induce large increases in variance, but significant disturbances occurred at the announcement of dividend changes.
A recent study by Grinblatt, Masulis, and Titman  examines the impact of both stock split and stock dividend announcements. The results indicate significantly positive announcement returns on day 0 and day 1 for the entire sample, for a sample of "pure" events that have no other announcements in the three-day period around the announcement day, and for a sample where no cash dividends were declared in the previous three years. They conclude that the abnormal return on the announcement day and the day after (day 0 and day 1) cannot be explained by forecasts of near term increases in cash dividends. The announcement effect is larger for the stock dividend sample than for the stock split sample.
Ohlson and Penman  analyze the behavior of stock-return volatilities preceding and following the ex-split date using a simple methodology. They find a 30% increase in the return standard deviations following the ex-date. This increased variance is not a temporary effect. Recently, Lamourex and Poon  find an increase in the noisiness of security returns around the time of a stock split. Our analysis goes further and examines both stock returns and return variance. We identify when the increased volatility begins and ends and what factors affect the length of this adjustment period using a sound statistical methodology.
Hillmer and Yu  devised a cumulative sum technique that can be used to measure the speed of adjustment of any market behavior variable, e.g., the mean or the variance of stock price changes, the frequency of transactions, the volume of transactions, etc. They measured adjustment intervals for five specific events. (1) They found that either the stock prices did not change following the announcements or the change was completed very rapidly. Hence, there was little or no opportunity to profit from the announcements. However, the market was found to be in an apparent state of disturbance. There was no evidence of excess returns, but increased variability was found with respect to each event. The size of the company appeared to be a factor in determining the speed of adjustment in their sample of five firms. The technique devised by Hillmer and Yu  will be used in our study and is discussed in the following section.
METHODOLOGY AND DATA
The cumulative sum tests that were first proposed by Page  have been traditionally concerned with detecting parameter changes. Hillmer and Yu  extend the ideas in cumulative sum tests to get an unbiased estimate of the disturbance interval. This methodology does not suffer from any of the criticisms of the market model. It is also able to detect a significant change in both mean and variance of returns simultaneously. The assumptions required are that price changes are independently and identically distributed. We state briefly the operational procedure of the cumulative sums tests below. (2)
Let([X.sub.t] ~t = [t.sub.s],..., [t.sub.1], [t.sub.1] + 1,... [t.sub.m])
be an observed sequence of market behavior of variable X. Then, define
[Mathematical Expression Omitted]
where [S.sub.[kappa]] is the cumulative sum of deviations from the mean and u is the mean value of variable X. From Donsker's theorem, [S.sub.t] for [t.sub.s] [is less than or equal to] [t.sub.1] is approximately a symmetric Weiner process, and [S.sub.t]-[S.sub.t1] for t [is greater than] [t.sub.1] is approximately a Weiner process with a drift [u.sub.c]-u, where [u.sub.c] is the new mean value. Let [alpha] be the probability of wrongly detecting a parameter change given that there was no change. Then,
[B.sub.[kappa]] = - [square root of [kappa]] [sigma] Z [alpha]/2,
where [[sigma].sup.2] is the variance in the non-announcement period. If [S.sub.k] [is less than] [B.sub.[kappa]] for some period, a change in parameter value is signaled from u to [u.sub.c]. [S.sub.[kappa]] fluctuates around zero till time [t.sub.1], but after [t.sub.1], [S.sub.[kappa]] drifts downwards, and at time T a statistically significant change in the parameter occurs. Then, an estimate of the change time is given by
[T.sub.1] = T - [B.sub.T]/([u.sub.c] - u),
where [B.sub.T/[u.sub.c] - u) is the first passage time, as shown by Cox and Miller . If we are interested in detecting a decrease in the mean return after information is released, a preliminary estimate of [t.sub.1], for example, [t'.sub.1], is obtained by observing the actual data. An estimate of [u.sub.c] is
[Mathematical Expression Omitted]
Next, we reestimate [u.sub.c] based on the new [t.sub.1]. The estimate of [t.sub.1] and [u.sub.c] is repeated till estimate of t converge.
In order to estimate [t.sub.2] (the ending time of adjustment), the cumulative sum technique is applied backwards from [t'.sub.2] [is greater than] [t.sub.2] until a change is signaled. When an increase in the parameter has to be tested, the only change is in the sign of [B.sub.[kappa]]. That is, [B.sub.[kappa]] = + [square root of [kappa]] [sigma] Z [alpha]/2. A change in the return variance can be detected by a similar procedure as outlined by Hillmer and Yu .
The above test procedure of adjustment time is applied to the data of stock split announcements given in the next section. Since no statistical package is available for the model, a computer program was written to do the modeling. Possible cases examined in our study are:
1) Mean increases (decreases) and variance is unchanged.
2) Mean is unchanged and variance increases (decreases).
3) Mean increases (decreases) and variance increases (decreases).
4) Mean and variance are unchanged.
Our sample consists of 571 stock split proposals during the period 1977 to 1981. The number of announcements each year is displayed in Table 1. Stock splits in which at least five shares are distributed for every four formerly outstanding are included in the sample. We use The Wall Street Journal Index and Moody's Dividend Record to identify the date of the first public announcement of a split proposal. The CRSP (Center for Research on Security Prices) tapes are used to obtain daily returns. The beginning and ending times of the adjustment process are estimated using the steps outlined in the previous section. The COMPUSTAT tapes provide the data on firm size and dividends for 170 stock splits. The measure of firm size used is the total market value of outstanding equity at the end of the year prior to the announcement date. The total sample is then divided into ten size categories, and the spread of adjustment is examined for each category. The sample is also divided into three groups: dividend increase, dividend decrease, and no change in dividends after the stock splits announcements. The adjustment process is then studied for each of these groups as well.
Mean and Variance Tests
The purpose of the mean and variance tests is to determine the duration of the change in mean returns and/or the changes in variability of stock returns that accompany stock split proposals. We draw inferences concerning the speed of adjustment by examining cumulative sum deviations from the mean of the pre-announcement period. The period examined is - 150 days to + 60 days, where day 0 is the date of the first public announcement of a split proposal. The pre-announcement period is considered to be - 150 days to - 50 days. The effect of information release is captured by allowing for a change in the mean and variance of daily returns. In order to examine the beginning time of adjustment, the mean and variance are estimated in the pre-announcement period, considered to be - 150 days to - 50 days. A pre-announcement period long before the actual proposal date (day 0) is used, keeping in mind that generally a stock split occurs because a company and its stock have performed well; therefore, the stock price has increased considerably over the past few months. Next, the cumulative sum of deviations becomes and the critical values are estimated from - 50 days onwards using a confidence level of 0.05. The point in time (T) when the cumulative sum of deviations becomes less than or equal to the critical value denotes a statistically significant change in the parameter. This estimate of T is then used as an unbiased estimate of the beginning time of adjustment. A similar procedure is used to estimate the ending point of adjustment. Table 2 reports the frequency of mean and variance changes around the announcement dates for the total sample of 388 cases as identified by the cumulative sum technique.
Only 12 out of 388 split announcements exhibit significant changes in mean returns. It is safe to say that the announcements did not result in an apparent shift in mean returns. This evidence suggests that there is no (or insignificant) apparent effect of acting on inside information concerning split announcements or subsequent dividends. The stationarity of the mean returns implies that any abnormal return arising from split announcements would rapidly disappear in efficient market. Grinblatt, Masulis, and Titman's  study indicates that abnormal returns exist on the split announcement day and one day subsequent to the announcement (day 0 and day 1 ), but we find a significant increase in mean returns for only 3 percent of our sample. In addition, a majority of stock split proposals (226 cases) do not cause any change in either the mean or the variance. This finding is consistent with the fact that technically a stock split is just an accounting change with no change in the value of the firm. However, the 156 cases of variance increase indicate that stock splits are associated with a period of increased risk and disturbance. Variance increases may reflect increases in market speculative activities during the period of stock split announcements.
To further examine the 156 cases of variance increases, we estimate the mean beginning and ending times of the adjustment process. This provides us information regarding the speed of adjustment of return variance in response to the information content of stock splits. The results for the combined sample and also for the contaminated and non-contaminated groups are repported in Table 3. A split announcement was considered "contaminated" if there had been other significant announcements made by the company during the five days around the actual split announcement day. The announcements considered to be significant were merger information, earnings reports, and cash dividend declarations.
The adjustment process based on the combined sample starts, on average, 18 days before the proposal announcement and continues for 63 days after that announcement. After a stock split has been proposed, it must be approved and declared. Investors are also interested in knowing whether dividends will change subsequent to the stock split. The quarterly dividend announcement can occur any time from the time of the split proposal to three months after the split proposal. This explains why the adjustment process continues for 63 days after the actual announcement. In addition, during this period of variance increases, there can be increased speculative activity in options written on the split stocks. Ohlson and Penman  find the average number of trading days between the announcement and split dates to be 52.06. We find the increase in variance starts building up prior to the actual proposal and persists for quite some time. It should be kept in mind that stock splits occur when a great deal of good news has been revealed about the firm and the stock price has risen.
Since stock split announcements are found to be contaminated with other announcements in a majority of the cases, the adjustment time is re-examined for contaminated and non-contaminated samples. The latter takes a shorter time (54 days) to complete adjustment since it is reacting to only one announcement. The contaminated group takes longer to adjust (88 days) since the market has to revise expectations based on more pieces of information. Most stock split studies that have been done in the past have not accounted for this contamination effect. In our sample, more than 85% of the announcements had some other significant simultaneous announcement. This suggests that the effect examined in some previous studies (e.g., Fama et al. , Charest , and Ohlson and Penman ) was not a pure stock split effect.
The Adjustment Time and Size Groups
Next, we divide the sample of 170 splits for which data was available on COMPUSTAT tapes into ten size categories. The purpose of the size classification is to examine how the relative adjustment time varies according to firm size. In general, larger firms are more closely followed by a large number of investors, security analysts, and the financial press, so more information is available about them. If information is readily available, then adjustment time should be shorter for larger firms. We test these hypotheses empirically.
The measure of firm size used is market value of common equity. Each equity size group consists of 17 splits. The composition of each size category in terms of average equity, the number of variance increases, and the adjustment times are presentd in Table 4. The smallest firm had equity of 1.275 million dollars and the largest had 34.78 billion dollars. The average equity ranges from 36.91 million dollars in the smallest size group to 5.07 billion dollars in the largest. In the smallest size group, 7 out of 17 cases exhibit an increase in return variance, but, in the largest size group, the number of variance increases are found to be 5 out of 17. The smaller size groups react more to the split announcement and result in a larger proportion of variance increases.
An examination of Table 4 shows that an increase in return variance starts anywhere from 50 days (group 10) to 9 days (group 3) before the actual announcement. It is interesting to note in Table 4 that the smallest firms take a total of 130 days for adjustment while the largest firms take 88 days. But, an examination of group 2 to group 9 indicates a consistent increase in the total adjustment time from 76 days to 113 days. It should also be noted that the total adjustment time for the 156 cases of variance increases in Table 3 is 81 days. However, the 82 cases of variance increases analyzed in Table 4 show a mean adjustment time of 98 days. Table 4 analyzes the 170 splits for which data were available on COMPUSTAT; therefore, these firms on average are larger than our overall sample. The conclusion, therefore, is that, in fact, larger firms take a larger adjustment time. This can be related to our results from the contaminated versus non-contaminated group. There are likely to be more simultaneous announcements by large firms, and adjustment times are larger. (6) In the next section, we divide the sample into firms that increased, decreased, and did not change dividends after the stock split. This allows us to examine how dividend changes around stock splits affect the adjustment times.
The Adjustment Time and Dividend Classification
The sample of 170 splits for which dividend data were available on COMPUSTAT was divided into three categories of dividend increase, dividend decrease, and no change in dividend. Firms were included in the dividend increase (decrease) category if the sum of dividends in four quarters immediately before the split announcement was less (greater) than the sum of dividends in the four quarters immediately after the split announcement. This classification allows an examination of how dividend changes affect adjustment times. A stock split by itself does not change firm value, but a stock split announcement effect may be the result of expected cash dividend increases after a split. The adjustment time should be shortest for the dividend decrease group that reacts to negative information. This question is empirically tested in this section.
An examination of the results reported in Table 5 shows 157 cases of dividend increases, 8 cases of no change in dividend, and 5 cases of dividend decreases. The dividend decrease category is the quickest to adjust. Investors react very quickly to adverse news, and the adjustment is complete in 62 days. (7) Moreover, the end of adjustment occurs very early for the dividend decrease group, 10 days after the announcement, as compared with 68 and 84 days, respectively, for the dividend increase and no change in dividend groups. The dividend increase group reacts faster than the no change group. Investors in the no change group continue to wait for a longer time in the hope that dividends will be increased eventually and thus stretch out the adjustment time much after the announcement. In addition, the percentage of variance increases is smaller for the dividend increase group than for the other two groups. This implies that investors react in a more significant way if dividends do not increase after a stock split, as is generally anticipated. These results must be interpreted carefully due to the limited number of dividend decreases and no change in dividends.
This paper examines the adjustment of stock returns to stock splits announcements. The beginning and ending times of the adjustment process are estimated using a statistical method proposed by Hillmer and Yu . In addition, the sample is dividend into subsets based on contaminated versus non-contaminated announcements, size of the firm, and changes in dividends after the split announcement in order to determine whether any of these factors systematically affect the variability of returns.
The findings clearly indicate that there are no excess returns associated with stock split proposal announcements. However, a disturbance in stock returns is present in the form of increased variability. This implies a period of increased volatility and uncertaintly for the underlying stock. These results are consistent with the findings of Hillmer and Yu , Patell and Wolfson , and Ohlson and Penman . The period of increased volatility is greater for larger firms and for firms that make many simultaneous announcements around the time of a split announcement. The dividends decrease group takes a shorter adjustment time than the dividends increase or no change in dividends groups. The adjustment process also ends very rapidly after the announcement for the dividends decrease group. Our results are consistent with the findings of Ohlson and Penman  and Lamourex and Poon . This study has further strengthened the present understanding of the price adjustment process to the announcement of stock splits.
We judge more empirical work is required in the area of return volatility. It would be interesting to examine volatility around the time of some other events such as merger announcements and discount rate changes announced by the Federal Reserve Board. Different financial events would lead to different adjustment times. In addition, it is important to determine what firm specific factors for each event tend to shorten or lengthen the process of price adjustment. Increased return volatility lasts for a long time period and is inconsistent with the efficient market hypothesis. The next logical question is whether any portfolio strategies deriving excess returns can be formulated based on this anomally.
(1) The five events were: reactions of Rockwell International and Boeing Co. to the news on June 30, 1977, that the B-1 bomber was going to be scrapped; IBM's report on April 13, 1977, of a 5.3% rise in first quarter earnings; General Motor's quarterly earnings report on February 8, 1978; and the announcement of an award of 150.8 million dollar defense contract on March 1, 1977, to Todd Shipyards.
(2) See Hillmer and Yu  for details.
(3) There were data available on CRSP for 388 splits.
(4) The simultaneous and non-simultaneous samples were not classified into size categories because there were only 26 cases of variance increases in the case of the non-simultaneous (or pure) group.
(5) The size data were available on COMPUSTAT for 170 splits, out of which 82 showed an increase in variance and are classified by size.
(6) Similar results are found using total assets for size.
(7) The mean of the beginning time for the total sample is 18 days in Table 3, but, for the three dividend groups in Table 5, it averages 30 days. It should be clarified that this occurs because diviend groups are for firms on COMPUSTAT; for these larger firms the adjustment process starts earlier.
[1.] Charest, G. "Split Information, Stock Returns and Market Efficiency -I." Journal of Financial Economics, 6, 213 (June/September 1978), 265-96.
[2.] Cox, D. R., and H. D. Miller. The Theory of Stochastic Processes. London: Methuen, 1970.
[3.] Fama, E. F., et al. "The Adjustment of Stock Prices to New Information." International Economic Review, 10, 1 (February, 1969), 1-21.
[4.] Grinblatt, M. D., R. W. Masulis, and S. Titman. "The Valuation Effects of Stock Splits and Stock Dividends." Journal of Financial Economics, 13, 4 (December, 1984), 46-90.
[5.] Hillmer, S. C., and P. L. Yu. "The Market Speed of Adjustment to New Information." Journal of Financial Economics, 7, 4 (December, 1979), 321-45.
[6.] Lamourex, C. G., and P. Poon. "The Market Reaction to Stock Splits." Journal of Finance, 42, 5 (December, 1987), 1347-70.
[7.] Ohlson, J. A., and S. H. Penman. "Volatility Increases Subsequent to Stock Splits: An Empirical Operation." Journal of Financial Economics, 14, 2 (June, 1985), 251-66.
[8.] Page, E. S. "Continuous Inspection Schemes." Biometrika, 41 (March, 1954), 100-14.
[9.] Patell, J. M., and M. A. Wolfson. "The Intraday Speed of Adjustment of Stock Prices to Earnings and Dividend Announcements." Journal of Financial Economics, 13, 2 (June, 1984), 223-52.
REENA AGGARAWAL is Assistant Professor of Finance at Georgetown University. SON-NAN CHEN is Professor of Finance at the University of Maryland at College Park.…